%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU653^2 : 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 : n019.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 10:45:59 AM UTC 2026
% Result : Theorem 0.07s 0.27s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 63 ( 51 unt; 0 typ; 5 def)
% Number of atoms : 309 ( 205 equ; 0 cnn)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 1058 ( 40 ~; 55 |; 0 &; 922 @)
% ( 0 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 12 con; 0-2 aty)
% Number of variables : 209 ( 0 ^; 209 !; 0 ?; 209 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_SX0,type,
sK1_SX0: $i ).
thf(tp_sK2_SY36,type,
sK2_SY36: $i ).
thf(tp_sK3_SY44,type,
sK3_SY44: $i ).
thf(tp_sK4_SY48,type,
sK4_SY48: $i ).
thf(tp_secondinupair,type,
secondinupair: $o ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setukpairinjL2,type,
setukpairinjL2: $o ).
thf(tp_setukpairinjR1,type,
setukpairinjR1: $o ).
thf(tp_upairequniteq,type,
upairequniteq: $o ).
thf(tp_upairset2E,type,
upairset2E: $o ).
thf(secondinupair,definition,
( secondinupair
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',secondinupair) ).
thf(setukpairinjL2,definition,
( setukpairinjL2
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(setukpairinjR1,definition,
( setukpairinjR1
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( ( Xz = Xu )
=> ( Xy = Xu ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR1) ).
thf(upairequniteq,definition,
( upairequniteq
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairequniteq) ).
thf(upairset2E,definition,
( upairset2E
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairset2E) ).
thf(1,conjecture,
( secondinupair
=> ( upairset2E
=> ( setukpairinjL2
=> ( setukpairinjR1
=> ( upairequniteq
=> ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xy = Xu ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR2) ).
thf(2,negated_conjecture,
( ( secondinupair
=> ( upairset2E
=> ( setukpairinjL2
=> ( setukpairinjR1
=> ( upairequniteq
=> ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xy = Xu ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( ( Xz = Xu )
=> ( Xy = Xu ) ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) )
=> ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xy = Xu ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,secondinupair,setukpairinjL2,setukpairinjR1,upairequniteq,upairset2E]) ).
thf(4,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( ( Xz = Xu )
=> ( Xy = Xu ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xy = Xu ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(10,plain,
( ( ~ ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xy = Xu ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[8]) ).
thf(12,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( ( Xz = Xu )
=> ( Xy = Xu ) ) ) )
= $true ),
inference(copy,[status(thm)],[7]) ).
thf(13,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) )
= $true ),
inference(copy,[status(thm)],[6]) ).
thf(14,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(15,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[4]) ).
thf(16,plain,
( ( ~ ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xy = Xu ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(17,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14,secondinupair,setukpairinjL2,setukpairinjR1,upairequniteq,upairset2E]) ).
thf(18,plain,
( ( ~ ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16,secondinupair,setukpairinjL2,setukpairinjR1,upairequniteq,upairset2E]) ).
thf(19,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13,secondinupair,setukpairinjL2,setukpairinjR1,upairequniteq,upairset2E]) ).
thf(20,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) )
| ( SX2 != SX3 )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12,secondinupair,setukpairinjL2,setukpairinjR1,upairequniteq,upairset2E]) ).
thf(21,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
!= ( setadjoin @ SX2 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11,secondinupair,setukpairinjL2,setukpairinjR1,upairequniteq,upairset2E]) ).
thf(22,plain,
! [SV1: $i] :
( ( ! [SY24: $i] : ( in @ SY24 @ ( setadjoin @ SV1 @ ( setadjoin @ SY24 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[15]) ).
thf(23,plain,
! [SV2: $i] :
( ( ! [SY25: $i,SY26: $i] :
( ~ ( in @ SY26 @ ( setadjoin @ SV2 @ ( setadjoin @ SY25 @ emptyset ) ) )
| ( SY26 = SV2 )
| ( SY26 = SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(24,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SX2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX2 @ ( setadjoin @ SX3 @ emptyset ) ) @ emptyset ) ) )
| ( SX1 = SX3 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[18]) ).
thf(25,plain,
! [SV3: $i] :
( ( ! [SY27: $i,SY28: $i,SY29: $i] :
( ( ( setadjoin @ ( setadjoin @ SV3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV3 @ ( setadjoin @ SY27 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY28 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY28 @ ( setadjoin @ SY29 @ emptyset ) ) @ emptyset ) ) )
| ( SV3 = SY28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(26,plain,
! [SV4: $i] :
( ( ! [SY30: $i,SY31: $i,SY32: $i] :
( ( ( setadjoin @ ( setadjoin @ SV4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV4 @ ( setadjoin @ SY30 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY31 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY31 @ ( setadjoin @ SY32 @ emptyset ) ) @ emptyset ) ) )
| ( SY31 != SY32 )
| ( SY30 = SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(27,plain,
! [SV5: $i] :
( ( ! [SY33: $i,SY34: $i] :
( ( ( setadjoin @ SV5 @ ( setadjoin @ SY33 @ emptyset ) )
!= ( setadjoin @ SY34 @ emptyset ) )
| ( SV5 = SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(28,plain,
! [SV1: $i,SV6: $i] :
( ( in @ SV6 @ ( setadjoin @ SV1 @ ( setadjoin @ SV6 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(29,plain,
! [SV7: $i,SV2: $i] :
( ( ! [SY35: $i] :
( ~ ( in @ SY35 @ ( setadjoin @ SV2 @ ( setadjoin @ SV7 @ emptyset ) ) )
| ( SY35 = SV2 )
| ( SY35 = SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(30,plain,
( ( ! [SY36: $i,SY37: $i,SY38: $i] :
( ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ SY36 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY37 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY37 @ ( setadjoin @ SY38 @ emptyset ) ) @ emptyset ) ) )
| ( SY36 = SY38 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[24]) ).
thf(31,plain,
! [SV8: $i,SV3: $i] :
( ( ! [SY39: $i,SY40: $i] :
( ( ( setadjoin @ ( setadjoin @ SV3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV3 @ ( setadjoin @ SV8 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY39 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY39 @ ( setadjoin @ SY40 @ emptyset ) ) @ emptyset ) ) )
| ( SV3 = SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(32,plain,
! [SV9: $i,SV4: $i] :
( ( ! [SY41: $i,SY42: $i] :
( ( ( setadjoin @ ( setadjoin @ SV4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV4 @ ( setadjoin @ SV9 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY41 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY41 @ ( setadjoin @ SY42 @ emptyset ) ) @ emptyset ) ) )
| ( SY41 != SY42 )
| ( SV9 = SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(33,plain,
! [SV10: $i,SV5: $i] :
( ( ! [SY43: $i] :
( ( ( setadjoin @ SV5 @ ( setadjoin @ SV10 @ emptyset ) )
!= ( setadjoin @ SY43 @ emptyset ) )
| ( SV5 = SV10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(34,plain,
! [SV7: $i,SV2: $i,SV11: $i] :
( ( ~ ( in @ SV11 @ ( setadjoin @ SV2 @ ( setadjoin @ SV7 @ emptyset ) ) )
| ( SV11 = SV2 )
| ( SV11 = SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(35,plain,
( ( ! [SY44: $i,SY45: $i] :
( ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK2_SY36 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY44 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY44 @ ( setadjoin @ SY45 @ emptyset ) ) @ emptyset ) ) )
| ( sK2_SY36 = SY45 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[30]) ).
thf(36,plain,
! [SV12: $i,SV8: $i,SV3: $i] :
( ( ! [SY46: $i] :
( ( ( setadjoin @ ( setadjoin @ SV3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV3 @ ( setadjoin @ SV8 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV12 @ ( setadjoin @ SY46 @ emptyset ) ) @ emptyset ) ) )
| ( SV3 = SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(37,plain,
! [SV13: $i,SV9: $i,SV4: $i] :
( ( ! [SY47: $i] :
( ( ( setadjoin @ ( setadjoin @ SV4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV4 @ ( setadjoin @ SV9 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV13 @ ( setadjoin @ SY47 @ emptyset ) ) @ emptyset ) ) )
| ( SV13 != SY47 )
| ( SV9 = SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(38,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ( ( setadjoin @ SV5 @ ( setadjoin @ SV10 @ emptyset ) )
!= ( setadjoin @ SV14 @ emptyset ) )
| ( SV5 = SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(39,plain,
! [SV7: $i,SV2: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ ( setadjoin @ SV2 @ ( setadjoin @ SV7 @ emptyset ) ) ) )
= $true )
| ( ( ( SV11 = SV2 )
| ( SV11 = SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[34]) ).
thf(40,plain,
( ( ! [SY48: $i] :
( ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK2_SY36 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK3_SY44 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY44 @ ( setadjoin @ SY48 @ emptyset ) ) @ emptyset ) ) )
| ( sK2_SY36 = SY48 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[35]) ).
thf(41,plain,
! [SV15: $i,SV12: $i,SV8: $i,SV3: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV3 @ ( setadjoin @ SV8 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV12 @ ( setadjoin @ SV15 @ emptyset ) ) @ emptyset ) ) )
| ( SV3 = SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(42,plain,
! [SV16: $i,SV13: $i,SV9: $i,SV4: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV4 @ ( setadjoin @ SV9 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV13 @ ( setadjoin @ SV16 @ emptyset ) ) @ emptyset ) ) )
| ( SV13 != SV16 )
| ( SV9 = SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(43,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ( ( setadjoin @ SV5 @ ( setadjoin @ SV10 @ emptyset ) )
!= ( setadjoin @ SV14 @ emptyset ) )
= $true )
| ( ( SV5 = SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(44,plain,
! [SV7: $i,SV2: $i,SV11: $i] :
( ( ( in @ SV11 @ ( setadjoin @ SV2 @ ( setadjoin @ SV7 @ emptyset ) ) )
= $false )
| ( ( ( SV11 = SV2 )
| ( SV11 = SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(45,plain,
( ( ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK2_SY36 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK3_SY44 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY44 @ ( setadjoin @ sK4_SY48 @ emptyset ) ) @ emptyset ) ) )
| ( sK2_SY36 = sK4_SY48 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[40]) ).
thf(46,plain,
! [SV15: $i,SV12: $i,SV8: $i,SV3: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV3 @ ( setadjoin @ SV8 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV12 @ ( setadjoin @ SV15 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( SV3 = SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(47,plain,
! [SV16: $i,SV13: $i,SV9: $i,SV4: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV4 @ ( setadjoin @ SV9 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV13 @ ( setadjoin @ SV16 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( ( SV13 != SV16 )
| ( SV9 = SV16 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(48,plain,
! [SV14: $i,SV10: $i,SV5: $i] :
( ( ( ( setadjoin @ SV5 @ ( setadjoin @ SV10 @ emptyset ) )
= ( setadjoin @ SV14 @ emptyset ) )
= $false )
| ( ( SV5 = SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(49,plain,
! [SV7: $i,SV2: $i,SV11: $i] :
( ( ( SV11 = SV2 )
= $true )
| ( ( SV11 = SV7 )
= $true )
| ( ( in @ SV11 @ ( setadjoin @ SV2 @ ( setadjoin @ SV7 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(50,plain,
( ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK2_SY36 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK3_SY44 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY44 @ ( setadjoin @ sK4_SY48 @ emptyset ) ) @ emptyset ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(51,plain,
( ( sK2_SY36 = sK4_SY48 )
= $false ),
inference(extcnf_or_neg,[status(thm)],[45]) ).
thf(52,plain,
! [SV15: $i,SV12: $i,SV8: $i,SV3: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV3 @ ( setadjoin @ SV8 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV12 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV12 @ ( setadjoin @ SV15 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV3 = SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(53,plain,
! [SV16: $i,SV13: $i,SV9: $i,SV4: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV4 @ ( setadjoin @ SV9 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV13 @ ( setadjoin @ SV16 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( ( SV13 != SV16 )
| ( SV9 = SV16 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(54,plain,
( ( ( setadjoin @ ( setadjoin @ sK1_SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_SX0 @ ( setadjoin @ sK2_SY36 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3_SY44 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY44 @ ( setadjoin @ sK4_SY48 @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[50]) ).
thf(55,plain,
! [SV4: $i,SV9: $i,SV16: $i,SV13: $i] :
( ( ( SV13 != SV16 )
= $true )
| ( ( SV9 = SV16 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV4 @ ( setadjoin @ SV9 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV13 @ ( setadjoin @ SV16 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[53]) ).
thf(56,plain,
! [SV4: $i,SV9: $i,SV16: $i,SV13: $i] :
( ( ( SV13 = SV16 )
= $false )
| ( ( SV9 = SV16 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV4 @ ( setadjoin @ SV9 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV13 @ ( setadjoin @ SV16 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(57,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,56,54,52,51,49,48]) ).
thf(58,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU653^2 : 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
% 0.07/0.18 % Computer : n019.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 15:30:16 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.27
% 0.07/0.27 No.of.Axioms: 0
% 0.07/0.27
% 0.07/0.27 Length.of.Defs: 1433
% 0.07/0.27
% 0.07/0.27 Contains.Choice.Funs: false
% 0.07/0.27 ...
% 0.07/0.27
% 0.07/0.27 ********************************
% 0.07/0.27 * All subproblems solved! *
% 0.07/0.27 ********************************
% 0.07/0.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:5,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:57,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.27
% 0.07/0.27 %**** Beginning of derivation protocol ****
% 0.07/0.27 % SZS output start CNFRefutation
% See solution above
% 0.07/0.28
% 0.07/0.28 %**** End of derivation protocol ****
% 0.07/0.28 %**** no. of clauses in derivation: 58 ****
% 0.07/0.28 %**** clause counter: 57 ****
% 0.07/0.28
% 0.07/0.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:5,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:57,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------