%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU807^2 : 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 : n001.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 10:48:27 AM UTC 2026
% Result : Theorem 0.31s 0.37s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of formulae : 83 ( 46 unt; 0 typ; 5 def)
% Number of atoms : 557 ( 217 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 857 ( 159 ~; 158 |; 12 &; 490 @)
% ( 3 <=>; 35 =>; 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 : 14 ( 11 usr; 10 con; 0-2 aty)
% Number of variables : 267 ( 0 ^; 258 !; 9 ?; 267 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_foundationAx,type,
foundationAx: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_in__Cong,type,
in__Cong: $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY20,type,
sK2_SY20: $i ).
thf(tp_sK3_B,type,
sK3_B: $i > $i ).
thf(tp_setadjoin,type,
setadjoin: $i > $i > $i ).
thf(tp_setadjoinIL,type,
setadjoinIL: $o ).
thf(tp_setadjoinIR,type,
setadjoinIR: $o ).
thf(tp_upairset2E,type,
upairset2E: $o ).
thf(foundationAx,definition,
( foundationAx
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',foundationAx) ).
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(setadjoinIL,definition,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(setadjoinIR,definition,
( setadjoinIR
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIR) ).
thf(upairset2E,definition,
( upairset2E
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2E) ).
thf(1,conjecture,
( foundationAx
=> ( setadjoinIL
=> ( setadjoinIR
=> ( in__Cong
=> ( upairset2E
=> ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinself2) ).
thf(2,negated_conjecture,
( ( foundationAx
=> ( setadjoinIL
=> ( setadjoinIR
=> ( in__Cong
=> ( upairset2E
=> ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) )
=> ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,foundationAx,in__Cong,setadjoinIL,setadjoinIR,upairset2E]) ).
thf(4,plain,
( ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,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(8,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(9,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(10,plain,
( ( ~ ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(11,plain,
( ( ( in @ sK1_A @ sK2_SY20 )
& ( in @ sK2_SY20 @ sK1_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(12,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
| ( ( in @ ( sK3_B @ A ) @ A )
& ! [SY21: $i] :
( ~ ( in @ SY21 @ ( sK3_B @ A ) )
| ~ ( in @ SY21 @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(13,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ~ ( in @ Xy @ A )
| ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(14,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ~ ( in @ Xx @ A )
| ( in @ Xy @ B ) )
& ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ~ ( in @ Xy @ B )
| ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(15,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ~ ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
| ( Xz = Xx )
| ( Xz = Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(16,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ~ ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
| ( Xz = Xx )
| ( Xz = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ~ ( in @ Xx @ A )
| ( in @ Xy @ B ) )
& ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ~ ( in @ Xy @ B )
| ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(18,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ~ ( in @ Xy @ A )
| ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(19,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(20,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
| ( ( in @ ( sK3_B @ A ) @ A )
& ! [SY21: $i] :
( ~ ( in @ SY21 @ ( sK3_B @ A ) )
| ~ ( in @ SY21 @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(21,plain,
( ( ( in @ sK1_A @ sK2_SY20 )
& ( in @ sK2_SY20 @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(22,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ~ ( ~ ( in @ ( sK3_B @ SX0 ) @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK3_B @ SX0 ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20,foundationAx,in__Cong,setadjoinIL,setadjoinIR,upairset2E]) ).
thf(23,plain,
( ( ~ ( ~ ( in @ sK1_A @ sK2_SY20 )
| ~ ( in @ sK2_SY20 @ sK1_A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21,foundationAx,in__Cong,setadjoinIL,setadjoinIR,upairset2E]) ).
thf(24,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17,foundationAx,in__Cong,setadjoinIL,setadjoinIR,upairset2E]) ).
thf(25,plain,
! [SV1: $i] :
( ( ! [SY22: $i,SY23: $i] :
( ~ ( in @ SY23 @ ( setadjoin @ SV1 @ ( setadjoin @ SY22 @ emptyset ) ) )
| ( SY23 = SV1 )
| ( SY23 = SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[16]) ).
thf(26,plain,
! [SV2: $i] :
( ( ! [SY24: $i,SY25: $i] :
( ~ ( in @ SY25 @ SY24 )
| ( in @ SY25 @ ( setadjoin @ SV2 @ SY24 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(27,plain,
! [SV3: $i] :
( ( ! [SY26: $i] : ( in @ SV3 @ ( setadjoin @ SV3 @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(28,plain,
! [SV4: $i] :
( ( ! [SY27: $i] :
~ ( in @ SY27 @ SV4 )
| ~ ( ~ ( in @ ( sK3_B @ SV4 ) @ SV4 )
| ~ ! [SY28: $i] :
( ~ ( in @ SY28 @ ( sK3_B @ SV4 ) )
| ~ ( in @ SY28 @ SV4 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(29,plain,
( ( ~ ( in @ sK1_A @ sK2_SY20 )
| ~ ( in @ sK2_SY20 @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(30,plain,
! [SV5: $i] :
( ( ! [SY29: $i] :
( ( SV5 != SY29 )
| ~ ( ~ ! [SY30: $i,SY31: $i] :
( ( SY30 != SY31 )
| ~ ( in @ SY30 @ SV5 )
| ( in @ SY31 @ SY29 ) )
| ~ ! [SY32: $i,SY33: $i] :
( ( SY32 != SY33 )
| ~ ( in @ SY33 @ SY29 )
| ( in @ SY32 @ SV5 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(31,plain,
! [SV6: $i,SV1: $i] :
( ( ! [SY34: $i] :
( ~ ( in @ SY34 @ ( setadjoin @ SV1 @ ( setadjoin @ SV6 @ emptyset ) ) )
| ( SY34 = SV1 )
| ( SY34 = SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(32,plain,
! [SV2: $i,SV7: $i] :
( ( ! [SY35: $i] :
( ~ ( in @ SY35 @ SV7 )
| ( in @ SY35 @ ( setadjoin @ SV2 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(33,plain,
! [SV8: $i,SV3: $i] :
( ( in @ SV3 @ ( setadjoin @ SV3 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(34,plain,
! [SV4: $i] :
( ( ( ! [SY27: $i] :
~ ( in @ SY27 @ SV4 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK3_B @ SV4 ) @ SV4 )
| ~ ! [SY28: $i] :
( ~ ( in @ SY28 @ ( sK3_B @ SV4 ) )
| ~ ( in @ SY28 @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(35,plain,
( ( ~ ( in @ sK1_A @ sK2_SY20 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(36,plain,
( ( ~ ( in @ sK2_SY20 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[29]) ).
thf(37,plain,
! [SV9: $i,SV5: $i] :
( ( ( SV5 != SV9 )
| ~ ( ~ ! [SY36: $i,SY37: $i] :
( ( SY36 != SY37 )
| ~ ( in @ SY36 @ SV5 )
| ( in @ SY37 @ SV9 ) )
| ~ ! [SY38: $i,SY39: $i] :
( ( SY38 != SY39 )
| ~ ( in @ SY39 @ SV9 )
| ( in @ SY38 @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(38,plain,
! [SV6: $i,SV1: $i,SV10: $i] :
( ( ~ ( in @ SV10 @ ( setadjoin @ SV1 @ ( setadjoin @ SV6 @ emptyset ) ) )
| ( SV10 = SV1 )
| ( SV10 = SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(39,plain,
! [SV2: $i,SV7: $i,SV11: $i] :
( ( ~ ( in @ SV11 @ SV7 )
| ( in @ SV11 @ ( setadjoin @ SV2 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(40,plain,
! [SV4: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV4 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK3_B @ SV4 ) @ SV4 )
| ~ ! [SY28: $i] :
( ~ ( in @ SY28 @ ( sK3_B @ SV4 ) )
| ~ ( in @ SY28 @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(41,plain,
( ( in @ sK1_A @ sK2_SY20 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(42,plain,
( ( in @ sK2_SY20 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[36]) ).
thf(43,plain,
! [SV9: $i,SV5: $i] :
( ( ( SV5 != SV9 )
= $true )
| ( ( ~ ( ~ ! [SY36: $i,SY37: $i] :
( ( SY36 != SY37 )
| ~ ( in @ SY36 @ SV5 )
| ( in @ SY37 @ SV9 ) )
| ~ ! [SY38: $i,SY39: $i] :
( ( SY38 != SY39 )
| ~ ( in @ SY39 @ SV9 )
| ( in @ SY38 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(44,plain,
! [SV6: $i,SV1: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ ( setadjoin @ SV1 @ ( setadjoin @ SV6 @ emptyset ) ) ) )
= $true )
| ( ( ( SV10 = SV1 )
| ( SV10 = SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(45,plain,
! [SV2: $i,SV7: $i,SV11: $i] :
( ( ( ~ ( in @ SV11 @ SV7 ) )
= $true )
| ( ( in @ SV11 @ ( setadjoin @ SV2 @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(46,plain,
! [SV4: $i,SV12: $i] :
( ( ( in @ SV12 @ SV4 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK3_B @ SV4 ) @ SV4 )
| ~ ! [SY28: $i] :
( ~ ( in @ SY28 @ ( sK3_B @ SV4 ) )
| ~ ( in @ SY28 @ SV4 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(47,plain,
! [SV9: $i,SV5: $i] :
( ( ( SV5 = SV9 )
= $false )
| ( ( ~ ( ~ ! [SY36: $i,SY37: $i] :
( ( SY36 != SY37 )
| ~ ( in @ SY36 @ SV5 )
| ( in @ SY37 @ SV9 ) )
| ~ ! [SY38: $i,SY39: $i] :
( ( SY38 != SY39 )
| ~ ( in @ SY39 @ SV9 )
| ( in @ SY38 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV6: $i,SV1: $i,SV10: $i] :
( ( ( in @ SV10 @ ( setadjoin @ SV1 @ ( setadjoin @ SV6 @ emptyset ) ) )
= $false )
| ( ( ( SV10 = SV1 )
| ( SV10 = SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV2: $i,SV7: $i,SV11: $i] :
( ( ( in @ SV11 @ SV7 )
= $false )
| ( ( in @ SV11 @ ( setadjoin @ SV2 @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(50,plain,
! [SV12: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK3_B @ SV4 ) @ SV4 )
| ~ ! [SY28: $i] :
( ~ ( in @ SY28 @ ( sK3_B @ SV4 ) )
| ~ ( in @ SY28 @ SV4 ) ) )
= $false )
| ( ( in @ SV12 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(51,plain,
! [SV9: $i,SV5: $i] :
( ( ( ~ ! [SY36: $i,SY37: $i] :
( ( SY36 != SY37 )
| ~ ( in @ SY36 @ SV5 )
| ( in @ SY37 @ SV9 ) )
| ~ ! [SY38: $i,SY39: $i] :
( ( SY38 != SY39 )
| ~ ( in @ SY39 @ SV9 )
| ( in @ SY38 @ SV5 ) ) )
= $false )
| ( ( SV5 = SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV6: $i,SV1: $i,SV10: $i] :
( ( ( SV10 = SV1 )
= $true )
| ( ( SV10 = SV6 )
= $true )
| ( ( in @ SV10 @ ( setadjoin @ SV1 @ ( setadjoin @ SV6 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV12: $i,SV4: $i] :
( ( ( ~ ( in @ ( sK3_B @ SV4 ) @ SV4 ) )
= $false )
| ( ( in @ SV12 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(54,plain,
! [SV12: $i,SV4: $i] :
( ( ( ~ ! [SY28: $i] :
( ~ ( in @ SY28 @ ( sK3_B @ SV4 ) )
| ~ ( in @ SY28 @ SV4 ) ) )
= $false )
| ( ( in @ SV12 @ SV4 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[50]) ).
thf(55,plain,
! [SV9: $i,SV5: $i] :
( ( ( ~ ! [SY36: $i,SY37: $i] :
( ( SY36 != SY37 )
| ~ ( in @ SY36 @ SV5 )
| ( in @ SY37 @ SV9 ) ) )
= $false )
| ( ( SV5 = SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(56,plain,
! [SV5: $i,SV9: $i] :
( ( ( ~ ! [SY38: $i,SY39: $i] :
( ( SY38 != SY39 )
| ~ ( in @ SY39 @ SV9 )
| ( in @ SY38 @ SV5 ) ) )
= $false )
| ( ( SV5 = SV9 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[51]) ).
thf(57,plain,
! [SV12: $i,SV4: $i] :
( ( ( in @ ( sK3_B @ SV4 ) @ SV4 )
= $true )
| ( ( in @ SV12 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[53]) ).
thf(58,plain,
! [SV12: $i,SV4: $i] :
( ( ( ! [SY28: $i] :
( ~ ( in @ SY28 @ ( sK3_B @ SV4 ) )
| ~ ( in @ SY28 @ SV4 ) ) )
= $true )
| ( ( in @ SV12 @ SV4 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(59,plain,
! [SV9: $i,SV5: $i] :
( ( ( ! [SY36: $i,SY37: $i] :
( ( SY36 != SY37 )
| ~ ( in @ SY36 @ SV5 )
| ( in @ SY37 @ SV9 ) ) )
= $true )
| ( ( SV5 = SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(60,plain,
! [SV5: $i,SV9: $i] :
( ( ( ! [SY38: $i,SY39: $i] :
( ( SY38 != SY39 )
| ~ ( in @ SY39 @ SV9 )
| ( in @ SY38 @ SV5 ) ) )
= $true )
| ( ( SV5 = SV9 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(61,plain,
! [SV12: $i,SV4: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ ( sK3_B @ SV4 ) )
| ~ ( in @ SV13 @ SV4 ) )
= $true )
| ( ( in @ SV12 @ SV4 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(62,plain,
! [SV9: $i,SV5: $i,SV14: $i] :
( ( ( ! [SY40: $i] :
( ( SV14 != SY40 )
| ~ ( in @ SV14 @ SV5 )
| ( in @ SY40 @ SV9 ) ) )
= $true )
| ( ( SV5 = SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(63,plain,
! [SV5: $i,SV9: $i,SV15: $i] :
( ( ( ! [SY41: $i] :
( ( SV15 != SY41 )
| ~ ( in @ SY41 @ SV9 )
| ( in @ SV15 @ SV5 ) ) )
= $true )
| ( ( SV5 = SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(64,plain,
! [SV12: $i,SV4: $i,SV13: $i] :
( ( ( ~ ( in @ SV13 @ ( sK3_B @ SV4 ) ) )
= $true )
| ( ( ~ ( in @ SV13 @ SV4 ) )
= $true )
| ( ( in @ SV12 @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(65,plain,
! [SV9: $i,SV5: $i,SV16: $i,SV14: $i] :
( ( ( ( SV14 != SV16 )
| ~ ( in @ SV14 @ SV5 )
| ( in @ SV16 @ SV9 ) )
= $true )
| ( ( SV5 = SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(66,plain,
! [SV5: $i,SV9: $i,SV17: $i,SV15: $i] :
( ( ( ( SV15 != SV17 )
| ~ ( in @ SV17 @ SV9 )
| ( in @ SV15 @ SV5 ) )
= $true )
| ( ( SV5 = SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(67,plain,
! [SV12: $i,SV4: $i,SV13: $i] :
( ( ( in @ SV13 @ ( sK3_B @ SV4 ) )
= $false )
| ( ( ~ ( in @ SV13 @ SV4 ) )
= $true )
| ( ( in @ SV12 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(68,plain,
! [SV9: $i,SV5: $i,SV16: $i,SV14: $i] :
( ( ( SV14 != SV16 )
= $true )
| ( ( ~ ( in @ SV14 @ SV5 )
| ( in @ SV16 @ SV9 ) )
= $true )
| ( ( SV5 = SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(69,plain,
! [SV5: $i,SV9: $i,SV17: $i,SV15: $i] :
( ( ( SV15 != SV17 )
= $true )
| ( ( ~ ( in @ SV17 @ SV9 )
| ( in @ SV15 @ SV5 ) )
= $true )
| ( ( SV5 = SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(70,plain,
! [SV12: $i,SV4: $i,SV13: $i] :
( ( ( in @ SV13 @ SV4 )
= $false )
| ( ( in @ SV13 @ ( sK3_B @ SV4 ) )
= $false )
| ( ( in @ SV12 @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(71,plain,
! [SV9: $i,SV5: $i,SV16: $i,SV14: $i] :
( ( ( SV14 = SV16 )
= $false )
| ( ( ~ ( in @ SV14 @ SV5 )
| ( in @ SV16 @ SV9 ) )
= $true )
| ( ( SV5 = SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(72,plain,
! [SV5: $i,SV9: $i,SV17: $i,SV15: $i] :
( ( ( SV15 = SV17 )
= $false )
| ( ( ~ ( in @ SV17 @ SV9 )
| ( in @ SV15 @ SV5 ) )
= $true )
| ( ( SV5 = SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(73,plain,
! [SV9: $i,SV16: $i,SV5: $i,SV14: $i] :
( ( ( ~ ( in @ SV14 @ SV5 ) )
= $true )
| ( ( in @ SV16 @ SV9 )
= $true )
| ( ( SV14 = SV16 )
= $false )
| ( ( SV5 = SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(74,plain,
! [SV5: $i,SV15: $i,SV9: $i,SV17: $i] :
( ( ( ~ ( in @ SV17 @ SV9 ) )
= $true )
| ( ( in @ SV15 @ SV5 )
= $true )
| ( ( SV15 = SV17 )
= $false )
| ( ( SV5 = SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(75,plain,
! [SV9: $i,SV16: $i,SV5: $i,SV14: $i] :
( ( ( in @ SV14 @ SV5 )
= $false )
| ( ( in @ SV16 @ SV9 )
= $true )
| ( ( SV14 = SV16 )
= $false )
| ( ( SV5 = SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(76,plain,
! [SV5: $i,SV15: $i,SV9: $i,SV17: $i] :
( ( ( in @ SV17 @ SV9 )
= $false )
| ( ( in @ SV15 @ SV5 )
= $true )
| ( ( SV15 = SV17 )
= $false )
| ( ( SV5 = SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(77,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[33,76,75,70,57,52,49,42,41]) ).
thf(78,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU807^2 : 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
% 0.07/0.19 % Computer : n001.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 15:41:39 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.31/0.37
% 0.31/0.37 No.of.Axioms: 0
% 0.31/0.37
% 0.31/0.37 Length.of.Defs: 1001
% 0.31/0.37
% 0.31/0.37 Contains.Choice.Funs: false
% 0.31/0.37 ..
% 0.31/0.37
% 0.31/0.37 ********************************
% 0.31/0.37 * All subproblems solved! *
% 0.31/0.37 ********************************
% 0.31/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:5,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:77,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.31/0.37
% 0.31/0.37 %**** Beginning of derivation protocol ****
% 0.31/0.37 % SZS output start CNFRefutation
% See solution above
% 0.31/0.37
% 0.31/0.37 %**** End of derivation protocol ****
% 0.31/0.37 %**** no. of clauses in derivation: 78 ****
% 0.31/0.37 %**** clause counter: 77 ****
% 0.31/0.37
% 0.31/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:5,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:77,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------