%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU142+2 : TPTP v9.3.1. Released v3.3.0.
% 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 : n011.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 10:43:02 AM UTC 2026
% Result : Theorem 0.55s 0.33s
% Output : CNFRefutation 0.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 125 ( 53 unt; 0 typ; 0 def)
% Number of atoms : 989 ( 587 equ; 0 cnn)
% Maximal formula atoms : 4 ( 7 avg)
% Number of connectives : 1574 ( 325 ~; 384 |; 0 &; 853 @)
% ( 12 <=>; 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 : 17 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 315 ( 0 ^; 315 !; 0 ?; 315 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
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_proper_subset,type,
proper_subset: $i > $i > $o ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY19,type,
sK2_SY19: $i > $i > $i ).
thf(tp_sK3_SY24,type,
sK3_SY24: $i > $i > $i > $i ).
thf(tp_set_difference,type,
set_difference: $i > $i > $i ).
thf(tp_set_intersection2,type,
set_intersection2: $i > $i > $i ).
thf(tp_set_union2,type,
set_union2: $i > $i > $i ).
thf(tp_singleton,type,
singleton: $i > $i ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_unordered_pair,type,
unordered_pair: $i > $i > $i ).
thf(19,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k4_xboole_0) ).
thf(20,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_xboole_0) ).
thf(21,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_xboole_0) ).
thf(22,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_tarski) ).
thf(23,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_xboole_0) ).
thf(24,axiom,
$true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tarski) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( unordered_pair @ A @ B ) )
<=> ! [D: $i] :
( ( in @ D @ C )
<=> ( ( D = A )
| ( D = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(63,conjecture,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
thf(64,negated_conjecture,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[63]) ).
thf(65,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $false ),
inference(unfold_def,[status(thm)],[64]) ).
thf(66,plain,
$true = $true,
inference(unfold_def,[status(thm)],[19]) ).
thf(67,plain,
$true = $true,
inference(unfold_def,[status(thm)],[20]) ).
thf(68,plain,
$true = $true,
inference(unfold_def,[status(thm)],[21]) ).
thf(69,plain,
$true = $true,
inference(unfold_def,[status(thm)],[22]) ).
thf(70,plain,
$true = $true,
inference(unfold_def,[status(thm)],[23]) ).
thf(71,plain,
$true = $true,
inference(unfold_def,[status(thm)],[24]) ).
thf(72,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)],[31]) ).
thf(73,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(74,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(75,plain,
( ( ( unordered_pair @ sK1_A @ sK1_A )
= ( singleton @ sK1_A ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[65]) ).
thf(76,plain,
( ( ( unordered_pair @ sK1_A @ sK1_A )
!= ( singleton @ sK1_A ) )
= $true ),
inference(polarity_switch,[status(thm)],[75]) ).
thf(77,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(78,plain,
( ( ! [A: $i,B: $i] :
( ( B
= ( singleton @ A ) )
<=> ! [C: $i] :
( ( in @ C @ B )
<=> ( C = A ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(79,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)],[72]) ).
thf(80,plain,
$true = $true,
inference(copy,[status(thm)],[71]) ).
thf(81,plain,
$true = $true,
inference(copy,[status(thm)],[70]) ).
thf(82,plain,
$true = $true,
inference(copy,[status(thm)],[69]) ).
thf(83,plain,
$true = $true,
inference(copy,[status(thm)],[68]) ).
thf(84,plain,
$true = $true,
inference(copy,[status(thm)],[67]) ).
thf(85,plain,
$true = $true,
inference(copy,[status(thm)],[66]) ).
thf(86,plain,
( ( ( unordered_pair @ sK1_A @ sK1_A )
!= ( singleton @ sK1_A ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(87,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)],[78]) ).
thf(88,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)],[79]) ).
thf(89,plain,
! [SV1: $i] :
( ( ! [SY10: $i] :
( ( unordered_pair @ SV1 @ SY10 )
= ( unordered_pair @ SY10 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(90,plain,
( ( ( unordered_pair @ sK1_A @ sK1_A )
= ( singleton @ sK1_A ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(91,plain,
! [SV2: $i] :
( ( ! [SY11: $i] :
~ ( ~ ( ( SY11
!= ( singleton @ SV2 ) )
| ! [SY12: $i] :
~ ( ~ ( ~ ( in @ SY12 @ SY11 )
| ( SY12 = SV2 ) )
| ~ ( ( SY12 != SV2 )
| ( in @ SY12 @ SY11 ) ) ) )
| ~ ( ~ ! [SY13: $i] :
~ ( ~ ( ~ ( in @ SY13 @ SY11 )
| ( SY13 = SV2 ) )
| ~ ( ( SY13 != SV2 )
| ( in @ SY13 @ SY11 ) ) )
| ( SY11
= ( singleton @ SV2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(92,plain,
! [SV3: $i] :
( ( ! [SY14: $i,SY15: $i] :
~ ( ~ ( ( SY15
!= ( unordered_pair @ SV3 @ SY14 ) )
| ! [SY16: $i] :
~ ( ~ ( ~ ( in @ SY16 @ SY15 )
| ( SY16 = SV3 )
| ( SY16 = SY14 ) )
| ~ ( ~ ( ( SY16 = SV3 )
| ( SY16 = SY14 ) )
| ( in @ SY16 @ SY15 ) ) ) )
| ~ ( ~ ! [SY17: $i] :
~ ( ~ ( ~ ( in @ SY17 @ SY15 )
| ( SY17 = SV3 )
| ( SY17 = SY14 ) )
| ~ ( ~ ( ( SY17 = SV3 )
| ( SY17 = SY14 ) )
| ( in @ SY17 @ SY15 ) ) )
| ( SY15
= ( unordered_pair @ SV3 @ SY14 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(93,plain,
! [SV4: $i,SV1: $i] :
( ( ( unordered_pair @ SV1 @ SV4 )
= ( unordered_pair @ SV4 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(94,plain,
! [SV2: $i,SV5: $i] :
( ( ~ ( ~ ( ( SV5
!= ( singleton @ SV2 ) )
| ! [SY18: $i] :
~ ( ~ ( ~ ( in @ SY18 @ SV5 )
| ( SY18 = SV2 ) )
| ~ ( ( SY18 != SV2 )
| ( in @ SY18 @ SV5 ) ) ) )
| ~ ( ~ ! [SY19: $i] :
~ ( ~ ( ~ ( in @ SY19 @ SV5 )
| ( SY19 = SV2 ) )
| ~ ( ( SY19 != SV2 )
| ( in @ SY19 @ SV5 ) ) )
| ( SV5
= ( singleton @ SV2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(95,plain,
! [SV6: $i,SV3: $i] :
( ( ! [SY20: $i] :
~ ( ~ ( ( SY20
!= ( unordered_pair @ SV3 @ SV6 ) )
| ! [SY21: $i] :
~ ( ~ ( ~ ( in @ SY21 @ SY20 )
| ( SY21 = SV3 )
| ( SY21 = SV6 ) )
| ~ ( ~ ( ( SY21 = SV3 )
| ( SY21 = SV6 ) )
| ( in @ SY21 @ SY20 ) ) ) )
| ~ ( ~ ! [SY22: $i] :
~ ( ~ ( ~ ( in @ SY22 @ SY20 )
| ( SY22 = SV3 )
| ( SY22 = SV6 ) )
| ~ ( ~ ( ( SY22 = SV3 )
| ( SY22 = SV6 ) )
| ( in @ SY22 @ SY20 ) ) )
| ( SY20
= ( unordered_pair @ SV3 @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(96,plain,
! [SV2: $i,SV5: $i] :
( ( ~ ( ( SV5
!= ( singleton @ SV2 ) )
| ! [SY18: $i] :
~ ( ~ ( ~ ( in @ SY18 @ SV5 )
| ( SY18 = SV2 ) )
| ~ ( ( SY18 != SV2 )
| ( in @ SY18 @ SV5 ) ) ) )
| ~ ( ~ ! [SY19: $i] :
~ ( ~ ( ~ ( in @ SY19 @ SV5 )
| ( SY19 = SV2 ) )
| ~ ( ( SY19 != SV2 )
| ( in @ SY19 @ SV5 ) ) )
| ( SV5
= ( singleton @ SV2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(97,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ~ ( ~ ( ( SV7
!= ( unordered_pair @ SV3 @ SV6 ) )
| ! [SY23: $i] :
~ ( ~ ( ~ ( in @ SY23 @ SV7 )
| ( SY23 = SV3 )
| ( SY23 = SV6 ) )
| ~ ( ~ ( ( SY23 = SV3 )
| ( SY23 = SV6 ) )
| ( in @ SY23 @ SV7 ) ) ) )
| ~ ( ~ ! [SY24: $i] :
~ ( ~ ( ~ ( in @ SY24 @ SV7 )
| ( SY24 = SV3 )
| ( SY24 = SV6 ) )
| ~ ( ~ ( ( SY24 = SV3 )
| ( SY24 = SV6 ) )
| ( in @ SY24 @ SV7 ) ) )
| ( SV7
= ( unordered_pair @ SV3 @ SV6 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(98,plain,
! [SV2: $i,SV5: $i] :
( ( ~ ( ( SV5
!= ( singleton @ SV2 ) )
| ! [SY18: $i] :
~ ( ~ ( ~ ( in @ SY18 @ SV5 )
| ( SY18 = SV2 ) )
| ~ ( ( SY18 != SV2 )
| ( in @ SY18 @ SV5 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(99,plain,
! [SV2: $i,SV5: $i] :
( ( ~ ( ~ ! [SY19: $i] :
~ ( ~ ( ~ ( in @ SY19 @ SV5 )
| ( SY19 = SV2 ) )
| ~ ( ( SY19 != SV2 )
| ( in @ SY19 @ SV5 ) ) )
| ( SV5
= ( singleton @ SV2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[96]) ).
thf(100,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ~ ( ( SV7
!= ( unordered_pair @ SV3 @ SV6 ) )
| ! [SY23: $i] :
~ ( ~ ( ~ ( in @ SY23 @ SV7 )
| ( SY23 = SV3 )
| ( SY23 = SV6 ) )
| ~ ( ~ ( ( SY23 = SV3 )
| ( SY23 = SV6 ) )
| ( in @ SY23 @ SV7 ) ) ) )
| ~ ( ~ ! [SY24: $i] :
~ ( ~ ( ~ ( in @ SY24 @ SV7 )
| ( SY24 = SV3 )
| ( SY24 = SV6 ) )
| ~ ( ~ ( ( SY24 = SV3 )
| ( SY24 = SV6 ) )
| ( in @ SY24 @ SV7 ) ) )
| ( SV7
= ( unordered_pair @ SV3 @ SV6 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(101,plain,
! [SV2: $i,SV5: $i] :
( ( ( SV5
!= ( singleton @ SV2 ) )
| ! [SY18: $i] :
~ ( ~ ( ~ ( in @ SY18 @ SV5 )
| ( SY18 = SV2 ) )
| ~ ( ( SY18 != SV2 )
| ( in @ SY18 @ SV5 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(102,plain,
! [SV2: $i,SV5: $i] :
( ( ~ ! [SY19: $i] :
~ ( ~ ( ~ ( in @ SY19 @ SV5 )
| ( SY19 = SV2 ) )
| ~ ( ( SY19 != SV2 )
| ( in @ SY19 @ SV5 ) ) )
| ( SV5
= ( singleton @ SV2 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[99]) ).
thf(103,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ~ ( ( SV7
!= ( unordered_pair @ SV3 @ SV6 ) )
| ! [SY23: $i] :
~ ( ~ ( ~ ( in @ SY23 @ SV7 )
| ( SY23 = SV3 )
| ( SY23 = SV6 ) )
| ~ ( ~ ( ( SY23 = SV3 )
| ( SY23 = SV6 ) )
| ( in @ SY23 @ SV7 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(104,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ~ ( ~ ! [SY24: $i] :
~ ( ~ ( ~ ( in @ SY24 @ SV7 )
| ( SY24 = SV3 )
| ( SY24 = SV6 ) )
| ~ ( ~ ( ( SY24 = SV3 )
| ( SY24 = SV6 ) )
| ( in @ SY24 @ SV7 ) ) )
| ( SV7
= ( unordered_pair @ SV3 @ SV6 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[100]) ).
thf(105,plain,
! [SV2: $i,SV5: $i] :
( ( ( SV5
!= ( singleton @ SV2 ) )
= $true )
| ( ( ! [SY18: $i] :
~ ( ~ ( ~ ( in @ SY18 @ SV5 )
| ( SY18 = SV2 ) )
| ~ ( ( SY18 != SV2 )
| ( in @ SY18 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[101]) ).
thf(106,plain,
! [SV2: $i,SV5: $i] :
( ( ( ~ ! [SY19: $i] :
~ ( ~ ( ~ ( in @ SY19 @ SV5 )
| ( SY19 = SV2 ) )
| ~ ( ( SY19 != SV2 )
| ( in @ SY19 @ SV5 ) ) ) )
= $true )
| ( ( SV5
= ( singleton @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(107,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ( SV7
!= ( unordered_pair @ SV3 @ SV6 ) )
| ! [SY23: $i] :
~ ( ~ ( ~ ( in @ SY23 @ SV7 )
| ( SY23 = SV3 )
| ( SY23 = SV6 ) )
| ~ ( ~ ( ( SY23 = SV3 )
| ( SY23 = SV6 ) )
| ( in @ SY23 @ SV7 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[103]) ).
thf(108,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ~ ! [SY24: $i] :
~ ( ~ ( ~ ( in @ SY24 @ SV7 )
| ( SY24 = SV3 )
| ( SY24 = SV6 ) )
| ~ ( ~ ( ( SY24 = SV3 )
| ( SY24 = SV6 ) )
| ( in @ SY24 @ SV7 ) ) )
| ( SV7
= ( unordered_pair @ SV3 @ SV6 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[104]) ).
thf(109,plain,
! [SV2: $i,SV5: $i] :
( ( ( SV5
= ( singleton @ SV2 ) )
= $false )
| ( ( ! [SY18: $i] :
~ ( ~ ( ~ ( in @ SY18 @ SV5 )
| ( SY18 = SV2 ) )
| ~ ( ( SY18 != SV2 )
| ( in @ SY18 @ SV5 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(110,plain,
! [SV2: $i,SV5: $i] :
( ( ( ! [SY19: $i] :
~ ( ~ ( ~ ( in @ SY19 @ SV5 )
| ( SY19 = SV2 ) )
| ~ ( ( SY19 != SV2 )
| ( in @ SY19 @ SV5 ) ) ) )
= $false )
| ( ( SV5
= ( singleton @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(111,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ( SV7
!= ( unordered_pair @ SV3 @ SV6 ) )
= $true )
| ( ( ! [SY23: $i] :
~ ( ~ ( ~ ( in @ SY23 @ SV7 )
| ( SY23 = SV3 )
| ( SY23 = SV6 ) )
| ~ ( ~ ( ( SY23 = SV3 )
| ( SY23 = SV6 ) )
| ( in @ SY23 @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(112,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ( ~ ! [SY24: $i] :
~ ( ~ ( ~ ( in @ SY24 @ SV7 )
| ( SY24 = SV3 )
| ( SY24 = SV6 ) )
| ~ ( ~ ( ( SY24 = SV3 )
| ( SY24 = SV6 ) )
| ( in @ SY24 @ SV7 ) ) ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(113,plain,
! [SV2: $i,SV5: $i,SV8: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV8 @ SV5 )
| ( SV8 = SV2 ) )
| ~ ( ( SV8 != SV2 )
| ( in @ SV8 @ SV5 ) ) ) )
= $true )
| ( ( SV5
= ( singleton @ SV2 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(114,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK2_SY19 @ SV2 @ SV5 ) @ SV5 )
| ( ( sK2_SY19 @ SV2 @ SV5 )
= SV2 ) )
| ~ ( ( ( sK2_SY19 @ SV2 @ SV5 )
!= SV2 )
| ( in @ ( sK2_SY19 @ SV2 @ SV5 ) @ SV5 ) ) ) )
= $false )
| ( ( SV5
= ( singleton @ SV2 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[110]) ).
thf(115,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false )
| ( ( ! [SY23: $i] :
~ ( ~ ( ~ ( in @ SY23 @ SV7 )
| ( SY23 = SV3 )
| ( SY23 = SV6 ) )
| ~ ( ~ ( ( SY23 = SV3 )
| ( SY23 = SV6 ) )
| ( in @ SY23 @ SV7 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(116,plain,
! [SV6: $i,SV3: $i,SV7: $i] :
( ( ( ! [SY24: $i] :
~ ( ~ ( ~ ( in @ SY24 @ SV7 )
| ( SY24 = SV3 )
| ( SY24 = SV6 ) )
| ~ ( ~ ( ( SY24 = SV3 )
| ( SY24 = SV6 ) )
| ( in @ SY24 @ SV7 ) ) ) )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(117,plain,
! [SV2: $i,SV5: $i,SV8: $i] :
( ( ( ~ ( ~ ( in @ SV8 @ SV5 )
| ( SV8 = SV2 ) )
| ~ ( ( SV8 != SV2 )
| ( in @ SV8 @ SV5 ) ) )
= $false )
| ( ( SV5
= ( singleton @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(118,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ( ~ ( in @ ( sK2_SY19 @ SV2 @ SV5 ) @ SV5 )
| ( ( sK2_SY19 @ SV2 @ SV5 )
= SV2 ) )
| ~ ( ( ( sK2_SY19 @ SV2 @ SV5 )
!= SV2 )
| ( in @ ( sK2_SY19 @ SV2 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5
= ( singleton @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[114]) ).
thf(119,plain,
! [SV6: $i,SV3: $i,SV7: $i,SV9: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV9 @ SV7 )
| ( SV9 = SV3 )
| ( SV9 = SV6 ) )
| ~ ( ~ ( ( SV9 = SV3 )
| ( SV9 = SV6 ) )
| ( in @ SV9 @ SV7 ) ) ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(120,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK3_SY24 @ SV6 @ SV3 @ SV7 ) @ SV7 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ~ ( ~ ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ( in @ ( sK3_SY24 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) ) )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[116]) ).
thf(121,plain,
! [SV2: $i,SV5: $i,SV8: $i] :
( ( ( ~ ( ~ ( in @ SV8 @ SV5 )
| ( SV8 = SV2 ) ) )
= $false )
| ( ( SV5
= ( singleton @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(122,plain,
! [SV5: $i,SV2: $i,SV8: $i] :
( ( ( ~ ( ( SV8 != SV2 )
| ( in @ SV8 @ SV5 ) ) )
= $false )
| ( ( SV5
= ( singleton @ SV2 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[117]) ).
thf(123,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ( ~ ( in @ ( sK2_SY19 @ SV2 @ SV5 ) @ SV5 )
| ( ( sK2_SY19 @ SV2 @ SV5 )
= SV2 ) ) )
= $true )
| ( ( ~ ( ( ( sK2_SY19 @ SV2 @ SV5 )
!= SV2 )
| ( in @ ( sK2_SY19 @ SV2 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5
= ( singleton @ SV2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(124,plain,
! [SV6: $i,SV3: $i,SV7: $i,SV9: $i] :
( ( ( ~ ( ~ ( in @ SV9 @ SV7 )
| ( SV9 = SV3 )
| ( SV9 = SV6 ) )
| ~ ( ~ ( ( SV9 = SV3 )
| ( SV9 = SV6 ) )
| ( in @ SV9 @ SV7 ) ) )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(125,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_SY24 @ SV6 @ SV3 @ SV7 ) @ SV7 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ~ ( ~ ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ( in @ ( sK3_SY24 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[120]) ).
thf(126,plain,
! [SV2: $i,SV5: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV5 )
| ( SV8 = SV2 ) )
= $true )
| ( ( SV5
= ( singleton @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[121]) ).
thf(127,plain,
! [SV5: $i,SV2: $i,SV8: $i] :
( ( ( ( SV8 != SV2 )
| ( in @ SV8 @ SV5 ) )
= $true )
| ( ( SV5
= ( singleton @ SV2 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[122]) ).
thf(128,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ( in @ ( sK2_SY19 @ SV2 @ SV5 ) @ SV5 )
| ( ( sK2_SY19 @ SV2 @ SV5 )
= SV2 ) )
= $false )
| ( ( ~ ( ( ( sK2_SY19 @ SV2 @ SV5 )
!= SV2 )
| ( in @ ( sK2_SY19 @ SV2 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5
= ( singleton @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(129,plain,
! [SV6: $i,SV3: $i,SV7: $i,SV9: $i] :
( ( ( ~ ( ~ ( in @ SV9 @ SV7 )
| ( SV9 = SV3 )
| ( SV9 = SV6 ) ) )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(130,plain,
! [SV7: $i,SV6: $i,SV3: $i,SV9: $i] :
( ( ( ~ ( ~ ( ( SV9 = SV3 )
| ( SV9 = SV6 ) )
| ( in @ SV9 @ SV7 ) ) )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[124]) ).
thf(131,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( ~ ( in @ ( sK3_SY24 @ SV6 @ SV3 @ SV7 ) @ SV7 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 ) ) )
= $true )
| ( ( ~ ( ~ ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ( in @ ( sK3_SY24 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(132,plain,
! [SV2: $i,SV5: $i,SV8: $i] :
( ( ( ~ ( in @ SV8 @ SV5 ) )
= $true )
| ( ( SV8 = SV2 )
= $true )
| ( ( SV5
= ( singleton @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(133,plain,
! [SV5: $i,SV2: $i,SV8: $i] :
( ( ( SV8 != SV2 )
= $true )
| ( ( in @ SV8 @ SV5 )
= $true )
| ( ( SV5
= ( singleton @ SV2 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(134,plain,
! [SV5: $i,SV2: $i] :
( ( ( ~ ( in @ ( sK2_SY19 @ SV2 @ SV5 ) @ SV5 ) )
= $false )
| ( ( ~ ( ( ( sK2_SY19 @ SV2 @ SV5 )
!= SV2 )
| ( in @ ( sK2_SY19 @ SV2 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5
= ( singleton @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(135,plain,
! [SV5: $i,SV2: $i] :
( ( ( ( sK2_SY19 @ SV2 @ SV5 )
= SV2 )
= $false )
| ( ( ~ ( ( ( sK2_SY19 @ SV2 @ SV5 )
!= SV2 )
| ( in @ ( sK2_SY19 @ SV2 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5
= ( singleton @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[128]) ).
thf(136,plain,
! [SV6: $i,SV3: $i,SV7: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV7 )
| ( SV9 = SV3 )
| ( SV9 = SV6 ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[129]) ).
thf(137,plain,
! [SV7: $i,SV6: $i,SV3: $i,SV9: $i] :
( ( ( ~ ( ( SV9 = SV3 )
| ( SV9 = SV6 ) )
| ( in @ SV9 @ SV7 ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[130]) ).
thf(138,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( in @ ( sK3_SY24 @ SV6 @ SV3 @ SV7 ) @ SV7 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ( in @ ( sK3_SY24 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(139,plain,
! [SV2: $i,SV5: $i,SV8: $i] :
( ( ( in @ SV8 @ SV5 )
= $false )
| ( ( SV8 = SV2 )
= $true )
| ( ( SV5
= ( singleton @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(140,plain,
! [SV5: $i,SV2: $i,SV8: $i] :
( ( ( SV8 = SV2 )
= $false )
| ( ( in @ SV8 @ SV5 )
= $true )
| ( ( SV5
= ( singleton @ SV2 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(141,plain,
! [SV5: $i,SV2: $i] :
( ( ( in @ ( sK2_SY19 @ SV2 @ SV5 ) @ SV5 )
= $true )
| ( ( ~ ( ( ( sK2_SY19 @ SV2 @ SV5 )
!= SV2 )
| ( in @ ( sK2_SY19 @ SV2 @ SV5 ) @ SV5 ) ) )
= $true )
| ( ( SV5
= ( singleton @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[134]) ).
thf(142,plain,
! [SV5: $i,SV2: $i] :
( ( ( ( ( sK2_SY19 @ SV2 @ SV5 )
!= SV2 )
| ( in @ ( sK2_SY19 @ SV2 @ SV5 ) @ SV5 ) )
= $false )
| ( ( ( sK2_SY19 @ SV2 @ SV5 )
= SV2 )
= $false )
| ( ( SV5
= ( singleton @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(143,plain,
! [SV6: $i,SV3: $i,SV7: $i,SV9: $i] :
( ( ( ~ ( in @ SV9 @ SV7 ) )
= $true )
| ( ( ( SV9 = SV3 )
| ( SV9 = SV6 ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[136]) ).
thf(144,plain,
! [SV7: $i,SV6: $i,SV3: $i,SV9: $i] :
( ( ( ~ ( ( SV9 = SV3 )
| ( SV9 = SV6 ) ) )
= $true )
| ( ( in @ SV9 @ SV7 )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[137]) ).
thf(145,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( in @ ( sK3_SY24 @ SV6 @ SV3 @ SV7 ) @ SV7 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ( in @ ( sK3_SY24 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(146,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
= $false )
| ( ( ~ ( ~ ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ( in @ ( sK3_SY24 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[138]) ).
thf(147,plain,
! [SV5: $i,SV2: $i] :
( ( ( ( ( sK2_SY19 @ SV2 @ SV5 )
!= SV2 )
| ( in @ ( sK2_SY19 @ SV2 @ SV5 ) @ SV5 ) )
= $false )
| ( ( in @ ( sK2_SY19 @ SV2 @ SV5 ) @ SV5 )
= $true )
| ( ( SV5
= ( singleton @ SV2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(148,plain,
! [SV5: $i,SV2: $i] :
( ( ( ( sK2_SY19 @ SV2 @ SV5 )
!= SV2 )
= $false )
| ( ( ( sK2_SY19 @ SV2 @ SV5 )
= SV2 )
= $false )
| ( ( SV5
= ( singleton @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(149,plain,
! [SV5: $i,SV2: $i] :
( ( ( in @ ( sK2_SY19 @ SV2 @ SV5 ) @ SV5 )
= $false )
| ( ( ( sK2_SY19 @ SV2 @ SV5 )
= SV2 )
= $false )
| ( ( SV5
= ( singleton @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[142]) ).
thf(150,plain,
! [SV6: $i,SV3: $i,SV7: $i,SV9: $i] :
( ( ( in @ SV9 @ SV7 )
= $false )
| ( ( ( SV9 = SV3 )
| ( SV9 = SV6 ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(151,plain,
! [SV7: $i,SV6: $i,SV3: $i,SV9: $i] :
( ( ( ( SV9 = SV3 )
| ( SV9 = SV6 ) )
= $false )
| ( ( in @ SV9 @ SV7 )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(152,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( in @ ( sK3_SY24 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( ~ ( ~ ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ( in @ ( sK3_SY24 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[145]) ).
thf(153,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
= $false )
| ( ( ~ ( ~ ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ( in @ ( sK3_SY24 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(154,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 )
= $false )
| ( ( ~ ( ~ ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ( in @ ( sK3_SY24 @ SV6 @ SV3 @ SV7 ) @ SV7 ) ) )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[146]) ).
thf(155,plain,
! [SV5: $i,SV2: $i] :
( ( ( ( sK2_SY19 @ SV2 @ SV5 )
!= SV2 )
= $false )
| ( ( in @ ( sK2_SY19 @ SV2 @ SV5 ) @ SV5 )
= $true )
| ( ( SV5
= ( singleton @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(156,plain,
! [SV5: $i,SV2: $i] :
( ( ( in @ ( sK2_SY19 @ SV2 @ SV5 ) @ SV5 )
= $false )
| ( ( in @ ( sK2_SY19 @ SV2 @ SV5 ) @ SV5 )
= $true )
| ( ( SV5
= ( singleton @ SV2 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[147]) ).
thf(157,plain,
! [SV5: $i,SV2: $i] :
( ( ( ( sK2_SY19 @ SV2 @ SV5 )
= SV2 )
= $true )
| ( ( ( sK2_SY19 @ SV2 @ SV5 )
= SV2 )
= $false )
| ( ( SV5
= ( singleton @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[148]) ).
thf(158,plain,
! [SV7: $i,SV6: $i,SV3: $i,SV9: $i] :
( ( ( SV9 = SV3 )
= $true )
| ( ( SV9 = SV6 )
= $true )
| ( ( in @ SV9 @ SV7 )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(159,plain,
! [SV6: $i,SV7: $i,SV3: $i,SV9: $i] :
( ( ( SV9 = SV3 )
= $false )
| ( ( in @ SV9 @ SV7 )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(160,plain,
! [SV3: $i,SV7: $i,SV6: $i,SV9: $i] :
( ( ( SV9 = SV6 )
= $false )
| ( ( in @ SV9 @ SV7 )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[151]) ).
thf(161,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ( in @ ( sK3_SY24 @ SV6 @ SV3 @ SV7 ) @ SV7 ) )
= $false )
| ( ( in @ ( sK3_SY24 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(162,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ( in @ ( sK3_SY24 @ SV6 @ SV3 @ SV7 ) @ SV7 ) )
= $false )
| ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(163,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
| ( in @ ( sK3_SY24 @ SV6 @ SV3 @ SV7 ) @ SV7 ) )
= $false )
| ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(164,plain,
! [SV5: $i,SV2: $i] :
( ( ( ( sK2_SY19 @ SV2 @ SV5 )
= SV2 )
= $true )
| ( ( in @ ( sK2_SY19 @ SV2 @ SV5 ) @ SV5 )
= $true )
| ( ( SV5
= ( singleton @ SV2 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[155]) ).
thf(165,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 ) ) )
= $false )
| ( ( in @ ( sK3_SY24 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(166,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( in @ ( sK3_SY24 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $false )
| ( ( in @ ( sK3_SY24 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[161]) ).
thf(167,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 ) ) )
= $false )
| ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[162]) ).
thf(168,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( in @ ( sK3_SY24 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $false )
| ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[162]) ).
thf(169,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ~ ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 ) ) )
= $false )
| ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(170,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( in @ ( sK3_SY24 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $false )
| ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[163]) ).
thf(171,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
= $true )
| ( ( in @ ( sK3_SY24 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(172,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
= $true )
| ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(173,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
| ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 ) )
= $true )
| ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[169]) ).
thf(174,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
= $true )
| ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 )
= $true )
| ( ( in @ ( sK3_SY24 @ SV6 @ SV3 @ SV7 ) @ SV7 )
= $true )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(175,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
= $true )
| ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 )
= $true )
| ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(176,plain,
! [SV7: $i,SV3: $i,SV6: $i] :
( ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV3 )
= $true )
| ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 )
= $true )
| ( ( ( sK3_SY24 @ SV6 @ SV3 @ SV7 )
= SV6 )
= $false )
| ( ( SV7
= ( unordered_pair @ SV3 @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(177,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[80,176,175,174,170,168,166,164,160,159,158,157,156,149,140,139,93,90,85,84,83,82,81]) ).
thf(178,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[177]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU142+2 : TPTP v9.3.1. Released v3.3.0.
% 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 : n011.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 15:01:36 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.55/0.33
% 0.55/0.33 No.of.Axioms: 9
% 0.55/0.33
% 0.55/0.33 Length.of.Defs: 0
% 0.55/0.33
% 0.55/0.33 Contains.Choice.Funs: false
% 0.55/0.33 ....
% 0.55/0.33
% 0.55/0.33 ********************************
% 0.55/0.33 * All subproblems solved! *
% 0.55/0.33 ********************************
% 0.55/0.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:9,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:177,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.55/0.33
% 0.55/0.33 %**** Beginning of derivation protocol ****
% 0.55/0.33 % SZS output start CNFRefutation
% See solution above
% 0.55/0.33
% 0.55/0.33 %**** End of derivation protocol ****
% 0.55/0.33 %**** no. of clauses in derivation: 125 ****
% 0.55/0.33 %**** clause counter: 177 ****
% 0.55/0.33
% 0.55/0.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:9,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:177,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------