TSTP Solution File: SEU664^2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU664^2 : 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 : n022.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 12:13:46 EDT 2022
% Result : Theorem 0.21s 0.53s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 17
% Syntax : Number of formulae : 73 ( 37 unt; 13 typ; 3 def)
% Number of atoms : 346 ( 139 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 835 ( 104 ~; 77 |; 12 &; 613 @)
% ( 0 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 188 ( 0 ^ 182 !; 6 ?; 188 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cartprod,type,
cartprod: $i > $i > $i ).
thf(tp_cartprodfstpairEq,type,
cartprodfstpairEq: $o ).
thf(tp_cartprodmempair1,type,
cartprodmempair1: $o ).
thf(tp_cartprodsndpairEq,type,
cartprodsndpairEq: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_kfst,type,
kfst: $i > $i ).
thf(tp_kpair,type,
kpair: $i > $i > $i ).
thf(tp_ksnd,type,
ksnd: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY19,type,
sK2_SY19: $i ).
thf(tp_sK3_SY21,type,
sK3_SY21: $i ).
thf(tp_sK4_Xx,type,
sK4_Xx: $i > $i > $i > $i ).
thf(tp_sK5_SY22,type,
sK5_SY22: $i > $i > $i > $i ).
thf(cartprodfstpairEq,definition,
( cartprodfstpairEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(cartprodmempair1,definition,
( cartprodmempair1
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xu
= ( kpair @ Xx @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodsndpairEq,definition,
( cartprodsndpairEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodsndpairEq) ).
thf(1,conjecture,
( cartprodmempair1
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
thf(2,negated_conjecture,
( ( cartprodmempair1
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xu
= ( kpair @ Xx @ Xy ) ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) )
=> ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,cartprodfstpairEq,cartprodmempair1,cartprodsndpairEq]) ).
thf(4,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xu
= ( kpair @ Xx @ Xy ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ~ ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( ( in @ sK3_SY21 @ ( cartprod @ sK1_A @ sK2_SY19 ) )
& ( ( kpair @ ( kfst @ sK3_SY21 ) @ ( ksnd @ sK3_SY21 ) )
!= sK3_SY21 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(10,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
| ( ( Xu
= ( kpair @ ( sK4_Xx @ Xu @ B @ A ) @ ( sK5_SY22 @ Xu @ B @ A ) ) )
& ( in @ ( sK5_SY22 @ Xu @ B @ A ) @ B )
& ( in @ ( sK4_Xx @ Xu @ B @ A ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(11,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(12,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(13,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(14,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(15,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
| ( ( Xu
= ( kpair @ ( sK4_Xx @ Xu @ B @ A ) @ ( sK5_SY22 @ Xu @ B @ A ) ) )
& ( in @ ( sK5_SY22 @ Xu @ B @ A ) @ B )
& ( in @ ( sK4_Xx @ Xu @ B @ A ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(16,plain,
( ( ( in @ sK3_SY21 @ ( cartprod @ sK1_A @ sK2_SY19 ) )
& ( ( kpair @ ( kfst @ sK3_SY21 ) @ ( ksnd @ sK3_SY21 ) )
!= sK3_SY21 ) )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(17,plain,
( ( ~ ( ~ ( in @ sK3_SY21 @ ( cartprod @ sK1_A @ sK2_SY19 ) )
| ~ ( ( ( kpair @ ( kfst @ sK3_SY21 ) @ ( ksnd @ sK3_SY21 ) )
!= sK3_SY21 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,cartprodfstpairEq,cartprodmempair1,cartprodsndpairEq]) ).
thf(18,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( ( SX2
!= ( kpair @ ( sK4_Xx @ SX2 @ SX1 @ SX0 ) @ ( sK5_SY22 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK5_SY22 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( sK4_Xx @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,cartprodfstpairEq,cartprodmempair1,cartprodsndpairEq]) ).
thf(19,plain,
! [SV1: $i] :
( ( ! [SY23: $i,SY24: $i] :
( ~ ( in @ SY24 @ SV1 )
| ! [Xy: $i] :
( ~ ( in @ Xy @ SY23 )
| ( ( ksnd @ ( kpair @ SY24 @ Xy ) )
= Xy ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[13]) ).
thf(20,plain,
! [SV2: $i] :
( ( ! [SY26: $i,SY27: $i] :
( ~ ( in @ SY27 @ SV2 )
| ! [Xy: $i] :
( ~ ( in @ Xy @ SY26 )
| ( ( kfst @ ( kpair @ SY27 @ Xy ) )
= SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(21,plain,
( ( ~ ( in @ sK3_SY21 @ ( cartprod @ sK1_A @ sK2_SY19 ) )
| ~ ( ( ( kpair @ ( kfst @ sK3_SY21 ) @ ( ksnd @ sK3_SY21 ) )
!= sK3_SY21 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(22,plain,
! [SV3: $i] :
( ( ! [SY29: $i,SY30: $i] :
( ~ ( in @ SY30 @ ( cartprod @ SV3 @ SY29 ) )
| ~ ( ~ ~ ( ( SY30
!= ( kpair @ ( sK4_Xx @ SY30 @ SY29 @ SV3 ) @ ( sK5_SY22 @ SY30 @ SY29 @ SV3 ) ) )
| ~ ( in @ ( sK5_SY22 @ SY30 @ SY29 @ SV3 ) @ SY29 ) )
| ~ ( in @ ( sK4_Xx @ SY30 @ SY29 @ SV3 ) @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV4: $i,SV1: $i] :
( ( ! [SY31: $i] :
( ~ ( in @ SY31 @ SV1 )
| ! [SY32: $i] :
( ~ ( in @ SY32 @ SV4 )
| ( ( ksnd @ ( kpair @ SY31 @ SY32 ) )
= SY32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
! [SV5: $i,SV2: $i] :
( ( ! [SY33: $i] :
( ~ ( in @ SY33 @ SV2 )
| ! [SY34: $i] :
( ~ ( in @ SY34 @ SV5 )
| ( ( kfst @ ( kpair @ SY33 @ SY34 ) )
= SY33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(25,plain,
( ( ~ ( in @ sK3_SY21 @ ( cartprod @ sK1_A @ sK2_SY19 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(26,plain,
( ( ~ ( ( ( kpair @ ( kfst @ sK3_SY21 ) @ ( ksnd @ sK3_SY21 ) )
!= sK3_SY21 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(27,plain,
! [SV6: $i,SV3: $i] :
( ( ! [SY35: $i] :
( ~ ( in @ SY35 @ ( cartprod @ SV3 @ SV6 ) )
| ~ ( ~ ~ ( ( SY35
!= ( kpair @ ( sK4_Xx @ SY35 @ SV6 @ SV3 ) @ ( sK5_SY22 @ SY35 @ SV6 @ SV3 ) ) )
| ~ ( in @ ( sK5_SY22 @ SY35 @ SV6 @ SV3 ) @ SV6 ) )
| ~ ( in @ ( sK4_Xx @ SY35 @ SV6 @ SV3 ) @ SV3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ~ ( in @ SV7 @ SV1 )
| ! [SY36: $i] :
( ~ ( in @ SY36 @ SV4 )
| ( ( ksnd @ ( kpair @ SV7 @ SY36 ) )
= SY36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV5: $i,SV2: $i,SV8: $i] :
( ( ~ ( in @ SV8 @ SV2 )
| ! [SY37: $i] :
( ~ ( in @ SY37 @ SV5 )
| ( ( kfst @ ( kpair @ SV8 @ SY37 ) )
= SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(30,plain,
( ( in @ sK3_SY21 @ ( cartprod @ sK1_A @ sK2_SY19 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(31,plain,
( ( ( ( kpair @ ( kfst @ sK3_SY21 ) @ ( ksnd @ sK3_SY21 ) )
!= sK3_SY21 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(32,plain,
! [SV6: $i,SV3: $i,SV9: $i] :
( ( ~ ( in @ SV9 @ ( cartprod @ SV3 @ SV6 ) )
| ~ ( ~ ~ ( ( SV9
!= ( kpair @ ( sK4_Xx @ SV9 @ SV6 @ SV3 ) @ ( sK5_SY22 @ SV9 @ SV6 @ SV3 ) ) )
| ~ ( in @ ( sK5_SY22 @ SV9 @ SV6 @ SV3 ) @ SV6 ) )
| ~ ( in @ ( sK4_Xx @ SV9 @ SV6 @ SV3 ) @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(33,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( ~ ( in @ SV7 @ SV1 ) )
= $true )
| ( ( ! [SY36: $i] :
( ~ ( in @ SY36 @ SV4 )
| ( ( ksnd @ ( kpair @ SV7 @ SY36 ) )
= SY36 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(34,plain,
! [SV5: $i,SV2: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV2 ) )
= $true )
| ( ( ! [SY37: $i] :
( ~ ( in @ SY37 @ SV5 )
| ( ( kfst @ ( kpair @ SV8 @ SY37 ) )
= SV8 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(35,plain,
( ( ( kpair @ ( kfst @ sK3_SY21 ) @ ( ksnd @ sK3_SY21 ) )
= sK3_SY21 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV6: $i,SV3: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ ( cartprod @ SV3 @ SV6 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV9
!= ( kpair @ ( sK4_Xx @ SV9 @ SV6 @ SV3 ) @ ( sK5_SY22 @ SV9 @ SV6 @ SV3 ) ) )
| ~ ( in @ ( sK5_SY22 @ SV9 @ SV6 @ SV3 ) @ SV6 ) )
| ~ ( in @ ( sK4_Xx @ SV9 @ SV6 @ SV3 ) @ SV3 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(37,plain,
! [SV4: $i,SV1: $i,SV7: $i] :
( ( ( in @ SV7 @ SV1 )
= $false )
| ( ( ! [SY36: $i] :
( ~ ( in @ SY36 @ SV4 )
| ( ( ksnd @ ( kpair @ SV7 @ SY36 ) )
= SY36 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(38,plain,
! [SV5: $i,SV2: $i,SV8: $i] :
( ( ( in @ SV8 @ SV2 )
= $false )
| ( ( ! [SY37: $i] :
( ~ ( in @ SY37 @ SV5 )
| ( ( kfst @ ( kpair @ SV8 @ SY37 ) )
= SV8 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV6: $i,SV3: $i,SV9: $i] :
( ( ( in @ SV9 @ ( cartprod @ SV3 @ SV6 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( SV9
!= ( kpair @ ( sK4_Xx @ SV9 @ SV6 @ SV3 ) @ ( sK5_SY22 @ SV9 @ SV6 @ SV3 ) ) )
| ~ ( in @ ( sK5_SY22 @ SV9 @ SV6 @ SV3 ) @ SV6 ) )
| ~ ( in @ ( sK4_Xx @ SV9 @ SV6 @ SV3 ) @ SV3 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(40,plain,
! [SV1: $i,SV7: $i,SV4: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV4 )
| ( ( ksnd @ ( kpair @ SV7 @ SV10 ) )
= SV10 ) )
= $true )
| ( ( in @ SV7 @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(41,plain,
! [SV2: $i,SV8: $i,SV5: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV5 )
| ( ( kfst @ ( kpair @ SV8 @ SV11 ) )
= SV8 ) )
= $true )
| ( ( in @ SV8 @ SV2 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(42,plain,
! [SV3: $i,SV6: $i,SV9: $i] :
( ( ( ~ ~ ( ( SV9
!= ( kpair @ ( sK4_Xx @ SV9 @ SV6 @ SV3 ) @ ( sK5_SY22 @ SV9 @ SV6 @ SV3 ) ) )
| ~ ( in @ ( sK5_SY22 @ SV9 @ SV6 @ SV3 ) @ SV6 ) )
| ~ ( in @ ( sK4_Xx @ SV9 @ SV6 @ SV3 ) @ SV3 ) )
= $false )
| ( ( in @ SV9 @ ( cartprod @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(43,plain,
! [SV1: $i,SV7: $i,SV4: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV4 ) )
= $true )
| ( ( ( ksnd @ ( kpair @ SV7 @ SV10 ) )
= SV10 )
= $true )
| ( ( in @ SV7 @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(44,plain,
! [SV2: $i,SV8: $i,SV5: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV5 ) )
= $true )
| ( ( ( kfst @ ( kpair @ SV8 @ SV11 ) )
= SV8 )
= $true )
| ( ( in @ SV8 @ SV2 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(45,plain,
! [SV3: $i,SV6: $i,SV9: $i] :
( ( ( ~ ~ ( ( SV9
!= ( kpair @ ( sK4_Xx @ SV9 @ SV6 @ SV3 ) @ ( sK5_SY22 @ SV9 @ SV6 @ SV3 ) ) )
| ~ ( in @ ( sK5_SY22 @ SV9 @ SV6 @ SV3 ) @ SV6 ) ) )
= $false )
| ( ( in @ SV9 @ ( cartprod @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(46,plain,
! [SV3: $i,SV6: $i,SV9: $i] :
( ( ( ~ ( in @ ( sK4_Xx @ SV9 @ SV6 @ SV3 ) @ SV3 ) )
= $false )
| ( ( in @ SV9 @ ( cartprod @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[42]) ).
thf(47,plain,
! [SV1: $i,SV7: $i,SV4: $i,SV10: $i] :
( ( ( in @ SV10 @ SV4 )
= $false )
| ( ( ( ksnd @ ( kpair @ SV7 @ SV10 ) )
= SV10 )
= $true )
| ( ( in @ SV7 @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV2: $i,SV8: $i,SV5: $i,SV11: $i] :
( ( ( in @ SV11 @ SV5 )
= $false )
| ( ( ( kfst @ ( kpair @ SV8 @ SV11 ) )
= SV8 )
= $true )
| ( ( in @ SV8 @ SV2 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV3: $i,SV6: $i,SV9: $i] :
( ( ( ~ ( ( SV9
!= ( kpair @ ( sK4_Xx @ SV9 @ SV6 @ SV3 ) @ ( sK5_SY22 @ SV9 @ SV6 @ SV3 ) ) )
| ~ ( in @ ( sK5_SY22 @ SV9 @ SV6 @ SV3 ) @ SV6 ) ) )
= $true )
| ( ( in @ SV9 @ ( cartprod @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(50,plain,
! [SV3: $i,SV6: $i,SV9: $i] :
( ( ( in @ ( sK4_Xx @ SV9 @ SV6 @ SV3 ) @ SV3 )
= $true )
| ( ( in @ SV9 @ ( cartprod @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(51,plain,
! [SV3: $i,SV6: $i,SV9: $i] :
( ( ( ( SV9
!= ( kpair @ ( sK4_Xx @ SV9 @ SV6 @ SV3 ) @ ( sK5_SY22 @ SV9 @ SV6 @ SV3 ) ) )
| ~ ( in @ ( sK5_SY22 @ SV9 @ SV6 @ SV3 ) @ SV6 ) )
= $false )
| ( ( in @ SV9 @ ( cartprod @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(52,plain,
! [SV3: $i,SV6: $i,SV9: $i] :
( ( ( ( SV9
!= ( kpair @ ( sK4_Xx @ SV9 @ SV6 @ SV3 ) @ ( sK5_SY22 @ SV9 @ SV6 @ SV3 ) ) ) )
= $false )
| ( ( in @ SV9 @ ( cartprod @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(53,plain,
! [SV3: $i,SV6: $i,SV9: $i] :
( ( ( ~ ( in @ ( sK5_SY22 @ SV9 @ SV6 @ SV3 ) @ SV6 ) )
= $false )
| ( ( in @ SV9 @ ( cartprod @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(54,plain,
! [SV3: $i,SV6: $i,SV9: $i] :
( ( ( SV9
= ( kpair @ ( sK4_Xx @ SV9 @ SV6 @ SV3 ) @ ( sK5_SY22 @ SV9 @ SV6 @ SV3 ) ) )
= $true )
| ( ( in @ SV9 @ ( cartprod @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(55,plain,
! [SV3: $i,SV6: $i,SV9: $i] :
( ( ( in @ ( sK5_SY22 @ SV9 @ SV6 @ SV3 ) @ SV6 )
= $true )
| ( ( in @ SV9 @ ( cartprod @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(56,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[30,55,54,50,48,47,35]) ).
thf(57,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU664^2 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n022.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 : Sun Jun 19 04:51:01 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: 731
% 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)...
% 0.21/0.53
% 0.21/0.53 ********************************
% 0.21/0.53 * All subproblems solved! *
% 0.21/0.53 ********************************
% 0.21/0.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,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:56,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.21/0.53
% 0.21/0.53 %**** Beginning of derivation protocol ****
% 0.21/0.53 % SZS output start CNFRefutation
% See solution above
% 0.21/0.53
% 0.21/0.53 %**** End of derivation protocol ****
% 0.21/0.53 %**** no. of clauses in derivation: 57 ****
% 0.21/0.53 %**** clause counter: 56 ****
% 0.21/0.53
% 0.21/0.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:3,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:56,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------