%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU638^2 : 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 : n003.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 10:45:48 AM UTC 2026
% Result : Theorem 0.47s 0.37s
% Output : CNFRefutation 0.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 5
% Syntax : Number of formulae : 58 ( 44 unt; 0 typ; 4 def)
% Number of atoms : 276 ( 88 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 578 ( 103 ~; 44 |; 11 &; 400 @)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 11 con; 0-2 aty)
% Number of variables : 183 ( 62 ^; 110 !; 11 ?; 183 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(tp_dsetconstrEL,type,
dsetconstrEL: $o ).
thf(tp_dsetconstrER,type,
dsetconstrER: $o ).
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_ex1,type,
ex1: $i > ( $i > $o ) > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK10_E,type,
sK10_E: ( $i > $o ) > $i ).
thf(tp_sK11_E,type,
sK11_E: ( $i > $i > $o ) > $i ).
thf(tp_sK12_E,type,
sK12_E: $i ).
thf(tp_sK13_E,type,
sK13_E: ( $i > $i > $i > $o ) > $i ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY34,type,
sK2_SY34: $i > $o ).
thf(tp_sK3_SY41,type,
sK3_SY41: $i ).
thf(tp_sK4_E,type,
sK4_E: ( $i > $o ) > $i ).
thf(tp_sK5_E,type,
sK5_E: ( $i > $i > $o ) > $i ).
thf(tp_sK6_E,type,
sK6_E: $i ).
thf(tp_sK7_E,type,
sK7_E: ( $i > $i > $i > $o ) > $i ).
thf(tp_sK8_E,type,
sK8_E: $i ).
thf(tp_sK9_E,type,
sK9_E: $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $o ).
thf(dsetconstrEL,definition,
( dsetconstrEL
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrER,definition,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(ex1,definition,
( ex1
= ( ^ [A: $i,Xphi: $i > $o] :
( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1) ).
thf(singleton,definition,
( singleton
= ( ^ [A: $i] :
? [Xx: $i] :
( ( in @ Xx @ A )
& ( A
= ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(1,conjecture,
( dsetconstrEL
=> ( dsetconstrER
=> ! [A: $i,Xphi: $i > $o] :
( ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E1) ).
thf(2,negated_conjecture,
( ( dsetconstrEL
=> ( dsetconstrER
=> ! [A: $i,Xphi: $i > $o] :
( ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) )
=> ! [SY0: $i,SY1: $i > $o] :
( ? [SY6: $i] :
( ( in @ SY6
@ ( dsetconstr @ SY0
@ ^ [SY7: $i] : ( SY1 @ SY7 ) ) )
& ( ( dsetconstr @ SY0
@ ^ [SY8: $i] : ( SY1 @ SY8 ) )
= ( setadjoin @ SY6 @ emptyset ) ) )
=> ? [Xx: $i] :
( ( in @ Xx @ SY0 )
& ( SY1 @ Xx ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,dsetconstrEL,dsetconstrER,ex1,singleton]) ).
thf(4,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [SY0: $i,SY1: $i > $o] :
( ? [SY6: $i] :
( ( in @ SY6
@ ( dsetconstr @ SY0
@ ^ [SY7: $i] : ( SY1 @ SY7 ) ) )
& ( ( dsetconstr @ SY0
@ ^ [SY8: $i] : ( SY1 @ SY8 ) )
= ( setadjoin @ SY6 @ emptyset ) ) )
=> ? [Xx: $i] :
( ( in @ Xx @ SY0 )
& ( SY1 @ Xx ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ~ ! [SY0: $i,SY1: $i > $o] :
( ? [SY6: $i] :
( ( in @ SY6
@ ( dsetconstr @ SY0
@ ^ [SY7: $i] : ( SY1 @ SY7 ) ) )
& ( ( dsetconstr @ SY0
@ ^ [SY8: $i] : ( SY1 @ SY8 ) )
= ( setadjoin @ SY6 @ emptyset ) ) )
=> ? [Xx: $i] :
( ( in @ Xx @ SY0 )
& ( SY1 @ Xx ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[6]) ).
thf(8,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(9,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(10,plain,
( ( ~ ! [SY0: $i,SY1: $i > $o] :
( ? [SY6: $i] :
( ( in @ SY6
@ ( dsetconstr @ SY0
@ ^ [SY7: $i] : ( SY1 @ SY7 ) ) )
& ( ( dsetconstr @ SY0
@ ^ [SY8: $i] : ( SY1 @ SY8 ) )
= ( setadjoin @ SY6 @ emptyset ) ) )
=> ? [Xx: $i] :
( ( in @ Xx @ SY0 )
& ( SY1 @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(11,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8,dsetconstrEL,dsetconstrER,ex1,singleton]) ).
thf(12,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9,dsetconstrEL,dsetconstrER,ex1,singleton]) ).
thf(13,plain,
( ( ~ ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) )
!= ( setadjoin @ SX2 @ emptyset ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10,dsetconstrEL,dsetconstrER,ex1,singleton]) ).
thf(14,plain,
! [SV1: $i] :
( ( ! [SY24: $i > $o,SY25: $i] :
( ~ ( in @ SY25
@ ( dsetconstr @ SV1
@ ^ [SX3: $i] : ( SY24 @ SX3 ) ) )
| ( SY24 @ SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(15,plain,
! [SV2: $i] :
( ( ! [SY27: $i > $o,SY28: $i] :
( ~ ( in @ SY28
@ ( dsetconstr @ SV2
@ ^ [SX3: $i] : ( SY27 @ SX3 ) ) )
| ( in @ SY28 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[12]) ).
thf(16,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) )
!= ( setadjoin @ SX2 @ emptyset ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[13]) ).
thf(17,plain,
! [SV3: $i > $o,SV1: $i] :
( ( ! [SY30: $i] :
( ~ ( in @ SY30
@ ( dsetconstr @ SV1
@ ^ [SY31: $i] : ( SV3 @ SY31 ) ) )
| ( SV3 @ SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[14]) ).
thf(18,plain,
! [SV4: $i > $o,SV2: $i] :
( ( ! [SY32: $i] :
( ~ ( in @ SY32
@ ( dsetconstr @ SV2
@ ^ [SY33: $i] : ( SV4 @ SY33 ) ) )
| ( in @ SY32 @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(19,plain,
( ( ! [SY34: $i > $o] :
( ~ ~ ! [SY35: $i] :
~ ~ ( ~ ( in @ SY35
@ ( dsetconstr @ sK1_SX0
@ ^ [SX3: $i] : ( SY34 @ SX3 ) ) )
| ( ( dsetconstr @ sK1_SX0
@ ^ [SX3: $i] : ( SY34 @ SX3 ) )
!= ( setadjoin @ SY35 @ emptyset ) ) )
| ~ ! [SY38: $i] :
~ ~ ( ~ ( in @ SY38 @ sK1_SX0 )
| ~ ( SY34 @ SY38 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[16]) ).
thf(20,plain,
! [SV3: $i > $o,SV1: $i,SV5: $i] :
( ( ~ ( in @ SV5
@ ( dsetconstr @ SV1
@ ^ [SY31: $i] : ( SV3 @ SY31 ) ) )
| ( SV3 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(21,plain,
! [SV4: $i > $o,SV2: $i,SV6: $i] :
( ( ~ ( in @ SV6
@ ( dsetconstr @ SV2
@ ^ [SY33: $i] : ( SV4 @ SY33 ) ) )
| ( in @ SV6 @ SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(22,plain,
( ( ~ ~ ! [SY41: $i] :
~ ~ ( ~ ( in @ SY41
@ ( dsetconstr @ sK1_SX0
@ ^ [SY42: $i] : ( sK2_SY34 @ SY42 ) ) )
| ( ( dsetconstr @ sK1_SX0
@ ^ [SY43: $i] : ( sK2_SY34 @ SY43 ) )
!= ( setadjoin @ SY41 @ emptyset ) ) )
| ~ ! [SY44: $i] :
~ ~ ( ~ ( in @ SY44 @ sK1_SX0 )
| ~ ( sK2_SY34 @ SY44 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[19]) ).
thf(23,plain,
! [SV3: $i > $o,SV1: $i,SV5: $i] :
( ( ( ~ ( in @ SV5
@ ( dsetconstr @ SV1
@ ^ [SY31: $i] : ( SV3 @ SY31 ) ) ) )
= $true )
| ( ( SV3 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[20]) ).
thf(24,plain,
! [SV4: $i > $o,SV2: $i,SV6: $i] :
( ( ( ~ ( in @ SV6
@ ( dsetconstr @ SV2
@ ^ [SY33: $i] : ( SV4 @ SY33 ) ) ) )
= $true )
| ( ( in @ SV6 @ SV2 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[21]) ).
thf(25,plain,
( ( ~ ~ ! [SY41: $i] :
~ ~ ( ~ ( in @ SY41
@ ( dsetconstr @ sK1_SX0
@ ^ [SY42: $i] : ( sK2_SY34 @ SY42 ) ) )
| ( ( dsetconstr @ sK1_SX0
@ ^ [SY43: $i] : ( sK2_SY34 @ SY43 ) )
!= ( setadjoin @ SY41 @ emptyset ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(26,plain,
( ( ~ ! [SY44: $i] :
~ ~ ( ~ ( in @ SY44 @ sK1_SX0 )
| ~ ( sK2_SY34 @ SY44 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[22]) ).
thf(27,plain,
! [SV3: $i > $o,SV1: $i,SV5: $i] :
( ( ( in @ SV5
@ ( dsetconstr @ SV1
@ ^ [SY31: $i] : ( SV3 @ SY31 ) ) )
= $false )
| ( ( SV3 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV4: $i > $o,SV2: $i,SV6: $i] :
( ( ( in @ SV6
@ ( dsetconstr @ SV2
@ ^ [SY33: $i] : ( SV4 @ SY33 ) ) )
= $false )
| ( ( in @ SV6 @ SV2 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(29,plain,
( ( ~ ! [SY41: $i] :
~ ~ ( ~ ( in @ SY41
@ ( dsetconstr @ sK1_SX0
@ ^ [SY42: $i] : ( sK2_SY34 @ SY42 ) ) )
| ( ( dsetconstr @ sK1_SX0
@ ^ [SY43: $i] : ( sK2_SY34 @ SY43 ) )
!= ( setadjoin @ SY41 @ emptyset ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[25]) ).
thf(30,plain,
( ( ! [SY44: $i] :
~ ~ ( ~ ( in @ SY44 @ sK1_SX0 )
| ~ ( sK2_SY34 @ SY44 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[26]) ).
thf(31,plain,
( ( ! [SY41: $i] :
~ ~ ( ~ ( in @ SY41
@ ( dsetconstr @ sK1_SX0
@ ^ [SY42: $i] : ( sK2_SY34 @ SY42 ) ) )
| ( ( dsetconstr @ sK1_SX0
@ ^ [SY43: $i] : ( sK2_SY34 @ SY43 ) )
!= ( setadjoin @ SY41 @ emptyset ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(32,plain,
! [SV7: $i] :
( ( ~ ~ ( ~ ( in @ SV7 @ sK1_SX0 )
| ~ ( sK2_SY34 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(33,plain,
( ( ~ ~ ( ~ ( in @ sK3_SY41
@ ( dsetconstr @ sK1_SX0
@ ^ [SY42: $i] : ( sK2_SY34 @ SY42 ) ) )
| ( ( dsetconstr @ sK1_SX0
@ ^ [SY43: $i] : ( sK2_SY34 @ SY43 ) )
!= ( setadjoin @ sK3_SY41 @ emptyset ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[31]) ).
thf(34,plain,
! [SV7: $i] :
( ( ~ ( ~ ( in @ SV7 @ sK1_SX0 )
| ~ ( sK2_SY34 @ SV7 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(35,plain,
( ( ~ ( ~ ( in @ sK3_SY41
@ ( dsetconstr @ sK1_SX0
@ ^ [SY42: $i] : ( sK2_SY34 @ SY42 ) ) )
| ( ( dsetconstr @ sK1_SX0
@ ^ [SY43: $i] : ( sK2_SY34 @ SY43 ) )
!= ( setadjoin @ sK3_SY41 @ emptyset ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[33]) ).
thf(36,plain,
! [SV7: $i] :
( ( ~ ( in @ SV7 @ sK1_SX0 )
| ~ ( sK2_SY34 @ SV7 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(37,plain,
( ( ~ ( in @ sK3_SY41
@ ( dsetconstr @ sK1_SX0
@ ^ [SY42: $i] : ( sK2_SY34 @ SY42 ) ) )
| ( ( dsetconstr @ sK1_SX0
@ ^ [SY43: $i] : ( sK2_SY34 @ SY43 ) )
!= ( setadjoin @ sK3_SY41 @ emptyset ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(38,plain,
! [SV7: $i] :
( ( ( ~ ( in @ SV7 @ sK1_SX0 ) )
= $true )
| ( ( ~ ( sK2_SY34 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(39,plain,
( ( ~ ( in @ sK3_SY41
@ ( dsetconstr @ sK1_SX0
@ ^ [SY42: $i] : ( sK2_SY34 @ SY42 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[37]) ).
thf(41,plain,
! [SV7: $i] :
( ( ( in @ SV7 @ sK1_SX0 )
= $false )
| ( ( ~ ( sK2_SY34 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(42,plain,
( ( in @ sK3_SY41
@ ( dsetconstr @ sK1_SX0
@ ^ [SY42: $i] : ( sK2_SY34 @ SY42 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(44,plain,
! [SV7: $i] :
( ( ( sK2_SY34 @ SV7 )
= $false )
| ( ( in @ SV7 @ sK1_SX0 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(85,plain,
! [SV15: $i > $o,SV16: $i,SV17: $i] :
( ( ( in @ SV17
@ ( dsetconstr @ SV16
@ ^ [SX0: $i] : ( SV15 @ SX0 ) ) )
= $false )
| ( ( SV15 @ SV17 )
= $true ) ),
inference(rename,[status(thm)],[27]) ).
thf(89,plain,
! [SV15: $i > $o,SV16: $i,SV17: $i] :
( ( ( ( in @ SV17
@ ( dsetconstr @ SV16
@ ^ [SX0: $i] : ( SV15 @ SX0 ) ) )
= ( in @ sK3_SY41
@ ( dsetconstr @ sK1_SX0
@ ^ [SY42: $i] : ( sK2_SY34 @ SY42 ) ) ) )
= $false )
| ( ( SV15 @ SV17 )
= $true ) ),
inference(res,[status(thm)],[85,42]) ).
thf(102,plain,
( ( sK2_SY34 @ sK3_SY41 )
= $true ),
inference(extuni,[status(esa)],[89:[bind(SV15,$thf( ^ [SX0: $i] : ( sK2_SY34 @ SX0 ) )),bind(SV16,$thf( sK1_SX0 )),bind(SV17,$thf( sK3_SY41 ))]]) ).
thf(123,plain,
! [SV59: $i > $o,SV60: $i,SV61: $i] :
( ( ( in @ SV61
@ ( dsetconstr @ SV60
@ ^ [SX0: $i] : ( SV59 @ SX0 ) ) )
= $false )
| ( ( in @ SV61 @ SV60 )
= $true ) ),
inference(rename,[status(thm)],[28]) ).
thf(130,plain,
! [SV59: $i > $o,SV60: $i,SV61: $i] :
( ( ( ( in @ SV61
@ ( dsetconstr @ SV60
@ ^ [SX0: $i] : ( SV59 @ SX0 ) ) )
= ( in @ sK3_SY41
@ ( dsetconstr @ sK1_SX0
@ ^ [SY42: $i] : ( sK2_SY34 @ SY42 ) ) ) )
= $false )
| ( ( in @ SV61 @ SV60 )
= $true ) ),
inference(res,[status(thm)],[123,42]) ).
thf(142,plain,
( ( in @ sK3_SY41 @ sK1_SX0 )
= $true ),
inference(extuni,[status(esa)],[130:[bind(SV59,$thf( ^ [SX0: $i] : ( sK2_SY34 @ SX0 ) )),bind(SV60,$thf( sK1_SX0 )),bind(SV61,$thf( sK3_SY41 ))]]) ).
thf(151,plain,
! [SV92: $i] :
( ( ( sK2_SY34 @ SV92 )
= $false )
| ( ( in @ SV92 @ sK1_SX0 )
= $false ) ),
inference(rename,[status(thm)],[44]) ).
thf(157,plain,
! [SV92: $i] :
( ( ( ( sK2_SY34 @ SV92 )
= ( sK2_SY34 @ sK3_SY41 ) )
= $false )
| ( ( in @ SV92 @ sK1_SX0 )
= $false ) ),
inference(res,[status(thm)],[151,102]) ).
thf(166,plain,
( ( in @ sK3_SY41 @ sK1_SX0 )
= $false ),
inference(extuni,[status(esa)],[157:[bind(SV92,$thf( sK3_SY41 ))]]) ).
thf(169,plain,
( ( ( in @ sK3_SY41 @ sK1_SX0 )
= ( in @ sK3_SY41 @ sK1_SX0 ) )
= $false ),
inference(res,[status(thm)],[166,142]) ).
thf(177,plain,
$false = $true,
inference(extuni,[status(esa)],[169]) ).
thf(178,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU638^2 : 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
% 0.09/0.17 % Computer : n003.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 15:31:39 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.47/0.37
% 0.47/0.37 No.of.Axioms: 0
% 0.47/0.37
% 0.47/0.37 Length.of.Defs: 780
% 0.47/0.37
% 0.47/0.37 Contains.Choice.Funs: false
% 0.47/0.37 ....
% 0.47/0.37
% 0.47/0.37 ********************************
% 0.47/0.37 * All subproblems solved! *
% 0.47/0.37 ********************************
% 0.47/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:2,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:177,loop_count:8,foatp_calls:3,translation:fof_full)
% 0.47/0.37
% 0.47/0.37 %**** Beginning of derivation protocol ****
% 0.47/0.37 % SZS output start CNFRefutation
% See solution above
% 0.47/0.37
% 0.47/0.37 %**** End of derivation protocol ****
% 0.47/0.37 %**** no. of clauses in derivation: 54 ****
% 0.47/0.37 %**** clause counter: 177 ****
% 0.47/0.37
% 0.47/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:2,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:177,loop_count:8,foatp_calls:3,translation:fof_full)
%------------------------------------------------------------------------------