TSTP Solution File: CAT009-3 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : CAT009-3 : 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 : n020.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 : Fri Jul 15 00:03:47 EDT 2022
% Result : Unsatisfiable 26.94s 27.17s
% Output : CNFRefutation 26.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 28
% Syntax : Number of formulae : 151 ( 86 unt; 8 typ; 0 def)
% Number of atoms : 673 ( 301 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 849 ( 127 ~; 174 |; 0 &; 548 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 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 : 240 ( 0 ^ 240 !; 0 ?; 240 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
thf(tp_codomain,type,
codomain: $i > $i ).
thf(tp_compose,type,
compose: $i > $i > $i ).
thf(tp_domain,type,
domain: $i > $i ).
thf(tp_equivalent,type,
equivalent: $i > $i > $o ).
thf(tp_f1,type,
f1: $i > $i > $i ).
thf(tp_there_exists,type,
there_exists: $i > $o ).
thf(1,axiom,
! [X: $i,Y: $i] :
( ( X
!= ( f1 @ X @ Y ) )
| ( Y
!= ( f1 @ X @ Y ) )
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',indiscernibles3) ).
thf(2,axiom,
! [X: $i,Y: $i] :
( ( X
= ( f1 @ X @ Y ) )
| ( Y
= ( f1 @ X @ Y ) )
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',indiscernibles2) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ( there_exists @ ( f1 @ X @ Y ) )
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',indiscernibles1) ).
thf(4,axiom,
! [X: $i,Y: $i] :
( ~ ( there_exists @ ( compose @ X @ Y ) )
| ( there_exists @ ( codomain @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_implies_codomain) ).
thf(5,axiom,
! [X: $i,Y: $i] :
( ~ ( there_exists @ X )
| ~ ( there_exists @ Y )
| ( X != Y )
| ( equivalent @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_and_equality_implies_equivalence2) ).
thf(6,axiom,
! [X: $i,Y: $i] :
( ~ ( equivalent @ X @ Y )
| ( there_exists @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_implies_existence3) ).
thf(7,axiom,
! [X: $i] :
( ( compose @ ( codomain @ X ) @ X )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_codomain) ).
thf(8,axiom,
! [X: $i] :
( ( compose @ X @ ( domain @ X ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compose_domain) ).
thf(9,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( compose @ X @ ( compose @ Y @ Z ) )
= ( compose @ ( compose @ X @ Y ) @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_compose) ).
thf(10,axiom,
! [X: $i,Y: $i] :
( ~ ( there_exists @ ( domain @ X ) )
| ( ( domain @ X )
!= ( codomain @ Y ) )
| ( there_exists @ ( compose @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_codomain_composition2) ).
thf(11,axiom,
! [X: $i,Y: $i] :
( ~ ( there_exists @ ( compose @ X @ Y ) )
| ( ( domain @ X )
= ( codomain @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_codomain_composition1) ).
thf(12,axiom,
! [X: $i,Y: $i] :
( ~ ( there_exists @ ( compose @ X @ Y ) )
| ( there_exists @ ( domain @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',composition_implies_domain) ).
thf(13,axiom,
! [X: $i] :
( ~ ( there_exists @ ( codomain @ X ) )
| ( there_exists @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain_has_elements) ).
thf(14,axiom,
! [X: $i] :
( ~ ( there_exists @ ( domain @ X ) )
| ( there_exists @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain_has_elements) ).
thf(15,axiom,
! [X: $i,Y: $i] :
( ~ ( there_exists @ X )
| ( X != Y )
| ( equivalent @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_and_equality_implies_equivalence1) ).
thf(16,axiom,
! [X: $i,Y: $i] :
( ~ ( equivalent @ X @ Y )
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_implies_existence2) ).
thf(17,axiom,
! [X: $i,Y: $i] :
( ~ ( equivalent @ X @ Y )
| ( there_exists @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equivalence_implies_existence1) ).
thf(18,axiom,
there_exists @ ( compose @ a @ b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_exists) ).
thf(19,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(20,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[19]) ).
thf(21,negated_conjecture,
( domain @ ( compose @ a @ b ) )
!= ( domain @ b ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_of_ab_equals_domain_of_b) ).
thf(22,plain,
$false = $false,
inference(unfold_def,[status(thm)],[20]) ).
thf(23,plain,
( ( ! [X: $i,Y: $i] :
( ( X
!= ( f1 @ X @ Y ) )
| ( Y
!= ( f1 @ X @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(24,plain,
( ( ! [X: $i,Y: $i] :
( ( X
= ( f1 @ X @ Y ) )
| ( Y
= ( f1 @ X @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(25,plain,
( ( ! [X: $i,Y: $i] :
( ( there_exists @ ( f1 @ X @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(26,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( there_exists @ ( compose @ X @ Y ) )
| ( there_exists @ ( codomain @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( there_exists @ X )
| ~ ( there_exists @ Y )
| ( X != Y )
| ( equivalent @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(28,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equivalent @ X @ Y )
| ( there_exists @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(29,plain,
( ( ! [X: $i] :
( ( compose @ ( codomain @ X ) @ X )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(30,plain,
( ( ! [X: $i] :
( ( compose @ X @ ( domain @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(31,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( compose @ X @ ( compose @ Y @ Z ) )
= ( compose @ ( compose @ X @ Y ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(32,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( there_exists @ ( domain @ X ) )
| ( ( domain @ X )
!= ( codomain @ Y ) )
| ( there_exists @ ( compose @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(33,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( there_exists @ ( compose @ X @ Y ) )
| ( ( domain @ X )
= ( codomain @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(34,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( there_exists @ ( compose @ X @ Y ) )
| ( there_exists @ ( domain @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(35,plain,
( ( ! [X: $i] :
( ~ ( there_exists @ ( codomain @ X ) )
| ( there_exists @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(36,plain,
( ( ! [X: $i] :
( ~ ( there_exists @ ( domain @ X ) )
| ( there_exists @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(37,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( there_exists @ X )
| ( X != Y )
| ( equivalent @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(38,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equivalent @ X @ Y )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equivalent @ X @ Y )
| ( there_exists @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(40,plain,
( ( there_exists @ ( compose @ a @ b ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(41,plain,
( ( ( ( domain @ ( compose @ a @ b ) )
!= ( domain @ b ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(42,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(43,plain,
( ( ! [X: $i,Y: $i] :
( ( X
!= ( f1 @ X @ Y ) )
| ( Y
!= ( f1 @ X @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(44,plain,
( ( ! [X: $i,Y: $i] :
( ( X = Y )
| ( there_exists @ ( f1 @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(45,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
~ ( there_exists @ ( compose @ X @ Y ) )
| ( there_exists @ ( codomain @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(46,plain,
( ( ! [X: $i] :
( ~ ( there_exists @ X )
| ! [Y: $i] :
( ~ ( there_exists @ Y )
| ( X != Y )
| ( equivalent @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(47,plain,
( ( ! [X: $i] :
( ~ ( there_exists @ ( domain @ X ) )
| ! [Y: $i] :
( ( ( domain @ X )
!= ( codomain @ Y ) )
| ( there_exists @ ( compose @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(48,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
~ ( there_exists @ ( compose @ X @ Y ) )
| ( there_exists @ ( domain @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(49,plain,
( ( ! [X: $i] :
( ~ ( there_exists @ X )
| ! [Y: $i] :
( ( X != Y )
| ( equivalent @ X @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[37]) ).
thf(50,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
~ ( equivalent @ X @ Y )
| ( there_exists @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(51,plain,
( ( ( ( domain @ ( compose @ a @ b ) )
!= ( domain @ b ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(52,plain,
( ( ( ( domain @ ( compose @ a @ b ) )
!= ( domain @ b ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(53,plain,
( ( there_exists @ ( compose @ a @ b ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(54,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
~ ( equivalent @ X @ Y )
| ( there_exists @ X ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(55,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equivalent @ X @ Y )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(56,plain,
( ( ! [X: $i] :
( ~ ( there_exists @ X )
| ! [Y: $i] :
( ( X != Y )
| ( equivalent @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(57,plain,
( ( ! [X: $i] :
( ~ ( there_exists @ ( domain @ X ) )
| ( there_exists @ X ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(58,plain,
( ( ! [X: $i] :
( ~ ( there_exists @ ( codomain @ X ) )
| ( there_exists @ X ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(59,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
~ ( there_exists @ ( compose @ X @ Y ) )
| ( there_exists @ ( domain @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(60,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( there_exists @ ( compose @ X @ Y ) )
| ( ( domain @ X )
= ( codomain @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(61,plain,
( ( ! [X: $i] :
( ~ ( there_exists @ ( domain @ X ) )
| ! [Y: $i] :
( ( ( domain @ X )
!= ( codomain @ Y ) )
| ( there_exists @ ( compose @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(62,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( compose @ X @ ( compose @ Y @ Z ) )
= ( compose @ ( compose @ X @ Y ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(63,plain,
( ( ! [X: $i] :
( ( compose @ X @ ( domain @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(64,plain,
( ( ! [X: $i] :
( ( compose @ ( codomain @ X ) @ X )
= X ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(65,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equivalent @ X @ Y )
| ( there_exists @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(66,plain,
( ( ! [X: $i] :
( ~ ( there_exists @ X )
| ! [Y: $i] :
( ~ ( there_exists @ Y )
| ( X != Y )
| ( equivalent @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(67,plain,
( ( ! [X: $i] :
( ! [Y: $i] :
~ ( there_exists @ ( compose @ X @ Y ) )
| ( there_exists @ ( codomain @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(68,plain,
( ( ! [X: $i,Y: $i] :
( ( X = Y )
| ( there_exists @ ( f1 @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(69,plain,
( ( ! [X: $i,Y: $i] :
( ( X
= ( f1 @ X @ Y ) )
| ( Y
= ( f1 @ X @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(70,plain,
( ( ! [X: $i,Y: $i] :
( ( X
!= ( f1 @ X @ Y ) )
| ( Y
!= ( f1 @ X @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(71,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(72,plain,
( ( ( domain @ ( compose @ a @ b ) )
= ( domain @ b ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[52]) ).
thf(73,plain,
! [SV1: $i] :
( ( ! [SY31: $i] :
~ ( equivalent @ SV1 @ SY31 )
| ( there_exists @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(74,plain,
! [SV2: $i] :
( ( ! [SY32: $i] :
( ~ ( equivalent @ SV2 @ SY32 )
| ( SV2 = SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(75,plain,
! [SV3: $i] :
( ( ~ ( there_exists @ SV3 )
| ! [SY33: $i] :
( ( SV3 != SY33 )
| ( equivalent @ SV3 @ SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(76,plain,
! [SV4: $i] :
( ( ~ ( there_exists @ ( domain @ SV4 ) )
| ( there_exists @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(77,plain,
! [SV5: $i] :
( ( ~ ( there_exists @ ( codomain @ SV5 ) )
| ( there_exists @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(78,plain,
! [SV6: $i] :
( ( ! [SY34: $i] :
~ ( there_exists @ ( compose @ SV6 @ SY34 ) )
| ( there_exists @ ( domain @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(79,plain,
! [SV7: $i] :
( ( ! [SY35: $i] :
( ~ ( there_exists @ ( compose @ SV7 @ SY35 ) )
| ( ( domain @ SV7 )
= ( codomain @ SY35 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(80,plain,
! [SV8: $i] :
( ( ~ ( there_exists @ ( domain @ SV8 ) )
| ! [SY36: $i] :
( ( ( domain @ SV8 )
!= ( codomain @ SY36 ) )
| ( there_exists @ ( compose @ SV8 @ SY36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(81,plain,
! [SV9: $i] :
( ( ! [SY37: $i,SY38: $i] :
( ( compose @ SV9 @ ( compose @ SY37 @ SY38 ) )
= ( compose @ ( compose @ SV9 @ SY37 ) @ SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(82,plain,
! [SV10: $i] :
( ( ( compose @ SV10 @ ( domain @ SV10 ) )
= SV10 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(83,plain,
! [SV11: $i] :
( ( ( compose @ ( codomain @ SV11 ) @ SV11 )
= SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(84,plain,
! [SV12: $i] :
( ( ! [SY39: $i] :
( ~ ( equivalent @ SV12 @ SY39 )
| ( there_exists @ SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(85,plain,
! [SV13: $i] :
( ( ~ ( there_exists @ SV13 )
| ! [SY40: $i] :
( ~ ( there_exists @ SY40 )
| ( SV13 != SY40 )
| ( equivalent @ SV13 @ SY40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(86,plain,
! [SV14: $i] :
( ( ! [SY41: $i] :
~ ( there_exists @ ( compose @ SV14 @ SY41 ) )
| ( there_exists @ ( codomain @ SV14 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(87,plain,
! [SV15: $i] :
( ( ! [SY42: $i] :
( ( SV15 = SY42 )
| ( there_exists @ ( f1 @ SV15 @ SY42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(88,plain,
! [SV16: $i] :
( ( ! [SY43: $i] :
( ( SV16
= ( f1 @ SV16 @ SY43 ) )
| ( SY43
= ( f1 @ SV16 @ SY43 ) )
| ( SV16 = SY43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(89,plain,
! [SV17: $i] :
( ( ! [SY44: $i] :
( ( SV17
!= ( f1 @ SV17 @ SY44 ) )
| ( SY44
!= ( f1 @ SV17 @ SY44 ) )
| ( SV17 = SY44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(90,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(91,plain,
! [SV1: $i] :
( ( ( ! [SY31: $i] :
~ ( equivalent @ SV1 @ SY31 ) )
= $true )
| ( ( there_exists @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(92,plain,
! [SV18: $i,SV2: $i] :
( ( ~ ( equivalent @ SV2 @ SV18 )
| ( SV2 = SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(93,plain,
! [SV3: $i] :
( ( ( ~ ( there_exists @ SV3 ) )
= $true )
| ( ( ! [SY33: $i] :
( ( SV3 != SY33 )
| ( equivalent @ SV3 @ SY33 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(94,plain,
! [SV4: $i] :
( ( ( ~ ( there_exists @ ( domain @ SV4 ) ) )
= $true )
| ( ( there_exists @ SV4 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(95,plain,
! [SV5: $i] :
( ( ( ~ ( there_exists @ ( codomain @ SV5 ) ) )
= $true )
| ( ( there_exists @ SV5 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(96,plain,
! [SV6: $i] :
( ( ( ! [SY34: $i] :
~ ( there_exists @ ( compose @ SV6 @ SY34 ) ) )
= $true )
| ( ( there_exists @ ( domain @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(97,plain,
! [SV19: $i,SV7: $i] :
( ( ~ ( there_exists @ ( compose @ SV7 @ SV19 ) )
| ( ( domain @ SV7 )
= ( codomain @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(98,plain,
! [SV8: $i] :
( ( ( ~ ( there_exists @ ( domain @ SV8 ) ) )
= $true )
| ( ( ! [SY36: $i] :
( ( ( domain @ SV8 )
!= ( codomain @ SY36 ) )
| ( there_exists @ ( compose @ SV8 @ SY36 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(99,plain,
! [SV20: $i,SV9: $i] :
( ( ! [SY45: $i] :
( ( compose @ SV9 @ ( compose @ SV20 @ SY45 ) )
= ( compose @ ( compose @ SV9 @ SV20 ) @ SY45 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(100,plain,
! [SV21: $i,SV12: $i] :
( ( ~ ( equivalent @ SV12 @ SV21 )
| ( there_exists @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(101,plain,
! [SV13: $i] :
( ( ( ~ ( there_exists @ SV13 ) )
= $true )
| ( ( ! [SY40: $i] :
( ~ ( there_exists @ SY40 )
| ( SV13 != SY40 )
| ( equivalent @ SV13 @ SY40 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[85]) ).
thf(102,plain,
! [SV14: $i] :
( ( ( ! [SY41: $i] :
~ ( there_exists @ ( compose @ SV14 @ SY41 ) ) )
= $true )
| ( ( there_exists @ ( codomain @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(103,plain,
! [SV22: $i,SV15: $i] :
( ( ( SV15 = SV22 )
| ( there_exists @ ( f1 @ SV15 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(104,plain,
! [SV23: $i,SV16: $i] :
( ( ( SV16
= ( f1 @ SV16 @ SV23 ) )
| ( SV23
= ( f1 @ SV16 @ SV23 ) )
| ( SV16 = SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(105,plain,
! [SV24: $i,SV17: $i] :
( ( ( SV17
!= ( f1 @ SV17 @ SV24 ) )
| ( SV24
!= ( f1 @ SV17 @ SV24 ) )
| ( SV17 = SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(106,plain,
! [SV25: $i,SV1: $i] :
( ( ( ~ ( equivalent @ SV1 @ SV25 ) )
= $true )
| ( ( there_exists @ SV1 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(107,plain,
! [SV18: $i,SV2: $i] :
( ( ( ~ ( equivalent @ SV2 @ SV18 ) )
= $true )
| ( ( SV2 = SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[92]) ).
thf(108,plain,
! [SV3: $i] :
( ( ( there_exists @ SV3 )
= $false )
| ( ( ! [SY33: $i] :
( ( SV3 != SY33 )
| ( equivalent @ SV3 @ SY33 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(109,plain,
! [SV4: $i] :
( ( ( there_exists @ ( domain @ SV4 ) )
= $false )
| ( ( there_exists @ SV4 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(110,plain,
! [SV5: $i] :
( ( ( there_exists @ ( codomain @ SV5 ) )
= $false )
| ( ( there_exists @ SV5 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(111,plain,
! [SV26: $i,SV6: $i] :
( ( ( ~ ( there_exists @ ( compose @ SV6 @ SV26 ) ) )
= $true )
| ( ( there_exists @ ( domain @ SV6 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(112,plain,
! [SV19: $i,SV7: $i] :
( ( ( ~ ( there_exists @ ( compose @ SV7 @ SV19 ) ) )
= $true )
| ( ( ( domain @ SV7 )
= ( codomain @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(113,plain,
! [SV8: $i] :
( ( ( there_exists @ ( domain @ SV8 ) )
= $false )
| ( ( ! [SY36: $i] :
( ( ( domain @ SV8 )
!= ( codomain @ SY36 ) )
| ( there_exists @ ( compose @ SV8 @ SY36 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(114,plain,
! [SV27: $i,SV20: $i,SV9: $i] :
( ( ( compose @ SV9 @ ( compose @ SV20 @ SV27 ) )
= ( compose @ ( compose @ SV9 @ SV20 ) @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(115,plain,
! [SV21: $i,SV12: $i] :
( ( ( ~ ( equivalent @ SV12 @ SV21 ) )
= $true )
| ( ( there_exists @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(116,plain,
! [SV13: $i] :
( ( ( there_exists @ SV13 )
= $false )
| ( ( ! [SY40: $i] :
( ~ ( there_exists @ SY40 )
| ( SV13 != SY40 )
| ( equivalent @ SV13 @ SY40 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(117,plain,
! [SV28: $i,SV14: $i] :
( ( ( ~ ( there_exists @ ( compose @ SV14 @ SV28 ) ) )
= $true )
| ( ( there_exists @ ( codomain @ SV14 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(118,plain,
! [SV22: $i,SV15: $i] :
( ( ( SV15 = SV22 )
= $true )
| ( ( there_exists @ ( f1 @ SV15 @ SV22 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[103]) ).
thf(119,plain,
! [SV23: $i,SV16: $i] :
( ( ( SV16
= ( f1 @ SV16 @ SV23 ) )
= $true )
| ( ( ( SV23
= ( f1 @ SV16 @ SV23 ) )
| ( SV16 = SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(120,plain,
! [SV24: $i,SV17: $i] :
( ( ( ( SV17
!= ( f1 @ SV17 @ SV24 ) ) )
= $true )
| ( ( ( SV24
!= ( f1 @ SV17 @ SV24 ) )
| ( SV17 = SV24 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(121,plain,
! [SV25: $i,SV1: $i] :
( ( ( equivalent @ SV1 @ SV25 )
= $false )
| ( ( there_exists @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(122,plain,
! [SV18: $i,SV2: $i] :
( ( ( equivalent @ SV2 @ SV18 )
= $false )
| ( ( SV2 = SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(123,plain,
! [SV29: $i,SV3: $i] :
( ( ( ( SV3 != SV29 )
| ( equivalent @ SV3 @ SV29 ) )
= $true )
| ( ( there_exists @ SV3 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(124,plain,
! [SV26: $i,SV6: $i] :
( ( ( there_exists @ ( compose @ SV6 @ SV26 ) )
= $false )
| ( ( there_exists @ ( domain @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(125,plain,
! [SV19: $i,SV7: $i] :
( ( ( there_exists @ ( compose @ SV7 @ SV19 ) )
= $false )
| ( ( ( domain @ SV7 )
= ( codomain @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(126,plain,
! [SV30: $i,SV8: $i] :
( ( ( ( ( domain @ SV8 )
!= ( codomain @ SV30 ) )
| ( there_exists @ ( compose @ SV8 @ SV30 ) ) )
= $true )
| ( ( there_exists @ ( domain @ SV8 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(127,plain,
! [SV21: $i,SV12: $i] :
( ( ( equivalent @ SV12 @ SV21 )
= $false )
| ( ( there_exists @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(128,plain,
! [SV13: $i,SV31: $i] :
( ( ( ~ ( there_exists @ SV31 )
| ( SV13 != SV31 )
| ( equivalent @ SV13 @ SV31 ) )
= $true )
| ( ( there_exists @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(129,plain,
! [SV28: $i,SV14: $i] :
( ( ( there_exists @ ( compose @ SV14 @ SV28 ) )
= $false )
| ( ( there_exists @ ( codomain @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(130,plain,
! [SV16: $i,SV23: $i] :
( ( ( SV23
= ( f1 @ SV16 @ SV23 ) )
= $true )
| ( ( SV16 = SV23 )
= $true )
| ( ( SV16
= ( f1 @ SV16 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(131,plain,
! [SV24: $i,SV17: $i] :
( ( ( SV17
= ( f1 @ SV17 @ SV24 ) )
= $false )
| ( ( ( SV24
!= ( f1 @ SV17 @ SV24 ) )
| ( SV17 = SV24 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[120]) ).
thf(132,plain,
! [SV29: $i,SV3: $i] :
( ( ( ( SV3 != SV29 ) )
= $true )
| ( ( equivalent @ SV3 @ SV29 )
= $true )
| ( ( there_exists @ SV3 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(133,plain,
! [SV30: $i,SV8: $i] :
( ( ( ( ( domain @ SV8 )
!= ( codomain @ SV30 ) ) )
= $true )
| ( ( there_exists @ ( compose @ SV8 @ SV30 ) )
= $true )
| ( ( there_exists @ ( domain @ SV8 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(134,plain,
! [SV13: $i,SV31: $i] :
( ( ( ~ ( there_exists @ SV31 ) )
= $true )
| ( ( ( SV13 != SV31 )
| ( equivalent @ SV13 @ SV31 ) )
= $true )
| ( ( there_exists @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(135,plain,
! [SV17: $i,SV24: $i] :
( ( ( ( SV24
!= ( f1 @ SV17 @ SV24 ) ) )
= $true )
| ( ( SV17 = SV24 )
= $true )
| ( ( SV17
= ( f1 @ SV17 @ SV24 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(136,plain,
! [SV29: $i,SV3: $i] :
( ( ( SV3 = SV29 )
= $false )
| ( ( equivalent @ SV3 @ SV29 )
= $true )
| ( ( there_exists @ SV3 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[132]) ).
thf(137,plain,
! [SV30: $i,SV8: $i] :
( ( ( ( domain @ SV8 )
= ( codomain @ SV30 ) )
= $false )
| ( ( there_exists @ ( compose @ SV8 @ SV30 ) )
= $true )
| ( ( there_exists @ ( domain @ SV8 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(138,plain,
! [SV13: $i,SV31: $i] :
( ( ( there_exists @ SV31 )
= $false )
| ( ( ( SV13 != SV31 )
| ( equivalent @ SV13 @ SV31 ) )
= $true )
| ( ( there_exists @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(139,plain,
! [SV17: $i,SV24: $i] :
( ( ( SV24
= ( f1 @ SV17 @ SV24 ) )
= $false )
| ( ( SV17 = SV24 )
= $true )
| ( ( SV17
= ( f1 @ SV17 @ SV24 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(140,plain,
! [SV31: $i,SV13: $i] :
( ( ( ( SV13 != SV31 ) )
= $true )
| ( ( equivalent @ SV13 @ SV31 )
= $true )
| ( ( there_exists @ SV31 )
= $false )
| ( ( there_exists @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(141,plain,
! [SV31: $i,SV13: $i] :
( ( ( SV13 = SV31 )
= $false )
| ( ( equivalent @ SV13 @ SV31 )
= $true )
| ( ( there_exists @ SV31 )
= $false )
| ( ( there_exists @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(142,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[53,141,139,137,136,130,129,127,125,124,122,121,118,114,110,109,90,83,82,72]) ).
thf(143,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[142]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : CAT009-3 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.33 % Computer : n020.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 20:21:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34
% 0.12/0.34 No.of.Axioms: 19
% 0.12/0.34
% 0.12/0.34 Length.of.Defs: 0
% 0.12/0.34
% 0.12/0.34 Contains.Choice.Funs: false
% 0.12/0.35 (rf:0,axioms:19,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:21,loop_count:0,foatp_calls:0,translation:fof_full)......
% 26.94/27.17
% 26.94/27.17 ********************************
% 26.94/27.17 * All subproblems solved! *
% 26.94/27.17 ********************************
% 26.94/27.17 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:19,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:142,loop_count:0,foatp_calls:1,translation:fof_full)
% 26.94/27.18
% 26.94/27.18 %**** Beginning of derivation protocol ****
% 26.94/27.18 % SZS output start CNFRefutation
% See solution above
% 26.94/27.18
% 26.94/27.18 %**** End of derivation protocol ****
% 26.94/27.18 %**** no. of clauses in derivation: 143 ****
% 26.94/27.18 %**** clause counter: 142 ****
% 26.94/27.18
% 26.94/27.18 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:19,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:142,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------