TSTP Solution File: SWV007-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SWV007-1 : 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 : n023.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 : Wed Jul 20 19:53:09 EDT 2022
% Result : Unsatisfiable 0.19s 0.48s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 33
% Syntax : Number of formulae : 159 ( 102 unt; 9 typ; 0 def)
% Number of atoms : 689 ( 261 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 929 ( 154 ~; 167 |; 0 &; 608 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 210 ( 0 ^ 210 !; 0 ?; 210 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i > $i ).
thf(tp_i,type,
i: $i ).
thf(tp_k,type,
k: $i ).
thf(tp_less_than,type,
less_than: $i > $i > $o ).
thf(tp_m,type,
m: $i ).
thf(tp_n,type,
n: $i ).
thf(tp_one,type,
one: $i ).
thf(tp_predecessor,type,
predecessor: $i > $i ).
thf(tp_successor,type,
successor: $i > $i ).
thf(1,axiom,
! [Z: $i,Y: $i,X: $i] :
( ( less_than @ Z @ Y )
| ( X != Y )
| ~ ( less_than @ Z @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_and_less_than_transitivity2) ).
thf(2,axiom,
! [Y: $i,Z: $i,X: $i] :
( ( less_than @ Y @ Z )
| ( X != Y )
| ~ ( less_than @ X @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_and_less_than_transitivity1) ).
thf(3,axiom,
! [X: $i,Y: $i] :
( ~ ( less_than @ X @ Y )
| ~ ( less_than @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',anti_symmetry_of_less_than) ).
thf(4,axiom,
! [X: $i] :
~ ( less_than @ X @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_not_less_than_x) ).
thf(5,axiom,
! [X: $i,Y: $i] :
( ( less_than @ X @ Y )
| ( less_than @ Y @ X )
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',all_related) ).
thf(6,axiom,
! [X: $i,Z: $i,Y: $i] :
( ( less_than @ X @ Z )
| ~ ( less_than @ X @ Y )
| ~ ( less_than @ Y @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_of_less_than) ).
thf(7,axiom,
! [X: $i] : ( less_than @ X @ ( successor @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less_than_successor) ).
thf(8,axiom,
! [X: $i] : ( less_than @ ( predecessor @ X ) @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',predecessor_less_than) ).
thf(9,axiom,
! [X: $i,Y: $i] :
( ( X = Y )
| ( ( successor @ X )
!= ( successor @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_defined_successor) ).
thf(10,axiom,
! [X: $i,Y: $i] :
( ( X = Y )
| ( ( predecessor @ X )
!= ( predecessor @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_defined_predecessor) ).
thf(11,axiom,
! [X: $i] :
( ( successor @ ( predecessor @ X ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_predecessor) ).
thf(12,axiom,
! [X: $i] :
( ( predecessor @ ( successor @ X ) )
= X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',predecessor_successor) ).
thf(13,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(14,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[13]) ).
thf(15,negated_conjecture,
! [X: $i] :
( ( less_than @ X @ i )
| ~ ( less_than @ X @ ( successor @ n ) )
| ~ ( less_than @ ( a @ X ) @ ( a @ k ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11) ).
thf(16,negated_conjecture,
! [X: $i] :
( ( less_than @ X @ i )
| ( less_than @ n @ X )
| ~ ( less_than @ one @ X )
| ~ ( less_than @ ( a @ X ) @ ( a @ ( predecessor @ i ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10) ).
thf(17,negated_conjecture,
! [X: $i] :
( ~ ( less_than @ one @ X )
| ~ ( less_than @ X @ i )
| ~ ( less_than @ ( a @ X ) @ ( a @ ( predecessor @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
thf(18,negated_conjecture,
less_than @ ( a @ m ) @ ( a @ k ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
thf(19,negated_conjecture,
k != m,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
thf(20,negated_conjecture,
~ ( less_than @ i @ one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
thf(21,negated_conjecture,
less_than @ i @ m,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
thf(22,negated_conjecture,
~ ( less_than @ n @ m ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
thf(23,negated_conjecture,
less_than @ i @ n,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
thf(24,negated_conjecture,
~ ( less_than @ k @ i ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
thf(25,negated_conjecture,
~ ( less_than @ n @ k ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
thf(26,plain,
$false = $false,
inference(unfold_def,[status(thm)],[14]) ).
thf(27,plain,
( ( ! [Z: $i,Y: $i,X: $i] :
( ( less_than @ Z @ Y )
| ( X != Y )
| ~ ( less_than @ Z @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(28,plain,
( ( ! [Y: $i,Z: $i,X: $i] :
( ( less_than @ Y @ Z )
| ( X != Y )
| ~ ( less_than @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(29,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_than @ X @ Y )
| ~ ( less_than @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(30,plain,
( ( ! [X: $i] :
~ ( less_than @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(31,plain,
( ( ! [X: $i,Y: $i] :
( ( less_than @ X @ Y )
| ( less_than @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(32,plain,
( ( ! [X: $i,Z: $i,Y: $i] :
( ( less_than @ X @ Z )
| ~ ( less_than @ X @ Y )
| ~ ( less_than @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(33,plain,
( ( ! [X: $i] : ( less_than @ X @ ( successor @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(34,plain,
( ( ! [X: $i] : ( less_than @ ( predecessor @ X ) @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(35,plain,
( ( ! [X: $i,Y: $i] :
( ( X = Y )
| ( ( successor @ X )
!= ( successor @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(36,plain,
( ( ! [X: $i,Y: $i] :
( ( X = Y )
| ( ( predecessor @ X )
!= ( predecessor @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(37,plain,
( ( ! [X: $i] :
( ( successor @ ( predecessor @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(38,plain,
( ( ! [X: $i] :
( ( predecessor @ ( successor @ X ) )
= X ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(39,plain,
( ( ! [X: $i] :
( ( less_than @ X @ i )
| ~ ( less_than @ X @ ( successor @ n ) )
| ~ ( less_than @ ( a @ X ) @ ( a @ k ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(40,plain,
( ( ! [X: $i] :
( ( less_than @ X @ i )
| ( less_than @ n @ X )
| ~ ( less_than @ one @ X )
| ~ ( less_than @ ( a @ X ) @ ( a @ ( predecessor @ i ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(41,plain,
( ( ! [X: $i] :
( ~ ( less_than @ one @ X )
| ~ ( less_than @ X @ i )
| ~ ( less_than @ ( a @ X ) @ ( a @ ( predecessor @ X ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(42,plain,
( ( less_than @ ( a @ m ) @ ( a @ k ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(43,plain,
( ( ( k != m ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(44,plain,
( ( ~ ( less_than @ i @ one ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(45,plain,
( ( less_than @ i @ m )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(46,plain,
( ( ~ ( less_than @ n @ m ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(47,plain,
( ( less_than @ i @ n )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(48,plain,
( ( ~ ( less_than @ k @ i ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(49,plain,
( ( ~ ( less_than @ n @ k ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(50,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[26]) ).
thf(51,plain,
( ( ! [Z: $i,Y: $i] :
( ( less_than @ Z @ Y )
| ! [X: $i] :
( ( X != Y )
| ~ ( less_than @ Z @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(52,plain,
( ( ! [Y: $i,Z: $i] :
( ( less_than @ Y @ Z )
| ! [X: $i] :
( ( X != Y )
| ~ ( less_than @ X @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(53,plain,
( ( ! [X: $i,Y: $i] :
( ( less_than @ X @ Y )
| ( X = Y )
| ( less_than @ Y @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(54,plain,
( ( ! [X: $i,Z: $i] :
( ( less_than @ X @ Z )
| ! [Y: $i] :
( ~ ( less_than @ X @ Y )
| ~ ( less_than @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(55,plain,
( ( ! [X: $i,Y: $i] :
( ( ( successor @ X )
!= ( successor @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(56,plain,
( ( ! [X: $i,Y: $i] :
( ( ( predecessor @ X )
!= ( predecessor @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(57,plain,
( ( ( k != m ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(58,plain,
( ( ~ ( less_than @ n @ k ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(59,plain,
( ( ~ ( less_than @ k @ i ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(60,plain,
( ( less_than @ i @ n )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(61,plain,
( ( ~ ( less_than @ n @ m ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(62,plain,
( ( less_than @ i @ m )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(63,plain,
( ( ~ ( less_than @ i @ one ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(64,plain,
( ( ( k != m ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(65,plain,
( ( less_than @ ( a @ m ) @ ( a @ k ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(66,plain,
( ( ! [X: $i] :
( ~ ( less_than @ one @ X )
| ~ ( less_than @ X @ i )
| ~ ( less_than @ ( a @ X ) @ ( a @ ( predecessor @ X ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(67,plain,
( ( ! [X: $i] :
( ( less_than @ X @ i )
| ( less_than @ n @ X )
| ~ ( less_than @ one @ X )
| ~ ( less_than @ ( a @ X ) @ ( a @ ( predecessor @ i ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(68,plain,
( ( ! [X: $i] :
( ( less_than @ X @ i )
| ~ ( less_than @ X @ ( successor @ n ) )
| ~ ( less_than @ ( a @ X ) @ ( a @ k ) ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(69,plain,
( ( ! [X: $i] :
( ( predecessor @ ( successor @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(70,plain,
( ( ! [X: $i] :
( ( successor @ ( predecessor @ X ) )
= X ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(71,plain,
( ( ! [X: $i,Y: $i] :
( ( ( predecessor @ X )
!= ( predecessor @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(72,plain,
( ( ! [X: $i,Y: $i] :
( ( ( successor @ X )
!= ( successor @ Y ) )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(73,plain,
( ( ! [X: $i] : ( less_than @ ( predecessor @ X ) @ X ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(74,plain,
( ( ! [X: $i] : ( less_than @ X @ ( successor @ X ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(75,plain,
( ( ! [X: $i,Z: $i] :
( ( less_than @ X @ Z )
| ! [Y: $i] :
( ~ ( less_than @ X @ Y )
| ~ ( less_than @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(76,plain,
( ( ! [X: $i,Y: $i] :
( ( less_than @ X @ Y )
| ( X = Y )
| ( less_than @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(77,plain,
( ( ! [X: $i] :
~ ( less_than @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(78,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( less_than @ X @ Y )
| ~ ( less_than @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(79,plain,
( ( ! [Y: $i,Z: $i] :
( ( less_than @ Y @ Z )
| ! [X: $i] :
( ( X != Y )
| ~ ( less_than @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(80,plain,
( ( ! [Z: $i,Y: $i] :
( ( less_than @ Z @ Y )
| ! [X: $i] :
( ( X != Y )
| ~ ( less_than @ Z @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(81,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(82,plain,
( ( less_than @ n @ k )
= $false ),
inference(extcnf_not_pos,[status(thm)],[58]) ).
thf(83,plain,
( ( less_than @ k @ i )
= $false ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(84,plain,
( ( less_than @ n @ m )
= $false ),
inference(extcnf_not_pos,[status(thm)],[61]) ).
thf(85,plain,
( ( less_than @ i @ one )
= $false ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(86,plain,
( ( k = m )
= $false ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(87,plain,
! [SV1: $i] :
( ( ~ ( less_than @ one @ SV1 )
| ~ ( less_than @ SV1 @ i )
| ~ ( less_than @ ( a @ SV1 ) @ ( a @ ( predecessor @ SV1 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(88,plain,
! [SV2: $i] :
( ( ( less_than @ SV2 @ i )
| ( less_than @ n @ SV2 )
| ~ ( less_than @ one @ SV2 )
| ~ ( less_than @ ( a @ SV2 ) @ ( a @ ( predecessor @ i ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(89,plain,
! [SV3: $i] :
( ( ( less_than @ SV3 @ i )
| ~ ( less_than @ SV3 @ ( successor @ n ) )
| ~ ( less_than @ ( a @ SV3 ) @ ( a @ k ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(90,plain,
! [SV4: $i] :
( ( ( predecessor @ ( successor @ SV4 ) )
= SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(91,plain,
! [SV5: $i] :
( ( ( successor @ ( predecessor @ SV5 ) )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(92,plain,
! [SV6: $i] :
( ( ! [SY25: $i] :
( ( ( predecessor @ SV6 )
!= ( predecessor @ SY25 ) )
| ( SV6 = SY25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(93,plain,
! [SV7: $i] :
( ( ! [SY26: $i] :
( ( ( successor @ SV7 )
!= ( successor @ SY26 ) )
| ( SV7 = SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(94,plain,
! [SV8: $i] :
( ( less_than @ ( predecessor @ SV8 ) @ SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(95,plain,
! [SV9: $i] :
( ( less_than @ SV9 @ ( successor @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(96,plain,
! [SV10: $i] :
( ( ! [SY27: $i] :
( ( less_than @ SV10 @ SY27 )
| ! [SY28: $i] :
( ~ ( less_than @ SV10 @ SY28 )
| ~ ( less_than @ SY28 @ SY27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(97,plain,
! [SV11: $i] :
( ( ! [SY29: $i] :
( ( less_than @ SV11 @ SY29 )
| ( SV11 = SY29 )
| ( less_than @ SY29 @ SV11 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(98,plain,
! [SV12: $i] :
( ( ~ ( less_than @ SV12 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(99,plain,
! [SV13: $i] :
( ( ! [SY30: $i] :
( ~ ( less_than @ SV13 @ SY30 )
| ~ ( less_than @ SY30 @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(100,plain,
! [SV14: $i] :
( ( ! [SY31: $i] :
( ( less_than @ SV14 @ SY31 )
| ! [SY32: $i] :
( ( SY32 != SV14 )
| ~ ( less_than @ SY32 @ SY31 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(101,plain,
! [SV15: $i] :
( ( ! [SY33: $i] :
( ( less_than @ SV15 @ SY33 )
| ! [SY34: $i] :
( ( SY34 != SY33 )
| ~ ( less_than @ SV15 @ SY34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(102,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(103,plain,
! [SV1: $i] :
( ( ( ~ ( less_than @ one @ SV1 ) )
= $true )
| ( ( ~ ( less_than @ SV1 @ i )
| ~ ( less_than @ ( a @ SV1 ) @ ( a @ ( predecessor @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(104,plain,
! [SV2: $i] :
( ( ( less_than @ SV2 @ i )
= $true )
| ( ( ( less_than @ n @ SV2 )
| ~ ( less_than @ one @ SV2 )
| ~ ( less_than @ ( a @ SV2 ) @ ( a @ ( predecessor @ i ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(105,plain,
! [SV3: $i] :
( ( ( less_than @ SV3 @ i )
= $true )
| ( ( ~ ( less_than @ SV3 @ ( successor @ n ) )
| ~ ( less_than @ ( a @ SV3 ) @ ( a @ k ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(106,plain,
! [SV16: $i,SV6: $i] :
( ( ( ( predecessor @ SV6 )
!= ( predecessor @ SV16 ) )
| ( SV6 = SV16 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(107,plain,
! [SV17: $i,SV7: $i] :
( ( ( ( successor @ SV7 )
!= ( successor @ SV17 ) )
| ( SV7 = SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(108,plain,
! [SV18: $i,SV10: $i] :
( ( ( less_than @ SV10 @ SV18 )
| ! [SY35: $i] :
( ~ ( less_than @ SV10 @ SY35 )
| ~ ( less_than @ SY35 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(109,plain,
! [SV19: $i,SV11: $i] :
( ( ( less_than @ SV11 @ SV19 )
| ( SV11 = SV19 )
| ( less_than @ SV19 @ SV11 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(110,plain,
! [SV12: $i] :
( ( less_than @ SV12 @ SV12 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(111,plain,
! [SV20: $i,SV13: $i] :
( ( ~ ( less_than @ SV13 @ SV20 )
| ~ ( less_than @ SV20 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(112,plain,
! [SV21: $i,SV14: $i] :
( ( ( less_than @ SV14 @ SV21 )
| ! [SY36: $i] :
( ( SY36 != SV14 )
| ~ ( less_than @ SY36 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(113,plain,
! [SV22: $i,SV15: $i] :
( ( ( less_than @ SV15 @ SV22 )
| ! [SY37: $i] :
( ( SY37 != SV22 )
| ~ ( less_than @ SV15 @ SY37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(114,plain,
! [SV1: $i] :
( ( ( less_than @ one @ SV1 )
= $false )
| ( ( ~ ( less_than @ SV1 @ i )
| ~ ( less_than @ ( a @ SV1 ) @ ( a @ ( predecessor @ SV1 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(115,plain,
! [SV2: $i] :
( ( ( less_than @ n @ SV2 )
= $true )
| ( ( ~ ( less_than @ one @ SV2 )
| ~ ( less_than @ ( a @ SV2 ) @ ( a @ ( predecessor @ i ) ) ) )
= $true )
| ( ( less_than @ SV2 @ i )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(116,plain,
! [SV3: $i] :
( ( ( ~ ( less_than @ SV3 @ ( successor @ n ) ) )
= $true )
| ( ( ~ ( less_than @ ( a @ SV3 ) @ ( a @ k ) ) )
= $true )
| ( ( less_than @ SV3 @ i )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(117,plain,
! [SV16: $i,SV6: $i] :
( ( ( ( ( predecessor @ SV6 )
!= ( predecessor @ SV16 ) ) )
= $true )
| ( ( SV6 = SV16 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(118,plain,
! [SV17: $i,SV7: $i] :
( ( ( ( ( successor @ SV7 )
!= ( successor @ SV17 ) ) )
= $true )
| ( ( SV7 = SV17 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(119,plain,
! [SV18: $i,SV10: $i] :
( ( ( less_than @ SV10 @ SV18 )
= $true )
| ( ( ! [SY35: $i] :
( ~ ( less_than @ SV10 @ SY35 )
| ~ ( less_than @ SY35 @ SV18 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(120,plain,
! [SV19: $i,SV11: $i] :
( ( ( less_than @ SV11 @ SV19 )
= $true )
| ( ( ( SV11 = SV19 )
| ( less_than @ SV19 @ SV11 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[109]) ).
thf(121,plain,
! [SV20: $i,SV13: $i] :
( ( ( ~ ( less_than @ SV13 @ SV20 ) )
= $true )
| ( ( ~ ( less_than @ SV20 @ SV13 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(122,plain,
! [SV21: $i,SV14: $i] :
( ( ( less_than @ SV14 @ SV21 )
= $true )
| ( ( ! [SY36: $i] :
( ( SY36 != SV14 )
| ~ ( less_than @ SY36 @ SV21 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(123,plain,
! [SV22: $i,SV15: $i] :
( ( ( less_than @ SV15 @ SV22 )
= $true )
| ( ( ! [SY37: $i] :
( ( SY37 != SV22 )
| ~ ( less_than @ SV15 @ SY37 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[113]) ).
thf(124,plain,
! [SV1: $i] :
( ( ( ~ ( less_than @ SV1 @ i ) )
= $true )
| ( ( ~ ( less_than @ ( a @ SV1 ) @ ( a @ ( predecessor @ SV1 ) ) ) )
= $true )
| ( ( less_than @ one @ SV1 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[114]) ).
thf(125,plain,
! [SV2: $i] :
( ( ( ~ ( less_than @ one @ SV2 ) )
= $true )
| ( ( ~ ( less_than @ ( a @ SV2 ) @ ( a @ ( predecessor @ i ) ) ) )
= $true )
| ( ( less_than @ n @ SV2 )
= $true )
| ( ( less_than @ SV2 @ i )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(126,plain,
! [SV3: $i] :
( ( ( less_than @ SV3 @ ( successor @ n ) )
= $false )
| ( ( ~ ( less_than @ ( a @ SV3 ) @ ( a @ k ) ) )
= $true )
| ( ( less_than @ SV3 @ i )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[116]) ).
thf(127,plain,
! [SV16: $i,SV6: $i] :
( ( ( ( predecessor @ SV6 )
= ( predecessor @ SV16 ) )
= $false )
| ( ( SV6 = SV16 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[117]) ).
thf(128,plain,
! [SV17: $i,SV7: $i] :
( ( ( ( successor @ SV7 )
= ( successor @ SV17 ) )
= $false )
| ( ( SV7 = SV17 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[118]) ).
thf(129,plain,
! [SV18: $i,SV23: $i,SV10: $i] :
( ( ( ~ ( less_than @ SV10 @ SV23 )
| ~ ( less_than @ SV23 @ SV18 ) )
= $true )
| ( ( less_than @ SV10 @ SV18 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(130,plain,
! [SV19: $i,SV11: $i] :
( ( ( SV11 = SV19 )
= $true )
| ( ( less_than @ SV19 @ SV11 )
= $true )
| ( ( less_than @ SV11 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[120]) ).
thf(131,plain,
! [SV20: $i,SV13: $i] :
( ( ( less_than @ SV13 @ SV20 )
= $false )
| ( ( ~ ( less_than @ SV20 @ SV13 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[121]) ).
thf(132,plain,
! [SV21: $i,SV14: $i,SV24: $i] :
( ( ( ( SV24 != SV14 )
| ~ ( less_than @ SV24 @ SV21 ) )
= $true )
| ( ( less_than @ SV14 @ SV21 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(133,plain,
! [SV15: $i,SV22: $i,SV25: $i] :
( ( ( ( SV25 != SV22 )
| ~ ( less_than @ SV15 @ SV25 ) )
= $true )
| ( ( less_than @ SV15 @ SV22 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(134,plain,
! [SV1: $i] :
( ( ( less_than @ SV1 @ i )
= $false )
| ( ( ~ ( less_than @ ( a @ SV1 ) @ ( a @ ( predecessor @ SV1 ) ) ) )
= $true )
| ( ( less_than @ one @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[124]) ).
thf(135,plain,
! [SV2: $i] :
( ( ( less_than @ one @ SV2 )
= $false )
| ( ( ~ ( less_than @ ( a @ SV2 ) @ ( a @ ( predecessor @ i ) ) ) )
= $true )
| ( ( less_than @ n @ SV2 )
= $true )
| ( ( less_than @ SV2 @ i )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[125]) ).
thf(136,plain,
! [SV3: $i] :
( ( ( less_than @ ( a @ SV3 ) @ ( a @ k ) )
= $false )
| ( ( less_than @ SV3 @ ( successor @ n ) )
= $false )
| ( ( less_than @ SV3 @ i )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(137,plain,
! [SV18: $i,SV23: $i,SV10: $i] :
( ( ( ~ ( less_than @ SV10 @ SV23 ) )
= $true )
| ( ( ~ ( less_than @ SV23 @ SV18 ) )
= $true )
| ( ( less_than @ SV10 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(138,plain,
! [SV13: $i,SV20: $i] :
( ( ( less_than @ SV20 @ SV13 )
= $false )
| ( ( less_than @ SV13 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[131]) ).
thf(139,plain,
! [SV21: $i,SV14: $i,SV24: $i] :
( ( ( ( SV24 != SV14 ) )
= $true )
| ( ( ~ ( less_than @ SV24 @ SV21 ) )
= $true )
| ( ( less_than @ SV14 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(140,plain,
! [SV15: $i,SV22: $i,SV25: $i] :
( ( ( ( SV25 != SV22 ) )
= $true )
| ( ( ~ ( less_than @ SV15 @ SV25 ) )
= $true )
| ( ( less_than @ SV15 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[133]) ).
thf(141,plain,
! [SV1: $i] :
( ( ( less_than @ ( a @ SV1 ) @ ( a @ ( predecessor @ SV1 ) ) )
= $false )
| ( ( less_than @ SV1 @ i )
= $false )
| ( ( less_than @ one @ SV1 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[134]) ).
thf(142,plain,
! [SV2: $i] :
( ( ( less_than @ ( a @ SV2 ) @ ( a @ ( predecessor @ i ) ) )
= $false )
| ( ( less_than @ one @ SV2 )
= $false )
| ( ( less_than @ n @ SV2 )
= $true )
| ( ( less_than @ SV2 @ i )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[135]) ).
thf(143,plain,
! [SV18: $i,SV23: $i,SV10: $i] :
( ( ( less_than @ SV10 @ SV23 )
= $false )
| ( ( ~ ( less_than @ SV23 @ SV18 ) )
= $true )
| ( ( less_than @ SV10 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(144,plain,
! [SV21: $i,SV14: $i,SV24: $i] :
( ( ( SV24 = SV14 )
= $false )
| ( ( ~ ( less_than @ SV24 @ SV21 ) )
= $true )
| ( ( less_than @ SV14 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(145,plain,
! [SV15: $i,SV22: $i,SV25: $i] :
( ( ( SV25 = SV22 )
= $false )
| ( ( ~ ( less_than @ SV15 @ SV25 ) )
= $true )
| ( ( less_than @ SV15 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(146,plain,
! [SV10: $i,SV18: $i,SV23: $i] :
( ( ( less_than @ SV23 @ SV18 )
= $false )
| ( ( less_than @ SV10 @ SV23 )
= $false )
| ( ( less_than @ SV10 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(147,plain,
! [SV14: $i,SV21: $i,SV24: $i] :
( ( ( less_than @ SV24 @ SV21 )
= $false )
| ( ( SV24 = SV14 )
= $false )
| ( ( less_than @ SV14 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(148,plain,
! [SV22: $i,SV25: $i,SV15: $i] :
( ( ( less_than @ SV15 @ SV25 )
= $false )
| ( ( SV25 = SV22 )
= $false )
| ( ( less_than @ SV15 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[145]) ).
thf(149,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[60,148,147,146,142,141,138,136,130,128,127,110,102,95,94,91,90,86,85,84,83,82,65,62]) ).
thf(150,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SWV007-1 : TPTP v8.1.0. Released v1.0.0.
% 0.10/0.14 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n023.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 : Wed Jun 15 10:17:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 23
% 0.13/0.36
% 0.13/0.36 Length.of.Defs: 0
% 0.13/0.36
% 0.13/0.36 Contains.Choice.Funs: false
% 0.13/0.36 (rf:0,axioms:23,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:25,loop_count:0,foatp_calls:0,translation:fof_full)......
% 0.19/0.48
% 0.19/0.48 ********************************
% 0.19/0.48 * All subproblems solved! *
% 0.19/0.48 ********************************
% 0.19/0.48 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:23,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:149,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.49
% 0.19/0.49 %**** Beginning of derivation protocol ****
% 0.19/0.49 % SZS output start CNFRefutation
% See solution above
% 0.19/0.49
% 0.19/0.49 %**** End of derivation protocol ****
% 0.19/0.49 %**** no. of clauses in derivation: 150 ****
% 0.19/0.49 %**** clause counter: 149 ****
% 0.19/0.49
% 0.19/0.49 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:23,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:149,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------