%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU706^2 : 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 : n015.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 10:46:27 AM UTC 2026
% Result : Theorem 0.07s 0.22s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 80 ( 54 unt; 0 typ; 6 def)
% Number of atoms : 499 ( 263 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 674 ( 142 ~; 119 |; 5 &; 353 @)
% ( 4 <=>; 51 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 211 ( 1 ^; 205 !; 5 ?; 211 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_in__Cong,type,
in__Cong: $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY30,type,
sK2_SY30: $i ).
thf(tp_sK3_SY29,type,
sK3_SY29: $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setadjoin__Cong,type,
setadjoin__Cong: $o ).
thf(tp_setunion,type,
setunion: $i > $i ).
thf(tp_setunion__Cong,type,
setunion__Cong: $o ).
thf(tp_setunionsingleton,type,
setunionsingleton: $o ).
thf(tp_singleton,type,
singleton: $i > $o ).
thf(tp_uniqinunit,type,
uniqinunit: $o ).
thf(in__Cong,definition,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in__Cong) ).
thf(setadjoin__Cong,definition,
( setadjoin__Cong
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(setunion__Cong,definition,
( setunion__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong) ).
thf(setunionsingleton,definition,
( setunionsingleton
= ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton) ).
thf(singleton,definition,
( singleton
= ( ^ [A: $i] :
? [Xx: $i] :
( ( in @ Xx @ A )
& ( A
= ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(uniqinunit,definition,
( uniqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(1,conjecture,
( uniqinunit
=> ( in__Cong
=> ( setadjoin__Cong
=> ( setunion__Cong
=> ( setunionsingleton
=> ! [X: $i] :
( ( singleton @ X )
=> ! [Xx: $i] :
( ( in @ Xx @ X )
=> ( ( setunion @ X )
= Xx ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theeq) ).
thf(2,negated_conjecture,
( ( uniqinunit
=> ( in__Cong
=> ( setadjoin__Cong
=> ( setunion__Cong
=> ( setunionsingleton
=> ! [X: $i] :
( ( singleton @ X )
=> ! [Xx: $i] :
( ( in @ Xx @ X )
=> ( ( setunion @ X )
= Xx ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) )
=> ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx )
=> ! [SY0: $i] :
( ? [SY1: $i] :
( ( in @ SY1 @ SY0 )
& ( SY0
= ( setadjoin @ SY1 @ emptyset ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY0 )
=> ( ( setunion @ SY0 )
= Xx ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,in__Cong,setadjoin__Cong,setunion__Cong,setunionsingleton,singleton,uniqinunit]) ).
thf(4,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( ! [SY0: $i] :
( ? [SY1: $i] :
( ( in @ SY1 @ SY0 )
& ( SY0
= ( setadjoin @ SY1 @ emptyset ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY0 )
=> ( ( setunion @ SY0 )
= Xx ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(10,plain,
( ( ~ ! [SY0: $i] :
( ? [SY1: $i] :
( ( in @ SY1 @ SY0 )
& ( SY0
= ( setadjoin @ SY1 @ emptyset ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY0 )
=> ( ( setunion @ SY0 )
= Xx ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(13,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(14,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(15,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(16,plain,
( ( ~ ! [SY0: $i] :
( ? [SY1: $i] :
( ( in @ SY1 @ SY0 )
& ( SY0
= ( setadjoin @ SY1 @ emptyset ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ SY0 )
=> ( ( setunion @ SY0 )
= Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(17,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ( ~ ( in @ SX3 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,in__Cong,setadjoin__Cong,setunion__Cong,setunionsingleton,singleton,uniqinunit]) ).
thf(18,plain,
( ( ~ ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ( SX0
!= ( setadjoin @ SX1 @ emptyset ) ) )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( ( setunion @ SX0 )
= SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,in__Cong,setadjoin__Cong,setunion__Cong,setunionsingleton,singleton,uniqinunit]) ).
thf(19,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ( ( setadjoin @ SX0 @ SX2 )
= ( setadjoin @ SX1 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,in__Cong,setadjoin__Cong,setunion__Cong,setunionsingleton,singleton,uniqinunit]) ).
thf(20,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setunion @ SX0 )
= ( setunion @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,in__Cong,setadjoin__Cong,setunion__Cong,setunionsingleton,singleton,uniqinunit]) ).
thf(21,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15,in__Cong,setadjoin__Cong,setunion__Cong,setunionsingleton,singleton,uniqinunit]) ).
thf(22,plain,
! [SV1: $i] :
( ( ( setunion @ ( setadjoin @ SV1 @ emptyset ) )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[11]) ).
thf(23,plain,
! [SV2: $i] :
( ( ! [SY19: $i] :
( ( SV2 != SY19 )
| ! [SY20: $i,SY21: $i] :
( ( SY20 != SY21 )
| ~ ( ~ ( ~ ( in @ SY20 @ SV2 )
| ( in @ SY21 @ SY19 ) )
| ~ ( ~ ( in @ SY21 @ SY19 )
| ( in @ SY20 @ SV2 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(24,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ( SX0
!= ( setadjoin @ SX1 @ emptyset ) ) )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( ( setunion @ SX0 )
= SX1 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(25,plain,
! [SV3: $i] :
( ( ! [SY22: $i] :
( ( SV3 != SY22 )
| ! [SY23: $i,SY24: $i] :
( ( SY23 != SY24 )
| ( ( setadjoin @ SV3 @ SY23 )
= ( setadjoin @ SY22 @ SY24 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(26,plain,
! [SV4: $i] :
( ( ! [SY25: $i] :
( ( SV4 != SY25 )
| ( ( setunion @ SV4 )
= ( setunion @ SY25 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(27,plain,
! [SV5: $i] :
( ( ! [SY26: $i] :
( ~ ( in @ SV5 @ ( setadjoin @ SY26 @ emptyset ) )
| ( SV5 = SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(28,plain,
! [SV6: $i,SV2: $i] :
( ( ( SV2 != SV6 )
| ! [SY27: $i,SY28: $i] :
( ( SY27 != SY28 )
| ~ ( ~ ( ~ ( in @ SY27 @ SV2 )
| ( in @ SY28 @ SV6 ) )
| ~ ( ~ ( in @ SY28 @ SV6 )
| ( in @ SY27 @ SV2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(29,plain,
( ( ~ ~ ! [SY29: $i] :
~ ~ ( ~ ( in @ SY29 @ sK1_SX0 )
| ( sK1_SX0
!= ( setadjoin @ SY29 @ emptyset ) ) )
| ! [SY30: $i] :
( ~ ( in @ SY30 @ sK1_SX0 )
| ( ( setunion @ sK1_SX0 )
= SY30 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[24]) ).
thf(30,plain,
! [SV7: $i,SV3: $i] :
( ( ( SV3 != SV7 )
| ! [SY31: $i,SY32: $i] :
( ( SY31 != SY32 )
| ( ( setadjoin @ SV3 @ SY31 )
= ( setadjoin @ SV7 @ SY32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(31,plain,
! [SV8: $i,SV4: $i] :
( ( ( SV4 != SV8 )
| ( ( setunion @ SV4 )
= ( setunion @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(32,plain,
! [SV9: $i,SV5: $i] :
( ( ~ ( in @ SV5 @ ( setadjoin @ SV9 @ emptyset ) )
| ( SV5 = SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(33,plain,
! [SV6: $i,SV2: $i] :
( ( ( SV2 != SV6 )
= $true )
| ( ( ! [SY27: $i,SY28: $i] :
( ( SY27 != SY28 )
| ~ ( ~ ( ~ ( in @ SY27 @ SV2 )
| ( in @ SY28 @ SV6 ) )
| ~ ( ~ ( in @ SY28 @ SV6 )
| ( in @ SY27 @ SV2 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(34,plain,
( ( ~ ~ ! [SY29: $i] :
~ ~ ( ~ ( in @ SY29 @ sK1_SX0 )
| ( sK1_SX0
!= ( setadjoin @ SY29 @ emptyset ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(35,plain,
( ( ! [SY30: $i] :
( ~ ( in @ SY30 @ sK1_SX0 )
| ( ( setunion @ sK1_SX0 )
= SY30 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(36,plain,
! [SV7: $i,SV3: $i] :
( ( ( SV3 != SV7 )
= $true )
| ( ( ! [SY31: $i,SY32: $i] :
( ( SY31 != SY32 )
| ( ( setadjoin @ SV3 @ SY31 )
= ( setadjoin @ SV7 @ SY32 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[30]) ).
thf(37,plain,
! [SV8: $i,SV4: $i] :
( ( ( SV4 != SV8 )
= $true )
| ( ( ( setunion @ SV4 )
= ( setunion @ SV8 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[31]) ).
thf(38,plain,
! [SV9: $i,SV5: $i] :
( ( ( ~ ( in @ SV5 @ ( setadjoin @ SV9 @ emptyset ) ) )
= $true )
| ( ( SV5 = SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(39,plain,
! [SV6: $i,SV2: $i] :
( ( ( SV2 = SV6 )
= $false )
| ( ( ! [SY27: $i,SY28: $i] :
( ( SY27 != SY28 )
| ~ ( ~ ( ~ ( in @ SY27 @ SV2 )
| ( in @ SY28 @ SV6 ) )
| ~ ( ~ ( in @ SY28 @ SV6 )
| ( in @ SY27 @ SV2 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(40,plain,
( ( ~ ! [SY29: $i] :
~ ~ ( ~ ( in @ SY29 @ sK1_SX0 )
| ( sK1_SX0
!= ( setadjoin @ SY29 @ emptyset ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(41,plain,
( ( ~ ( in @ sK2_SY30 @ sK1_SX0 )
| ( ( setunion @ sK1_SX0 )
= sK2_SY30 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[35]) ).
thf(42,plain,
! [SV7: $i,SV3: $i] :
( ( ( SV3 = SV7 )
= $false )
| ( ( ! [SY31: $i,SY32: $i] :
( ( SY31 != SY32 )
| ( ( setadjoin @ SV3 @ SY31 )
= ( setadjoin @ SV7 @ SY32 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(43,plain,
! [SV8: $i,SV4: $i] :
( ( ( SV4 = SV8 )
= $false )
| ( ( ( setunion @ SV4 )
= ( setunion @ SV8 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(44,plain,
! [SV9: $i,SV5: $i] :
( ( ( in @ SV5 @ ( setadjoin @ SV9 @ emptyset ) )
= $false )
| ( ( SV5 = SV9 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(45,plain,
! [SV6: $i,SV2: $i,SV10: $i] :
( ( ( ! [SY33: $i] :
( ( SV10 != SY33 )
| ~ ( ~ ( ~ ( in @ SV10 @ SV2 )
| ( in @ SY33 @ SV6 ) )
| ~ ( ~ ( in @ SY33 @ SV6 )
| ( in @ SV10 @ SV2 ) ) ) ) )
= $true )
| ( ( SV2 = SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(46,plain,
( ( ! [SY29: $i] :
~ ~ ( ~ ( in @ SY29 @ sK1_SX0 )
| ( sK1_SX0
!= ( setadjoin @ SY29 @ emptyset ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(47,plain,
( ( ~ ( in @ sK2_SY30 @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(48,plain,
( ( ( setunion @ sK1_SX0 )
= sK2_SY30 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[41]) ).
thf(49,plain,
! [SV7: $i,SV3: $i,SV11: $i] :
( ( ( ! [SY34: $i] :
( ( SV11 != SY34 )
| ( ( setadjoin @ SV3 @ SV11 )
= ( setadjoin @ SV7 @ SY34 ) ) ) )
= $true )
| ( ( SV3 = SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(50,plain,
! [SV6: $i,SV2: $i,SV12: $i,SV10: $i] :
( ( ( ( SV10 != SV12 )
| ~ ( ~ ( ~ ( in @ SV10 @ SV2 )
| ( in @ SV12 @ SV6 ) )
| ~ ( ~ ( in @ SV12 @ SV6 )
| ( in @ SV10 @ SV2 ) ) ) )
= $true )
| ( ( SV2 = SV6 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(51,plain,
( ( ~ ~ ( ~ ( in @ sK3_SY29 @ sK1_SX0 )
| ( sK1_SX0
!= ( setadjoin @ sK3_SY29 @ emptyset ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[46]) ).
thf(52,plain,
( ( in @ sK2_SY30 @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[47]) ).
thf(53,plain,
! [SV7: $i,SV3: $i,SV13: $i,SV11: $i] :
( ( ( ( SV11 != SV13 )
| ( ( setadjoin @ SV3 @ SV11 )
= ( setadjoin @ SV7 @ SV13 ) ) )
= $true )
| ( ( SV3 = SV7 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(54,plain,
! [SV6: $i,SV2: $i,SV12: $i,SV10: $i] :
( ( ( SV10 != SV12 )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV10 @ SV2 )
| ( in @ SV12 @ SV6 ) )
| ~ ( ~ ( in @ SV12 @ SV6 )
| ( in @ SV10 @ SV2 ) ) ) )
= $true )
| ( ( SV2 = SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(55,plain,
( ( ~ ( ~ ( in @ sK3_SY29 @ sK1_SX0 )
| ( sK1_SX0
!= ( setadjoin @ sK3_SY29 @ emptyset ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[51]) ).
thf(56,plain,
! [SV7: $i,SV3: $i,SV13: $i,SV11: $i] :
( ( ( SV11 != SV13 )
= $true )
| ( ( ( setadjoin @ SV3 @ SV11 )
= ( setadjoin @ SV7 @ SV13 ) )
= $true )
| ( ( SV3 = SV7 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(57,plain,
! [SV6: $i,SV2: $i,SV12: $i,SV10: $i] :
( ( ( SV10 = SV12 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV10 @ SV2 )
| ( in @ SV12 @ SV6 ) )
| ~ ( ~ ( in @ SV12 @ SV6 )
| ( in @ SV10 @ SV2 ) ) ) )
= $true )
| ( ( SV2 = SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(58,plain,
( ( ~ ( in @ sK3_SY29 @ sK1_SX0 )
| ( sK1_SX0
!= ( setadjoin @ sK3_SY29 @ emptyset ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(59,plain,
! [SV7: $i,SV3: $i,SV13: $i,SV11: $i] :
( ( ( SV11 = SV13 )
= $false )
| ( ( ( setadjoin @ SV3 @ SV11 )
= ( setadjoin @ SV7 @ SV13 ) )
= $true )
| ( ( SV3 = SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(60,plain,
! [SV6: $i,SV12: $i,SV2: $i,SV10: $i] :
( ( ( ~ ( ~ ( in @ SV10 @ SV2 )
| ( in @ SV12 @ SV6 ) )
| ~ ( ~ ( in @ SV12 @ SV6 )
| ( in @ SV10 @ SV2 ) ) )
= $false )
| ( ( SV10 = SV12 )
= $false )
| ( ( SV2 = SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(61,plain,
( ( ~ ( in @ sK3_SY29 @ sK1_SX0 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(62,plain,
( ( sK1_SX0
!= ( setadjoin @ sK3_SY29 @ emptyset ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[58]) ).
thf(63,plain,
! [SV6: $i,SV12: $i,SV2: $i,SV10: $i] :
( ( ( ~ ( ~ ( in @ SV10 @ SV2 )
| ( in @ SV12 @ SV6 ) ) )
= $false )
| ( ( SV10 = SV12 )
= $false )
| ( ( SV2 = SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(64,plain,
! [SV2: $i,SV10: $i,SV6: $i,SV12: $i] :
( ( ( ~ ( ~ ( in @ SV12 @ SV6 )
| ( in @ SV10 @ SV2 ) ) )
= $false )
| ( ( SV10 = SV12 )
= $false )
| ( ( SV2 = SV6 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(65,plain,
( ( in @ sK3_SY29 @ sK1_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[61]) ).
thf(66,plain,
( ( sK1_SX0
= ( setadjoin @ sK3_SY29 @ emptyset ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(67,plain,
! [SV6: $i,SV12: $i,SV2: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV2 )
| ( in @ SV12 @ SV6 ) )
= $true )
| ( ( SV10 = SV12 )
= $false )
| ( ( SV2 = SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(68,plain,
! [SV2: $i,SV10: $i,SV6: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV6 )
| ( in @ SV10 @ SV2 ) )
= $true )
| ( ( SV10 = SV12 )
= $false )
| ( ( SV2 = SV6 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[64]) ).
thf(69,plain,
! [SV6: $i,SV12: $i,SV2: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV2 ) )
= $true )
| ( ( in @ SV12 @ SV6 )
= $true )
| ( ( SV10 = SV12 )
= $false )
| ( ( SV2 = SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(70,plain,
! [SV2: $i,SV10: $i,SV6: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV6 ) )
= $true )
| ( ( in @ SV10 @ SV2 )
= $true )
| ( ( SV10 = SV12 )
= $false )
| ( ( SV2 = SV6 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(71,plain,
! [SV6: $i,SV12: $i,SV2: $i,SV10: $i] :
( ( ( in @ SV10 @ SV2 )
= $false )
| ( ( in @ SV12 @ SV6 )
= $true )
| ( ( SV10 = SV12 )
= $false )
| ( ( SV2 = SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(72,plain,
! [SV2: $i,SV10: $i,SV6: $i,SV12: $i] :
( ( ( in @ SV12 @ SV6 )
= $false )
| ( ( in @ SV10 @ SV2 )
= $true )
| ( ( SV10 = SV12 )
= $false )
| ( ( SV2 = SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(73,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[22,72,71,66,65,59,52,48,44,43]) ).
thf(74,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU706^2 : 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
% 0.07/0.18 % Computer : n015.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 15:36:24 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.22
% 0.07/0.22 No.of.Axioms: 0
% 0.07/0.22
% 0.07/0.22 Length.of.Defs: 1180
% 0.07/0.22
% 0.07/0.22 Contains.Choice.Funs: false
% 0.07/0.22 ..
% 0.07/0.22
% 0.07/0.22 ********************************
% 0.07/0.22 * All subproblems solved! *
% 0.07/0.22 ********************************
% 0.07/0.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:5,ps:3,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:73,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.22
% 0.07/0.22 %**** Beginning of derivation protocol ****
% 0.07/0.22 % SZS output start CNFRefutation
% See solution above
% 0.07/0.22
% 0.07/0.22 %**** End of derivation protocol ****
% 0.07/0.22 %**** no. of clauses in derivation: 74 ****
% 0.07/0.22 %**** clause counter: 73 ****
% 0.07/0.22
% 0.07/0.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:5,ps:3,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:73,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------