%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU156+3 : 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 : n017.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 10:43:07 AM UTC 2026
% Result : Theorem 0.85s 0.49s
% Output : CNFRefutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of formulae : 170 ( 135 unt; 0 typ; 0 def)
% Number of atoms : 701 ( 441 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 913 ( 266 ~; 98 |; 16 &; 514 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 374 ( 0 ^; 366 !; 8 ?; 374 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_empty,type,
empty: $i > $o ).
thf(tp_ordered_pair,type,
ordered_pair: $i > $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK2_SY27,type,
sK2_SY27: $i ).
thf(tp_sK3_SY30,type,
sK3_SY30: $i ).
thf(tp_sK4_SY32,type,
sK4_SY32: $i ).
thf(tp_sK5_SX0,type,
sK5_SX0: $i ).
thf(tp_sK6_SX0,type,
sK6_SX0: $i ).
thf(tp_sK7_SX0,type,
sK7_SX0: $i ).
thf(tp_sK8_SX0,type,
sK8_SX0: $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(1,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(2,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(4,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(6,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(7,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(8,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(9,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(12,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_zfmisc_1) ).
thf(13,negated_conjecture,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[12]) ).
thf(14,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ordered_pair @ A @ B )
= ( ordered_pair @ C @ D ) )
=> ( ( A = C )
& ( B = D ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[13]) ).
thf(15,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(16,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(17,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(19,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(20,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(21,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(22,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(23,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(26,plain,
( ( ! [SY27: $i,SY28: $i,SY29: $i] :
( ( ( ordered_pair @ sK1_A @ SY27 )
= ( ordered_pair @ SY28 @ SY29 ) )
=> ( ( sK1_A = SY28 )
& ( SY27 = SY29 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[14]) ).
thf(27,plain,
( ( ! [SY30: $i,SY31: $i] :
( ( ( ordered_pair @ sK1_A @ sK2_SY27 )
= ( ordered_pair @ SY30 @ SY31 ) )
=> ( ( sK1_A = SY30 )
& ( sK2_SY27 = SY31 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[26]) ).
thf(28,plain,
( ( ! [SY32: $i] :
( ( ( ordered_pair @ sK1_A @ sK2_SY27 )
= ( ordered_pair @ sK3_SY30 @ SY32 ) )
=> ( ( sK1_A = sK3_SY30 )
& ( sK2_SY27 = SY32 ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[27]) ).
thf(29,plain,
( ( ( ( ordered_pair @ sK1_A @ sK2_SY27 )
= ( ordered_pair @ sK3_SY30 @ sK4_SY32 ) )
=> ( ( sK1_A = sK3_SY30 )
& ( sK2_SY27 = sK4_SY32 ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[28]) ).
thf(30,plain,
( ( ( ordered_pair @ sK1_A @ sK2_SY27 )
= ( ordered_pair @ sK3_SY30 @ sK4_SY32 ) )
= $true ),
inference(standard_cnf,[status(thm)],[29]) ).
thf(31,plain,
( ( ( sK1_A = sK3_SY30 )
& ( sK2_SY27 = sK4_SY32 ) )
= $false ),
inference(standard_cnf,[status(thm)],[29]) ).
thf(32,plain,
( ( sK1_A = sK3_SY30 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[31]) ).
thf(33,plain,
( ( sK2_SY27 = sK4_SY32 )
= $false ),
inference(split_conjecture,[split_conjecture(split,[])],[31]) ).
thf(34,plain,
( ( sK1_A != sK3_SY30 )
= $true ),
inference(polarity_switch,[status(thm)],[32]) ).
thf(35,plain,
( ( sK2_SY27 != sK4_SY32 )
= $true ),
inference(polarity_switch,[status(thm)],[33]) ).
thf(36,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(39,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(40,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(41,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(42,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(43,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(44,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(45,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(46,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(47,plain,
( ( ( ordered_pair @ sK1_A @ sK2_SY27 )
= ( ordered_pair @ sK3_SY30 @ sK4_SY32 ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(48,plain,
( ( sK1_A != sK3_SY30 )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(49,plain,
( ( ~ ! [SX0: $i] :
~ ( empty @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(50,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( singleton @ SX0 )
!= ( unordered_pair @ SX1 @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(51,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ~ ( ~ ~ ( ( ( unordered_pair @ SX0 @ SX1 )
!= ( unordered_pair @ SX2 @ SX3 ) )
| ~ ( ( SX0 != SX2 ) ) )
| ~ ( ( SX0 != SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(52,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(53,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( singleton @ SX0 )
!= ( unordered_pair @ SX1 @ SX2 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(54,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( empty @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(55,plain,
! [SV1: $i] :
( ( ! [SY33: $i] :
( ( unordered_pair @ SV1 @ SY33 )
= ( unordered_pair @ SY33 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(56,plain,
! [SV2: $i] :
( ( ! [SY34: $i] :
( ( ordered_pair @ SV2 @ SY34 )
= ( unordered_pair @ ( unordered_pair @ SV2 @ SY34 ) @ ( singleton @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(57,plain,
! [SV3: $i] :
( ( ! [SY35: $i] :
~ ( empty @ ( ordered_pair @ SV3 @ SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(58,plain,
! [SV4: $i] :
( ( ! [SY36: $i] : ( subset @ SV4 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(59,plain,
! [SV5: $i] :
( ( ( unordered_pair @ SV5 @ SV5 )
= ( singleton @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(60,plain,
( ( sK1_A = sK3_SY30 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(61,plain,
( ( ! [SX0: $i] :
~ ( empty @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(62,plain,
! [SV6: $i] :
( ( ! [SY37: $i,SY38: $i] :
( ( ( singleton @ SV6 )
!= ( unordered_pair @ SY37 @ SY38 ) )
| ( SY37 = SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(63,plain,
! [SV7: $i] :
( ( ! [SY39: $i,SY40: $i,SY41: $i] :
~ ~ ( ~ ~ ( ( ( unordered_pair @ SV7 @ SY39 )
!= ( unordered_pair @ SY40 @ SY41 ) )
| ~ ( ( SV7 != SY40 ) ) )
| ~ ( ( SV7 != SY41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(64,plain,
! [SV8: $i] :
( ( ! [SY42: $i] :
( ~ ( subset @ ( singleton @ SV8 ) @ ( singleton @ SY42 ) )
| ( SV8 = SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(65,plain,
! [SV9: $i] :
( ( ! [SY43: $i,SY44: $i] :
( ( ( singleton @ SV9 )
!= ( unordered_pair @ SY43 @ SY44 ) )
| ( SV9 = SY43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(66,plain,
( ( ! [SX0: $i] :
~ ~ ( empty @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[54]) ).
thf(67,plain,
! [SV10: $i,SV1: $i] :
( ( ( unordered_pair @ SV1 @ SV10 )
= ( unordered_pair @ SV10 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(68,plain,
! [SV11: $i,SV2: $i] :
( ( ( ordered_pair @ SV2 @ SV11 )
= ( unordered_pair @ ( unordered_pair @ SV2 @ SV11 ) @ ( singleton @ SV2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(69,plain,
! [SV12: $i,SV3: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV3 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(70,plain,
! [SV4: $i] :
( ( subset @ SV4 @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(71,plain,
( ( ~ ( empty @ sK5_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[61]) ).
thf(72,plain,
! [SV14: $i,SV6: $i] :
( ( ! [SY45: $i] :
( ( ( singleton @ SV6 )
!= ( unordered_pair @ SV14 @ SY45 ) )
| ( SV14 = SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(73,plain,
! [SV15: $i,SV7: $i] :
( ( ! [SY46: $i,SY47: $i] :
~ ~ ( ~ ~ ( ( ( unordered_pair @ SV7 @ SV15 )
!= ( unordered_pair @ SY46 @ SY47 ) )
| ~ ( ( SV7 != SY46 ) ) )
| ~ ( ( SV7 != SY47 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(74,plain,
! [SV16: $i,SV8: $i] :
( ( ~ ( subset @ ( singleton @ SV8 ) @ ( singleton @ SV16 ) )
| ( SV8 = SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(75,plain,
! [SV17: $i,SV9: $i] :
( ( ! [SY48: $i] :
( ( ( singleton @ SV9 )
!= ( unordered_pair @ SV17 @ SY48 ) )
| ( SV9 = SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(76,plain,
( ( ~ ~ ( empty @ sK6_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[66]) ).
thf(77,plain,
! [SV12: $i,SV3: $i] :
( ( empty @ ( ordered_pair @ SV3 @ SV12 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(78,plain,
( ( empty @ sK5_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[71]) ).
thf(79,plain,
! [SV18: $i,SV14: $i,SV6: $i] :
( ( ( ( singleton @ SV6 )
!= ( unordered_pair @ SV14 @ SV18 ) )
| ( SV14 = SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(80,plain,
! [SV19: $i,SV15: $i,SV7: $i] :
( ( ! [SY49: $i] :
~ ~ ( ~ ~ ( ( ( unordered_pair @ SV7 @ SV15 )
!= ( unordered_pair @ SV19 @ SY49 ) )
| ~ ( ( SV7 != SV19 ) ) )
| ~ ( ( SV7 != SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(81,plain,
! [SV16: $i,SV8: $i] :
( ( ( ~ ( subset @ ( singleton @ SV8 ) @ ( singleton @ SV16 ) ) )
= $true )
| ( ( SV8 = SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(82,plain,
! [SV20: $i,SV17: $i,SV9: $i] :
( ( ( ( singleton @ SV9 )
!= ( unordered_pair @ SV17 @ SV20 ) )
| ( SV9 = SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(83,plain,
( ( ~ ( empty @ sK6_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[76]) ).
thf(84,plain,
! [SV18: $i,SV14: $i,SV6: $i] :
( ( ( ( singleton @ SV6 )
!= ( unordered_pair @ SV14 @ SV18 ) )
= $true )
| ( ( SV14 = SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(85,plain,
! [SV21: $i,SV19: $i,SV15: $i,SV7: $i] :
( ( ~ ~ ( ~ ~ ( ( ( unordered_pair @ SV7 @ SV15 )
!= ( unordered_pair @ SV19 @ SV21 ) )
| ~ ( ( SV7 != SV19 ) ) )
| ~ ( ( SV7 != SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(86,plain,
! [SV16: $i,SV8: $i] :
( ( ( subset @ ( singleton @ SV8 ) @ ( singleton @ SV16 ) )
= $false )
| ( ( SV8 = SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(87,plain,
! [SV20: $i,SV17: $i,SV9: $i] :
( ( ( ( singleton @ SV9 )
!= ( unordered_pair @ SV17 @ SV20 ) )
= $true )
| ( ( SV9 = SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[82]) ).
thf(88,plain,
( ( empty @ sK6_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(89,plain,
! [SV18: $i,SV14: $i,SV6: $i] :
( ( ( ( singleton @ SV6 )
= ( unordered_pair @ SV14 @ SV18 ) )
= $false )
| ( ( SV14 = SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(90,plain,
! [SV21: $i,SV19: $i,SV15: $i,SV7: $i] :
( ( ~ ( ~ ~ ( ( ( unordered_pair @ SV7 @ SV15 )
!= ( unordered_pair @ SV19 @ SV21 ) )
| ~ ( ( SV7 != SV19 ) ) )
| ~ ( ( SV7 != SV21 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(91,plain,
! [SV20: $i,SV17: $i,SV9: $i] :
( ( ( ( singleton @ SV9 )
= ( unordered_pair @ SV17 @ SV20 ) )
= $false )
| ( ( SV9 = SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(92,plain,
! [SV21: $i,SV19: $i,SV15: $i,SV7: $i] :
( ( ~ ~ ( ( ( unordered_pair @ SV7 @ SV15 )
!= ( unordered_pair @ SV19 @ SV21 ) )
| ~ ( ( SV7 != SV19 ) ) )
| ~ ( ( SV7 != SV21 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[90]) ).
thf(93,plain,
! [SV21: $i,SV19: $i,SV15: $i,SV7: $i] :
( ( ( ~ ~ ( ( ( unordered_pair @ SV7 @ SV15 )
!= ( unordered_pair @ SV19 @ SV21 ) )
| ~ ( ( SV7 != SV19 ) ) ) )
= $true )
| ( ( ~ ( ( SV7 != SV21 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(94,plain,
! [SV21: $i,SV19: $i,SV15: $i,SV7: $i] :
( ( ( ~ ( ( ( unordered_pair @ SV7 @ SV15 )
!= ( unordered_pair @ SV19 @ SV21 ) )
| ~ ( ( SV7 != SV19 ) ) ) )
= $false )
| ( ( ~ ( ( SV7 != SV21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(95,plain,
! [SV21: $i,SV19: $i,SV15: $i,SV7: $i] :
( ( ( ( ( unordered_pair @ SV7 @ SV15 )
!= ( unordered_pair @ SV19 @ SV21 ) )
| ~ ( ( SV7 != SV19 ) ) )
= $true )
| ( ( ~ ( ( SV7 != SV21 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[94]) ).
thf(96,plain,
! [SV21: $i,SV19: $i,SV15: $i,SV7: $i] :
( ( ( ( unordered_pair @ SV7 @ SV15 )
!= ( unordered_pair @ SV19 @ SV21 ) )
= $true )
| ( ( ~ ( ( SV7 != SV19 ) ) )
= $true )
| ( ( ~ ( ( SV7 != SV21 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(97,plain,
! [SV21: $i,SV19: $i,SV15: $i,SV7: $i] :
( ( ( ( unordered_pair @ SV7 @ SV15 )
= ( unordered_pair @ SV19 @ SV21 ) )
= $false )
| ( ( ~ ( ( SV7 != SV19 ) ) )
= $true )
| ( ( ~ ( ( SV7 != SV21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(98,plain,
! [SV21: $i,SV15: $i,SV19: $i,SV7: $i] :
( ( ( SV7 != SV19 )
= $false )
| ( ( ( unordered_pair @ SV7 @ SV15 )
= ( unordered_pair @ SV19 @ SV21 ) )
= $false )
| ( ( ~ ( ( SV7 != SV21 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(99,plain,
! [SV21: $i,SV15: $i,SV19: $i,SV7: $i] :
( ( ( SV7 = SV19 )
= $true )
| ( ( ( unordered_pair @ SV7 @ SV15 )
= ( unordered_pair @ SV19 @ SV21 ) )
= $false )
| ( ( ~ ( ( SV7 != SV21 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[98]) ).
thf(100,plain,
! [SV19: $i,SV15: $i,SV21: $i,SV7: $i] :
( ( ( SV7 != SV21 )
= $false )
| ( ( ( unordered_pair @ SV7 @ SV15 )
= ( unordered_pair @ SV19 @ SV21 ) )
= $false )
| ( ( SV7 = SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(101,plain,
! [SV19: $i,SV15: $i,SV21: $i,SV7: $i] :
( ( ( SV7 = SV21 )
= $true )
| ( ( ( unordered_pair @ SV7 @ SV15 )
= ( unordered_pair @ SV19 @ SV21 ) )
= $false )
| ( ( SV7 = SV19 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[100]) ).
thf(102,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[47,101,91,89,88,86,78,77,70,68,67,60,59]) ).
thf(103,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(104,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(105,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(106,plain,
( ( ? [A: $i] : ( empty @ A ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(107,plain,
( ( ? [A: $i] :
~ ( empty @ A ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(108,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(109,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( ( unordered_pair @ A @ B )
= ( unordered_pair @ C @ D ) )
& ( A != C )
& ( A != D ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(110,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(111,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(112,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(113,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
= ( unordered_pair @ B @ C ) )
=> ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(114,plain,
( ( ( ordered_pair @ sK1_A @ sK2_SY27 )
= ( ordered_pair @ sK3_SY30 @ sK4_SY32 ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(115,plain,
( ( sK2_SY27 != sK4_SY32 )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(116,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( singleton @ SX0 )
!= ( unordered_pair @ SX1 @ SX2 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[112]) ).
thf(117,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( singleton @ SX0 )
!= ( unordered_pair @ SX1 @ SX2 ) )
| ( SX1 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[113]) ).
thf(118,plain,
( ( ~ ! [SX0: $i] :
~ ~ ( empty @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[107]) ).
thf(119,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
~ ~ ( ~ ~ ( ( ( unordered_pair @ SX0 @ SX1 )
!= ( unordered_pair @ SX2 @ SX3 ) )
| ~ ( ( SX0 != SX2 ) ) )
| ~ ( ( SX0 != SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(120,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ ( singleton @ SX0 ) @ ( singleton @ SX1 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[111]) ).
thf(121,plain,
( ( ~ ! [SX0: $i] :
~ ( empty @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(122,plain,
! [SV22: $i] :
( ( ! [SY50: $i] :
( ( unordered_pair @ SV22 @ SY50 )
= ( unordered_pair @ SY50 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(123,plain,
! [SV23: $i] :
( ( ! [SY51: $i] :
( ( ordered_pair @ SV23 @ SY51 )
= ( unordered_pair @ ( unordered_pair @ SV23 @ SY51 ) @ ( singleton @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(124,plain,
! [SV24: $i] :
( ( ! [SY52: $i] :
~ ( empty @ ( ordered_pair @ SV24 @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(125,plain,
! [SV25: $i] :
( ( ! [SY53: $i] : ( subset @ SV25 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(126,plain,
! [SV26: $i] :
( ( ( unordered_pair @ SV26 @ SV26 )
= ( singleton @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(127,plain,
( ( sK2_SY27 = sK4_SY32 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(128,plain,
! [SV27: $i] :
( ( ! [SY54: $i,SY55: $i] :
( ( ( singleton @ SV27 )
!= ( unordered_pair @ SY54 @ SY55 ) )
| ( SV27 = SY54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(129,plain,
! [SV28: $i] :
( ( ! [SY56: $i,SY57: $i] :
( ( ( singleton @ SV28 )
!= ( unordered_pair @ SY56 @ SY57 ) )
| ( SY56 = SY57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(130,plain,
( ( ! [SX0: $i] :
~ ~ ( empty @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(131,plain,
! [SV29: $i] :
( ( ! [SY58: $i,SY59: $i,SY60: $i] :
~ ~ ( ~ ~ ( ( ( unordered_pair @ SV29 @ SY58 )
!= ( unordered_pair @ SY59 @ SY60 ) )
| ~ ( ( SV29 != SY59 ) ) )
| ~ ( ( SV29 != SY60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(132,plain,
! [SV30: $i] :
( ( ! [SY61: $i] :
( ~ ( subset @ ( singleton @ SV30 ) @ ( singleton @ SY61 ) )
| ( SV30 = SY61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(133,plain,
( ( ! [SX0: $i] :
~ ( empty @ SX0 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(134,plain,
! [SV31: $i,SV22: $i] :
( ( ( unordered_pair @ SV22 @ SV31 )
= ( unordered_pair @ SV31 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(135,plain,
! [SV32: $i,SV23: $i] :
( ( ( ordered_pair @ SV23 @ SV32 )
= ( unordered_pair @ ( unordered_pair @ SV23 @ SV32 ) @ ( singleton @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(136,plain,
! [SV33: $i,SV24: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV24 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(137,plain,
! [SV25: $i] :
( ( subset @ SV25 @ SV25 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(138,plain,
! [SV35: $i,SV27: $i] :
( ( ! [SY62: $i] :
( ( ( singleton @ SV27 )
!= ( unordered_pair @ SV35 @ SY62 ) )
| ( SV27 = SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(139,plain,
! [SV36: $i,SV28: $i] :
( ( ! [SY63: $i] :
( ( ( singleton @ SV28 )
!= ( unordered_pair @ SV36 @ SY63 ) )
| ( SV36 = SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(140,plain,
( ( ~ ~ ( empty @ sK7_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[130]) ).
thf(141,plain,
! [SV37: $i,SV29: $i] :
( ( ! [SY64: $i,SY65: $i] :
~ ~ ( ~ ~ ( ( ( unordered_pair @ SV29 @ SV37 )
!= ( unordered_pair @ SY64 @ SY65 ) )
| ~ ( ( SV29 != SY64 ) ) )
| ~ ( ( SV29 != SY65 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(142,plain,
! [SV38: $i,SV30: $i] :
( ( ~ ( subset @ ( singleton @ SV30 ) @ ( singleton @ SV38 ) )
| ( SV30 = SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(143,plain,
( ( ~ ( empty @ sK8_SX0 ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[133]) ).
thf(144,plain,
! [SV33: $i,SV24: $i] :
( ( empty @ ( ordered_pair @ SV24 @ SV33 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(145,plain,
! [SV39: $i,SV35: $i,SV27: $i] :
( ( ( ( singleton @ SV27 )
!= ( unordered_pair @ SV35 @ SV39 ) )
| ( SV27 = SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(146,plain,
! [SV40: $i,SV36: $i,SV28: $i] :
( ( ( ( singleton @ SV28 )
!= ( unordered_pair @ SV36 @ SV40 ) )
| ( SV36 = SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(147,plain,
( ( ~ ( empty @ sK7_SX0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[140]) ).
thf(148,plain,
! [SV41: $i,SV37: $i,SV29: $i] :
( ( ! [SY66: $i] :
~ ~ ( ~ ~ ( ( ( unordered_pair @ SV29 @ SV37 )
!= ( unordered_pair @ SV41 @ SY66 ) )
| ~ ( ( SV29 != SV41 ) ) )
| ~ ( ( SV29 != SY66 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(149,plain,
! [SV38: $i,SV30: $i] :
( ( ( ~ ( subset @ ( singleton @ SV30 ) @ ( singleton @ SV38 ) ) )
= $true )
| ( ( SV30 = SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(150,plain,
( ( empty @ sK8_SX0 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[143]) ).
thf(151,plain,
! [SV39: $i,SV35: $i,SV27: $i] :
( ( ( ( singleton @ SV27 )
!= ( unordered_pair @ SV35 @ SV39 ) )
= $true )
| ( ( SV27 = SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(152,plain,
! [SV40: $i,SV36: $i,SV28: $i] :
( ( ( ( singleton @ SV28 )
!= ( unordered_pair @ SV36 @ SV40 ) )
= $true )
| ( ( SV36 = SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(153,plain,
( ( empty @ sK7_SX0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(154,plain,
! [SV42: $i,SV41: $i,SV37: $i,SV29: $i] :
( ( ~ ~ ( ~ ~ ( ( ( unordered_pair @ SV29 @ SV37 )
!= ( unordered_pair @ SV41 @ SV42 ) )
| ~ ( ( SV29 != SV41 ) ) )
| ~ ( ( SV29 != SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(155,plain,
! [SV38: $i,SV30: $i] :
( ( ( subset @ ( singleton @ SV30 ) @ ( singleton @ SV38 ) )
= $false )
| ( ( SV30 = SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(156,plain,
! [SV39: $i,SV35: $i,SV27: $i] :
( ( ( ( singleton @ SV27 )
= ( unordered_pair @ SV35 @ SV39 ) )
= $false )
| ( ( SV27 = SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(157,plain,
! [SV40: $i,SV36: $i,SV28: $i] :
( ( ( ( singleton @ SV28 )
= ( unordered_pair @ SV36 @ SV40 ) )
= $false )
| ( ( SV36 = SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[152]) ).
thf(158,plain,
! [SV42: $i,SV41: $i,SV37: $i,SV29: $i] :
( ( ~ ( ~ ~ ( ( ( unordered_pair @ SV29 @ SV37 )
!= ( unordered_pair @ SV41 @ SV42 ) )
| ~ ( ( SV29 != SV41 ) ) )
| ~ ( ( SV29 != SV42 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(159,plain,
! [SV42: $i,SV41: $i,SV37: $i,SV29: $i] :
( ( ~ ~ ( ( ( unordered_pair @ SV29 @ SV37 )
!= ( unordered_pair @ SV41 @ SV42 ) )
| ~ ( ( SV29 != SV41 ) ) )
| ~ ( ( SV29 != SV42 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[158]) ).
thf(160,plain,
! [SV42: $i,SV41: $i,SV37: $i,SV29: $i] :
( ( ( ~ ~ ( ( ( unordered_pair @ SV29 @ SV37 )
!= ( unordered_pair @ SV41 @ SV42 ) )
| ~ ( ( SV29 != SV41 ) ) ) )
= $true )
| ( ( ~ ( ( SV29 != SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[159]) ).
thf(161,plain,
! [SV42: $i,SV41: $i,SV37: $i,SV29: $i] :
( ( ( ~ ( ( ( unordered_pair @ SV29 @ SV37 )
!= ( unordered_pair @ SV41 @ SV42 ) )
| ~ ( ( SV29 != SV41 ) ) ) )
= $false )
| ( ( ~ ( ( SV29 != SV42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(162,plain,
! [SV42: $i,SV41: $i,SV37: $i,SV29: $i] :
( ( ( ( ( unordered_pair @ SV29 @ SV37 )
!= ( unordered_pair @ SV41 @ SV42 ) )
| ~ ( ( SV29 != SV41 ) ) )
= $true )
| ( ( ~ ( ( SV29 != SV42 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[161]) ).
thf(163,plain,
! [SV42: $i,SV41: $i,SV37: $i,SV29: $i] :
( ( ( ( unordered_pair @ SV29 @ SV37 )
!= ( unordered_pair @ SV41 @ SV42 ) )
= $true )
| ( ( ~ ( ( SV29 != SV41 ) ) )
= $true )
| ( ( ~ ( ( SV29 != SV42 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(164,plain,
! [SV42: $i,SV41: $i,SV37: $i,SV29: $i] :
( ( ( ( unordered_pair @ SV29 @ SV37 )
= ( unordered_pair @ SV41 @ SV42 ) )
= $false )
| ( ( ~ ( ( SV29 != SV41 ) ) )
= $true )
| ( ( ~ ( ( SV29 != SV42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[163]) ).
thf(165,plain,
! [SV42: $i,SV37: $i,SV41: $i,SV29: $i] :
( ( ( SV29 != SV41 )
= $false )
| ( ( ( unordered_pair @ SV29 @ SV37 )
= ( unordered_pair @ SV41 @ SV42 ) )
= $false )
| ( ( ~ ( ( SV29 != SV42 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[164]) ).
thf(166,plain,
! [SV42: $i,SV37: $i,SV41: $i,SV29: $i] :
( ( ( SV29 = SV41 )
= $true )
| ( ( ( unordered_pair @ SV29 @ SV37 )
= ( unordered_pair @ SV41 @ SV42 ) )
= $false )
| ( ( ~ ( ( SV29 != SV42 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[165]) ).
thf(167,plain,
! [SV41: $i,SV37: $i,SV42: $i,SV29: $i] :
( ( ( SV29 != SV42 )
= $false )
| ( ( ( unordered_pair @ SV29 @ SV37 )
= ( unordered_pair @ SV41 @ SV42 ) )
= $false )
| ( ( SV29 = SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(168,plain,
! [SV41: $i,SV37: $i,SV42: $i,SV29: $i] :
( ( ( SV29 = SV42 )
= $true )
| ( ( ( unordered_pair @ SV29 @ SV37 )
= ( unordered_pair @ SV41 @ SV42 ) )
= $false )
| ( ( SV29 = SV41 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[167]) ).
thf(169,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[114,168,157,156,155,153,150,144,137,135,134,127,126]) ).
thf(170,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[169,102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU156+3 : 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
% 0.07/0.18 % Computer : n017.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 14:57:45 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.85/0.49
% 0.85/0.49 No.of.Axioms: 11
% 0.85/0.49
% 0.85/0.49 Length.of.Defs: 0
% 0.85/0.49
% 0.85/0.49 Contains.Choice.Funs: false
% 0.85/0.49 ....
% 0.85/0.49
% 0.85/0.49 ********************************
% 0.85/0.49 * All subproblems solved! *
% 0.85/0.49 ********************************
% 0.85/0.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:12,ps:3,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:169,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.85/0.49
% 0.85/0.49 %**** Beginning of derivation protocol ****
% 0.85/0.49 % SZS output start CNFRefutation
% See solution above
% 1.42/0.49
% 1.42/0.49 %**** End of derivation protocol ****
% 1.42/0.49 %**** no. of clauses in derivation: 170 ****
% 1.42/0.49 %**** clause counter: 169 ****
% 1.42/0.49
% 1.42/0.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:12,ps:3,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:169,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------