TSTP Solution File: TOP005-2 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : TOP005-2 : 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 : n019.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 21:31:41 EDT 2022
% Result : Unsatisfiable 0.18s 0.44s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 24
% Syntax : Number of formulae : 124 ( 62 unt; 11 typ; 0 def)
% Number of atoms : 622 ( 160 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 1173 ( 143 ~; 189 |; 0 &; 841 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 274 ( 0 ^ 274 !; 0 ?; 274 :)
% Comments :
%------------------------------------------------------------------------------
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_f,type,
f: $i ).
thf(tp_f1,type,
f1: $i > $i > $i ).
thf(tp_f10,type,
f10: $i > $i > $i > $i ).
thf(tp_f11,type,
f11: $i > $i > $i ).
thf(tp_g,type,
g: $i ).
thf(tp_subset_collections,type,
subset_collections: $i > $i > $o ).
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,U: $i] :
( ~ ( subset_collections @ X @ Y )
| ~ ( element_of_collection @ U @ X )
| ( element_of_collection @ U @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_theory_21) ).
thf(2,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( subset_sets @ X @ Y )
| ~ ( element_of_collection @ Y @ Z )
| ( subset_sets @ X @ ( union_of_members @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_theory_20) ).
thf(3,axiom,
! [X: $i,Y: $i,U: $i] :
( ( subset_sets @ X @ Y )
| ~ ( element_of_set @ U @ X )
| ( element_of_set @ U @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_theory_19) ).
thf(4,axiom,
! [U: $i,Vf: $i,Uu11: $i] :
( ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ~ ( element_of_set @ ( f11 @ Vf @ U ) @ Uu11 )
| ~ ( element_of_collection @ Uu11 @ Vf )
| ~ ( subset_sets @ Uu11 @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_41) ).
thf(5,axiom,
! [U: $i,Vf: $i] :
( ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ( element_of_set @ ( f11 @ Vf @ U ) @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_40) ).
thf(6,axiom,
! [U: $i,Vf: $i,X: $i] :
( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ~ ( element_of_set @ X @ U )
| ( subset_sets @ ( f10 @ Vf @ U @ X ) @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_39) ).
thf(7,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/sandbox2/benchmark/theBenchmark.p',topology_generated_38) ).
thf(8,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/sandbox2/benchmark/theBenchmark.p',topology_generated_37) ).
thf(9,axiom,
! [U: $i,Vf: $i] :
( ~ ( element_of_set @ U @ ( union_of_members @ Vf ) )
| ( element_of_collection @ ( f1 @ Vf @ U ) @ Vf ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_of_members_2) ).
thf(10,axiom,
! [U: $i,Vf: $i] :
( ~ ( element_of_set @ U @ ( union_of_members @ Vf ) )
| ( element_of_set @ U @ ( f1 @ Vf @ U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_of_members_1) ).
thf(11,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(12,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[11]) ).
thf(13,negated_conjecture,
~ ( element_of_collection @ ( union_of_members @ g ) @ ( top_of_basis @ f ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1e_3) ).
thf(14,negated_conjecture,
subset_collections @ g @ ( top_of_basis @ f ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1e_2) ).
thf(15,plain,
$false = $false,
inference(unfold_def,[status(thm)],[12]) ).
thf(16,plain,
( ( ! [X: $i,Y: $i,U: $i] :
( ~ ( subset_collections @ X @ Y )
| ~ ( element_of_collection @ U @ X )
| ( element_of_collection @ U @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(17,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( subset_sets @ X @ Y )
| ~ ( element_of_collection @ Y @ Z )
| ( subset_sets @ X @ ( union_of_members @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(18,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)],[3]) ).
thf(19,plain,
( ( ! [U: $i,Vf: $i,Uu11: $i] :
( ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ~ ( element_of_set @ ( f11 @ Vf @ U ) @ Uu11 )
| ~ ( element_of_collection @ Uu11 @ Vf )
| ~ ( subset_sets @ Uu11 @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(20,plain,
( ( ! [U: $i,Vf: $i] :
( ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ( element_of_set @ ( f11 @ Vf @ U ) @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(21,plain,
( ( ! [U: $i,Vf: $i,X: $i] :
( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ~ ( element_of_set @ X @ U )
| ( subset_sets @ ( f10 @ Vf @ U @ X ) @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
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)],[7]) ).
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)],[8]) ).
thf(24,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)],[9]) ).
thf(25,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)],[10]) ).
thf(26,plain,
( ( ~ ( element_of_collection @ ( union_of_members @ g ) @ ( top_of_basis @ f ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(27,plain,
( ( subset_collections @ g @ ( top_of_basis @ f ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(28,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[15]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( subset_collections @ X @ Y )
| ! [U: $i] :
( ~ ( element_of_collection @ U @ X )
| ( element_of_collection @ U @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(30,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( subset_sets @ X @ Y )
| ! [Z: $i] :
( ~ ( element_of_collection @ Y @ Z )
| ( subset_sets @ X @ ( union_of_members @ Z ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(31,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)],[18]) ).
thf(32,plain,
( ( ! [U: $i,Vf: $i] :
( ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ! [Uu11: $i] :
( ~ ( element_of_set @ ( f11 @ Vf @ U ) @ Uu11 )
| ~ ( element_of_collection @ Uu11 @ Vf )
| ~ ( subset_sets @ Uu11 @ U ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(33,plain,
( ( ! [U: $i,Vf: $i] :
( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ! [X: $i] :
( ~ ( element_of_set @ X @ U )
| ( subset_sets @ ( f10 @ Vf @ U @ X ) @ U ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(34,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(35,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(36,plain,
( ( subset_collections @ g @ ( top_of_basis @ f ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(37,plain,
( ( ~ ( element_of_collection @ ( union_of_members @ g ) @ ( top_of_basis @ f ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
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)],[25]) ).
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)],[24]) ).
thf(40,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)],[35]) ).
thf(41,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)],[34]) ).
thf(42,plain,
( ( ! [U: $i,Vf: $i] :
( ~ ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ! [X: $i] :
( ~ ( element_of_set @ X @ U )
| ( subset_sets @ ( f10 @ Vf @ U @ X ) @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(43,plain,
( ( ! [U: $i,Vf: $i] :
( ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ( element_of_set @ ( f11 @ Vf @ U ) @ U ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(44,plain,
( ( ! [U: $i,Vf: $i] :
( ( element_of_collection @ U @ ( top_of_basis @ Vf ) )
| ! [Uu11: $i] :
( ~ ( element_of_set @ ( f11 @ Vf @ U ) @ Uu11 )
| ~ ( element_of_collection @ Uu11 @ Vf )
| ~ ( subset_sets @ Uu11 @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
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)],[31]) ).
thf(46,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( subset_sets @ X @ Y )
| ! [Z: $i] :
( ~ ( element_of_collection @ Y @ Z )
| ( subset_sets @ X @ ( union_of_members @ Z ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(47,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( subset_collections @ X @ Y )
| ! [U: $i] :
( ~ ( element_of_collection @ U @ X )
| ( element_of_collection @ U @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(48,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(49,plain,
( ( element_of_collection @ ( union_of_members @ g ) @ ( top_of_basis @ f ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(50,plain,
! [SV1: $i] :
( ( ! [SY27: $i] :
( ~ ( element_of_set @ SV1 @ ( union_of_members @ SY27 ) )
| ( element_of_set @ SV1 @ ( f1 @ SY27 @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(51,plain,
! [SV2: $i] :
( ( ! [SY28: $i] :
( ~ ( element_of_set @ SV2 @ ( union_of_members @ SY28 ) )
| ( element_of_collection @ ( f1 @ SY28 @ SV2 ) @ SY28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(52,plain,
! [SV3: $i] :
( ( ! [SY29: $i] :
( ~ ( element_of_collection @ SV3 @ ( top_of_basis @ SY29 ) )
| ! [SY30: $i] :
( ~ ( element_of_set @ SY30 @ SV3 )
| ( element_of_set @ SY30 @ ( f10 @ SY29 @ SV3 @ SY30 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(53,plain,
! [SV4: $i] :
( ( ! [SY31: $i] :
( ~ ( element_of_collection @ SV4 @ ( top_of_basis @ SY31 ) )
| ! [SY32: $i] :
( ~ ( element_of_set @ SY32 @ SV4 )
| ( element_of_collection @ ( f10 @ SY31 @ SV4 @ SY32 ) @ SY31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(54,plain,
! [SV5: $i] :
( ( ! [SY33: $i] :
( ~ ( element_of_collection @ SV5 @ ( top_of_basis @ SY33 ) )
| ! [SY34: $i] :
( ~ ( element_of_set @ SY34 @ SV5 )
| ( subset_sets @ ( f10 @ SY33 @ SV5 @ SY34 ) @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(55,plain,
! [SV6: $i] :
( ( ! [SY35: $i] :
( ( element_of_collection @ SV6 @ ( top_of_basis @ SY35 ) )
| ( element_of_set @ ( f11 @ SY35 @ SV6 ) @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(56,plain,
! [SV7: $i] :
( ( ! [SY36: $i] :
( ( element_of_collection @ SV7 @ ( top_of_basis @ SY36 ) )
| ! [SY37: $i] :
( ~ ( element_of_set @ ( f11 @ SY36 @ SV7 ) @ SY37 )
| ~ ( element_of_collection @ SY37 @ SY36 )
| ~ ( subset_sets @ SY37 @ SV7 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(57,plain,
! [SV8: $i] :
( ( ! [SY38: $i] :
( ( subset_sets @ SV8 @ SY38 )
| ! [SY39: $i] :
( ~ ( element_of_set @ SY39 @ SV8 )
| ( element_of_set @ SY39 @ SY38 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(58,plain,
! [SV9: $i] :
( ( ! [SY40: $i] :
( ~ ( subset_sets @ SV9 @ SY40 )
| ! [SY41: $i] :
( ~ ( element_of_collection @ SY40 @ SY41 )
| ( subset_sets @ SV9 @ ( union_of_members @ SY41 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(59,plain,
! [SV10: $i] :
( ( ! [SY42: $i] :
( ~ ( subset_collections @ SV10 @ SY42 )
| ! [SY43: $i] :
( ~ ( element_of_collection @ SY43 @ SV10 )
| ( element_of_collection @ SY43 @ SY42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(60,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(61,plain,
! [SV11: $i,SV1: $i] :
( ( ~ ( element_of_set @ SV1 @ ( union_of_members @ SV11 ) )
| ( element_of_set @ SV1 @ ( f1 @ SV11 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(62,plain,
! [SV12: $i,SV2: $i] :
( ( ~ ( element_of_set @ SV2 @ ( union_of_members @ SV12 ) )
| ( element_of_collection @ ( f1 @ SV12 @ SV2 ) @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(63,plain,
! [SV13: $i,SV3: $i] :
( ( ~ ( element_of_collection @ SV3 @ ( top_of_basis @ SV13 ) )
| ! [SY44: $i] :
( ~ ( element_of_set @ SY44 @ SV3 )
| ( element_of_set @ SY44 @ ( f10 @ SV13 @ SV3 @ SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(64,plain,
! [SV14: $i,SV4: $i] :
( ( ~ ( element_of_collection @ SV4 @ ( top_of_basis @ SV14 ) )
| ! [SY45: $i] :
( ~ ( element_of_set @ SY45 @ SV4 )
| ( element_of_collection @ ( f10 @ SV14 @ SV4 @ SY45 ) @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(65,plain,
! [SV15: $i,SV5: $i] :
( ( ~ ( element_of_collection @ SV5 @ ( top_of_basis @ SV15 ) )
| ! [SY46: $i] :
( ~ ( element_of_set @ SY46 @ SV5 )
| ( subset_sets @ ( f10 @ SV15 @ SV5 @ SY46 ) @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(66,plain,
! [SV16: $i,SV6: $i] :
( ( ( element_of_collection @ SV6 @ ( top_of_basis @ SV16 ) )
| ( element_of_set @ ( f11 @ SV16 @ SV6 ) @ SV6 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(67,plain,
! [SV17: $i,SV7: $i] :
( ( ( element_of_collection @ SV7 @ ( top_of_basis @ SV17 ) )
| ! [SY47: $i] :
( ~ ( element_of_set @ ( f11 @ SV17 @ SV7 ) @ SY47 )
| ~ ( element_of_collection @ SY47 @ SV17 )
| ~ ( subset_sets @ SY47 @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(68,plain,
! [SV18: $i,SV8: $i] :
( ( ( subset_sets @ SV8 @ SV18 )
| ! [SY48: $i] :
( ~ ( element_of_set @ SY48 @ SV8 )
| ( element_of_set @ SY48 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(69,plain,
! [SV19: $i,SV9: $i] :
( ( ~ ( subset_sets @ SV9 @ SV19 )
| ! [SY49: $i] :
( ~ ( element_of_collection @ SV19 @ SY49 )
| ( subset_sets @ SV9 @ ( union_of_members @ SY49 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(70,plain,
! [SV20: $i,SV10: $i] :
( ( ~ ( subset_collections @ SV10 @ SV20 )
| ! [SY50: $i] :
( ~ ( element_of_collection @ SY50 @ SV10 )
| ( element_of_collection @ SY50 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(71,plain,
! [SV11: $i,SV1: $i] :
( ( ( ~ ( element_of_set @ SV1 @ ( union_of_members @ SV11 ) ) )
= $true )
| ( ( element_of_set @ SV1 @ ( f1 @ SV11 @ SV1 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[61]) ).
thf(72,plain,
! [SV12: $i,SV2: $i] :
( ( ( ~ ( element_of_set @ SV2 @ ( union_of_members @ SV12 ) ) )
= $true )
| ( ( element_of_collection @ ( f1 @ SV12 @ SV2 ) @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(73,plain,
! [SV13: $i,SV3: $i] :
( ( ( ~ ( element_of_collection @ SV3 @ ( top_of_basis @ SV13 ) ) )
= $true )
| ( ( ! [SY44: $i] :
( ~ ( element_of_set @ SY44 @ SV3 )
| ( element_of_set @ SY44 @ ( f10 @ SV13 @ SV3 @ SY44 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(74,plain,
! [SV14: $i,SV4: $i] :
( ( ( ~ ( element_of_collection @ SV4 @ ( top_of_basis @ SV14 ) ) )
= $true )
| ( ( ! [SY45: $i] :
( ~ ( element_of_set @ SY45 @ SV4 )
| ( element_of_collection @ ( f10 @ SV14 @ SV4 @ SY45 ) @ SV14 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(75,plain,
! [SV15: $i,SV5: $i] :
( ( ( ~ ( element_of_collection @ SV5 @ ( top_of_basis @ SV15 ) ) )
= $true )
| ( ( ! [SY46: $i] :
( ~ ( element_of_set @ SY46 @ SV5 )
| ( subset_sets @ ( f10 @ SV15 @ SV5 @ SY46 ) @ SV5 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(76,plain,
! [SV16: $i,SV6: $i] :
( ( ( element_of_collection @ SV6 @ ( top_of_basis @ SV16 ) )
= $true )
| ( ( element_of_set @ ( f11 @ SV16 @ SV6 ) @ SV6 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(77,plain,
! [SV17: $i,SV7: $i] :
( ( ( element_of_collection @ SV7 @ ( top_of_basis @ SV17 ) )
= $true )
| ( ( ! [SY47: $i] :
( ~ ( element_of_set @ ( f11 @ SV17 @ SV7 ) @ SY47 )
| ~ ( element_of_collection @ SY47 @ SV17 )
| ~ ( subset_sets @ SY47 @ SV7 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(78,plain,
! [SV18: $i,SV8: $i] :
( ( ( subset_sets @ SV8 @ SV18 )
= $true )
| ( ( ! [SY48: $i] :
( ~ ( element_of_set @ SY48 @ SV8 )
| ( element_of_set @ SY48 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(79,plain,
! [SV19: $i,SV9: $i] :
( ( ( ~ ( subset_sets @ SV9 @ SV19 ) )
= $true )
| ( ( ! [SY49: $i] :
( ~ ( element_of_collection @ SV19 @ SY49 )
| ( subset_sets @ SV9 @ ( union_of_members @ SY49 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[69]) ).
thf(80,plain,
! [SV20: $i,SV10: $i] :
( ( ( ~ ( subset_collections @ SV10 @ SV20 ) )
= $true )
| ( ( ! [SY50: $i] :
( ~ ( element_of_collection @ SY50 @ SV10 )
| ( element_of_collection @ SY50 @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(81,plain,
! [SV11: $i,SV1: $i] :
( ( ( element_of_set @ SV1 @ ( union_of_members @ SV11 ) )
= $false )
| ( ( element_of_set @ SV1 @ ( f1 @ SV11 @ SV1 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(82,plain,
! [SV12: $i,SV2: $i] :
( ( ( element_of_set @ SV2 @ ( union_of_members @ SV12 ) )
= $false )
| ( ( element_of_collection @ ( f1 @ SV12 @ SV2 ) @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(83,plain,
! [SV13: $i,SV3: $i] :
( ( ( element_of_collection @ SV3 @ ( top_of_basis @ SV13 ) )
= $false )
| ( ( ! [SY44: $i] :
( ~ ( element_of_set @ SY44 @ SV3 )
| ( element_of_set @ SY44 @ ( f10 @ SV13 @ SV3 @ SY44 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(84,plain,
! [SV14: $i,SV4: $i] :
( ( ( element_of_collection @ SV4 @ ( top_of_basis @ SV14 ) )
= $false )
| ( ( ! [SY45: $i] :
( ~ ( element_of_set @ SY45 @ SV4 )
| ( element_of_collection @ ( f10 @ SV14 @ SV4 @ SY45 ) @ SV14 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(85,plain,
! [SV15: $i,SV5: $i] :
( ( ( element_of_collection @ SV5 @ ( top_of_basis @ SV15 ) )
= $false )
| ( ( ! [SY46: $i] :
( ~ ( element_of_set @ SY46 @ SV5 )
| ( subset_sets @ ( f10 @ SV15 @ SV5 @ SY46 ) @ SV5 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(86,plain,
! [SV21: $i,SV7: $i,SV17: $i] :
( ( ( ~ ( element_of_set @ ( f11 @ SV17 @ SV7 ) @ SV21 )
| ~ ( element_of_collection @ SV21 @ SV17 )
| ~ ( subset_sets @ SV21 @ SV7 ) )
= $true )
| ( ( element_of_collection @ SV7 @ ( top_of_basis @ SV17 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(87,plain,
! [SV18: $i,SV8: $i,SV22: $i] :
( ( ( ~ ( element_of_set @ SV22 @ SV8 )
| ( element_of_set @ SV22 @ SV18 ) )
= $true )
| ( ( subset_sets @ SV8 @ SV18 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(88,plain,
! [SV19: $i,SV9: $i] :
( ( ( subset_sets @ SV9 @ SV19 )
= $false )
| ( ( ! [SY49: $i] :
( ~ ( element_of_collection @ SV19 @ SY49 )
| ( subset_sets @ SV9 @ ( union_of_members @ SY49 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(89,plain,
! [SV20: $i,SV10: $i] :
( ( ( subset_collections @ SV10 @ SV20 )
= $false )
| ( ( ! [SY50: $i] :
( ~ ( element_of_collection @ SY50 @ SV10 )
| ( element_of_collection @ SY50 @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(90,plain,
! [SV13: $i,SV3: $i,SV23: $i] :
( ( ( ~ ( element_of_set @ SV23 @ SV3 )
| ( element_of_set @ SV23 @ ( f10 @ SV13 @ SV3 @ SV23 ) ) )
= $true )
| ( ( element_of_collection @ SV3 @ ( top_of_basis @ SV13 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(91,plain,
! [SV14: $i,SV4: $i,SV24: $i] :
( ( ( ~ ( element_of_set @ SV24 @ SV4 )
| ( element_of_collection @ ( f10 @ SV14 @ SV4 @ SV24 ) @ SV14 ) )
= $true )
| ( ( element_of_collection @ SV4 @ ( top_of_basis @ SV14 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(92,plain,
! [SV15: $i,SV5: $i,SV25: $i] :
( ( ( ~ ( element_of_set @ SV25 @ SV5 )
| ( subset_sets @ ( f10 @ SV15 @ SV5 @ SV25 ) @ SV5 ) )
= $true )
| ( ( element_of_collection @ SV5 @ ( top_of_basis @ SV15 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(93,plain,
! [SV21: $i,SV7: $i,SV17: $i] :
( ( ( ~ ( element_of_set @ ( f11 @ SV17 @ SV7 ) @ SV21 ) )
= $true )
| ( ( ~ ( element_of_collection @ SV21 @ SV17 )
| ~ ( subset_sets @ SV21 @ SV7 ) )
= $true )
| ( ( element_of_collection @ SV7 @ ( top_of_basis @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(94,plain,
! [SV18: $i,SV8: $i,SV22: $i] :
( ( ( ~ ( element_of_set @ SV22 @ SV8 ) )
= $true )
| ( ( element_of_set @ SV22 @ SV18 )
= $true )
| ( ( subset_sets @ SV8 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(95,plain,
! [SV9: $i,SV26: $i,SV19: $i] :
( ( ( ~ ( element_of_collection @ SV19 @ SV26 )
| ( subset_sets @ SV9 @ ( union_of_members @ SV26 ) ) )
= $true )
| ( ( subset_sets @ SV9 @ SV19 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(96,plain,
! [SV20: $i,SV10: $i,SV27: $i] :
( ( ( ~ ( element_of_collection @ SV27 @ SV10 )
| ( element_of_collection @ SV27 @ SV20 ) )
= $true )
| ( ( subset_collections @ SV10 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(97,plain,
! [SV13: $i,SV3: $i,SV23: $i] :
( ( ( ~ ( element_of_set @ SV23 @ SV3 ) )
= $true )
| ( ( element_of_set @ SV23 @ ( f10 @ SV13 @ SV3 @ SV23 ) )
= $true )
| ( ( element_of_collection @ SV3 @ ( top_of_basis @ SV13 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(98,plain,
! [SV14: $i,SV4: $i,SV24: $i] :
( ( ( ~ ( element_of_set @ SV24 @ SV4 ) )
= $true )
| ( ( element_of_collection @ ( f10 @ SV14 @ SV4 @ SV24 ) @ SV14 )
= $true )
| ( ( element_of_collection @ SV4 @ ( top_of_basis @ SV14 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(99,plain,
! [SV15: $i,SV5: $i,SV25: $i] :
( ( ( ~ ( element_of_set @ SV25 @ SV5 ) )
= $true )
| ( ( subset_sets @ ( f10 @ SV15 @ SV5 @ SV25 ) @ SV5 )
= $true )
| ( ( element_of_collection @ SV5 @ ( top_of_basis @ SV15 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(100,plain,
! [SV21: $i,SV7: $i,SV17: $i] :
( ( ( element_of_set @ ( f11 @ SV17 @ SV7 ) @ SV21 )
= $false )
| ( ( ~ ( element_of_collection @ SV21 @ SV17 )
| ~ ( subset_sets @ SV21 @ SV7 ) )
= $true )
| ( ( element_of_collection @ SV7 @ ( top_of_basis @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(101,plain,
! [SV18: $i,SV8: $i,SV22: $i] :
( ( ( element_of_set @ SV22 @ SV8 )
= $false )
| ( ( element_of_set @ SV22 @ SV18 )
= $true )
| ( ( subset_sets @ SV8 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(102,plain,
! [SV9: $i,SV26: $i,SV19: $i] :
( ( ( ~ ( element_of_collection @ SV19 @ SV26 ) )
= $true )
| ( ( subset_sets @ SV9 @ ( union_of_members @ SV26 ) )
= $true )
| ( ( subset_sets @ SV9 @ SV19 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(103,plain,
! [SV20: $i,SV10: $i,SV27: $i] :
( ( ( ~ ( element_of_collection @ SV27 @ SV10 ) )
= $true )
| ( ( element_of_collection @ SV27 @ SV20 )
= $true )
| ( ( subset_collections @ SV10 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(104,plain,
! [SV13: $i,SV3: $i,SV23: $i] :
( ( ( element_of_set @ SV23 @ SV3 )
= $false )
| ( ( element_of_set @ SV23 @ ( f10 @ SV13 @ SV3 @ SV23 ) )
= $true )
| ( ( element_of_collection @ SV3 @ ( top_of_basis @ SV13 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(105,plain,
! [SV14: $i,SV4: $i,SV24: $i] :
( ( ( element_of_set @ SV24 @ SV4 )
= $false )
| ( ( element_of_collection @ ( f10 @ SV14 @ SV4 @ SV24 ) @ SV14 )
= $true )
| ( ( element_of_collection @ SV4 @ ( top_of_basis @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(106,plain,
! [SV15: $i,SV5: $i,SV25: $i] :
( ( ( element_of_set @ SV25 @ SV5 )
= $false )
| ( ( subset_sets @ ( f10 @ SV15 @ SV5 @ SV25 ) @ SV5 )
= $true )
| ( ( element_of_collection @ SV5 @ ( top_of_basis @ SV15 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(107,plain,
! [SV7: $i,SV17: $i,SV21: $i] :
( ( ( ~ ( element_of_collection @ SV21 @ SV17 ) )
= $true )
| ( ( ~ ( subset_sets @ SV21 @ SV7 ) )
= $true )
| ( ( element_of_set @ ( f11 @ SV17 @ SV7 ) @ SV21 )
= $false )
| ( ( element_of_collection @ SV7 @ ( top_of_basis @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(108,plain,
! [SV9: $i,SV26: $i,SV19: $i] :
( ( ( element_of_collection @ SV19 @ SV26 )
= $false )
| ( ( subset_sets @ SV9 @ ( union_of_members @ SV26 ) )
= $true )
| ( ( subset_sets @ SV9 @ SV19 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(109,plain,
! [SV20: $i,SV10: $i,SV27: $i] :
( ( ( element_of_collection @ SV27 @ SV10 )
= $false )
| ( ( element_of_collection @ SV27 @ SV20 )
= $true )
| ( ( subset_collections @ SV10 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(110,plain,
! [SV7: $i,SV17: $i,SV21: $i] :
( ( ( element_of_collection @ SV21 @ SV17 )
= $false )
| ( ( ~ ( subset_sets @ SV21 @ SV7 ) )
= $true )
| ( ( element_of_set @ ( f11 @ SV17 @ SV7 ) @ SV21 )
= $false )
| ( ( element_of_collection @ SV7 @ ( top_of_basis @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(111,plain,
! [SV17: $i,SV7: $i,SV21: $i] :
( ( ( subset_sets @ SV21 @ SV7 )
= $false )
| ( ( element_of_collection @ SV21 @ SV17 )
= $false )
| ( ( element_of_set @ ( f11 @ SV17 @ SV7 ) @ SV21 )
= $false )
| ( ( element_of_collection @ SV7 @ ( top_of_basis @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[110]) ).
thf(112,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[36,111,109,108,106,105,104,101,82,81,76,60,49]) ).
thf(113,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : TOP005-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun May 29 12:28:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.35
% 0.12/0.35 No.of.Axioms: 12
% 0.12/0.35
% 0.12/0.35 Length.of.Defs: 0
% 0.12/0.35
% 0.12/0.35 Contains.Choice.Funs: false
% 0.12/0.36 (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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:14,loop_count:0,foatp_calls:0,translation:fof_full)......
% 0.18/0.44
% 0.18/0.44 ********************************
% 0.18/0.44 * All subproblems solved! *
% 0.18/0.44 ********************************
% 0.18/0.44 % SZS status Unsatisfiable 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:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:112,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.18/0.44
% 0.18/0.44 %**** Beginning of derivation protocol ****
% 0.18/0.44 % SZS output start CNFRefutation
% See solution above
% 0.18/0.44
% 0.18/0.44 %**** End of derivation protocol ****
% 0.18/0.44 %**** no. of clauses in derivation: 113 ****
% 0.18/0.44 %**** clause counter: 112 ****
% 0.18/0.44
% 0.18/0.44 % SZS status Unsatisfiable 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:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:112,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------