TSTP Solution File: SEU662^2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU662^2 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 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 : 600s
% DateTime : Tue Jul 19 12:13:45 EDT 2022
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 47 ( 30 unt; 9 typ; 2 def)
% Number of atoms : 185 ( 71 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 277 ( 47 ~; 27 |; 4 &; 177 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 84 ( 0 ^ 84 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cartprodmempaircEq,type,
cartprodmempaircEq: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_kfst,type,
kfst: $i > $i ).
thf(tp_kfstpairEq,type,
kfstpairEq: $o ).
thf(tp_kpair,type,
kpair: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY14,type,
sK2_SY14: $i ).
thf(tp_sK3_SY17,type,
sK3_SY17: $i ).
thf(tp_sK4_SY19,type,
sK4_SY19: $i ).
thf(cartprodmempaircEq,definition,
( cartprodmempaircEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kpair @ Xx @ Xy )
= ( kpair @ Xx @ Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempaircEq) ).
thf(kfstpairEq,definition,
( kfstpairEq
= ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kfstpairEq) ).
thf(1,conjecture,
( kfstpairEq
=> ( cartprodmempaircEq
=> ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(2,negated_conjecture,
( ( kfstpairEq
=> ( cartprodmempaircEq
=> ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kpair @ Xx @ Xy )
= ( kpair @ Xx @ Xy ) ) ) )
=> ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,cartprodmempaircEq,kfstpairEq]) ).
thf(4,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kpair @ Xx @ Xy )
= ( kpair @ Xx @ Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ( in @ sK3_SY17 @ sK1_A )
& ( in @ sK4_SY19 @ sK2_SY14 )
& ( ( kfst @ ( kpair @ sK3_SY17 @ sK4_SY19 ) )
!= sK3_SY17 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(9,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
| ! [B: $i,Xy: $i] :
~ ( in @ Xy @ B )
| $true ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(10,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
| ! [B: $i,Xy: $i] :
~ ( in @ Xy @ B )
| $true ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(12,plain,
( ( ( in @ sK3_SY17 @ sK1_A )
& ( in @ sK4_SY19 @ sK2_SY14 )
& ( ( kfst @ ( kpair @ sK3_SY17 @ sK4_SY19 ) )
!= sK3_SY17 ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
( ( ~ ( ~ ( in @ sK3_SY17 @ sK1_A )
| ~ ~ ( ~ ( in @ sK4_SY19 @ sK2_SY14 )
| ~ ( ( ( kfst @ ( kpair @ sK3_SY17 @ sK4_SY19 ) )
!= sK3_SY17 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,cartprodmempaircEq,kfstpairEq]) ).
thf(14,plain,
! [SV1: $i] :
( ( ! [SY20: $i] :
~ ( in @ SY20 @ SV1 )
| ! [B: $i,Xy: $i] :
~ ( in @ Xy @ B )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(15,plain,
! [SV2: $i] :
( ( ! [SY23: $i] :
( ( kfst @ ( kpair @ SV2 @ SY23 ) )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(16,plain,
( ( ~ ( in @ sK3_SY17 @ sK1_A )
| ~ ~ ( ~ ( in @ sK4_SY19 @ sK2_SY14 )
| ~ ( ( ( kfst @ ( kpair @ sK3_SY17 @ sK4_SY19 ) )
!= sK3_SY17 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV1: $i] :
( ( ( ! [SY20: $i] :
~ ( in @ SY20 @ SV1 ) )
= $true )
| ( ( ! [B: $i,Xy: $i] :
~ ( in @ Xy @ B )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV3: $i,SV2: $i] :
( ( ( kfst @ ( kpair @ SV2 @ SV3 ) )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( ~ ( in @ sK3_SY17 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(20,plain,
( ( ~ ~ ( ~ ( in @ sK4_SY19 @ sK2_SY14 )
| ~ ( ( ( kfst @ ( kpair @ sK3_SY17 @ sK4_SY19 ) )
!= sK3_SY17 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[16]) ).
thf(21,plain,
! [SV1: $i,SV4: $i] :
( ( ( ~ ( in @ SV4 @ SV1 ) )
= $true )
| ( ( ! [B: $i,Xy: $i] :
~ ( in @ Xy @ B )
| $true )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(22,plain,
( ( in @ sK3_SY17 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(23,plain,
( ( ~ ( ~ ( in @ sK4_SY19 @ sK2_SY14 )
| ~ ( ( ( kfst @ ( kpair @ sK3_SY17 @ sK4_SY19 ) )
!= sK3_SY17 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[20]) ).
thf(24,plain,
! [SV1: $i,SV4: $i] :
( ( ( in @ SV4 @ SV1 )
= $false )
| ( ( ! [B: $i,Xy: $i] :
~ ( in @ Xy @ B )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(25,plain,
( ( ~ ( in @ sK4_SY19 @ sK2_SY14 )
| ~ ( ( ( kfst @ ( kpair @ sK3_SY17 @ sK4_SY19 ) )
!= sK3_SY17 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(26,plain,
! [SV1: $i,SV4: $i] :
( ( ( ! [B: $i,Xy: $i] :
~ ( in @ Xy @ B ) )
= $true )
| ( $true = $true )
| ( ( in @ SV4 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[24]) ).
thf(27,plain,
( ( ~ ( in @ sK4_SY19 @ sK2_SY14 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(28,plain,
( ( ~ ( ( ( kfst @ ( kpair @ sK3_SY17 @ sK4_SY19 ) )
!= sK3_SY17 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[25]) ).
thf(29,plain,
! [SV1: $i,SV4: $i,SV5: $i] :
( ( ( ! [SY24: $i] :
~ ( in @ SY24 @ SV5 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV4 @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(30,plain,
( ( in @ sK4_SY19 @ sK2_SY14 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[27]) ).
thf(31,plain,
( ( ( ( kfst @ ( kpair @ sK3_SY17 @ sK4_SY19 ) )
!= sK3_SY17 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(32,plain,
! [SV1: $i,SV4: $i,SV5: $i,SV6: $i] :
( ( ( ~ ( in @ SV6 @ SV5 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV4 @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(33,plain,
( ( ( kfst @ ( kpair @ sK3_SY17 @ sK4_SY19 ) )
= sK3_SY17 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV1: $i,SV4: $i,SV5: $i,SV6: $i] :
( ( ( in @ SV6 @ SV5 )
= $false )
| ( $true = $true )
| ( ( in @ SV4 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(35,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[18,34,33,30,22]) ).
thf(36,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU662^2 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n015.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 : Sat Jun 18 21:01:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 0
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 402
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.35 (rf:0,axioms:0,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)..
% 0.13/0.38
% 0.13/0.38 ********************************
% 0.13/0.38 * All subproblems solved! *
% 0.13/0.38 ********************************
% 0.13/0.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:35,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.13/0.38
% 0.13/0.38 %**** Beginning of derivation protocol ****
% 0.13/0.38 % SZS output start CNFRefutation
% See solution above
% 0.13/0.38
% 0.13/0.38 %**** End of derivation protocol ****
% 0.13/0.38 %**** no. of clauses in derivation: 36 ****
% 0.13/0.38 %**** clause counter: 35 ****
% 0.13/0.38
% 0.13/0.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:35,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------