TSTP Solution File: SET015-4 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SET015-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n011.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 02:57:54 EDT 2022
% Result : Unsatisfiable 0.91s 1.17s
% Output : CNFRefutation 0.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 28
% Syntax : Number of formulae : 122 ( 73 unt; 12 typ; 0 def)
% Number of atoms : 482 ( 168 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 730 ( 88 ~; 116 |; 0 &; 526 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 198 ( 0 ^ 198 !; 0 ?; 198 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_as,type,
as: $i ).
thf(tp_bs,type,
bs: $i ).
thf(tp_complement,type,
complement: $i > $i ).
thf(tp_cs,type,
cs: $i ).
thf(tp_ds,type,
ds: $i ).
thf(tp_empty_set,type,
empty_set: $i ).
thf(tp_f1,type,
f1: $i > $i > $i ).
thf(tp_intersection,type,
intersection: $i > $i > $i ).
thf(tp_little_set,type,
little_set: $i > $o ).
thf(tp_member,type,
member: $i > $i > $o ).
thf(tp_union,type,
union: $i > $i > $i ).
thf(tp_universal_set,type,
universal_set: $i ).
thf(1,axiom,
! [Z: $i] :
( ( member @ Z @ universal_set )
| ~ ( little_set @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',universal_set) ).
thf(2,axiom,
! [Z: $i] :
~ ( member @ Z @ empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ( union @ X @ Y )
= ( complement @ ( intersection @ ( complement @ X ) @ ( complement @ Y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
thf(4,axiom,
! [Z: $i,X: $i] :
( ( member @ Z @ ( complement @ X ) )
| ~ ( little_set @ Z )
| ( member @ Z @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement2) ).
thf(5,axiom,
! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( complement @ X ) )
| ~ ( member @ Z @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement1) ).
thf(6,axiom,
! [Z: $i,X: $i,Y: $i] :
( ( member @ Z @ ( intersection @ X @ Y ) )
| ~ ( member @ Z @ X )
| ~ ( member @ Z @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection3) ).
thf(7,axiom,
! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection2) ).
thf(8,axiom,
! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection1) ).
thf(9,axiom,
! [X: $i,Y: $i] :
( ~ ( member @ ( f1 @ X @ Y ) @ X )
| ~ ( member @ ( f1 @ X @ Y ) @ Y )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality3) ).
thf(10,axiom,
! [X: $i,Y: $i] :
( ( member @ ( f1 @ X @ Y ) @ X )
| ( member @ ( f1 @ X @ Y ) @ Y )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality2) ).
thf(11,axiom,
! [X: $i,Y: $i] :
( ( little_set @ ( f1 @ X @ Y ) )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',extensionality1) ).
thf(12,axiom,
! [X: $i,Y: $i] :
( ~ ( member @ X @ Y )
| ( little_set @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
thf(13,axiom,
( ( union @ bs @ as )
= ds ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_union_a_is_d) ).
thf(14,axiom,
( ( union @ as @ bs )
= cs ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_union_b_is_c) ).
thf(15,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(16,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[15]) ).
thf(17,negated_conjecture,
cs != ds,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_equals_d) ).
thf(18,plain,
$false = $false,
inference(unfold_def,[status(thm)],[16]) ).
thf(19,plain,
( ( ! [Z: $i] :
( ( member @ Z @ universal_set )
| ~ ( little_set @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(20,plain,
( ( ! [Z: $i] :
~ ( member @ Z @ empty_set ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(21,plain,
( ( ! [X: $i,Y: $i] :
( ( union @ X @ Y )
= ( complement @ ( intersection @ ( complement @ X ) @ ( complement @ Y ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(22,plain,
( ( ! [Z: $i,X: $i] :
( ( member @ Z @ ( complement @ X ) )
| ~ ( little_set @ Z )
| ( member @ Z @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(23,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( complement @ X ) )
| ~ ( member @ Z @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(24,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ( member @ Z @ ( intersection @ X @ Y ) )
| ~ ( member @ Z @ X )
| ~ ( member @ Z @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(25,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(26,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ ( f1 @ X @ Y ) @ X )
| ~ ( member @ ( f1 @ X @ Y ) @ Y )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(28,plain,
( ( ! [X: $i,Y: $i] :
( ( member @ ( f1 @ X @ Y ) @ X )
| ( member @ ( f1 @ X @ Y ) @ Y )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i] :
( ( little_set @ ( f1 @ X @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(30,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ X @ Y )
| ( little_set @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(31,plain,
( ( ( union @ bs @ as )
= ds )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(32,plain,
( ( ( union @ as @ bs )
= cs )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(33,plain,
( ( ( cs != ds ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(34,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[18]) ).
thf(35,plain,
( ( ! [Z: $i,X: $i] :
( ! [Y: $i] :
~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(36,plain,
( ( ! [X: $i,Y: $i] :
( ( member @ ( f1 @ X @ Y ) @ X )
| ( X = Y )
| ( member @ ( f1 @ X @ Y ) @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(37,plain,
( ( ! [X: $i,Y: $i] :
( ( X = Y )
| ( little_set @ ( f1 @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(38,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
~ ( member @ X @ Y )
| ( little_set @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(39,plain,
( ( ( cs != ds ) )
= $true ),
inference(extcnf_combined,[status(esa)],[33]) ).
thf(40,plain,
( ( ( cs != ds ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(41,plain,
( ( ( union @ as @ bs )
= cs )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(42,plain,
( ( ( union @ bs @ as )
= ds )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(43,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
~ ( member @ X @ Y )
| ( little_set @ X ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(44,plain,
( ( ! [X: $i,Y: $i] :
( ( X = Y )
| ( little_set @ ( f1 @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(45,plain,
( ( ! [X: $i,Y: $i] :
( ( member @ ( f1 @ X @ Y ) @ X )
| ( X = Y )
| ( member @ ( f1 @ X @ Y ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(46,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( member @ ( f1 @ X @ Y ) @ X )
| ~ ( member @ ( f1 @ X @ Y ) @ Y )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(47,plain,
( ( ! [Z: $i,X: $i] :
( ! [Y: $i] :
~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ X ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(48,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( member @ Z @ ( intersection @ X @ Y ) )
| ( member @ Z @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(49,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ( member @ Z @ ( intersection @ X @ Y ) )
| ~ ( member @ Z @ X )
| ~ ( member @ Z @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(50,plain,
( ( ! [Z: $i,X: $i] :
( ~ ( member @ Z @ ( complement @ X ) )
| ~ ( member @ Z @ X ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(51,plain,
( ( ! [Z: $i,X: $i] :
( ( member @ Z @ ( complement @ X ) )
| ~ ( little_set @ Z )
| ( member @ Z @ X ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(52,plain,
( ( ! [X: $i,Y: $i] :
( ( union @ X @ Y )
= ( complement @ ( intersection @ ( complement @ X ) @ ( complement @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(53,plain,
( ( ! [Z: $i] :
~ ( member @ Z @ empty_set ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(54,plain,
( ( ! [Z: $i] :
( ( member @ Z @ universal_set )
| ~ ( little_set @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(55,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(56,plain,
( ( cs = ds )
= $false ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(57,plain,
! [SV1: $i] :
( ( ! [SY25: $i] :
~ ( member @ SV1 @ SY25 )
| ( little_set @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(58,plain,
! [SV2: $i] :
( ( ! [SY26: $i] :
( ( SV2 = SY26 )
| ( little_set @ ( f1 @ SV2 @ SY26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(59,plain,
! [SV3: $i] :
( ( ! [SY27: $i] :
( ( member @ ( f1 @ SV3 @ SY27 ) @ SV3 )
| ( SV3 = SY27 )
| ( member @ ( f1 @ SV3 @ SY27 ) @ SY27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(60,plain,
! [SV4: $i] :
( ( ! [SY28: $i] :
( ~ ( member @ ( f1 @ SV4 @ SY28 ) @ SV4 )
| ~ ( member @ ( f1 @ SV4 @ SY28 ) @ SY28 )
| ( SV4 = SY28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(61,plain,
! [SV5: $i] :
( ( ! [SY29: $i] :
( ! [SY30: $i] :
~ ( member @ SV5 @ ( intersection @ SY29 @ SY30 ) )
| ( member @ SV5 @ SY29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(62,plain,
! [SV6: $i] :
( ( ! [SY31: $i,SY32: $i] :
( ~ ( member @ SV6 @ ( intersection @ SY31 @ SY32 ) )
| ( member @ SV6 @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(63,plain,
! [SV7: $i] :
( ( ! [SY33: $i,SY34: $i] :
( ( member @ SV7 @ ( intersection @ SY33 @ SY34 ) )
| ~ ( member @ SV7 @ SY33 )
| ~ ( member @ SV7 @ SY34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(64,plain,
! [SV8: $i] :
( ( ! [SY35: $i] :
( ~ ( member @ SV8 @ ( complement @ SY35 ) )
| ~ ( member @ SV8 @ SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(65,plain,
! [SV9: $i] :
( ( ! [SY36: $i] :
( ( member @ SV9 @ ( complement @ SY36 ) )
| ~ ( little_set @ SV9 )
| ( member @ SV9 @ SY36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(66,plain,
! [SV10: $i] :
( ( ! [SY37: $i] :
( ( union @ SV10 @ SY37 )
= ( complement @ ( intersection @ ( complement @ SV10 ) @ ( complement @ SY37 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(67,plain,
! [SV11: $i] :
( ( ~ ( member @ SV11 @ empty_set ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(68,plain,
! [SV12: $i] :
( ( ( member @ SV12 @ universal_set )
| ~ ( little_set @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(69,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(70,plain,
! [SV1: $i] :
( ( ( ! [SY25: $i] :
~ ( member @ SV1 @ SY25 ) )
= $true )
| ( ( little_set @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(71,plain,
! [SV13: $i,SV2: $i] :
( ( ( SV2 = SV13 )
| ( little_set @ ( f1 @ SV2 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(72,plain,
! [SV14: $i,SV3: $i] :
( ( ( member @ ( f1 @ SV3 @ SV14 ) @ SV3 )
| ( SV3 = SV14 )
| ( member @ ( f1 @ SV3 @ SV14 ) @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(73,plain,
! [SV15: $i,SV4: $i] :
( ( ~ ( member @ ( f1 @ SV4 @ SV15 ) @ SV4 )
| ~ ( member @ ( f1 @ SV4 @ SV15 ) @ SV15 )
| ( SV4 = SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(74,plain,
! [SV16: $i,SV5: $i] :
( ( ! [SY38: $i] :
~ ( member @ SV5 @ ( intersection @ SV16 @ SY38 ) )
| ( member @ SV5 @ SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(75,plain,
! [SV17: $i,SV6: $i] :
( ( ! [SY39: $i] :
( ~ ( member @ SV6 @ ( intersection @ SV17 @ SY39 ) )
| ( member @ SV6 @ SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(76,plain,
! [SV18: $i,SV7: $i] :
( ( ! [SY40: $i] :
( ( member @ SV7 @ ( intersection @ SV18 @ SY40 ) )
| ~ ( member @ SV7 @ SV18 )
| ~ ( member @ SV7 @ SY40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(77,plain,
! [SV19: $i,SV8: $i] :
( ( ~ ( member @ SV8 @ ( complement @ SV19 ) )
| ~ ( member @ SV8 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(78,plain,
! [SV20: $i,SV9: $i] :
( ( ( member @ SV9 @ ( complement @ SV20 ) )
| ~ ( little_set @ SV9 )
| ( member @ SV9 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(79,plain,
! [SV21: $i,SV10: $i] :
( ( ( union @ SV10 @ SV21 )
= ( complement @ ( intersection @ ( complement @ SV10 ) @ ( complement @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(80,plain,
! [SV11: $i] :
( ( member @ SV11 @ empty_set )
= $false ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(81,plain,
! [SV12: $i] :
( ( ( member @ SV12 @ universal_set )
= $true )
| ( ( ~ ( little_set @ SV12 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(82,plain,
! [SV22: $i,SV1: $i] :
( ( ( ~ ( member @ SV1 @ SV22 ) )
= $true )
| ( ( little_set @ SV1 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(83,plain,
! [SV13: $i,SV2: $i] :
( ( ( SV2 = SV13 )
= $true )
| ( ( little_set @ ( f1 @ SV2 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(84,plain,
! [SV14: $i,SV3: $i] :
( ( ( member @ ( f1 @ SV3 @ SV14 ) @ SV3 )
= $true )
| ( ( ( SV3 = SV14 )
| ( member @ ( f1 @ SV3 @ SV14 ) @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(85,plain,
! [SV15: $i,SV4: $i] :
( ( ( ~ ( member @ ( f1 @ SV4 @ SV15 ) @ SV4 ) )
= $true )
| ( ( ~ ( member @ ( f1 @ SV4 @ SV15 ) @ SV15 )
| ( SV4 = SV15 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(86,plain,
! [SV16: $i,SV5: $i] :
( ( ( ! [SY38: $i] :
~ ( member @ SV5 @ ( intersection @ SV16 @ SY38 ) ) )
= $true )
| ( ( member @ SV5 @ SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(87,plain,
! [SV23: $i,SV17: $i,SV6: $i] :
( ( ~ ( member @ SV6 @ ( intersection @ SV17 @ SV23 ) )
| ( member @ SV6 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(88,plain,
! [SV24: $i,SV18: $i,SV7: $i] :
( ( ( member @ SV7 @ ( intersection @ SV18 @ SV24 ) )
| ~ ( member @ SV7 @ SV18 )
| ~ ( member @ SV7 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(89,plain,
! [SV19: $i,SV8: $i] :
( ( ( ~ ( member @ SV8 @ ( complement @ SV19 ) ) )
= $true )
| ( ( ~ ( member @ SV8 @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(90,plain,
! [SV20: $i,SV9: $i] :
( ( ( member @ SV9 @ ( complement @ SV20 ) )
= $true )
| ( ( ~ ( little_set @ SV9 )
| ( member @ SV9 @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(91,plain,
! [SV12: $i] :
( ( ( little_set @ SV12 )
= $false )
| ( ( member @ SV12 @ universal_set )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(92,plain,
! [SV22: $i,SV1: $i] :
( ( ( member @ SV1 @ SV22 )
= $false )
| ( ( little_set @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(93,plain,
! [SV14: $i,SV3: $i] :
( ( ( SV3 = SV14 )
= $true )
| ( ( member @ ( f1 @ SV3 @ SV14 ) @ SV14 )
= $true )
| ( ( member @ ( f1 @ SV3 @ SV14 ) @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[84]) ).
thf(94,plain,
! [SV15: $i,SV4: $i] :
( ( ( member @ ( f1 @ SV4 @ SV15 ) @ SV4 )
= $false )
| ( ( ~ ( member @ ( f1 @ SV4 @ SV15 ) @ SV15 )
| ( SV4 = SV15 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(95,plain,
! [SV25: $i,SV16: $i,SV5: $i] :
( ( ( ~ ( member @ SV5 @ ( intersection @ SV16 @ SV25 ) ) )
= $true )
| ( ( member @ SV5 @ SV16 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(96,plain,
! [SV23: $i,SV17: $i,SV6: $i] :
( ( ( ~ ( member @ SV6 @ ( intersection @ SV17 @ SV23 ) ) )
= $true )
| ( ( member @ SV6 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(97,plain,
! [SV24: $i,SV18: $i,SV7: $i] :
( ( ( member @ SV7 @ ( intersection @ SV18 @ SV24 ) )
= $true )
| ( ( ~ ( member @ SV7 @ SV18 )
| ~ ( member @ SV7 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(98,plain,
! [SV19: $i,SV8: $i] :
( ( ( member @ SV8 @ ( complement @ SV19 ) )
= $false )
| ( ( ~ ( member @ SV8 @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(99,plain,
! [SV20: $i,SV9: $i] :
( ( ( ~ ( little_set @ SV9 ) )
= $true )
| ( ( member @ SV9 @ SV20 )
= $true )
| ( ( member @ SV9 @ ( complement @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(100,plain,
! [SV15: $i,SV4: $i] :
( ( ( ~ ( member @ ( f1 @ SV4 @ SV15 ) @ SV15 ) )
= $true )
| ( ( SV4 = SV15 )
= $true )
| ( ( member @ ( f1 @ SV4 @ SV15 ) @ SV4 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(101,plain,
! [SV25: $i,SV16: $i,SV5: $i] :
( ( ( member @ SV5 @ ( intersection @ SV16 @ SV25 ) )
= $false )
| ( ( member @ SV5 @ SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(102,plain,
! [SV23: $i,SV17: $i,SV6: $i] :
( ( ( member @ SV6 @ ( intersection @ SV17 @ SV23 ) )
= $false )
| ( ( member @ SV6 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(103,plain,
! [SV24: $i,SV18: $i,SV7: $i] :
( ( ( ~ ( member @ SV7 @ SV18 ) )
= $true )
| ( ( ~ ( member @ SV7 @ SV24 ) )
= $true )
| ( ( member @ SV7 @ ( intersection @ SV18 @ SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(104,plain,
! [SV19: $i,SV8: $i] :
( ( ( member @ SV8 @ SV19 )
= $false )
| ( ( member @ SV8 @ ( complement @ SV19 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(105,plain,
! [SV20: $i,SV9: $i] :
( ( ( little_set @ SV9 )
= $false )
| ( ( member @ SV9 @ SV20 )
= $true )
| ( ( member @ SV9 @ ( complement @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(106,plain,
! [SV15: $i,SV4: $i] :
( ( ( member @ ( f1 @ SV4 @ SV15 ) @ SV15 )
= $false )
| ( ( SV4 = SV15 )
= $true )
| ( ( member @ ( f1 @ SV4 @ SV15 ) @ SV4 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(107,plain,
! [SV24: $i,SV18: $i,SV7: $i] :
( ( ( member @ SV7 @ SV18 )
= $false )
| ( ( ~ ( member @ SV7 @ SV24 ) )
= $true )
| ( ( member @ SV7 @ ( intersection @ SV18 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(108,plain,
! [SV18: $i,SV24: $i,SV7: $i] :
( ( ( member @ SV7 @ SV24 )
= $false )
| ( ( member @ SV7 @ SV18 )
= $false )
| ( ( member @ SV7 @ ( intersection @ SV18 @ SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(109,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[41,108,106,105,104,102,101,93,92,91,83,80,79,69,56,42]) ).
thf(110,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET015-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jul 10 22:47:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 15
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.36 (rf:0,axioms:15,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:17,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.91/1.17
% 0.91/1.17 ********************************
% 0.91/1.17 * All subproblems solved! *
% 0.91/1.17 ********************************
% 0.91/1.17 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:15,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:109,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.99/1.17
% 0.99/1.17 %**** Beginning of derivation protocol ****
% 0.99/1.17 % SZS output start CNFRefutation
% See solution above
% 0.99/1.17
% 0.99/1.17 %**** End of derivation protocol ****
% 0.99/1.17 %**** no. of clauses in derivation: 110 ****
% 0.99/1.17 %**** clause counter: 109 ****
% 0.99/1.17
% 0.99/1.17 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:15,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:109,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------