TSTP Solution File: SEU156+3 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SEU156+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 12:07:17 EDT 2022
% Result : Theorem 0.41s 0.59s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 23
% Syntax : Number of formulae : 146 ( 110 unt; 11 typ; 0 def)
% Number of atoms : 523 ( 332 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 585 ( 69 ~; 71 |; 12 &; 420 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 281 ( 0 ^ 277 !; 4 ?; 281 :)
% 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_A,type,
sK5_A: $i ).
thf(tp_sK6_A,type,
sK6_A: $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/sandbox/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/sandbox/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(4,axiom,
! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(6,axiom,
! [A: $i,B: $i] : ( subset @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(7,axiom,
? [A: $i] :
~ ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(8,axiom,
? [A: $i] : ( empty @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(9,axiom,
! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ),
file('/export/starexec/sandbox/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/sandbox/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,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(37,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(39,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( A = D )
| ( A = C )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ C @ D ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(40,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(41,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(42,plain,
( ( empty @ sK6_A )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(43,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(44,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(45,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(46,plain,
( ( empty @ sK6_A )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(47,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(48,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(49,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( A = D )
| ( A = C )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(50,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(51,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(52,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(53,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(54,plain,
( ( ( ordered_pair @ sK1_A @ sK2_SY27 )
= ( ordered_pair @ sK3_SY30 @ sK4_SY32 ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(55,plain,
( ( ( sK1_A != sK3_SY30 ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(56,plain,
! [SV1: $i] :
( ( ! [SY33: $i] :
( ( unordered_pair @ SV1 @ SY33 )
= ( unordered_pair @ SY33 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(57,plain,
! [SV2: $i] :
( ( ! [SY34: $i] :
( ( ordered_pair @ SV2 @ SY34 )
= ( unordered_pair @ ( unordered_pair @ SV2 @ SY34 ) @ ( singleton @ SV2 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(58,plain,
! [SV3: $i] :
( ( ! [SY35: $i] :
~ ( empty @ ( ordered_pair @ SV3 @ SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(59,plain,
( ( empty @ sK5_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(60,plain,
! [SV4: $i] :
( ( subset @ SV4 @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(61,plain,
! [SV5: $i] :
( ( ! [SY36: $i,SY37: $i,SY38: $i] :
( ( SV5 = SY38 )
| ( SV5 = SY37 )
| ( ( unordered_pair @ SV5 @ SY36 )
!= ( unordered_pair @ SY37 @ SY38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(62,plain,
! [SV6: $i] :
( ( ( unordered_pair @ SV6 @ SV6 )
= ( singleton @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(63,plain,
! [SV7: $i] :
( ( ! [SY39: $i] :
( ~ ( subset @ ( singleton @ SV7 ) @ ( singleton @ SY39 ) )
| ( SV7 = SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(64,plain,
! [SV8: $i] :
( ( ! [SY40: $i] :
( ! [SY41: $i] :
( ( singleton @ SV8 )
!= ( unordered_pair @ SY40 @ SY41 ) )
| ( SV8 = SY40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(65,plain,
! [SV9: $i] :
( ( ! [SY42: $i,SY43: $i] :
( ( ( singleton @ SV9 )
!= ( unordered_pair @ SY42 @ SY43 ) )
| ( SY42 = SY43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(66,plain,
( ( sK1_A = sK3_SY30 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(67,plain,
! [SV10: $i,SV1: $i] :
( ( ( unordered_pair @ SV1 @ SV10 )
= ( unordered_pair @ SV10 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
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)],[57]) ).
thf(69,plain,
! [SV12: $i,SV3: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV3 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(70,plain,
! [SV13: $i,SV5: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ( SV5 = SY45 )
| ( SV5 = SY44 )
| ( ( unordered_pair @ SV5 @ SV13 )
!= ( unordered_pair @ SY44 @ SY45 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(71,plain,
! [SV14: $i,SV7: $i] :
( ( ~ ( subset @ ( singleton @ SV7 ) @ ( singleton @ SV14 ) )
| ( SV7 = SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(72,plain,
! [SV15: $i,SV8: $i] :
( ( ! [SY46: $i] :
( ( singleton @ SV8 )
!= ( unordered_pair @ SV15 @ SY46 ) )
| ( SV8 = SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(73,plain,
! [SV16: $i,SV9: $i] :
( ( ! [SY47: $i] :
( ( ( singleton @ SV9 )
!= ( unordered_pair @ SV16 @ SY47 ) )
| ( SV16 = SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(74,plain,
! [SV12: $i,SV3: $i] :
( ( empty @ ( ordered_pair @ SV3 @ SV12 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(75,plain,
! [SV13: $i,SV17: $i,SV5: $i] :
( ( ! [SY48: $i] :
( ( SV5 = SY48 )
| ( SV5 = SV17 )
| ( ( unordered_pair @ SV5 @ SV13 )
!= ( unordered_pair @ SV17 @ SY48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(76,plain,
! [SV14: $i,SV7: $i] :
( ( ( ~ ( subset @ ( singleton @ SV7 ) @ ( singleton @ SV14 ) ) )
= $true )
| ( ( SV7 = SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(77,plain,
! [SV15: $i,SV8: $i] :
( ( ( ! [SY46: $i] :
( ( singleton @ SV8 )
!= ( unordered_pair @ SV15 @ SY46 ) ) )
= $true )
| ( ( SV8 = SV15 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(78,plain,
! [SV18: $i,SV16: $i,SV9: $i] :
( ( ( ( singleton @ SV9 )
!= ( unordered_pair @ SV16 @ SV18 ) )
| ( SV16 = SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(79,plain,
! [SV13: $i,SV17: $i,SV19: $i,SV5: $i] :
( ( ( SV5 = SV19 )
| ( SV5 = SV17 )
| ( ( unordered_pair @ SV5 @ SV13 )
!= ( unordered_pair @ SV17 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(80,plain,
! [SV14: $i,SV7: $i] :
( ( ( subset @ ( singleton @ SV7 ) @ ( singleton @ SV14 ) )
= $false )
| ( ( SV7 = SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(81,plain,
! [SV20: $i,SV15: $i,SV8: $i] :
( ( ( ( ( singleton @ SV8 )
!= ( unordered_pair @ SV15 @ SV20 ) ) )
= $true )
| ( ( SV8 = SV15 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(82,plain,
! [SV18: $i,SV16: $i,SV9: $i] :
( ( ( ( ( singleton @ SV9 )
!= ( unordered_pair @ SV16 @ SV18 ) ) )
= $true )
| ( ( SV16 = SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(83,plain,
! [SV13: $i,SV17: $i,SV19: $i,SV5: $i] :
( ( ( SV5 = SV19 )
= $true )
| ( ( ( SV5 = SV17 )
| ( ( unordered_pair @ SV5 @ SV13 )
!= ( unordered_pair @ SV17 @ SV19 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(84,plain,
! [SV20: $i,SV15: $i,SV8: $i] :
( ( ( ( singleton @ SV8 )
= ( unordered_pair @ SV15 @ SV20 ) )
= $false )
| ( ( SV8 = SV15 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(85,plain,
! [SV18: $i,SV16: $i,SV9: $i] :
( ( ( ( singleton @ SV9 )
= ( unordered_pair @ SV16 @ SV18 ) )
= $false )
| ( ( SV16 = SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(86,plain,
! [SV19: $i,SV13: $i,SV17: $i,SV5: $i] :
( ( ( SV5 = SV17 )
= $true )
| ( ( ( ( unordered_pair @ SV5 @ SV13 )
!= ( unordered_pair @ SV17 @ SV19 ) ) )
= $true )
| ( ( SV5 = SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(87,plain,
! [SV19: $i,SV17: $i,SV13: $i,SV5: $i] :
( ( ( ( unordered_pair @ SV5 @ SV13 )
= ( unordered_pair @ SV17 @ SV19 ) )
= $false )
| ( ( SV5 = SV17 )
= $true )
| ( ( SV5 = SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(88,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[46,87,85,84,80,74,68,67,66,62,60,59,54]) ).
thf(89,plain,
( ( ! [A: $i,B: $i] :
( ( unordered_pair @ A @ B )
= ( unordered_pair @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(90,plain,
( ( ! [A: $i,B: $i] :
( ( ordered_pair @ A @ B )
= ( unordered_pair @ ( unordered_pair @ A @ B ) @ ( singleton @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(91,plain,
( ( ! [A: $i,B: $i] :
~ ( empty @ ( ordered_pair @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(92,plain,
( ( empty @ sK6_A )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(93,plain,
( ( ~ ( empty @ sK5_A ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(94,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(95,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ( A = D )
| ( A = C )
| ( ( unordered_pair @ A @ B )
!= ( unordered_pair @ C @ D ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(96,plain,
( ( ! [A: $i] :
( ( unordered_pair @ A @ A )
= ( singleton @ A ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(97,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ ( singleton @ A ) @ ( singleton @ B ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(98,plain,
( ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(99,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( ( singleton @ A )
!= ( unordered_pair @ B @ C ) )
| ( B = C ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(100,plain,
( ( ( ordered_pair @ sK1_A @ sK2_SY27 )
= ( ordered_pair @ sK3_SY30 @ sK4_SY32 ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(101,plain,
( ( ( sK2_SY27 != sK4_SY32 ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(102,plain,
! [SV21: $i] :
( ( ! [SY49: $i] :
( ( unordered_pair @ SV21 @ SY49 )
= ( unordered_pair @ SY49 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(103,plain,
! [SV22: $i] :
( ( ! [SY50: $i] :
( ( ordered_pair @ SV22 @ SY50 )
= ( unordered_pair @ ( unordered_pair @ SV22 @ SY50 ) @ ( singleton @ SV22 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(104,plain,
! [SV23: $i] :
( ( ! [SY51: $i] :
~ ( empty @ ( ordered_pair @ SV23 @ SY51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(105,plain,
( ( empty @ sK5_A )
= $false ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(106,plain,
! [SV24: $i] :
( ( subset @ SV24 @ SV24 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(107,plain,
! [SV25: $i] :
( ( ! [SY52: $i,SY53: $i,SY54: $i] :
( ( SV25 = SY54 )
| ( SV25 = SY53 )
| ( ( unordered_pair @ SV25 @ SY52 )
!= ( unordered_pair @ SY53 @ SY54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(108,plain,
! [SV26: $i] :
( ( ( unordered_pair @ SV26 @ SV26 )
= ( singleton @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(109,plain,
! [SV27: $i] :
( ( ! [SY55: $i] :
( ~ ( subset @ ( singleton @ SV27 ) @ ( singleton @ SY55 ) )
| ( SV27 = SY55 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(110,plain,
! [SV28: $i] :
( ( ! [SY56: $i] :
( ! [SY57: $i] :
( ( singleton @ SV28 )
!= ( unordered_pair @ SY56 @ SY57 ) )
| ( SV28 = SY56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(111,plain,
! [SV29: $i] :
( ( ! [SY58: $i,SY59: $i] :
( ( ( singleton @ SV29 )
!= ( unordered_pair @ SY58 @ SY59 ) )
| ( SY58 = SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(112,plain,
( ( sK2_SY27 = sK4_SY32 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(113,plain,
! [SV30: $i,SV21: $i] :
( ( ( unordered_pair @ SV21 @ SV30 )
= ( unordered_pair @ SV30 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(114,plain,
! [SV31: $i,SV22: $i] :
( ( ( ordered_pair @ SV22 @ SV31 )
= ( unordered_pair @ ( unordered_pair @ SV22 @ SV31 ) @ ( singleton @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(115,plain,
! [SV32: $i,SV23: $i] :
( ( ~ ( empty @ ( ordered_pair @ SV23 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(116,plain,
! [SV33: $i,SV25: $i] :
( ( ! [SY60: $i,SY61: $i] :
( ( SV25 = SY61 )
| ( SV25 = SY60 )
| ( ( unordered_pair @ SV25 @ SV33 )
!= ( unordered_pair @ SY60 @ SY61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(117,plain,
! [SV34: $i,SV27: $i] :
( ( ~ ( subset @ ( singleton @ SV27 ) @ ( singleton @ SV34 ) )
| ( SV27 = SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(118,plain,
! [SV35: $i,SV28: $i] :
( ( ! [SY62: $i] :
( ( singleton @ SV28 )
!= ( unordered_pair @ SV35 @ SY62 ) )
| ( SV28 = SV35 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(119,plain,
! [SV36: $i,SV29: $i] :
( ( ! [SY63: $i] :
( ( ( singleton @ SV29 )
!= ( unordered_pair @ SV36 @ SY63 ) )
| ( SV36 = SY63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(120,plain,
! [SV32: $i,SV23: $i] :
( ( empty @ ( ordered_pair @ SV23 @ SV32 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(121,plain,
! [SV33: $i,SV37: $i,SV25: $i] :
( ( ! [SY64: $i] :
( ( SV25 = SY64 )
| ( SV25 = SV37 )
| ( ( unordered_pair @ SV25 @ SV33 )
!= ( unordered_pair @ SV37 @ SY64 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(122,plain,
! [SV34: $i,SV27: $i] :
( ( ( ~ ( subset @ ( singleton @ SV27 ) @ ( singleton @ SV34 ) ) )
= $true )
| ( ( SV27 = SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[117]) ).
thf(123,plain,
! [SV35: $i,SV28: $i] :
( ( ( ! [SY62: $i] :
( ( singleton @ SV28 )
!= ( unordered_pair @ SV35 @ SY62 ) ) )
= $true )
| ( ( SV28 = SV35 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[118]) ).
thf(124,plain,
! [SV38: $i,SV36: $i,SV29: $i] :
( ( ( ( singleton @ SV29 )
!= ( unordered_pair @ SV36 @ SV38 ) )
| ( SV36 = SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(125,plain,
! [SV33: $i,SV37: $i,SV39: $i,SV25: $i] :
( ( ( SV25 = SV39 )
| ( SV25 = SV37 )
| ( ( unordered_pair @ SV25 @ SV33 )
!= ( unordered_pair @ SV37 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(126,plain,
! [SV34: $i,SV27: $i] :
( ( ( subset @ ( singleton @ SV27 ) @ ( singleton @ SV34 ) )
= $false )
| ( ( SV27 = SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[122]) ).
thf(127,plain,
! [SV40: $i,SV35: $i,SV28: $i] :
( ( ( ( ( singleton @ SV28 )
!= ( unordered_pair @ SV35 @ SV40 ) ) )
= $true )
| ( ( SV28 = SV35 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(128,plain,
! [SV38: $i,SV36: $i,SV29: $i] :
( ( ( ( ( singleton @ SV29 )
!= ( unordered_pair @ SV36 @ SV38 ) ) )
= $true )
| ( ( SV36 = SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(129,plain,
! [SV33: $i,SV37: $i,SV39: $i,SV25: $i] :
( ( ( SV25 = SV39 )
= $true )
| ( ( ( SV25 = SV37 )
| ( ( unordered_pair @ SV25 @ SV33 )
!= ( unordered_pair @ SV37 @ SV39 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(130,plain,
! [SV40: $i,SV35: $i,SV28: $i] :
( ( ( ( singleton @ SV28 )
= ( unordered_pair @ SV35 @ SV40 ) )
= $false )
| ( ( SV28 = SV35 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(131,plain,
! [SV38: $i,SV36: $i,SV29: $i] :
( ( ( ( singleton @ SV29 )
= ( unordered_pair @ SV36 @ SV38 ) )
= $false )
| ( ( SV36 = SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(132,plain,
! [SV39: $i,SV33: $i,SV37: $i,SV25: $i] :
( ( ( SV25 = SV37 )
= $true )
| ( ( ( ( unordered_pair @ SV25 @ SV33 )
!= ( unordered_pair @ SV37 @ SV39 ) ) )
= $true )
| ( ( SV25 = SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(133,plain,
! [SV39: $i,SV37: $i,SV33: $i,SV25: $i] :
( ( ( ( unordered_pair @ SV25 @ SV33 )
= ( unordered_pair @ SV37 @ SV39 ) )
= $false )
| ( ( SV25 = SV37 )
= $true )
| ( ( SV25 = SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(134,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[92,133,131,130,126,120,114,113,112,108,106,105,100]) ).
thf(135,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[134,88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SEU156+3 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n017.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sun Jun 19 01:08:28 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 11
% 0.13/0.34
% 0.13/0.34 Length.of.Defs: 0
% 0.13/0.34
% 0.13/0.34 Contains.Choice.Funs: false
% 0.13/0.35 (rf:0,axioms:11,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:13,loop_count:0,foatp_calls:0,translation:fof_full).....
% 0.41/0.59
% 0.41/0.59 ********************************
% 0.41/0.59 * All subproblems solved! *
% 0.41/0.59 ********************************
% 0.41/0.59 % SZS status Theorem for /export/starexec/sandbox/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:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:134,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.41/0.59
% 0.41/0.59 %**** Beginning of derivation protocol ****
% 0.41/0.59 % SZS output start CNFRefutation
% See solution above
% 0.41/0.59
% 0.41/0.59 %**** End of derivation protocol ****
% 0.41/0.59 %**** no. of clauses in derivation: 135 ****
% 0.41/0.59 %**** clause counter: 134 ****
% 0.41/0.59
% 0.41/0.59 % SZS status Theorem for /export/starexec/sandbox/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:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:134,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------