TSTP Solution File: SEU777^2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU777^2 : 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 : n021.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 12:14:38 EDT 2022
% Result : Theorem 76.59s 76.84s
% Output : CNFRefutation 76.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 38
% Syntax : Number of formulae : 154 ( 49 unt; 33 typ; 4 def)
% Number of atoms : 750 ( 321 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 1669 ( 155 ~; 144 |; 8 &;1343 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 156 ( 156 >; 0 *; 0 +; 0 <<)
% Number of symbols : 36 ( 33 usr; 17 con; 0-3 aty)
% Number of variables : 513 ( 187 ^ 326 !; 0 ?; 513 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_breln,type,
breln: $i > $i > $i > $o ).
thf(tp_breln1,type,
breln1: $i > $i > $o ).
thf(tp_breln1invset,type,
breln1invset: $i > $i > $i ).
thf(tp_cartprod,type,
cartprod: $i > $i > $i ).
thf(tp_dpsetconstr,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_dpsetconstrER,type,
dpsetconstrER: $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 ).
thf(tp_sK11_E,type,
sK11_E: $i ).
thf(tp_sK12_E,type,
sK12_E: $i ).
thf(tp_sK13_E,type,
sK13_E: $i ).
thf(tp_sK14_E,type,
sK14_E: $i ).
thf(tp_sK15_E,type,
sK15_E: $i > $i > $i ).
thf(tp_sK16_E,type,
sK16_E: $i > $i > $i ).
thf(tp_sK17_E,type,
sK17_E: $i ).
thf(tp_sK18_E,type,
sK18_E: $i ).
thf(tp_sK19_E,type,
sK19_E: $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_E,type,
sK20_E: $i ).
thf(tp_sK21_E,type,
sK21_E: ( $i > $i > $o ) > $i ).
thf(tp_sK22_E,type,
sK22_E: ( $i > $i > $o ) > $i ).
thf(tp_sK23_E,type,
sK23_E: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK24_E,type,
sK24_E: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK2_SY402,type,
sK2_SY402: $i ).
thf(tp_sK3_SY405,type,
sK3_SY405: $i ).
thf(tp_sK4_SY407,type,
sK4_SY407: $i ).
thf(tp_sK5_E,type,
sK5_E: ( $i > $i > $o ) > $i ).
thf(tp_sK6_E,type,
sK6_E: ( $i > $i > $o ) > $i ).
thf(tp_sK7_E,type,
sK7_E: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK8_E,type,
sK8_E: ( $i > $i > $o ) > $i > $i > $i ).
thf(tp_sK9_E,type,
sK9_E: $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(breln,definition,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).
thf(breln1,definition,
( breln1
= ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1) ).
thf(breln1invset,definition,
( breln1invset
= ( ^ [A: $i,R: $i] :
( dpsetconstr @ A @ A
@ ^ [Xx: $i,Xy: $i] : ( in @ ( kpair @ Xy @ Xx ) @ R ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1invset) ).
thf(dpsetconstrER,definition,
( dpsetconstrER
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( Xphi @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrER) ).
thf(1,conjecture,
( dpsetconstrER
=> ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1invE) ).
thf(2,negated_conjecture,
( ( dpsetconstrER
=> ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
dpsetconstrER = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[2]) ).
thf(5,plain,
( ( ~ ! [A: $i,R: $i] :
( ( breln1 @ A @ R )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( in @ ( kpair @ Xy @ Xx ) @ ( breln1invset @ A @ R ) )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[4]) ).
thf(6,plain,
( ( ( breln1 @ sK1_A @ sK2_SY402 )
& ( in @ sK3_SY405 @ sK1_A )
& ( in @ sK4_SY407 @ sK1_A )
& ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 ) @ ( breln1invset @ sK1_A @ sK2_SY402 ) )
& ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[5]) ).
thf(7,plain,
dpsetconstrER = $true,
inference(copy,[status(thm)],[3]) ).
thf(8,plain,
( ( ( breln1 @ sK1_A @ sK2_SY402 )
& ( in @ sK3_SY405 @ sK1_A )
& ( in @ sK4_SY407 @ sK1_A )
& ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 ) @ ( breln1invset @ sK1_A @ sK2_SY402 ) )
& ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ( ~ ( subset @ sK2_SY402 @ ( cartprod @ sK1_A @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK3_SY405 @ sK1_A )
| ~ ~ ( ~ ( in @ sK4_SY407 @ sK1_A )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
@ ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
| ~ ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,breln,breln1,breln1invset,dpsetconstrER]) ).
thf(10,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $o,SX3: $i,SX4: $i] :
( ~ ( in @ ( kpair @ SX3 @ SX4 )
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX5: $i,SX6: $i] : ( SX2 @ SX5 @ SX6 ) ) )
| ( SX2 @ SX3 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7,breln,breln1,breln1invset,dpsetconstrER]) ).
thf(11,plain,
( ( ~ ( subset @ sK2_SY402 @ ( cartprod @ sK1_A @ sK1_A ) )
| ~ ~ ( ~ ( in @ sK3_SY405 @ sK1_A )
| ~ ~ ( ~ ( in @ sK4_SY407 @ sK1_A )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
@ ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
| ~ ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: $i] :
( ( ! [SY408: $i,SY409: $i > $i > $o,SY410: $i,SY411: $i] :
( ~ ( in @ ( kpair @ SY410 @ SY411 )
@ ( dpsetconstr @ SV1 @ SY408
@ ^ [SX5: $i,SX6: $i] : ( SY409 @ SX5 @ SX6 ) ) )
| ( SY409 @ SY410 @ SY411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ~ ( subset @ sK2_SY402 @ ( cartprod @ sK1_A @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ~ ( ~ ( in @ sK3_SY405 @ sK1_A )
| ~ ~ ( ~ ( in @ sK4_SY407 @ sK1_A )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
@ ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
| ~ ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[11]) ).
thf(15,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY414: $i > $i > $o,SY415: $i,SY416: $i] :
( ~ ( in @ ( kpair @ SY415 @ SY416 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SX5: $i,SX6: $i] : ( SY414 @ SX5 @ SX6 ) ) )
| ( SY414 @ SY415 @ SY416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(16,plain,
( ( subset @ sK2_SY402 @ ( cartprod @ sK1_A @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[13]) ).
thf(17,plain,
( ( ~ ( ~ ( in @ sK3_SY405 @ sK1_A )
| ~ ~ ( ~ ( in @ sK4_SY407 @ sK1_A )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
@ ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
| ~ ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[14]) ).
thf(18,plain,
! [SV3: $i > $i > $o,SV2: $i,SV1: $i] :
( ( ! [SY419: $i,SY420: $i] :
( ~ ( in @ ( kpair @ SY419 @ SY420 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY421: $i,SY422: $i] : ( SV3 @ SY421 @ SY422 ) ) )
| ( SV3 @ SY419 @ SY420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( ~ ( in @ sK3_SY405 @ sK1_A )
| ~ ~ ( ~ ( in @ sK4_SY407 @ sK1_A )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
@ ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
| ~ ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(20,plain,
! [SV3: $i > $i > $o,SV2: $i,SV1: $i,SV4: $i] :
( ( ! [SY423: $i] :
( ~ ( in @ ( kpair @ SV4 @ SY423 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY421: $i,SY422: $i] : ( SV3 @ SY421 @ SY422 ) ) )
| ( SV3 @ SV4 @ SY423 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(21,plain,
( ( ~ ( in @ sK3_SY405 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(22,plain,
( ( ~ ~ ( ~ ( in @ sK4_SY407 @ sK1_A )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
@ ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
| ~ ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(23,plain,
! [SV3: $i > $i > $o,SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
( ( ~ ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY421: $i,SY422: $i] : ( SV3 @ SY421 @ SY422 ) ) )
| ( SV3 @ SV4 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( in @ sK3_SY405 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(25,plain,
( ( ~ ( ~ ( in @ sK4_SY407 @ sK1_A )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
@ ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
| ~ ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(26,plain,
! [SV3: $i > $i > $o,SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
( ( ( ~ ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY421: $i,SY422: $i] : ( SV3 @ SY421 @ SY422 ) ) ) )
= $true )
| ( ( SV3 @ SV4 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[23]) ).
thf(27,plain,
( ( ~ ( in @ sK4_SY407 @ sK1_A )
| ~ ~ ( ~ ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
@ ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
| ~ ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(28,plain,
! [SV3: $i > $i > $o,SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
( ( ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY421: $i,SY422: $i] : ( SV3 @ SY421 @ SY422 ) ) )
= $false )
| ( ( SV3 @ SV4 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(29,plain,
( ( ~ ( in @ sK4_SY407 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(30,plain,
( ( ~ ~ ( ~ ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
@ ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
| ~ ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(31,plain,
( ( in @ sK4_SY407 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(32,plain,
( ( ~ ( ~ ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
@ ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
| ~ ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[30]) ).
thf(33,plain,
( ( ~ ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
@ ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
| ~ ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(34,plain,
( ( ~ ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
@ ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(35,plain,
( ( ~ ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[33]) ).
thf(36,plain,
( ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
@ ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(37,plain,
( ( ~ ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(38,plain,
( ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
( ( ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SX0: $i,SX1: $i] : $false ) )
= $false )
| ( $false = $true ) ),
inference(prim_subst,[status(thm)],[28:[bind(SV3,$thf( ^ [SV9: $i] : ^ [SV10: $i] : $false ))]]) ).
thf(41,plain,
! [SV8: $i > $i > $o,SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
( ( ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SX0: $i,SX1: $i] :
~ ( SV8 @ SX0 @ SX1 ) ) )
= $false )
| ( ( ~ ( SV8 @ SV4 @ SV5 ) )
= $true ) ),
inference(prim_subst,[status(thm)],[28:[bind(SV3,$thf( ^ [SV6: $i] : ^ [SV7: $i] : ~ ( SV8 @ SV6 @ SV7 ) ))]]) ).
thf(42,plain,
! [SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
( ( ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
= $false )
| ( ( ( SV4 != SV5 ) )
= $true ) ),
inference(prim_subst,[status(thm)],[28:[bind(SV3,$thf( ^ [SY434: $i] : ^ [SY435: $i] : ( SY434 != SY435 ) ))]]) ).
thf(43,plain,
! [SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
( ( ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $false )
| ( ( SV4 = SV5 )
= $true ) ),
inference(prim_subst,[status(thm)],[28:[bind(SV3,$thf( ^ [SV14: $i] : ^ [SV13: $i] : ( SV14 = SV13 ) ))]]) ).
thf(44,plain,
! [SV3: $i > $i > $o,SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
( ( ( SV3 @ SV4 @ SV5 )
= $true )
| ( ( ( SV3 @ SV4 @ SV5 )
= ( ~ ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY421: $i,SY422: $i] : ( SV3 @ SY421 @ SY422 ) ) ) ) )
= $false ) ),
inference(fac_restr,[status(thm)],[28]) ).
thf(45,plain,
! [SV2: $i,SV1: $i,SV5: $i,SV4: $i,SV3: $i > $i > $o] :
( ( ( ~ ( ( SV3 @ SV4 @ SV5 )
| ~ ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY421: $i,SY422: $i] : ( SV3 @ SY421 @ SY422 ) ) ) )
| ~ ( ~ ( SV3 @ SV4 @ SV5 )
| ~ ~ ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY421: $i,SY422: $i] : ( SV3 @ SY421 @ SY422 ) ) ) ) )
= $false )
| ( ( SV3 @ SV4 @ SV5 )
= $true ) ),
inference(extcnf_equal_neg,[status(thm)],[44]) ).
thf(47,plain,
! [SV2: $i,SV1: $i,SV5: $i,SV4: $i,SV3: $i > $i > $o] :
( ( ( ~ ( ( SV3 @ SV4 @ SV5 )
| ~ ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY421: $i,SY422: $i] : ( SV3 @ SY421 @ SY422 ) ) ) ) )
= $false )
| ( ( SV3 @ SV4 @ SV5 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(49,plain,
! [SV2: $i,SV1: $i,SV5: $i,SV4: $i,SV3: $i > $i > $o] :
( ( ( ( SV3 @ SV4 @ SV5 )
| ~ ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY421: $i,SY422: $i] : ( SV3 @ SY421 @ SY422 ) ) ) )
= $true )
| ( ( SV3 @ SV4 @ SV5 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(51,plain,
! [SV2: $i,SV1: $i,SV5: $i,SV4: $i,SV3: $i > $i > $o] :
( ( ( SV3 @ SV4 @ SV5 )
= $true )
| ( ( ~ ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY421: $i,SY422: $i] : ( SV3 @ SY421 @ SY422 ) ) ) )
= $true )
| ( ( SV3 @ SV4 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[49]) ).
thf(53,plain,
! [SV3: $i > $i > $o,SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
( ( ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY421: $i,SY422: $i] : ( SV3 @ SY421 @ SY422 ) ) )
= $false )
| ( ( SV3 @ SV4 @ SV5 )
= $true )
| ( ( SV3 @ SV4 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(57,plain,
! [SV2: $i,SV1: $i,SV5: $i,SV4: $i,SV8: $i > $i > $o] :
( ( ( SV8 @ SV4 @ SV5 )
= $false )
| ( ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SX0: $i,SX1: $i] :
~ ( SV8 @ SX0 @ SX1 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(58,plain,
! [SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
( ( ( SV4 = SV5 )
= $false )
| ( ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(59,plain,
! [SV2: $i,SV1: $i,SV5: $i] :
( ( in @ ( kpair @ SV5 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
= $false ),
inference(extuni,[status(esa)],[58:[bind(SV4,$thf( SV5 ))]]) ).
thf(60,plain,
! [SV3: $i > $i > $o,SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
( ( ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY421: $i,SY422: $i] : ( SV3 @ SY421 @ SY422 ) ) )
= $false )
| ( ( SV3 @ SV4 @ SV5 )
= $true ) ),
inference(sim,[status(thm)],[53]) ).
thf(61,plain,
! [SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
( ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SX0: $i,SX1: $i] : $false ) )
= $false ),
inference(sim,[status(thm)],[40]) ).
thf(62,plain,
! [SV20: $i > $i > $o,SV21: $i,SV22: $i,SV23: $i,SV24: $i] :
( ( ( in @ ( kpair @ SV24 @ SV23 )
@ ( dpsetconstr @ SV22 @ SV21
@ ^ [SX0: $i,SX1: $i] : ( SV20 @ SX0 @ SX1 ) ) )
= $false )
| ( ( SV20 @ SV24 @ SV23 )
= $true ) ),
inference(rename,[status(thm)],[28]) ).
thf(65,plain,
! [SV20: $i > $i > $o,SV21: $i,SV22: $i,SV23: $i,SV24: $i] :
( ( ( ( in @ ( kpair @ SV24 @ SV23 )
@ ( dpsetconstr @ SV22 @ SV21
@ ^ [SX0: $i,SX1: $i] : ( SV20 @ SX0 @ SX1 ) ) )
= ( in @ sK3_SY405 @ sK1_A ) )
= $false )
| ( ( SV20 @ SV24 @ SV23 )
= $true ) ),
inference(res,[status(thm)],[62,24]) ).
thf(68,plain,
! [SV21: $i,SV22: $i,SV23: $i,SV24: $i] :
( ( ( in @ ( kpair @ SV24 @ SV23 )
@ ( dpsetconstr @ SV22 @ SV21
@ ^ [SX0: $i,SX1: $i] : $false ) )
= $false )
| ( $false = $true ) ),
inference(prim_subst,[status(thm)],[62:[bind(SV20,$thf( ^ [SV28: $i] : ^ [SV29: $i] : $false ))]]) ).
thf(69,plain,
! [SV21: $i,SV22: $i,SV23: $i,SV24: $i] :
( ( in @ ( kpair @ SV24 @ SV23 )
@ ( dpsetconstr @ SV22 @ SV21
@ ^ [SX0: $i,SX1: $i] : $false ) )
= $false ),
inference(sim,[status(thm)],[68]) ).
thf(70,plain,
! [SV27: $i > $i > $o,SV21: $i,SV22: $i,SV23: $i,SV24: $i] :
( ( ( in @ ( kpair @ SV24 @ SV23 )
@ ( dpsetconstr @ SV22 @ SV21
@ ^ [SX0: $i,SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) ) )
= $false )
| ( ( ~ ( SV27 @ SV24 @ SV23 ) )
= $true ) ),
inference(prim_subst,[status(thm)],[62:[bind(SV20,$thf( ^ [SV25: $i] : ^ [SV26: $i] : ~ ( SV27 @ SV25 @ SV26 ) ))]]) ).
thf(71,plain,
! [SV21: $i,SV22: $i,SV23: $i,SV24: $i] :
( ( ( in @ ( kpair @ SV24 @ SV23 )
@ ( dpsetconstr @ SV22 @ SV21
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
= $false )
| ( ( ( SV24 != SV23 ) )
= $true ) ),
inference(prim_subst,[status(thm)],[62:[bind(SV20,$thf( ^ [SY447: $i] : ^ [SY448: $i] : ( SY447 != SY448 ) ))]]) ).
thf(72,plain,
! [SV21: $i,SV22: $i,SV23: $i,SV24: $i] :
( ( ( in @ ( kpair @ SV24 @ SV23 )
@ ( dpsetconstr @ SV22 @ SV21
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $false )
| ( ( SV24 = SV23 )
= $true ) ),
inference(prim_subst,[status(thm)],[62:[bind(SV20,$thf( ^ [SV33: $i] : ^ [SV32: $i] : ( SV33 = SV32 ) ))]]) ).
thf(74,plain,
! [SV21: $i,SV22: $i,SV23: $i,SV24: $i,SV20: $i > $i > $o] :
( ( ( SV20 @ SV24 @ SV23 )
= $true )
| ( ( ( dpsetconstr @ SV22 @ SV21
@ ^ [SX0: $i,SX1: $i] : ( SV20 @ SX0 @ SX1 ) )
= sK1_A )
= $false )
| ( ( ( kpair @ SV24 @ SV23 )
= sK3_SY405 )
= $false ) ),
inference(extuni,[status(esa)],[65]) ).
thf(75,plain,
! [SV21: $i,SV22: $i,SV23: $i,SV24: $i,SV27: $i > $i > $o] :
( ( ( SV27 @ SV24 @ SV23 )
= $false )
| ( ( in @ ( kpair @ SV24 @ SV23 )
@ ( dpsetconstr @ SV22 @ SV21
@ ^ [SX0: $i,SX1: $i] :
~ ( SV27 @ SX0 @ SX1 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(76,plain,
! [SV21: $i,SV22: $i,SV23: $i,SV24: $i] :
( ( ( SV24 = SV23 )
= $false )
| ( ( in @ ( kpair @ SV24 @ SV23 )
@ ( dpsetconstr @ SV22 @ SV21
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(77,plain,
! [SV20: $i > $i > $o,SV21: $i,SV22: $i,SV23: $i,SV24: $i] :
( ( ( ( in @ sK4_SY407 @ sK1_A )
= ( in @ ( kpair @ SV24 @ SV23 )
@ ( dpsetconstr @ SV22 @ SV21
@ ^ [SX0: $i,SX1: $i] : ( SV20 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( SV20 @ SV24 @ SV23 )
= $true ) ),
inference(res,[status(thm)],[31,62]) ).
thf(78,plain,
! [SV21: $i,SV22: $i,SV23: $i,SV24: $i,SV20: $i > $i > $o] :
( ( ( SV20 @ SV24 @ SV23 )
= $true )
| ( ( sK1_A
= ( dpsetconstr @ SV22 @ SV21
@ ^ [SX0: $i,SX1: $i] : ( SV20 @ SX0 @ SX1 ) ) )
= $false )
| ( ( sK4_SY407
= ( kpair @ SV24 @ SV23 ) )
= $false ) ),
inference(extuni,[status(esa)],[77]) ).
thf(79,plain,
! [SV20: $i > $i > $o,SV21: $i,SV22: $i,SV23: $i,SV24: $i] :
( ( ( ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
@ ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
= ( in @ ( kpair @ SV24 @ SV23 )
@ ( dpsetconstr @ SV22 @ SV21
@ ^ [SX0: $i,SX1: $i] : ( SV20 @ SX0 @ SX1 ) ) ) )
= $false )
| ( ( SV20 @ SV24 @ SV23 )
= $true ) ),
inference(res,[status(thm)],[36,62]) ).
thf(80,plain,
! [SV20: $i > $i > $o] :
( ( ( SV20 @ sK4_SY407 @ sK3_SY405 )
= $true )
| ( ( in @ ( kpair @ ( sK6_E @ SV20 ) @ ( sK5_E @ SV20 ) ) @ sK2_SY402 )
= $true )
| ( ( SV20 @ ( sK5_E @ SV20 ) @ ( sK6_E @ SV20 ) )
= $true ) ),
inference(extuni,[status(esa)],[79:[bind(SV21,$thf( sK1_A )),bind(SV22,$thf( sK1_A )),bind(SV23,$thf( sK3_SY405 )),bind(SV24,$thf( sK4_SY407 ))]]) ).
thf(81,plain,
! [SV20: $i > $i > $o] :
( ( ( SV20 @ sK4_SY407 @ sK3_SY405 )
= $true )
| ( ( in @ ( kpair @ ( sK6_E @ SV20 ) @ ( sK5_E @ SV20 ) ) @ sK2_SY402 )
= $false )
| ( ( SV20 @ ( sK5_E @ SV20 ) @ ( sK6_E @ SV20 ) )
= $false ) ),
inference(extuni,[status(esa)],[79:[bind(SV21,$thf( sK1_A )),bind(SV22,$thf( sK1_A )),bind(SV23,$thf( sK3_SY405 )),bind(SV24,$thf( sK4_SY407 ))]]) ).
thf(82,plain,
! [SV21: $i,SV22: $i,SV20: $i > $i > $o] :
( ( ( SV20 @ sK4_SY407 @ sK3_SY405 )
= $true )
| ( ( ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) )
= ( dpsetconstr @ SV22 @ SV21
@ ^ [SX0: $i,SX1: $i] : ( SV20 @ SX0 @ SX1 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[79:[bind(SV23,$thf( sK3_SY405 )),bind(SV24,$thf( sK4_SY407 ))]]) ).
thf(83,plain,
! [SV23: $i,SV24: $i,SV20: $i > $i > $o] :
( ( ( SV20 @ SV24 @ SV23 )
= $true )
| ( ( in @ ( kpair @ ( sK8_E @ SV20 @ SV24 @ SV23 ) @ ( sK7_E @ SV23 @ SV24 @ SV20 ) ) @ sK2_SY402 )
= $true )
| ( ( SV20 @ ( sK7_E @ SV23 @ SV24 @ SV20 ) @ ( sK8_E @ SV20 @ SV24 @ SV23 ) )
= $true )
| ( ( ( kpair @ sK4_SY407 @ sK3_SY405 )
= ( kpair @ SV24 @ SV23 ) )
= $false ) ),
inference(extuni,[status(esa)],[79:[bind(SV21,$thf( sK1_A )),bind(SV22,$thf( sK1_A ))]]) ).
thf(84,plain,
! [SV23: $i,SV24: $i,SV20: $i > $i > $o] :
( ( ( SV20 @ SV24 @ SV23 )
= $true )
| ( ( in @ ( kpair @ ( sK8_E @ SV20 @ SV24 @ SV23 ) @ ( sK7_E @ SV23 @ SV24 @ SV20 ) ) @ sK2_SY402 )
= $false )
| ( ( SV20 @ ( sK7_E @ SV23 @ SV24 @ SV20 ) @ ( sK8_E @ SV20 @ SV24 @ SV23 ) )
= $false )
| ( ( ( kpair @ sK4_SY407 @ sK3_SY405 )
= ( kpair @ SV24 @ SV23 ) )
= $false ) ),
inference(extuni,[status(esa)],[79:[bind(SV21,$thf( sK1_A )),bind(SV22,$thf( sK1_A ))]]) ).
thf(85,plain,
! [SV21: $i,SV22: $i,SV23: $i,SV24: $i,SV20: $i > $i > $o] :
( ( ( SV20 @ SV24 @ SV23 )
= $true )
| ( ( ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) )
= ( dpsetconstr @ SV22 @ SV21
@ ^ [SX0: $i,SX1: $i] : ( SV20 @ SX0 @ SX1 ) ) )
= $false )
| ( ( ( kpair @ sK4_SY407 @ sK3_SY405 )
= ( kpair @ SV24 @ SV23 ) )
= $false ) ),
inference(extuni,[status(esa)],[79]) ).
thf(87,plain,
( ( ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 )
= ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
@ ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) ) )
= $false ),
inference(res,[status(thm)],[38,36]) ).
thf(88,plain,
( ( ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 )
= ( in @ sK4_SY407 @ sK1_A ) )
= $false ),
inference(res,[status(thm)],[38,31]) ).
thf(89,plain,
( ( ( in @ ( kpair @ sK3_SY405 @ sK4_SY407 ) @ sK2_SY402 )
= ( in @ sK3_SY405 @ sK1_A ) )
= $false ),
inference(res,[status(thm)],[38,24]) ).
thf(91,plain,
( ( ( sK2_SY402 = sK1_A )
= $false )
| ( ( ( kpair @ sK3_SY405 @ sK4_SY407 )
= sK3_SY405 )
= $false ) ),
inference(extuni,[status(esa)],[89]) ).
thf(92,plain,
( ( ( sK2_SY402 = sK1_A )
= $false )
| ( ( ( kpair @ sK3_SY405 @ sK4_SY407 )
= sK4_SY407 )
= $false ) ),
inference(extuni,[status(esa)],[88]) ).
thf(93,plain,
( ( ( sK2_SY402
= ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
= $false )
| ( ( sK4_SY407 = sK3_SY405 )
= $false )
| ( ( sK3_SY405 = sK4_SY407 )
= $false ) ),
inference(extuni,[status(esa)],[87]) ).
thf(94,plain,
( ( ( sK2_SY402
= ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
= $false )
| ( ( ( kpair @ sK3_SY405 @ sK4_SY407 )
= ( kpair @ sK4_SY407 @ sK3_SY405 ) )
= $false ) ),
inference(extuni,[status(esa)],[87]) ).
thf(95,plain,
! [SV81: $i,SV82: $i,SV83: $i,SV84: $i] :
( ( ( in @ ( kpair @ SV84 @ SV83 )
@ ( dpsetconstr @ SV82 @ SV81
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= $false )
| ( ( SV84 = SV83 )
= $true ) ),
inference(rename,[status(thm)],[43]) ).
thf(101,plain,
! [SV81: $i,SV82: $i,SV83: $i,SV84: $i] :
( ( ( ( in @ ( kpair @ SV84 @ SV83 )
@ ( dpsetconstr @ SV82 @ SV81
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
@ ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) ) )
= $false )
| ( ( SV84 = SV83 )
= $true ) ),
inference(res,[status(thm)],[95,36]) ).
thf(102,plain,
! [SV81: $i,SV82: $i,SV83: $i,SV84: $i] :
( ( ( ( in @ ( kpair @ SV84 @ SV83 )
@ ( dpsetconstr @ SV82 @ SV81
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= ( in @ sK4_SY407 @ sK1_A ) )
= $false )
| ( ( SV84 = SV83 )
= $true ) ),
inference(res,[status(thm)],[95,31]) ).
thf(103,plain,
! [SV81: $i,SV82: $i,SV83: $i,SV84: $i] :
( ( ( ( in @ ( kpair @ SV84 @ SV83 )
@ ( dpsetconstr @ SV82 @ SV81
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) ) )
= ( in @ sK3_SY405 @ sK1_A ) )
= $false )
| ( ( SV84 = SV83 )
= $true ) ),
inference(res,[status(thm)],[95,24]) ).
thf(105,plain,
! [SV81: $i,SV82: $i,SV83: $i,SV84: $i] :
( ( ( SV84 = SV83 )
= $true )
| ( ( ( dpsetconstr @ SV82 @ SV81
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
= sK1_A )
= $false )
| ( ( ( kpair @ SV84 @ SV83 )
= sK3_SY405 )
= $false ) ),
inference(extuni,[status(esa)],[103]) ).
thf(106,plain,
! [SV81: $i,SV82: $i,SV83: $i,SV84: $i] :
( ( ( SV84 = SV83 )
= $true )
| ( ( ( dpsetconstr @ SV82 @ SV81
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
= sK1_A )
= $false )
| ( ( ( kpair @ SV84 @ SV83 )
= sK4_SY407 )
= $false ) ),
inference(extuni,[status(esa)],[102]) ).
thf(107,plain,
( ( ( sK4_SY407 = sK3_SY405 )
= $true )
| ( ( sK13_E = sK14_E )
= $true )
| ( ( in @ ( kpair @ sK14_E @ sK13_E ) @ sK2_SY402 )
= $true ) ),
inference(extuni,[status(esa)],[101:[bind(SV81,$thf( sK1_A )),bind(SV82,$thf( sK1_A )),bind(SV83,$thf( sK3_SY405 )),bind(SV84,$thf( sK4_SY407 ))]]) ).
thf(108,plain,
( ( ( sK4_SY407 = sK3_SY405 )
= $true )
| ( ( sK13_E = sK14_E )
= $false )
| ( ( in @ ( kpair @ sK14_E @ sK13_E ) @ sK2_SY402 )
= $false ) ),
inference(extuni,[status(esa)],[101:[bind(SV81,$thf( sK1_A )),bind(SV82,$thf( sK1_A )),bind(SV83,$thf( sK3_SY405 )),bind(SV84,$thf( sK4_SY407 ))]]) ).
thf(109,plain,
! [SV81: $i,SV82: $i] :
( ( ( sK4_SY407 = sK3_SY405 )
= $true )
| ( ( ( dpsetconstr @ SV82 @ SV81
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
= ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[101:[bind(SV83,$thf( sK3_SY405 )),bind(SV84,$thf( sK4_SY407 ))]]) ).
thf(110,plain,
! [SV83: $i,SV84: $i] :
( ( ( SV84 = SV83 )
= $true )
| ( ( ( sK15_E @ SV83 @ SV84 )
= ( sK16_E @ SV84 @ SV83 ) )
= $true )
| ( ( in @ ( kpair @ ( sK16_E @ SV84 @ SV83 ) @ ( sK15_E @ SV83 @ SV84 ) ) @ sK2_SY402 )
= $true )
| ( ( ( kpair @ SV84 @ SV83 )
= ( kpair @ sK4_SY407 @ sK3_SY405 ) )
= $false ) ),
inference(extuni,[status(esa)],[101:[bind(SV81,$thf( sK1_A )),bind(SV82,$thf( sK1_A ))]]) ).
thf(111,plain,
! [SV83: $i,SV84: $i] :
( ( ( SV84 = SV83 )
= $true )
| ( ( ( sK15_E @ SV83 @ SV84 )
= ( sK16_E @ SV84 @ SV83 ) )
= $false )
| ( ( in @ ( kpair @ ( sK16_E @ SV84 @ SV83 ) @ ( sK15_E @ SV83 @ SV84 ) ) @ sK2_SY402 )
= $false )
| ( ( ( kpair @ SV84 @ SV83 )
= ( kpair @ sK4_SY407 @ sK3_SY405 ) )
= $false ) ),
inference(extuni,[status(esa)],[101:[bind(SV81,$thf( sK1_A )),bind(SV82,$thf( sK1_A ))]]) ).
thf(112,plain,
! [SV81: $i,SV82: $i,SV83: $i,SV84: $i] :
( ( ( SV84 = SV83 )
= $true )
| ( ( ( dpsetconstr @ SV82 @ SV81
@ ^ [SX0: $i,SX1: $i] : ( SX0 = SX1 ) )
= ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
= $false )
| ( ( ( kpair @ SV84 @ SV83 )
= ( kpair @ sK4_SY407 @ sK3_SY405 ) )
= $false ) ),
inference(extuni,[status(esa)],[101]) ).
thf(113,plain,
! [SV85: $i,SV86: $i,SV87: $i,SV88: $i,SV89: $i > $i > $o] :
( ( ( SV89 @ SV88 @ SV87 )
= $false )
| ( ( in @ ( kpair @ SV88 @ SV87 )
@ ( dpsetconstr @ SV86 @ SV85
@ ^ [SX0: $i,SX1: $i] :
~ ( SV89 @ SX0 @ SX1 ) ) )
= $false ) ),
inference(rename,[status(thm)],[57]) ).
thf(118,plain,
! [SV85: $i,SV86: $i,SV87: $i,SV88: $i,SV89: $i > $i > $o] :
( ( ( ( in @ ( kpair @ SV88 @ SV87 )
@ ( dpsetconstr @ SV86 @ SV85
@ ^ [SX0: $i,SX1: $i] :
~ ( SV89 @ SX0 @ SX1 ) ) )
= ( in @ ( kpair @ sK4_SY407 @ sK3_SY405 )
@ ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) ) )
= $false )
| ( ( SV89 @ SV88 @ SV87 )
= $false ) ),
inference(res,[status(thm)],[113,36]) ).
thf(120,plain,
! [SV85: $i,SV86: $i,SV87: $i,SV88: $i,SV89: $i > $i > $o] :
( ( ( ( in @ ( kpair @ SV88 @ SV87 )
@ ( dpsetconstr @ SV86 @ SV85
@ ^ [SX0: $i,SX1: $i] :
~ ( SV89 @ SX0 @ SX1 ) ) )
= ( in @ sK4_SY407 @ sK1_A ) )
= $false )
| ( ( SV89 @ SV88 @ SV87 )
= $false ) ),
inference(res,[status(thm)],[113,31]) ).
thf(122,plain,
! [SV85: $i,SV86: $i,SV87: $i,SV88: $i,SV89: $i > $i > $o] :
( ( ( ( in @ ( kpair @ SV88 @ SV87 )
@ ( dpsetconstr @ SV86 @ SV85
@ ^ [SX0: $i,SX1: $i] :
~ ( SV89 @ SX0 @ SX1 ) ) )
= ( in @ sK3_SY405 @ sK1_A ) )
= $false )
| ( ( SV89 @ SV88 @ SV87 )
= $false ) ),
inference(res,[status(thm)],[113,24]) ).
thf(126,plain,
! [SV85: $i,SV86: $i,SV87: $i,SV88: $i] :
( ( $true = $false )
| ( ( in @ ( kpair @ SV88 @ SV87 )
@ ( dpsetconstr @ SV86 @ SV85
@ ^ [SX0: $i,SX1: $i] : ~ $true ) )
= $false ) ),
inference(prim_subst,[status(thm)],[113:[bind(SV89,$thf( ^ [SV95: $i] : ^ [SV96: $i] : $true ))]]) ).
thf(127,plain,
! [SV85: $i,SV86: $i,SV87: $i,SV88: $i] :
( ( in @ ( kpair @ SV88 @ SV87 )
@ ( dpsetconstr @ SV86 @ SV85
@ ^ [SX0: $i,SX1: $i] : ~ $true ) )
= $false ),
inference(sim,[status(thm)],[126]) ).
thf(129,plain,
! [SV85: $i,SV86: $i,SV87: $i,SV88: $i,SV92: $i > $i > $o] :
( ( ( ~ ( SV92 @ SV88 @ SV87 ) )
= $false )
| ( ( in @ ( kpair @ SV88 @ SV87 )
@ ( dpsetconstr @ SV86 @ SV85
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV92 @ SX0 @ SX1 ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[113:[bind(SV89,$thf( ^ [SV90: $i] : ^ [SV91: $i] : ~ ( SV92 @ SV90 @ SV91 ) ))]]) ).
thf(130,plain,
! [SV85: $i,SV86: $i,SV87: $i,SV88: $i] :
( ( ( ( SV88 != SV87 ) )
= $false )
| ( ( in @ ( kpair @ SV88 @ SV87 )
@ ( dpsetconstr @ SV86 @ SV85
@ ^ [SX0: $i,SX1: $i] :
~ ( ( SX0 != SX1 ) ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[113:[bind(SV89,$thf( ^ [SY499: $i] : ^ [SY500: $i] : ( SY499 != SY500 ) ))]]) ).
thf(131,plain,
! [SV85: $i,SV86: $i,SV87: $i,SV88: $i] :
( ( ( SV88 = SV87 )
= $false )
| ( ( in @ ( kpair @ SV88 @ SV87 )
@ ( dpsetconstr @ SV86 @ SV85
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
= $false ) ),
inference(prim_subst,[status(thm)],[113:[bind(SV89,$thf( ^ [SV98: $i] : ^ [SV97: $i] : ( SV98 = SV97 ) ))]]) ).
thf(133,plain,
! [SV85: $i,SV86: $i,SV87: $i,SV88: $i,SV89: $i > $i > $o] :
( ( ( SV89 @ SV88 @ SV87 )
= $false )
| ( ( ( dpsetconstr @ SV86 @ SV85
@ ^ [SX0: $i,SX1: $i] :
~ ( SV89 @ SX0 @ SX1 ) )
= sK1_A )
= $false )
| ( ( ( kpair @ SV88 @ SV87 )
= sK3_SY405 )
= $false ) ),
inference(extuni,[status(esa)],[122]) ).
thf(134,plain,
! [SV85: $i,SV86: $i,SV87: $i,SV88: $i,SV89: $i > $i > $o] :
( ( ( SV89 @ SV88 @ SV87 )
= $false )
| ( ( ( dpsetconstr @ SV86 @ SV85
@ ^ [SX0: $i,SX1: $i] :
~ ( SV89 @ SX0 @ SX1 ) )
= sK1_A )
= $false )
| ( ( ( kpair @ SV88 @ SV87 )
= sK4_SY407 )
= $false ) ),
inference(extuni,[status(esa)],[120]) ).
thf(135,plain,
! [SV89: $i > $i > $o] :
( ( ( SV89 @ sK4_SY407 @ sK3_SY405 )
= $false )
| ( ( ~ ( SV89 @ ( sK21_E @ SV89 ) @ ( sK22_E @ SV89 ) ) )
= $true )
| ( ( in @ ( kpair @ ( sK22_E @ SV89 ) @ ( sK21_E @ SV89 ) ) @ sK2_SY402 )
= $true ) ),
inference(extuni,[status(esa)],[118:[bind(SV85,$thf( sK1_A )),bind(SV86,$thf( sK1_A )),bind(SV87,$thf( sK3_SY405 )),bind(SV88,$thf( sK4_SY407 ))]]) ).
thf(136,plain,
! [SV89: $i > $i > $o] :
( ( ( SV89 @ sK4_SY407 @ sK3_SY405 )
= $false )
| ( ( ~ ( SV89 @ ( sK21_E @ SV89 ) @ ( sK22_E @ SV89 ) ) )
= $false )
| ( ( in @ ( kpair @ ( sK22_E @ SV89 ) @ ( sK21_E @ SV89 ) ) @ sK2_SY402 )
= $false ) ),
inference(extuni,[status(esa)],[118:[bind(SV85,$thf( sK1_A )),bind(SV86,$thf( sK1_A )),bind(SV87,$thf( sK3_SY405 )),bind(SV88,$thf( sK4_SY407 ))]]) ).
thf(137,plain,
! [SV85: $i,SV86: $i,SV89: $i > $i > $o] :
( ( ( SV89 @ sK4_SY407 @ sK3_SY405 )
= $false )
| ( ( ( dpsetconstr @ SV86 @ SV85
@ ^ [SX0: $i,SX1: $i] :
~ ( SV89 @ SX0 @ SX1 ) )
= ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[118:[bind(SV87,$thf( sK3_SY405 )),bind(SV88,$thf( sK4_SY407 ))]]) ).
thf(138,plain,
! [SV87: $i,SV88: $i,SV89: $i > $i > $o] :
( ( ( SV89 @ SV88 @ SV87 )
= $false )
| ( ( ~ ( SV89 @ ( sK23_E @ SV87 @ SV88 @ SV89 ) @ ( sK24_E @ SV88 @ SV87 @ SV89 ) ) )
= $true )
| ( ( in @ ( kpair @ ( sK24_E @ SV88 @ SV87 @ SV89 ) @ ( sK23_E @ SV87 @ SV88 @ SV89 ) ) @ sK2_SY402 )
= $true )
| ( ( ( kpair @ SV88 @ SV87 )
= ( kpair @ sK4_SY407 @ sK3_SY405 ) )
= $false ) ),
inference(extuni,[status(esa)],[118:[bind(SV85,$thf( sK1_A )),bind(SV86,$thf( sK1_A ))]]) ).
thf(139,plain,
! [SV87: $i,SV88: $i,SV89: $i > $i > $o] :
( ( ( SV89 @ SV88 @ SV87 )
= $false )
| ( ( ~ ( SV89 @ ( sK23_E @ SV87 @ SV88 @ SV89 ) @ ( sK24_E @ SV88 @ SV87 @ SV89 ) ) )
= $false )
| ( ( in @ ( kpair @ ( sK24_E @ SV88 @ SV87 @ SV89 ) @ ( sK23_E @ SV87 @ SV88 @ SV89 ) ) @ sK2_SY402 )
= $false )
| ( ( ( kpair @ SV88 @ SV87 )
= ( kpair @ sK4_SY407 @ sK3_SY405 ) )
= $false ) ),
inference(extuni,[status(esa)],[118:[bind(SV85,$thf( sK1_A )),bind(SV86,$thf( sK1_A ))]]) ).
thf(140,plain,
! [SV85: $i,SV86: $i,SV87: $i,SV88: $i,SV89: $i > $i > $o] :
( ( ( SV89 @ SV88 @ SV87 )
= $false )
| ( ( ( dpsetconstr @ SV86 @ SV85
@ ^ [SX0: $i,SX1: $i] :
~ ( SV89 @ SX0 @ SX1 ) )
= ( dpsetconstr @ sK1_A @ sK1_A
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY402 ) ) )
= $false )
| ( ( ( kpair @ SV88 @ SV87 )
= ( kpair @ sK4_SY407 @ sK3_SY405 ) )
= $false ) ),
inference(extuni,[status(esa)],[118]) ).
thf(141,plain,
! [SV85: $i,SV86: $i,SV87: $i] :
( ( in @ ( kpair @ SV87 @ SV87 )
@ ( dpsetconstr @ SV86 @ SV85
@ ^ [SX0: $i,SX1: $i] : ( SX0 != SX1 ) ) )
= $false ),
inference(extuni,[status(esa)],[131:[bind(SV88,$thf( SV87 ))]]) ).
thf(142,plain,
! [SV88: $i,SV87: $i,SV89: $i > $i > $o] :
( ( ( SV89 @ ( sK23_E @ SV87 @ SV88 @ SV89 ) @ ( sK24_E @ SV88 @ SV87 @ SV89 ) )
= $true )
| ( ( SV89 @ SV88 @ SV87 )
= $false )
| ( ( in @ ( kpair @ ( sK24_E @ SV88 @ SV87 @ SV89 ) @ ( sK23_E @ SV87 @ SV88 @ SV89 ) ) @ sK2_SY402 )
= $false )
| ( ( ( kpair @ SV88 @ SV87 )
= ( kpair @ sK4_SY407 @ sK3_SY405 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[139]) ).
thf(143,plain,
! [SV88: $i,SV87: $i,SV89: $i > $i > $o] :
( ( ( SV89 @ ( sK23_E @ SV87 @ SV88 @ SV89 ) @ ( sK24_E @ SV88 @ SV87 @ SV89 ) )
= $false )
| ( ( SV89 @ SV88 @ SV87 )
= $false )
| ( ( in @ ( kpair @ ( sK24_E @ SV88 @ SV87 @ SV89 ) @ ( sK23_E @ SV87 @ SV88 @ SV89 ) ) @ sK2_SY402 )
= $true )
| ( ( ( kpair @ SV88 @ SV87 )
= ( kpair @ sK4_SY407 @ sK3_SY405 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(144,plain,
! [SV89: $i > $i > $o] :
( ( ( SV89 @ ( sK21_E @ SV89 ) @ ( sK22_E @ SV89 ) )
= $true )
| ( ( SV89 @ sK4_SY407 @ sK3_SY405 )
= $false )
| ( ( in @ ( kpair @ ( sK22_E @ SV89 ) @ ( sK21_E @ SV89 ) ) @ sK2_SY402 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[136]) ).
thf(145,plain,
! [SV89: $i > $i > $o] :
( ( ( SV89 @ ( sK21_E @ SV89 ) @ ( sK22_E @ SV89 ) )
= $false )
| ( ( SV89 @ sK4_SY407 @ sK3_SY405 )
= $false )
| ( ( in @ ( kpair @ ( sK22_E @ SV89 ) @ ( sK21_E @ SV89 ) ) @ sK2_SY402 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(146,plain,
! [SV85: $i,SV86: $i,SV87: $i,SV88: $i,SV92: $i > $i > $o] :
( ( ( SV92 @ SV88 @ SV87 )
= $true )
| ( ( in @ ( kpair @ SV88 @ SV87 )
@ ( dpsetconstr @ SV86 @ SV85
@ ^ [SX0: $i,SX1: $i] :
~ ~ ( SV92 @ SX0 @ SX1 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(147,plain,
! [SV85: $i,SV86: $i,SV87: $i,SV88: $i] :
( ( ( SV88 = SV87 )
= $true )
| ( ( in @ ( kpair @ SV88 @ SV87 )
@ ( dpsetconstr @ SV86 @ SV85
@ ^ [SX0: $i,SX1: $i] :
~ ( ( SX0 != SX1 ) ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(148,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[16,147,146,145,144,143,142,141,140,137,134,133,127,113,112,111,110,109,108,107,106,105,95,94,93,92,91,85,84,83,82,81,80,78,76,75,74,72,69,62,61,60,59,38,36,31,24]) ).
thf(149,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU777^2 : TPTP v8.1.0. Released v3.7.0.
% 0.06/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 19 19:17:33 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 0
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 750
% 0.13/0.34
% 0.13/0.34 Contains.Choice.Funs: false
% 0.13/0.34 (rf:0,axioms:0,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)...
% 1.07/1.25
% 1.07/1.25 Prim_subst applied to clause
% 1.07/1.25
% 1.07/1.25 91:[ 0:<(in@((kpair@SV62)@SV61))@(((dpsetconstr@SV60)@SV59)@(^[SX0:$i,SX1:$i]: ((SV58@SX0)@SX1))) = $false>-w(1)-i() 1:<(SV58@SV62)@SV61 = $true>-w(1)-i() ]-mln(2)-w(2)-i(rename 28)-o(AXIOM)-fv([ SV58 SV59 SV60 SV61 SV62 ])
% 1.12/1.34 .........
% 75.46/75.66 (rf:0,axioms:0,ps:2,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:2,loop_count:0,foatp_calls:0,translation:fof_full)..
% 75.58/75.76
% 75.58/75.76 Prim_subst applied to clause
% 75.58/75.76
% 75.58/75.76 62:[ 0:<(in@((kpair@SV24)@SV23))@(((dpsetconstr@SV22)@SV21)@(^[SX0:$i,SX1:$i]: ((SV20@SX0)@SX1))) = $false>-w(1)-i() 1:<(SV20@SV24)@SV23 = $true>-w(1)-i() ]-mln(2)-w(2)-i(rename 28)-o(AXIOM)-fv([ SV20 SV21 SV22 SV23 SV24 ])
% 75.60/75.78 ...
% 76.21/76.40
% 76.21/76.40 Prim_subst applied to clause
% 76.21/76.40
% 76.21/76.40 113:[ 0:<(SV89@SV88)@SV87 = $false>-w(1)-i() 1:<(in@((kpair@SV88)@SV87))@(((dpsetconstr@SV86)@SV85)@(^[SX0:$i,SX1:$i]: (~ ((SV89@SX0)@SX1)))) = $false>-w(1)-i() ]-mln(2)-w(2)-i(rename 57)-o(AXIOM)-fv([ SV85 SV86 SV87 SV88 SV89 ])
% 76.59/76.84
% 76.59/76.84 ********************************
% 76.59/76.84 * All subproblems solved! *
% 76.59/76.84 ********************************
% 76.59/76.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:148,loop_count:8,foatp_calls:3,translation:fof_full)
% 76.59/76.86
% 76.59/76.86 %**** Beginning of derivation protocol ****
% 76.59/76.86 % SZS output start CNFRefutation
% See solution above
% 76.59/76.86
% 76.59/76.86 %**** End of derivation protocol ****
% 76.59/76.86 %**** no. of clauses in derivation: 117 ****
% 76.59/76.86 %**** clause counter: 148 ****
% 76.59/76.86
% 76.59/76.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,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:148,loop_count:8,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------