TSTP Solution File: SEU797^2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU797^2 : 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 : n003.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 12:14:49 EDT 2022
% Result : Theorem 201.88s 202.15s
% Output : CNFRefutation 201.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 25
% Syntax : Number of formulae : 128 ( 38 unt; 23 typ; 1 def)
% Number of atoms : 749 ( 302 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 1456 ( 106 ~; 155 |; 16 &;1168 @)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 159 ( 159 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 11 con; 0-5 aty)
% Number of variables : 480 ( 133 ^ 339 !; 8 ?; 480 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_image1,type,
image1: $i > ( $i > $i ) > $i ).
thf(tp_image1Equiv,type,
image1Equiv: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK10_E,type,
sK10_E: $i ).
thf(tp_sK11_E,type,
sK11_E: $i > $i > ( $i > $i ) > ( $i > $i ) > $i ).
thf(tp_sK12_E,type,
sK12_E: $i > $i > ( $i > $i ) > ( $i > $i ) > $i ).
thf(tp_sK13_E,type,
sK13_E: $i ).
thf(tp_sK14_E,type,
sK14_E: $i > ( $i > $i ) > $i ).
thf(tp_sK15_E,type,
sK15_E: $i > ( $i > $i ) > $i ).
thf(tp_sK16_E,type,
sK16_E: $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 > $i > ( $i > $i ) > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_E,type,
sK20_E: $i > $i > ( $i > $i ) > $i ).
thf(tp_sK2_SY430,type,
sK2_SY430: $i > $i ).
thf(tp_sK3_SY434,type,
sK3_SY434: $i ).
thf(tp_sK4_SY437,type,
sK4_SY437: $i ).
thf(tp_sK5_Xy,type,
sK5_Xy: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK6_E,type,
sK6_E: $i > ( $i > $i ) > $i ).
thf(tp_sK7_E,type,
sK7_E: $i > $i > $i > ( $i > $i ) > ( $i > $i ) > $i ).
thf(tp_sK8_E,type,
sK8_E: $i > $i > $i > ( $i > $i ) > ( $i > $i ) > $i ).
thf(tp_sK9_E,type,
sK9_E: $i > $i ).
thf(image1Equiv,definition,
( image1Equiv
= ( ! [A: $i,Xf: $i > $i,Xx: $i] :
( ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image1Equiv) ).
thf(1,conjecture,
( image1Equiv
=> ! [A: $i,Xf: $i > $i,Xx: $i] :
( ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) )
=> ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',image1I) ).
thf(2,negated_conjecture,
( ( image1Equiv
=> ! [A: $i,Xf: $i > $i,Xx: $i] :
( ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) )
=> ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,Xf: $i > $i,Xx: $i] :
( ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) ) )
=> ! [A: $i,Xf: $i > $i,Xx: $i] :
( ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) )
=> ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,image1Equiv]) ).
thf(4,plain,
( ( ! [A: $i,Xf: $i > $i,Xx: $i] :
( ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,Xf: $i > $i,Xx: $i] :
( ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) )
=> ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [A: $i,Xf: $i > $i,Xx: $i] :
( ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xx
= ( Xf @ Xy ) ) )
=> ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ( sK3_SY434
= ( sK2_SY430 @ sK4_SY437 ) )
& ( in @ sK4_SY437 @ sK1_A )
& ~ ( in @ sK3_SY434
@ ( image1 @ sK1_A
@ ^ [SY436: $i] : ( sK2_SY430 @ SY436 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(8,plain,
( ( ! [A: $i] :
( ! [Xf: $i > $i,Xx: $i] :
( ! [Xy: $i] :
( ( Xx
!= ( Xf @ Xy ) )
| ~ ( in @ Xy @ A ) )
| ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) ) )
& ! [Xf: $i > $i,Xx: $i] :
( ~ ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) )
| ( ( Xx
= ( Xf @ ( sK5_Xy @ Xx @ Xf @ A ) ) )
& ( in @ ( sK5_Xy @ Xx @ Xf @ A ) @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(9,plain,
( ( ! [A: $i] :
( ! [Xf: $i > $i,Xx: $i] :
( ! [Xy: $i] :
( ( Xx
!= ( Xf @ Xy ) )
| ~ ( in @ Xy @ A ) )
| ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) ) )
& ! [Xf: $i > $i,Xx: $i] :
( ~ ( in @ Xx
@ ( image1 @ A
@ ^ [Xy: $i] : ( Xf @ Xy ) ) )
| ( ( Xx
= ( Xf @ ( sK5_Xy @ Xx @ Xf @ A ) ) )
& ( in @ ( sK5_Xy @ Xx @ Xf @ A ) @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(10,plain,
( ( ( sK3_SY434
= ( sK2_SY430 @ sK4_SY437 ) )
& ( in @ sK4_SY437 @ sK1_A )
& ~ ( in @ sK3_SY434
@ ( image1 @ sK1_A
@ ^ [SY436: $i] : ( sK2_SY430 @ SY436 ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i > $i,SX2: $i] :
( ! [SX3: $i] :
( ( SX2
!= ( SX1 @ SX3 ) )
| ~ ( in @ SX3 @ SX0 ) )
| ( in @ SX2
@ ( image1 @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) )
| ~ ! [SX1: $i > $i,SX2: $i] :
( ~ ( in @ SX2
@ ( image1 @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ~ ( ( SX2
!= ( SX1 @ ( sK5_Xy @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( in @ ( sK5_Xy @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,image1Equiv]) ).
thf(12,plain,
( ( ~ ( ~ ~ ( ( sK3_SY434
!= ( sK2_SY430 @ sK4_SY437 ) )
| ~ ( in @ sK4_SY437 @ sK1_A ) )
| ~ ~ ( in @ sK3_SY434
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY430 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,image1Equiv]) ).
thf(13,plain,
! [SV1: $i] :
( ( ~ ( ~ ! [SY439: $i > $i,SY440: $i] :
( ! [SY441: $i] :
( ( SY440
!= ( SY439 @ SY441 ) )
| ~ ( in @ SY441 @ SV1 ) )
| ( in @ SY440
@ ( image1 @ SV1
@ ^ [SX3: $i] : ( SY439 @ SX3 ) ) ) )
| ~ ! [SY443: $i > $i,SY444: $i] :
( ~ ( in @ SY444
@ ( image1 @ SV1
@ ^ [SX3: $i] : ( SY443 @ SX3 ) ) )
| ~ ( ( SY444
!= ( SY443 @ ( sK5_Xy @ SY444 @ SY443 @ SV1 ) ) )
| ~ ( in @ ( sK5_Xy @ SY444 @ SY443 @ SV1 ) @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ~ ( ( sK3_SY434
!= ( sK2_SY430 @ sK4_SY437 ) )
| ~ ( in @ sK4_SY437 @ sK1_A ) )
| ~ ~ ( in @ sK3_SY434
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY430 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV1: $i] :
( ( ~ ! [SY439: $i > $i,SY440: $i] :
( ! [SY441: $i] :
( ( SY440
!= ( SY439 @ SY441 ) )
| ~ ( in @ SY441 @ SV1 ) )
| ( in @ SY440
@ ( image1 @ SV1
@ ^ [SX3: $i] : ( SY439 @ SX3 ) ) ) )
| ~ ! [SY443: $i > $i,SY444: $i] :
( ~ ( in @ SY444
@ ( image1 @ SV1
@ ^ [SX3: $i] : ( SY443 @ SX3 ) ) )
| ~ ( ( SY444
!= ( SY443 @ ( sK5_Xy @ SY444 @ SY443 @ SV1 ) ) )
| ~ ( in @ ( sK5_Xy @ SY444 @ SY443 @ SV1 ) @ SV1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ~ ( ( sK3_SY434
!= ( sK2_SY430 @ sK4_SY437 ) )
| ~ ( in @ sK4_SY437 @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ~ ( in @ sK3_SY434
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY430 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
! [SV1: $i] :
( ( ~ ! [SY439: $i > $i,SY440: $i] :
( ! [SY441: $i] :
( ( SY440
!= ( SY439 @ SY441 ) )
| ~ ( in @ SY441 @ SV1 ) )
| ( in @ SY440
@ ( image1 @ SV1
@ ^ [SX3: $i] : ( SY439 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(19,plain,
! [SV1: $i] :
( ( ~ ! [SY443: $i > $i,SY444: $i] :
( ~ ( in @ SY444
@ ( image1 @ SV1
@ ^ [SX3: $i] : ( SY443 @ SX3 ) ) )
| ~ ( ( SY444
!= ( SY443 @ ( sK5_Xy @ SY444 @ SY443 @ SV1 ) ) )
| ~ ( in @ ( sK5_Xy @ SY444 @ SY443 @ SV1 ) @ SV1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(20,plain,
( ( ~ ( ( sK3_SY434
!= ( sK2_SY430 @ sK4_SY437 ) )
| ~ ( in @ sK4_SY437 @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(21,plain,
( ( ~ ( in @ sK3_SY434
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY430 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(22,plain,
! [SV1: $i] :
( ( ! [SY439: $i > $i,SY440: $i] :
( ! [SY441: $i] :
( ( SY440
!= ( SY439 @ SY441 ) )
| ~ ( in @ SY441 @ SV1 ) )
| ( in @ SY440
@ ( image1 @ SV1
@ ^ [SX3: $i] : ( SY439 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(23,plain,
! [SV1: $i] :
( ( ! [SY443: $i > $i,SY444: $i] :
( ~ ( in @ SY444
@ ( image1 @ SV1
@ ^ [SX3: $i] : ( SY443 @ SX3 ) ) )
| ~ ( ( SY444
!= ( SY443 @ ( sK5_Xy @ SY444 @ SY443 @ SV1 ) ) )
| ~ ( in @ ( sK5_Xy @ SY444 @ SY443 @ SV1 ) @ SV1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(24,plain,
( ( ( sK3_SY434
!= ( sK2_SY430 @ sK4_SY437 ) )
| ~ ( in @ sK4_SY437 @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(25,plain,
( ( in @ sK3_SY434
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY430 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV1: $i,SV2: $i > $i] :
( ( ! [SY446: $i] :
( ! [SY447: $i] :
( ( SY446
!= ( SV2 @ SY447 ) )
| ~ ( in @ SY447 @ SV1 ) )
| ( in @ SY446
@ ( image1 @ SV1
@ ^ [SY448: $i] : ( SV2 @ SY448 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV3: $i > $i,SV1: $i] :
( ( ! [SY449: $i] :
( ~ ( in @ SY449
@ ( image1 @ SV1
@ ^ [SY450: $i] : ( SV3 @ SY450 ) ) )
| ~ ( ( SY449
!= ( SV3 @ ( sK5_Xy @ SY449 @ SV3 @ SV1 ) ) )
| ~ ( in @ ( sK5_Xy @ SY449 @ SV3 @ SV1 ) @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(28,plain,
( ( ( sK3_SY434
!= ( sK2_SY430 @ sK4_SY437 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(29,plain,
( ( ~ ( in @ sK4_SY437 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(30,plain,
! [SV1: $i,SV2: $i > $i,SV4: $i] :
( ( ! [SY451: $i] :
( ( SV4
!= ( SV2 @ SY451 ) )
| ~ ( in @ SY451 @ SV1 ) )
| ( in @ SV4
@ ( image1 @ SV1
@ ^ [SY448: $i] : ( SV2 @ SY448 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV3: $i > $i,SV1: $i,SV5: $i] :
( ( ~ ( in @ SV5
@ ( image1 @ SV1
@ ^ [SY450: $i] : ( SV3 @ SY450 ) ) )
| ~ ( ( SV5
!= ( SV3 @ ( sK5_Xy @ SV5 @ SV3 @ SV1 ) ) )
| ~ ( in @ ( sK5_Xy @ SV5 @ SV3 @ SV1 ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(32,plain,
( ( sK3_SY434
= ( sK2_SY430 @ sK4_SY437 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(33,plain,
( ( in @ sK4_SY437 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(34,plain,
! [SV1: $i,SV2: $i > $i,SV4: $i] :
( ( ( ! [SY451: $i] :
( ( SV4
!= ( SV2 @ SY451 ) )
| ~ ( in @ SY451 @ SV1 ) ) )
= $true )
| ( ( in @ SV4
@ ( image1 @ SV1
@ ^ [SY448: $i] : ( SV2 @ SY448 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV3: $i > $i,SV1: $i,SV5: $i] :
( ( ( ~ ( in @ SV5
@ ( image1 @ SV1
@ ^ [SY450: $i] : ( SV3 @ SY450 ) ) ) )
= $true )
| ( ( ~ ( ( SV5
!= ( SV3 @ ( sK5_Xy @ SV5 @ SV3 @ SV1 ) ) )
| ~ ( in @ ( sK5_Xy @ SV5 @ SV3 @ SV1 ) @ SV1 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(36,plain,
! [SV1: $i,SV6: $i,SV2: $i > $i,SV4: $i] :
( ( ( ( SV4
!= ( SV2 @ SV6 ) )
| ~ ( in @ SV6 @ SV1 ) )
= $true )
| ( ( in @ SV4
@ ( image1 @ SV1
@ ^ [SY448: $i] : ( SV2 @ SY448 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV3: $i > $i,SV1: $i,SV5: $i] :
( ( ( in @ SV5
@ ( image1 @ SV1
@ ^ [SY450: $i] : ( SV3 @ SY450 ) ) )
= $false )
| ( ( ~ ( ( SV5
!= ( SV3 @ ( sK5_Xy @ SV5 @ SV3 @ SV1 ) ) )
| ~ ( in @ ( sK5_Xy @ SV5 @ SV3 @ SV1 ) @ SV1 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV1: $i,SV6: $i,SV2: $i > $i,SV4: $i] :
( ( ( ( SV4
!= ( SV2 @ SV6 ) ) )
= $true )
| ( ( ~ ( in @ SV6 @ SV1 ) )
= $true )
| ( ( in @ SV4
@ ( image1 @ SV1
@ ^ [SY448: $i] : ( SV2 @ SY448 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(39,plain,
! [SV1: $i,SV3: $i > $i,SV5: $i] :
( ( ( ( SV5
!= ( SV3 @ ( sK5_Xy @ SV5 @ SV3 @ SV1 ) ) )
| ~ ( in @ ( sK5_Xy @ SV5 @ SV3 @ SV1 ) @ SV1 ) )
= $false )
| ( ( in @ SV5
@ ( image1 @ SV1
@ ^ [SY450: $i] : ( SV3 @ SY450 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(40,plain,
! [SV1: $i,SV6: $i,SV2: $i > $i,SV4: $i] :
( ( ( SV4
= ( SV2 @ SV6 ) )
= $false )
| ( ( ~ ( in @ SV6 @ SV1 ) )
= $true )
| ( ( in @ SV4
@ ( image1 @ SV1
@ ^ [SY448: $i] : ( SV2 @ SY448 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(41,plain,
! [SV1: $i,SV3: $i > $i,SV5: $i] :
( ( ( ( SV5
!= ( SV3 @ ( sK5_Xy @ SV5 @ SV3 @ SV1 ) ) ) )
= $false )
| ( ( in @ SV5
@ ( image1 @ SV1
@ ^ [SY450: $i] : ( SV3 @ SY450 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(42,plain,
! [SV1: $i,SV3: $i > $i,SV5: $i] :
( ( ( ~ ( in @ ( sK5_Xy @ SV5 @ SV3 @ SV1 ) @ SV1 ) )
= $false )
| ( ( in @ SV5
@ ( image1 @ SV1
@ ^ [SY450: $i] : ( SV3 @ SY450 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[39]) ).
thf(43,plain,
! [SV2: $i > $i,SV4: $i,SV1: $i,SV6: $i] :
( ( ( in @ SV6 @ SV1 )
= $false )
| ( ( SV4
= ( SV2 @ SV6 ) )
= $false )
| ( ( in @ SV4
@ ( image1 @ SV1
@ ^ [SY448: $i] : ( SV2 @ SY448 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(44,plain,
! [SV1: $i,SV3: $i > $i,SV5: $i] :
( ( ( SV5
= ( SV3 @ ( sK5_Xy @ SV5 @ SV3 @ SV1 ) ) )
= $true )
| ( ( in @ SV5
@ ( image1 @ SV1
@ ^ [SY450: $i] : ( SV3 @ SY450 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(45,plain,
! [SV1: $i,SV3: $i > $i,SV5: $i] :
( ( ( in @ ( sK5_Xy @ SV5 @ SV3 @ SV1 ) @ SV1 )
= $true )
| ( ( in @ SV5
@ ( image1 @ SV1
@ ^ [SY450: $i] : ( SV3 @ SY450 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[42]) ).
thf(46,plain,
! [SV1: $i,SV6: $i,SV2: $i > $i] :
( ( ( in @ ( SV2 @ SV6 )
@ ( image1 @ SV1
@ ^ [SX0: $i] : ( SV2 @ SX0 ) ) )
= $true )
| ( ( in @ SV6 @ SV1 )
= $false ) ),
inference(extuni,[status(esa)],[43:[bind(SV4,$thf( SV2 @ SV6 ))]]) ).
thf(49,plain,
! [SV7: $i > $i,SV8: $i,SV9: $i,SV10: $i] :
( ( ( in @ SV10 @ SV9 )
= $false )
| ( ( SV8
= ( SV7 @ SV10 ) )
= $false )
| ( ( in @ SV8
@ ( image1 @ SV9
@ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
= $true ) ),
inference(rename,[status(thm)],[43]) ).
thf(55,plain,
! [SV7: $i > $i,SV8: $i,SV9: $i,SV10: $i] :
( ( ( ( in @ SV10 @ SV9 )
= ( in @ sK4_SY437 @ sK1_A ) )
= $false )
| ( ( SV8
= ( SV7 @ SV10 ) )
= $false )
| ( ( in @ SV8
@ ( image1 @ SV9
@ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[49,33]) ).
thf(56,plain,
! [SV7: $i > $i,SV8: $i,SV9: $i,SV10: $i] :
( ( ( ( SV8
= ( SV7 @ SV10 ) )
= ( sK3_SY434
= ( sK2_SY430 @ sK4_SY437 ) ) )
= $false )
| ( ( in @ SV10 @ SV9 )
= $false )
| ( ( in @ SV8
@ ( image1 @ SV9
@ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[49,32]) ).
thf(59,plain,
! [SV9: $i] :
( ( ( in @ ( sK2_SY430 @ sK4_SY437 )
@ ( image1 @ SV9
@ ^ [SX0: $i] : SX0 ) )
= $true )
| ( ( in @ sK3_SY434 @ SV9 )
= $false ) ),
inference(extuni,[status(esa)],[56:[bind(SV8,$thf( sK2_SY430 @ sK4_SY437 )),bind(SV10,$thf( sK3_SY434 )),bind(SV7,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(60,plain,
! [SV10: $i,SV9: $i] :
( ( ( in @ ( sK2_SY430 @ sK4_SY437 )
@ ( image1 @ SV9
@ ^ [SX0: $i] : sK3_SY434 ) )
= $true )
| ( ( in @ SV10 @ SV9 )
= $false ) ),
inference(extuni,[status(esa)],[56:[bind(SV8,$thf( sK2_SY430 @ sK4_SY437 )),bind(SV7,$thf( ^ [SX0: $i] : sK3_SY434 ))]]) ).
thf(61,plain,
! [SV9: $i] :
( ( ( in @ sK3_SY434
@ ( image1 @ SV9
@ ^ [SX0: $i] : ( sK2_SY430 @ SX0 ) ) )
= $true )
| ( ( in @ sK4_SY437 @ SV9 )
= $false ) ),
inference(extuni,[status(esa)],[56:[bind(SV10,$thf( sK4_SY437 )),bind(SV7,$thf( ^ [SX0: $i] : ( sK2_SY430 @ SX0 ) )),bind(SV8,$thf( sK3_SY434 ))]]) ).
thf(62,plain,
! [SV10: $i,SV9: $i] :
( ( ( in @ sK3_SY434
@ ( image1 @ SV9
@ ^ [SX0: $i] : ( sK2_SY430 @ sK4_SY437 ) ) )
= $true )
| ( ( in @ SV10 @ SV9 )
= $false ) ),
inference(extuni,[status(esa)],[56:[bind(SV7,$thf( ^ [SX0: $i] : ( sK2_SY430 @ sK4_SY437 ) )),bind(SV8,$thf( sK3_SY434 ))]]) ).
thf(63,plain,
! [SV9: $i] :
( ( ( in @ sK3_SY434
@ ( image1 @ SV9
@ ^ [SX0: $i] : SX0 ) )
= $true )
| ( ( in @ ( sK2_SY430 @ sK4_SY437 ) @ SV9 )
= $false ) ),
inference(extuni,[status(esa)],[56:[bind(SV10,$thf( sK2_SY430 @ sK4_SY437 )),bind(SV7,$thf( ^ [SX0: $i] : SX0 )),bind(SV8,$thf( sK3_SY434 ))]]) ).
thf(64,plain,
! [SV7: $i > $i] :
( ( in @ ( SV7 @ sK4_SY437 )
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
= $true ),
inference(extuni,[status(esa)],[55:[bind(SV8,$thf( SV7 @ sK4_SY437 )),bind(SV9,$thf( sK1_A )),bind(SV10,$thf( sK4_SY437 ))]]) ).
thf(65,plain,
! [SV9: $i,SV10: $i,SV7: $i > $i] :
( ( ( in @ ( SV7 @ SV10 )
@ ( image1 @ SV9
@ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
= $true )
| ( ( in @ SV10 @ SV9 )
= $false ) ),
inference(extuni,[status(esa)],[49:[bind(SV8,$thf( SV7 @ SV10 ))]]) ).
thf(66,plain,
! [SV25: $i,SV26: $i > $i,SV27: $i] :
( ( ( SV27
= ( SV26 @ ( sK5_Xy @ SV27 @ SV26 @ SV25 ) ) )
= $true )
| ( ( in @ SV27
@ ( image1 @ SV25
@ ^ [SX0: $i] : ( SV26 @ SX0 ) ) )
= $false ) ),
inference(rename,[status(thm)],[44]) ).
thf(69,plain,
! [SV25: $i,SV26: $i > $i,SV27: $i,SV7: $i > $i,SV8: $i,SV9: $i,SV10: $i] :
( ( ( ( in @ SV27
@ ( image1 @ SV25
@ ^ [SX0: $i] : ( SV26 @ SX0 ) ) )
= ( in @ SV8
@ ( image1 @ SV9
@ ^ [SX0: $i] : ( SV7 @ SX0 ) ) ) )
= $false )
| ( ( SV27
= ( SV26 @ ( sK5_Xy @ SV27 @ SV26 @ SV25 ) ) )
= $true )
| ( ( in @ SV10 @ SV9 )
= $false )
| ( ( SV8
= ( SV7 @ SV10 ) )
= $false ) ),
inference(res,[status(thm)],[66,49]) ).
thf(70,plain,
! [SV25: $i,SV26: $i > $i,SV27: $i,SV7: $i > $i,SV8: $i,SV9: $i,SV10: $i] :
( ( ( ( SV27
= ( SV26 @ ( sK5_Xy @ SV27 @ SV26 @ SV25 ) ) )
= ( SV8
= ( SV7 @ SV10 ) ) )
= $false )
| ( ( in @ SV27
@ ( image1 @ SV25
@ ^ [SX0: $i] : ( SV26 @ SX0 ) ) )
= $false )
| ( ( in @ SV10 @ SV9 )
= $false )
| ( ( in @ SV8
@ ( image1 @ SV9
@ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[66,49]) ).
thf(75,plain,
! [SV9: $i,SV25: $i,SV10: $i,SV7: $i > $i,SV26: $i > $i] :
( ( ( in @ ( SV26 @ ( sK5_Xy @ ( SV7 @ SV10 ) @ SV26 @ SV25 ) )
@ ( image1 @ SV9
@ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
= $true )
| ( ( in @ SV10 @ SV9 )
= $false )
| ( ( in @ ( SV7 @ SV10 )
@ ( image1 @ SV25
@ ^ [SX0: $i] : ( SV26 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[70:[bind(SV27,$thf( SV7 @ SV10 )),bind(SV8,$thf( SV26 @ ( sK5_Xy @ ( SV7 @ SV10 ) @ SV26 @ SV25 ) ))]]) ).
thf(76,plain,
! [SV9: $i,SV10: $i,SV7: $i > $i,SV25: $i,SV8: $i,SV26: $i > $i] :
( ( ( in @ SV8
@ ( image1 @ SV9
@ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
= $true )
| ( ( in @ SV10 @ SV9 )
= $false )
| ( ( in @ SV8
@ ( image1 @ SV25
@ ^ [SX0: $i] : ( SV26 @ SX0 ) ) )
= $false )
| ( ( ( SV26 @ ( sK5_Xy @ SV8 @ SV26 @ SV25 ) )
= ( SV7 @ SV10 ) )
= $false ) ),
inference(extuni,[status(esa)],[70:[bind(SV27,$thf( SV8 ))]]) ).
thf(77,plain,
! [SV7: $i > $i,SV9: $i,SV10: $i,SV26: $i > $i] :
( ( ( in @ SV10 @ SV9 )
= $false )
| ( ( ( SV7 @ SV10 )
= ( SV26 @ ( sK5_Xy @ ( SV7 @ SV10 ) @ SV26 @ SV9 ) ) )
= $true )
| ( ( ( SV26 @ ( sK7_E @ SV10 @ SV9 @ ( SV7 @ SV10 ) @ SV7 @ SV26 ) )
= ( SV7 @ ( sK7_E @ SV10 @ SV9 @ ( SV7 @ SV10 ) @ SV7 @ SV26 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[69:[bind(SV8,$thf( SV7 @ SV10 )),bind(SV25,$thf( SV9 )),bind(SV27,$thf( SV7 @ SV10 ))]]) ).
thf(78,plain,
! [SV28: $i,SV29: $i > $i,SV30: $i] :
( ( ( in @ ( sK5_Xy @ SV30 @ SV29 @ SV28 ) @ SV28 )
= $true )
| ( ( in @ SV30
@ ( image1 @ SV28
@ ^ [SX0: $i] : ( SV29 @ SX0 ) ) )
= $false ) ),
inference(rename,[status(thm)],[45]) ).
thf(81,plain,
! [SV28: $i,SV29: $i > $i,SV30: $i,SV25: $i,SV26: $i > $i,SV27: $i] :
( ( ( ( in @ ( sK5_Xy @ SV30 @ SV29 @ SV28 ) @ SV28 )
= ( in @ SV27
@ ( image1 @ SV25
@ ^ [SX0: $i] : ( SV26 @ SX0 ) ) ) )
= $false )
| ( ( in @ SV30
@ ( image1 @ SV28
@ ^ [SX0: $i] : ( SV29 @ SX0 ) ) )
= $false )
| ( ( SV27
= ( SV26 @ ( sK5_Xy @ SV27 @ SV26 @ SV25 ) ) )
= $true ) ),
inference(res,[status(thm)],[78,66]) ).
thf(83,plain,
! [SV28: $i,SV29: $i > $i,SV30: $i,SV7: $i > $i,SV8: $i,SV9: $i,SV10: $i] :
( ( ( ( in @ SV30
@ ( image1 @ SV28
@ ^ [SX0: $i] : ( SV29 @ SX0 ) ) )
= ( in @ SV8
@ ( image1 @ SV9
@ ^ [SX0: $i] : ( SV7 @ SX0 ) ) ) )
= $false )
| ( ( in @ ( sK5_Xy @ SV30 @ SV29 @ SV28 ) @ SV28 )
= $true )
| ( ( in @ SV10 @ SV9 )
= $false )
| ( ( SV8
= ( SV7 @ SV10 ) )
= $false ) ),
inference(res,[status(thm)],[78,49]) ).
thf(85,plain,
! [SV28: $i,SV29: $i > $i,SV30: $i,SV7: $i > $i,SV8: $i,SV9: $i,SV10: $i] :
( ( ( ( in @ ( sK5_Xy @ SV30 @ SV29 @ SV28 ) @ SV28 )
= ( in @ SV10 @ SV9 ) )
= $false )
| ( ( in @ SV30
@ ( image1 @ SV28
@ ^ [SX0: $i] : ( SV29 @ SX0 ) ) )
= $false )
| ( ( SV8
= ( SV7 @ SV10 ) )
= $false )
| ( ( in @ SV8
@ ( image1 @ SV9
@ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[78,49]) ).
thf(89,plain,
! [SV9: $i,SV29: $i > $i,SV30: $i,SV7: $i > $i] :
( ( ( in @ ( SV7 @ ( sK5_Xy @ SV30 @ SV29 @ SV9 ) )
@ ( image1 @ SV9
@ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
= $true )
| ( ( in @ SV30
@ ( image1 @ SV9
@ ^ [SX0: $i] : ( SV29 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[85:[bind(SV8,$thf( SV7 @ ( sK5_Xy @ SV30 @ SV29 @ SV9 ) )),bind(SV28,$thf( SV9 )),bind(SV10,$thf( sK5_Xy @ SV30 @ SV29 @ SV9 ))]]) ).
thf(90,plain,
! [SV7: $i > $i,SV9: $i,SV10: $i,SV29: $i > $i] :
( ( ( in @ SV10 @ SV9 )
= $false )
| ( ( in @ ( sK5_Xy @ ( SV7 @ SV10 ) @ SV29 @ SV9 ) @ SV9 )
= $true )
| ( ( ( SV29 @ ( sK8_E @ SV10 @ SV9 @ ( SV7 @ SV10 ) @ SV7 @ SV29 ) )
= ( SV7 @ ( sK8_E @ SV10 @ SV9 @ ( SV7 @ SV10 ) @ SV7 @ SV29 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[83:[bind(SV8,$thf( SV7 @ SV10 )),bind(SV28,$thf( SV9 )),bind(SV30,$thf( SV7 @ SV10 ))]]) ).
thf(91,plain,
! [SV26: $i > $i,SV25: $i,SV29: $i > $i,SV30: $i] :
( ( ( ( sK5_Xy @ SV30 @ SV29
@ ( image1 @ SV25
@ ^ [SX0: $i] : ( SV26 @ SX0 ) ) )
= ( SV26
@ ( sK5_Xy
@ ( sK5_Xy @ SV30 @ SV29
@ ( image1 @ SV25
@ ^ [SX0: $i] : ( SV26 @ SX0 ) ) )
@ SV26
@ SV25 ) ) )
= $true )
| ( ( in @ SV30
@ ( image1
@ ( image1 @ SV25
@ ^ [SX0: $i] : ( SV26 @ SX0 ) )
@ ^ [SX0: $i] : ( SV29 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[81:[bind(SV28,$thf( image1 @ SV25 @ ^ [SX0: $i] : ( SV26 @ SX0 ) )),bind(SV27,$thf( sK5_Xy @ SV30 @ SV29 @ ( image1 @ SV25 @ ^ [SX0: $i] : ( SV26 @ SX0 ) ) ))]]) ).
thf(92,plain,
! [SV31: $i,SV32: $i,SV33: $i > $i] :
( ( ( in @ ( SV33 @ SV32 )
@ ( image1 @ SV31
@ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
= $true )
| ( ( in @ SV32 @ SV31 )
= $false ) ),
inference(rename,[status(thm)],[46]) ).
thf(95,plain,
! [SV31: $i,SV32: $i,SV33: $i > $i,SV28: $i,SV29: $i > $i,SV30: $i] :
( ( ( ( in @ ( SV33 @ SV32 )
@ ( image1 @ SV31
@ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
= ( in @ SV30
@ ( image1 @ SV28
@ ^ [SX0: $i] : ( SV29 @ SX0 ) ) ) )
= $false )
| ( ( in @ SV32 @ SV31 )
= $false )
| ( ( in @ ( sK5_Xy @ SV30 @ SV29 @ SV28 ) @ SV28 )
= $true ) ),
inference(res,[status(thm)],[92,78]) ).
thf(96,plain,
! [SV31: $i,SV32: $i,SV33: $i > $i,SV28: $i,SV29: $i > $i,SV30: $i] :
( ( ( ( in @ SV32 @ SV31 )
= ( in @ ( sK5_Xy @ SV30 @ SV29 @ SV28 ) @ SV28 ) )
= $false )
| ( ( in @ ( SV33 @ SV32 )
@ ( image1 @ SV31
@ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
= $true )
| ( ( in @ SV30
@ ( image1 @ SV28
@ ^ [SX0: $i] : ( SV29 @ SX0 ) ) )
= $false ) ),
inference(res,[status(thm)],[92,78]) ).
thf(97,plain,
! [SV31: $i,SV32: $i,SV33: $i > $i,SV25: $i,SV26: $i > $i,SV27: $i] :
( ( ( ( in @ ( SV33 @ SV32 )
@ ( image1 @ SV31
@ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
= ( in @ SV27
@ ( image1 @ SV25
@ ^ [SX0: $i] : ( SV26 @ SX0 ) ) ) )
= $false )
| ( ( in @ SV32 @ SV31 )
= $false )
| ( ( SV27
= ( SV26 @ ( sK5_Xy @ SV27 @ SV26 @ SV25 ) ) )
= $true ) ),
inference(res,[status(thm)],[92,66]) ).
thf(99,plain,
! [SV31: $i,SV32: $i,SV33: $i > $i,SV7: $i > $i,SV8: $i,SV9: $i,SV10: $i] :
( ( ( ( in @ SV32 @ SV31 )
= ( in @ SV8
@ ( image1 @ SV9
@ ^ [SX0: $i] : ( SV7 @ SX0 ) ) ) )
= $false )
| ( ( in @ ( SV33 @ SV32 )
@ ( image1 @ SV31
@ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
= $true )
| ( ( in @ SV10 @ SV9 )
= $false )
| ( ( SV8
= ( SV7 @ SV10 ) )
= $false ) ),
inference(res,[status(thm)],[92,49]) ).
thf(101,plain,
! [SV31: $i,SV32: $i,SV33: $i > $i,SV7: $i > $i,SV8: $i,SV9: $i,SV10: $i] :
( ( ( ( in @ ( SV33 @ SV32 )
@ ( image1 @ SV31
@ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
= ( in @ SV10 @ SV9 ) )
= $false )
| ( ( in @ SV32 @ SV31 )
= $false )
| ( ( SV8
= ( SV7 @ SV10 ) )
= $false )
| ( ( in @ SV8
@ ( image1 @ SV9
@ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[92,49]) ).
thf(102,plain,
! [SV31: $i,SV32: $i,SV33: $i > $i] :
( ( ( ( in @ SV32 @ SV31 )
= ( in @ sK4_SY437 @ sK1_A ) )
= $false )
| ( ( in @ ( SV33 @ SV32 )
@ ( image1 @ SV31
@ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[92,33]) ).
thf(105,plain,
! [SV33: $i > $i] :
( ( in @ ( SV33 @ sK4_SY437 )
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
= $true ),
inference(extuni,[status(esa)],[102:[bind(SV31,$thf( sK1_A )),bind(SV32,$thf( sK4_SY437 ))]]) ).
thf(106,plain,
! [SV31: $i,SV32: $i,SV33: $i > $i,SV7: $i > $i] :
( ( ( in @ ( SV7 @ ( SV33 @ SV32 ) )
@ ( image1
@ ( image1 @ SV31
@ ^ [SX0: $i] : ( SV33 @ SX0 ) )
@ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
= $true )
| ( ( in @ SV32 @ SV31 )
= $false ) ),
inference(extuni,[status(esa)],[101:[bind(SV8,$thf( SV7 @ ( SV33 @ SV32 ) )),bind(SV9,$thf( image1 @ SV31 @ ^ [SX0: $i] : ( SV33 @ SX0 ) )),bind(SV10,$thf( SV33 @ SV32 ))]]) ).
thf(107,plain,
! [SV7: $i > $i,SV33: $i > $i,SV9: $i,SV10: $i] :
( ( ( in @ SV10 @ SV9 )
= $false )
| ( ( in @ ( SV33 @ ( SV7 @ SV10 ) )
@ ( image1
@ ( image1 @ SV9
@ ^ [SX0: $i] : ( SV7 @ SX0 ) )
@ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[99:[bind(SV8,$thf( SV7 @ SV10 )),bind(SV31,$thf( image1 @ SV9 @ ^ [SX0: $i] : ( SV7 @ SX0 ) )),bind(SV32,$thf( SV7 @ SV10 ))]]) ).
thf(108,plain,
! [SV26: $i > $i,SV32: $i,SV25: $i,SV33: $i > $i] :
( ( ( ( SV33 @ SV32 )
= ( SV26 @ ( sK5_Xy @ ( SV33 @ SV32 ) @ SV26 @ SV25 ) ) )
= $true )
| ( ( in @ SV32 @ SV25 )
= $false )
| ( ( ( SV33 @ ( sK11_E @ SV25 @ SV32 @ SV26 @ SV33 ) )
= ( SV26 @ ( sK11_E @ SV25 @ SV32 @ SV26 @ SV33 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[97:[bind(SV31,$thf( SV25 )),bind(SV27,$thf( SV33 @ SV32 ))]]) ).
thf(109,plain,
! [SV33: $i > $i,SV29: $i > $i,SV28: $i,SV30: $i] :
( ( ( in @ SV30
@ ( image1 @ SV28
@ ^ [SX0: $i] : ( SV29 @ SX0 ) ) )
= $false )
| ( ( in @ ( SV33 @ ( sK5_Xy @ SV30 @ SV29 @ SV28 ) )
@ ( image1 @ SV28
@ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
= $true ) ),
inference(extuni,[status(esa)],[96:[bind(SV31,$thf( SV28 )),bind(SV32,$thf( sK5_Xy @ SV30 @ SV29 @ SV28 ))]]) ).
thf(110,plain,
! [SV29: $i > $i,SV32: $i,SV28: $i,SV33: $i > $i] :
( ( ( in @ ( sK5_Xy @ ( SV33 @ SV32 ) @ SV29 @ SV28 ) @ SV28 )
= $true )
| ( ( in @ SV32 @ SV28 )
= $false )
| ( ( ( SV33 @ ( sK12_E @ SV28 @ SV32 @ SV29 @ SV33 ) )
= ( SV29 @ ( sK12_E @ SV28 @ SV32 @ SV29 @ SV33 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[95:[bind(SV31,$thf( SV28 )),bind(SV30,$thf( SV33 @ SV32 ))]]) ).
thf(111,plain,
! [SV36: $i] :
( ( ( in @ ( sK2_SY430 @ sK4_SY437 )
@ ( image1 @ SV36
@ ^ [SX0: $i] : SX0 ) )
= $true )
| ( ( in @ sK3_SY434 @ SV36 )
= $false ) ),
inference(rename,[status(thm)],[59]) ).
thf(114,plain,
! [SV36: $i,SV31: $i,SV32: $i,SV33: $i > $i] :
( ( ( ( in @ ( sK2_SY430 @ sK4_SY437 )
@ ( image1 @ SV36
@ ^ [SX0: $i] : SX0 ) )
= ( in @ SV32 @ SV31 ) )
= $false )
| ( ( in @ sK3_SY434 @ SV36 )
= $false )
| ( ( in @ ( SV33 @ SV32 )
@ ( image1 @ SV31
@ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[111,92]) ).
thf(122,plain,
! [SV36: $i,SV7: $i > $i,SV8: $i,SV9: $i,SV10: $i] :
( ( ( ( in @ ( sK2_SY430 @ sK4_SY437 )
@ ( image1 @ SV36
@ ^ [SX0: $i] : SX0 ) )
= ( in @ SV10 @ SV9 ) )
= $false )
| ( ( in @ sK3_SY434 @ SV36 )
= $false )
| ( ( SV8
= ( SV7 @ SV10 ) )
= $false )
| ( ( in @ SV8
@ ( image1 @ SV9
@ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[111,49]) ).
thf(126,plain,
! [SV36: $i,SV7: $i > $i] :
( ( ( in @ ( SV7 @ ( sK2_SY430 @ sK4_SY437 ) )
@ ( image1
@ ( image1 @ SV36
@ ^ [SX0: $i] : SX0 )
@ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
= $true )
| ( ( in @ sK3_SY434 @ SV36 )
= $false ) ),
inference(extuni,[status(esa)],[122:[bind(SV8,$thf( SV7 @ ( sK2_SY430 @ sK4_SY437 ) )),bind(SV9,$thf( image1 @ SV36 @ ^ [SX0: $i] : SX0 )),bind(SV10,$thf( sK2_SY430 @ sK4_SY437 ))]]) ).
thf(127,plain,
! [SV36: $i,SV33: $i > $i] :
( ( ( in @ ( SV33 @ ( sK2_SY430 @ sK4_SY437 ) )
@ ( image1
@ ( image1 @ SV36
@ ^ [SX0: $i] : SX0 )
@ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
= $true )
| ( ( in @ sK3_SY434 @ SV36 )
= $false ) ),
inference(extuni,[status(esa)],[114:[bind(SV31,$thf( image1 @ SV36 @ ^ [SX0: $i] : SX0 )),bind(SV32,$thf( sK2_SY430 @ sK4_SY437 ))]]) ).
thf(128,plain,
! [SV37: $i,SV38: $i] :
( ( ( in @ ( sK2_SY430 @ sK4_SY437 )
@ ( image1 @ SV38
@ ^ [SX0: $i] : sK3_SY434 ) )
= $true )
| ( ( in @ SV37 @ SV38 )
= $false ) ),
inference(rename,[status(thm)],[60]) ).
thf(132,plain,
! [SV37: $i,SV38: $i,SV36: $i] :
( ( ( ( in @ SV37 @ SV38 )
= ( in @ ( sK2_SY430 @ sK4_SY437 )
@ ( image1 @ SV36
@ ^ [SX0: $i] : SX0 ) ) )
= $false )
| ( ( in @ ( sK2_SY430 @ sK4_SY437 )
@ ( image1 @ SV38
@ ^ [SX0: $i] : sK3_SY434 ) )
= $true )
| ( ( in @ sK3_SY434 @ SV36 )
= $false ) ),
inference(res,[status(thm)],[128,111]) ).
thf(133,plain,
! [SV37: $i,SV38: $i,SV31: $i,SV32: $i,SV33: $i > $i] :
( ( ( ( in @ ( sK2_SY430 @ sK4_SY437 )
@ ( image1 @ SV38
@ ^ [SX0: $i] : sK3_SY434 ) )
= ( in @ SV32 @ SV31 ) )
= $false )
| ( ( in @ SV37 @ SV38 )
= $false )
| ( ( in @ ( SV33 @ SV32 )
@ ( image1 @ SV31
@ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[128,92]) ).
thf(134,plain,
! [SV37: $i,SV38: $i,SV31: $i,SV32: $i,SV33: $i > $i] :
( ( ( ( in @ SV37 @ SV38 )
= ( in @ ( SV33 @ SV32 )
@ ( image1 @ SV31
@ ^ [SX0: $i] : ( SV33 @ SX0 ) ) ) )
= $false )
| ( ( in @ ( sK2_SY430 @ sK4_SY437 )
@ ( image1 @ SV38
@ ^ [SX0: $i] : sK3_SY434 ) )
= $true )
| ( ( in @ SV32 @ SV31 )
= $false ) ),
inference(res,[status(thm)],[128,92]) ).
thf(136,plain,
! [SV37: $i,SV38: $i,SV28: $i,SV29: $i > $i,SV30: $i] :
( ( ( ( in @ SV37 @ SV38 )
= ( in @ ( sK5_Xy @ SV30 @ SV29 @ SV28 ) @ SV28 ) )
= $false )
| ( ( in @ ( sK2_SY430 @ sK4_SY437 )
@ ( image1 @ SV38
@ ^ [SX0: $i] : sK3_SY434 ) )
= $true )
| ( ( in @ SV30
@ ( image1 @ SV28
@ ^ [SX0: $i] : ( SV29 @ SX0 ) ) )
= $false ) ),
inference(res,[status(thm)],[128,78]) ).
thf(139,plain,
! [SV37: $i,SV38: $i,SV7: $i > $i,SV8: $i,SV9: $i,SV10: $i] :
( ( ( ( in @ SV37 @ SV38 )
= ( in @ SV8
@ ( image1 @ SV9
@ ^ [SX0: $i] : ( SV7 @ SX0 ) ) ) )
= $false )
| ( ( in @ ( sK2_SY430 @ sK4_SY437 )
@ ( image1 @ SV38
@ ^ [SX0: $i] : sK3_SY434 ) )
= $true )
| ( ( in @ SV10 @ SV9 )
= $false )
| ( ( SV8
= ( SV7 @ SV10 ) )
= $false ) ),
inference(res,[status(thm)],[128,49]) ).
thf(141,plain,
! [SV37: $i,SV38: $i,SV7: $i > $i,SV8: $i,SV9: $i,SV10: $i] :
( ( ( ( in @ ( sK2_SY430 @ sK4_SY437 )
@ ( image1 @ SV38
@ ^ [SX0: $i] : sK3_SY434 ) )
= ( in @ SV10 @ SV9 ) )
= $false )
| ( ( in @ SV37 @ SV38 )
= $false )
| ( ( SV8
= ( SV7 @ SV10 ) )
= $false )
| ( ( in @ SV8
@ ( image1 @ SV9
@ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[128,49]) ).
thf(142,plain,
! [SV37: $i,SV38: $i] :
( ( ( ( in @ SV37 @ SV38 )
= ( in @ sK4_SY437 @ sK1_A ) )
= $false )
| ( ( in @ ( sK2_SY430 @ sK4_SY437 )
@ ( image1 @ SV38
@ ^ [SX0: $i] : sK3_SY434 ) )
= $true ) ),
inference(res,[status(thm)],[128,33]) ).
thf(145,plain,
( ( in @ ( sK2_SY430 @ sK4_SY437 )
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : sK3_SY434 ) )
= $true ),
inference(extuni,[status(esa)],[142:[bind(SV38,$thf( sK1_A )),bind(SV37,$thf( sK4_SY437 ))]]) ).
thf(146,plain,
! [SV37: $i,SV38: $i,SV7: $i > $i] :
( ( ( in @ ( SV7 @ ( sK2_SY430 @ sK4_SY437 ) )
@ ( image1
@ ( image1 @ SV38
@ ^ [SX0: $i] : sK3_SY434 )
@ ^ [SX0: $i] : ( SV7 @ SX0 ) ) )
= $true )
| ( ( in @ SV37 @ SV38 )
= $false ) ),
inference(extuni,[status(esa)],[141:[bind(SV8,$thf( SV7 @ ( sK2_SY430 @ sK4_SY437 ) )),bind(SV9,$thf( image1 @ SV38 @ ^ [SX0: $i] : sK3_SY434 )),bind(SV10,$thf( sK2_SY430 @ sK4_SY437 ))]]) ).
thf(147,plain,
! [SV7: $i > $i,SV9: $i,SV10: $i] :
( ( ( in @ SV10 @ SV9 )
= $false )
| ( ( in @ ( sK2_SY430 @ sK4_SY437 )
@ ( image1
@ ( image1 @ SV9
@ ^ [SX0: $i] : ( SV7 @ SX0 ) )
@ ^ [SX0: $i] : sK3_SY434 ) )
= $true ) ),
inference(extuni,[status(esa)],[139:[bind(SV8,$thf( SV7 @ SV10 )),bind(SV38,$thf( image1 @ SV9 @ ^ [SX0: $i] : ( SV7 @ SX0 ) )),bind(SV37,$thf( SV7 @ SV10 ))]]) ).
thf(148,plain,
! [SV29: $i > $i,SV28: $i,SV30: $i] :
( ( ( in @ SV30
@ ( image1 @ SV28
@ ^ [SX0: $i] : ( SV29 @ SX0 ) ) )
= $false )
| ( ( in @ ( sK2_SY430 @ sK4_SY437 )
@ ( image1 @ SV28
@ ^ [SX0: $i] : sK3_SY434 ) )
= $true ) ),
inference(extuni,[status(esa)],[136:[bind(SV38,$thf( SV28 )),bind(SV37,$thf( sK5_Xy @ SV30 @ SV29 @ SV28 ))]]) ).
thf(149,plain,
! [SV33: $i > $i,SV31: $i,SV32: $i] :
( ( ( in @ SV32 @ SV31 )
= $false )
| ( ( in @ ( sK2_SY430 @ sK4_SY437 )
@ ( image1
@ ( image1 @ SV31
@ ^ [SX0: $i] : ( SV33 @ SX0 ) )
@ ^ [SX0: $i] : sK3_SY434 ) )
= $true ) ),
inference(extuni,[status(esa)],[134:[bind(SV38,$thf( image1 @ SV31 @ ^ [SX0: $i] : ( SV33 @ SX0 ) )),bind(SV37,$thf( SV33 @ SV32 ))]]) ).
thf(150,plain,
! [SV37: $i,SV38: $i,SV33: $i > $i] :
( ( ( in @ ( SV33 @ ( sK2_SY430 @ sK4_SY437 ) )
@ ( image1
@ ( image1 @ SV38
@ ^ [SX0: $i] : sK3_SY434 )
@ ^ [SX0: $i] : ( SV33 @ SX0 ) ) )
= $true )
| ( ( in @ SV37 @ SV38 )
= $false ) ),
inference(extuni,[status(esa)],[133:[bind(SV31,$thf( image1 @ SV38 @ ^ [SX0: $i] : sK3_SY434 )),bind(SV32,$thf( sK2_SY430 @ sK4_SY437 ))]]) ).
thf(151,plain,
! [SV36: $i] :
( ( ( in @ sK3_SY434 @ SV36 )
= $false )
| ( ( in @ ( sK2_SY430 @ sK4_SY437 )
@ ( image1
@ ( image1 @ SV36
@ ^ [SX0: $i] : SX0 )
@ ^ [SX0: $i] : sK3_SY434 ) )
= $true ) ),
inference(extuni,[status(esa)],[132:[bind(SV38,$thf( image1 @ SV36 @ ^ [SX0: $i] : SX0 )),bind(SV37,$thf( sK2_SY430 @ sK4_SY437 ))]]) ).
thf(152,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,151,150,149,148,147,146,145,128,127,126,111,110,109,108,107,106,105,92,91,90,89,78,77,76,75,66,65,64,63,62,61,49,33,32]) ).
thf(153,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[152]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU797^2 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n003.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 : Mon Jun 20 07:39:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 0
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 236
% 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)...eprover: CPU time limit exceeded, terminating
% 50.16/50.41 eprover: CPU time limit exceeded, terminating
% 50.48/50.69 .........
% 75.07/75.29 (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
% 125.11/125.32 eprover: CPU time limit exceeded, terminating
% 125.14/125.34 ...eprover: CPU time limit exceeded, terminating
% 149.55/149.78 .
% 150.17/150.39 (rf:0,axioms:0,ps:3,u:8,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,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
% 200.13/200.45 eprover: CPU time limit exceeded, terminating
% 200.25/200.47 ....
% 201.88/202.15
% 201.88/202.15 ********************************
% 201.88/202.15 * All subproblems solved! *
% 201.88/202.15 ********************************
% 201.88/202.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:8,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:23,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:152,loop_count:10,foatp_calls:3,translation:fof_full)
% 201.93/202.16
% 201.93/202.16 %**** Beginning of derivation protocol ****
% 201.93/202.16 % SZS output start CNFRefutation
% See solution above
% 201.93/202.16
% 201.93/202.16 %**** End of derivation protocol ****
% 201.93/202.16 %**** no. of clauses in derivation: 104 ****
% 201.93/202.16 %**** clause counter: 152 ****
% 201.93/202.16
% 201.93/202.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:1,ps:3,u:8,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:false,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:23,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:152,loop_count:10,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------