TSTP Solution File: GRP114-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GRP114-1 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n008.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 : Sat Jul 16 10:15:57 EDT 2022
% Result : Unsatisfiable 2.29s 2.48s
% Output : CNFRefutation 2.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 30
% Syntax : Number of formulae : 119 ( 111 unt; 8 typ; 0 def)
% Number of atoms : 287 ( 191 equ; 0 cnn)
% Maximal formula atoms : 1 ( 2 avg)
% Number of connectives : 596 ( 6 ~; 0 |; 0 &; 590 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 204 ( 0 ^ 204 !; 0 ?; 204 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_identity,type,
identity: $i ).
thf(tp_intersection,type,
intersection: $i > $i > $i ).
thf(tp_inverse,type,
inverse: $i > $i ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(tp_negative_part,type,
negative_part: $i > $i ).
thf(tp_positive_part,type,
positive_part: $i > $i ).
thf(tp_union,type,
union: $i > $i > $i ).
thf(1,axiom,
! [X: $i] :
( ( negative_part @ X )
= ( intersection @ X @ identity ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',negative_part) ).
thf(2,axiom,
! [X: $i] :
( ( positive_part @ X )
= ( union @ X @ identity ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',positive_part) ).
thf(3,axiom,
! [Y: $i,Z: $i,X: $i] :
( ( multiply @ ( intersection @ Y @ Z ) @ X )
= ( intersection @ ( multiply @ Y @ X ) @ ( multiply @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_intersection2) ).
thf(4,axiom,
! [Y: $i,Z: $i,X: $i] :
( ( multiply @ ( union @ Y @ Z ) @ X )
= ( union @ ( multiply @ Y @ X ) @ ( multiply @ Z @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_union2) ).
thf(5,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( intersection @ Y @ Z ) )
= ( intersection @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_intersection1) ).
thf(6,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( union @ Y @ Z ) )
= ( union @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply_union1) ).
thf(7,axiom,
! [X: $i,Y: $i] :
( ( intersection @ ( union @ X @ Y ) @ Y )
= Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_union_absorbtion) ).
thf(8,axiom,
! [X: $i,Y: $i] :
( ( union @ ( intersection @ X @ Y ) @ Y )
= Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_intersection_absorbtion) ).
thf(9,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( union @ X @ ( union @ Y @ Z ) )
= ( union @ ( union @ X @ Y ) @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_associative) ).
thf(10,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( intersection @ X @ ( intersection @ Y @ Z ) )
= ( intersection @ ( intersection @ X @ Y ) @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_associative) ).
thf(11,axiom,
! [X: $i,Y: $i] :
( ( union @ X @ Y )
= ( union @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_commutative) ).
thf(12,axiom,
! [X: $i,Y: $i] :
( ( intersection @ X @ Y )
= ( intersection @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_commutative) ).
thf(13,axiom,
! [X: $i] :
( ( union @ X @ X )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_idempotent) ).
thf(14,axiom,
! [X: $i] :
( ( intersection @ X @ X )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_idempotent) ).
thf(15,axiom,
! [X: $i,Y: $i] :
( ( inverse @ ( multiply @ X @ Y ) )
= ( multiply @ ( inverse @ Y ) @ ( inverse @ X ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_product_lemma) ).
thf(16,axiom,
! [X: $i] :
( ( inverse @ ( inverse @ X ) )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_involution) ).
thf(17,axiom,
( ( inverse @ identity )
= identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_of_identity) ).
thf(18,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
thf(19,axiom,
! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
thf(20,axiom,
! [X: $i] :
( ( multiply @ identity @ X )
= X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
thf(21,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(22,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[21]) ).
thf(23,negated_conjecture,
( multiply @ ( positive_part @ a ) @ ( negative_part @ a ) )
!= a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_product) ).
thf(24,plain,
$false = $false,
inference(unfold_def,[status(thm)],[22]) ).
thf(25,plain,
( ( ! [X: $i] :
( ( negative_part @ X )
= ( intersection @ X @ identity ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(26,plain,
( ( ! [X: $i] :
( ( positive_part @ X )
= ( union @ X @ identity ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(27,plain,
( ( ! [Y: $i,Z: $i,X: $i] :
( ( multiply @ ( intersection @ Y @ Z ) @ X )
= ( intersection @ ( multiply @ Y @ X ) @ ( multiply @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(28,plain,
( ( ! [Y: $i,Z: $i,X: $i] :
( ( multiply @ ( union @ Y @ Z ) @ X )
= ( union @ ( multiply @ Y @ X ) @ ( multiply @ Z @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( intersection @ Y @ Z ) )
= ( intersection @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(30,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( union @ Y @ Z ) )
= ( union @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(31,plain,
( ( ! [X: $i,Y: $i] :
( ( intersection @ ( union @ X @ Y ) @ Y )
= Y ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(32,plain,
( ( ! [X: $i,Y: $i] :
( ( union @ ( intersection @ X @ Y ) @ Y )
= Y ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(33,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( union @ X @ ( union @ Y @ Z ) )
= ( union @ ( union @ X @ Y ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(34,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( intersection @ X @ ( intersection @ Y @ Z ) )
= ( intersection @ ( intersection @ X @ Y ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(35,plain,
( ( ! [X: $i,Y: $i] :
( ( union @ X @ Y )
= ( union @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(36,plain,
( ( ! [X: $i,Y: $i] :
( ( intersection @ X @ Y )
= ( intersection @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(37,plain,
( ( ! [X: $i] :
( ( union @ X @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(38,plain,
( ( ! [X: $i] :
( ( intersection @ X @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i] :
( ( inverse @ ( multiply @ X @ Y ) )
= ( multiply @ ( inverse @ Y ) @ ( inverse @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(40,plain,
( ( ! [X: $i] :
( ( inverse @ ( inverse @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(41,plain,
( ( ( inverse @ identity )
= identity )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(42,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(43,plain,
( ( ! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= identity ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(44,plain,
( ( ! [X: $i] :
( ( multiply @ identity @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(45,plain,
( ( ( ( multiply @ ( positive_part @ a ) @ ( negative_part @ a ) )
!= a ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(46,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[24]) ).
thf(47,plain,
( ( ( ( multiply @ ( positive_part @ a ) @ ( negative_part @ a ) )
!= a ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(48,plain,
( ( ( ( multiply @ ( positive_part @ a ) @ ( negative_part @ a ) )
!= a ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(49,plain,
( ( ! [X: $i] :
( ( multiply @ identity @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(50,plain,
( ( ! [X: $i] :
( ( multiply @ ( inverse @ X ) @ X )
= identity ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(51,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ ( multiply @ X @ Y ) @ Z )
= ( multiply @ X @ ( multiply @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(52,plain,
( ( ( inverse @ identity )
= identity )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(53,plain,
( ( ! [X: $i] :
( ( inverse @ ( inverse @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(54,plain,
( ( ! [X: $i,Y: $i] :
( ( inverse @ ( multiply @ X @ Y ) )
= ( multiply @ ( inverse @ Y ) @ ( inverse @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(55,plain,
( ( ! [X: $i] :
( ( intersection @ X @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(56,plain,
( ( ! [X: $i] :
( ( union @ X @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(57,plain,
( ( ! [X: $i,Y: $i] :
( ( intersection @ X @ Y )
= ( intersection @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(58,plain,
( ( ! [X: $i,Y: $i] :
( ( union @ X @ Y )
= ( union @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(59,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( intersection @ X @ ( intersection @ Y @ Z ) )
= ( intersection @ ( intersection @ X @ Y ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(60,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( union @ X @ ( union @ Y @ Z ) )
= ( union @ ( union @ X @ Y ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(61,plain,
( ( ! [X: $i,Y: $i] :
( ( union @ ( intersection @ X @ Y ) @ Y )
= Y ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(62,plain,
( ( ! [X: $i,Y: $i] :
( ( intersection @ ( union @ X @ Y ) @ Y )
= Y ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(63,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( union @ Y @ Z ) )
= ( union @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(64,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( multiply @ X @ ( intersection @ Y @ Z ) )
= ( intersection @ ( multiply @ X @ Y ) @ ( multiply @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(65,plain,
( ( ! [Y: $i,Z: $i,X: $i] :
( ( multiply @ ( union @ Y @ Z ) @ X )
= ( union @ ( multiply @ Y @ X ) @ ( multiply @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(66,plain,
( ( ! [Y: $i,Z: $i,X: $i] :
( ( multiply @ ( intersection @ Y @ Z ) @ X )
= ( intersection @ ( multiply @ Y @ X ) @ ( multiply @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(67,plain,
( ( ! [X: $i] :
( ( positive_part @ X )
= ( union @ X @ identity ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(68,plain,
( ( ! [X: $i] :
( ( negative_part @ X )
= ( intersection @ X @ identity ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(69,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(70,plain,
( ( ( multiply @ ( positive_part @ a ) @ ( negative_part @ a ) )
= a )
= $false ),
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(71,plain,
! [SV1: $i] :
( ( ( multiply @ identity @ SV1 )
= SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(72,plain,
! [SV2: $i] :
( ( ( multiply @ ( inverse @ SV2 ) @ SV2 )
= identity )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(73,plain,
! [SV3: $i] :
( ( ! [SY38: $i,SY39: $i] :
( ( multiply @ ( multiply @ SV3 @ SY38 ) @ SY39 )
= ( multiply @ SV3 @ ( multiply @ SY38 @ SY39 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(74,plain,
! [SV4: $i] :
( ( ( inverse @ ( inverse @ SV4 ) )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(75,plain,
! [SV5: $i] :
( ( ! [SY40: $i] :
( ( inverse @ ( multiply @ SV5 @ SY40 ) )
= ( multiply @ ( inverse @ SY40 ) @ ( inverse @ SV5 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(76,plain,
! [SV6: $i] :
( ( ( intersection @ SV6 @ SV6 )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(77,plain,
! [SV7: $i] :
( ( ( union @ SV7 @ SV7 )
= SV7 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(78,plain,
! [SV8: $i] :
( ( ! [SY41: $i] :
( ( intersection @ SV8 @ SY41 )
= ( intersection @ SY41 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(79,plain,
! [SV9: $i] :
( ( ! [SY42: $i] :
( ( union @ SV9 @ SY42 )
= ( union @ SY42 @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(80,plain,
! [SV10: $i] :
( ( ! [SY43: $i,SY44: $i] :
( ( intersection @ SV10 @ ( intersection @ SY43 @ SY44 ) )
= ( intersection @ ( intersection @ SV10 @ SY43 ) @ SY44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(81,plain,
! [SV11: $i] :
( ( ! [SY45: $i,SY46: $i] :
( ( union @ SV11 @ ( union @ SY45 @ SY46 ) )
= ( union @ ( union @ SV11 @ SY45 ) @ SY46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(82,plain,
! [SV12: $i] :
( ( ! [SY47: $i] :
( ( union @ ( intersection @ SV12 @ SY47 ) @ SY47 )
= SY47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(83,plain,
! [SV13: $i] :
( ( ! [SY48: $i] :
( ( intersection @ ( union @ SV13 @ SY48 ) @ SY48 )
= SY48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(84,plain,
! [SV14: $i] :
( ( ! [SY49: $i,SY50: $i] :
( ( multiply @ SV14 @ ( union @ SY49 @ SY50 ) )
= ( union @ ( multiply @ SV14 @ SY49 ) @ ( multiply @ SV14 @ SY50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(85,plain,
! [SV15: $i] :
( ( ! [SY51: $i,SY52: $i] :
( ( multiply @ SV15 @ ( intersection @ SY51 @ SY52 ) )
= ( intersection @ ( multiply @ SV15 @ SY51 ) @ ( multiply @ SV15 @ SY52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(86,plain,
! [SV16: $i] :
( ( ! [SY53: $i,SY54: $i] :
( ( multiply @ ( union @ SV16 @ SY53 ) @ SY54 )
= ( union @ ( multiply @ SV16 @ SY54 ) @ ( multiply @ SY53 @ SY54 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(87,plain,
! [SV17: $i] :
( ( ! [SY55: $i,SY56: $i] :
( ( multiply @ ( intersection @ SV17 @ SY55 ) @ SY56 )
= ( intersection @ ( multiply @ SV17 @ SY56 ) @ ( multiply @ SY55 @ SY56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(88,plain,
! [SV18: $i] :
( ( ( positive_part @ SV18 )
= ( union @ SV18 @ identity ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(89,plain,
! [SV19: $i] :
( ( ( negative_part @ SV19 )
= ( intersection @ SV19 @ identity ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(90,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(91,plain,
! [SV20: $i,SV3: $i] :
( ( ! [SY57: $i] :
( ( multiply @ ( multiply @ SV3 @ SV20 ) @ SY57 )
= ( multiply @ SV3 @ ( multiply @ SV20 @ SY57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(92,plain,
! [SV21: $i,SV5: $i] :
( ( ( inverse @ ( multiply @ SV5 @ SV21 ) )
= ( multiply @ ( inverse @ SV21 ) @ ( inverse @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(93,plain,
! [SV22: $i,SV8: $i] :
( ( ( intersection @ SV8 @ SV22 )
= ( intersection @ SV22 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(94,plain,
! [SV23: $i,SV9: $i] :
( ( ( union @ SV9 @ SV23 )
= ( union @ SV23 @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(95,plain,
! [SV24: $i,SV10: $i] :
( ( ! [SY58: $i] :
( ( intersection @ SV10 @ ( intersection @ SV24 @ SY58 ) )
= ( intersection @ ( intersection @ SV10 @ SV24 ) @ SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(96,plain,
! [SV25: $i,SV11: $i] :
( ( ! [SY59: $i] :
( ( union @ SV11 @ ( union @ SV25 @ SY59 ) )
= ( union @ ( union @ SV11 @ SV25 ) @ SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(97,plain,
! [SV26: $i,SV12: $i] :
( ( ( union @ ( intersection @ SV12 @ SV26 ) @ SV26 )
= SV26 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(98,plain,
! [SV27: $i,SV13: $i] :
( ( ( intersection @ ( union @ SV13 @ SV27 ) @ SV27 )
= SV27 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(99,plain,
! [SV28: $i,SV14: $i] :
( ( ! [SY60: $i] :
( ( multiply @ SV14 @ ( union @ SV28 @ SY60 ) )
= ( union @ ( multiply @ SV14 @ SV28 ) @ ( multiply @ SV14 @ SY60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(100,plain,
! [SV29: $i,SV15: $i] :
( ( ! [SY61: $i] :
( ( multiply @ SV15 @ ( intersection @ SV29 @ SY61 ) )
= ( intersection @ ( multiply @ SV15 @ SV29 ) @ ( multiply @ SV15 @ SY61 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(101,plain,
! [SV30: $i,SV16: $i] :
( ( ! [SY62: $i] :
( ( multiply @ ( union @ SV16 @ SV30 ) @ SY62 )
= ( union @ ( multiply @ SV16 @ SY62 ) @ ( multiply @ SV30 @ SY62 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(102,plain,
! [SV31: $i,SV17: $i] :
( ( ! [SY63: $i] :
( ( multiply @ ( intersection @ SV17 @ SV31 ) @ SY63 )
= ( intersection @ ( multiply @ SV17 @ SY63 ) @ ( multiply @ SV31 @ SY63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(103,plain,
! [SV32: $i,SV20: $i,SV3: $i] :
( ( ( multiply @ ( multiply @ SV3 @ SV20 ) @ SV32 )
= ( multiply @ SV3 @ ( multiply @ SV20 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(104,plain,
! [SV33: $i,SV24: $i,SV10: $i] :
( ( ( intersection @ SV10 @ ( intersection @ SV24 @ SV33 ) )
= ( intersection @ ( intersection @ SV10 @ SV24 ) @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(105,plain,
! [SV34: $i,SV25: $i,SV11: $i] :
( ( ( union @ SV11 @ ( union @ SV25 @ SV34 ) )
= ( union @ ( union @ SV11 @ SV25 ) @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(106,plain,
! [SV35: $i,SV28: $i,SV14: $i] :
( ( ( multiply @ SV14 @ ( union @ SV28 @ SV35 ) )
= ( union @ ( multiply @ SV14 @ SV28 ) @ ( multiply @ SV14 @ SV35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(107,plain,
! [SV36: $i,SV29: $i,SV15: $i] :
( ( ( multiply @ SV15 @ ( intersection @ SV29 @ SV36 ) )
= ( intersection @ ( multiply @ SV15 @ SV29 ) @ ( multiply @ SV15 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(108,plain,
! [SV37: $i,SV30: $i,SV16: $i] :
( ( ( multiply @ ( union @ SV16 @ SV30 ) @ SV37 )
= ( union @ ( multiply @ SV16 @ SV37 ) @ ( multiply @ SV30 @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(109,plain,
! [SV38: $i,SV31: $i,SV17: $i] :
( ( ( multiply @ ( intersection @ SV17 @ SV31 ) @ SV38 )
= ( intersection @ ( multiply @ SV17 @ SV38 ) @ ( multiply @ SV31 @ SV38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(110,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[52,109,108,107,106,105,104,103,98,97,94,93,92,90,89,88,77,76,74,72,71,70]) ).
thf(111,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP114-1 : TPTP v8.1.0. Released v1.2.0.
% 0.07/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n008.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 : Tue Jun 14 01:43:37 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34
% 0.13/0.34 No.of.Axioms: 21
% 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:21,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:23,loop_count:0,foatp_calls:0,translation:fof_full)......
% 2.29/2.48
% 2.29/2.48 ********************************
% 2.29/2.48 * All subproblems solved! *
% 2.29/2.48 ********************************
% 2.29/2.48 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:21,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:110,loop_count:0,foatp_calls:1,translation:fof_full)
% 2.29/2.48
% 2.29/2.48 %**** Beginning of derivation protocol ****
% 2.29/2.48 % SZS output start CNFRefutation
% See solution above
% 2.29/2.48
% 2.29/2.48 %**** End of derivation protocol ****
% 2.29/2.48 %**** no. of clauses in derivation: 111 ****
% 2.29/2.48 %**** clause counter: 110 ****
% 2.29/2.48
% 2.29/2.48 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:21,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:110,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------