## TSTP Solution File: GRP125-1.003 by E-SAT---3.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : E-SAT---3.0
% Problem  : GRP125-1.003 : TPTP v8.1.0. Released v1.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n015.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  : 300s
% DateTime : Fri Sep 16 21:22:18 EDT 2022

% Result   : Unsatisfiable 0.19s 0.47s
% Output   : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   49 (  22 unt;   6 typ;   0 def)
%            Number of atoms       :   84 (   0 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   75 (  34   ~;  41   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    3 (   3 usr;   3 con; 0-0 aty)
%            Number of variables   :   40 (   0 sgn   0   !;   0   ?;   0   :)

%------------------------------------------------------------------------------
tff(decl_22,type,
e_1: \$i ).

tff(decl_23,type,
group_element: \$i > \$o ).

tff(decl_24,type,
e_2: \$i ).

tff(decl_25,type,
e_3: \$i ).

tff(decl_26,type,
equalish: ( \$i * \$i ) > \$o ).

tff(decl_27,type,
product: ( \$i * \$i * \$i ) > \$o ).

cnf(product_total_function1,axiom,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| product(X1,X2,e_3)
| ~ group_element(X1)
| ~ group_element(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_total_function1) ).

cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_3) ).

cnf(product_right_cancellation,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).

cnf(product_idempotence,axiom,
product(X1,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_idempotence) ).

cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_1) ).

cnf(product_left_cancellation,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).

cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_3_is_not_e_1) ).

cnf(e_1_is_not_e_3,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_1_is_not_e_3) ).

cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_2) ).

cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_3) ).

cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e_2_is_not_e_1) ).

cnf(qg3,negated_conjecture,
( product(X3,X4,X1)
| ~ product(X1,X2,X3)
| ~ product(X2,X1,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qg3) ).

cnf(c_0_12,axiom,
( product(X1,X2,e_1)
| product(X1,X2,e_2)
| product(X1,X2,e_3)
| ~ group_element(X1)
| ~ group_element(X2) ),
product_total_function1 ).

cnf(c_0_13,axiom,
group_element(e_3),
element_3 ).

cnf(c_0_14,axiom,
( equalish(X2,X4)
| ~ product(X1,X2,X3)
| ~ product(X1,X4,X3) ),
product_right_cancellation ).

cnf(c_0_15,axiom,
product(X1,X1,X1),
product_idempotence ).

cnf(c_0_16,plain,
( product(X1,e_3,e_3)
| product(X1,e_3,e_2)
| product(X1,e_3,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_17,axiom,
group_element(e_1),
element_1 ).

cnf(c_0_18,axiom,
( equalish(X1,X4)
| ~ product(X1,X2,X3)
| ~ product(X4,X2,X3) ),
product_left_cancellation ).

cnf(c_0_19,plain,
( equalish(X1,X2)
| ~ product(X2,X1,X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_20,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_21,axiom,
~ equalish(e_3,e_1),
e_3_is_not_e_1 ).

cnf(c_0_22,plain,
( equalish(X1,X2)
| ~ product(X1,X2,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).

cnf(c_0_23,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).

cnf(c_0_24,axiom,
~ equalish(e_1,e_3),
e_1_is_not_e_3 ).

cnf(c_0_25,plain,
product(e_1,e_3,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).

cnf(c_0_26,axiom,
group_element(e_2),
element_2 ).

cnf(c_0_27,axiom,
~ equalish(e_2,e_3),
e_2_is_not_e_3 ).

cnf(c_0_28,plain,
( equalish(X1,e_3)
| ~ product(e_1,X1,e_2) ),
inference(spm,[status(thm)],[c_0_14,c_0_25]) ).

cnf(c_0_29,plain,
( product(X1,e_2,e_3)
| product(X1,e_2,e_2)
| product(X1,e_2,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_26]) ).

cnf(c_0_30,plain,
~ product(e_1,e_2,e_2),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_31,plain,
( product(X1,e_1,e_3)
| product(X1,e_1,e_2)
| product(X1,e_1,e_1)
| ~ group_element(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).

cnf(c_0_32,plain,
( product(e_1,e_2,e_1)
| product(e_1,e_2,e_3) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_17]),c_0_30]) ).

cnf(c_0_33,axiom,
~ equalish(e_2,e_1),
e_2_is_not_e_1 ).

cnf(c_0_34,plain,
( product(e_3,e_1,e_1)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_31,c_0_13]) ).

cnf(c_0_35,plain,
product(e_1,e_2,e_3),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_32]),c_0_33]) ).

cnf(c_0_36,negated_conjecture,
( product(X3,X4,X1)
| ~ product(X1,X2,X3)
| ~ product(X2,X1,X4) ),
qg3 ).

cnf(c_0_37,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_34]),c_0_21]) ).

cnf(c_0_38,plain,
( equalish(X1,e_1)
| ~ product(X1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_18,c_0_35]) ).

cnf(c_0_39,negated_conjecture,
( product(X1,e_2,e_3)
| ~ product(e_3,e_1,X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_25]) ).

cnf(c_0_40,plain,
product(e_3,e_1,e_2),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_37]),c_0_24]) ).

cnf(c_0_41,plain,
~ product(e_2,e_2,e_3),
inference(spm,[status(thm)],[c_0_33,c_0_38]) ).

cnf(c_0_42,negated_conjecture,
\$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),
[proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : GRP125-1.003 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.14  % Command    : run_E %s %d THM
% 0.14/0.34  % Computer : n015.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Wed Aug 31 15:08:22 EDT 2022
% 0.14/0.34  % CPUTime    :
% 0.19/0.46  Running first-order on 8 cores model finding
% 0.19/0.46  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46  # Version: 3.0pre003
% 0.19/0.47  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.47  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.47  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.47  # Starting new_bool_3 with 300s (1) cores
% 0.19/0.47  # Starting new_bool_1 with 300s (1) cores
% 0.19/0.47  # Starting sh5l with 300s (1) cores
% 0.19/0.47  # new_bool_3 with pid 3255 completed with status 0
% 0.19/0.47  # Result found by new_bool_3
% 0.19/0.47  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.47  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.47  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.47  # Starting new_bool_3 with 300s (1) cores
% 0.19/0.47  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.47  # ...ProofStateSinE()=15/15
% 0.19/0.47  # Search class: FGUNF-FFSS00-SFFFFFNN
% 0.19/0.47  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.47  # Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 0.19/0.47  # SAT001_MinMin_p005000_rr_RG with pid 3260 completed with status 0
% 0.19/0.47  # Result found by SAT001_MinMin_p005000_rr_RG
% 0.19/0.47  # Preprocessing class: FSMSSMSSSSSNFFN.
% 0.19/0.47  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.19/0.47  # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.19/0.47  # Starting new_bool_3 with 300s (1) cores
% 0.19/0.47  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.19/0.47  # ...ProofStateSinE()=15/15
% 0.19/0.47  # Search class: FGUNF-FFSS00-SFFFFFNN
% 0.19/0.47  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.19/0.47  # Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 0.19/0.47  # Preprocessing time       : 0.001 s
% 0.19/0.47  # Presaturation interreduction done
% 0.19/0.47
% 0.19/0.47  # Proof found!
% 0.19/0.47  # SZS status Unsatisfiable
% 0.19/0.47  # SZS output start CNFRefutation
% See solution above
% 0.19/0.47  # Parsed axioms                        : 15
% 0.19/0.47  # Removed by relevancy pruning/SinE    : 0
% 0.19/0.47  # Initial clauses                      : 15
% 0.19/0.47  # Removed in clause preprocessing      : 0
% 0.19/0.47  # Initial clauses in saturation        : 15
% 0.19/0.47  # Processed clauses                    : 76
% 0.19/0.47  # ...of these trivial                  : 0
% 0.19/0.47  # ...subsumed                          : 3
% 0.19/0.47  # ...remaining for further processing  : 73
% 0.19/0.47  # Other redundant clauses eliminated   : 0
% 0.19/0.47  # Clauses deleted for lack of memory   : 0
% 0.19/0.47  # Backward-subsumed                    : 3
% 0.19/0.47  # Backward-rewritten                   : 3
% 0.19/0.47  # Generated clauses                    : 96
% 0.19/0.47  # ...of the previous two non-redundant : 87
% 0.19/0.47  # ...aggressively subsumed             : 0
% 0.19/0.47  # Contextual simplify-reflections      : 0
% 0.19/0.47  # Paramodulations                      : 94
% 0.19/0.47  # Factorizations                       : 0
% 0.19/0.47  # NegExts                              : 0
% 0.19/0.47  # Equation resolutions                 : 0
% 0.19/0.47  # Propositional unsat checks           : 0
% 0.19/0.47  #    Propositional check models        : 0
% 0.19/0.47  #    Propositional check unsatisfiable : 0
% 0.19/0.47  #    Propositional clauses             : 0
% 0.19/0.47  #    Propositional clauses after purity: 0
% 0.19/0.47  #    Propositional unsat core size     : 0
% 0.19/0.47  #    Propositional preprocessing time  : 0.000
% 0.19/0.47  #    Propositional encoding time       : 0.000
% 0.19/0.47  #    Propositional solver time         : 0.000
% 0.19/0.47  #    Success case prop preproc time    : 0.000
% 0.19/0.47  #    Success case prop encoding time   : 0.000
% 0.19/0.47  #    Success case prop solver time     : 0.000
% 0.19/0.47  # Current number of processed clauses  : 50
% 0.19/0.47  #    Positive orientable unit clauses  : 8
% 0.19/0.47  #    Positive unorientable unit clauses: 0
% 0.19/0.47  #    Negative unit clauses             : 17
% 0.19/0.47  #    Non-unit-clauses                  : 25
% 0.19/0.47  # Current number of unprocessed clauses: 25
% 0.19/0.47  # ...number of literals in the above   : 82
% 0.19/0.47  # Current number of archived formulas  : 0
% 0.19/0.47  # Current number of archived clauses   : 23
% 0.19/0.47  # Clause-clause subsumption calls (NU) : 140
% 0.19/0.47  # Rec. Clause-clause subsumption calls : 134
% 0.19/0.47  # Non-unit clause-clause subsumptions  : 2
% 0.19/0.47  # Unit Clause-clause subsumption calls : 35
% 0.19/0.47  # Rewrite failures with RHS unbound    : 0
% 0.19/0.47  # BW rewrite match attempts            : 15
% 0.19/0.47  # BW rewrite match successes           : 3
% 0.19/0.47  # Condensation attempts                : 0
% 0.19/0.47  # Condensation successes               : 0
% 0.19/0.47  # Termbank termtop insertions          : 1323
% 0.19/0.47
% 0.19/0.47  # -------------------------------------------------
% 0.19/0.47  # User time                : 0.004 s
% 0.19/0.47  # System time              : 0.002 s
% 0.19/0.47  # Total time               : 0.006 s
% 0.19/0.47  # Maximum resident set size: 1632 pages
% 0.19/0.47
% 0.19/0.47  # -------------------------------------------------
% 0.19/0.47  # User time                : 0.004 s
% 0.19/0.47  # System time              : 0.004 s
% 0.19/0.47  # Total time               : 0.008 s
% 0.19/0.47  # Maximum resident set size: 1704 pages
%------------------------------------------------------------------------------
```