%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU797^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:48:25 AM UTC 2026
% Result : Theorem 270.52s 45.47s
% Output : CNFRefutation 270.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 2
% Syntax : Number of formulae : 115 ( 52 unt; 0 typ; 1 def)
% Number of atoms : 706 ( 339 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 1367 ( 106 ~; 134 |; 16 &;1100 @)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 105 ( 105 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 11 con; 0-5 aty)
% Number of variables : 422 ( 148 ^; 266 !; 8 ?; 422 :)
% 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 > $i ) > ( $i > $i ) > $i ).
thf(tp_sK11_E,type,
sK11_E: $i ).
thf(tp_sK12_E,type,
sK12_E: ( $i > $i ) > $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 > $i ) > ( $i > $i ) > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY15,type,
sK2_SY15: $i > $i ).
thf(tp_sK3_SY19,type,
sK3_SY19: $i ).
thf(tp_sK4_SY22,type,
sK4_SY22: $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 ).
thf(tp_sK9_E,type,
sK9_E: $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/sandbox2/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/sandbox2/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_SY19
= ( sK2_SY15 @ sK4_SY22 ) )
& ( in @ sK4_SY22 @ sK1_A )
& ~ ( in @ sK3_SY19
@ ( image1 @ sK1_A
@ ^ [SY21: $i] : ( sK2_SY15 @ SY21 ) ) ) )
= $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_SY19
= ( sK2_SY15 @ sK4_SY22 ) )
& ( in @ sK4_SY22 @ sK1_A )
& ~ ( in @ sK3_SY19
@ ( image1 @ sK1_A
@ ^ [SY21: $i] : ( sK2_SY15 @ SY21 ) ) ) )
= $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_SY19
!= ( sK2_SY15 @ sK4_SY22 ) )
| ~ ( in @ sK4_SY22 @ sK1_A ) )
| ~ ~ ( in @ sK3_SY19
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,image1Equiv]) ).
thf(13,plain,
! [SV1: $i] :
( ( ~ ( ~ ! [SY24: $i > $i,SY25: $i] :
( ! [SY26: $i] :
( ( SY25
!= ( SY24 @ SY26 ) )
| ~ ( in @ SY26 @ SV1 ) )
| ( in @ SY25
@ ( image1 @ SV1
@ ^ [SX3: $i] : ( SY24 @ SX3 ) ) ) )
| ~ ! [SY28: $i > $i,SY29: $i] :
( ~ ( in @ SY29
@ ( image1 @ SV1
@ ^ [SX3: $i] : ( SY28 @ SX3 ) ) )
| ~ ( ( SY29
!= ( SY28 @ ( sK5_Xy @ SY29 @ SY28 @ SV1 ) ) )
| ~ ( in @ ( sK5_Xy @ SY29 @ SY28 @ SV1 ) @ SV1 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(14,plain,
( ( ~ ~ ( ( sK3_SY19
!= ( sK2_SY15 @ sK4_SY22 ) )
| ~ ( in @ sK4_SY22 @ sK1_A ) )
| ~ ~ ( in @ sK3_SY19
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[12]) ).
thf(15,plain,
! [SV1: $i] :
( ( ~ ! [SY24: $i > $i,SY25: $i] :
( ! [SY26: $i] :
( ( SY25
!= ( SY24 @ SY26 ) )
| ~ ( in @ SY26 @ SV1 ) )
| ( in @ SY25
@ ( image1 @ SV1
@ ^ [SX3: $i] : ( SY24 @ SX3 ) ) ) )
| ~ ! [SY28: $i > $i,SY29: $i] :
( ~ ( in @ SY29
@ ( image1 @ SV1
@ ^ [SX3: $i] : ( SY28 @ SX3 ) ) )
| ~ ( ( SY29
!= ( SY28 @ ( sK5_Xy @ SY29 @ SY28 @ SV1 ) ) )
| ~ ( in @ ( sK5_Xy @ SY29 @ SY28 @ SV1 ) @ SV1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(16,plain,
( ( ~ ~ ( ( sK3_SY19
!= ( sK2_SY15 @ sK4_SY22 ) )
| ~ ( in @ sK4_SY22 @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(17,plain,
( ( ~ ~ ( in @ sK3_SY19
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[14]) ).
thf(18,plain,
! [SV1: $i] :
( ( ~ ! [SY24: $i > $i,SY25: $i] :
( ! [SY26: $i] :
( ( SY25
!= ( SY24 @ SY26 ) )
| ~ ( in @ SY26 @ SV1 ) )
| ( in @ SY25
@ ( image1 @ SV1
@ ^ [SX3: $i] : ( SY24 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(19,plain,
! [SV1: $i] :
( ( ~ ! [SY28: $i > $i,SY29: $i] :
( ~ ( in @ SY29
@ ( image1 @ SV1
@ ^ [SX3: $i] : ( SY28 @ SX3 ) ) )
| ~ ( ( SY29
!= ( SY28 @ ( sK5_Xy @ SY29 @ SY28 @ SV1 ) ) )
| ~ ( in @ ( sK5_Xy @ SY29 @ SY28 @ SV1 ) @ SV1 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(20,plain,
( ( ~ ( ( sK3_SY19
!= ( sK2_SY15 @ sK4_SY22 ) )
| ~ ( in @ sK4_SY22 @ sK1_A ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[16]) ).
thf(21,plain,
( ( ~ ( in @ sK3_SY19
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[17]) ).
thf(22,plain,
! [SV1: $i] :
( ( ! [SY24: $i > $i,SY25: $i] :
( ! [SY26: $i] :
( ( SY25
!= ( SY24 @ SY26 ) )
| ~ ( in @ SY26 @ SV1 ) )
| ( in @ SY25
@ ( image1 @ SV1
@ ^ [SX3: $i] : ( SY24 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[18]) ).
thf(23,plain,
! [SV1: $i] :
( ( ! [SY28: $i > $i,SY29: $i] :
( ~ ( in @ SY29
@ ( image1 @ SV1
@ ^ [SX3: $i] : ( SY28 @ SX3 ) ) )
| ~ ( ( SY29
!= ( SY28 @ ( sK5_Xy @ SY29 @ SY28 @ SV1 ) ) )
| ~ ( in @ ( sK5_Xy @ SY29 @ SY28 @ SV1 ) @ SV1 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[19]) ).
thf(24,plain,
( ( ( sK3_SY19
!= ( sK2_SY15 @ sK4_SY22 ) )
| ~ ( in @ sK4_SY22 @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(25,plain,
( ( in @ sK3_SY19
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(26,plain,
! [SV1: $i,SV2: $i > $i] :
( ( ! [SY31: $i] :
( ! [SY32: $i] :
( ( SY31
!= ( SV2 @ SY32 ) )
| ~ ( in @ SY32 @ SV1 ) )
| ( in @ SY31
@ ( image1 @ SV1
@ ^ [SY33: $i] : ( SV2 @ SY33 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV3: $i > $i,SV1: $i] :
( ( ! [SY34: $i] :
( ~ ( in @ SY34
@ ( image1 @ SV1
@ ^ [SY35: $i] : ( SV3 @ SY35 ) ) )
| ~ ( ( SY34
!= ( SV3 @ ( sK5_Xy @ SY34 @ SV3 @ SV1 ) ) )
| ~ ( in @ ( sK5_Xy @ SY34 @ SV3 @ SV1 ) @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(28,plain,
( ( sK3_SY19
!= ( sK2_SY15 @ sK4_SY22 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(29,plain,
( ( ~ ( in @ sK4_SY22 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[24]) ).
thf(30,plain,
! [SV1: $i,SV2: $i > $i,SV4: $i] :
( ( ! [SY36: $i] :
( ( SV4
!= ( SV2 @ SY36 ) )
| ~ ( in @ SY36 @ SV1 ) )
| ( in @ SV4
@ ( image1 @ SV1
@ ^ [SY33: $i] : ( SV2 @ SY33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(31,plain,
! [SV3: $i > $i,SV1: $i,SV5: $i] :
( ( ~ ( in @ SV5
@ ( image1 @ SV1
@ ^ [SY35: $i] : ( SV3 @ SY35 ) ) )
| ~ ( ( 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_SY19
= ( sK2_SY15 @ sK4_SY22 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(33,plain,
( ( in @ sK4_SY22 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(34,plain,
! [SV1: $i,SV2: $i > $i,SV4: $i] :
( ( ( ! [SY36: $i] :
( ( SV4
!= ( SV2 @ SY36 ) )
| ~ ( in @ SY36 @ SV1 ) ) )
= $true )
| ( ( in @ SV4
@ ( image1 @ SV1
@ ^ [SY33: $i] : ( SV2 @ SY33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(35,plain,
! [SV3: $i > $i,SV1: $i,SV5: $i] :
( ( ( ~ ( in @ SV5
@ ( image1 @ SV1
@ ^ [SY35: $i] : ( SV3 @ SY35 ) ) ) )
= $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
@ ^ [SY33: $i] : ( SV2 @ SY33 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV3: $i > $i,SV1: $i,SV5: $i] :
( ( ( in @ SV5
@ ( image1 @ SV1
@ ^ [SY35: $i] : ( SV3 @ SY35 ) ) )
= $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
@ ^ [SY33: $i] : ( SV2 @ SY33 ) ) )
= $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
@ ^ [SY35: $i] : ( SV3 @ SY35 ) ) )
= $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
@ ^ [SY33: $i] : ( SV2 @ SY33 ) ) )
= $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
@ ^ [SY35: $i] : ( SV3 @ SY35 ) ) )
= $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
@ ^ [SY35: $i] : ( SV3 @ SY35 ) ) )
= $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
@ ^ [SY33: $i] : ( SV2 @ SY33 ) ) )
= $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
@ ^ [SY35: $i] : ( SV3 @ SY35 ) ) )
= $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
@ ^ [SY35: $i] : ( SV3 @ SY35 ) ) )
= $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(48,plain,
( ( ( in @ sK4_SY22 @ sK1_A )
= ( in @ sK3_SY19
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) ) ) )
= $false ),
inference(res,[status(thm)],[33,25]) ).
thf(49,plain,
( ( ( sK1_A
= ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) ) )
= $false )
| ( ( sK4_SY22 = sK3_SY19 )
= $false ) ),
inference(extuni,[status(esa)],[48]) ).
thf(50,plain,
! [SV7: $i,SV8: $i > $i,SV9: $i] :
( ( ( SV9
= ( SV8 @ ( sK5_Xy @ SV9 @ SV8 @ SV7 ) ) )
= $true )
| ( ( in @ SV9
@ ( image1 @ SV7
@ ^ [SX0: $i] : ( SV8 @ SX0 ) ) )
= $false ) ),
inference(rename,[status(thm)],[44]) ).
thf(53,plain,
! [SV7: $i,SV8: $i > $i,SV9: $i] :
( ( ( ( in @ SV9
@ ( image1 @ SV7
@ ^ [SX0: $i] : ( SV8 @ SX0 ) ) )
= ( in @ sK4_SY22 @ sK1_A ) )
= $false )
| ( ( SV9
= ( SV8 @ ( sK5_Xy @ SV9 @ SV8 @ SV7 ) ) )
= $true ) ),
inference(res,[status(thm)],[50,33]) ).
thf(56,plain,
! [SV7: $i,SV8: $i > $i] :
( ( ( sK4_SY22
= ( SV8 @ ( sK5_Xy @ sK4_SY22 @ SV8 @ SV7 ) ) )
= $true )
| ( ( ( image1 @ SV7
@ ^ [SX0: $i] : ( SV8 @ SX0 ) )
= sK1_A )
= $false ) ),
inference(extuni,[status(esa)],[53:[bind(SV9,$thf( sK4_SY22 ))]]) ).
thf(57,plain,
! [SV10: $i > $i,SV11: $i,SV12: $i,SV13: $i] :
( ( ( in @ SV13 @ SV12 )
= $false )
| ( ( SV11
= ( SV10 @ SV13 ) )
= $false )
| ( ( in @ SV11
@ ( image1 @ SV12
@ ^ [SX0: $i] : ( SV10 @ SX0 ) ) )
= $true ) ),
inference(rename,[status(thm)],[43]) ).
thf(62,plain,
! [SV10: $i > $i,SV11: $i,SV12: $i,SV13: $i,SV7: $i,SV8: $i > $i,SV9: $i] :
( ( ( ( in @ SV11
@ ( image1 @ SV12
@ ^ [SX0: $i] : ( SV10 @ SX0 ) ) )
= ( in @ SV9
@ ( image1 @ SV7
@ ^ [SX0: $i] : ( SV8 @ SX0 ) ) ) )
= $false )
| ( ( in @ SV13 @ SV12 )
= $false )
| ( ( SV11
= ( SV10 @ SV13 ) )
= $false )
| ( ( SV9
= ( SV8 @ ( sK5_Xy @ SV9 @ SV8 @ SV7 ) ) )
= $true ) ),
inference(res,[status(thm)],[57,50]) ).
thf(63,plain,
! [SV10: $i > $i,SV11: $i,SV12: $i,SV13: $i,SV7: $i,SV8: $i > $i,SV9: $i] :
( ( ( ( SV11
= ( SV10 @ SV13 ) )
= ( SV9
= ( SV8 @ ( sK5_Xy @ SV9 @ SV8 @ SV7 ) ) ) )
= $false )
| ( ( in @ SV13 @ SV12 )
= $false )
| ( ( in @ SV11
@ ( image1 @ SV12
@ ^ [SX0: $i] : ( SV10 @ SX0 ) ) )
= $true )
| ( ( in @ SV9
@ ( image1 @ SV7
@ ^ [SX0: $i] : ( SV8 @ SX0 ) ) )
= $false ) ),
inference(res,[status(thm)],[57,50]) ).
thf(66,plain,
! [SV10: $i > $i,SV11: $i,SV12: $i,SV13: $i] :
( ( ( ( in @ SV13 @ SV12 )
= ( in @ sK4_SY22 @ sK1_A ) )
= $false )
| ( ( SV11
= ( SV10 @ SV13 ) )
= $false )
| ( ( in @ SV11
@ ( image1 @ SV12
@ ^ [SX0: $i] : ( SV10 @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[57,33]) ).
thf(67,plain,
! [SV10: $i > $i,SV11: $i,SV12: $i,SV13: $i] :
( ( ( ( SV11
= ( SV10 @ SV13 ) )
= ( sK3_SY19
= ( sK2_SY15 @ sK4_SY22 ) ) )
= $false )
| ( ( in @ SV13 @ SV12 )
= $false )
| ( ( in @ SV11
@ ( image1 @ SV12
@ ^ [SX0: $i] : ( SV10 @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[57,32]) ).
thf(69,plain,
! [SV10: $i > $i,SV11: $i,SV12: $i,SV13: $i] :
( ( ( ( in @ SV11
@ ( image1 @ SV12
@ ^ [SX0: $i] : ( SV10 @ SX0 ) ) )
= ( in @ sK3_SY19
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) ) ) )
= $false )
| ( ( in @ SV13 @ SV12 )
= $false )
| ( ( SV11
= ( SV10 @ SV13 ) )
= $false ) ),
inference(res,[status(thm)],[57,25]) ).
thf(70,plain,
! [SV20: $i > $i > $i,SV13: $i,SV19: $i > $i] :
( ( ( sK3_SY19
= ( sK2_SY15 @ ( sK6_E @ ( SV19 @ SV13 ) @ ( SV20 @ SV13 ) ) ) )
= $false )
| ( ( in @ SV13 @ sK1_A )
= $false )
| ( ( ( sK6_E
@ ( SV19
@ ( sK6_E @ SV13
@ ^ [SX0: $i] : ( sK2_SY15 @ ( sK6_E @ ( SV19 @ SX0 ) @ ( SV20 @ SX0 ) ) ) ) )
@ ( SV20
@ ( sK6_E @ SV13
@ ^ [SX0: $i] : ( sK2_SY15 @ ( sK6_E @ ( SV19 @ SX0 ) @ ( SV20 @ SX0 ) ) ) ) ) )
= ( sK6_E @ SV13
@ ^ [SX0: $i] : ( sK2_SY15 @ ( sK6_E @ ( SV19 @ SX0 ) @ ( SV20 @ SX0 ) ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[69:[bind(SV10,$thf( ^ [SX0: $i] : ( sK2_SY15 @ ( sK6_E @ ( SV19 @ SX0 ) @ ( SV20 @ SX0 ) ) ) )),bind(SV12,$thf( sK1_A )),bind(SV11,$thf( sK3_SY19 ))]]) ).
thf(71,plain,
! [SV13: $i] :
( ( ( sK3_SY19
= ( sK2_SY15 @ SV13 ) )
= $false )
| ( ( in @ SV13 @ sK1_A )
= $false ) ),
inference(extuni,[status(esa)],[69:[bind(SV10,$thf( ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) )),bind(SV12,$thf( sK1_A )),bind(SV11,$thf( sK3_SY19 ))]]) ).
thf(72,plain,
! [SV13: $i,SV16: $i > $i] :
( ( ( sK3_SY19
= ( sK2_SY15 @ ( SV16 @ SV13 ) ) )
= $false )
| ( ( in @ SV13 @ sK1_A )
= $false )
| ( ( ( sK2_SY15
@ ( SV16
@ ( sK6_E @ SV13
@ ^ [SX0: $i] : ( sK2_SY15 @ ( SV16 @ SX0 ) ) ) ) )
= ( sK2_SY15
@ ( sK6_E @ SV13
@ ^ [SX0: $i] : ( sK2_SY15 @ ( SV16 @ SX0 ) ) ) ) )
= $false ) ),
inference(extuni,[status(esa)],[69:[bind(SV10,$thf( ^ [SX0: $i] : ( sK2_SY15 @ ( SV16 @ SX0 ) ) )),bind(SV12,$thf( sK1_A )),bind(SV11,$thf( sK3_SY19 ))]]) ).
thf(73,plain,
( ( ( in @ sK3_SY19 @ sK1_A )
= $false )
| ( ( ( sK6_E @ sK3_SY19
@ ^ [SX0: $i] : SX0 )
= ( sK2_SY15
@ ( sK6_E @ sK3_SY19
@ ^ [SX0: $i] : SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[69:[bind(SV13,$thf( sK3_SY19 )),bind(SV10,$thf( ^ [SX0: $i] : SX0 )),bind(SV12,$thf( sK1_A )),bind(SV11,$thf( sK3_SY19 ))]]) ).
thf(74,plain,
! [SV12: $i,SV13: $i,SV10: $i > $i] :
( ( ( sK3_SY19
= ( SV10 @ SV13 ) )
= $false )
| ( ( in @ SV13 @ SV12 )
= $false )
| ( ( ( image1 @ SV12
@ ^ [SX0: $i] : ( SV10 @ SX0 ) )
= ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[69:[bind(SV11,$thf( sK3_SY19 ))]]) ).
thf(75,plain,
! [SV12: $i] :
( ( ( in @ ( sK2_SY15 @ sK4_SY22 )
@ ( image1 @ SV12
@ ^ [SX0: $i] : SX0 ) )
= $true )
| ( ( in @ sK3_SY19 @ SV12 )
= $false ) ),
inference(extuni,[status(esa)],[67:[bind(SV11,$thf( sK2_SY15 @ sK4_SY22 )),bind(SV13,$thf( sK3_SY19 )),bind(SV10,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(76,plain,
! [SV13: $i,SV12: $i] :
( ( ( in @ ( sK2_SY15 @ sK4_SY22 )
@ ( image1 @ SV12
@ ^ [SX0: $i] : sK3_SY19 ) )
= $true )
| ( ( in @ SV13 @ SV12 )
= $false ) ),
inference(extuni,[status(esa)],[67:[bind(SV11,$thf( sK2_SY15 @ sK4_SY22 )),bind(SV10,$thf( ^ [SX0: $i] : sK3_SY19 ))]]) ).
thf(77,plain,
! [SV12: $i] :
( ( ( in @ sK3_SY19
@ ( image1 @ SV12
@ ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) ) )
= $true )
| ( ( in @ sK4_SY22 @ SV12 )
= $false ) ),
inference(extuni,[status(esa)],[67:[bind(SV13,$thf( sK4_SY22 )),bind(SV10,$thf( ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) )),bind(SV11,$thf( sK3_SY19 ))]]) ).
thf(78,plain,
! [SV13: $i,SV12: $i] :
( ( ( in @ sK3_SY19
@ ( image1 @ SV12
@ ^ [SX0: $i] : ( sK2_SY15 @ sK4_SY22 ) ) )
= $true )
| ( ( in @ SV13 @ SV12 )
= $false ) ),
inference(extuni,[status(esa)],[67:[bind(SV10,$thf( ^ [SX0: $i] : ( sK2_SY15 @ sK4_SY22 ) )),bind(SV11,$thf( sK3_SY19 ))]]) ).
thf(79,plain,
! [SV13: $i,SV25: $i > $i,SV12: $i] :
( ( ( in @ sK3_SY19
@ ( image1 @ SV12
@ ^ [SX0: $i] : ( sK2_SY15 @ ( SV25 @ SX0 ) ) ) )
= $true )
| ( ( in @ SV13 @ SV12 )
= $false )
| ( ( ( sK2_SY15 @ ( SV25 @ SV13 ) )
= ( sK2_SY15 @ sK4_SY22 ) )
= $false ) ),
inference(extuni,[status(esa)],[67:[bind(SV10,$thf( ^ [SX0: $i] : ( sK2_SY15 @ ( SV25 @ SX0 ) ) )),bind(SV11,$thf( sK3_SY19 ))]]) ).
thf(80,plain,
! [SV12: $i] :
( ( ( in @ sK3_SY19
@ ( image1 @ SV12
@ ^ [SX0: $i] : SX0 ) )
= $true )
| ( ( in @ ( sK2_SY15 @ sK4_SY22 ) @ SV12 )
= $false ) ),
inference(extuni,[status(esa)],[67:[bind(SV13,$thf( sK2_SY15 @ sK4_SY22 )),bind(SV10,$thf( ^ [SX0: $i] : SX0 )),bind(SV11,$thf( sK3_SY19 ))]]) ).
thf(81,plain,
! [SV10: $i > $i] :
( ( in @ ( SV10 @ sK4_SY22 )
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( SV10 @ SX0 ) ) )
= $true ),
inference(extuni,[status(esa)],[66:[bind(SV11,$thf( SV10 @ sK4_SY22 )),bind(SV12,$thf( sK1_A )),bind(SV13,$thf( sK4_SY22 ))]]) ).
thf(82,plain,
! [SV12: $i,SV8: $i > $i,SV7: $i,SV13: $i,SV10: $i > $i] :
( ( ( in @ ( SV10 @ SV13 )
@ ( image1 @ SV7
@ ^ [SX0: $i] : ( SV8 @ SX0 ) ) )
= $false )
| ( ( in @ ( SV8 @ ( sK5_Xy @ ( SV10 @ SV13 ) @ SV8 @ SV7 ) )
@ ( image1 @ SV12
@ ^ [SX0: $i] : ( SV10 @ SX0 ) ) )
= $true )
| ( ( in @ SV13 @ SV12 )
= $false ) ),
inference(extuni,[status(esa)],[63:[bind(SV11,$thf( SV8 @ ( sK5_Xy @ ( SV10 @ SV13 ) @ SV8 @ SV7 ) )),bind(SV9,$thf( SV10 @ SV13 ))]]) ).
thf(83,plain,
! [SV12: $i,SV7: $i,SV9: $i,SV8: $i > $i,SV13: $i,SV10: $i > $i] :
( ( ( in @ SV9
@ ( image1 @ SV7
@ ^ [SX0: $i] : ( SV8 @ SX0 ) ) )
= $false )
| ( ( in @ SV9
@ ( image1 @ SV12
@ ^ [SX0: $i] : ( SV10 @ SX0 ) ) )
= $true )
| ( ( in @ SV13 @ SV12 )
= $false )
| ( ( ( SV10 @ SV13 )
= ( SV8 @ ( sK5_Xy @ SV9 @ SV8 @ SV7 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[63:[bind(SV11,$thf( SV9 ))]]) ).
thf(84,plain,
! [SV8: $i > $i,SV7: $i,SV13: $i,SV10: $i > $i] :
( ( ( ( SV10 @ SV13 )
= ( SV8 @ ( sK5_Xy @ ( SV10 @ SV13 ) @ SV8 @ SV7 ) ) )
= $true )
| ( ( in @ SV13 @ SV7 )
= $false )
| ( ( ( SV10 @ ( sK7_E @ ( SV10 @ SV13 ) @ SV7 @ SV13 @ SV8 @ SV10 ) )
= ( SV8 @ ( sK7_E @ ( SV10 @ SV13 ) @ SV7 @ SV13 @ SV8 @ SV10 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[62:[bind(SV9,$thf( SV10 @ SV13 )),bind(SV12,$thf( SV7 )),bind(SV11,$thf( SV10 @ SV13 ))]]) ).
thf(85,plain,
! [SV12: $i,SV7: $i,SV8: $i > $i,SV13: $i,SV10: $i > $i] :
( ( ( ( SV10 @ SV13 )
= ( SV8 @ ( sK5_Xy @ ( SV10 @ SV13 ) @ SV8 @ SV7 ) ) )
= $true )
| ( ( in @ SV13 @ SV12 )
= $false )
| ( ( ( image1 @ SV12
@ ^ [SX0: $i] : ( SV10 @ SX0 ) )
= ( image1 @ SV7
@ ^ [SX0: $i] : ( SV8 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[62:[bind(SV9,$thf( SV10 @ SV13 )),bind(SV11,$thf( SV10 @ SV13 ))]]) ).
thf(86,plain,
! [SV12: $i,SV13: $i,SV10: $i > $i] :
( ( ( in @ ( SV10 @ SV13 )
@ ( image1 @ SV12
@ ^ [SX0: $i] : ( SV10 @ SX0 ) ) )
= $true )
| ( ( in @ SV13 @ SV12 )
= $false ) ),
inference(extuni,[status(esa)],[57:[bind(SV11,$thf( SV10 @ SV13 ))]]) ).
thf(87,plain,
! [SV28: $i > $i] :
( ( in @ ( SV28 @ sK4_SY22 )
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( SV28 @ SX0 ) ) )
= $true ),
inference(rename,[status(thm)],[81]) ).
thf(89,plain,
! [SV28: $i > $i,SV10: $i > $i,SV11: $i,SV12: $i,SV13: $i] :
( ( ( ( in @ ( SV28 @ sK4_SY22 )
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( SV28 @ SX0 ) ) )
= ( in @ SV13 @ SV12 ) )
= $false )
| ( ( SV11
= ( SV10 @ SV13 ) )
= $false )
| ( ( in @ SV11
@ ( image1 @ SV12
@ ^ [SX0: $i] : ( SV10 @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[87,57]) ).
thf(90,plain,
! [SV28: $i > $i,SV7: $i,SV8: $i > $i,SV9: $i] :
( ( ( ( in @ ( SV28 @ sK4_SY22 )
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( SV28 @ SX0 ) ) )
= ( in @ SV9
@ ( image1 @ SV7
@ ^ [SX0: $i] : ( SV8 @ SX0 ) ) ) )
= $false )
| ( ( SV9
= ( SV8 @ ( sK5_Xy @ SV9 @ SV8 @ SV7 ) ) )
= $true ) ),
inference(res,[status(thm)],[87,50]) ).
thf(91,plain,
! [SV28: $i > $i] :
( ( ( in @ ( SV28 @ sK4_SY22 )
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( SV28 @ SX0 ) ) )
= ( in @ sK3_SY19
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) ) ) )
= $false ),
inference(res,[status(thm)],[87,25]) ).
thf(92,plain,
( ( ( sK9_E
= ( sK2_SY15 @ sK9_E ) )
= $false )
| ( ( sK4_SY22 = sK3_SY19 )
= $false ) ),
inference(extuni,[status(esa)],[91:[bind(SV28,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(93,plain,
( ( ( ( image1 @ sK1_A
@ ^ [SX0: $i] : SX0 )
= ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) ) )
= $false )
| ( ( sK4_SY22 = sK3_SY19 )
= $false ) ),
inference(extuni,[status(esa)],[91:[bind(SV28,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(94,plain,
( ( sK3_SY19
= ( sK2_SY15 @ sK8_E ) )
= $false ),
inference(extuni,[status(esa)],[91:[bind(SV28,$thf( ^ [SX0: $i] : sK3_SY19 ))]]) ).
thf(95,plain,
( ( ( image1 @ sK1_A
@ ^ [SX0: $i] : sK3_SY19 )
= ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) ) )
= $false ),
inference(extuni,[status(esa)],[91:[bind(SV28,$thf( ^ [SX0: $i] : sK3_SY19 ))]]) ).
thf(96,plain,
! [SV8: $i > $i,SV28: $i > $i] :
( ( ( ( SV28 @ sK4_SY22 )
= ( SV8 @ ( sK5_Xy @ ( SV28 @ sK4_SY22 ) @ SV8 @ sK1_A ) ) )
= $true )
| ( ( ( SV28 @ ( sK10_E @ SV8 @ SV28 ) )
= ( SV8 @ ( sK10_E @ SV8 @ SV28 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[90:[bind(SV7,$thf( sK1_A )),bind(SV9,$thf( SV28 @ sK4_SY22 ))]]) ).
thf(97,plain,
! [SV7: $i,SV8: $i > $i,SV28: $i > $i] :
( ( ( ( SV28 @ sK4_SY22 )
= ( SV8 @ ( sK5_Xy @ ( SV28 @ sK4_SY22 ) @ SV8 @ SV7 ) ) )
= $true )
| ( ( ( image1 @ sK1_A
@ ^ [SX0: $i] : ( SV28 @ SX0 ) )
= ( image1 @ SV7
@ ^ [SX0: $i] : ( SV8 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[90:[bind(SV9,$thf( SV28 @ sK4_SY22 ))]]) ).
thf(98,plain,
! [SV28: $i > $i,SV10: $i > $i] :
( ( in @ ( SV10 @ ( SV28 @ sK4_SY22 ) )
@ ( image1
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( SV28 @ SX0 ) )
@ ^ [SX0: $i] : ( SV10 @ SX0 ) ) )
= $true ),
inference(extuni,[status(esa)],[89:[bind(SV11,$thf( SV10 @ ( SV28 @ sK4_SY22 ) )),bind(SV12,$thf( image1 @ sK1_A @ ^ [SX0: $i] : ( SV28 @ SX0 ) )),bind(SV13,$thf( SV28 @ sK4_SY22 ))]]) ).
thf(101,plain,
! [SV7: $i,SV8: $i > $i,SV9: $i] :
( ( ( ( sK3_SY19
= ( sK2_SY15 @ sK8_E ) )
= ( SV9
= ( SV8 @ ( sK5_Xy @ SV9 @ SV8 @ SV7 ) ) ) )
= $false )
| ( ( in @ SV9
@ ( image1 @ SV7
@ ^ [SX0: $i] : ( SV8 @ SX0 ) ) )
= $false ) ),
inference(res,[status(thm)],[94,50]) ).
thf(103,plain,
( ( ( sK3_SY19
= ( sK2_SY15 @ sK8_E ) )
= ( sK3_SY19
= ( sK2_SY15 @ sK4_SY22 ) ) )
= $false ),
inference(res,[status(thm)],[94,32]) ).
thf(104,plain,
( ( ( sK3_SY19
= ( sK2_SY15 @ sK4_SY22 ) )
= $false )
| ( ( ( sK2_SY15 @ sK8_E )
= sK3_SY19 )
= $false ) ),
inference(extuni,[status(esa)],[103]) ).
thf(105,plain,
( ( sK8_E = sK4_SY22 )
= $false ),
inference(extuni,[status(esa)],[103]) ).
thf(106,plain,
( ( ( sK2_SY15 @ sK8_E )
= ( sK2_SY15 @ sK4_SY22 ) )
= $false ),
inference(extuni,[status(esa)],[103]) ).
thf(107,plain,
! [SV8: $i > $i,SV7: $i] :
( ( ( in @ ( sK2_SY15 @ sK8_E )
@ ( image1 @ SV7
@ ^ [SX0: $i] : ( SV8 @ SX0 ) ) )
= $false )
| ( ( sK3_SY19
= ( SV8 @ ( sK5_Xy @ ( sK2_SY15 @ sK8_E ) @ SV8 @ SV7 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[101:[bind(SV9,$thf( sK2_SY15 @ sK8_E ))]]) ).
thf(108,plain,
! [SV8: $i > $i,SV7: $i] :
( ( ( in @ sK3_SY19
@ ( image1 @ SV7
@ ^ [SX0: $i] : ( SV8 @ SX0 ) ) )
= $false )
| ( ( ( sK2_SY15 @ sK8_E )
= ( SV8 @ ( sK5_Xy @ sK3_SY19 @ SV8 @ SV7 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[101:[bind(SV9,$thf( sK3_SY19 ))]]) ).
thf(111,plain,
! [SV7: $i,SV8: $i > $i,SV9: $i] :
( ( ( ( ( image1 @ sK1_A
@ ^ [SX0: $i] : sK3_SY19 )
= ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) ) )
= ( SV9
= ( SV8 @ ( sK5_Xy @ SV9 @ SV8 @ SV7 ) ) ) )
= $false )
| ( ( in @ SV9
@ ( image1 @ SV7
@ ^ [SX0: $i] : ( SV8 @ SX0 ) ) )
= $false ) ),
inference(res,[status(thm)],[95,50]) ).
thf(113,plain,
( ( ( ( image1 @ sK1_A
@ ^ [SX0: $i] : sK3_SY19 )
= ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) ) )
= ( sK3_SY19
= ( sK2_SY15 @ sK4_SY22 ) ) )
= $false ),
inference(res,[status(thm)],[95,32]) ).
thf(114,plain,
( ( ( ( image1 @ sK1_A
@ ^ [SX0: $i] : sK3_SY19 )
= ( sK2_SY15 @ sK4_SY22 ) )
= $false )
| ( ( ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) )
= sK3_SY19 )
= $false ) ),
inference(extuni,[status(esa)],[113]) ).
thf(115,plain,
( ( ( ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) )
= ( sK2_SY15 @ sK4_SY22 ) )
= $false )
| ( ( ( image1 @ sK1_A
@ ^ [SX0: $i] : sK3_SY19 )
= sK3_SY19 )
= $false ) ),
inference(extuni,[status(esa)],[113]) ).
thf(116,plain,
! [SV8: $i > $i,SV7: $i] :
( ( ( in
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) )
@ ( image1 @ SV7
@ ^ [SX0: $i] : ( SV8 @ SX0 ) ) )
= $false )
| ( ( ( image1 @ sK1_A
@ ^ [SX0: $i] : sK3_SY19 )
= ( SV8
@ ( sK5_Xy
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) )
@ SV8
@ SV7 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[111:[bind(SV9,$thf( image1 @ sK1_A @ ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) ))]]) ).
thf(117,plain,
! [SV8: $i > $i,SV7: $i] :
( ( ( in
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : sK3_SY19 )
@ ( image1 @ SV7
@ ^ [SX0: $i] : ( SV8 @ SX0 ) ) )
= $false )
| ( ( ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) )
= ( SV8
@ ( sK5_Xy
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : sK3_SY19 )
@ SV8
@ SV7 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[111:[bind(SV9,$thf( image1 @ sK1_A @ ^ [SX0: $i] : sK3_SY19 ))]]) ).
thf(118,plain,
( ( sK3_SY19
= ( sK2_SY15 @ sK11_E ) )
= $false ),
inference(extuni,[status(esa)],[95]) ).
thf(119,plain,
! [SV31: $i > $i,SV32: $i > $i] :
( ( in @ ( SV32 @ ( SV31 @ sK4_SY22 ) )
@ ( image1
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( SV31 @ SX0 ) )
@ ^ [SX0: $i] : ( SV32 @ SX0 ) ) )
= $true ),
inference(rename,[status(thm)],[98]) ).
thf(123,plain,
! [SV31: $i > $i,SV32: $i > $i,SV10: $i > $i,SV11: $i,SV12: $i,SV13: $i] :
( ( ( ( in @ ( SV32 @ ( SV31 @ sK4_SY22 ) )
@ ( image1
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( SV31 @ SX0 ) )
@ ^ [SX0: $i] : ( SV32 @ SX0 ) ) )
= ( in @ SV13 @ SV12 ) )
= $false )
| ( ( SV11
= ( SV10 @ SV13 ) )
= $false )
| ( ( in @ SV11
@ ( image1 @ SV12
@ ^ [SX0: $i] : ( SV10 @ SX0 ) ) )
= $true ) ),
inference(res,[status(thm)],[119,57]) ).
thf(124,plain,
! [SV31: $i > $i,SV32: $i > $i,SV7: $i,SV8: $i > $i,SV9: $i] :
( ( ( ( in @ ( SV32 @ ( SV31 @ sK4_SY22 ) )
@ ( image1
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( SV31 @ SX0 ) )
@ ^ [SX0: $i] : ( SV32 @ SX0 ) ) )
= ( in @ SV9
@ ( image1 @ SV7
@ ^ [SX0: $i] : ( SV8 @ SX0 ) ) ) )
= $false )
| ( ( SV9
= ( SV8 @ ( sK5_Xy @ SV9 @ SV8 @ SV7 ) ) )
= $true ) ),
inference(res,[status(thm)],[119,50]) ).
thf(125,plain,
! [SV31: $i > $i,SV32: $i > $i] :
( ( ( in @ ( SV32 @ ( SV31 @ sK4_SY22 ) )
@ ( image1
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( SV31 @ SX0 ) )
@ ^ [SX0: $i] : ( SV32 @ SX0 ) ) )
= ( in @ sK3_SY19
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) ) ) )
= $false ),
inference(res,[status(thm)],[119,25]) ).
thf(126,plain,
( ( ( sK14_E
= ( sK2_SY15 @ sK14_E ) )
= $false )
| ( ( ( image1 @ sK1_A
@ ^ [SX0: $i] : SX0 )
= sK1_A )
= $false )
| ( ( sK4_SY22 = sK3_SY19 )
= $false ) ),
inference(extuni,[status(esa)],[125:[bind(SV31,$thf( ^ [SX0: $i] : SX0 )),bind(SV32,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(127,plain,
( ( ( ( image1
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : SX0 )
@ ^ [SX0: $i] : SX0 )
= ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) ) )
= $false )
| ( ( sK4_SY22 = sK3_SY19 )
= $false ) ),
inference(extuni,[status(esa)],[125:[bind(SV31,$thf( ^ [SX0: $i] : SX0 )),bind(SV32,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(128,plain,
( ( ( sK13_E
= ( sK2_SY15 @ sK13_E ) )
= $false )
| ( ( ( image1 @ sK1_A
@ ^ [SX0: $i] : sK3_SY19 )
= sK1_A )
= $false ) ),
inference(extuni,[status(esa)],[125:[bind(SV31,$thf( ^ [SX0: $i] : sK3_SY19 )),bind(SV32,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(129,plain,
( ( ( image1
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : sK3_SY19 )
@ ^ [SX0: $i] : SX0 )
= ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) ) )
= $false ),
inference(extuni,[status(esa)],[125:[bind(SV31,$thf( ^ [SX0: $i] : sK3_SY19 )),bind(SV32,$thf( ^ [SX0: $i] : SX0 ))]]) ).
thf(130,plain,
! [SV31: $i > $i] :
( ( ( sK3_SY19
= ( sK2_SY15 @ ( sK12_E @ SV31 ) ) )
= $false )
| ( ( ( image1 @ sK1_A
@ ^ [SX0: $i] : ( SV31 @ SX0 ) )
= sK1_A )
= $false ) ),
inference(extuni,[status(esa)],[125:[bind(SV32,$thf( ^ [SX0: $i] : sK3_SY19 ))]]) ).
thf(131,plain,
! [SV31: $i > $i] :
( ( ( image1
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( SV31 @ SX0 ) )
@ ^ [SX0: $i] : sK3_SY19 )
= ( image1 @ sK1_A
@ ^ [SX0: $i] : ( sK2_SY15 @ SX0 ) ) )
= $false ),
inference(extuni,[status(esa)],[125:[bind(SV32,$thf( ^ [SX0: $i] : sK3_SY19 ))]]) ).
thf(132,plain,
! [SV8: $i > $i,SV31: $i > $i,SV32: $i > $i] :
( ( ( ( SV32 @ ( SV31 @ sK4_SY22 ) )
= ( SV8
@ ( sK5_Xy @ ( SV32 @ ( SV31 @ sK4_SY22 ) ) @ SV8
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( SV31 @ SX0 ) ) ) ) )
= $true )
| ( ( ( SV32 @ ( sK15_E @ SV31 @ SV8 @ SV32 ) )
= ( SV8 @ ( sK15_E @ SV31 @ SV8 @ SV32 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[124:[bind(SV7,$thf( image1 @ sK1_A @ ^ [SX0: $i] : ( SV31 @ SX0 ) )),bind(SV9,$thf( SV32 @ ( SV31 @ sK4_SY22 ) ))]]) ).
thf(133,plain,
! [SV7: $i,SV8: $i > $i,SV31: $i > $i,SV32: $i > $i] :
( ( ( ( SV32 @ ( SV31 @ sK4_SY22 ) )
= ( SV8 @ ( sK5_Xy @ ( SV32 @ ( SV31 @ sK4_SY22 ) ) @ SV8 @ SV7 ) ) )
= $true )
| ( ( ( image1
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( SV31 @ SX0 ) )
@ ^ [SX0: $i] : ( SV32 @ SX0 ) )
= ( image1 @ SV7
@ ^ [SX0: $i] : ( SV8 @ SX0 ) ) )
= $false ) ),
inference(extuni,[status(esa)],[124:[bind(SV9,$thf( SV32 @ ( SV31 @ sK4_SY22 ) ))]]) ).
thf(134,plain,
! [SV31: $i > $i,SV32: $i > $i,SV10: $i > $i] :
( ( in @ ( SV10 @ ( SV32 @ ( SV31 @ sK4_SY22 ) ) )
@ ( image1
@ ( image1
@ ( image1 @ sK1_A
@ ^ [SX0: $i] : ( SV31 @ SX0 ) )
@ ^ [SX0: $i] : ( SV32 @ SX0 ) )
@ ^ [SX0: $i] : ( SV10 @ SX0 ) ) )
= $true ),
inference(extuni,[status(esa)],[123:[bind(SV11,$thf( SV10 @ ( SV32 @ ( SV31 @ sK4_SY22 ) ) )),bind(SV12,$thf( image1 @ ( image1 @ sK1_A @ ^ [SX0: $i] : ( SV31 @ SX0 ) ) @ ^ [SX0: $i] : ( SV32 @ SX0 ) )),bind(SV13,$thf( SV32 @ ( SV31 @ sK4_SY22 ) ))]]) ).
thf(135,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[25,134,133,132,131,130,129,128,127,126,119,118,117,116,115,114,108,107,106,105,104,97,96,95,94,93,92,87,86,85,84,83,82,80,79,78,77,76,75,74,73,72,71,70,57,56,50,49,46,45,33,32]) ).
thf(136,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU797^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n026.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 15:38:02 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 270.52/45.47
% 270.52/45.47 No.of.Axioms: 0
% 270.52/45.47
% 270.52/45.47 Length.of.Defs: 237
% 270.52/45.47
% 270.52/45.47 Contains.Choice.Funs: false
% 270.52/45.47 .eprover: CPU time limit exceeded, terminating
% 270.52/45.47 .eprover: CPU time limit exceeded, terminating
% 270.52/45.47 eprover: CPU time limit exceeded, terminating
% 270.52/45.47 .
% 270.52/45.47
% 270.52/45.47 ********************************
% 270.52/45.47 * All subproblems solved! *
% 270.52/45.47 ********************************
% 270.52/45.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:135,loop_count:10,foatp_calls:4,translation:fof_experiment)
% 270.52/45.47
% 270.52/45.47 %**** Beginning of derivation protocol ****
% 270.52/45.47 % SZS output start CNFRefutation
% See solution above
% 270.52/45.47
% 270.52/45.47 %**** End of derivation protocol ****
% 270.52/45.47 %**** no. of clauses in derivation: 114 ****
% 270.52/45.47 %**** clause counter: 135 ****
% 270.52/45.47
% 270.52/45.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:1,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:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:135,loop_count:10,foatp_calls:4,translation:fof_experiment)
%------------------------------------------------------------------------------