%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU672^2 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/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 10:46:11 AM UTC 2026
% Result : Theorem 0.40s 0.29s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 48 ( 31 unt; 0 typ; 4 def)
% Number of atoms : 332 ( 103 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 872 ( 46 ~; 34 |; 21 &; 751 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 8 con; 0-3 aty)
% Number of variables : 152 ( 87 ^; 53 !; 12 ?; 152 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_breln,type,
breln: $i > $i > $i > $o ).
thf(tp_cartprod,type,
cartprod: $i > $i > $i ).
thf(tp_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_ex1,type,
ex1: $i > ( $i > $o ) > $o ).
thf(tp_func,type,
func: $i > $i > $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_kpair,type,
kpair: $i > $i > $i ).
thf(tp_sK1_SY0,type,
sK1_SY0: $i ).
thf(tp_sK2_SY39,type,
sK2_SY39: $i ).
thf(tp_sK3_SY49,type,
sK3_SY49: $i ).
thf(tp_sK4_SY62,type,
sK4_SY62: $i ).
thf(tp_sK5_SY59,type,
sK5_SY59: $i > $i ).
thf(tp_sK6_E,type,
sK6_E: $i ).
thf(tp_sK7_E,type,
sK7_E: $i > $i > $i ).
thf(tp_sK8_E,type,
sK8_E: $i > $i ).
thf(tp_sK9_E,type,
sK9_E: $i > $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(breln,definition,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).
thf(ex1,definition,
( ex1
= ( ^ [A: $i,Xphi: $i > $o] :
( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1) ).
thf(func,definition,
( func
= ( ^ [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
& ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ex1 @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',func) ).
thf(singleton,definition,
( singleton
= ( ^ [A: $i] :
? [Xx: $i] :
( ( in @ Xx @ A )
& ( A
= ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(1,conjecture,
! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( singleton
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton) ).
thf(2,negated_conjecture,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( singleton
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [SY0: $i,SY1: $i,SY2: $i] :
( ( ( subset @ SY2 @ ( cartprod @ SY0 @ SY1 ) )
& ! [SY21: $i] :
( ( in @ SY21 @ SY0 )
=> ? [SY22: $i] :
( ( in @ SY22
@ ( dsetconstr @ SY1
@ ^ [SY23: $i] : ( in @ ( kpair @ SY21 @ SY23 ) @ SY2 ) ) )
& ( ( dsetconstr @ SY1
@ ^ [SY24: $i] : ( in @ ( kpair @ SY21 @ SY24 ) @ SY2 ) )
= ( setadjoin @ SY22 @ emptyset ) ) ) ) )
=> ! [SY25: $i] :
( ( in @ SY25 @ SY0 )
=> ? [SY27: $i] :
( ( in @ SY27
@ ( dsetconstr @ SY1
@ ^ [Xy: $i] : ( in @ ( kpair @ SY25 @ Xy ) @ SY2 ) ) )
& ( ( dsetconstr @ SY1
@ ^ [Xy: $i] : ( in @ ( kpair @ SY25 @ Xy ) @ SY2 ) )
= ( setadjoin @ SY27 @ emptyset ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,breln,ex1,func,singleton]) ).
thf(4,plain,
( ( ! [SY39: $i,SY40: $i] :
( ( ( subset @ SY40 @ ( cartprod @ sK1_SY0 @ SY39 ) )
& ! [SY41: $i] :
( ( in @ SY41 @ sK1_SY0 )
=> ? [SY22: $i] :
( ( in @ SY22
@ ( dsetconstr @ SY39
@ ^ [SY23: $i] : ( in @ ( kpair @ SY41 @ SY23 ) @ SY40 ) ) )
& ( ( dsetconstr @ SY39
@ ^ [SY24: $i] : ( in @ ( kpair @ SY41 @ SY24 ) @ SY40 ) )
= ( setadjoin @ SY22 @ emptyset ) ) ) ) )
=> ! [SY45: $i] :
( ( in @ SY45 @ sK1_SY0 )
=> ? [SY27: $i] :
( ( in @ SY27
@ ( dsetconstr @ SY39
@ ^ [Xy: $i] : ( in @ ( kpair @ SY45 @ Xy ) @ SY40 ) ) )
& ( ( dsetconstr @ SY39
@ ^ [Xy: $i] : ( in @ ( kpair @ SY45 @ Xy ) @ SY40 ) )
= ( setadjoin @ SY27 @ emptyset ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[3]) ).
thf(5,plain,
( ( ! [SY49: $i] :
( ( ( subset @ SY49 @ ( cartprod @ sK1_SY0 @ sK2_SY39 ) )
& ! [SY50: $i] :
( ( in @ SY50 @ sK1_SY0 )
=> ? [SY51: $i] :
( ( in @ SY51
@ ( dsetconstr @ sK2_SY39
@ ^ [SY23: $i] : ( in @ ( kpair @ SY50 @ SY23 ) @ SY49 ) ) )
& ( ( dsetconstr @ sK2_SY39
@ ^ [SY24: $i] : ( in @ ( kpair @ SY50 @ SY24 ) @ SY49 ) )
= ( setadjoin @ SY51 @ emptyset ) ) ) ) )
=> ! [SY54: $i] :
( ( in @ SY54 @ sK1_SY0 )
=> ? [SY55: $i] :
( ( in @ SY55
@ ( dsetconstr @ sK2_SY39
@ ^ [Xy: $i] : ( in @ ( kpair @ SY54 @ Xy ) @ SY49 ) ) )
& ( ( dsetconstr @ sK2_SY39
@ ^ [Xy: $i] : ( in @ ( kpair @ SY54 @ Xy ) @ SY49 ) )
= ( setadjoin @ SY55 @ emptyset ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[4]) ).
thf(6,plain,
( ( ( ( subset @ sK3_SY49 @ ( cartprod @ sK1_SY0 @ sK2_SY39 ) )
& ! [SY58: $i] :
( ( in @ SY58 @ sK1_SY0 )
=> ? [SY59: $i] :
( ( in @ SY59
@ ( dsetconstr @ sK2_SY39
@ ^ [SY60: $i] : ( in @ ( kpair @ SY58 @ SY60 ) @ sK3_SY49 ) ) )
& ( ( dsetconstr @ sK2_SY39
@ ^ [SY61: $i] : ( in @ ( kpair @ SY58 @ SY61 ) @ sK3_SY49 ) )
= ( setadjoin @ SY59 @ emptyset ) ) ) ) )
=> ! [SY62: $i] :
( ( in @ SY62 @ sK1_SY0 )
=> ? [SY63: $i] :
( ( in @ SY63
@ ( dsetconstr @ sK2_SY39
@ ^ [SY64: $i] : ( in @ ( kpair @ SY62 @ SY64 ) @ sK3_SY49 ) ) )
& ( ( dsetconstr @ sK2_SY39
@ ^ [SY65: $i] : ( in @ ( kpair @ SY62 @ SY65 ) @ sK3_SY49 ) )
= ( setadjoin @ SY63 @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[5]) ).
thf(8,plain,
( ( ! [SY58: $i] :
( ( in @ SY58 @ sK1_SY0 )
=> ? [SY59: $i] :
( ( in @ SY59
@ ( dsetconstr @ sK2_SY39
@ ^ [SY60: $i] : ( in @ ( kpair @ SY58 @ SY60 ) @ sK3_SY49 ) ) )
& ( ( dsetconstr @ sK2_SY39
@ ^ [SY61: $i] : ( in @ ( kpair @ SY58 @ SY61 ) @ sK3_SY49 ) )
= ( setadjoin @ SY59 @ emptyset ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(9,plain,
( ( ! [SY62: $i] :
( ( in @ SY62 @ sK1_SY0 )
=> ? [SY63: $i] :
( ( in @ SY63
@ ( dsetconstr @ sK2_SY39
@ ^ [SY64: $i] : ( in @ ( kpair @ SY62 @ SY64 ) @ sK3_SY49 ) ) )
& ( ( dsetconstr @ sK2_SY39
@ ^ [SY65: $i] : ( in @ ( kpair @ SY62 @ SY65 ) @ sK3_SY49 ) )
= ( setadjoin @ SY63 @ emptyset ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[6]) ).
thf(10,plain,
( ( ~ ! [SY62: $i] :
( ( in @ SY62 @ sK1_SY0 )
=> ? [SY63: $i] :
( ( in @ SY63
@ ( dsetconstr @ sK2_SY39
@ ^ [SY64: $i] : ( in @ ( kpair @ SY62 @ SY64 ) @ sK3_SY49 ) ) )
& ( ( dsetconstr @ sK2_SY39
@ ^ [SY65: $i] : ( in @ ( kpair @ SY62 @ SY65 ) @ sK3_SY49 ) )
= ( setadjoin @ SY63 @ emptyset ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(11,plain,
( ( ( in @ sK4_SY62 @ sK1_SY0 )
& ! [SY66: $i] :
( ( ( dsetconstr @ sK2_SY39
@ ^ [SY67: $i] : ( in @ ( kpair @ sK4_SY62 @ SY67 ) @ sK3_SY49 ) )
!= ( setadjoin @ SY66 @ emptyset ) )
| ~ ( in @ SY66
@ ( dsetconstr @ sK2_SY39
@ ^ [SY68: $i] : ( in @ ( kpair @ sK4_SY62 @ SY68 ) @ sK3_SY49 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(12,plain,
( ( ! [SY58: $i] :
( ~ ( in @ SY58 @ sK1_SY0 )
| ( ( ( dsetconstr @ sK2_SY39
@ ^ [SY61: $i] : ( in @ ( kpair @ SY58 @ SY61 ) @ sK3_SY49 ) )
= ( setadjoin @ ( sK5_SY59 @ SY58 ) @ emptyset ) )
& ( in @ ( sK5_SY59 @ SY58 )
@ ( dsetconstr @ sK2_SY39
@ ^ [SY60: $i] : ( in @ ( kpair @ SY58 @ SY60 ) @ sK3_SY49 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(13,plain,
( ( ! [SY58: $i] :
( ~ ( in @ SY58 @ sK1_SY0 )
| ( ( ( dsetconstr @ sK2_SY39
@ ^ [SY61: $i] : ( in @ ( kpair @ SY58 @ SY61 ) @ sK3_SY49 ) )
= ( setadjoin @ ( sK5_SY59 @ SY58 ) @ emptyset ) )
& ( in @ ( sK5_SY59 @ SY58 )
@ ( dsetconstr @ sK2_SY39
@ ^ [SY60: $i] : ( in @ ( kpair @ SY58 @ SY60 ) @ sK3_SY49 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(15,plain,
( ( ( in @ sK4_SY62 @ sK1_SY0 )
& ! [SY66: $i] :
( ( ( dsetconstr @ sK2_SY39
@ ^ [SY67: $i] : ( in @ ( kpair @ sK4_SY62 @ SY67 ) @ sK3_SY49 ) )
!= ( setadjoin @ SY66 @ emptyset ) )
| ~ ( in @ SY66
@ ( dsetconstr @ sK2_SY39
@ ^ [SY68: $i] : ( in @ ( kpair @ sK4_SY62 @ SY68 ) @ sK3_SY49 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(16,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ sK1_SY0 )
| ~ ( ( ( dsetconstr @ sK2_SY39
@ ^ [SX1: $i] : ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY49 ) )
!= ( setadjoin @ ( sK5_SY59 @ SX0 ) @ emptyset ) )
| ~ ( in @ ( sK5_SY59 @ SX0 )
@ ( dsetconstr @ sK2_SY39
@ ^ [SX1: $i] : ( in @ ( kpair @ SX0 @ SX1 ) @ sK3_SY49 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,breln,ex1,func,singleton]) ).
thf(17,plain,
( ( ~ ( ~ ( in @ sK4_SY62 @ sK1_SY0 )
| ~ ! [SX0: $i] :
( ( ( dsetconstr @ sK2_SY39
@ ^ [SX1: $i] : ( in @ ( kpair @ sK4_SY62 @ SX1 ) @ sK3_SY49 ) )
!= ( setadjoin @ SX0 @ emptyset ) )
| ~ ( in @ SX0
@ ( dsetconstr @ sK2_SY39
@ ^ [SX1: $i] : ( in @ ( kpair @ sK4_SY62 @ SX1 ) @ sK3_SY49 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,breln,ex1,func,singleton]) ).
thf(18,plain,
! [SV1: $i] :
( ( ~ ( in @ SV1 @ sK1_SY0 )
| ~ ( ( ( dsetconstr @ sK2_SY39
@ ^ [SY71: $i] : ( in @ ( kpair @ SV1 @ SY71 ) @ sK3_SY49 ) )
!= ( setadjoin @ ( sK5_SY59 @ SV1 ) @ emptyset ) )
| ~ ( in @ ( sK5_SY59 @ SV1 )
@ ( dsetconstr @ sK2_SY39
@ ^ [SY72: $i] : ( in @ ( kpair @ SV1 @ SY72 ) @ sK3_SY49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(19,plain,
( ( ~ ( in @ sK4_SY62 @ sK1_SY0 )
| ~ ! [SX0: $i] :
( ( ( dsetconstr @ sK2_SY39
@ ^ [SX1: $i] : ( in @ ( kpair @ sK4_SY62 @ SX1 ) @ sK3_SY49 ) )
!= ( setadjoin @ SX0 @ emptyset ) )
| ~ ( in @ SX0
@ ( dsetconstr @ sK2_SY39
@ ^ [SX1: $i] : ( in @ ( kpair @ sK4_SY62 @ SX1 ) @ sK3_SY49 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(20,plain,
! [SV1: $i] :
( ( ( ~ ( in @ SV1 @ sK1_SY0 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ sK2_SY39
@ ^ [SY71: $i] : ( in @ ( kpair @ SV1 @ SY71 ) @ sK3_SY49 ) )
!= ( setadjoin @ ( sK5_SY59 @ SV1 ) @ emptyset ) )
| ~ ( in @ ( sK5_SY59 @ SV1 )
@ ( dsetconstr @ sK2_SY39
@ ^ [SY72: $i] : ( in @ ( kpair @ SV1 @ SY72 ) @ sK3_SY49 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[18]) ).
thf(21,plain,
( ( ~ ( in @ sK4_SY62 @ sK1_SY0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(22,plain,
( ( ~ ! [SX0: $i] :
( ( ( dsetconstr @ sK2_SY39
@ ^ [SX1: $i] : ( in @ ( kpair @ sK4_SY62 @ SX1 ) @ sK3_SY49 ) )
!= ( setadjoin @ SX0 @ emptyset ) )
| ~ ( in @ SX0
@ ( dsetconstr @ sK2_SY39
@ ^ [SX1: $i] : ( in @ ( kpair @ sK4_SY62 @ SX1 ) @ sK3_SY49 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[19]) ).
thf(23,plain,
! [SV1: $i] :
( ( ( in @ SV1 @ sK1_SY0 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ sK2_SY39
@ ^ [SY71: $i] : ( in @ ( kpair @ SV1 @ SY71 ) @ sK3_SY49 ) )
!= ( setadjoin @ ( sK5_SY59 @ SV1 ) @ emptyset ) )
| ~ ( in @ ( sK5_SY59 @ SV1 )
@ ( dsetconstr @ sK2_SY39
@ ^ [SY72: $i] : ( in @ ( kpair @ SV1 @ SY72 ) @ sK3_SY49 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(24,plain,
( ( in @ sK4_SY62 @ sK1_SY0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[21]) ).
thf(25,plain,
( ( ! [SX0: $i] :
( ( ( dsetconstr @ sK2_SY39
@ ^ [SX1: $i] : ( in @ ( kpair @ sK4_SY62 @ SX1 ) @ sK3_SY49 ) )
!= ( setadjoin @ SX0 @ emptyset ) )
| ~ ( in @ SX0
@ ( dsetconstr @ sK2_SY39
@ ^ [SX1: $i] : ( in @ ( kpair @ sK4_SY62 @ SX1 ) @ sK3_SY49 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[22]) ).
thf(26,plain,
! [SV1: $i] :
( ( ( ( ( dsetconstr @ sK2_SY39
@ ^ [SY71: $i] : ( in @ ( kpair @ SV1 @ SY71 ) @ sK3_SY49 ) )
!= ( setadjoin @ ( sK5_SY59 @ SV1 ) @ emptyset ) )
| ~ ( in @ ( sK5_SY59 @ SV1 )
@ ( dsetconstr @ sK2_SY39
@ ^ [SY72: $i] : ( in @ ( kpair @ SV1 @ SY72 ) @ sK3_SY49 ) ) ) )
= $false )
| ( ( in @ SV1 @ sK1_SY0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV2: $i] :
( ( ( ( dsetconstr @ sK2_SY39
@ ^ [SX1: $i] : ( in @ ( kpair @ sK4_SY62 @ SX1 ) @ sK3_SY49 ) )
!= ( setadjoin @ SV2 @ emptyset ) )
| ~ ( in @ SV2
@ ( dsetconstr @ sK2_SY39
@ ^ [SX1: $i] : ( in @ ( kpair @ sK4_SY62 @ SX1 ) @ sK3_SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(28,plain,
! [SV1: $i] :
( ( ( ( dsetconstr @ sK2_SY39
@ ^ [SY71: $i] : ( in @ ( kpair @ SV1 @ SY71 ) @ sK3_SY49 ) )
!= ( setadjoin @ ( sK5_SY59 @ SV1 ) @ emptyset ) )
= $false )
| ( ( in @ SV1 @ sK1_SY0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(29,plain,
! [SV1: $i] :
( ( ( ~ ( in @ ( sK5_SY59 @ SV1 )
@ ( dsetconstr @ sK2_SY39
@ ^ [SY72: $i] : ( in @ ( kpair @ SV1 @ SY72 ) @ sK3_SY49 ) ) ) )
= $false )
| ( ( in @ SV1 @ sK1_SY0 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[26]) ).
thf(30,plain,
! [SV2: $i] :
( ( ( ( dsetconstr @ sK2_SY39
@ ^ [SX1: $i] : ( in @ ( kpair @ sK4_SY62 @ SX1 ) @ sK3_SY49 ) )
!= ( setadjoin @ SV2 @ emptyset ) )
= $true )
| ( ( ~ ( in @ SV2
@ ( dsetconstr @ sK2_SY39
@ ^ [SX1: $i] : ( in @ ( kpair @ sK4_SY62 @ SX1 ) @ sK3_SY49 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV1: $i] :
( ( ( ( dsetconstr @ sK2_SY39
@ ^ [SY71: $i] : ( in @ ( kpair @ SV1 @ SY71 ) @ sK3_SY49 ) )
= ( setadjoin @ ( sK5_SY59 @ SV1 ) @ emptyset ) )
= $true )
| ( ( in @ SV1 @ sK1_SY0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[28]) ).
thf(32,plain,
! [SV1: $i] :
( ( ( in @ ( sK5_SY59 @ SV1 )
@ ( dsetconstr @ sK2_SY39
@ ^ [SY72: $i] : ( in @ ( kpair @ SV1 @ SY72 ) @ sK3_SY49 ) ) )
= $true )
| ( ( in @ SV1 @ sK1_SY0 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[29]) ).
thf(33,plain,
! [SV2: $i] :
( ( ( ( dsetconstr @ sK2_SY39
@ ^ [SX1: $i] : ( in @ ( kpair @ sK4_SY62 @ SX1 ) @ sK3_SY49 ) )
= ( setadjoin @ SV2 @ emptyset ) )
= $false )
| ( ( ~ ( in @ SV2
@ ( dsetconstr @ sK2_SY39
@ ^ [SX1: $i] : ( in @ ( kpair @ sK4_SY62 @ SX1 ) @ sK3_SY49 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV2: $i] :
( ( ( in @ SV2
@ ( dsetconstr @ sK2_SY39
@ ^ [SX1: $i] : ( in @ ( kpair @ sK4_SY62 @ SX1 ) @ sK3_SY49 ) ) )
= $false )
| ( ( ( dsetconstr @ sK2_SY39
@ ^ [SX1: $i] : ( in @ ( kpair @ sK4_SY62 @ SX1 ) @ sK3_SY49 ) )
= ( setadjoin @ SV2 @ emptyset ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(46,plain,
! [SV3: $i] :
( ( ( ( dsetconstr @ sK2_SY39
@ ^ [SX0: $i] : ( in @ ( kpair @ SV3 @ SX0 ) @ sK3_SY49 ) )
= ( setadjoin @ ( sK5_SY59 @ SV3 ) @ emptyset ) )
= $true )
| ( ( in @ SV3 @ sK1_SY0 )
= $false ) ),
inference(rename,[status(thm)],[31]) ).
thf(49,plain,
! [SV3: $i] :
( ( ( ( in @ SV3 @ sK1_SY0 )
= ( in @ sK4_SY62 @ sK1_SY0 ) )
= $false )
| ( ( ( dsetconstr @ sK2_SY39
@ ^ [SX0: $i] : ( in @ ( kpair @ SV3 @ SX0 ) @ sK3_SY49 ) )
= ( setadjoin @ ( sK5_SY59 @ SV3 ) @ emptyset ) )
= $true ) ),
inference(res,[status(thm)],[46,24]) ).
thf(51,plain,
( ( ( dsetconstr @ sK2_SY39
@ ^ [SX0: $i] : ( in @ ( kpair @ sK4_SY62 @ SX0 ) @ sK3_SY49 ) )
= ( setadjoin @ ( sK5_SY59 @ sK4_SY62 ) @ emptyset ) )
= $true ),
inference(extuni,[status(esa)],[49:[bind(SV3,$thf( sK4_SY62 ))]]) ).
thf(53,plain,
! [SV4: $i] :
( ( ( in @ ( sK5_SY59 @ SV4 )
@ ( dsetconstr @ sK2_SY39
@ ^ [SX0: $i] : ( in @ ( kpair @ SV4 @ SX0 ) @ sK3_SY49 ) ) )
= $true )
| ( ( in @ SV4 @ sK1_SY0 )
= $false ) ),
inference(rename,[status(thm)],[32]) ).
thf(59,plain,
! [SV4: $i] :
( ( ( ( in @ SV4 @ sK1_SY0 )
= ( in @ sK4_SY62 @ sK1_SY0 ) )
= $false )
| ( ( in @ ( sK5_SY59 @ SV4 )
@ ( dsetconstr @ sK2_SY39
@ ^ [SX0: $i] : ( in @ ( kpair @ SV4 @ SX0 ) @ sK3_SY49 ) ) )
= $true ) ),
inference(res,[status(thm)],[53,24]) ).
thf(61,plain,
( ( in @ ( sK5_SY59 @ sK4_SY62 )
@ ( dsetconstr @ sK2_SY39
@ ^ [SX0: $i] : ( in @ ( kpair @ sK4_SY62 @ SX0 ) @ sK3_SY49 ) ) )
= $true ),
inference(extuni,[status(esa)],[59:[bind(SV4,$thf( sK4_SY62 ))]]) ).
thf(67,plain,
! [SV5: $i] :
( ( ( in @ SV5
@ ( dsetconstr @ sK2_SY39
@ ^ [SX0: $i] : ( in @ ( kpair @ sK4_SY62 @ SX0 ) @ sK3_SY49 ) ) )
= $false )
| ( ( ( dsetconstr @ sK2_SY39
@ ^ [SX0: $i] : ( in @ ( kpair @ sK4_SY62 @ SX0 ) @ sK3_SY49 ) )
= ( setadjoin @ SV5 @ emptyset ) )
= $false ) ),
inference(rename,[status(thm)],[34]) ).
thf(72,plain,
! [SV5: $i] :
( ( ( ( ( dsetconstr @ sK2_SY39
@ ^ [SX0: $i] : ( in @ ( kpair @ sK4_SY62 @ SX0 ) @ sK3_SY49 ) )
= ( setadjoin @ SV5 @ emptyset ) )
= ( ( dsetconstr @ sK2_SY39
@ ^ [SX0: $i] : ( in @ ( kpair @ sK4_SY62 @ SX0 ) @ sK3_SY49 ) )
= ( setadjoin @ ( sK5_SY59 @ sK4_SY62 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV5
@ ( dsetconstr @ sK2_SY39
@ ^ [SX0: $i] : ( in @ ( kpair @ sK4_SY62 @ SX0 ) @ sK3_SY49 ) ) )
= $false ) ),
inference(res,[status(thm)],[67,51]) ).
thf(94,plain,
( ( in @ ( sK5_SY59 @ sK4_SY62 )
@ ( dsetconstr @ sK2_SY39
@ ^ [SX0: $i] : ( in @ ( kpair @ sK4_SY62 @ SX0 ) @ sK3_SY49 ) ) )
= $false ),
inference(extuni,[status(esa)],[72:[bind(SV5,$thf( sK5_SY59 @ sK4_SY62 ))]]) ).
thf(102,plain,
( ( ( in @ ( sK5_SY59 @ sK4_SY62 )
@ ( dsetconstr @ sK2_SY39
@ ^ [SX0: $i] : ( in @ ( kpair @ sK4_SY62 @ SX0 ) @ sK3_SY49 ) ) )
= ( in @ ( sK5_SY59 @ sK4_SY62 )
@ ( dsetconstr @ sK2_SY39
@ ^ [SX0: $i] : ( in @ ( kpair @ sK4_SY62 @ SX0 ) @ sK3_SY49 ) ) ) )
= $false ),
inference(res,[status(thm)],[94,61]) ).
thf(115,plain,
$false = $true,
inference(extuni,[status(esa)],[102]) ).
thf(116,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU672^2 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.19 % Computer : n026.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Oct 6 15:33:31 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.40/0.29
% 0.40/0.29 No.of.Axioms: 0
% 0.40/0.29
% 0.40/0.29 Length.of.Defs: 711
% 0.40/0.29
% 0.40/0.29 Contains.Choice.Funs: false
% 0.40/0.29 ...
% 0.40/0.29
% 0.40/0.29 ********************************
% 0.40/0.29 * All subproblems solved! *
% 0.40/0.29 ********************************
% 0.40/0.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:115,loop_count:8,foatp_calls:2,translation:fof_experiment)
% 0.40/0.29
% 0.40/0.29 %**** Beginning of derivation protocol ****
% 0.40/0.29 % SZS output start CNFRefutation
% See solution above
% 0.40/0.29
% 0.40/0.29 %**** End of derivation protocol ****
% 0.40/0.29 %**** no. of clauses in derivation: 44 ****
% 0.40/0.29 %**** clause counter: 115 ****
% 0.40/0.29
% 0.40/0.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:2,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:115,loop_count:8,foatp_calls:2,translation:fof_experiment)
%------------------------------------------------------------------------------