TSTP Solution File: SEU668^2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU668^2 : 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 : n016.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 12:13:48 EDT 2022
% Result : Theorem 129.64s 129.85s
% Output : CNFRefutation 129.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 26
% Syntax : Number of formulae : 212 ( 56 unt; 21 typ; 4 def)
% Number of atoms : 1461 ( 637 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 3157 ( 800 ~; 471 |; 9 &;1856 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 149 ( 149 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 11 con; 0-3 aty)
% Number of variables : 549 ( 77 ^ 470 !; 2 ?; 549 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_cartprod,type,
cartprod: $i > $i > $i ).
thf(tp_dpsetconstr,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(tp_dsetconstrER,type,
dsetconstrER: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_kpair,type,
kpair: $i > $i > $i ).
thf(tp_sK10_E,type,
sK10_E: ( $i > $o ) > $i ).
thf(tp_sK11_SY199,type,
sK11_SY199: ( $i > $o ) > $i ).
thf(tp_sK12_SY206,type,
sK12_SY206: ( $i > $o ) > $i ).
thf(tp_sK13_E,type,
sK13_E: $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY118,type,
sK2_SY118: $i ).
thf(tp_sK3_SY124,type,
sK3_SY124: $i > $i > $o ).
thf(tp_sK4_SY129,type,
sK4_SY129: $i ).
thf(tp_sK5_SY133,type,
sK5_SY133: $i ).
thf(tp_sK6_E,type,
sK6_E: ( $i > $o ) > $i ).
thf(tp_sK7_SY177,type,
sK7_SY177: ( $i > $o ) > $i ).
thf(tp_sK8_SY180,type,
sK8_SY180: ( $i > $o ) > $i ).
thf(tp_sK9_E,type,
sK9_E: $i ).
thf(tp_setukpairinjL,type,
setukpairinjL: $o ).
thf(tp_setukpairinjR,type,
setukpairinjR: $o ).
thf(dpsetconstr,definition,
( dpsetconstr
= ( ^ [A: $i,B: $i,Xphi: $i > $i > $o] :
( dsetconstr @ ( cartprod @ A @ B )
@ ^ [Xu: $i] :
? [Xx: $i] :
( ( in @ Xx @ A )
& ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xphi @ Xx @ Xy )
& ( Xu
= ( kpair @ Xx @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstr) ).
thf(dsetconstrER,definition,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(setukpairinjL,definition,
( setukpairinjL
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xx = Xz ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL) ).
thf(setukpairinjR,definition,
( setukpairinjR
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xy = Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR) ).
thf(1,conjecture,
( dsetconstrER
=> ( setukpairinjL
=> ( setukpairinjR
=> ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( Xphi @ Xx @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrERa) ).
thf(2,negated_conjecture,
( ( dsetconstrER
=> ( setukpairinjL
=> ( setukpairinjR
=> ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( Xphi @ Xx @ Xy ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
dsetconstrER = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(4,plain,
setukpairinjL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(5,plain,
setukpairinjR = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(6,plain,
( ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( Xphi @ Xx @ Xy ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[2]) ).
thf(7,plain,
( ( ~ ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( Xphi @ Xx @ Xy ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ( in @ sK4_SY129 @ sK1_A )
& ( in @ sK5_SY133 @ sK2_SY118 )
& ( in @ ( kpair @ sK4_SY129 @ sK5_SY133 )
@ ( dpsetconstr @ sK1_A @ sK2_SY118
@ ^ [SY131: $i,SY132: $i] : ( sK3_SY124 @ SY131 @ SY132 ) ) )
& ~ ( sK3_SY124 @ sK4_SY129 @ sK5_SY133 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(9,plain,
setukpairinjR = $true,
inference(copy,[status(thm)],[5]) ).
thf(10,plain,
setukpairinjL = $true,
inference(copy,[status(thm)],[4]) ).
thf(11,plain,
dsetconstrER = $true,
inference(copy,[status(thm)],[3]) ).
thf(12,plain,
( ( ( in @ sK4_SY129 @ sK1_A )
& ( in @ sK5_SY133 @ sK2_SY118 )
& ( in @ ( kpair @ sK4_SY129 @ sK5_SY133 )
@ ( dpsetconstr @ sK1_A @ sK2_SY118
@ ^ [SY131: $i,SY132: $i] : ( sK3_SY124 @ SY131 @ SY132 ) ) )
& ~ ( sK3_SY124 @ sK4_SY129 @ sK5_SY133 ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(13,plain,
( ( ~ ( ~ ( in @ sK4_SY129 @ sK1_A )
| ~ ~ ( ~ ( in @ sK5_SY133 @ sK2_SY118 )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY129 @ sK5_SY133 )
@ ( dsetconstr @ ( cartprod @ sK1_A @ sK2_SY118 )
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ sK1_A )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX2 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SX1 @ SX2 ) )
| ( SX0
!= ( kpair @ SX1 @ SX2 ) ) ) ) ) )
| ~ ~ ( sK3_SY124 @ sK4_SY129 @ sK5_SY133 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,dpsetconstr,dsetconstrER,setukpairinjL,setukpairinjR]) ).
thf(14,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( kpair @ SX0 @ SX1 )
!= ( kpair @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,dpsetconstr,dsetconstrER,setukpairinjL,setukpairinjR]) ).
thf(15,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,dpsetconstr,dsetconstrER,setukpairinjL,setukpairinjR]) ).
thf(16,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( kpair @ SX0 @ SX1 )
!= ( kpair @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,dpsetconstr,dsetconstrER,setukpairinjL,setukpairinjR]) ).
thf(17,plain,
( ( ~ ( in @ sK4_SY129 @ sK1_A )
| ~ ~ ( ~ ( in @ sK5_SY133 @ sK2_SY118 )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY129 @ sK5_SY133 )
@ ( dsetconstr @ ( cartprod @ sK1_A @ sK2_SY118 )
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ sK1_A )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX2 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SX1 @ SX2 ) )
| ( SX0
!= ( kpair @ SX1 @ SX2 ) ) ) ) ) )
| ~ ~ ( sK3_SY124 @ sK4_SY129 @ sK5_SY133 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(18,plain,
! [SV1: $i] :
( ( ! [SY138: $i,SY139: $i,SY140: $i] :
( ( ( kpair @ SV1 @ SY138 )
!= ( kpair @ SY139 @ SY140 ) )
| ( SY138 = SY140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(19,plain,
! [SV2: $i] :
( ( ! [SY141: $i > $o,SY142: $i] :
( ~ ( in @ SY142
@ ( dsetconstr @ SV2
@ ^ [SX3: $i] : ( SY141 @ SX3 ) ) )
| ( SY141 @ SY142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(20,plain,
! [SV3: $i] :
( ( ! [SY144: $i,SY145: $i,SY146: $i] :
( ( ( kpair @ SV3 @ SY144 )
!= ( kpair @ SY145 @ SY146 ) )
| ( SV3 = SY145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(21,plain,
( ( ~ ( in @ sK4_SY129 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(22,plain,
( ( ~ ~ ( ~ ( in @ sK5_SY133 @ sK2_SY118 )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY129 @ sK5_SY133 )
@ ( dsetconstr @ ( cartprod @ sK1_A @ sK2_SY118 )
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ sK1_A )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX2 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SX1 @ SX2 ) )
| ( SX0
!= ( kpair @ SX1 @ SX2 ) ) ) ) ) )
| ~ ~ ( sK3_SY124 @ sK4_SY129 @ sK5_SY133 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[17]) ).
thf(23,plain,
! [SV4: $i,SV1: $i] :
( ( ! [SY147: $i,SY148: $i] :
( ( ( kpair @ SV1 @ SV4 )
!= ( kpair @ SY147 @ SY148 ) )
| ( SV4 = SY148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(24,plain,
! [SV5: $i > $o,SV2: $i] :
( ( ! [SY149: $i] :
( ~ ( in @ SY149
@ ( dsetconstr @ SV2
@ ^ [SY150: $i] : ( SV5 @ SY150 ) ) )
| ( SV5 @ SY149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(25,plain,
! [SV6: $i,SV3: $i] :
( ( ! [SY151: $i,SY152: $i] :
( ( ( kpair @ SV3 @ SV6 )
!= ( kpair @ SY151 @ SY152 ) )
| ( SV3 = SY151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(26,plain,
( ( in @ sK4_SY129 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(27,plain,
( ( ~ ( ~ ( in @ sK5_SY133 @ sK2_SY118 )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY129 @ sK5_SY133 )
@ ( dsetconstr @ ( cartprod @ sK1_A @ sK2_SY118 )
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ sK1_A )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX2 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SX1 @ SX2 ) )
| ( SX0
!= ( kpair @ SX1 @ SX2 ) ) ) ) ) )
| ~ ~ ( sK3_SY124 @ sK4_SY129 @ sK5_SY133 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(28,plain,
! [SV7: $i,SV4: $i,SV1: $i] :
( ( ! [SY153: $i] :
( ( ( kpair @ SV1 @ SV4 )
!= ( kpair @ SV7 @ SY153 ) )
| ( SV4 = SY153 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(29,plain,
! [SV5: $i > $o,SV2: $i,SV8: $i] :
( ( ~ ( in @ SV8
@ ( dsetconstr @ SV2
@ ^ [SY150: $i] : ( SV5 @ SY150 ) ) )
| ( SV5 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(30,plain,
! [SV9: $i,SV6: $i,SV3: $i] :
( ( ! [SY155: $i] :
( ( ( kpair @ SV3 @ SV6 )
!= ( kpair @ SV9 @ SY155 ) )
| ( SV3 = SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(31,plain,
( ( ~ ( in @ sK5_SY133 @ sK2_SY118 )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY129 @ sK5_SY133 )
@ ( dsetconstr @ ( cartprod @ sK1_A @ sK2_SY118 )
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ sK1_A )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX2 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SX1 @ SX2 ) )
| ( SX0
!= ( kpair @ SX1 @ SX2 ) ) ) ) ) )
| ~ ~ ( sK3_SY124 @ sK4_SY129 @ sK5_SY133 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(32,plain,
! [SV10: $i,SV7: $i,SV4: $i,SV1: $i] :
( ( ( ( kpair @ SV1 @ SV4 )
!= ( kpair @ SV7 @ SV10 ) )
| ( SV4 = SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV5: $i > $o,SV2: $i,SV8: $i] :
( ( ( ~ ( in @ SV8
@ ( dsetconstr @ SV2
@ ^ [SY150: $i] : ( SV5 @ SY150 ) ) ) )
= $true )
| ( ( SV5 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[29]) ).
thf(34,plain,
! [SV11: $i,SV9: $i,SV6: $i,SV3: $i] :
( ( ( ( kpair @ SV3 @ SV6 )
!= ( kpair @ SV9 @ SV11 ) )
| ( SV3 = SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(35,plain,
( ( ~ ( in @ sK5_SY133 @ sK2_SY118 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(36,plain,
( ( ~ ~ ( ~ ( in @ ( kpair @ sK4_SY129 @ sK5_SY133 )
@ ( dsetconstr @ ( cartprod @ sK1_A @ sK2_SY118 )
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ sK1_A )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX2 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SX1 @ SX2 ) )
| ( SX0
!= ( kpair @ SX1 @ SX2 ) ) ) ) ) )
| ~ ~ ( sK3_SY124 @ sK4_SY129 @ sK5_SY133 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[31]) ).
thf(37,plain,
! [SV10: $i,SV7: $i,SV4: $i,SV1: $i] :
( ( ( ( ( kpair @ SV1 @ SV4 )
!= ( kpair @ SV7 @ SV10 ) ) )
= $true )
| ( ( SV4 = SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(38,plain,
! [SV5: $i > $o,SV2: $i,SV8: $i] :
( ( ( in @ SV8
@ ( dsetconstr @ SV2
@ ^ [SY150: $i] : ( SV5 @ SY150 ) ) )
= $false )
| ( ( SV5 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(39,plain,
! [SV11: $i,SV9: $i,SV6: $i,SV3: $i] :
( ( ( ( ( kpair @ SV3 @ SV6 )
!= ( kpair @ SV9 @ SV11 ) ) )
= $true )
| ( ( SV3 = SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(40,plain,
( ( in @ sK5_SY133 @ sK2_SY118 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(41,plain,
( ( ~ ( ~ ( in @ ( kpair @ sK4_SY129 @ sK5_SY133 )
@ ( dsetconstr @ ( cartprod @ sK1_A @ sK2_SY118 )
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ sK1_A )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX2 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SX1 @ SX2 ) )
| ( SX0
!= ( kpair @ SX1 @ SX2 ) ) ) ) ) )
| ~ ~ ( sK3_SY124 @ sK4_SY129 @ sK5_SY133 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(42,plain,
! [SV10: $i,SV7: $i,SV4: $i,SV1: $i] :
( ( ( ( kpair @ SV1 @ SV4 )
= ( kpair @ SV7 @ SV10 ) )
= $false )
| ( ( SV4 = SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(43,plain,
! [SV11: $i,SV9: $i,SV6: $i,SV3: $i] :
( ( ( ( kpair @ SV3 @ SV6 )
= ( kpair @ SV9 @ SV11 ) )
= $false )
| ( ( SV3 = SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(44,plain,
( ( ~ ( in @ ( kpair @ sK4_SY129 @ sK5_SY133 )
@ ( dsetconstr @ ( cartprod @ sK1_A @ sK2_SY118 )
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ sK1_A )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX2 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SX1 @ SX2 ) )
| ( SX0
!= ( kpair @ SX1 @ SX2 ) ) ) ) ) )
| ~ ~ ( sK3_SY124 @ sK4_SY129 @ sK5_SY133 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(45,plain,
( ( ~ ( in @ ( kpair @ sK4_SY129 @ sK5_SY133 )
@ ( dsetconstr @ ( cartprod @ sK1_A @ sK2_SY118 )
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ sK1_A )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX2 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SX1 @ SX2 ) )
| ( SX0
!= ( kpair @ SX1 @ SX2 ) ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(46,plain,
( ( ~ ~ ( sK3_SY124 @ sK4_SY129 @ sK5_SY133 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[44]) ).
thf(47,plain,
( ( in @ ( kpair @ sK4_SY129 @ sK5_SY133 )
@ ( dsetconstr @ ( cartprod @ sK1_A @ sK2_SY118 )
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ sK1_A )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX2 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SX1 @ SX2 ) )
| ( SX0
!= ( kpair @ SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[45]) ).
thf(48,plain,
( ( ~ ( sK3_SY124 @ sK4_SY129 @ sK5_SY133 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[46]) ).
thf(49,plain,
( ( sK3_SY124 @ sK4_SY129 @ sK5_SY133 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(51,plain,
! [SV2: $i,SV8: $i] :
( ( ( in @ SV8
@ ( dsetconstr @ SV2
@ ^ [SX0: $i] : $false ) )
= $false )
| ( $false = $true ) ),
inference(prim_subst,[status(thm)],[38:[bind(SV5,$thf( ^ [SV14: $i] : $false ))]]) ).
thf(52,plain,
! [SV13: $i > $o,SV2: $i,SV8: $i] :
( ( ( in @ SV8
@ ( dsetconstr @ SV2
@ ^ [SX0: $i] :
~ ( SV13 @ SX0 ) ) )
= $false )
| ( ( ~ ( SV13 @ SV8 ) )
= $true ) ),
inference(prim_subst,[status(thm)],[38:[bind(SV5,$thf( ^ [SV12: $i] : ~ ( SV13 @ SV12 ) ))]]) ).
thf(68,plain,
! [SV2: $i,SV8: $i,SV13: $i > $o] :
( ( ( SV13 @ SV8 )
= $false )
| ( ( in @ SV8
@ ( dsetconstr @ SV2
@ ^ [SX0: $i] :
~ ( SV13 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(70,plain,
! [SV2: $i,SV8: $i] :
( ( in @ SV8
@ ( dsetconstr @ SV2
@ ^ [SX0: $i] : $false ) )
= $false ),
inference(sim,[status(thm)],[51]) ).
thf(71,plain,
! [SV23: $i > $o,SV24: $i,SV25: $i] :
( ( ( in @ SV25
@ ( dsetconstr @ SV24
@ ^ [SX0: $i] : ( SV23 @ SX0 ) ) )
= $false )
| ( ( SV23 @ SV25 )
= $true ) ),
inference(rename,[status(thm)],[38]) ).
thf(74,plain,
! [SV23: $i > $o,SV24: $i,SV25: $i] :
( ( ( ( in @ SV25
@ ( dsetconstr @ SV24
@ ^ [SX0: $i] : ( SV23 @ SX0 ) ) )
= ( in @ sK4_SY129 @ sK1_A ) )
= $false )
| ( ( SV23 @ SV25 )
= $true ) ),
inference(res,[status(thm)],[71,26]) ).
thf(76,plain,
! [SV24: $i,SV25: $i] :
( ( ( in @ SV25
@ ( dsetconstr @ SV24
@ ^ [SX0: $i] : $false ) )
= $false )
| ( $false = $true ) ),
inference(prim_subst,[status(thm)],[71:[bind(SV23,$thf( ^ [SV28: $i] : $false ))]]) ).
thf(77,plain,
! [SV24: $i,SV25: $i] :
( ( in @ SV25
@ ( dsetconstr @ SV24
@ ^ [SX0: $i] : $false ) )
= $false ),
inference(sim,[status(thm)],[76]) ).
thf(78,plain,
! [SV27: $i > $o,SV24: $i,SV25: $i] :
( ( ( in @ SV25
@ ( dsetconstr @ SV24
@ ^ [SX0: $i] :
~ ( SV27 @ SX0 ) ) )
= $false )
| ( ( ~ ( SV27 @ SV25 ) )
= $true ) ),
inference(prim_subst,[status(thm)],[71:[bind(SV23,$thf( ^ [SV26: $i] : ~ ( SV27 @ SV26 ) ))]]) ).
thf(79,plain,
! [SV24: $i,SV25: $i] :
( ( ( in @ SV25
@ ( dsetconstr @ SV24
@ ^ [SX0: $i] : ( SX0 = sK1_A ) ) )
= $false )
| ( ( SV25 = sK1_A )
= $true ) ),
inference(prim_subst,[status(thm)],[71:[bind(SV23,$thf( ^ [SV30: $i] : ( SV30 = sK1_A ) ))]]) ).
thf(80,plain,
! [SV24: $i,SV25: $i] :
( ( ( in @ SV25
@ ( dsetconstr @ SV24
@ ^ [SX0: $i] : ( SX0 = sK4_SY129 ) ) )
= $false )
| ( ( SV25 = sK4_SY129 )
= $true ) ),
inference(prim_subst,[status(thm)],[71:[bind(SV23,$thf( ^ [SV31: $i] : ( SV31 = sK4_SY129 ) ))]]) ).
thf(81,plain,
! [SV24: $i,SV25: $i] :
( ( ( in @ SV25
@ ( dsetconstr @ SV24
@ ^ [SX0: $i] : ( SX0 = sK5_SY133 ) ) )
= $false )
| ( ( SV25 = sK5_SY133 )
= $true ) ),
inference(prim_subst,[status(thm)],[71:[bind(SV23,$thf( ^ [SV32: $i] : ( SV32 = sK5_SY133 ) ))]]) ).
thf(82,plain,
! [SV24: $i,SV25: $i] :
( ( ( in @ SV25
@ ( dsetconstr @ SV24
@ ^ [SX0: $i] : ( SX0 = sK2_SY118 ) ) )
= $false )
| ( ( SV25 = sK2_SY118 )
= $true ) ),
inference(prim_subst,[status(thm)],[71:[bind(SV23,$thf( ^ [SV33: $i] : ( SV33 = sK2_SY118 ) ))]]) ).
thf(84,plain,
! [SV24: $i,SV23: $i > $o] :
( ( ( SV23 @ sK4_SY129 )
= $true )
| ( ( ( dsetconstr @ SV24
@ ^ [SX0: $i] : ( SV23 @ SX0 ) )
= sK1_A )
= $false ) ),
inference(extuni,[status(esa)],[74:[bind(SV25,$thf( sK4_SY129 ))]]) ).
thf(85,plain,
! [SV24: $i,SV25: $i,SV27: $i > $o] :
( ( ( SV27 @ SV25 )
= $false )
| ( ( in @ SV25
@ ( dsetconstr @ SV24
@ ^ [SX0: $i] :
~ ( SV27 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(86,plain,
! [SV23: $i > $o,SV24: $i,SV25: $i] :
( ( ( ( in @ sK5_SY133 @ sK2_SY118 )
= ( in @ SV25
@ ( dsetconstr @ SV24
@ ^ [SX0: $i] : ( SV23 @ SX0 ) ) ) )
= $false )
| ( ( SV23 @ SV25 )
= $true ) ),
inference(res,[status(thm)],[40,71]) ).
thf(87,plain,
! [SV24: $i,SV23: $i > $o] :
( ( ( SV23 @ sK5_SY133 )
= $true )
| ( ( sK2_SY118
= ( dsetconstr @ SV24
@ ^ [SX0: $i] : ( SV23 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[86:[bind(SV25,$thf( sK5_SY133 ))]]) ).
thf(88,plain,
! [SV67: $i,SV68: $i,SV69: $i,SV70: $i] :
( ( ( ( kpair @ SV70 @ SV69 )
= ( kpair @ SV68 @ SV67 ) )
= $false )
| ( ( SV69 = SV67 )
= $true ) ),
inference(rename,[status(thm)],[42]) ).
thf(96,plain,
! [SV71: $i,SV72: $i,SV73: $i,SV74: $i] :
( ( ( ( kpair @ SV74 @ SV73 )
= ( kpair @ SV72 @ SV71 ) )
= $false )
| ( ( SV74 = SV72 )
= $true ) ),
inference(rename,[status(thm)],[43]) ).
thf(99,plain,
! [SV71: $i,SV72: $i,SV73: $i,SV74: $i,SV67: $i,SV68: $i,SV69: $i,SV70: $i] :
( ( ( ( ( kpair @ SV74 @ SV73 )
= ( kpair @ SV72 @ SV71 ) )
= ( SV69 = SV67 ) )
= $false )
| ( ( SV74 = SV72 )
= $true )
| ( ( ( kpair @ SV70 @ SV69 )
= ( kpair @ SV68 @ SV67 ) )
= $false ) ),
inference(res,[status(thm)],[96,88]) ).
thf(100,plain,
! [SV71: $i,SV72: $i,SV73: $i,SV74: $i,SV67: $i,SV68: $i,SV69: $i,SV70: $i] :
( ( ( ( SV74 = SV72 )
= ( ( kpair @ SV70 @ SV69 )
= ( kpair @ SV68 @ SV67 ) ) )
= $false )
| ( ( ( kpair @ SV74 @ SV73 )
= ( kpair @ SV72 @ SV71 ) )
= $false )
| ( ( SV69 = SV67 )
= $true ) ),
inference(res,[status(thm)],[96,88]) ).
thf(106,plain,
! [SV70: $i,SV68: $i,SV67: $i,SV69: $i] :
( ( ( SV69 = SV67 )
= $true )
| ( ( ( kpair @ SV68 @ SV67 )
= ( kpair @ SV70 @ SV69 ) )
= $false ) ),
inference(extuni,[status(esa)],[100:[bind(SV73,$thf( SV71 )),bind(SV74,$thf( kpair @ SV68 @ SV67 )),bind(SV72,$thf( kpair @ SV70 @ SV69 ))]]) ).
thf(107,plain,
! [SV71: $i,SV70: $i,SV73: $i,SV68: $i,SV67: $i,SV69: $i] :
( ( ( SV69 = SV67 )
= $true )
| ( ( ( kpair @ ( kpair @ SV68 @ SV67 ) @ SV73 )
= ( kpair @ ( kpair @ SV70 @ SV69 ) @ SV71 ) )
= $false ) ),
inference(extuni,[status(esa)],[100:[bind(SV74,$thf( kpair @ SV68 @ SV67 )),bind(SV72,$thf( kpair @ SV70 @ SV69 ))]]) ).
thf(109,plain,
! [SV68: $i,SV70: $i,SV67: $i,SV69: $i] :
( ( ( SV69 = SV67 )
= $true )
| ( ( ( kpair @ SV70 @ SV69 )
= ( kpair @ SV68 @ SV67 ) )
= $false ) ),
inference(extuni,[status(esa)],[100:[bind(SV73,$thf( SV71 )),bind(SV72,$thf( kpair @ SV68 @ SV67 )),bind(SV74,$thf( kpair @ SV70 @ SV69 ))]]) ).
thf(110,plain,
! [SV71: $i,SV68: $i,SV73: $i,SV70: $i,SV67: $i,SV69: $i] :
( ( ( SV69 = SV67 )
= $true )
| ( ( ( kpair @ ( kpair @ SV70 @ SV69 ) @ SV73 )
= ( kpair @ ( kpair @ SV68 @ SV67 ) @ SV71 ) )
= $false ) ),
inference(extuni,[status(esa)],[100:[bind(SV72,$thf( kpair @ SV68 @ SV67 )),bind(SV74,$thf( kpair @ SV70 @ SV69 ))]]) ).
thf(112,plain,
! [SV73: $i,SV74: $i,SV71: $i,SV72: $i] :
( ( ( ( kpair @ SV72 @ SV71 )
= ( kpair @ SV74 @ SV73 ) )
= $false )
| ( ( SV74 = SV72 )
= $true ) ),
inference(extuni,[status(esa)],[99:[bind(SV70,$thf( SV68 )),bind(SV67,$thf( kpair @ SV74 @ SV73 )),bind(SV69,$thf( kpair @ SV72 @ SV71 ))]]) ).
thf(113,plain,
! [SV73: $i,SV74: $i,SV68: $i,SV71: $i,SV72: $i,SV70: $i] :
( ( ( ( kpair @ SV70 @ ( kpair @ SV72 @ SV71 ) )
= ( kpair @ SV68 @ ( kpair @ SV74 @ SV73 ) ) )
= $false )
| ( ( SV74 = SV72 )
= $true ) ),
inference(extuni,[status(esa)],[99:[bind(SV67,$thf( kpair @ SV74 @ SV73 )),bind(SV69,$thf( kpair @ SV72 @ SV71 ))]]) ).
thf(115,plain,
! [SV71: $i,SV72: $i,SV73: $i,SV74: $i] :
( ( ( ( kpair @ SV74 @ SV73 )
= ( kpair @ SV72 @ SV71 ) )
= $false )
| ( ( SV74 = SV72 )
= $true ) ),
inference(extuni,[status(esa)],[99:[bind(SV70,$thf( SV68 )),bind(SV67,$thf( kpair @ SV72 @ SV71 )),bind(SV69,$thf( kpair @ SV74 @ SV73 ))]]) ).
thf(116,plain,
! [SV71: $i,SV72: $i,SV68: $i,SV73: $i,SV74: $i,SV70: $i] :
( ( ( ( kpair @ SV70 @ ( kpair @ SV74 @ SV73 ) )
= ( kpair @ SV68 @ ( kpair @ SV72 @ SV71 ) ) )
= $false )
| ( ( SV74 = SV72 )
= $true ) ),
inference(extuni,[status(esa)],[99:[bind(SV67,$thf( kpair @ SV72 @ SV71 )),bind(SV69,$thf( kpair @ SV74 @ SV73 ))]]) ).
thf(120,plain,
! [SV23: $i > $o,SV24: $i,SV25: $i] :
( ( ( ( in @ ( kpair @ sK4_SY129 @ sK5_SY133 )
@ ( dsetconstr @ ( cartprod @ sK1_A @ sK2_SY118 )
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ sK1_A )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX2 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SX1 @ SX2 ) )
| ( SX0
!= ( kpair @ SX1 @ SX2 ) ) ) ) ) )
= ( in @ SV25
@ ( dsetconstr @ SV24
@ ^ [SX0: $i] : ( SV23 @ SX0 ) ) ) )
= $false )
| ( ( SV23 @ SV25 )
= $true ) ),
inference(res,[status(thm)],[47,71]) ).
thf(121,plain,
! [SV23: $i > $o] :
( ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( ~ ! [SY177: $i] :
~ ~ ( ~ ( in @ SY177 @ sK1_A )
| ~ ~ ! [SY178: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY178 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SY177 @ SY178 ) )
| ( ( sK6_E @ SV23 )
!= ( kpair @ SY177 @ SY178 ) ) ) ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $true ) ),
inference(extuni,[status(esa)],[120:[bind(SV24,$thf( cartprod @ sK1_A @ sK2_SY118 )),bind(SV25,$thf( kpair @ sK4_SY129 @ sK5_SY133 ))]]) ).
thf(122,plain,
! [SV23: $i > $o] :
( ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( ~ ! [SY177: $i] :
~ ~ ( ~ ( in @ SY177 @ sK1_A )
| ~ ~ ! [SY178: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY178 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SY177 @ SY178 ) )
| ( ( sK6_E @ SV23 )
!= ( kpair @ SY177 @ SY178 ) ) ) ) )
= $false )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $false ) ),
inference(extuni,[status(esa)],[120:[bind(SV24,$thf( cartprod @ sK1_A @ sK2_SY118 )),bind(SV25,$thf( kpair @ sK4_SY129 @ sK5_SY133 ))]]) ).
thf(123,plain,
! [SV24: $i,SV23: $i > $o] :
( ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( ( dsetconstr @ ( cartprod @ sK1_A @ sK2_SY118 )
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ sK1_A )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX2 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SX1 @ SX2 ) )
| ( SX0
!= ( kpair @ SX1 @ SX2 ) ) ) ) )
= ( dsetconstr @ SV24
@ ^ [SX0: $i] : ( SV23 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[120:[bind(SV25,$thf( kpair @ sK4_SY129 @ sK5_SY133 ))]]) ).
thf(124,plain,
! [SV23: $i > $o] :
( ( ( ! [SY177: $i] :
~ ~ ( ~ ( in @ SY177 @ sK1_A )
| ~ ~ ! [SY178: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY178 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SY177 @ SY178 ) )
| ( ( sK6_E @ SV23 )
!= ( kpair @ SY177 @ SY178 ) ) ) ) )
= $true )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(125,plain,
! [SV23: $i > $o] :
( ( ( ! [SY177: $i] :
~ ~ ( ~ ( in @ SY177 @ sK1_A )
| ~ ~ ! [SY178: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY178 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SY177 @ SY178 ) )
| ( ( sK6_E @ SV23 )
!= ( kpair @ SY177 @ SY178 ) ) ) ) )
= $false )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(126,plain,
! [SV23: $i > $o,SV75: $i] :
( ( ( ~ ~ ( ~ ( in @ SV75 @ sK1_A )
| ~ ~ ! [SY179: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY179 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SV75 @ SY179 ) )
| ( ( sK6_E @ SV23 )
!= ( kpair @ SV75 @ SY179 ) ) ) ) )
= $true )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(127,plain,
! [SV23: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK7_SY177 @ SV23 ) @ sK1_A )
| ~ ~ ! [SY180: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY180 @ sK2_SY118 )
| ~ ( sK3_SY124 @ ( sK7_SY177 @ SV23 ) @ SY180 ) )
| ( ( sK6_E @ SV23 )
!= ( kpair @ ( sK7_SY177 @ SV23 ) @ SY180 ) ) ) ) )
= $false )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[125]) ).
thf(128,plain,
! [SV23: $i > $o,SV75: $i] :
( ( ( ~ ( ~ ( in @ SV75 @ sK1_A )
| ~ ~ ! [SY179: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY179 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SV75 @ SY179 ) )
| ( ( sK6_E @ SV23 )
!= ( kpair @ SV75 @ SY179 ) ) ) ) )
= $false )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(129,plain,
! [SV23: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK7_SY177 @ SV23 ) @ sK1_A )
| ~ ~ ! [SY180: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY180 @ sK2_SY118 )
| ~ ( sK3_SY124 @ ( sK7_SY177 @ SV23 ) @ SY180 ) )
| ( ( sK6_E @ SV23 )
!= ( kpair @ ( sK7_SY177 @ SV23 ) @ SY180 ) ) ) ) )
= $true )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[127]) ).
thf(130,plain,
! [SV23: $i > $o,SV75: $i] :
( ( ( ~ ( in @ SV75 @ sK1_A )
| ~ ~ ! [SY179: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY179 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SV75 @ SY179 ) )
| ( ( sK6_E @ SV23 )
!= ( kpair @ SV75 @ SY179 ) ) ) )
= $true )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[128]) ).
thf(131,plain,
! [SV23: $i > $o] :
( ( ( ~ ( in @ ( sK7_SY177 @ SV23 ) @ sK1_A )
| ~ ~ ! [SY180: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY180 @ sK2_SY118 )
| ~ ( sK3_SY124 @ ( sK7_SY177 @ SV23 ) @ SY180 ) )
| ( ( sK6_E @ SV23 )
!= ( kpair @ ( sK7_SY177 @ SV23 ) @ SY180 ) ) ) )
= $false )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[129]) ).
thf(132,plain,
! [SV23: $i > $o,SV75: $i] :
( ( ( ~ ( in @ SV75 @ sK1_A ) )
= $true )
| ( ( ~ ~ ! [SY179: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY179 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SV75 @ SY179 ) )
| ( ( sK6_E @ SV23 )
!= ( kpair @ SV75 @ SY179 ) ) ) )
= $true )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(133,plain,
! [SV23: $i > $o] :
( ( ( ~ ( in @ ( sK7_SY177 @ SV23 ) @ sK1_A ) )
= $false )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(134,plain,
! [SV23: $i > $o] :
( ( ( ~ ~ ! [SY180: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY180 @ sK2_SY118 )
| ~ ( sK3_SY124 @ ( sK7_SY177 @ SV23 ) @ SY180 ) )
| ( ( sK6_E @ SV23 )
!= ( kpair @ ( sK7_SY177 @ SV23 ) @ SY180 ) ) ) )
= $false )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[131]) ).
thf(135,plain,
! [SV23: $i > $o,SV75: $i] :
( ( ( in @ SV75 @ sK1_A )
= $false )
| ( ( ~ ~ ! [SY179: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY179 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SV75 @ SY179 ) )
| ( ( sK6_E @ SV23 )
!= ( kpair @ SV75 @ SY179 ) ) ) )
= $true )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(136,plain,
! [SV23: $i > $o] :
( ( ( in @ ( sK7_SY177 @ SV23 ) @ sK1_A )
= $true )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[133]) ).
thf(137,plain,
! [SV23: $i > $o] :
( ( ( ~ ! [SY180: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY180 @ sK2_SY118 )
| ~ ( sK3_SY124 @ ( sK7_SY177 @ SV23 ) @ SY180 ) )
| ( ( sK6_E @ SV23 )
!= ( kpair @ ( sK7_SY177 @ SV23 ) @ SY180 ) ) ) )
= $true )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(138,plain,
! [SV23: $i > $o,SV75: $i] :
( ( ( ~ ! [SY179: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY179 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SV75 @ SY179 ) )
| ( ( sK6_E @ SV23 )
!= ( kpair @ SV75 @ SY179 ) ) ) )
= $false )
| ( ( in @ SV75 @ sK1_A )
= $false )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(139,plain,
! [SV23: $i > $o] :
( ( ( ! [SY180: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY180 @ sK2_SY118 )
| ~ ( sK3_SY124 @ ( sK7_SY177 @ SV23 ) @ SY180 ) )
| ( ( sK6_E @ SV23 )
!= ( kpair @ ( sK7_SY177 @ SV23 ) @ SY180 ) ) ) )
= $false )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(140,plain,
! [SV23: $i > $o,SV75: $i] :
( ( ( ! [SY179: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY179 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SV75 @ SY179 ) )
| ( ( sK6_E @ SV23 )
!= ( kpair @ SV75 @ SY179 ) ) ) )
= $true )
| ( ( in @ SV75 @ sK1_A )
= $false )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[138]) ).
thf(141,plain,
! [SV23: $i > $o] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK8_SY180 @ SV23 ) @ sK2_SY118 )
| ~ ( sK3_SY124 @ ( sK7_SY177 @ SV23 ) @ ( sK8_SY180 @ SV23 ) ) )
| ( ( sK6_E @ SV23 )
!= ( kpair @ ( sK7_SY177 @ SV23 ) @ ( sK8_SY180 @ SV23 ) ) ) ) )
= $false )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[139]) ).
thf(142,plain,
! [SV23: $i > $o,SV75: $i,SV76: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV76 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SV75 @ SV76 ) )
| ( ( sK6_E @ SV23 )
!= ( kpair @ SV75 @ SV76 ) ) ) )
= $true )
| ( ( in @ SV75 @ sK1_A )
= $false )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(143,plain,
! [SV23: $i > $o] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_SY180 @ SV23 ) @ sK2_SY118 )
| ~ ( sK3_SY124 @ ( sK7_SY177 @ SV23 ) @ ( sK8_SY180 @ SV23 ) ) )
| ( ( sK6_E @ SV23 )
!= ( kpair @ ( sK7_SY177 @ SV23 ) @ ( sK8_SY180 @ SV23 ) ) ) ) )
= $true )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[141]) ).
thf(144,plain,
! [SV23: $i > $o,SV75: $i,SV76: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV76 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SV75 @ SV76 ) )
| ( ( sK6_E @ SV23 )
!= ( kpair @ SV75 @ SV76 ) ) ) )
= $false )
| ( ( in @ SV75 @ sK1_A )
= $false )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(145,plain,
! [SV23: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK8_SY180 @ SV23 ) @ sK2_SY118 )
| ~ ( sK3_SY124 @ ( sK7_SY177 @ SV23 ) @ ( sK8_SY180 @ SV23 ) ) )
| ( ( sK6_E @ SV23 )
!= ( kpair @ ( sK7_SY177 @ SV23 ) @ ( sK8_SY180 @ SV23 ) ) ) )
= $false )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(146,plain,
! [SV23: $i > $o,SV75: $i,SV76: $i] :
( ( ( ~ ~ ( ~ ( in @ SV76 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SV75 @ SV76 ) )
| ( ( sK6_E @ SV23 )
!= ( kpair @ SV75 @ SV76 ) ) )
= $true )
| ( ( in @ SV75 @ sK1_A )
= $false )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[144]) ).
thf(147,plain,
! [SV23: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK8_SY180 @ SV23 ) @ sK2_SY118 )
| ~ ( sK3_SY124 @ ( sK7_SY177 @ SV23 ) @ ( sK8_SY180 @ SV23 ) ) ) )
= $false )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(148,plain,
! [SV23: $i > $o] :
( ( ( ( ( sK6_E @ SV23 )
!= ( kpair @ ( sK7_SY177 @ SV23 ) @ ( sK8_SY180 @ SV23 ) ) ) )
= $false )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[145]) ).
thf(149,plain,
! [SV23: $i > $o,SV75: $i,SV76: $i] :
( ( ( ~ ~ ( ~ ( in @ SV76 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SV75 @ SV76 ) ) )
= $true )
| ( ( ( ( sK6_E @ SV23 )
!= ( kpair @ SV75 @ SV76 ) ) )
= $true )
| ( ( in @ SV75 @ sK1_A )
= $false )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(150,plain,
! [SV23: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK8_SY180 @ SV23 ) @ sK2_SY118 )
| ~ ( sK3_SY124 @ ( sK7_SY177 @ SV23 ) @ ( sK8_SY180 @ SV23 ) ) ) )
= $true )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[147]) ).
thf(151,plain,
! [SV23: $i > $o] :
( ( ( ( sK6_E @ SV23 )
= ( kpair @ ( sK7_SY177 @ SV23 ) @ ( sK8_SY180 @ SV23 ) ) )
= $true )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(152,plain,
! [SV23: $i > $o,SV75: $i,SV76: $i] :
( ( ( ~ ( ~ ( in @ SV76 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SV75 @ SV76 ) ) )
= $false )
| ( ( ( ( sK6_E @ SV23 )
!= ( kpair @ SV75 @ SV76 ) ) )
= $true )
| ( ( in @ SV75 @ sK1_A )
= $false )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(153,plain,
! [SV23: $i > $o] :
( ( ( ~ ( in @ ( sK8_SY180 @ SV23 ) @ sK2_SY118 )
| ~ ( sK3_SY124 @ ( sK7_SY177 @ SV23 ) @ ( sK8_SY180 @ SV23 ) ) )
= $false )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(154,plain,
! [SV23: $i > $o,SV75: $i,SV76: $i] :
( ( ( ~ ( in @ SV76 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SV75 @ SV76 ) )
= $true )
| ( ( ( ( sK6_E @ SV23 )
!= ( kpair @ SV75 @ SV76 ) ) )
= $true )
| ( ( in @ SV75 @ sK1_A )
= $false )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[152]) ).
thf(155,plain,
! [SV23: $i > $o] :
( ( ( ~ ( in @ ( sK8_SY180 @ SV23 ) @ sK2_SY118 ) )
= $false )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(156,plain,
! [SV23: $i > $o] :
( ( ( ~ ( sK3_SY124 @ ( sK7_SY177 @ SV23 ) @ ( sK8_SY180 @ SV23 ) ) )
= $false )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[153]) ).
thf(157,plain,
! [SV23: $i > $o,SV75: $i,SV76: $i] :
( ( ( ~ ( in @ SV76 @ sK2_SY118 ) )
= $true )
| ( ( ~ ( sK3_SY124 @ SV75 @ SV76 ) )
= $true )
| ( ( ( ( sK6_E @ SV23 )
!= ( kpair @ SV75 @ SV76 ) ) )
= $true )
| ( ( in @ SV75 @ sK1_A )
= $false )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(158,plain,
! [SV23: $i > $o] :
( ( ( in @ ( sK8_SY180 @ SV23 ) @ sK2_SY118 )
= $true )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[155]) ).
thf(159,plain,
! [SV23: $i > $o] :
( ( ( sK3_SY124 @ ( sK7_SY177 @ SV23 ) @ ( sK8_SY180 @ SV23 ) )
= $true )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[156]) ).
thf(160,plain,
! [SV23: $i > $o,SV75: $i,SV76: $i] :
( ( ( in @ SV76 @ sK2_SY118 )
= $false )
| ( ( ~ ( sK3_SY124 @ SV75 @ SV76 ) )
= $true )
| ( ( ( ( sK6_E @ SV23 )
!= ( kpair @ SV75 @ SV76 ) ) )
= $true )
| ( ( in @ SV75 @ sK1_A )
= $false )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(161,plain,
! [SV23: $i > $o,SV76: $i,SV75: $i] :
( ( ( sK3_SY124 @ SV75 @ SV76 )
= $false )
| ( ( in @ SV76 @ sK2_SY118 )
= $false )
| ( ( ( ( sK6_E @ SV23 )
!= ( kpair @ SV75 @ SV76 ) ) )
= $true )
| ( ( in @ SV75 @ sK1_A )
= $false )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(162,plain,
! [SV76: $i,SV75: $i,SV23: $i > $o] :
( ( ( ( sK6_E @ SV23 )
= ( kpair @ SV75 @ SV76 ) )
= $false )
| ( ( in @ SV76 @ sK2_SY118 )
= $false )
| ( ( sK3_SY124 @ SV75 @ SV76 )
= $false )
| ( ( in @ SV75 @ sK1_A )
= $false )
| ( ( SV23 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $true )
| ( ( SV23 @ ( sK6_E @ SV23 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(169,plain,
! [SV77: $i,SV78: $i,SV79: $i > $o] :
( ( ( SV79 @ SV78 )
= $false )
| ( ( in @ SV78
@ ( dsetconstr @ SV77
@ ^ [SX0: $i] :
~ ( SV79 @ SX0 ) ) )
= $false ) ),
inference(rename,[status(thm)],[68]) ).
thf(176,plain,
! [SV77: $i,SV78: $i,SV79: $i > $o] :
( ( ( ( in @ SV78
@ ( dsetconstr @ SV77
@ ^ [SX0: $i] :
~ ( SV79 @ SX0 ) ) )
= ( in @ ( kpair @ sK4_SY129 @ sK5_SY133 )
@ ( dsetconstr @ ( cartprod @ sK1_A @ sK2_SY118 )
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ sK1_A )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX2 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SX1 @ SX2 ) )
| ( SX0
!= ( kpair @ SX1 @ SX2 ) ) ) ) ) ) )
= $false )
| ( ( SV79 @ SV78 )
= $false ) ),
inference(res,[status(thm)],[169,47]) ).
thf(178,plain,
! [SV77: $i,SV78: $i,SV79: $i > $o] :
( ( ( ( in @ SV78
@ ( dsetconstr @ SV77
@ ^ [SX0: $i] :
~ ( SV79 @ SX0 ) ) )
= ( in @ sK5_SY133 @ sK2_SY118 ) )
= $false )
| ( ( SV79 @ SV78 )
= $false ) ),
inference(res,[status(thm)],[169,40]) ).
thf(180,plain,
! [SV77: $i,SV78: $i,SV79: $i > $o] :
( ( ( ( in @ SV78
@ ( dsetconstr @ SV77
@ ^ [SX0: $i] :
~ ( SV79 @ SX0 ) ) )
= ( in @ sK4_SY129 @ sK1_A ) )
= $false )
| ( ( SV79 @ SV78 )
= $false ) ),
inference(res,[status(thm)],[169,26]) ).
thf(182,plain,
! [SV77: $i,SV78: $i] :
( ( $true = $false )
| ( ( in @ SV78
@ ( dsetconstr @ SV77
@ ^ [SX0: $i] : ~ $true ) )
= $false ) ),
inference(prim_subst,[status(thm)],[169:[bind(SV79,$thf( ^ [SV83: $i] : $true ))]]) ).
thf(183,plain,
! [SV77: $i,SV78: $i] :
( ( in @ SV78
@ ( dsetconstr @ SV77
@ ^ [SX0: $i] : ~ $true ) )
= $false ),
inference(sim,[status(thm)],[182]) ).
thf(185,plain,
! [SV77: $i,SV78: $i,SV81: $i > $o] :
( ( ( ~ ( SV81 @ SV78 ) )
= $false )
| ( ( in @ SV78
@ ( dsetconstr @ SV77
@ ^ [SX0: $i] :
~ ~ ( SV81 @ SX0 ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[169:[bind(SV79,$thf( ^ [SV80: $i] : ~ ( SV81 @ SV80 ) ))]]) ).
thf(186,plain,
! [SV77: $i,SV78: $i] :
( ( ( SV78 = sK9_E )
= $false )
| ( ( in @ SV78
@ ( dsetconstr @ SV77
@ ^ [SX0: $i] : ( SX0 != sK9_E ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[169:[bind(SV79,$thf( ^ [SV84: $i] : ( SV84 = sK9_E ) ))]]) ).
thf(187,plain,
! [SV77: $i,SV78: $i] :
( ( ( SV78 = sK4_SY129 )
= $false )
| ( ( in @ SV78
@ ( dsetconstr @ SV77
@ ^ [SX0: $i] : ( SX0 != sK4_SY129 ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[169:[bind(SV79,$thf( ^ [SV85: $i] : ( SV85 = sK4_SY129 ) ))]]) ).
thf(188,plain,
! [SV77: $i,SV78: $i] :
( ( ( SV78 = sK5_SY133 )
= $false )
| ( ( in @ SV78
@ ( dsetconstr @ SV77
@ ^ [SX0: $i] : ( SX0 != sK5_SY133 ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[169:[bind(SV79,$thf( ^ [SV86: $i] : ( SV86 = sK5_SY133 ) ))]]) ).
thf(189,plain,
! [SV77: $i,SV78: $i] :
( ( ( SV78 = sK2_SY118 )
= $false )
| ( ( in @ SV78
@ ( dsetconstr @ SV77
@ ^ [SX0: $i] : ( SX0 != sK2_SY118 ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[169:[bind(SV79,$thf( ^ [SV87: $i] : ( SV87 = sK2_SY118 ) ))]]) ).
thf(190,plain,
! [SV77: $i,SV78: $i] :
( ( ( SV78 = sK1_A )
= $false )
| ( ( in @ SV78
@ ( dsetconstr @ SV77
@ ^ [SX0: $i] : ( SX0 != sK1_A ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[169:[bind(SV79,$thf( ^ [SV88: $i] : ( SV88 = sK1_A ) ))]]) ).
thf(192,plain,
! [SV77: $i,SV79: $i > $o] :
( ( ( SV79 @ sK4_SY129 )
= $false )
| ( ( ( dsetconstr @ SV77
@ ^ [SX0: $i] :
~ ( SV79 @ SX0 ) )
= sK1_A )
= $false ) ),
inference(extuni,[status(esa)],[180:[bind(SV78,$thf( sK4_SY129 ))]]) ).
thf(193,plain,
! [SV77: $i,SV79: $i > $o] :
( ( ( SV79 @ sK5_SY133 )
= $false )
| ( ( ( dsetconstr @ SV77
@ ^ [SX0: $i] :
~ ( SV79 @ SX0 ) )
= sK2_SY118 )
= $false ) ),
inference(extuni,[status(esa)],[178:[bind(SV78,$thf( sK5_SY133 ))]]) ).
thf(194,plain,
! [SV79: $i > $o] :
( ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( ~ ( SV79 @ ( sK10_E @ SV79 ) ) )
= $true )
| ( ( ~ ! [SY199: $i] :
~ ~ ( ~ ( in @ SY199 @ sK1_A )
| ~ ~ ! [SY200: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY200 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SY199 @ SY200 ) )
| ( ( sK10_E @ SV79 )
!= ( kpair @ SY199 @ SY200 ) ) ) ) )
= $true ) ),
inference(extuni,[status(esa)],[176:[bind(SV77,$thf( cartprod @ sK1_A @ sK2_SY118 )),bind(SV78,$thf( kpair @ sK4_SY129 @ sK5_SY133 ))]]) ).
thf(195,plain,
! [SV79: $i > $o] :
( ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( ~ ( SV79 @ ( sK10_E @ SV79 ) ) )
= $false )
| ( ( ~ ! [SY199: $i] :
~ ~ ( ~ ( in @ SY199 @ sK1_A )
| ~ ~ ! [SY200: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY200 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SY199 @ SY200 ) )
| ( ( sK10_E @ SV79 )
!= ( kpair @ SY199 @ SY200 ) ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[176:[bind(SV77,$thf( cartprod @ sK1_A @ sK2_SY118 )),bind(SV78,$thf( kpair @ sK4_SY129 @ sK5_SY133 ))]]) ).
thf(196,plain,
! [SV77: $i,SV79: $i > $o] :
( ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( ( dsetconstr @ SV77
@ ^ [SX0: $i] :
~ ( SV79 @ SX0 ) )
= ( dsetconstr @ ( cartprod @ sK1_A @ sK2_SY118 )
@ ^ [SX0: $i] :
~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ sK1_A )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SX2 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SX1 @ SX2 ) )
| ( SX0
!= ( kpair @ SX1 @ SX2 ) ) ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[176:[bind(SV78,$thf( kpair @ sK4_SY129 @ sK5_SY133 ))]]) ).
thf(197,plain,
! [SV77: $i] :
( ( in @ sK9_E
@ ( dsetconstr @ SV77
@ ^ [SX0: $i] : ( SX0 != sK9_E ) ) )
= $false ),
inference(extuni,[status(esa)],[186:[bind(SV78,$thf( sK9_E ))]]) ).
thf(198,plain,
! [SV77: $i] :
( ( in @ sK4_SY129
@ ( dsetconstr @ SV77
@ ^ [SX0: $i] : ( SX0 != sK4_SY129 ) ) )
= $false ),
inference(extuni,[status(esa)],[187:[bind(SV78,$thf( sK4_SY129 ))]]) ).
thf(199,plain,
! [SV77: $i] :
( ( in @ sK5_SY133
@ ( dsetconstr @ SV77
@ ^ [SX0: $i] : ( SX0 != sK5_SY133 ) ) )
= $false ),
inference(extuni,[status(esa)],[188:[bind(SV78,$thf( sK5_SY133 ))]]) ).
thf(200,plain,
! [SV77: $i] :
( ( in @ sK2_SY118
@ ( dsetconstr @ SV77
@ ^ [SX0: $i] : ( SX0 != sK2_SY118 ) ) )
= $false ),
inference(extuni,[status(esa)],[189:[bind(SV78,$thf( sK2_SY118 ))]]) ).
thf(201,plain,
! [SV77: $i] :
( ( in @ sK1_A
@ ( dsetconstr @ SV77
@ ^ [SX0: $i] : ( SX0 != sK1_A ) ) )
= $false ),
inference(extuni,[status(esa)],[190:[bind(SV78,$thf( sK1_A ))]]) ).
thf(202,plain,
! [SV79: $i > $o] :
( ( ( SV79 @ ( sK10_E @ SV79 ) )
= $true )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( ~ ! [SY199: $i] :
~ ~ ( ~ ( in @ SY199 @ sK1_A )
| ~ ~ ! [SY200: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY200 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SY199 @ SY200 ) )
| ( ( sK10_E @ SV79 )
!= ( kpair @ SY199 @ SY200 ) ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[195]) ).
thf(203,plain,
! [SV79: $i > $o] :
( ( ( SV79 @ ( sK10_E @ SV79 ) )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( ~ ! [SY199: $i] :
~ ~ ( ~ ( in @ SY199 @ sK1_A )
| ~ ~ ! [SY200: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY200 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SY199 @ SY200 ) )
| ( ( sK10_E @ SV79 )
!= ( kpair @ SY199 @ SY200 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(204,plain,
! [SV77: $i,SV78: $i,SV81: $i > $o] :
( ( ( SV81 @ SV78 )
= $true )
| ( ( in @ SV78
@ ( dsetconstr @ SV77
@ ^ [SX0: $i] :
~ ~ ( SV81 @ SX0 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[185]) ).
thf(205,plain,
! [SV79: $i > $o] :
( ( ( ! [SY199: $i] :
~ ~ ( ~ ( in @ SY199 @ sK1_A )
| ~ ~ ! [SY200: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY200 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SY199 @ SY200 ) )
| ( ( sK10_E @ SV79 )
!= ( kpair @ SY199 @ SY200 ) ) ) ) )
= $true )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[202]) ).
thf(206,plain,
! [SV79: $i > $o] :
( ( ( ! [SY199: $i] :
~ ~ ( ~ ( in @ SY199 @ sK1_A )
| ~ ~ ! [SY200: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY200 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SY199 @ SY200 ) )
| ( ( sK10_E @ SV79 )
!= ( kpair @ SY199 @ SY200 ) ) ) ) )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(207,plain,
! [SV79: $i > $o,SV142: $i] :
( ( ( ~ ~ ( ~ ( in @ SV142 @ sK1_A )
| ~ ~ ! [SY205: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY205 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SV142 @ SY205 ) )
| ( ( sK10_E @ SV79 )
!= ( kpair @ SV142 @ SY205 ) ) ) ) )
= $true )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(208,plain,
! [SV79: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK11_SY199 @ SV79 ) @ sK1_A )
| ~ ~ ! [SY206: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY206 @ sK2_SY118 )
| ~ ( sK3_SY124 @ ( sK11_SY199 @ SV79 ) @ SY206 ) )
| ( ( sK10_E @ SV79 )
!= ( kpair @ ( sK11_SY199 @ SV79 ) @ SY206 ) ) ) ) )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[206]) ).
thf(209,plain,
! [SV79: $i > $o,SV142: $i] :
( ( ( ~ ( ~ ( in @ SV142 @ sK1_A )
| ~ ~ ! [SY205: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY205 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SV142 @ SY205 ) )
| ( ( sK10_E @ SV79 )
!= ( kpair @ SV142 @ SY205 ) ) ) ) )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(210,plain,
! [SV79: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK11_SY199 @ SV79 ) @ sK1_A )
| ~ ~ ! [SY206: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY206 @ sK2_SY118 )
| ~ ( sK3_SY124 @ ( sK11_SY199 @ SV79 ) @ SY206 ) )
| ( ( sK10_E @ SV79 )
!= ( kpair @ ( sK11_SY199 @ SV79 ) @ SY206 ) ) ) ) )
= $true )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[208]) ).
thf(211,plain,
! [SV79: $i > $o,SV142: $i] :
( ( ( ~ ( in @ SV142 @ sK1_A )
| ~ ~ ! [SY205: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY205 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SV142 @ SY205 ) )
| ( ( sK10_E @ SV79 )
!= ( kpair @ SV142 @ SY205 ) ) ) )
= $true )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[209]) ).
thf(212,plain,
! [SV79: $i > $o] :
( ( ( ~ ( in @ ( sK11_SY199 @ SV79 ) @ sK1_A )
| ~ ~ ! [SY206: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY206 @ sK2_SY118 )
| ~ ( sK3_SY124 @ ( sK11_SY199 @ SV79 ) @ SY206 ) )
| ( ( sK10_E @ SV79 )
!= ( kpair @ ( sK11_SY199 @ SV79 ) @ SY206 ) ) ) )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(213,plain,
! [SV79: $i > $o,SV142: $i] :
( ( ( ~ ( in @ SV142 @ sK1_A ) )
= $true )
| ( ( ~ ~ ! [SY205: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY205 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SV142 @ SY205 ) )
| ( ( sK10_E @ SV79 )
!= ( kpair @ SV142 @ SY205 ) ) ) )
= $true )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(214,plain,
! [SV79: $i > $o] :
( ( ( ~ ( in @ ( sK11_SY199 @ SV79 ) @ sK1_A ) )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(215,plain,
! [SV79: $i > $o] :
( ( ( ~ ~ ! [SY206: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY206 @ sK2_SY118 )
| ~ ( sK3_SY124 @ ( sK11_SY199 @ SV79 ) @ SY206 ) )
| ( ( sK10_E @ SV79 )
!= ( kpair @ ( sK11_SY199 @ SV79 ) @ SY206 ) ) ) )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[212]) ).
thf(216,plain,
! [SV79: $i > $o,SV142: $i] :
( ( ( in @ SV142 @ sK1_A )
= $false )
| ( ( ~ ~ ! [SY205: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY205 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SV142 @ SY205 ) )
| ( ( sK10_E @ SV79 )
!= ( kpair @ SV142 @ SY205 ) ) ) )
= $true )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(217,plain,
! [SV79: $i > $o] :
( ( ( in @ ( sK11_SY199 @ SV79 ) @ sK1_A )
= $true )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[214]) ).
thf(218,plain,
! [SV79: $i > $o] :
( ( ( ~ ! [SY206: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY206 @ sK2_SY118 )
| ~ ( sK3_SY124 @ ( sK11_SY199 @ SV79 ) @ SY206 ) )
| ( ( sK10_E @ SV79 )
!= ( kpair @ ( sK11_SY199 @ SV79 ) @ SY206 ) ) ) )
= $true )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[215]) ).
thf(219,plain,
! [SV79: $i > $o,SV142: $i] :
( ( ( ~ ! [SY205: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY205 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SV142 @ SY205 ) )
| ( ( sK10_E @ SV79 )
!= ( kpair @ SV142 @ SY205 ) ) ) )
= $false )
| ( ( in @ SV142 @ sK1_A )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(220,plain,
! [SV79: $i > $o] :
( ( ( ! [SY206: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY206 @ sK2_SY118 )
| ~ ( sK3_SY124 @ ( sK11_SY199 @ SV79 ) @ SY206 ) )
| ( ( sK10_E @ SV79 )
!= ( kpair @ ( sK11_SY199 @ SV79 ) @ SY206 ) ) ) )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(221,plain,
! [SV79: $i > $o,SV142: $i] :
( ( ( ! [SY205: $i] :
~ ~ ( ~ ~ ( ~ ( in @ SY205 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SV142 @ SY205 ) )
| ( ( sK10_E @ SV79 )
!= ( kpair @ SV142 @ SY205 ) ) ) )
= $true )
| ( ( in @ SV142 @ sK1_A )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[219]) ).
thf(222,plain,
! [SV79: $i > $o] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK12_SY206 @ SV79 ) @ sK2_SY118 )
| ~ ( sK3_SY124 @ ( sK11_SY199 @ SV79 ) @ ( sK12_SY206 @ SV79 ) ) )
| ( ( sK10_E @ SV79 )
!= ( kpair @ ( sK11_SY199 @ SV79 ) @ ( sK12_SY206 @ SV79 ) ) ) ) )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[220]) ).
thf(223,plain,
! [SV79: $i > $o,SV142: $i,SV143: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ SV143 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SV142 @ SV143 ) )
| ( ( sK10_E @ SV79 )
!= ( kpair @ SV142 @ SV143 ) ) ) )
= $true )
| ( ( in @ SV142 @ sK1_A )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(224,plain,
! [SV79: $i > $o] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK12_SY206 @ SV79 ) @ sK2_SY118 )
| ~ ( sK3_SY124 @ ( sK11_SY199 @ SV79 ) @ ( sK12_SY206 @ SV79 ) ) )
| ( ( sK10_E @ SV79 )
!= ( kpair @ ( sK11_SY199 @ SV79 ) @ ( sK12_SY206 @ SV79 ) ) ) ) )
= $true )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[222]) ).
thf(225,plain,
! [SV79: $i > $o,SV142: $i,SV143: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ SV143 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SV142 @ SV143 ) )
| ( ( sK10_E @ SV79 )
!= ( kpair @ SV142 @ SV143 ) ) ) )
= $false )
| ( ( in @ SV142 @ sK1_A )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(226,plain,
! [SV79: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK12_SY206 @ SV79 ) @ sK2_SY118 )
| ~ ( sK3_SY124 @ ( sK11_SY199 @ SV79 ) @ ( sK12_SY206 @ SV79 ) ) )
| ( ( sK10_E @ SV79 )
!= ( kpair @ ( sK11_SY199 @ SV79 ) @ ( sK12_SY206 @ SV79 ) ) ) )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(227,plain,
! [SV79: $i > $o,SV142: $i,SV143: $i] :
( ( ( ~ ~ ( ~ ( in @ SV143 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SV142 @ SV143 ) )
| ( ( sK10_E @ SV79 )
!= ( kpair @ SV142 @ SV143 ) ) )
= $true )
| ( ( in @ SV142 @ sK1_A )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[225]) ).
thf(228,plain,
! [SV79: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK12_SY206 @ SV79 ) @ sK2_SY118 )
| ~ ( sK3_SY124 @ ( sK11_SY199 @ SV79 ) @ ( sK12_SY206 @ SV79 ) ) ) )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(229,plain,
! [SV79: $i > $o] :
( ( ( ( ( sK10_E @ SV79 )
!= ( kpair @ ( sK11_SY199 @ SV79 ) @ ( sK12_SY206 @ SV79 ) ) ) )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[226]) ).
thf(230,plain,
! [SV79: $i > $o,SV142: $i,SV143: $i] :
( ( ( ~ ~ ( ~ ( in @ SV143 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SV142 @ SV143 ) ) )
= $true )
| ( ( ( ( sK10_E @ SV79 )
!= ( kpair @ SV142 @ SV143 ) ) )
= $true )
| ( ( in @ SV142 @ sK1_A )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(231,plain,
! [SV79: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK12_SY206 @ SV79 ) @ sK2_SY118 )
| ~ ( sK3_SY124 @ ( sK11_SY199 @ SV79 ) @ ( sK12_SY206 @ SV79 ) ) ) )
= $true )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[228]) ).
thf(232,plain,
! [SV79: $i > $o] :
( ( ( ( sK10_E @ SV79 )
= ( kpair @ ( sK11_SY199 @ SV79 ) @ ( sK12_SY206 @ SV79 ) ) )
= $true )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[229]) ).
thf(233,plain,
! [SV79: $i > $o,SV142: $i,SV143: $i] :
( ( ( ~ ( ~ ( in @ SV143 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SV142 @ SV143 ) ) )
= $false )
| ( ( ( ( sK10_E @ SV79 )
!= ( kpair @ SV142 @ SV143 ) ) )
= $true )
| ( ( in @ SV142 @ sK1_A )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(234,plain,
! [SV79: $i > $o] :
( ( ( ~ ( in @ ( sK12_SY206 @ SV79 ) @ sK2_SY118 )
| ~ ( sK3_SY124 @ ( sK11_SY199 @ SV79 ) @ ( sK12_SY206 @ SV79 ) ) )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(235,plain,
! [SV79: $i > $o,SV142: $i,SV143: $i] :
( ( ( ~ ( in @ SV143 @ sK2_SY118 )
| ~ ( sK3_SY124 @ SV142 @ SV143 ) )
= $true )
| ( ( ( ( sK10_E @ SV79 )
!= ( kpair @ SV142 @ SV143 ) ) )
= $true )
| ( ( in @ SV142 @ sK1_A )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[233]) ).
thf(236,plain,
! [SV79: $i > $o] :
( ( ( ~ ( in @ ( sK12_SY206 @ SV79 ) @ sK2_SY118 ) )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[234]) ).
thf(237,plain,
! [SV79: $i > $o] :
( ( ( ~ ( sK3_SY124 @ ( sK11_SY199 @ SV79 ) @ ( sK12_SY206 @ SV79 ) ) )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[234]) ).
thf(238,plain,
! [SV79: $i > $o,SV142: $i,SV143: $i] :
( ( ( ~ ( in @ SV143 @ sK2_SY118 ) )
= $true )
| ( ( ~ ( sK3_SY124 @ SV142 @ SV143 ) )
= $true )
| ( ( ( ( sK10_E @ SV79 )
!= ( kpair @ SV142 @ SV143 ) ) )
= $true )
| ( ( in @ SV142 @ sK1_A )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(239,plain,
! [SV79: $i > $o] :
( ( ( in @ ( sK12_SY206 @ SV79 ) @ sK2_SY118 )
= $true )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[236]) ).
thf(240,plain,
! [SV79: $i > $o] :
( ( ( sK3_SY124 @ ( sK11_SY199 @ SV79 ) @ ( sK12_SY206 @ SV79 ) )
= $true )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[237]) ).
thf(241,plain,
! [SV79: $i > $o,SV142: $i,SV143: $i] :
( ( ( in @ SV143 @ sK2_SY118 )
= $false )
| ( ( ~ ( sK3_SY124 @ SV142 @ SV143 ) )
= $true )
| ( ( ( ( sK10_E @ SV79 )
!= ( kpair @ SV142 @ SV143 ) ) )
= $true )
| ( ( in @ SV142 @ sK1_A )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(242,plain,
! [SV79: $i > $o,SV143: $i,SV142: $i] :
( ( ( sK3_SY124 @ SV142 @ SV143 )
= $false )
| ( ( in @ SV143 @ sK2_SY118 )
= $false )
| ( ( ( ( sK10_E @ SV79 )
!= ( kpair @ SV142 @ SV143 ) ) )
= $true )
| ( ( in @ SV142 @ sK1_A )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(243,plain,
! [SV143: $i,SV142: $i,SV79: $i > $o] :
( ( ( ( sK10_E @ SV79 )
= ( kpair @ SV142 @ SV143 ) )
= $false )
| ( ( in @ SV143 @ sK2_SY118 )
= $false )
| ( ( sK3_SY124 @ SV142 @ SV143 )
= $false )
| ( ( in @ SV142 @ sK1_A )
= $false )
| ( ( SV79 @ ( kpair @ sK4_SY129 @ sK5_SY133 ) )
= $false )
| ( ( SV79 @ ( sK10_E @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(245,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[26,243,240,239,232,217,204,201,200,199,198,197,196,193,192,183,169,162,159,158,151,136,123,116,115,113,112,110,109,107,106,96,88,87,85,84,82,81,80,79,77,71,70,49,47,40]) ).
thf(246,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[245]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU668^2 : TPTP v8.1.0. Released v3.7.0.
% 0.08/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Mon Jun 20 03:53:54 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.37
% 0.14/0.37 No.of.Axioms: 0
% 0.14/0.37
% 0.14/0.37 Length.of.Defs: 911
% 0.14/0.37
% 0.14/0.37 Contains.Choice.Funs: false
% 0.14/0.37 (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)......eprover: CPU time limit exceeded, terminating
% 25.26/25.47 ..eprover: CPU time limit exceeded, terminating
% 50.48/50.73
% 50.48/50.73
% 50.48/50.73 Prim_subst applied to clause
% 50.48/50.73
% 50.48/50.73 90:[ 0:<(in@SV29)@((dsetconstr@SV28)@(^[SX0:$i]: (SV27@SX0))) = $false>-w(1)-i() 1:<SV27@SV29 = $true>-w(1)-i() ]-mln(2)-w(2)-i(rename 38)-o(AXIOM)-fv([ SV27 SV28 SV29 ])
% 50.63/50.85 .............eprover: CPU time limit exceeded, terminating
% 75.41/75.64 .
% 75.41/75.64 (rf:0,axioms:0,ps:2,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)....eprover: CPU time limit exceeded, terminating
% 100.47/100.69 ..eprover: CPU time limit exceeded, terminating
% 125.66/125.86 .
% 125.66/125.86
% 125.66/125.86 Prim_subst applied to clause
% 125.66/125.86
% 125.66/125.86 71:[ 0:<(in@SV25)@((dsetconstr@SV24)@(^[SX0:$i]: (SV23@SX0))) = $false>-w(1)-i() 1:<SV23@SV25 = $true>-w(1)-i() ]-mln(2)-w(2)-i(rename 38)-o(AXIOM)-fv([ SV23 SV24 SV25 ])
% 126.58/126.75 ......
% 126.88/127.07
% 126.88/127.07 Prim_subst applied to clause
% 126.88/127.07
% 126.88/127.07 169:[ 0:<SV79@SV78 = $false>-w(1)-i() 1:<(in@SV78)@((dsetconstr@SV77)@(^[SX0:$i]: (~ (SV79@SX0)))) = $false>-w(1)-i() ]-mln(2)-w(2)-i(rename 68)-o(AXIOM)-fv([ SV77 SV78 SV79 ])
% 126.92/127.11 ....
% 129.64/129.85
% 129.64/129.85 ********************************
% 129.64/129.85 * All subproblems solved! *
% 129.64/129.85 ********************************
% 129.64/129.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,ps:2,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:22,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:245,loop_count:10,foatp_calls:3,translation:fof_full)
% 129.68/129.88
% 129.68/129.88 %**** Beginning of derivation protocol ****
% 129.68/129.88 % SZS output start CNFRefutation
% See solution above
% 129.68/129.88
% 129.68/129.88 %**** End of derivation protocol ****
% 129.68/129.88 %**** no. of clauses in derivation: 187 ****
% 129.68/129.88 %**** clause counter: 245 ****
% 129.68/129.88
% 129.68/129.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:3,ps:2,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:22,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:245,loop_count:10,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------