## TSTP Solution File: SYN969+1 by iProverMo---2.5-0.1

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : iProverMo---2.5-0.1
% Problem  : SYN969+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : iprover_modulo %s %d

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Thu Jul 21 07:43:37 EDT 2022

% Result   : Theorem 0.20s 0.42s
% Output   : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   18 (   7 unt;   0 def)
%            Number of atoms       :   41 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   38 (  15   ~;  10   |;   5   &)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-1 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   14 (   0 sgn   8   !;   0   ?)

%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy Equiv(ClausalAll)
% Orienting axioms whose shape is orientable
% Start CNF derivation
% End CNF derivation
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0,conjecture,
! [X1] :
( ( ! [X2] :
( p(X2)
=> q(X2) )
& r(X1) )
=> ( ! [X3] :
( r(X3)
=> p(X3) )
=> q(X1) ) ),
file('<stdin>',prove_this) ).

fof(c_0_1,negated_conjecture,
~ ! [X1] :
( ( ! [X2] :
( p(X2)
=> q(X2) )
& r(X1) )
=> ( ! [X3] :
( r(X3)
=> p(X3) )
=> q(X1) ) ),
inference(assume_negation,[status(cth)],[c_0_0]) ).

fof(c_0_2,negated_conjecture,
! [X5,X6] :
( ( ~ p(X5)
| q(X5) )
& r(esk1_0)
& ( ~ r(X6)
| p(X6) )
& ~ q(esk1_0) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])])]) ).

cnf(c_0_3,negated_conjecture,
( q(X1)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_4,negated_conjecture,
( p(X1)
| ~ r(X1) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_5,negated_conjecture,
~ q(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_6,negated_conjecture,
r(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_7,negated_conjecture,
( q(X1)
| ~ p(X1) ),
c_0_3,
[final] ).

cnf(c_0_8,negated_conjecture,
( p(X1)
| ~ r(X1) ),
c_0_4,
[final] ).

cnf(c_0_9,negated_conjecture,
~ q(esk1_0),
c_0_5,
[final] ).

cnf(c_0_10,negated_conjecture,
r(esk1_0),
c_0_6,
[final] ).

% End CNF derivation

%-------------------------------------------------------------
% Proof by iprover

cnf(c_0,negated_conjecture,
( q(X0)
| ~ p(X0) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_547b20.p',c_0_7) ).

cnf(c_5,plain,
( q(sk3_esk1_0)
| ~ p(sk3_esk1_0) ),
inference(instantiation,[status(thm)],[c_0]) ).

cnf(c_1,negated_conjecture,
( p(X0)
| ~ r(X0) ),
file('/export/starexec/sandbox2/tmp/iprover_modulo_547b20.p',c_0_8) ).

cnf(c_4,plain,
( p(sk3_esk1_0)
| ~ r(sk3_esk1_0) ),
inference(instantiation,[status(thm)],[c_1]) ).

cnf(c_2,negated_conjecture,
~ q(sk3_esk1_0),
file('/export/starexec/sandbox2/tmp/iprover_modulo_547b20.p',c_0_9) ).

cnf(c_3,negated_conjecture,
r(sk3_esk1_0),
file('/export/starexec/sandbox2/tmp/iprover_modulo_547b20.p',c_0_10) ).

\$false,
inference(minisat,[status(thm)],[c_5,c_4,c_2,c_3]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SYN969+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13  % Command  : iprover_modulo %s %d
% 0.13/0.34  % Computer : n007.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jul 11 12:34:03 EDT 2022
% 0.13/0.34  % CPUTime  :
% 0.13/0.35  % Running in mono-core mode
% 0.20/0.40  % Orienting using strategy Equiv(ClausalAll)
% 0.20/0.40  % FOF problem with conjecture
% 0.20/0.40  % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format  " --proof_out_file /export/starexec/sandbox2/tmp/iprover_proof_06271d.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox2/tmp/iprover_modulo_547b20.p | tee /export/starexec/sandbox2/tmp/iprover_modulo_out_59c7b1 | grep -v "SZS"
% 0.20/0.42
% 0.20/0.42  %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.20/0.42
% 0.20/0.42  %
% 0.20/0.42  % ------  iProver source info
% 0.20/0.42
% 0.20/0.42  % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.20/0.42  % git: non_committed_changes: true
% 0.20/0.42  % git: last_make_outside_of_git: true
% 0.20/0.42
% 0.20/0.42  %
% 0.20/0.42  % ------ Input Options
% 0.20/0.42
% 0.20/0.42  % --out_options                         all
% 0.20/0.42  % --tptp_safe_out                       true
% 0.20/0.42  % --problem_path                        ""
% 0.20/0.42  % --include_path                        ""
% 0.20/0.42  % --clausifier                          .//eprover
% 0.20/0.42  % --clausifier_options                  --tstp-format
% 0.20/0.42  % --stdin                               false
% 0.20/0.42  % --dbg_backtrace                       false
% 0.20/0.42  % --dbg_dump_prop_clauses               false
% 0.20/0.42  % --dbg_dump_prop_clauses_file          -
% 0.20/0.42  % --dbg_out_stat                        false
% 0.20/0.42
% 0.20/0.42  % ------ General Options
% 0.20/0.42
% 0.20/0.42  % --fof                                 false
% 0.20/0.42  % --time_out_real                       150.
% 0.20/0.42  % --time_out_prep_mult                  0.2
% 0.20/0.42  % --time_out_virtual                    -1.
% 0.20/0.42  % --schedule                            none
% 0.20/0.42  % --ground_splitting                    input
% 0.20/0.42  % --splitting_nvd                       16
% 0.20/0.42  % --non_eq_to_eq                        false
% 0.20/0.42  % --prep_gs_sim                         true
% 0.20/0.42  % --prep_unflatten                      false
% 0.20/0.42  % --prep_res_sim                        true
% 0.20/0.42  % --prep_upred                          true
% 0.20/0.42  % --res_sim_input                       true
% 0.20/0.42  % --clause_weak_htbl                    true
% 0.20/0.42  % --gc_record_bc_elim                   false
% 0.20/0.42  % --symbol_type_check                   false
% 0.20/0.42  % --clausify_out                        false
% 0.20/0.42  % --large_theory_mode                   false
% 0.20/0.42  % --prep_sem_filter                     none
% 0.20/0.42  % --prep_sem_filter_out                 false
% 0.20/0.42  % --preprocessed_out                    false
% 0.20/0.42  % --sub_typing                          false
% 0.20/0.42  % --brand_transform                     false
% 0.20/0.42  % --pure_diseq_elim                     true
% 0.20/0.42  % --min_unsat_core                      false
% 0.20/0.42  % --pred_elim                           true
% 0.20/0.42  % --soft_assumptions                    false
% 0.20/0.42  % --reset_solvers                       false
% 0.20/0.42  % --bc_imp_inh                          []
% 0.20/0.42  % --conj_cone_tolerance                 1.5
% 0.20/0.42  % --prolific_symb_bound                 500
% 0.20/0.42  % --lt_threshold                        2000
% 0.20/0.42
% 0.20/0.42  % ------ SAT Options
% 0.20/0.42
% 0.20/0.42  % --sat_mode                            false
% 0.20/0.42  % --sat_fm_restart_options              ""
% 0.20/0.42  % --sat_gr_def                          false
% 0.20/0.42  % --sat_epr_types                       true
% 0.20/0.42  % --sat_non_cyclic_types                false
% 0.20/0.42  % --sat_finite_models                   false
% 0.20/0.42  % --sat_fm_lemmas                       false
% 0.20/0.42  % --sat_fm_prep                         false
% 0.20/0.42  % --sat_fm_uc_incr                      true
% 0.20/0.42  % --sat_out_model                       small
% 0.20/0.42  % --sat_out_clauses                     false
% 0.20/0.42
% 0.20/0.42  % ------ QBF Options
% 0.20/0.42
% 0.20/0.42  % --qbf_mode                            false
% 0.20/0.42  % --qbf_elim_univ                       true
% 0.20/0.42  % --qbf_sk_in                           true
% 0.20/0.42  % --qbf_pred_elim                       true
% 0.20/0.42  % --qbf_split                           32
% 0.20/0.42
% 0.20/0.42  % ------ BMC1 Options
% 0.20/0.42
% 0.20/0.42  % --bmc1_incremental                    false
% 0.20/0.42  % --bmc1_axioms                         reachable_all
% 0.20/0.42  % --bmc1_min_bound                      0
% 0.20/0.42  % --bmc1_max_bound                      -1
% 0.20/0.42  % --bmc1_max_bound_default              -1
% 0.20/0.42  % --bmc1_symbol_reachability            true
% 0.20/0.42  % --bmc1_property_lemmas                false
% 0.20/0.42  % --bmc1_k_induction                    false
% 0.20/0.42  % --bmc1_non_equiv_states               false
% 0.20/0.42  % --bmc1_ucm                            false
% 0.20/0.42  % --bmc1_unsat_core_children            false
% 0.20/0.42  % --bmc1_unsat_core_extrapolate_axioms  false
% 0.20/0.42  % --bmc1_out_stat                       full
% 0.20/0.42  % --bmc1_ground_init                    false
% 0.20/0.42  % --bmc1_pre_inst_next_state            false
% 0.20/0.42  % --bmc1_pre_inst_state                 false
% 0.20/0.42  % --bmc1_pre_inst_reach_state           false
% 0.20/0.42  % --bmc1_out_unsat_core                 false
% 0.20/0.42  % --bmc1_aig_witness_out                false
% 0.20/0.42  % --bmc1_verbose                        false
% 0.20/0.42  % --bmc1_dump_clauses_tptp              false
% 0.20/0.42  % --bmc1_dump_unsat_core_tptp           false
% 0.20/0.42  % --bmc1_dump_file                      -
% 0.20/0.42  % --bmc1_ucm_expand_uc_limit            128
% 0.20/0.42  % --bmc1_ucm_n_expand_iterations        6
% 0.20/0.42  % --bmc1_ucm_extend_mode                1
% 0.20/0.42  % --bmc1_ucm_init_mode                  2
% 0.20/0.42  % --bmc1_ucm_cone_mode                  none
% 0.20/0.42  % --bmc1_ucm_reduced_relation_type      0
% 0.20/0.42  % --bmc1_ucm_relax_model                4
% 0.20/0.42  % --bmc1_ucm_full_tr_after_sat          true
% 0.20/0.42  % --bmc1_ucm_expand_neg_assumptions     false
% 0.20/0.42  % --bmc1_ucm_layered_model              none
% 0.20/0.42  % --bmc1_ucm_max_lemma_size             10
% 0.20/0.42
% 0.20/0.42  % ------ AIG Options
% 0.20/0.42
% 0.20/0.42  % --aig_mode                            false
% 0.20/0.42
% 0.20/0.42  % ------ Instantiation Options
% 0.20/0.42
% 0.20/0.42  % --instantiation_flag                  true
% 0.20/0.42  % --inst_lit_sel                        [+prop;+sign;+ground;-num_var;-num_symb]
% 0.20/0.42  % --inst_solver_per_active              750
% 0.20/0.42  % --inst_solver_calls_frac              0.5
% 0.20/0.42  % --inst_passive_queue_type             priority_queues
% 0.20/0.42  % --inst_passive_queues                 [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.20/0.42  % --inst_passive_queues_freq            [25;2]
% 0.20/0.42  % --inst_dismatching                    true
% 0.20/0.42  % --inst_eager_unprocessed_to_passive   true
% 0.20/0.42  % --inst_prop_sim_given                 true
% 0.20/0.42  % --inst_prop_sim_new                   false
% 0.20/0.42  % --inst_orphan_elimination             true
% 0.20/0.42  % --inst_learning_loop_flag             true
% 0.20/0.42  % --inst_learning_start                 3000
% 0.20/0.42  % --inst_learning_factor                2
% 0.20/0.42  % --inst_start_prop_sim_after_learn     3
% 0.20/0.42  % --inst_sel_renew                      solver
% 0.20/0.42  % --inst_lit_activity_flag              true
% 0.20/0.42  % --inst_out_proof                      true
% 0.20/0.42
% 0.20/0.42  % ------ Resolution Options
% 0.20/0.42
% 0.20/0.42  % --resolution_flag                     true
% 0.20/0.42  % --res_lit_sel                         kbo_max
% 0.20/0.42  % --res_to_prop_solver                  none
% 0.20/0.42  % --res_prop_simpl_new                  false
% 0.20/0.42  % --res_prop_simpl_given                false
% 0.20/0.42  % --res_passive_queue_type              priority_queues
% 0.20/0.42  % --res_passive_queues                  [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.20/0.42  % --res_passive_queues_freq             [15;5]
% 0.20/0.42  % --res_forward_subs                    full
% 0.20/0.42  % --res_backward_subs                   full
% 0.20/0.42  % --res_forward_subs_resolution         true
% 0.20/0.42  % --res_backward_subs_resolution        true
% 0.20/0.42  % --res_orphan_elimination              false
% 0.20/0.42  % --res_time_limit                      1000.
% 0.20/0.42  % --res_out_proof                       true
% 0.20/0.42  % --proof_out_file                      /export/starexec/sandbox2/tmp/iprover_proof_06271d.s
% 0.20/0.42  % --modulo                              true
% 0.20/0.42
% 0.20/0.42  % ------ Combination Options
% 0.20/0.42
% 0.20/0.42  % --comb_res_mult                       1000
% 0.20/0.42  % --comb_inst_mult                      300
% 0.20/0.42  % ------
% 0.20/0.42
% 0.20/0.42  % ------ Parsing...% successful
% 0.20/0.42
% 0.20/0.42  %
% 0.20/0.42
% 0.20/0.42
% 0.20/0.42  % ------                             Statistics
% 0.20/0.42
% 0.20/0.42  % ------ General
% 0.20/0.42
% 0.20/0.42  % num_of_input_clauses:                 4
% 0.20/0.42  % num_of_input_neg_conjectures:         4
% 0.20/0.42  % num_of_splits:                        0
% 0.20/0.42  % num_of_split_atoms:                   0
% 0.20/0.42  % num_of_sem_filtered_clauses:          0
% 0.20/0.42  % num_of_subtypes:                      0
% 0.20/0.42  % monotx_restored_types:                0
% 0.20/0.42  % sat_num_of_epr_types:                 0
% 0.20/0.42  % sat_num_of_non_cyclic_types:          0
% 0.20/0.42  % sat_guarded_non_collapsed_types:      0
% 0.20/0.42  % is_epr:                               0
% 0.20/0.42  % is_horn:                              0
% 0.20/0.42  % has_eq:                               0
% 0.20/0.42  % num_pure_diseq_elim:                  0
% 0.20/0.42  % simp_replaced_by:                     0
% 0.20/0.42  % res_preprocessed:                     0
% 0.20/0.42  % prep_upred:                           0
% 0.20/0.42  % prep_unflattend:                      0
% 0.20/0.42  % pred_elim_cands:                      0
% 0.20/0.42  % pred_elim:                            0
% 0.20/0.42  % pred_elim_cl:                         0
% 0.20/0.42  % pred_elim_cycles:                     0
% 0.20/0.42  % forced_gc_time:                       0
% 0.20/0.42  % gc_basic_clause_elim:                 0
% 0.20/0.42  % parsing_time:                         0.
% 0.20/0.42  % sem_filter_time:                      0.
% 0.20/0.42  % pred_elim_time:                       0.
% 0.20/0.42  % out_proof_time:                       0.
% 0.20/0.42  % monotx_time:                          0.
% 0.20/0.42  % subtype_inf_time:                     0.
% 0.20/0.42  % unif_index_cands_time:                0.
% 0.20/0.42  % total_time:                           0.018
% 0.20/0.42  % num_of_symbols:                       29
% 0.20/0.42  % num_of_terms:                         21
% 0.20/0.42
% 0.20/0.42  % ------ Propositional Solver
% 0.20/0.42
% 0.20/0.42  % prop_solver_calls:                    0
% 0.20/0.42  % prop_fast_solver_calls:               0
% 0.20/0.42  % prop_num_of_clauses:                  5
% 0.20/0.42  % prop_preprocess_simplified:           0
% 0.20/0.42  % prop_fo_subsumed:                     0
% 0.20/0.42  % prop_solver_time:                     0.
% 0.20/0.42  % prop_fast_solver_time:                0.
% 0.20/0.42  % prop_unsat_core_time:                 0.
% 0.20/0.42
% 0.20/0.42  % ------ QBF
% 0.20/0.42
% 0.20/0.42  % qbf_q_res:                            0
% 0.20/0.42  % qbf_num_tautologies:                  0
% 0.20/0.42  % qbf_prep_cycles:                      0
% 0.20/0.42
% 0.20/0.42  % ------ BMC1
% 0.20/0.42
% 0.20/0.42  % bmc1_current_bound:                   -1
% 0.20/0.42  % bmc1_last_solved_bound:               -1
% 0.20/0.42  % bmc1_unsat_core_size:                 -1
% 0.20/0.42  % bmc1_unsat_core_parents_size:         -1
% 0.20/0.42  % bmc1_merge_next_fun:                  0
% 0.20/0.42  % bmc1_unsat_core_clauses_time:         0.
% 0.20/0.42
% 0.20/0.42  % ------ Instantiation
% 0.20/0.42
% 0.20/0.42  % inst_num_of_clauses:                  undef
% 0.20/0.42  % inst_num_in_passive:                  undef
% 0.20/0.42  % inst_num_in_active:                   0
% 0.20/0.42  % inst_num_in_unprocessed:              0
% 0.20/0.42  % inst_num_of_loops:                    0
% 0.20/0.42  % inst_num_of_learning_restarts:        0
% 0.20/0.42  % inst_num_moves_active_passive:        0
% 0.20/0.42  % inst_lit_activity:                    0
% 0.20/0.42  % inst_lit_activity_moves:              0
% 0.20/0.42  % inst_num_tautologies:                 0
% 0.20/0.42  % inst_num_prop_implied:                0
% 0.20/0.42  % inst_num_existing_simplified:         0
% 0.20/0.42  % inst_num_eq_res_simplified:           0
% 0.20/0.42  % inst_num_child_elim:                  0
% 0.20/0.42  % inst_num_of_dismatching_blockings:    0
% 0.20/0.42  % inst_num_of_non_proper_insts:         0
% 0.20/0.42  % inst_num_of_duplicates:               0
% 0.20/0.42  % inst_inst_num_from_inst_to_res:       0
% 0.20/0.42  % inst_dismatching_checking_time:       0.
% 0.20/0.42
% 0.20/0.42  % ------ Resolution
% 0.20/0.42
% 0.20/0.42  % res_num_of_clauses:                   undef
% 0.20/0.42  % res_num_in_passive:                   undef
% 0.20/0.42  % res_num_in_active:                    0
% 0.20/0.42  % res_num_of_loops:                     0
% 0.20/0.42  % res_forward_subset_subsumed:          0
% 0.20/0.42  % res_backward_subset_subsumed:         0
% 0.20/0.42  % res_forward_subsumed:                 0
% 0.20/0.42  % res_backward_subsumed:                0
% 0.20/0.42  % res_forward_subsumption_resolution:   0
% 0.20/0.42  % res_backward_subsumption_resolution:  0
% 0.20/0.42  % res_clause_to_clause_subsumption:     0
% 0.20/0.42  % res_orphan_elimination:               0
% 0.20/0.42  % res_tautology_del:                    0
% 0.20/0.42  % res_num_eq_res_simplified:            0
% 0.20/0.42  % res_num_sel_changes:                  0
% 0.20/0.42  % res_moves_from_active_to_pass:        0
% 0.20/0.42
% 0.20/0.42  % Status Unsatisfiable
% 0.20/0.42  % SZS status Theorem
% 0.20/0.42  % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------
```