TSTP Solution File: MSC007-2.005 by LEO-II---1.7.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : MSC007-2.005 : 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 : 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 : Sun Jul 17 22:50:21 EDT 2022
% Result : Unsatisfiable 0.70s 0.89s
% Output : CNFRefutation 0.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 46
% Syntax : Number of formulae : 190 ( 143 unt; 13 typ; 0 def)
% Number of atoms : 740 ( 384 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 522 ( 162 ~; 163 |; 0 &; 197 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 125 ( 0 ^ 125 !; 0 ?; 125 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_hole,type,
hole: $i > $o ).
thf(tp_hole_1,type,
hole_1: $i ).
thf(tp_hole_2,type,
hole_2: $i ).
thf(tp_hole_3,type,
hole_3: $i ).
thf(tp_hole_4,type,
hole_4: $i ).
thf(tp_hole_of,type,
hole_of: $i > $i ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_pigeon,type,
pigeon: $i > $o ).
thf(tp_pigeon_1,type,
pigeon_1: $i ).
thf(tp_pigeon_2,type,
pigeon_2: $i ).
thf(tp_pigeon_3,type,
pigeon_3: $i ).
thf(tp_pigeon_4,type,
pigeon_4: $i ).
thf(tp_pigeon_5,type,
pigeon_5: $i ).
thf(1,axiom,
! [X: $i] :
( ~ ( pigeon @ X )
| ( in @ X @ ( hole_of @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',each_pigeons_hole2) ).
thf(2,axiom,
! [X: $i] :
( ~ ( pigeon @ X )
| ( hole @ ( hole_of @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',each_pigeons_hole1) ).
thf(3,axiom,
! [Hole: $i] :
( ~ ( hole @ Hole )
| ( Hole = hole_1 )
| ( Hole = hole_2 )
| ( Hole = hole_3 )
| ( Hole = hole_4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',all_holes) ).
thf(4,axiom,
hole_3 != hole_4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hole_3_is_not_hole_4) ).
thf(5,axiom,
hole_2 != hole_4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hole_2_is_not_hole_4) ).
thf(6,axiom,
hole_2 != hole_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hole_2_is_not_hole_3) ).
thf(7,axiom,
hole_1 != hole_4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hole_1_is_not_hole_4) ).
thf(8,axiom,
hole_1 != hole_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hole_1_is_not_hole_3) ).
thf(9,axiom,
hole_1 != hole_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hole_1_is_not_hole_2) ).
thf(10,axiom,
hole @ hole_4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hole_4) ).
thf(11,axiom,
hole @ hole_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hole_3) ).
thf(12,axiom,
hole @ hole_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hole_2) ).
thf(13,axiom,
hole @ hole_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',hole_1) ).
thf(14,axiom,
pigeon_4 != pigeon_5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pigeon_4_is_not_pigeon_5) ).
thf(15,axiom,
pigeon_3 != pigeon_5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pigeon_3_is_not_pigeon_5) ).
thf(16,axiom,
pigeon_3 != pigeon_4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pigeon_3_is_not_pigeon_4) ).
thf(17,axiom,
pigeon_2 != pigeon_5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pigeon_2_is_not_pigeon_5) ).
thf(18,axiom,
pigeon_2 != pigeon_4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pigeon_2_is_not_pigeon_4) ).
thf(19,axiom,
pigeon_2 != pigeon_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pigeon_2_is_not_pigeon_3) ).
thf(20,axiom,
pigeon_1 != pigeon_5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pigeon_1_is_not_pigeon_5) ).
thf(21,axiom,
pigeon_1 != pigeon_4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pigeon_1_is_not_pigeon_4) ).
thf(22,axiom,
pigeon_1 != pigeon_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pigeon_1_is_not_pigeon_3) ).
thf(23,axiom,
pigeon_1 != pigeon_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pigeon_1_is_not_pigeon_2) ).
thf(24,axiom,
pigeon @ pigeon_5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pigeon_5) ).
thf(25,axiom,
pigeon @ pigeon_4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pigeon_4) ).
thf(26,axiom,
pigeon @ pigeon_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pigeon_3) ).
thf(27,axiom,
pigeon @ pigeon_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pigeon_2) ).
thf(28,axiom,
pigeon @ pigeon_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pigeon_1) ).
thf(29,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( X != Y )
| ( Y != Z )
| ( X = Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(30,axiom,
! [X: $i,Y: $i] :
( ( X != Y )
| ( Y = X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry) ).
thf(31,axiom,
! [X: $i] : ( X = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(32,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(33,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[32]) ).
thf(34,negated_conjecture,
! [Hole: $i,Pigeon1: $i,Pigeon2: $i] :
( ~ ( hole @ Hole )
| ~ ( pigeon @ Pigeon1 )
| ~ ( pigeon @ Pigeon2 )
| ~ ( in @ Pigeon1 @ Hole )
| ~ ( in @ Pigeon2 @ Hole )
| ( Pigeon1 = Pigeon2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',only_one_per_hole) ).
thf(35,plain,
$false = $false,
inference(unfold_def,[status(thm)],[33]) ).
thf(36,plain,
( ( ! [X: $i] :
( ~ ( pigeon @ X )
| ( in @ X @ ( hole_of @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(37,plain,
( ( ! [X: $i] :
( ~ ( pigeon @ X )
| ( hole @ ( hole_of @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(38,plain,
( ( ! [Hole: $i] :
( ~ ( hole @ Hole )
| ( Hole = hole_1 )
| ( Hole = hole_2 )
| ( Hole = hole_3 )
| ( Hole = hole_4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(39,plain,
( ( ( hole_3 != hole_4 ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(40,plain,
( ( ( hole_2 != hole_4 ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(41,plain,
( ( ( hole_2 != hole_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(42,plain,
( ( ( hole_1 != hole_4 ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(43,plain,
( ( ( hole_1 != hole_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(44,plain,
( ( ( hole_1 != hole_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(45,plain,
( ( hole @ hole_4 )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(46,plain,
( ( hole @ hole_3 )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(47,plain,
( ( hole @ hole_2 )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(48,plain,
( ( hole @ hole_1 )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(49,plain,
( ( ( pigeon_4 != pigeon_5 ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(50,plain,
( ( ( pigeon_3 != pigeon_5 ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(51,plain,
( ( ( pigeon_3 != pigeon_4 ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(52,plain,
( ( ( pigeon_2 != pigeon_5 ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(53,plain,
( ( ( pigeon_2 != pigeon_4 ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(54,plain,
( ( ( pigeon_2 != pigeon_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(55,plain,
( ( ( pigeon_1 != pigeon_5 ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(56,plain,
( ( ( pigeon_1 != pigeon_4 ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(57,plain,
( ( ( pigeon_1 != pigeon_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(58,plain,
( ( ( pigeon_1 != pigeon_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(59,plain,
( ( pigeon @ pigeon_5 )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(60,plain,
( ( pigeon @ pigeon_4 )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(61,plain,
( ( pigeon @ pigeon_3 )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(62,plain,
( ( pigeon @ pigeon_2 )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(63,plain,
( ( pigeon @ pigeon_1 )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(64,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( X != Y )
| ( Y != Z )
| ( X = Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(65,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( Y = X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(66,plain,
( ( ! [X: $i] : ( X = X ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(67,plain,
( ( ! [Hole: $i,Pigeon1: $i,Pigeon2: $i] :
( ~ ( hole @ Hole )
| ~ ( pigeon @ Pigeon1 )
| ~ ( pigeon @ Pigeon2 )
| ~ ( in @ Pigeon1 @ Hole )
| ~ ( in @ Pigeon2 @ Hole )
| ( Pigeon1 = Pigeon2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(68,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[35]) ).
thf(69,plain,
( ( ( hole_3 != hole_4 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(70,plain,
( ( ( hole_2 != hole_4 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[40]) ).
thf(71,plain,
( ( ( hole_2 != hole_3 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(72,plain,
( ( ( hole_1 != hole_4 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(73,plain,
( ( ( hole_1 != hole_3 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(74,plain,
( ( ( hole_1 != hole_2 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(75,plain,
( ( ( pigeon_4 != pigeon_5 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(76,plain,
( ( ( pigeon_3 != pigeon_5 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(77,plain,
( ( ( pigeon_3 != pigeon_4 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(78,plain,
( ( ( pigeon_2 != pigeon_5 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[52]) ).
thf(79,plain,
( ( ( pigeon_2 != pigeon_4 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(80,plain,
( ( ( pigeon_2 != pigeon_3 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(81,plain,
( ( ( pigeon_1 != pigeon_5 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(82,plain,
( ( ( pigeon_1 != pigeon_4 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(83,plain,
( ( ( pigeon_1 != pigeon_3 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(84,plain,
( ( ( pigeon_1 != pigeon_2 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[58]) ).
thf(85,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ! [Z: $i] :
( ( Y != Z )
| ( X = Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(86,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( Y = X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[65]) ).
thf(87,plain,
( ( ! [X: $i] : $true )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(88,plain,
( ( ! [Hole: $i] :
( ~ ( hole @ Hole )
| ! [Pigeon1: $i] :
( ~ ( pigeon @ Pigeon1 )
| ! [Pigeon2: $i] :
( ~ ( pigeon @ Pigeon2 )
| ~ ( in @ Pigeon1 @ Hole )
| ~ ( in @ Pigeon2 @ Hole )
| ( Pigeon1 = Pigeon2 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(89,plain,
( ( ! [Hole: $i] :
( ~ ( hole @ Hole )
| ! [Pigeon1: $i] :
( ~ ( pigeon @ Pigeon1 )
| ! [Pigeon2: $i] :
( ~ ( pigeon @ Pigeon2 )
| ~ ( in @ Pigeon1 @ Hole )
| ~ ( in @ Pigeon2 @ Hole )
| ( Pigeon1 = Pigeon2 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(90,plain,
( ( ! [X: $i] : $true )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(91,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ( Y = X ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(92,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ! [Z: $i] :
( ( Y != Z )
| ( X = Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(93,plain,
( ( pigeon @ pigeon_1 )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(94,plain,
( ( pigeon @ pigeon_2 )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(95,plain,
( ( pigeon @ pigeon_3 )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(96,plain,
( ( pigeon @ pigeon_4 )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(97,plain,
( ( pigeon @ pigeon_5 )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(98,plain,
( ( ( pigeon_1 != pigeon_2 ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(99,plain,
( ( ( pigeon_1 != pigeon_3 ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(100,plain,
( ( ( pigeon_1 != pigeon_4 ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(101,plain,
( ( ( pigeon_1 != pigeon_5 ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(102,plain,
( ( ( pigeon_2 != pigeon_3 ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(103,plain,
( ( ( pigeon_2 != pigeon_4 ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(104,plain,
( ( ( pigeon_2 != pigeon_5 ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(105,plain,
( ( ( pigeon_3 != pigeon_4 ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(106,plain,
( ( ( pigeon_3 != pigeon_5 ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(107,plain,
( ( ( pigeon_4 != pigeon_5 ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(108,plain,
( ( hole @ hole_1 )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(109,plain,
( ( hole @ hole_2 )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(110,plain,
( ( hole @ hole_3 )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(111,plain,
( ( hole @ hole_4 )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(112,plain,
( ( ( hole_1 != hole_2 ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(113,plain,
( ( ( hole_1 != hole_3 ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(114,plain,
( ( ( hole_1 != hole_4 ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(115,plain,
( ( ( hole_2 != hole_3 ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(116,plain,
( ( ( hole_2 != hole_4 ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(117,plain,
( ( ( hole_3 != hole_4 ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(118,plain,
( ( ! [Hole: $i] :
( ~ ( hole @ Hole )
| ( Hole = hole_1 )
| ( Hole = hole_2 )
| ( Hole = hole_3 )
| ( Hole = hole_4 ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(119,plain,
( ( ! [X: $i] :
( ~ ( pigeon @ X )
| ( hole @ ( hole_of @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(120,plain,
( ( ! [X: $i] :
( ~ ( pigeon @ X )
| ( in @ X @ ( hole_of @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(121,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(122,plain,
! [SV1: $i] :
( ( ~ ( hole @ SV1 )
| ! [SY12: $i] :
( ~ ( pigeon @ SY12 )
| ! [SY13: $i] :
( ~ ( pigeon @ SY13 )
| ~ ( in @ SY12 @ SV1 )
| ~ ( in @ SY13 @ SV1 )
| ( SY12 = SY13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(123,plain,
$true = $true,
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(124,plain,
! [SV3: $i] :
( ( ! [SY14: $i] :
( ( SV3 != SY14 )
| ( SY14 = SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(125,plain,
! [SV4: $i] :
( ( ! [SY15: $i] :
( ( SV4 != SY15 )
| ! [SY16: $i] :
( ( SY15 != SY16 )
| ( SV4 = SY16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(126,plain,
( ( pigeon_1 = pigeon_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(127,plain,
( ( pigeon_1 = pigeon_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(128,plain,
( ( pigeon_1 = pigeon_4 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(129,plain,
( ( pigeon_1 = pigeon_5 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(130,plain,
( ( pigeon_2 = pigeon_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(131,plain,
( ( pigeon_2 = pigeon_4 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(132,plain,
( ( pigeon_2 = pigeon_5 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(133,plain,
( ( pigeon_3 = pigeon_4 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(134,plain,
( ( pigeon_3 = pigeon_5 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[106]) ).
thf(135,plain,
( ( pigeon_4 = pigeon_5 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(136,plain,
( ( hole_1 = hole_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[112]) ).
thf(137,plain,
( ( hole_1 = hole_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(138,plain,
( ( hole_1 = hole_4 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(139,plain,
( ( hole_2 = hole_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[115]) ).
thf(140,plain,
( ( hole_2 = hole_4 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(141,plain,
( ( hole_3 = hole_4 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(142,plain,
! [SV5: $i] :
( ( ~ ( hole @ SV5 )
| ( SV5 = hole_1 )
| ( SV5 = hole_2 )
| ( SV5 = hole_3 )
| ( SV5 = hole_4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(143,plain,
! [SV6: $i] :
( ( ~ ( pigeon @ SV6 )
| ( hole @ ( hole_of @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(144,plain,
! [SV7: $i] :
( ( ~ ( pigeon @ SV7 )
| ( in @ SV7 @ ( hole_of @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(145,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(146,plain,
! [SV1: $i] :
( ( ( ~ ( hole @ SV1 ) )
= $true )
| ( ( ! [SY12: $i] :
( ~ ( pigeon @ SY12 )
| ! [SY13: $i] :
( ~ ( pigeon @ SY13 )
| ~ ( in @ SY12 @ SV1 )
| ~ ( in @ SY13 @ SV1 )
| ( SY12 = SY13 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(147,plain,
! [SV8: $i,SV3: $i] :
( ( ( SV3 != SV8 )
| ( SV8 = SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(148,plain,
! [SV9: $i,SV4: $i] :
( ( ( SV4 != SV9 )
| ! [SY17: $i] :
( ( SV9 != SY17 )
| ( SV4 = SY17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(149,plain,
! [SV5: $i] :
( ( ( ~ ( hole @ SV5 ) )
= $true )
| ( ( ( SV5 = hole_1 )
| ( SV5 = hole_2 )
| ( SV5 = hole_3 )
| ( SV5 = hole_4 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(150,plain,
! [SV6: $i] :
( ( ( ~ ( pigeon @ SV6 ) )
= $true )
| ( ( hole @ ( hole_of @ SV6 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(151,plain,
! [SV7: $i] :
( ( ( ~ ( pigeon @ SV7 ) )
= $true )
| ( ( in @ SV7 @ ( hole_of @ SV7 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(152,plain,
! [SV1: $i] :
( ( ( hole @ SV1 )
= $false )
| ( ( ! [SY12: $i] :
( ~ ( pigeon @ SY12 )
| ! [SY13: $i] :
( ~ ( pigeon @ SY13 )
| ~ ( in @ SY12 @ SV1 )
| ~ ( in @ SY13 @ SV1 )
| ( SY12 = SY13 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(153,plain,
! [SV8: $i,SV3: $i] :
( ( ( ( SV3 != SV8 ) )
= $true )
| ( ( SV8 = SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(154,plain,
! [SV9: $i,SV4: $i] :
( ( ( ( SV4 != SV9 ) )
= $true )
| ( ( ! [SY17: $i] :
( ( SV9 != SY17 )
| ( SV4 = SY17 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(155,plain,
! [SV5: $i] :
( ( ( hole @ SV5 )
= $false )
| ( ( ( SV5 = hole_1 )
| ( SV5 = hole_2 )
| ( SV5 = hole_3 )
| ( SV5 = hole_4 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(156,plain,
! [SV6: $i] :
( ( ( pigeon @ SV6 )
= $false )
| ( ( hole @ ( hole_of @ SV6 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(157,plain,
! [SV7: $i] :
( ( ( pigeon @ SV7 )
= $false )
| ( ( in @ SV7 @ ( hole_of @ SV7 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(158,plain,
! [SV1: $i,SV10: $i] :
( ( ( ~ ( pigeon @ SV10 )
| ! [SY18: $i] :
( ~ ( pigeon @ SY18 )
| ~ ( in @ SV10 @ SV1 )
| ~ ( in @ SY18 @ SV1 )
| ( SV10 = SY18 ) ) )
= $true )
| ( ( hole @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(159,plain,
! [SV8: $i,SV3: $i] :
( ( ( SV3 = SV8 )
= $false )
| ( ( SV8 = SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[153]) ).
thf(160,plain,
! [SV9: $i,SV4: $i] :
( ( ( SV4 = SV9 )
= $false )
| ( ( ! [SY17: $i] :
( ( SV9 != SY17 )
| ( SV4 = SY17 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[154]) ).
thf(161,plain,
! [SV5: $i] :
( ( ( SV5 = hole_1 )
= $true )
| ( ( ( SV5 = hole_2 )
| ( SV5 = hole_3 )
| ( SV5 = hole_4 ) )
= $true )
| ( ( hole @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(162,plain,
! [SV1: $i,SV10: $i] :
( ( ( ~ ( pigeon @ SV10 ) )
= $true )
| ( ( ! [SY18: $i] :
( ~ ( pigeon @ SY18 )
| ~ ( in @ SV10 @ SV1 )
| ~ ( in @ SY18 @ SV1 )
| ( SV10 = SY18 ) ) )
= $true )
| ( ( hole @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(163,plain,
! [SV4: $i,SV11: $i,SV9: $i] :
( ( ( ( SV9 != SV11 )
| ( SV4 = SV11 ) )
= $true )
| ( ( SV4 = SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(164,plain,
! [SV5: $i] :
( ( ( SV5 = hole_2 )
= $true )
| ( ( ( SV5 = hole_3 )
| ( SV5 = hole_4 ) )
= $true )
| ( ( SV5 = hole_1 )
= $true )
| ( ( hole @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(165,plain,
! [SV1: $i,SV10: $i] :
( ( ( pigeon @ SV10 )
= $false )
| ( ( ! [SY18: $i] :
( ~ ( pigeon @ SY18 )
| ~ ( in @ SV10 @ SV1 )
| ~ ( in @ SY18 @ SV1 )
| ( SV10 = SY18 ) ) )
= $true )
| ( ( hole @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(166,plain,
! [SV4: $i,SV11: $i,SV9: $i] :
( ( ( ( SV9 != SV11 ) )
= $true )
| ( ( SV4 = SV11 )
= $true )
| ( ( SV4 = SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(167,plain,
! [SV5: $i] :
( ( ( SV5 = hole_3 )
= $true )
| ( ( SV5 = hole_4 )
= $true )
| ( ( SV5 = hole_2 )
= $true )
| ( ( SV5 = hole_1 )
= $true )
| ( ( hole @ SV5 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(168,plain,
! [SV1: $i,SV10: $i,SV12: $i] :
( ( ( ~ ( pigeon @ SV12 )
| ~ ( in @ SV10 @ SV1 )
| ~ ( in @ SV12 @ SV1 )
| ( SV10 = SV12 ) )
= $true )
| ( ( pigeon @ SV10 )
= $false )
| ( ( hole @ SV1 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(169,plain,
! [SV4: $i,SV11: $i,SV9: $i] :
( ( ( SV9 = SV11 )
= $false )
| ( ( SV4 = SV11 )
= $true )
| ( ( SV4 = SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(170,plain,
! [SV1: $i,SV10: $i,SV12: $i] :
( ( ( ~ ( pigeon @ SV12 ) )
= $true )
| ( ( ~ ( in @ SV10 @ SV1 )
| ~ ( in @ SV12 @ SV1 )
| ( SV10 = SV12 ) )
= $true )
| ( ( pigeon @ SV10 )
= $false )
| ( ( hole @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(171,plain,
! [SV1: $i,SV10: $i,SV12: $i] :
( ( ( pigeon @ SV12 )
= $false )
| ( ( ~ ( in @ SV10 @ SV1 )
| ~ ( in @ SV12 @ SV1 )
| ( SV10 = SV12 ) )
= $true )
| ( ( pigeon @ SV10 )
= $false )
| ( ( hole @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(172,plain,
! [SV12: $i,SV1: $i,SV10: $i] :
( ( ( ~ ( in @ SV10 @ SV1 ) )
= $true )
| ( ( ~ ( in @ SV12 @ SV1 )
| ( SV10 = SV12 ) )
= $true )
| ( ( pigeon @ SV12 )
= $false )
| ( ( pigeon @ SV10 )
= $false )
| ( ( hole @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(173,plain,
! [SV12: $i,SV1: $i,SV10: $i] :
( ( ( in @ SV10 @ SV1 )
= $false )
| ( ( ~ ( in @ SV12 @ SV1 )
| ( SV10 = SV12 ) )
= $true )
| ( ( pigeon @ SV12 )
= $false )
| ( ( pigeon @ SV10 )
= $false )
| ( ( hole @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[172]) ).
thf(174,plain,
! [SV10: $i,SV1: $i,SV12: $i] :
( ( ( ~ ( in @ SV12 @ SV1 ) )
= $true )
| ( ( SV10 = SV12 )
= $true )
| ( ( in @ SV10 @ SV1 )
= $false )
| ( ( pigeon @ SV12 )
= $false )
| ( ( pigeon @ SV10 )
= $false )
| ( ( hole @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(175,plain,
! [SV10: $i,SV1: $i,SV12: $i] :
( ( ( in @ SV12 @ SV1 )
= $false )
| ( ( SV10 = SV12 )
= $true )
| ( ( in @ SV10 @ SV1 )
= $false )
| ( ( pigeon @ SV12 )
= $false )
| ( ( pigeon @ SV10 )
= $false )
| ( ( hole @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[174]) ).
thf(176,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[93,175,169,167,159,157,156,145,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,123,111,110,109,108,97,96,95,94]) ).
thf(177,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : MSC007-2.005 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jul 1 15:13:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.35
% 0.19/0.35 No.of.Axioms: 32
% 0.19/0.35
% 0.19/0.35 Length.of.Defs: 0
% 0.19/0.35
% 0.19/0.35 Contains.Choice.Funs: false
% 0.19/0.36 (rf:0,axioms:32,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:34,loop_count:0,foatp_calls:0,translation:fof_full).....
% 0.70/0.89
% 0.70/0.89 ********************************
% 0.70/0.89 * All subproblems solved! *
% 0.70/0.89 ********************************
% 0.70/0.89 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:32,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:176,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.70/0.90
% 0.70/0.90 %**** Beginning of derivation protocol ****
% 0.70/0.90 % SZS output start CNFRefutation
% See solution above
% 0.70/0.90
% 0.70/0.90 %**** End of derivation protocol ****
% 0.70/0.90 %**** no. of clauses in derivation: 177 ****
% 0.70/0.90 %**** clause counter: 176 ****
% 0.70/0.90
% 0.70/0.90 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:32,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:176,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------