%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SET881+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 : 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 10:42:28 AM UTC 2026
% Result : Theorem 0.08s 0.23s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 86 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 680 ( 418 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 1183 ( 201 ~; 269 |; 0 &; 704 @)
% ( 9 <=>; 0 =>; 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 : 12 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 240 ( 0 ^; 240 !; 0 ?; 240 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_empty_set,type,
empty_set: $i ).
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_SY21,type,
sK3_SY21: $i > $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] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set )
<=> ( in @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).
thf(4,axiom,
empty @ empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(8,conjecture,
! [A: $i,B: $i] :
( ( set_difference @ ( singleton @ A ) @ ( unordered_pair @ A @ B ) )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_zfmisc_1) ).
thf(9,negated_conjecture,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( singleton @ A ) @ ( unordered_pair @ A @ B ) )
= empty_set ) )
= $false ),
inference(negate_conjecture,[status(cth)],[8]) ).
thf(10,plain,
( ( ! [A: $i,B: $i] :
( ( set_difference @ ( singleton @ A ) @ ( unordered_pair @ A @ B ) )
= empty_set ) )
= $false ),
inference(unfold_def,[status(thm)],[9]) ).
thf(11,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set )
<=> ( in @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(12,plain,
( ( empty @ empty_set )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(14,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(15,plain,
( ( ! [SY10: $i] :
( ( set_difference @ ( singleton @ sK1_A ) @ ( unordered_pair @ sK1_A @ SY10 ) )
= empty_set ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[10]) ).
thf(16,plain,
( ( ( set_difference @ ( singleton @ sK1_A ) @ ( unordered_pair @ sK1_A @ sK2_SY10 ) )
= empty_set )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[15]) ).
thf(17,plain,
( ( ( set_difference @ ( singleton @ sK1_A ) @ ( unordered_pair @ sK1_A @ sK2_SY10 ) )
!= empty_set )
= $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)],[14]) ).
thf(19,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(20,plain,
( ( empty @ empty_set )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(21,plain,
( ( ! [A: $i,B: $i] :
( ( ( set_difference @ ( singleton @ A ) @ B )
= empty_set )
<=> ( in @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(22,plain,
( ( ( set_difference @ ( singleton @ sK1_A ) @ ( unordered_pair @ sK1_A @ sK2_SY10 ) )
!= empty_set )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(23,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ( ( ( set_difference @ ( singleton @ SX0 ) @ SX1 )
!= empty_set )
| ( in @ SX0 @ SX1 ) )
| ~ ( ~ ( in @ SX0 @ SX1 )
| ( ( set_difference @ ( singleton @ SX0 ) @ SX1 )
= empty_set ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(24,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
~ ( ~ ( ( SX2
!= ( unordered_pair @ SX0 @ SX1 ) )
| ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ( ~ ( ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ( in @ SX3 @ SX2 ) ) ) )
| ~ ( ~ ! [SX3: $i] :
~ ( ~ ( ~ ( in @ SX3 @ SX2 )
| ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ~ ( ~ ( ( SX3 = SX0 )
| ( SX3 = SX1 ) )
| ( in @ SX3 @ SX2 ) ) )
| ( SX2
= ( unordered_pair @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(25,plain,
! [SV1: $i] :
( ( ! [SY11: $i] :
( ( unordered_pair @ SV1 @ SY11 )
= ( unordered_pair @ SY11 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(26,plain,
( ( ( set_difference @ ( singleton @ sK1_A ) @ ( unordered_pair @ sK1_A @ sK2_SY10 ) )
= empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(27,plain,
! [SV2: $i] :
( ( ! [SY12: $i] :
~ ( ~ ( ( ( set_difference @ ( singleton @ SV2 ) @ SY12 )
!= empty_set )
| ( in @ SV2 @ SY12 ) )
| ~ ( ~ ( in @ SV2 @ SY12 )
| ( ( set_difference @ ( singleton @ SV2 ) @ SY12 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(28,plain,
! [SV3: $i] :
( ( ! [SY13: $i,SY14: $i] :
~ ( ~ ( ( SY14
!= ( unordered_pair @ SV3 @ SY13 ) )
| ! [SY15: $i] :
~ ( ~ ( ~ ( in @ SY15 @ SY14 )
| ( SY15 = SV3 )
| ( SY15 = SY13 ) )
| ~ ( ~ ( ( SY15 = SV3 )
| ( SY15 = SY13 ) )
| ( in @ SY15 @ SY14 ) ) ) )
| ~ ( ~ ! [SY16: $i] :
~ ( ~ ( ~ ( in @ SY16 @ SY14 )
| ( SY16 = SV3 )
| ( SY16 = SY13 ) )
| ~ ( ~ ( ( SY16 = SV3 )
| ( SY16 = SY13 ) )
| ( in @ SY16 @ SY14 ) ) )
| ( SY14
= ( unordered_pair @ SV3 @ SY13 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(29,plain,
! [SV4: $i,SV1: $i] :
( ( ( unordered_pair @ SV1 @ SV4 )
= ( unordered_pair @ SV4 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(30,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ~ ( ( ( set_difference @ ( singleton @ SV2 ) @ SV5 )
!= empty_set )
| ( in @ SV2 @ SV5 ) )
| ~ ( ~ ( in @ SV2 @ SV5 )
| ( ( set_difference @ ( singleton @ SV2 ) @ SV5 )
= empty_set ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(31,plain,
! [SV6: $i,SV3: $i] :
( ( ! [SY17: $i] :
~ ( ~ ( ( SY17
!= ( unordered_pair @ SV3 @ SV6 ) )
| ! [SY18: $i] :
~ ( ~ ( ~ ( in @ SY18 @ SY17 )
| ( SY18 = SV3 )
| ( SY18 = SV6 ) )
| ~ ( ~ ( ( SY18 = SV3 )
| ( SY18 = SV6 ) )
| ( in @ SY18 @ SY17 ) ) ) )
| ~ ( ~ ! [SY19: $i] :
~ ( ~ ( ~ ( in @ SY19 @ SY17 )
| ( SY19 = SV3 )
| ( SY19 = SV6 ) )
| ~ ( ~ ( ( SY19 = SV3 )
| ( SY19 = SV6 ) )
| ( in @ SY19 @ SY17 ) ) )
| ( SY17
= ( unordered_pair @ SV3 @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(32,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ( ( set_difference @ ( singleton @ SV2 ) @ SV5 )
!= empty_set )
| ( in @ SV2 @ SV5 ) )
| ~ ( ~ ( in @ SV2 @ SV5 )
| ( ( set_difference @ ( singleton @ SV2 ) @ SV5 )
= empty_set ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ~ ( ~ ( ( SV7
!= ( unordered_pair @ SV3 @ SV6 ) )
| ! [SY20: $i] :
~ ( ~ ( ~ ( in @ SY20 @ SV7 )
| ( SY20 = SV3 )
| ( SY20 = SV6 ) )
| ~ ( ~ ( ( SY20 = SV3 )
| ( SY20 = SV6 ) )
| ( in @ SY20 @ SV7 ) ) ) )
| ~ ( ~ ! [SY21: $i] :
~ ( ~ ( ~ ( in @ SY21 @ SV7 )
| ( SY21 = SV3 )
| ( SY21 = SV6 ) )
| ~ ( ~ ( ( SY21 = SV3 )
| ( SY21 = SV6 ) )
| ( in @ SY21 @ SV7 ) ) )
| ( SV7
= ( unordered_pair @ SV3 @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(34,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ( ( set_difference @ ( singleton @ SV2 ) @ SV5 )
!= empty_set )
| ( in @ SV2 @ SV5 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(35,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( ~ ( in @ SV2 @ SV5 )
| ( ( set_difference @ ( singleton @ SV2 ) @ SV5 )
= empty_set ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[32]) ).
thf(36,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ~ ( ( SV7
!= ( unordered_pair @ SV3 @ SV6 ) )
| ! [SY20: $i] :
~ ( ~ ( ~ ( in @ SY20 @ SV7 )
| ( SY20 = SV3 )
| ( SY20 = SV6 ) )
| ~ ( ~ ( ( SY20 = SV3 )
| ( SY20 = SV6 ) )
| ( in @ SY20 @ SV7 ) ) ) )
| ~ ( ~ ! [SY21: $i] :
~ ( ~ ( ~ ( in @ SY21 @ SV7 )
| ( SY21 = SV3 )
| ( SY21 = SV6 ) )
| ~ ( ~ ( ( SY21 = SV3 )
| ( SY21 = SV6 ) )
| ( in @ SY21 @ SV7 ) ) )
| ( SV7
= ( unordered_pair @ SV3 @ SV6 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(37,plain,
! [SV5: $i,SV2: $i] :
( ( ( ( set_difference @ ( singleton @ SV2 ) @ SV5 )
!= empty_set )
| ( in @ SV2 @ SV5 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[34]) ).
thf(38,plain,
! [SV5: $i,SV2: $i] :
( ( ~ ( in @ SV2 @ SV5 )
| ( ( set_difference @ ( singleton @ SV2 ) @ SV5 )
= empty_set ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[35]) ).
thf(39,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ~ ( ( SV7
!= ( unordered_pair @ SV3 @ SV6 ) )
| ! [SY20: $i] :
~ ( ~ ( ~ ( in @ SY20 @ SV7 )
| ( SY20 = SV3 )
| ( SY20 = SV6 ) )
| ~ ( ~ ( ( SY20 = SV3 )
| ( SY20 = SV6 ) )
| ( in @ SY20 @ SV7 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(40,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ~ ( ~ ! [SY21: $i] :
~ ( ~ ( ~ ( in @ SY21 @ SV7 )
| ( SY21 = SV3 )
| ( SY21 = SV6 ) )
| ~ ( ~ ( ( SY21 = SV3 )
| ( SY21 = SV6 ) )
| ( in @ SY21 @ SV7 ) ) )
| ( SV7
= ( unordered_pair @ SV3 @ SV6 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[36]) ).
thf(41,plain,
! [SV5: $i,SV2: $i] :
( ( ( ( set_difference @ ( singleton @ SV2 ) @ SV5 )
!= empty_set )
= $true )
| ( ( in @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ( in @ SV2 @ SV5 ) )
= $true )
| ( ( ( set_difference @ ( singleton @ SV2 ) @ SV5 )
= empty_set )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ( SV7
!= ( unordered_pair @ SV3 @ SV6 ) )
| ! [SY20: $i] :
~ ( ~ ( ~ ( in @ SY20 @ SV7 )
| ( SY20 = SV3 )
| ( SY20 = SV6 ) )
| ~ ( ~ ( ( SY20 = SV3 )
| ( SY20 = SV6 ) )
| ( in @ SY20 @ SV7 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[39]) ).
thf(44,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ~ ! [SY21: $i] :
~ ( ~ ( ~ ( in @ SY21 @ SV7 )
| ( SY21 = SV3 )
| ( SY21 = SV6 ) )
| ~ ( ~ ( ( SY21 = SV3 )
| ( SY21 = SV6 ) )
| ( in @ SY21 @ SV7 ) ) )
| ( SV7
= ( unordered_pair @ SV3 @ SV6 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[40]) ).
thf(45,plain,
! [SV5: $i,SV2: $i] :
( ( ( ( set_difference @ ( singleton @ SV2 ) @ SV5 )
= empty_set )
= $false )
| ( ( in @ SV2 @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV5: $i,SV2: $i] :
( ( ( in @ SV2 @ SV5 )
= $false )
| ( ( ( set_difference @ ( singleton @ SV2 ) @ SV5 )
= empty_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(47,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ( SV7
!= ( unordered_pair @ SV3 @ SV6 ) )
= $true )
| ( ( ! [SY20: $i] :
~ ( ~ ( ~ ( in @ SY20 @ SV7 )
| ( SY20 = SV3 )
| ( SY20 = SV6 ) )
| ~ ( ~ ( ( SY20 = SV3 )
| ( SY20 = SV6 ) )
| ( in @ SY20 @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(48,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ( ~ ! [SY21: $i] :
~ ( ~ ( ~ ( in @ SY21 @ SV7 )
| ( SY21 = SV3 )
| ( SY21 = SV6 ) )
| ~ ( ~ ( ( SY21 = SV3 )
| ( SY21 = SV6 ) )
| ( in @ SY21 @ SV7 ) ) ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[44]) ).
thf(49,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false )
| ( ( ! [SY20: $i] :
~ ( ~ ( ~ ( in @ SY20 @ SV7 )
| ( SY20 = SV3 )
| ( SY20 = SV6 ) )
| ~ ( ~ ( ( SY20 = SV3 )
| ( SY20 = SV6 ) )
| ( in @ SY20 @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(50,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ( ! [SY21: $i] :
~ ( ~ ( ~ ( in @ SY21 @ SV7 )
| ( SY21 = SV3 )
| ( SY21 = SV6 ) )
| ~ ( ~ ( ( SY21 = SV3 )
| ( SY21 = SV6 ) )
| ( in @ SY21 @ SV7 ) ) ) )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(51,plain,
! [SV6: $i,SV3: $i,SV7: $i,SV8: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV8 @ SV7 )
| ( SV8 = SV3 )
| ( SV8 = SV6 ) )
| ~ ( ~ ( ( SV8 = SV3 )
| ( SV8 = SV6 ) )
| ( in @ SV8 @ SV7 ) ) ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(52,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK3_SY21 @ SV6 @ SV3 @ SV7 ) @ SV7 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ~ ( ~ ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ( in @ ( sK3_SY21 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) ) )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[50]) ).
thf(53,plain,
! [SV6: $i,SV3: $i,SV7: $i,SV8: $i] :
( ( ( ~ ( ~ ( in @ SV8 @ SV7 )
| ( SV8 = SV3 )
| ( SV8 = SV6 ) )
| ~ ( ~ ( ( SV8 = SV3 )
| ( SV8 = SV6 ) )
| ( in @ SV8 @ SV7 ) ) )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(54,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_SY21 @ SV6 @ SV3 @ SV7 ) @ SV7 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ~ ( ~ ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ( in @ ( sK3_SY21 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[52]) ).
thf(55,plain,
! [SV6: $i,SV3: $i,SV7: $i,SV8: $i] :
( ( ( ~ ( ~ ( in @ SV8 @ SV7 )
| ( SV8 = SV3 )
| ( SV8 = SV6 ) ) )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(56,plain,
! [SV7: $i,SV6: $i,SV3: $i,SV8: $i] :
( ( ( ~ ( ~ ( ( SV8 = SV3 )
| ( SV8 = SV6 ) )
| ( in @ SV8 @ SV7 ) ) )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[53]) ).
thf(57,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_SY21 @ SV6 @ SV3 @ SV7 ) @ SV7 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ( in @ ( sK3_SY21 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(58,plain,
! [SV6: $i,SV3: $i,SV7: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV7 )
| ( SV8 = SV3 )
| ( SV8 = SV6 ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[55]) ).
thf(59,plain,
! [SV7: $i,SV6: $i,SV3: $i,SV8: $i] :
( ( ( ~ ( ( SV8 = SV3 )
| ( SV8 = SV6 ) )
| ( in @ SV8 @ SV7 ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[56]) ).
thf(60,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( in @ ( sK3_SY21 @ SV6 @ SV3 @ SV7 ) @ SV7 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ( in @ ( sK3_SY21 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(61,plain,
! [SV6: $i,SV3: $i,SV7: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV7 ) )
= $true )
| ( ( ( SV8 = SV3 )
| ( SV8 = SV6 ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(62,plain,
! [SV7: $i,SV6: $i,SV3: $i,SV8: $i] :
( ( ( ~ ( ( SV8 = SV3 )
| ( SV8 = SV6 ) ) )
= $true )
| ( ( in @ SV8 @ SV7 )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(63,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( in @ ( sK3_SY21 @ SV6 @ SV3 @ SV7 ) @ SV7 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ( in @ ( sK3_SY21 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(64,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ( in @ ( sK3_SY21 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[60]) ).
thf(65,plain,
! [SV6: $i,SV3: $i,SV7: $i,SV8: $i] :
( ( ( in @ SV8 @ SV7 )
= $false )
| ( ( ( SV8 = SV3 )
| ( SV8 = SV6 ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(66,plain,
! [SV7: $i,SV6: $i,SV3: $i,SV8: $i] :
( ( ( ( SV8 = SV3 )
| ( SV8 = SV6 ) )
= $false )
| ( ( in @ SV8 @ SV7 )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( in @ ( sK3_SY21 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( ~ ( ~ ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ( in @ ( sK3_SY21 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[63]) ).
thf(68,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
= $false )
| ( ( ~ ( ~ ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ( in @ ( sK3_SY21 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(69,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 )
= $false )
| ( ( ~ ( ~ ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ( in @ ( sK3_SY21 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[64]) ).
thf(70,plain,
! [SV7: $i,SV6: $i,SV3: $i,SV8: $i] :
( ( ( SV8 = SV3 )
= $true )
| ( ( SV8 = SV6 )
= $true )
| ( ( in @ SV8 @ SV7 )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(71,plain,
! [SV6: $i,SV7: $i,SV3: $i,SV8: $i] :
( ( ( SV8 = SV3 )
= $false )
| ( ( in @ SV8 @ SV7 )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(72,plain,
! [SV3: $i,SV7: $i,SV6: $i,SV8: $i] :
( ( ( SV8 = SV6 )
= $false )
| ( ( in @ SV8 @ SV7 )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[66]) ).
thf(73,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ( in @ ( sK3_SY21 @ SV6 @ SV3 @ SV7 ) @ SV7 ) )
= $false )
| ( ( in @ ( sK3_SY21 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(74,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ( in @ ( sK3_SY21 @ SV6 @ SV3 @ SV7 ) @ SV7 ) )
= $false )
| ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(75,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ( in @ ( sK3_SY21 @ SV6 @ SV3 @ SV7 ) @ SV7 ) )
= $false )
| ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(76,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 ) ) )
= $false )
| ( ( in @ ( sK3_SY21 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(77,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( in @ ( sK3_SY21 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $false )
| ( ( in @ ( sK3_SY21 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[73]) ).
thf(78,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 ) ) )
= $false )
| ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(79,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( in @ ( sK3_SY21 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $false )
| ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[74]) ).
thf(80,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 ) ) )
= $false )
| ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(81,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( in @ ( sK3_SY21 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $false )
| ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[75]) ).
thf(82,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
= $true )
| ( ( in @ ( sK3_SY21 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(83,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
= $true )
| ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[78]) ).
thf(84,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
= $true )
| ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[80]) ).
thf(85,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
= $true )
| ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 )
= $true )
| ( ( in @ ( sK3_SY21 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(86,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
= $true )
| ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 )
= $true )
| ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(87,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV3 )
= $true )
| ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 )
= $true )
| ( ( ( sK3_SY21 @ SV6 @ SV3 @ SV7 )
= SV6 )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(88,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[20,87,86,85,81,79,77,72,71,70,46,45,29,26]) ).
thf(89,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET881+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.19 % Computer : n019.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Oct 6 14:55:46 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.23
% 0.08/0.23 No.of.Axioms: 4
% 0.08/0.23
% 0.08/0.23 Length.of.Defs: 0
% 0.08/0.23
% 0.08/0.23 Contains.Choice.Funs: false
% 0.08/0.23 ..
% 0.08/0.23
% 0.08/0.23 ********************************
% 0.08/0.23 * All subproblems solved! *
% 0.08/0.23 ********************************
% 0.08/0.23 % 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:88,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.08/0.23
% 0.08/0.23 %**** Beginning of derivation protocol ****
% 0.08/0.23 % SZS output start CNFRefutation
% See solution above
% 0.08/0.23
% 0.08/0.23 %**** End of derivation protocol ****
% 0.08/0.23 %**** no. of clauses in derivation: 86 ****
% 0.08/0.23 %**** clause counter: 88 ****
% 0.08/0.23
% 0.08/0.23 % 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:88,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------