## TSTP Solution File: SEU163+1 by LEO-II---1.7.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : LEO-II---1.7.0
% Problem  : SEU163+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s

% Computer : n011.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 : Tue Jul 19 12:07:25 EDT 2022

% Result   : Theorem 0.15s 0.41s
% Output   : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   43 (  30 unt;   5 typ;   0 def)
%            Number of atoms       :  134 (  37 equ;   0 cnn)
%            Maximal formula atoms :    2 (   3 avg)
%            Number of connectives :  169 (  20   ~;  13   |;   0   &; 127   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    5 (   5   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    8 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   48 (   0   ^  48   !;   0   ?;  48   :)

%------------------------------------------------------------------------------
thf(tp_in,type,
in: \$i > \$i > \$o ).

thf(tp_sK1_A,type,
sK1_A: \$i ).

thf(tp_sK2_SY8,type,
sK2_SY8: \$i ).

thf(tp_subset,type,
subset: \$i > \$i > \$o ).

thf(tp_union,type,
union: \$i > \$i ).

thf(1,axiom,
! [A: \$i,B: \$i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l50_zfmisc_1) ).

thf(2,axiom,
\$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_tarski) ).

thf(3,axiom,
! [A: \$i,B: \$i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

thf(4,axiom,
! [A: \$i,B: \$i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

thf(5,conjecture,
! [A: \$i,B: \$i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).

thf(6,negated_conjecture,
( ( ! [A: \$i,B: \$i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= \$false ),
inference(negate_conjecture,[status(cth)],[5]) ).

thf(7,plain,
( ( ! [A: \$i,B: \$i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= \$false ),
inference(unfold_def,[status(thm)],[6]) ).

thf(8,plain,
( ( ! [A: \$i,B: \$i] :
( ( in @ A @ B )
=> ( subset @ A @ ( union @ B ) ) ) )
= \$true ),
inference(unfold_def,[status(thm)],[1]) ).

thf(9,plain,
\$true = \$true,
inference(unfold_def,[status(thm)],[2]) ).

thf(10,plain,
( ( ! [A: \$i,B: \$i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= \$true ),
inference(unfold_def,[status(thm)],[3]) ).

thf(11,plain,
( ( ! [A: \$i,B: \$i] : ( subset @ A @ A ) )
= \$true ),
inference(unfold_def,[status(thm)],[4]) ).

thf(12,plain,
( ( ! [SY8: \$i] :
( ( in @ sK1_A @ SY8 )
=> ( subset @ sK1_A @ ( union @ SY8 ) ) ) )
= \$false ),
inference(extcnf_forall_neg,[status(esa)],[7]) ).

thf(13,plain,
( ( ( in @ sK1_A @ sK2_SY8 )
=> ( subset @ sK1_A @ ( union @ sK2_SY8 ) ) )
= \$false ),
inference(extcnf_forall_neg,[status(esa)],[12]) ).

thf(14,plain,
( ( in @ sK1_A @ sK2_SY8 )
= \$true ),
inference(standard_cnf,[status(thm)],[13]) ).

thf(15,plain,
( ( subset @ sK1_A @ ( union @ sK2_SY8 ) )
= \$false ),
inference(standard_cnf,[status(thm)],[13]) ).

thf(16,plain,
( ( ~ ( subset @ sK1_A @ ( union @ sK2_SY8 ) ) )
= \$true ),
inference(polarity_switch,[status(thm)],[15]) ).

thf(17,plain,
( ( ! [A: \$i,B: \$i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= \$true ),
inference(extcnf_combined,[status(esa)],[8]) ).

thf(18,plain,
( ( ! [A: \$i,B: \$i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= \$true ),
inference(extcnf_combined,[status(esa)],[10]) ).

thf(19,plain,
( ( ! [A: \$i] : ( subset @ A @ A ) )
= \$true ),
inference(extcnf_combined,[status(esa)],[11]) ).

thf(20,plain,
( ( ! [A: \$i] : ( subset @ A @ A ) )
= \$true ),
inference(copy,[status(thm)],[19]) ).

thf(21,plain,
( ( ! [A: \$i,B: \$i] :
( ~ ( in @ A @ B )
| ~ ( in @ B @ A ) ) )
= \$true ),
inference(copy,[status(thm)],[18]) ).

thf(22,plain,
\$true = \$true,
inference(copy,[status(thm)],[9]) ).

thf(23,plain,
( ( ! [A: \$i,B: \$i] :
( ~ ( in @ A @ B )
| ( subset @ A @ ( union @ B ) ) ) )
= \$true ),
inference(copy,[status(thm)],[17]) ).

thf(24,plain,
( ( in @ sK1_A @ sK2_SY8 )
= \$true ),
inference(copy,[status(thm)],[14]) ).

thf(25,plain,
( ( ~ ( subset @ sK1_A @ ( union @ sK2_SY8 ) ) )
= \$true ),
inference(copy,[status(thm)],[16]) ).

thf(26,plain,
! [SV1: \$i] :
( ( subset @ SV1 @ SV1 )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).

thf(27,plain,
! [SV2: \$i] :
( ( ! [SY9: \$i] :
( ~ ( in @ SV2 @ SY9 )
| ~ ( in @ SY9 @ SV2 ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).

thf(28,plain,
! [SV3: \$i] :
( ( ! [SY10: \$i] :
( ~ ( in @ SV3 @ SY10 )
| ( subset @ SV3 @ ( union @ SY10 ) ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).

thf(29,plain,
( ( subset @ sK1_A @ ( union @ sK2_SY8 ) )
= \$false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).

thf(30,plain,
! [SV4: \$i,SV2: \$i] :
( ( ~ ( in @ SV2 @ SV4 )
| ~ ( in @ SV4 @ SV2 ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).

thf(31,plain,
! [SV5: \$i,SV3: \$i] :
( ( ~ ( in @ SV3 @ SV5 )
| ( subset @ SV3 @ ( union @ SV5 ) ) )
= \$true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).

thf(32,plain,
! [SV4: \$i,SV2: \$i] :
( ( ( ~ ( in @ SV2 @ SV4 ) )
= \$true )
| ( ( ~ ( in @ SV4 @ SV2 ) )
= \$true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).

thf(33,plain,
! [SV5: \$i,SV3: \$i] :
( ( ( ~ ( in @ SV3 @ SV5 ) )
= \$true )
| ( ( subset @ SV3 @ ( union @ SV5 ) )
= \$true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).

thf(34,plain,
! [SV4: \$i,SV2: \$i] :
( ( ( in @ SV2 @ SV4 )
= \$false )
| ( ( ~ ( in @ SV4 @ SV2 ) )
= \$true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).

thf(35,plain,
! [SV5: \$i,SV3: \$i] :
( ( ( in @ SV3 @ SV5 )
= \$false )
| ( ( subset @ SV3 @ ( union @ SV5 ) )
= \$true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).

thf(36,plain,
! [SV2: \$i,SV4: \$i] :
( ( ( in @ SV4 @ SV2 )
= \$false )
| ( ( in @ SV2 @ SV4 )
= \$false ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).

thf(37,plain,
\$false = \$true,
inference(fo_atp_e,[status(thm)],[22,36,35,29,26,24]) ).

thf(38,plain,
\$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[37]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : SEU163+1 : TPTP v8.1.0. Released v3.3.0.
% 0.14/0.15  % Command  : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.15/0.37  % Computer : n011.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 600
% 0.15/0.37  % DateTime : Sun Jun 19 00:38:53 EDT 2022
% 0.15/0.37  % CPUTime  :
% 0.15/0.37
% 0.15/0.37   No.of.Axioms: 4
% 0.15/0.37
% 0.15/0.37   Length.of.Defs: 0
% 0.15/0.37
% 0.15/0.37   Contains.Choice.Funs: false
% 0.15/0.38  (rf:0,axioms:4,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:6,loop_count:0,foatp_calls:0,translation:fof_full).
% 0.15/0.41
% 0.15/0.41  ********************************
% 0.15/0.41  *   All subproblems solved!    *
% 0.15/0.41  ********************************
% 0.15/0.41  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:37,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.15/0.41
% 0.15/0.41  %**** Beginning of derivation protocol ****
% 0.15/0.41  % SZS output start CNFRefutation
% See solution above
% 0.15/0.41
% 0.15/0.41  %**** End of derivation protocol ****
% 0.15/0.41  %**** no. of clauses in derivation: 38 ****
% 0.15/0.41  %**** clause counter: 37 ****
% 0.15/0.41
% 0.15/0.41  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:5,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:37,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------
```