%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET882+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n006.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 10:42:28 AM UTC 2026
% Result : Theorem 0.09s 0.23s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of formulae : 90 ( 40 unt; 0 typ; 0 def)
% Number of atoms : 647 ( 358 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 1170 ( 284 ~; 228 |; 3 &; 641 @)
% ( 9 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 216 ( 0 ^; 216 !; 0 ?; 216 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY10,type,
sK2_SY10: $i ).
thf(tp_sK3_SY19,type,
sK3_SY19: $i > $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= ( singleton @ A ) )
<=> ( ~ ( in @ A @ C )
& ( ( in @ B @ C )
| ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l39_zfmisc_1) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(7,conjecture,
! [A: $i,B: $i] :
( ( A != B )
=> ( ( set_difference @ ( unordered_pair @ A @ B ) @ ( singleton @ B ) )
= ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_zfmisc_1) ).
thf(8,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( A != B )
=> ( ( set_difference @ ( unordered_pair @ A @ B ) @ ( singleton @ B ) )
= ( singleton @ A ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[7]) ).
thf(9,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
=> ( ( set_difference @ ( unordered_pair @ A @ B ) @ ( singleton @ B ) )
= ( singleton @ A ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[8]) ).
thf(10,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= ( singleton @ A ) )
<=> ( ~ ( in @ A @ C )
& ( ( in @ B @ C )
| ( A = B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(12,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(13,plain,
( ( ! [SY10: $i] :
( ( sK1_A != SY10 )
=> ( ( set_difference @ ( unordered_pair @ sK1_A @ SY10 ) @ ( singleton @ SY10 ) )
= ( singleton @ sK1_A ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[9]) ).
thf(14,plain,
( ( ( sK1_A != sK2_SY10 )
=> ( ( set_difference @ ( unordered_pair @ sK1_A @ sK2_SY10 ) @ ( singleton @ sK2_SY10 ) )
= ( singleton @ sK1_A ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[13]) ).
thf(15,plain,
( ( sK1_A != sK2_SY10 )
= $true ),
inference(standard_cnf,[status(thm)],[14]) ).
thf(16,plain,
( ( ( set_difference @ ( unordered_pair @ sK1_A @ sK2_SY10 ) @ ( singleton @ sK2_SY10 ) )
= ( singleton @ sK1_A ) )
= $false ),
inference(standard_cnf,[status(thm)],[14]) ).
thf(17,plain,
( ( ( set_difference @ ( unordered_pair @ sK1_A @ sK2_SY10 ) @ ( singleton @ sK2_SY10 ) )
!= ( singleton @ sK1_A ) )
= $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(18,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(19,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(20,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( set_difference @ ( unordered_pair @ A @ B ) @ C )
= ( singleton @ A ) )
<=> ( ~ ( in @ A @ C )
& ( ( in @ B @ C )
| ( A = B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(21,plain,
( ( sK1_A != sK2_SY10 )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(22,plain,
( ( ( set_difference @ ( unordered_pair @ sK1_A @ sK2_SY10 ) @ ( singleton @ sK2_SY10 ) )
!= ( singleton @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(23,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( ( set_difference @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
!= ( singleton @ SX0 ) )
| ~ ( ~ ~ ( in @ SX0 @ SX2 )
| ~ ( ( in @ SX1 @ SX2 )
| ( SX0 = SX1 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( in @ SX0 @ SX2 )
| ~ ( ( in @ SX1 @ SX2 )
| ( SX0 = SX1 ) ) )
| ( ( set_difference @ ( unordered_pair @ SX0 @ SX1 ) @ SX2 )
= ( singleton @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(24,plain,
( ( sK1_A != sK2_SY10 )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(25,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( SX1
!= ( singleton @ SX0 ) )
| ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) ) )
| ~ ( ~ ! [SX2: $i] :
~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( SX2 = SX0 ) )
| ~ ( ( SX2 != SX0 )
| ( in @ SX2 @ SX1 ) ) )
| ( SX1
= ( singleton @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(26,plain,
! [SV1: $i] :
( ( ! [SY11: $i] :
( ( unordered_pair @ SV1 @ SY11 )
= ( unordered_pair @ SY11 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(27,plain,
( ( ( set_difference @ ( unordered_pair @ sK1_A @ sK2_SY10 ) @ ( singleton @ sK2_SY10 ) )
= ( singleton @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(28,plain,
! [SV2: $i] :
( ( ! [SY12: $i,SY13: $i] :
~ ( ~ ( ( ( set_difference @ ( unordered_pair @ SV2 @ SY12 ) @ SY13 )
!= ( singleton @ SV2 ) )
| ~ ( ~ ~ ( in @ SV2 @ SY13 )
| ~ ( ( in @ SY12 @ SY13 )
| ( SV2 = SY12 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( in @ SV2 @ SY13 )
| ~ ( ( in @ SY12 @ SY13 )
| ( SV2 = SY12 ) ) )
| ( ( set_difference @ ( unordered_pair @ SV2 @ SY12 ) @ SY13 )
= ( singleton @ SV2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(29,plain,
( ( sK1_A = sK2_SY10 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[24]) ).
thf(30,plain,
! [SV3: $i] :
( ( ! [SY14: $i] :
~ ( ~ ( ( SY14
!= ( singleton @ SV3 ) )
| ! [SY15: $i] :
~ ( ~ ( ~ ( in @ SY15 @ SY14 )
| ( SY15 = SV3 ) )
| ~ ( ( SY15 != SV3 )
| ( in @ SY15 @ SY14 ) ) ) )
| ~ ( ~ ! [SY16: $i] :
~ ( ~ ( ~ ( in @ SY16 @ SY14 )
| ( SY16 = SV3 ) )
| ~ ( ( SY16 != SV3 )
| ( in @ SY16 @ SY14 ) ) )
| ( SY14
= ( singleton @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(31,plain,
! [SV4: $i,SV1: $i] :
( ( ( unordered_pair @ SV1 @ SV4 )
= ( unordered_pair @ SV4 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(32,plain,
! [SV5: $i,SV2: $i] :
( ( ! [SY17: $i] :
~ ( ~ ( ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SY17 )
!= ( singleton @ SV2 ) )
| ~ ( ~ ~ ( in @ SV2 @ SY17 )
| ~ ( ( in @ SV5 @ SY17 )
| ( SV2 = SV5 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( in @ SV2 @ SY17 )
| ~ ( ( in @ SV5 @ SY17 )
| ( SV2 = SV5 ) ) )
| ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SY17 )
= ( singleton @ SV2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(33,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ( ~ ( ( SV6
!= ( singleton @ SV3 ) )
| ! [SY18: $i] :
~ ( ~ ( ~ ( in @ SY18 @ SV6 )
| ( SY18 = SV3 ) )
| ~ ( ( SY18 != SV3 )
| ( in @ SY18 @ SV6 ) ) ) )
| ~ ( ~ ! [SY19: $i] :
~ ( ~ ( ~ ( in @ SY19 @ SV6 )
| ( SY19 = SV3 ) )
| ~ ( ( SY19 != SV3 )
| ( in @ SY19 @ SV6 ) ) )
| ( SV6
= ( singleton @ SV3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(34,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ~ ( ~ ( ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SV7 )
!= ( singleton @ SV2 ) )
| ~ ( ~ ~ ( in @ SV2 @ SV7 )
| ~ ( ( in @ SV5 @ SV7 )
| ( SV2 = SV5 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( in @ SV2 @ SV7 )
| ~ ( ( in @ SV5 @ SV7 )
| ( SV2 = SV5 ) ) )
| ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SV7 )
= ( singleton @ SV2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(35,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ( ( SV6
!= ( singleton @ SV3 ) )
| ! [SY18: $i] :
~ ( ~ ( ~ ( in @ SY18 @ SV6 )
| ( SY18 = SV3 ) )
| ~ ( ( SY18 != SV3 )
| ( in @ SY18 @ SV6 ) ) ) )
| ~ ( ~ ! [SY19: $i] :
~ ( ~ ( ~ ( in @ SY19 @ SV6 )
| ( SY19 = SV3 ) )
| ~ ( ( SY19 != SV3 )
| ( in @ SY19 @ SV6 ) ) )
| ( SV6
= ( singleton @ SV3 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(36,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ~ ( ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SV7 )
!= ( singleton @ SV2 ) )
| ~ ( ~ ~ ( in @ SV2 @ SV7 )
| ~ ( ( in @ SV5 @ SV7 )
| ( SV2 = SV5 ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( in @ SV2 @ SV7 )
| ~ ( ( in @ SV5 @ SV7 )
| ( SV2 = SV5 ) ) )
| ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SV7 )
= ( singleton @ SV2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(37,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ( ( SV6
!= ( singleton @ SV3 ) )
| ! [SY18: $i] :
~ ( ~ ( ~ ( in @ SY18 @ SV6 )
| ( SY18 = SV3 ) )
| ~ ( ( SY18 != SV3 )
| ( in @ SY18 @ SV6 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(38,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ( ~ ! [SY19: $i] :
~ ( ~ ( ~ ( in @ SY19 @ SV6 )
| ( SY19 = SV3 ) )
| ~ ( ( SY19 != SV3 )
| ( in @ SY19 @ SV6 ) ) )
| ( SV6
= ( singleton @ SV3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[35]) ).
thf(39,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ~ ( ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SV7 )
!= ( singleton @ SV2 ) )
| ~ ( ~ ~ ( in @ SV2 @ SV7 )
| ~ ( ( in @ SV5 @ SV7 )
| ( SV2 = SV5 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(40,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( in @ SV2 @ SV7 )
| ~ ( ( in @ SV5 @ SV7 )
| ( SV2 = SV5 ) ) )
| ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SV7 )
= ( singleton @ SV2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(41,plain,
! [SV3: $i,SV6: $i] :
( ( ( SV6
!= ( singleton @ SV3 ) )
| ! [SY18: $i] :
~ ( ~ ( ~ ( in @ SY18 @ SV6 )
| ( SY18 = SV3 ) )
| ~ ( ( SY18 != SV3 )
| ( in @ SY18 @ SV6 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[37]) ).
thf(42,plain,
! [SV3: $i,SV6: $i] :
( ( ~ ! [SY19: $i] :
~ ( ~ ( ~ ( in @ SY19 @ SV6 )
| ( SY19 = SV3 ) )
| ~ ( ( SY19 != SV3 )
| ( in @ SY19 @ SV6 ) ) )
| ( SV6
= ( singleton @ SV3 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[38]) ).
thf(43,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SV7 )
!= ( singleton @ SV2 ) )
| ~ ( ~ ~ ( in @ SV2 @ SV7 )
| ~ ( ( in @ SV5 @ SV7 )
| ( SV2 = SV5 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(44,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ~ ~ ( ~ ~ ( in @ SV2 @ SV7 )
| ~ ( ( in @ SV5 @ SV7 )
| ( SV2 = SV5 ) ) )
| ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SV7 )
= ( singleton @ SV2 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(45,plain,
! [SV3: $i,SV6: $i] :
( ( ( SV6
!= ( singleton @ SV3 ) )
= $true )
| ( ( ! [SY18: $i] :
~ ( ~ ( ~ ( in @ SY18 @ SV6 )
| ( SY18 = SV3 ) )
| ~ ( ( SY18 != SV3 )
| ( in @ SY18 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV3: $i,SV6: $i] :
( ( ( ~ ! [SY19: $i] :
~ ( ~ ( ~ ( in @ SY19 @ SV6 )
| ( SY19 = SV3 ) )
| ~ ( ( SY19 != SV3 )
| ( in @ SY19 @ SV6 ) ) ) )
= $true )
| ( ( SV6
= ( singleton @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SV7 )
!= ( singleton @ SV2 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV2 @ SV7 )
| ~ ( ( in @ SV5 @ SV7 )
| ( SV2 = SV5 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ( ~ ~ ( ~ ~ ( in @ SV2 @ SV7 )
| ~ ( ( in @ SV5 @ SV7 )
| ( SV2 = SV5 ) ) ) )
= $true )
| ( ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SV7 )
= ( singleton @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV3: $i,SV6: $i] :
( ( ( SV6
= ( singleton @ SV3 ) )
= $false )
| ( ( ! [SY18: $i] :
~ ( ~ ( ~ ( in @ SY18 @ SV6 )
| ( SY18 = SV3 ) )
| ~ ( ( SY18 != SV3 )
| ( in @ SY18 @ SV6 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[45]) ).
thf(50,plain,
! [SV3: $i,SV6: $i] :
( ( ( ! [SY19: $i] :
~ ( ~ ( ~ ( in @ SY19 @ SV6 )
| ( SY19 = SV3 ) )
| ~ ( ( SY19 != SV3 )
| ( in @ SY19 @ SV6 ) ) ) )
= $false )
| ( ( SV6
= ( singleton @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[46]) ).
thf(51,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SV7 )
= ( singleton @ SV2 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV2 @ SV7 )
| ~ ( ( in @ SV5 @ SV7 )
| ( SV2 = SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(52,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( ~ ~ ( in @ SV2 @ SV7 )
| ~ ( ( in @ SV5 @ SV7 )
| ( SV2 = SV5 ) ) ) )
= $false )
| ( ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SV7 )
= ( singleton @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(53,plain,
! [SV3: $i,SV6: $i,SV8: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV8 @ SV6 )
| ( SV8 = SV3 ) )
| ~ ( ( SV8 != SV3 )
| ( in @ SV8 @ SV6 ) ) ) )
= $true )
| ( ( SV6
= ( singleton @ SV3 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(54,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK3_SY19 @ SV3 @ SV6 ) @ SV6 )
| ( ( sK3_SY19 @ SV3 @ SV6 )
= SV3 ) )
| ~ ( ( ( sK3_SY19 @ SV3 @ SV6 )
!= SV3 )
| ( in @ ( sK3_SY19 @ SV3 @ SV6 ) @ SV6 ) ) ) )
= $false )
| ( ( SV6
= ( singleton @ SV3 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[50]) ).
thf(55,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ( ~ ~ ( in @ SV2 @ SV7 )
| ~ ( ( in @ SV5 @ SV7 )
| ( SV2 = SV5 ) ) )
= $false )
| ( ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SV7 )
= ( singleton @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(56,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ( ~ ~ ( in @ SV2 @ SV7 )
| ~ ( ( in @ SV5 @ SV7 )
| ( SV2 = SV5 ) ) )
= $true )
| ( ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SV7 )
= ( singleton @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(57,plain,
! [SV3: $i,SV6: $i,SV8: $i] :
( ( ( ~ ( ~ ( in @ SV8 @ SV6 )
| ( SV8 = SV3 ) )
| ~ ( ( SV8 != SV3 )
| ( in @ SV8 @ SV6 ) ) )
= $false )
| ( ( SV6
= ( singleton @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[53]) ).
thf(58,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_SY19 @ SV3 @ SV6 ) @ SV6 )
| ( ( sK3_SY19 @ SV3 @ SV6 )
= SV3 ) )
| ~ ( ( ( sK3_SY19 @ SV3 @ SV6 )
!= SV3 )
| ( in @ ( sK3_SY19 @ SV3 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6
= ( singleton @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[54]) ).
thf(59,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ( ~ ~ ( in @ SV2 @ SV7 ) )
= $false )
| ( ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SV7 )
= ( singleton @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(60,plain,
! [SV2: $i,SV7: $i,SV5: $i] :
( ( ( ~ ( ( in @ SV5 @ SV7 )
| ( SV2 = SV5 ) ) )
= $false )
| ( ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SV7 )
= ( singleton @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[55]) ).
thf(61,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ( ~ ~ ( in @ SV2 @ SV7 ) )
= $true )
| ( ( ~ ( ( in @ SV5 @ SV7 )
| ( SV2 = SV5 ) ) )
= $true )
| ( ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SV7 )
= ( singleton @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(62,plain,
! [SV3: $i,SV6: $i,SV8: $i] :
( ( ( ~ ( ~ ( in @ SV8 @ SV6 )
| ( SV8 = SV3 ) ) )
= $false )
| ( ( SV6
= ( singleton @ SV3 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(63,plain,
! [SV6: $i,SV3: $i,SV8: $i] :
( ( ( ~ ( ( SV8 != SV3 )
| ( in @ SV8 @ SV6 ) ) )
= $false )
| ( ( SV6
= ( singleton @ SV3 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[57]) ).
thf(64,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_SY19 @ SV3 @ SV6 ) @ SV6 )
| ( ( sK3_SY19 @ SV3 @ SV6 )
= SV3 ) ) )
= $true )
| ( ( ~ ( ( ( sK3_SY19 @ SV3 @ SV6 )
!= SV3 )
| ( in @ ( sK3_SY19 @ SV3 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6
= ( singleton @ SV3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(65,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( in @ SV2 @ SV7 ) )
= $true )
| ( ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SV7 )
= ( singleton @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[59]) ).
thf(66,plain,
! [SV2: $i,SV7: $i,SV5: $i] :
( ( ( ( in @ SV5 @ SV7 )
| ( SV2 = SV5 ) )
= $true )
| ( ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SV7 )
= ( singleton @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[60]) ).
thf(67,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( in @ SV2 @ SV7 ) )
= $false )
| ( ( ~ ( ( in @ SV5 @ SV7 )
| ( SV2 = SV5 ) ) )
= $true )
| ( ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SV7 )
= ( singleton @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(68,plain,
! [SV3: $i,SV6: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV6 )
| ( SV8 = SV3 ) )
= $true )
| ( ( SV6
= ( singleton @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[62]) ).
thf(69,plain,
! [SV6: $i,SV3: $i,SV8: $i] :
( ( ( ( SV8 != SV3 )
| ( in @ SV8 @ SV6 ) )
= $true )
| ( ( SV6
= ( singleton @ SV3 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(70,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( in @ ( sK3_SY19 @ SV3 @ SV6 ) @ SV6 )
| ( ( sK3_SY19 @ SV3 @ SV6 )
= SV3 ) )
= $false )
| ( ( ~ ( ( ( sK3_SY19 @ SV3 @ SV6 )
!= SV3 )
| ( in @ ( sK3_SY19 @ SV3 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6
= ( singleton @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(71,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ( in @ SV2 @ SV7 )
= $false )
| ( ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SV7 )
= ( singleton @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[65]) ).
thf(72,plain,
! [SV2: $i,SV7: $i,SV5: $i] :
( ( ( in @ SV5 @ SV7 )
= $true )
| ( ( SV2 = SV5 )
= $true )
| ( ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SV7 )
= ( singleton @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(73,plain,
! [SV5: $i,SV7: $i,SV2: $i] :
( ( ( in @ SV2 @ SV7 )
= $true )
| ( ( ~ ( ( in @ SV5 @ SV7 )
| ( SV2 = SV5 ) ) )
= $true )
| ( ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SV7 )
= ( singleton @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[67]) ).
thf(74,plain,
! [SV3: $i,SV6: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV6 ) )
= $true )
| ( ( SV8 = SV3 )
= $true )
| ( ( SV6
= ( singleton @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(75,plain,
! [SV6: $i,SV3: $i,SV8: $i] :
( ( ( SV8 != SV3 )
= $true )
| ( ( in @ SV8 @ SV6 )
= $true )
| ( ( SV6
= ( singleton @ SV3 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(76,plain,
! [SV6: $i,SV3: $i] :
( ( ( ~ ( in @ ( sK3_SY19 @ SV3 @ SV6 ) @ SV6 ) )
= $false )
| ( ( ~ ( ( ( sK3_SY19 @ SV3 @ SV6 )
!= SV3 )
| ( in @ ( sK3_SY19 @ SV3 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6
= ( singleton @ SV3 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(77,plain,
! [SV6: $i,SV3: $i] :
( ( ( ( sK3_SY19 @ SV3 @ SV6 )
= SV3 )
= $false )
| ( ( ~ ( ( ( sK3_SY19 @ SV3 @ SV6 )
!= SV3 )
| ( in @ ( sK3_SY19 @ SV3 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6
= ( singleton @ SV3 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[70]) ).
thf(78,plain,
! [SV2: $i,SV7: $i,SV5: $i] :
( ( ( ( in @ SV5 @ SV7 )
| ( SV2 = SV5 ) )
= $false )
| ( ( in @ SV2 @ SV7 )
= $true )
| ( ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SV7 )
= ( singleton @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(79,plain,
! [SV3: $i,SV6: $i,SV8: $i] :
( ( ( in @ SV8 @ SV6 )
= $false )
| ( ( SV8 = SV3 )
= $true )
| ( ( SV6
= ( singleton @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(80,plain,
! [SV6: $i,SV3: $i,SV8: $i] :
( ( ( SV8 = SV3 )
= $false )
| ( ( in @ SV8 @ SV6 )
= $true )
| ( ( SV6
= ( singleton @ SV3 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(81,plain,
! [SV6: $i,SV3: $i] :
( ( ( in @ ( sK3_SY19 @ SV3 @ SV6 ) @ SV6 )
= $true )
| ( ( ~ ( ( ( sK3_SY19 @ SV3 @ SV6 )
!= SV3 )
| ( in @ ( sK3_SY19 @ SV3 @ SV6 ) @ SV6 ) ) )
= $true )
| ( ( SV6
= ( singleton @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(82,plain,
! [SV6: $i,SV3: $i] :
( ( ( ( ( sK3_SY19 @ SV3 @ SV6 )
!= SV3 )
| ( in @ ( sK3_SY19 @ SV3 @ SV6 ) @ SV6 ) )
= $false )
| ( ( ( sK3_SY19 @ SV3 @ SV6 )
= SV3 )
= $false )
| ( ( SV6
= ( singleton @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(83,plain,
! [SV2: $i,SV7: $i,SV5: $i] :
( ( ( in @ SV5 @ SV7 )
= $false )
| ( ( in @ SV2 @ SV7 )
= $true )
| ( ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SV7 )
= ( singleton @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(84,plain,
! [SV7: $i,SV5: $i,SV2: $i] :
( ( ( SV2 = SV5 )
= $false )
| ( ( in @ SV2 @ SV7 )
= $true )
| ( ( ( set_difference @ ( unordered_pair @ SV2 @ SV5 ) @ SV7 )
= ( singleton @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[78]) ).
thf(85,plain,
! [SV6: $i,SV3: $i] :
( ( ( ( ( sK3_SY19 @ SV3 @ SV6 )
!= SV3 )
| ( in @ ( sK3_SY19 @ SV3 @ SV6 ) @ SV6 ) )
= $false )
| ( ( in @ ( sK3_SY19 @ SV3 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6
= ( singleton @ SV3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(86,plain,
! [SV6: $i,SV3: $i] :
( ( ( ( sK3_SY19 @ SV3 @ SV6 )
!= SV3 )
= $false )
| ( ( ( sK3_SY19 @ SV3 @ SV6 )
= SV3 )
= $false )
| ( ( SV6
= ( singleton @ SV3 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(87,plain,
! [SV6: $i,SV3: $i] :
( ( ( in @ ( sK3_SY19 @ SV3 @ SV6 ) @ SV6 )
= $false )
| ( ( ( sK3_SY19 @ SV3 @ SV6 )
= SV3 )
= $false )
| ( ( SV6
= ( singleton @ SV3 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[82]) ).
thf(88,plain,
! [SV6: $i,SV3: $i] :
( ( ( ( sK3_SY19 @ SV3 @ SV6 )
!= SV3 )
= $false )
| ( ( in @ ( sK3_SY19 @ SV3 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6
= ( singleton @ SV3 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(89,plain,
! [SV6: $i,SV3: $i] :
( ( ( in @ ( sK3_SY19 @ SV3 @ SV6 ) @ SV6 )
= $false )
| ( ( in @ ( sK3_SY19 @ SV3 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6
= ( singleton @ SV3 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[85]) ).
thf(90,plain,
! [SV6: $i,SV3: $i] :
( ( ( ( sK3_SY19 @ SV3 @ SV6 )
= SV3 )
= $true )
| ( ( ( sK3_SY19 @ SV3 @ SV6 )
= SV3 )
= $false )
| ( ( SV6
= ( singleton @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[86]) ).
thf(91,plain,
! [SV6: $i,SV3: $i] :
( ( ( ( sK3_SY19 @ SV3 @ SV6 )
= SV3 )
= $true )
| ( ( in @ ( sK3_SY19 @ SV3 @ SV6 ) @ SV6 )
= $true )
| ( ( SV6
= ( singleton @ SV3 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[88]) ).
thf(92,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[27,91,90,89,87,84,83,80,79,72,71,31,29]) ).
thf(93,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET882+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.17 % Computer : n006.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Oct 6 14:55:22 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.23
% 0.09/0.23 No.of.Axioms: 3
% 0.09/0.23
% 0.09/0.23 Length.of.Defs: 0
% 0.09/0.23
% 0.09/0.23 Contains.Choice.Funs: false
% 0.09/0.23 ..
% 0.09/0.23
% 0.09/0.23 ********************************
% 0.09/0.23 * All subproblems solved! *
% 0.09/0.23 ********************************
% 0.09/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:4,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:92,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.23
% 0.09/0.23 %**** Beginning of derivation protocol ****
% 0.09/0.23 % SZS output start CNFRefutation
% See solution above
% 0.09/0.23
% 0.09/0.23 %**** End of derivation protocol ****
% 0.09/0.23 %**** no. of clauses in derivation: 90 ****
% 0.09/0.23 %**** clause counter: 92 ****
% 0.09/0.23
% 0.09/0.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:4,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:92,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------