%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU777^2 : 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 : n006.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 10:48:12 AM UTC 2026
% Result : Theorem 3.28s 0.83s
% Output : CNFRefutation 3.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 34 unt; 0 typ; 4 def)
% Number of atoms : 197 ( 43 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 651 ( 38 ~; 37 |; 0 &; 545 @)
% ( 0 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 7 con; 0-7 aty)
% Number of variables : 192 ( 75 ^; 117 !; 0 ?; 192 :)
% 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 > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $i > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK11_E,type,
sK11_E: ( $i > $i > $o ) > $i ).
thf(tp_sK12_E,type,
sK12_E: ( $i > $i > $o ) > $i ).
thf(tp_sK13_E,type,
sK13_E: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK14_E,type,
sK14_E: ( $i > $i > $o ) > $i > $i > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY32,type,
sK2_SY32: $i ).
thf(tp_sK3_SY42,type,
sK3_SY42: $i ).
thf(tp_sK4_SY53,type,
sK4_SY53: $i ).
thf(tp_sK5_E,type,
sK5_E: ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $i > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK6_E,type,
sK6_E: ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $i > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK7_E,type,
sK7_E: ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $i > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK8_E,type,
sK8_E: ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $i > ( $i > $i > $i > $i > $o ) > $i ).
thf(tp_sK9_E,type,
sK9_E: ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > ( $i > $i > $i ) > $i > $i > ( $i > $i > $i > $i > $o ) > $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/sandbox2/benchmark/theBenchmark.p',breln) ).
thf(breln1,definition,
( breln1
= ( ^ [A: $i,R: $i] : ( breln @ A @ A @ R ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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,
( ( ! [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 ) )
=> ! [SY0: $i,SY1: $i] :
( ( subset @ SY1 @ ( cartprod @ SY0 @ SY0 ) )
=> ! [SY6: $i] :
( ( in @ SY6 @ SY0 )
=> ! [SY7: $i] :
( ( in @ SY7 @ SY0 )
=> ( ( in @ ( kpair @ SY7 @ SY6 )
@ ( dpsetconstr @ SY0 @ SY0
@ ^ [SY11: $i,SY12: $i] : ( in @ ( kpair @ SY12 @ SY11 ) @ SY1 ) ) )
=> ( in @ ( kpair @ SY6 @ SY7 ) @ SY1 ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,breln,breln1,breln1invset,dpsetconstrER]) ).
thf(4,plain,
( ( ! [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 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [SY0: $i,SY1: $i] :
( ( subset @ SY1 @ ( cartprod @ SY0 @ SY0 ) )
=> ! [SY6: $i] :
( ( in @ SY6 @ SY0 )
=> ! [SY7: $i] :
( ( in @ SY7 @ SY0 )
=> ( ( in @ ( kpair @ SY7 @ SY6 )
@ ( dpsetconstr @ SY0 @ SY0
@ ^ [SY11: $i,SY12: $i] : ( in @ ( kpair @ SY12 @ SY11 ) @ SY1 ) ) )
=> ( in @ ( kpair @ SY6 @ SY7 ) @ SY1 ) ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ~ ! [SY0: $i,SY1: $i] :
( ( subset @ SY1 @ ( cartprod @ SY0 @ SY0 ) )
=> ! [SY6: $i] :
( ( in @ SY6 @ SY0 )
=> ! [SY7: $i] :
( ( in @ SY7 @ SY0 )
=> ( ( in @ ( kpair @ SY7 @ SY6 )
@ ( dpsetconstr @ SY0 @ SY0
@ ^ [SY11: $i,SY12: $i] : ( in @ ( kpair @ SY12 @ SY11 ) @ SY1 ) ) )
=> ( in @ ( kpair @ SY6 @ SY7 ) @ SY1 ) ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[5]) ).
thf(7,plain,
( ( ! [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 ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(8,plain,
( ( ~ ! [SY0: $i,SY1: $i] :
( ( subset @ SY1 @ ( cartprod @ SY0 @ SY0 ) )
=> ! [SY6: $i] :
( ( in @ SY6 @ SY0 )
=> ! [SY7: $i] :
( ( in @ SY7 @ SY0 )
=> ( ( in @ ( kpair @ SY7 @ SY6 )
@ ( dpsetconstr @ SY0 @ SY0
@ ^ [SY11: $i,SY12: $i] : ( in @ ( kpair @ SY12 @ SY11 ) @ SY1 ) ) )
=> ( in @ ( kpair @ SY6 @ SY7 ) @ SY1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(9,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX1 @ ( cartprod @ SX0 @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX2 )
@ ( dpsetconstr @ SX0 @ SX0
@ ^ [SX4: $i,SX5: $i] : ( in @ ( kpair @ SX5 @ SX4 ) @ SX1 ) ) )
| ( in @ ( kpair @ SX2 @ SX3 ) @ SX1 ) ) ) ) )
= $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,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX1 @ ( cartprod @ SX0 @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( in @ ( kpair @ SX3 @ SX2 )
@ ( dpsetconstr @ SX0 @ SX0
@ ^ [SX4: $i,SX5: $i] : ( in @ ( kpair @ SX5 @ SX4 ) @ SX1 ) ) )
| ( in @ ( kpair @ SX2 @ SX3 ) @ SX1 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[9]) ).
thf(12,plain,
! [SV1: $i] :
( ( ! [SY26: $i,SY27: $i > $i > $o,SY28: $i,SY29: $i] :
( ~ ( in @ ( kpair @ SY28 @ SY29 )
@ ( dpsetconstr @ SV1 @ SY26
@ ^ [SX5: $i,SX6: $i] : ( SY27 @ SX5 @ SX6 ) ) )
| ( SY27 @ SY28 @ SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[10]) ).
thf(13,plain,
( ( ! [SY32: $i] :
( ~ ( subset @ SY32 @ ( cartprod @ sK1_SX0 @ sK1_SX0 ) )
| ! [SY33: $i] :
( ~ ( in @ SY33 @ sK1_SX0 )
| ! [SY34: $i] :
( ~ ( in @ SY34 @ sK1_SX0 )
| ~ ( in @ ( kpair @ SY34 @ SY33 )
@ ( dpsetconstr @ sK1_SX0 @ sK1_SX0
@ ^ [SX4: $i,SX5: $i] : ( in @ ( kpair @ SX5 @ SX4 ) @ SY32 ) ) )
| ( in @ ( kpair @ SY33 @ SY34 ) @ SY32 ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[11]) ).
thf(14,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY37: $i > $i > $o,SY38: $i,SY39: $i] :
( ~ ( in @ ( kpair @ SY38 @ SY39 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SX5: $i,SX6: $i] : ( SY37 @ SX5 @ SX6 ) ) )
| ( SY37 @ SY38 @ SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(15,plain,
( ( ~ ( subset @ sK2_SY32 @ ( cartprod @ sK1_SX0 @ sK1_SX0 ) )
| ! [SY42: $i] :
( ~ ( in @ SY42 @ sK1_SX0 )
| ! [SY43: $i] :
( ~ ( in @ SY43 @ sK1_SX0 )
| ~ ( in @ ( kpair @ SY43 @ SY42 )
@ ( dpsetconstr @ sK1_SX0 @ sK1_SX0
@ ^ [SY44: $i,SY45: $i] : ( in @ ( kpair @ SY45 @ SY44 ) @ sK2_SY32 ) ) )
| ( in @ ( kpair @ SY42 @ SY43 ) @ sK2_SY32 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(16,plain,
! [SV3: $i > $i > $o,SV2: $i,SV1: $i] :
( ( ! [SY46: $i,SY47: $i] :
( ~ ( in @ ( kpair @ SY46 @ SY47 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY48: $i,SY49: $i] : ( SV3 @ SY48 @ SY49 ) ) )
| ( SV3 @ SY46 @ SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
( ( ! [SY42: $i] :
( ~ ( in @ SY42 @ sK1_SX0 )
| ! [SY43: $i] :
( ~ ( in @ SY43 @ sK1_SX0 )
| ~ ( in @ ( kpair @ SY43 @ SY42 )
@ ( dpsetconstr @ sK1_SX0 @ sK1_SX0
@ ^ [SY44: $i,SY45: $i] : ( in @ ( kpair @ SY45 @ SY44 ) @ sK2_SY32 ) ) )
| ( in @ ( kpair @ SY42 @ SY43 ) @ sK2_SY32 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[15]) ).
thf(19,plain,
! [SV3: $i > $i > $o,SV2: $i,SV1: $i,SV4: $i] :
( ( ! [SY50: $i] :
( ~ ( in @ ( kpair @ SV4 @ SY50 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY48: $i,SY49: $i] : ( SV3 @ SY48 @ SY49 ) ) )
| ( SV3 @ SV4 @ SY50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(21,plain,
( ( ~ ( in @ sK3_SY42 @ sK1_SX0 )
| ! [SY53: $i] :
( ~ ( in @ SY53 @ sK1_SX0 )
| ~ ( in @ ( kpair @ SY53 @ sK3_SY42 )
@ ( dpsetconstr @ sK1_SX0 @ sK1_SX0
@ ^ [SY44: $i,SY45: $i] : ( in @ ( kpair @ SY45 @ SY44 ) @ sK2_SY32 ) ) )
| ( in @ ( kpair @ sK3_SY42 @ SY53 ) @ sK2_SY32 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[18]) ).
thf(22,plain,
! [SV3: $i > $i > $o,SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
( ( ~ ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY48: $i,SY49: $i] : ( SV3 @ SY48 @ SY49 ) ) )
| ( SV3 @ SV4 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
( ( ! [SY53: $i] :
( ~ ( in @ SY53 @ sK1_SX0 )
| ~ ( in @ ( kpair @ SY53 @ sK3_SY42 )
@ ( dpsetconstr @ sK1_SX0 @ sK1_SX0
@ ^ [SY44: $i,SY45: $i] : ( in @ ( kpair @ SY45 @ SY44 ) @ sK2_SY32 ) ) )
| ( in @ ( kpair @ sK3_SY42 @ SY53 ) @ sK2_SY32 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[21]) ).
thf(25,plain,
! [SV3: $i > $i > $o,SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
( ( ( ~ ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY48: $i,SY49: $i] : ( SV3 @ SY48 @ SY49 ) ) ) )
= $true )
| ( ( SV3 @ SV4 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[22]) ).
thf(27,plain,
( ( ~ ( in @ sK4_SY53 @ sK1_SX0 )
| ~ ( in @ ( kpair @ sK4_SY53 @ sK3_SY42 )
@ ( dpsetconstr @ sK1_SX0 @ sK1_SX0
@ ^ [SY44: $i,SY45: $i] : ( in @ ( kpair @ SY45 @ SY44 ) @ sK2_SY32 ) ) )
| ( in @ ( kpair @ sK3_SY42 @ sK4_SY53 ) @ sK2_SY32 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[24]) ).
thf(28,plain,
! [SV3: $i > $i > $o,SV2: $i,SV1: $i,SV5: $i,SV4: $i] :
( ( ( in @ ( kpair @ SV4 @ SV5 )
@ ( dpsetconstr @ SV1 @ SV2
@ ^ [SY48: $i,SY49: $i] : ( SV3 @ SY48 @ SY49 ) ) )
= $false )
| ( ( SV3 @ SV4 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[25]) ).
thf(30,plain,
( ( ~ ( in @ ( kpair @ sK4_SY53 @ sK3_SY42 )
@ ( dpsetconstr @ sK1_SX0 @ sK1_SX0
@ ^ [SY44: $i,SY45: $i] : ( in @ ( kpair @ SY45 @ SY44 ) @ sK2_SY32 ) ) )
| ( in @ ( kpair @ sK3_SY42 @ sK4_SY53 ) @ sK2_SY32 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[27]) ).
thf(32,plain,
( ( ~ ( in @ ( kpair @ sK4_SY53 @ sK3_SY42 )
@ ( dpsetconstr @ sK1_SX0 @ sK1_SX0
@ ^ [SY44: $i,SY45: $i] : ( in @ ( kpair @ SY45 @ SY44 ) @ sK2_SY32 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(33,plain,
( ( in @ ( kpair @ sK3_SY42 @ sK4_SY53 ) @ sK2_SY32 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[30]) ).
thf(34,plain,
( ( in @ ( kpair @ sK4_SY53 @ sK3_SY42 )
@ ( dpsetconstr @ sK1_SX0 @ sK1_SX0
@ ^ [SY44: $i,SY45: $i] : ( in @ ( kpair @ SY45 @ SY44 ) @ sK2_SY32 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[32]) ).
thf(82,plain,
! [SV49: $i > $i > $o,SV50: $i,SV51: $i,SV52: $i,SV53: $i] :
( ( ( in @ ( kpair @ SV53 @ SV52 )
@ ( dpsetconstr @ SV51 @ SV50
@ ^ [SX0: $i,SX1: $i] : ( SV49 @ SX0 @ SX1 ) ) )
= $false )
| ( ( SV49 @ SV53 @ SV52 )
= $true ) ),
inference(rename,[status(thm)],[28]) ).
thf(85,plain,
! [SV49: $i > $i > $o,SV50: $i,SV51: $i,SV52: $i,SV53: $i] :
( ( ( ( SV49 @ SV53 @ SV52 )
= ( in @ ( kpair @ sK3_SY42 @ sK4_SY53 ) @ sK2_SY32 ) )
= $false )
| ( ( in @ ( kpair @ SV53 @ SV52 )
@ ( dpsetconstr @ SV51 @ SV50
@ ^ [SX0: $i,SX1: $i] : ( SV49 @ SX0 @ SX1 ) ) )
= $false ) ),
inference(res,[status(thm)],[82,33]) ).
thf(97,plain,
! [SV50: $i,SV51: $i] :
( ( in @ ( kpair @ sK4_SY53 @ sK3_SY42 )
@ ( dpsetconstr @ SV51 @ SV50
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY32 ) ) )
= $false ),
inference(extuni,[status(esa)],[85:[bind(SV53,$thf( sK4_SY53 )),bind(SV52,$thf( sK3_SY42 )),bind(SV49,$thf( ^ [SX0: $i] : ^ [SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY32 ) ))]]) ).
thf(175,plain,
! [SV256: $i,SV257: $i] :
( ( in @ ( kpair @ sK4_SY53 @ sK3_SY42 )
@ ( dpsetconstr @ SV257 @ SV256
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY32 ) ) )
= $false ),
inference(rename,[status(thm)],[97]) ).
thf(177,plain,
! [SV256: $i,SV257: $i] :
( ( ( in @ ( kpair @ sK4_SY53 @ sK3_SY42 )
@ ( dpsetconstr @ SV257 @ SV256
@ ^ [SX0: $i,SX1: $i] : ( in @ ( kpair @ SX1 @ SX0 ) @ sK2_SY32 ) ) )
= ( in @ ( kpair @ sK4_SY53 @ sK3_SY42 )
@ ( dpsetconstr @ sK1_SX0 @ sK1_SX0
@ ^ [SY44: $i,SY45: $i] : ( in @ ( kpair @ SY45 @ SY44 ) @ sK2_SY32 ) ) ) )
= $false ),
inference(res,[status(thm)],[175,34]) ).
thf(183,plain,
$false = $true,
inference(extuni,[status(esa)],[177:[bind(SV256,$thf( sK1_SX0 )),bind(SV257,$thf( sK1_SX0 ))]]) ).
thf(184,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU777^2 : 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
% 0.10/0.19 % Computer : n006.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Oct 6 15:33:52 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.28/0.83
% 3.28/0.83 No.of.Axioms: 0
% 3.28/0.83
% 3.28/0.83 Length.of.Defs: 754
% 3.28/0.83
% 3.28/0.83 Contains.Choice.Funs: false
% 3.28/0.83 .....
% 3.28/0.83
% 3.28/0.83 ********************************
% 3.28/0.83 * All subproblems solved! *
% 3.28/0.83 ********************************
% 3.28/0.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:183,loop_count:7,foatp_calls:3,translation:fof_full)
% 3.28/0.83
% 3.28/0.83 %**** Beginning of derivation protocol ****
% 3.28/0.83 % SZS output start CNFRefutation
% See solution above
% 3.28/0.83
% 3.28/0.83 %**** End of derivation protocol ****
% 3.28/0.83 %**** no. of clauses in derivation: 35 ****
% 3.28/0.83 %**** clause counter: 183 ****
% 3.28/0.83
% 3.28/0.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:1,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:183,loop_count:7,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------