TSTP Solution File: TOP001-2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : TOP001-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n024.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 : Thu Jul 21 21:31:40 EDT 2022
% Result : Unsatisfiable 0.20s 0.41s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 26
% Syntax : Number of formulae : 117 ( 64 unt; 12 typ; 0 def)
% Number of atoms : 495 ( 130 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 873 ( 105 ~; 130 |; 0 &; 638 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 220 ( 0 ^ 220 !; 0 ?; 220 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_basis,type,
basis: $i > $i > $o ).
thf(tp_cx,type,
cx: $i ).
thf(tp_element_of_collection,type,
element_of_collection: $i > $i > $o ).
thf(tp_element_of_set,type,
element_of_set: $i > $i > $o ).
thf(tp_equal_sets,type,
equal_sets: $i > $i > $o ).
thf(tp_f,type,
f: $i ).
thf(tp_f1,type,
f1: $i > $i > $i ).
thf(tp_f10,type,
f10: $i > $i > $i > $i ).
thf(tp_in_1st_set,type,
in_1st_set: $i > $i > $i ).
thf(tp_subset_sets,type,
subset_sets: $i > $i > $o ).
thf(tp_top_of_basis,type,
top_of_basis: $i > $i ).
thf(tp_union_of_members,type,
union_of_members: $i > $i ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ( subset_sets @ X @ Y )
| ~ ( element_of_set @ ( in_1st_set @ X @ Y ) @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_5) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ( subset_sets @ X @ Y )
| ( element_of_set @ ( in_1st_set @ X @ Y ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_4) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ~ ( equal_sets @ X @ Y )
| ( subset_sets @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_3) ).
thf(4,axiom,
! [X: $i,Y: $i,U: $i] :
( ~ ( subset_sets @ X @ Y )
| ~ ( element_of_set @ U @ X )
| ( element_of_set @ U @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_2) ).
thf(5,axiom,
! [X: $i] : ( subset_sets @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_theory_1) ).
thf(6,axiom,
! [U: $i,Vf: $i,X: $i] :
( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ~ ( element_of_set @ X @ U )
| ( element_of_collection @ ( f10 @ Vf @ U @ X ) @ Vf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topology_generated_38) ).
thf(7,axiom,
! [U: $i,Vf: $i,X: $i] :
( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ~ ( element_of_set @ X @ U )
| ( element_of_set @ X @ ( f10 @ Vf @ U @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',topology_generated_37) ).
thf(8,axiom,
! [X: $i,Vf: $i] :
( ~ ( basis @ X @ Vf )
| ( equal_sets @ ( union_of_members @ Vf ) @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_for_topology_28) ).
thf(9,axiom,
! [U: $i,Vf: $i,Uu1: $i] :
( ( element_of_set @ U @ ( union_of_members @ Vf ) )
| ~ ( element_of_set @ U @ Uu1 )
| ~ ( element_of_collection @ Uu1 @ Vf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_of_members_3) ).
thf(10,axiom,
! [U: $i,Vf: $i] :
( ~ ( element_of_set @ U @ ( union_of_members @ Vf ) )
| ( element_of_collection @ ( f1 @ Vf @ U ) @ Vf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_of_members_2) ).
thf(11,axiom,
! [U: $i,Vf: $i] :
( ~ ( element_of_set @ U @ ( union_of_members @ Vf ) )
| ( element_of_set @ U @ ( f1 @ Vf @ U ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_of_members_1) ).
thf(12,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(13,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[12]) ).
thf(14,negated_conjecture,
~ ( subset_sets @ ( union_of_members @ ( top_of_basis @ f ) ) @ cx ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1a_2) ).
thf(15,negated_conjecture,
basis @ cx @ f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lemma_1a_1) ).
thf(16,plain,
$false = $false,
inference(unfold_def,[status(thm)],[13]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i] :
( ( subset_sets @ X @ Y )
| ~ ( element_of_set @ ( in_1st_set @ X @ Y ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(18,plain,
( ( ! [X: $i,Y: $i] :
( ( subset_sets @ X @ Y )
| ( element_of_set @ ( in_1st_set @ X @ Y ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(19,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equal_sets @ X @ Y )
| ( subset_sets @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( subset_sets @ X @ Y )
| ~ ( element_of_set @ U @ X )
| ( element_of_set @ U @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(21,plain,
( ( ! [X: $i] : ( subset_sets @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(22,plain,
( ( ! [U: $i,Vf: $i,X: $i] :
( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ~ ( element_of_set @ X @ U )
| ( element_of_collection @ ( f10 @ Vf @ U @ X ) @ Vf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(23,plain,
( ( ! [U: $i,Vf: $i,X: $i] :
( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ~ ( element_of_set @ X @ U )
| ( element_of_set @ X @ ( f10 @ Vf @ U @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(24,plain,
( ( ! [X: $i,Vf: $i] :
( ~ ( basis @ X @ Vf )
| ( equal_sets @ ( union_of_members @ Vf ) @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(25,plain,
( ( ! [U: $i,Vf: $i,Uu1: $i] :
( ( element_of_set @ U @ ( union_of_members @ Vf ) )
| ~ ( element_of_set @ U @ Uu1 )
| ~ ( element_of_collection @ Uu1 @ Vf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(26,plain,
( ( ! [U: $i,Vf: $i] :
( ~ ( element_of_set @ U @ ( union_of_members @ Vf ) )
| ( element_of_collection @ ( f1 @ Vf @ U ) @ Vf ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(27,plain,
( ( ! [U: $i,Vf: $i] :
( ~ ( element_of_set @ U @ ( union_of_members @ Vf ) )
| ( element_of_set @ U @ ( f1 @ Vf @ U ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(28,plain,
( ( ~ ( subset_sets @ ( union_of_members @ ( top_of_basis @ f ) ) @ cx ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(29,plain,
( ( basis @ cx @ f )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(30,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(31,plain,
( ( ! [X: $i,Y: $i] :
( ( element_of_set @ ( in_1st_set @ X @ Y ) @ X )
| ( subset_sets @ X @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(32,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( subset_sets @ X @ Y )
| ! [U: $i] :
( ~ ( element_of_set @ U @ X )
| ( element_of_set @ U @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(33,plain,
( ( ! [U: $i,Vf: $i] :
( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ! [X: $i] :
( ~ ( element_of_set @ X @ U )
| ( element_of_collection @ ( f10 @ Vf @ U @ X ) @ Vf ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(34,plain,
( ( ! [U: $i,Vf: $i] :
( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ! [X: $i] :
( ~ ( element_of_set @ X @ U )
| ( element_of_set @ X @ ( f10 @ Vf @ U @ X ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(35,plain,
( ( ! [U: $i,Vf: $i] :
( ( element_of_set @ U @ ( union_of_members @ Vf ) )
| ! [Uu1: $i] :
( ~ ( element_of_set @ U @ Uu1 )
| ~ ( element_of_collection @ Uu1 @ Vf ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(36,plain,
( ( basis @ cx @ f )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(37,plain,
( ( ~ ( subset_sets @ ( union_of_members @ ( top_of_basis @ f ) ) @ cx ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(38,plain,
( ( ! [U: $i,Vf: $i] :
( ~ ( element_of_set @ U @ ( union_of_members @ Vf ) )
| ( element_of_set @ U @ ( f1 @ Vf @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(39,plain,
( ( ! [U: $i,Vf: $i] :
( ~ ( element_of_set @ U @ ( union_of_members @ Vf ) )
| ( element_of_collection @ ( f1 @ Vf @ U ) @ Vf ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(40,plain,
( ( ! [U: $i,Vf: $i] :
( ( element_of_set @ U @ ( union_of_members @ Vf ) )
| ! [Uu1: $i] :
( ~ ( element_of_set @ U @ Uu1 )
| ~ ( element_of_collection @ Uu1 @ Vf ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(41,plain,
( ( ! [X: $i,Vf: $i] :
( ~ ( basis @ X @ Vf )
| ( equal_sets @ ( union_of_members @ Vf ) @ X ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(42,plain,
( ( ! [U: $i,Vf: $i] :
( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ! [X: $i] :
( ~ ( element_of_set @ X @ U )
| ( element_of_set @ X @ ( f10 @ Vf @ U @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(43,plain,
( ( ! [U: $i,Vf: $i] :
( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ! [X: $i] :
( ~ ( element_of_set @ X @ U )
| ( element_of_collection @ ( f10 @ Vf @ U @ X ) @ Vf ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(44,plain,
( ( ! [X: $i] : ( subset_sets @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(45,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( subset_sets @ X @ Y )
| ! [U: $i] :
( ~ ( element_of_set @ U @ X )
| ( element_of_set @ U @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(46,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equal_sets @ X @ Y )
| ( subset_sets @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(47,plain,
( ( ! [X: $i,Y: $i] :
( ( element_of_set @ ( in_1st_set @ X @ Y ) @ X )
| ( subset_sets @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(48,plain,
( ( ! [X: $i,Y: $i] :
( ( subset_sets @ X @ Y )
| ~ ( element_of_set @ ( in_1st_set @ X @ Y ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(49,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(50,plain,
( ( subset_sets @ ( union_of_members @ ( top_of_basis @ f ) ) @ cx )
= $false ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(51,plain,
! [SV1: $i] :
( ( ! [SY25: $i] :
( ~ ( element_of_set @ SV1 @ ( union_of_members @ SY25 ) )
| ( element_of_set @ SV1 @ ( f1 @ SY25 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(52,plain,
! [SV2: $i] :
( ( ! [SY26: $i] :
( ~ ( element_of_set @ SV2 @ ( union_of_members @ SY26 ) )
| ( element_of_collection @ ( f1 @ SY26 @ SV2 ) @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(53,plain,
! [SV3: $i] :
( ( ! [SY27: $i] :
( ( element_of_set @ SV3 @ ( union_of_members @ SY27 ) )
| ! [SY28: $i] :
( ~ ( element_of_set @ SV3 @ SY28 )
| ~ ( element_of_collection @ SY28 @ SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(54,plain,
! [SV4: $i] :
( ( ! [SY29: $i] :
( ~ ( basis @ SV4 @ SY29 )
| ( equal_sets @ ( union_of_members @ SY29 ) @ SV4 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(55,plain,
! [SV5: $i] :
( ( ! [SY30: $i] :
( ~ ( element_of_collection @ SV5 @ ( top_of_basis @ SY30 ) )
| ! [SY31: $i] :
( ~ ( element_of_set @ SY31 @ SV5 )
| ( element_of_set @ SY31 @ ( f10 @ SY30 @ SV5 @ SY31 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(56,plain,
! [SV6: $i] :
( ( ! [SY32: $i] :
( ~ ( element_of_collection @ SV6 @ ( top_of_basis @ SY32 ) )
| ! [SY33: $i] :
( ~ ( element_of_set @ SY33 @ SV6 )
| ( element_of_collection @ ( f10 @ SY32 @ SV6 @ SY33 ) @ SY32 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(57,plain,
! [SV7: $i] :
( ( subset_sets @ SV7 @ SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(58,plain,
! [SV8: $i] :
( ( ! [SY34: $i] :
( ~ ( subset_sets @ SV8 @ SY34 )
| ! [SY35: $i] :
( ~ ( element_of_set @ SY35 @ SV8 )
| ( element_of_set @ SY35 @ SY34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(59,plain,
! [SV9: $i] :
( ( ! [SY36: $i] :
( ~ ( equal_sets @ SV9 @ SY36 )
| ( subset_sets @ SV9 @ SY36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(60,plain,
! [SV10: $i] :
( ( ! [SY37: $i] :
( ( element_of_set @ ( in_1st_set @ SV10 @ SY37 ) @ SV10 )
| ( subset_sets @ SV10 @ SY37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(61,plain,
! [SV11: $i] :
( ( ! [SY38: $i] :
( ( subset_sets @ SV11 @ SY38 )
| ~ ( element_of_set @ ( in_1st_set @ SV11 @ SY38 ) @ SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(62,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(63,plain,
! [SV12: $i,SV1: $i] :
( ( ~ ( element_of_set @ SV1 @ ( union_of_members @ SV12 ) )
| ( element_of_set @ SV1 @ ( f1 @ SV12 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(64,plain,
! [SV13: $i,SV2: $i] :
( ( ~ ( element_of_set @ SV2 @ ( union_of_members @ SV13 ) )
| ( element_of_collection @ ( f1 @ SV13 @ SV2 ) @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(65,plain,
! [SV14: $i,SV3: $i] :
( ( ( element_of_set @ SV3 @ ( union_of_members @ SV14 ) )
| ! [SY39: $i] :
( ~ ( element_of_set @ SV3 @ SY39 )
| ~ ( element_of_collection @ SY39 @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(66,plain,
! [SV15: $i,SV4: $i] :
( ( ~ ( basis @ SV4 @ SV15 )
| ( equal_sets @ ( union_of_members @ SV15 ) @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(67,plain,
! [SV16: $i,SV5: $i] :
( ( ~ ( element_of_collection @ SV5 @ ( top_of_basis @ SV16 ) )
| ! [SY40: $i] :
( ~ ( element_of_set @ SY40 @ SV5 )
| ( element_of_set @ SY40 @ ( f10 @ SV16 @ SV5 @ SY40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(68,plain,
! [SV17: $i,SV6: $i] :
( ( ~ ( element_of_collection @ SV6 @ ( top_of_basis @ SV17 ) )
| ! [SY41: $i] :
( ~ ( element_of_set @ SY41 @ SV6 )
| ( element_of_collection @ ( f10 @ SV17 @ SV6 @ SY41 ) @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(69,plain,
! [SV18: $i,SV8: $i] :
( ( ~ ( subset_sets @ SV8 @ SV18 )
| ! [SY42: $i] :
( ~ ( element_of_set @ SY42 @ SV8 )
| ( element_of_set @ SY42 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(70,plain,
! [SV19: $i,SV9: $i] :
( ( ~ ( equal_sets @ SV9 @ SV19 )
| ( subset_sets @ SV9 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(71,plain,
! [SV20: $i,SV10: $i] :
( ( ( element_of_set @ ( in_1st_set @ SV10 @ SV20 ) @ SV10 )
| ( subset_sets @ SV10 @ SV20 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(72,plain,
! [SV21: $i,SV11: $i] :
( ( ( subset_sets @ SV11 @ SV21 )
| ~ ( element_of_set @ ( in_1st_set @ SV11 @ SV21 ) @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(73,plain,
! [SV12: $i,SV1: $i] :
( ( ( ~ ( element_of_set @ SV1 @ ( union_of_members @ SV12 ) ) )
= $true )
| ( ( element_of_set @ SV1 @ ( f1 @ SV12 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(74,plain,
! [SV13: $i,SV2: $i] :
( ( ( ~ ( element_of_set @ SV2 @ ( union_of_members @ SV13 ) ) )
= $true )
| ( ( element_of_collection @ ( f1 @ SV13 @ SV2 ) @ SV13 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(75,plain,
! [SV14: $i,SV3: $i] :
( ( ( element_of_set @ SV3 @ ( union_of_members @ SV14 ) )
= $true )
| ( ( ! [SY39: $i] :
( ~ ( element_of_set @ SV3 @ SY39 )
| ~ ( element_of_collection @ SY39 @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(76,plain,
! [SV15: $i,SV4: $i] :
( ( ( ~ ( basis @ SV4 @ SV15 ) )
= $true )
| ( ( equal_sets @ ( union_of_members @ SV15 ) @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(77,plain,
! [SV16: $i,SV5: $i] :
( ( ( ~ ( element_of_collection @ SV5 @ ( top_of_basis @ SV16 ) ) )
= $true )
| ( ( ! [SY40: $i] :
( ~ ( element_of_set @ SY40 @ SV5 )
| ( element_of_set @ SY40 @ ( f10 @ SV16 @ SV5 @ SY40 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(78,plain,
! [SV17: $i,SV6: $i] :
( ( ( ~ ( element_of_collection @ SV6 @ ( top_of_basis @ SV17 ) ) )
= $true )
| ( ( ! [SY41: $i] :
( ~ ( element_of_set @ SY41 @ SV6 )
| ( element_of_collection @ ( f10 @ SV17 @ SV6 @ SY41 ) @ SV17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(79,plain,
! [SV18: $i,SV8: $i] :
( ( ( ~ ( subset_sets @ SV8 @ SV18 ) )
= $true )
| ( ( ! [SY42: $i] :
( ~ ( element_of_set @ SY42 @ SV8 )
| ( element_of_set @ SY42 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(80,plain,
! [SV19: $i,SV9: $i] :
( ( ( ~ ( equal_sets @ SV9 @ SV19 ) )
= $true )
| ( ( subset_sets @ SV9 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(81,plain,
! [SV20: $i,SV10: $i] :
( ( ( element_of_set @ ( in_1st_set @ SV10 @ SV20 ) @ SV10 )
= $true )
| ( ( subset_sets @ SV10 @ SV20 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(82,plain,
! [SV21: $i,SV11: $i] :
( ( ( subset_sets @ SV11 @ SV21 )
= $true )
| ( ( ~ ( element_of_set @ ( in_1st_set @ SV11 @ SV21 ) @ SV21 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(83,plain,
! [SV12: $i,SV1: $i] :
( ( ( element_of_set @ SV1 @ ( union_of_members @ SV12 ) )
= $false )
| ( ( element_of_set @ SV1 @ ( f1 @ SV12 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(84,plain,
! [SV13: $i,SV2: $i] :
( ( ( element_of_set @ SV2 @ ( union_of_members @ SV13 ) )
= $false )
| ( ( element_of_collection @ ( f1 @ SV13 @ SV2 ) @ SV13 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(85,plain,
! [SV14: $i,SV22: $i,SV3: $i] :
( ( ( ~ ( element_of_set @ SV3 @ SV22 )
| ~ ( element_of_collection @ SV22 @ SV14 ) )
= $true )
| ( ( element_of_set @ SV3 @ ( union_of_members @ SV14 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(86,plain,
! [SV15: $i,SV4: $i] :
( ( ( basis @ SV4 @ SV15 )
= $false )
| ( ( equal_sets @ ( union_of_members @ SV15 ) @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(87,plain,
! [SV16: $i,SV5: $i] :
( ( ( element_of_collection @ SV5 @ ( top_of_basis @ SV16 ) )
= $false )
| ( ( ! [SY40: $i] :
( ~ ( element_of_set @ SY40 @ SV5 )
| ( element_of_set @ SY40 @ ( f10 @ SV16 @ SV5 @ SY40 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(88,plain,
! [SV17: $i,SV6: $i] :
( ( ( element_of_collection @ SV6 @ ( top_of_basis @ SV17 ) )
= $false )
| ( ( ! [SY41: $i] :
( ~ ( element_of_set @ SY41 @ SV6 )
| ( element_of_collection @ ( f10 @ SV17 @ SV6 @ SY41 ) @ SV17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(89,plain,
! [SV18: $i,SV8: $i] :
( ( ( subset_sets @ SV8 @ SV18 )
= $false )
| ( ( ! [SY42: $i] :
( ~ ( element_of_set @ SY42 @ SV8 )
| ( element_of_set @ SY42 @ SV18 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(90,plain,
! [SV19: $i,SV9: $i] :
( ( ( equal_sets @ SV9 @ SV19 )
= $false )
| ( ( subset_sets @ SV9 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(91,plain,
! [SV21: $i,SV11: $i] :
( ( ( element_of_set @ ( in_1st_set @ SV11 @ SV21 ) @ SV21 )
= $false )
| ( ( subset_sets @ SV11 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(92,plain,
! [SV14: $i,SV22: $i,SV3: $i] :
( ( ( ~ ( element_of_set @ SV3 @ SV22 ) )
= $true )
| ( ( ~ ( element_of_collection @ SV22 @ SV14 ) )
= $true )
| ( ( element_of_set @ SV3 @ ( union_of_members @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(93,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ( ~ ( element_of_set @ SV23 @ SV5 )
| ( element_of_set @ SV23 @ ( f10 @ SV16 @ SV5 @ SV23 ) ) )
= $true )
| ( ( element_of_collection @ SV5 @ ( top_of_basis @ SV16 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(94,plain,
! [SV17: $i,SV6: $i,SV24: $i] :
( ( ( ~ ( element_of_set @ SV24 @ SV6 )
| ( element_of_collection @ ( f10 @ SV17 @ SV6 @ SV24 ) @ SV17 ) )
= $true )
| ( ( element_of_collection @ SV6 @ ( top_of_basis @ SV17 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(95,plain,
! [SV18: $i,SV8: $i,SV25: $i] :
( ( ( ~ ( element_of_set @ SV25 @ SV8 )
| ( element_of_set @ SV25 @ SV18 ) )
= $true )
| ( ( subset_sets @ SV8 @ SV18 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(96,plain,
! [SV14: $i,SV22: $i,SV3: $i] :
( ( ( element_of_set @ SV3 @ SV22 )
= $false )
| ( ( ~ ( element_of_collection @ SV22 @ SV14 ) )
= $true )
| ( ( element_of_set @ SV3 @ ( union_of_members @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(97,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ( ~ ( element_of_set @ SV23 @ SV5 ) )
= $true )
| ( ( element_of_set @ SV23 @ ( f10 @ SV16 @ SV5 @ SV23 ) )
= $true )
| ( ( element_of_collection @ SV5 @ ( top_of_basis @ SV16 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[93]) ).
thf(98,plain,
! [SV17: $i,SV6: $i,SV24: $i] :
( ( ( ~ ( element_of_set @ SV24 @ SV6 ) )
= $true )
| ( ( element_of_collection @ ( f10 @ SV17 @ SV6 @ SV24 ) @ SV17 )
= $true )
| ( ( element_of_collection @ SV6 @ ( top_of_basis @ SV17 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(99,plain,
! [SV18: $i,SV8: $i,SV25: $i] :
( ( ( ~ ( element_of_set @ SV25 @ SV8 ) )
= $true )
| ( ( element_of_set @ SV25 @ SV18 )
= $true )
| ( ( subset_sets @ SV8 @ SV18 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(100,plain,
! [SV3: $i,SV14: $i,SV22: $i] :
( ( ( element_of_collection @ SV22 @ SV14 )
= $false )
| ( ( element_of_set @ SV3 @ SV22 )
= $false )
| ( ( element_of_set @ SV3 @ ( union_of_members @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(101,plain,
! [SV16: $i,SV5: $i,SV23: $i] :
( ( ( element_of_set @ SV23 @ SV5 )
= $false )
| ( ( element_of_set @ SV23 @ ( f10 @ SV16 @ SV5 @ SV23 ) )
= $true )
| ( ( element_of_collection @ SV5 @ ( top_of_basis @ SV16 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(102,plain,
! [SV17: $i,SV6: $i,SV24: $i] :
( ( ( element_of_set @ SV24 @ SV6 )
= $false )
| ( ( element_of_collection @ ( f10 @ SV17 @ SV6 @ SV24 ) @ SV17 )
= $true )
| ( ( element_of_collection @ SV6 @ ( top_of_basis @ SV17 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(103,plain,
! [SV18: $i,SV8: $i,SV25: $i] :
( ( ( element_of_set @ SV25 @ SV8 )
= $false )
| ( ( element_of_set @ SV25 @ SV18 )
= $true )
| ( ( subset_sets @ SV8 @ SV18 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(104,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[36,103,102,101,100,91,90,86,84,83,81,62,57,50]) ).
thf(105,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[104]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : TOP001-2 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n024.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 May 29 14:13:36 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 13
% 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:13,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:15,loop_count:0,foatp_calls:0,translation:fof_full).....
% 0.20/0.41
% 0.20/0.41 ********************************
% 0.20/0.41 * All subproblems solved! *
% 0.20/0.41 ********************************
% 0.20/0.41 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:13,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:104,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.20/0.42
% 0.20/0.42 %**** Beginning of derivation protocol ****
% 0.20/0.42 % SZS output start CNFRefutation
% See solution above
% 0.20/0.42
% 0.20/0.42 %**** End of derivation protocol ****
% 0.20/0.42 %**** no. of clauses in derivation: 105 ****
% 0.20/0.42 %**** clause counter: 104 ****
% 0.20/0.42
% 0.20/0.42 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:13,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:104,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------