%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET959+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 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 10:42:39 AM UTC 2026
% Result : Theorem 0.07s 0.24s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 87 ( 48 unt; 0 typ; 0 def)
% Number of atoms : 503 ( 197 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 942 ( 180 ~; 109 |; 24 &; 608 @)
% ( 10 <=>; 11 =>; 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 : 15 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 221 ( 0 ^; 221 !; 0 ?; 221 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY17,type,
sK2_SY17: $i ).
thf(tp_sK3_SY43,type,
sK3_SY43: $i > $i > $i ).
thf(tp_sK4_SY35,type,
sK4_SY35: $i > $i ).
thf(tp_sK5_SY39,type,
sK5_SY39: $i > $i ).
thf(tp_sK6_SY44,type,
sK6_SY44: $i > $i ).
thf(tp_sK7_SY45,type,
sK7_SY45: $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(8,conjecture,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ( in @ C @ A )
& ! [D: $i,E: $i] :
( C
!= ( ordered_pair @ D @ E ) ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i,E: $i] :
( C
!= ( ordered_pair @ D @ E ) ) )
& ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
<=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t112_zfmisc_1) ).
thf(9,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ( in @ C @ A )
& ! [D: $i,E: $i] :
( C
!= ( ordered_pair @ D @ E ) ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i,E: $i] :
( C
!= ( ordered_pair @ D @ E ) ) )
& ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
<=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) )
=> ( A = B ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[8]) ).
thf(10,plain,
( ( ! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( ( in @ C @ A )
& ! [D: $i,E: $i] :
( C
!= ( ordered_pair @ D @ E ) ) )
& ! [C: $i] :
~ ( ( in @ C @ B )
& ! [D: $i,E: $i] :
( C
!= ( ordered_pair @ D @ E ) ) )
& ! [C: $i,D: $i] :
( ( in @ ( ordered_pair @ C @ D ) @ A )
<=> ( in @ ( ordered_pair @ C @ D ) @ B ) ) )
=> ( A = B ) ) )
= $false ),
inference(unfold_def,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(12,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(14,plain,
( ( ! [SY17: $i] :
( ( ! [SY18: $i] :
~ ( ( in @ SY18 @ sK1_A )
& ! [D: $i,E: $i] :
( SY18
!= ( ordered_pair @ D @ E ) ) )
& ! [C: $i] :
~ ( ( in @ C @ SY17 )
& ! [D: $i,E: $i] :
( C
!= ( ordered_pair @ D @ E ) ) )
& ! [SY24: $i,SY25: $i] :
( ( in @ ( ordered_pair @ SY24 @ SY25 ) @ sK1_A )
<=> ( in @ ( ordered_pair @ SY24 @ SY25 ) @ SY17 ) ) )
=> ( sK1_A = SY17 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(15,plain,
( ( ( ! [SY18: $i] :
~ ( ( in @ SY18 @ sK1_A )
& ! [D: $i,E: $i] :
( SY18
!= ( ordered_pair @ D @ E ) ) )
& ! [SY29: $i] :
~ ( ( in @ SY29 @ sK2_SY17 )
& ! [D: $i,E: $i] :
( SY29
!= ( ordered_pair @ D @ E ) ) )
& ! [SY32: $i,SY33: $i] :
( ( in @ ( ordered_pair @ SY32 @ SY33 ) @ sK1_A )
<=> ( in @ ( ordered_pair @ SY32 @ SY33 ) @ sK2_SY17 ) ) )
=> ( sK1_A = sK2_SY17 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(16,plain,
( ( ! [SY18: $i] :
~ ( ( in @ SY18 @ sK1_A )
& ! [D: $i,E: $i] :
( SY18
!= ( ordered_pair @ D @ E ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[15]) ).
thf(17,plain,
( ( ! [SY29: $i] :
~ ( ( in @ SY29 @ sK2_SY17 )
& ! [D: $i,E: $i] :
( SY29
!= ( ordered_pair @ D @ E ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[15]) ).
thf(18,plain,
( ( ! [SY32: $i,SY33: $i] :
( ( in @ ( ordered_pair @ SY32 @ SY33 ) @ sK1_A )
<=> ( in @ ( ordered_pair @ SY32 @ SY33 ) @ sK2_SY17 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[15]) ).
thf(19,plain,
( ( sK1_A = sK2_SY17 )
= $false ),
inference(standard_cnf,[status(thm)],[15]) ).
thf(20,plain,
( ( sK1_A != sK2_SY17 )
= $true ),
inference(polarity_switch,[status(thm)],[19]) ).
thf(21,plain,
( ( ! [A: $i,B: $i] :
( ( in @ A @ B )
=> ~ ( in @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(22,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(23,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
<=> ( in @ C @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(24,plain,
( ( ! [SY32: $i,SY33: $i] :
( ( in @ ( ordered_pair @ SY32 @ SY33 ) @ sK1_A )
<=> ( in @ ( ordered_pair @ SY32 @ SY33 ) @ sK2_SY17 ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(25,plain,
( ( ! [SY29: $i] :
~ ( ( in @ SY29 @ sK2_SY17 )
& ! [D: $i,E: $i] :
( SY29
!= ( ordered_pair @ D @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(26,plain,
( ( ! [SY18: $i] :
~ ( ( in @ SY18 @ sK1_A )
& ! [D: $i,E: $i] :
( SY18
!= ( ordered_pair @ D @ E ) ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(27,plain,
( ( sK1_A != sK2_SY17 )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(28,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( in @ SX0 @ sK1_A )
| ~ ! [SX1: $i,SX2: $i] :
( SX0
!= ( ordered_pair @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(29,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ SX1 )
| ~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(30,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ sK1_A )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ sK2_SY17 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SX0 @ SX1 ) @ sK2_SY17 )
| ( in @ ( ordered_pair @ SX0 @ SX1 ) @ sK1_A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(31,plain,
( ( ! [SX0: $i] :
~ ~ ( ~ ( in @ SX0 @ sK2_SY17 )
| ~ ! [SX1: $i,SX2: $i] :
( SX0
!= ( ordered_pair @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(32,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(33,plain,
! [SV1: $i] :
( ( ! [SY34: $i] :
~ ( empty @ ( ordered_pair @ SV1 @ SY34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(34,plain,
( ( sK1_A = sK2_SY17 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(35,plain,
! [SV2: $i] :
( ( ~ ~ ( ~ ( in @ SV2 @ sK1_A )
| ~ ! [SY35: $i,SY36: $i] :
( SV2
!= ( ordered_pair @ SY35 @ SY36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(36,plain,
! [SV3: $i] :
( ( ! [SY37: $i] :
( ~ ( in @ SV3 @ SY37 )
| ~ ( in @ SY37 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(37,plain,
! [SV4: $i] :
( ( ! [SY38: $i] :
~ ( ~ ( ~ ( in @ ( ordered_pair @ SV4 @ SY38 ) @ sK1_A )
| ( in @ ( ordered_pair @ SV4 @ SY38 ) @ sK2_SY17 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV4 @ SY38 ) @ sK2_SY17 )
| ( in @ ( ordered_pair @ SV4 @ SY38 ) @ sK1_A ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(38,plain,
! [SV5: $i] :
( ( ~ ~ ( ~ ( in @ SV5 @ sK2_SY17 )
| ~ ! [SY39: $i,SY40: $i] :
( SV5
!= ( ordered_pair @ SY39 @ SY40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(39,plain,
! [SV6: $i] :
( ( ! [SY41: $i] :
( ~ ! [SY42: $i] :
~ ( ~ ( ~ ( in @ SY42 @ SV6 )
| ( in @ SY42 @ SY41 ) )
| ~ ( ~ ( in @ SY42 @ SY41 )
| ( in @ SY42 @ SV6 ) ) )
| ( SV6 = SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(40,plain,
! [SV7: $i,SV1: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV1 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(41,plain,
! [SV2: $i] :
( ( ~ ( ~ ( in @ SV2 @ sK1_A )
| ~ ! [SY35: $i,SY36: $i] :
( SV2
!= ( ordered_pair @ SY35 @ SY36 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[35]) ).
thf(42,plain,
! [SV8: $i,SV3: $i] :
( ( ~ ( in @ SV3 @ SV8 )
| ~ ( in @ SV8 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(43,plain,
! [SV9: $i,SV4: $i] :
( ( ~ ( ~ ( ~ ( in @ ( ordered_pair @ SV4 @ SV9 ) @ sK1_A )
| ( in @ ( ordered_pair @ SV4 @ SV9 ) @ sK2_SY17 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV4 @ SV9 ) @ sK2_SY17 )
| ( in @ ( ordered_pair @ SV4 @ SV9 ) @ sK1_A ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(44,plain,
! [SV5: $i] :
( ( ~ ( ~ ( in @ SV5 @ sK2_SY17 )
| ~ ! [SY39: $i,SY40: $i] :
( SV5
!= ( ordered_pair @ SY39 @ SY40 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(45,plain,
! [SV10: $i,SV6: $i] :
( ( ~ ! [SY43: $i] :
~ ( ~ ( ~ ( in @ SY43 @ SV6 )
| ( in @ SY43 @ SV10 ) )
| ~ ( ~ ( in @ SY43 @ SV10 )
| ( in @ SY43 @ SV6 ) ) )
| ( SV6 = SV10 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(46,plain,
! [SV7: $i,SV1: $i] :
( ( empty @ ( ordered_pair @ SV1 @ SV7 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(47,plain,
! [SV2: $i] :
( ( ~ ( in @ SV2 @ sK1_A )
| ~ ! [SY35: $i,SY36: $i] :
( SV2
!= ( ordered_pair @ SY35 @ SY36 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[41]) ).
thf(48,plain,
! [SV8: $i,SV3: $i] :
( ( ( ~ ( in @ SV3 @ SV8 ) )
= $true )
| ( ( ~ ( in @ SV8 @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(49,plain,
! [SV9: $i,SV4: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV4 @ SV9 ) @ sK1_A )
| ( in @ ( ordered_pair @ SV4 @ SV9 ) @ sK2_SY17 ) )
| ~ ( ~ ( in @ ( ordered_pair @ SV4 @ SV9 ) @ sK2_SY17 )
| ( in @ ( ordered_pair @ SV4 @ SV9 ) @ sK1_A ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(50,plain,
! [SV5: $i] :
( ( ~ ( in @ SV5 @ sK2_SY17 )
| ~ ! [SY39: $i,SY40: $i] :
( SV5
!= ( ordered_pair @ SY39 @ SY40 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[44]) ).
thf(51,plain,
! [SV10: $i,SV6: $i] :
( ( ( ~ ! [SY43: $i] :
~ ( ~ ( ~ ( in @ SY43 @ SV6 )
| ( in @ SY43 @ SV10 ) )
| ~ ( ~ ( in @ SY43 @ SV10 )
| ( in @ SY43 @ SV6 ) ) ) )
= $true )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[45]) ).
thf(52,plain,
! [SV2: $i] :
( ( ( ~ ( in @ SV2 @ sK1_A ) )
= $true )
| ( ( ~ ! [SY35: $i,SY36: $i] :
( SV2
!= ( ordered_pair @ SY35 @ SY36 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[47]) ).
thf(53,plain,
! [SV8: $i,SV3: $i] :
( ( ( in @ SV3 @ SV8 )
= $false )
| ( ( ~ ( in @ SV8 @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(54,plain,
! [SV9: $i,SV4: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV4 @ SV9 ) @ sK1_A )
| ( in @ ( ordered_pair @ SV4 @ SV9 ) @ sK2_SY17 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(55,plain,
! [SV9: $i,SV4: $i] :
( ( ~ ( ~ ( in @ ( ordered_pair @ SV4 @ SV9 ) @ sK2_SY17 )
| ( in @ ( ordered_pair @ SV4 @ SV9 ) @ sK1_A ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[49]) ).
thf(56,plain,
! [SV5: $i] :
( ( ( ~ ( in @ SV5 @ sK2_SY17 ) )
= $true )
| ( ( ~ ! [SY39: $i,SY40: $i] :
( SV5
!= ( ordered_pair @ SY39 @ SY40 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(57,plain,
! [SV10: $i,SV6: $i] :
( ( ( ! [SY43: $i] :
~ ( ~ ( ~ ( in @ SY43 @ SV6 )
| ( in @ SY43 @ SV10 ) )
| ~ ( ~ ( in @ SY43 @ SV10 )
| ( in @ SY43 @ SV6 ) ) ) )
= $false )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(58,plain,
! [SV2: $i] :
( ( ( in @ SV2 @ sK1_A )
= $false )
| ( ( ~ ! [SY35: $i,SY36: $i] :
( SV2
!= ( ordered_pair @ SY35 @ SY36 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(59,plain,
! [SV3: $i,SV8: $i] :
( ( ( in @ SV8 @ SV3 )
= $false )
| ( ( in @ SV3 @ SV8 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(60,plain,
! [SV9: $i,SV4: $i] :
( ( ~ ( in @ ( ordered_pair @ SV4 @ SV9 ) @ sK1_A )
| ( in @ ( ordered_pair @ SV4 @ SV9 ) @ sK2_SY17 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(61,plain,
! [SV9: $i,SV4: $i] :
( ( ~ ( in @ ( ordered_pair @ SV4 @ SV9 ) @ sK2_SY17 )
| ( in @ ( ordered_pair @ SV4 @ SV9 ) @ sK1_A ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(62,plain,
! [SV5: $i] :
( ( ( in @ SV5 @ sK2_SY17 )
= $false )
| ( ( ~ ! [SY39: $i,SY40: $i] :
( SV5
!= ( ordered_pair @ SY39 @ SY40 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(63,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV6 )
| ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV10 ) )
| ~ ( ~ ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV10 )
| ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV6 ) ) ) )
= $false )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[57]) ).
thf(64,plain,
! [SV2: $i] :
( ( ( ! [SY35: $i,SY36: $i] :
( SV2
!= ( ordered_pair @ SY35 @ SY36 ) ) )
= $false )
| ( ( in @ SV2 @ sK1_A )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(65,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV4 @ SV9 ) @ sK1_A ) )
= $true )
| ( ( in @ ( ordered_pair @ SV4 @ SV9 ) @ sK2_SY17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[60]) ).
thf(66,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( in @ ( ordered_pair @ SV4 @ SV9 ) @ sK2_SY17 ) )
= $true )
| ( ( in @ ( ordered_pair @ SV4 @ SV9 ) @ sK1_A )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(67,plain,
! [SV5: $i] :
( ( ( ! [SY39: $i,SY40: $i] :
( SV5
!= ( ordered_pair @ SY39 @ SY40 ) ) )
= $false )
| ( ( in @ SV5 @ sK2_SY17 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(68,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV6 )
| ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV10 ) )
| ~ ( ~ ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV10 )
| ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(69,plain,
! [SV2: $i] :
( ( ( ! [SY44: $i] :
( SV2
!= ( ordered_pair @ ( sK4_SY35 @ SV2 ) @ SY44 ) ) )
= $false )
| ( ( in @ SV2 @ sK1_A )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[64]) ).
thf(70,plain,
! [SV9: $i,SV4: $i] :
( ( ( in @ ( ordered_pair @ SV4 @ SV9 ) @ sK1_A )
= $false )
| ( ( in @ ( ordered_pair @ SV4 @ SV9 ) @ sK2_SY17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(71,plain,
! [SV9: $i,SV4: $i] :
( ( ( in @ ( ordered_pair @ SV4 @ SV9 ) @ sK2_SY17 )
= $false )
| ( ( in @ ( ordered_pair @ SV4 @ SV9 ) @ sK1_A )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(72,plain,
! [SV5: $i] :
( ( ( ! [SY45: $i] :
( SV5
!= ( ordered_pair @ ( sK5_SY39 @ SV5 ) @ SY45 ) ) )
= $false )
| ( ( in @ SV5 @ sK2_SY17 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[67]) ).
thf(73,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV6 )
| ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV10 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV10 )
| ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(74,plain,
! [SV2: $i] :
( ( ( SV2
!= ( ordered_pair @ ( sK4_SY35 @ SV2 ) @ ( sK6_SY44 @ SV2 ) ) )
= $false )
| ( ( in @ SV2 @ sK1_A )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[69]) ).
thf(75,plain,
! [SV5: $i] :
( ( ( SV5
!= ( ordered_pair @ ( sK5_SY39 @ SV5 ) @ ( sK7_SY45 @ SV5 ) ) )
= $false )
| ( ( in @ SV5 @ sK2_SY17 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[72]) ).
thf(76,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV6 )
| ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV10 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV10 )
| ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(77,plain,
! [SV2: $i] :
( ( ( SV2
= ( ordered_pair @ ( sK4_SY35 @ SV2 ) @ ( sK6_SY44 @ SV2 ) ) )
= $true )
| ( ( in @ SV2 @ sK1_A )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[74]) ).
thf(78,plain,
! [SV5: $i] :
( ( ( SV5
= ( ordered_pair @ ( sK5_SY39 @ SV5 ) @ ( sK7_SY45 @ SV5 ) ) )
= $true )
| ( ( in @ SV5 @ sK2_SY17 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[75]) ).
thf(79,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV6 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV10 )
| ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(80,plain,
! [SV6: $i,SV10: $i] :
( ( ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV10 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV10 )
| ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[76]) ).
thf(81,plain,
! [SV6: $i,SV10: $i] :
( ( ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV6 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV10 )
| ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[79]) ).
thf(82,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV10 )
| ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV6 ) )
= $false )
| ( ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV10 )
= $false )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(83,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV10 )
| ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV6 ) )
= $false )
| ( ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(84,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV10 ) )
= $false )
| ( ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV10 )
= $false )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(85,plain,
! [SV6: $i,SV10: $i] :
( ( ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV6 )
= $false )
| ( ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV10 )
= $false )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(86,plain,
! [SV6: $i,SV10: $i] :
( ( ( ~ ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV10 ) )
= $false )
| ( ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(87,plain,
! [SV6: $i,SV10: $i] :
( ( ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV6 )
= $false )
| ( ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[83]) ).
thf(88,plain,
! [SV6: $i,SV10: $i] :
( ( ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV10 )
= $true )
| ( ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV10 )
= $false )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[84]) ).
thf(89,plain,
! [SV6: $i,SV10: $i] :
( ( ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV10 )
= $true )
| ( ( in @ ( sK3_SY43 @ SV10 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6 = SV10 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(90,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[34,89,88,87,85,78,77,71,70,59,46]) ).
thf(91,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET959+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 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 : n026.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 15:00:32 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.24
% 0.07/0.24 No.of.Axioms: 3
% 0.07/0.24
% 0.07/0.24 Length.of.Defs: 0
% 0.07/0.24
% 0.07/0.24 Contains.Choice.Funs: false
% 0.07/0.24 ..
% 0.07/0.24
% 0.07/0.24 ********************************
% 0.07/0.24 * All subproblems solved! *
% 0.07/0.24 ********************************
% 0.07/0.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:6,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:90,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.24
% 0.07/0.24 %**** Beginning of derivation protocol ****
% 0.07/0.24 % SZS output start CNFRefutation
% See solution above
% 0.07/0.24
% 0.07/0.24 %**** End of derivation protocol ****
% 0.07/0.24 %**** no. of clauses in derivation: 87 ****
% 0.07/0.24 %**** clause counter: 90 ****
% 0.07/0.24
% 0.07/0.24 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:6,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:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:90,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------