TSTP Solution File: NUM024-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM024-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n027.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 : Mon Jul 18 11:46:28 EDT 2022
% Result : Unsatisfiable 0.19s 0.46s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 25
% Syntax : Number of formulae : 117 ( 79 unt; 8 typ; 0 def)
% Number of atoms : 431 ( 117 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 769 ( 78 ~; 88 |; 0 &; 603 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 217 ( 0 ^ 217 !; 0 ?; 217 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_add,type,
add: $i > $i > $i ).
thf(tp_equalish,type,
equalish: $i > $i > $o ).
thf(tp_less,type,
less: $i > $i > $o ).
thf(tp_multiply,type,
multiply: $i > $i > $i ).
thf(tp_n0,type,
n0: $i ).
thf(tp_predecessor_of_1st_minus_2nd,type,
predecessor_of_1st_minus_2nd: $i > $i > $i ).
thf(tp_successor,type,
successor: $i > $i ).
thf(1,axiom,
! [A: $i,B: $i] : ( equalish @ ( add @ A @ B ) @ ( add @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_plus) ).
thf(2,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( equalish @ ( add @ A @ B ) @ ( add @ C @ B ) )
| ( equalish @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_substitution) ).
thf(3,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( equalish @ Y @ Z )
| ( equalish @ X @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(4,axiom,
! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ Y @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry) ).
thf(5,axiom,
! [X: $i] : ( equalish @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ~ ( less @ A @ B )
| ( equalish @ ( add @ ( successor @ ( predecessor_of_1st_minus_2nd @ B @ A ) ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_lemma) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( equalish @ ( add @ ( successor @ A ) @ B ) @ C )
| ( less @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',smaller_number) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( less @ A @ B )
| ~ ( less @ C @ A )
| ( less @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( successor @ A ) @ ( successor @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_substitution) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ~ ( equalish @ ( successor @ A ) @ ( successor @ B ) )
| ( equalish @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_equality1) ).
thf(11,axiom,
! [A: $i,B: $i] : ( equalish @ ( multiply @ A @ ( successor @ B ) ) @ ( add @ ( multiply @ A @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times) ).
thf(12,axiom,
! [A: $i] : ( equalish @ ( multiply @ A @ n0 ) @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',times_zero) ).
thf(13,axiom,
! [A: $i,B: $i] : ( equalish @ ( add @ A @ ( successor @ B ) ) @ ( successor @ ( add @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition) ).
thf(14,axiom,
! [A: $i] : ( equalish @ ( add @ A @ n0 ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',adding_zero) ).
thf(15,axiom,
less @ a @ a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',impossible_a_is_less_than_itself) ).
thf(16,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(17,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[16]) ).
thf(18,negated_conjecture,
! [A: $i] :
~ ( equalish @ ( successor @ A ) @ n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_contradiction) ).
thf(19,plain,
$false = $false,
inference(unfold_def,[status(thm)],[17]) ).
thf(20,plain,
( ( ! [A: $i,B: $i] : ( equalish @ ( add @ A @ B ) @ ( add @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(21,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( equalish @ ( add @ A @ B ) @ ( add @ C @ B ) )
| ( equalish @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(22,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equalish @ X @ Y )
| ~ ( equalish @ Y @ Z )
| ( equalish @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(23,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(24,plain,
( ( ! [X: $i] : ( equalish @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ~ ( less @ A @ B )
| ( equalish @ ( add @ ( successor @ ( predecessor_of_1st_minus_2nd @ B @ A ) ) @ A ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(26,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( equalish @ ( add @ ( successor @ A ) @ B ) @ C )
| ( less @ B @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(27,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( less @ A @ B )
| ~ ( less @ C @ A )
| ( less @ C @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(28,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( successor @ A ) @ ( successor @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(29,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ ( successor @ A ) @ ( successor @ B ) )
| ( equalish @ A @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(30,plain,
( ( ! [A: $i,B: $i] : ( equalish @ ( multiply @ A @ ( successor @ B ) ) @ ( add @ ( multiply @ A @ B ) @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(31,plain,
( ( ! [A: $i] : ( equalish @ ( multiply @ A @ n0 ) @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(32,plain,
( ( ! [A: $i,B: $i] : ( equalish @ ( add @ A @ ( successor @ B ) ) @ ( successor @ ( add @ A @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(33,plain,
( ( ! [A: $i] : ( equalish @ ( add @ A @ n0 ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(34,plain,
( ( less @ a @ a )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(35,plain,
( ( ! [A: $i] :
~ ( equalish @ ( successor @ A ) @ n0 ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(36,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[19]) ).
thf(37,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [Z: $i] :
( ~ ( equalish @ Y @ Z )
| ( equalish @ X @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ~ ( less @ A @ B )
| ! [C: $i] :
( ~ ( less @ C @ A )
| ( less @ C @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(39,plain,
( ( ! [A: $i] :
~ ( equalish @ ( successor @ A ) @ n0 ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(40,plain,
( ( less @ a @ a )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(41,plain,
( ( ! [A: $i] : ( equalish @ ( add @ A @ n0 ) @ A ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(42,plain,
( ( ! [A: $i,B: $i] : ( equalish @ ( add @ A @ ( successor @ B ) ) @ ( successor @ ( add @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(43,plain,
( ( ! [A: $i] : ( equalish @ ( multiply @ A @ n0 ) @ n0 ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(44,plain,
( ( ! [A: $i,B: $i] : ( equalish @ ( multiply @ A @ ( successor @ B ) ) @ ( add @ ( multiply @ A @ B ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(45,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ ( successor @ A ) @ ( successor @ B ) )
| ( equalish @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(46,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ A @ B )
| ( equalish @ ( successor @ A ) @ ( successor @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(47,plain,
( ( ! [A: $i,B: $i] :
( ~ ( less @ A @ B )
| ! [C: $i] :
( ~ ( less @ C @ A )
| ( less @ C @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(48,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( equalish @ ( add @ ( successor @ A ) @ B ) @ C )
| ( less @ B @ C ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(49,plain,
( ( ! [A: $i,B: $i] :
( ~ ( less @ A @ B )
| ( equalish @ ( add @ ( successor @ ( predecessor_of_1st_minus_2nd @ B @ A ) ) @ A ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(50,plain,
( ( ! [X: $i] : ( equalish @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(51,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ( equalish @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(52,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( equalish @ X @ Y )
| ! [Z: $i] :
( ~ ( equalish @ Y @ Z )
| ( equalish @ X @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(53,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( equalish @ ( add @ A @ B ) @ ( add @ C @ B ) )
| ( equalish @ A @ C ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(54,plain,
( ( ! [A: $i,B: $i] : ( equalish @ ( add @ A @ B ) @ ( add @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(55,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(56,plain,
! [SV1: $i] :
( ( ~ ( equalish @ ( successor @ SV1 ) @ n0 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(57,plain,
! [SV2: $i] :
( ( equalish @ ( add @ SV2 @ n0 ) @ SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(58,plain,
! [SV3: $i] :
( ( ! [SY30: $i] : ( equalish @ ( add @ SV3 @ ( successor @ SY30 ) ) @ ( successor @ ( add @ SV3 @ SY30 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(59,plain,
! [SV4: $i] :
( ( equalish @ ( multiply @ SV4 @ n0 ) @ n0 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(60,plain,
! [SV5: $i] :
( ( ! [SY31: $i] : ( equalish @ ( multiply @ SV5 @ ( successor @ SY31 ) ) @ ( add @ ( multiply @ SV5 @ SY31 ) @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(61,plain,
! [SV6: $i] :
( ( ! [SY32: $i] :
( ~ ( equalish @ ( successor @ SV6 ) @ ( successor @ SY32 ) )
| ( equalish @ SV6 @ SY32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(62,plain,
! [SV7: $i] :
( ( ! [SY33: $i] :
( ~ ( equalish @ SV7 @ SY33 )
| ( equalish @ ( successor @ SV7 ) @ ( successor @ SY33 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(63,plain,
! [SV8: $i] :
( ( ! [SY34: $i] :
( ~ ( less @ SV8 @ SY34 )
| ! [SY35: $i] :
( ~ ( less @ SY35 @ SV8 )
| ( less @ SY35 @ SY34 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(64,plain,
! [SV9: $i] :
( ( ! [SY36: $i,SY37: $i] :
( ~ ( equalish @ ( add @ ( successor @ SV9 ) @ SY36 ) @ SY37 )
| ( less @ SY36 @ SY37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(65,plain,
! [SV10: $i] :
( ( ! [SY38: $i] :
( ~ ( less @ SV10 @ SY38 )
| ( equalish @ ( add @ ( successor @ ( predecessor_of_1st_minus_2nd @ SY38 @ SV10 ) ) @ SV10 ) @ SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(66,plain,
! [SV11: $i] :
( ( equalish @ SV11 @ SV11 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(67,plain,
! [SV12: $i] :
( ( ! [SY39: $i] :
( ~ ( equalish @ SV12 @ SY39 )
| ( equalish @ SY39 @ SV12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(68,plain,
! [SV13: $i] :
( ( ! [SY40: $i] :
( ~ ( equalish @ SV13 @ SY40 )
| ! [SY41: $i] :
( ~ ( equalish @ SY40 @ SY41 )
| ( equalish @ SV13 @ SY41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(69,plain,
! [SV14: $i] :
( ( ! [SY42: $i,SY43: $i] :
( ~ ( equalish @ ( add @ SV14 @ SY42 ) @ ( add @ SY43 @ SY42 ) )
| ( equalish @ SV14 @ SY43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(70,plain,
! [SV15: $i] :
( ( ! [SY44: $i] : ( equalish @ ( add @ SV15 @ SY44 ) @ ( add @ SY44 @ SV15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(71,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[55]) ).
thf(72,plain,
! [SV1: $i] :
( ( equalish @ ( successor @ SV1 ) @ n0 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(73,plain,
! [SV16: $i,SV3: $i] :
( ( equalish @ ( add @ SV3 @ ( successor @ SV16 ) ) @ ( successor @ ( add @ SV3 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(74,plain,
! [SV17: $i,SV5: $i] :
( ( equalish @ ( multiply @ SV5 @ ( successor @ SV17 ) ) @ ( add @ ( multiply @ SV5 @ SV17 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(75,plain,
! [SV18: $i,SV6: $i] :
( ( ~ ( equalish @ ( successor @ SV6 ) @ ( successor @ SV18 ) )
| ( equalish @ SV6 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(76,plain,
! [SV19: $i,SV7: $i] :
( ( ~ ( equalish @ SV7 @ SV19 )
| ( equalish @ ( successor @ SV7 ) @ ( successor @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(77,plain,
! [SV20: $i,SV8: $i] :
( ( ~ ( less @ SV8 @ SV20 )
| ! [SY45: $i] :
( ~ ( less @ SY45 @ SV8 )
| ( less @ SY45 @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(78,plain,
! [SV21: $i,SV9: $i] :
( ( ! [SY46: $i] :
( ~ ( equalish @ ( add @ ( successor @ SV9 ) @ SV21 ) @ SY46 )
| ( less @ SV21 @ SY46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(79,plain,
! [SV22: $i,SV10: $i] :
( ( ~ ( less @ SV10 @ SV22 )
| ( equalish @ ( add @ ( successor @ ( predecessor_of_1st_minus_2nd @ SV22 @ SV10 ) ) @ SV10 ) @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(80,plain,
! [SV23: $i,SV12: $i] :
( ( ~ ( equalish @ SV12 @ SV23 )
| ( equalish @ SV23 @ SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(81,plain,
! [SV24: $i,SV13: $i] :
( ( ~ ( equalish @ SV13 @ SV24 )
| ! [SY47: $i] :
( ~ ( equalish @ SV24 @ SY47 )
| ( equalish @ SV13 @ SY47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(82,plain,
! [SV25: $i,SV14: $i] :
( ( ! [SY48: $i] :
( ~ ( equalish @ ( add @ SV14 @ SV25 ) @ ( add @ SY48 @ SV25 ) )
| ( equalish @ SV14 @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(83,plain,
! [SV26: $i,SV15: $i] :
( ( equalish @ ( add @ SV15 @ SV26 ) @ ( add @ SV26 @ SV15 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(84,plain,
! [SV18: $i,SV6: $i] :
( ( ( ~ ( equalish @ ( successor @ SV6 ) @ ( successor @ SV18 ) ) )
= $true )
| ( ( equalish @ SV6 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(85,plain,
! [SV19: $i,SV7: $i] :
( ( ( ~ ( equalish @ SV7 @ SV19 ) )
= $true )
| ( ( equalish @ ( successor @ SV7 ) @ ( successor @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[76]) ).
thf(86,plain,
! [SV20: $i,SV8: $i] :
( ( ( ~ ( less @ SV8 @ SV20 ) )
= $true )
| ( ( ! [SY45: $i] :
( ~ ( less @ SY45 @ SV8 )
| ( less @ SY45 @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[77]) ).
thf(87,plain,
! [SV27: $i,SV21: $i,SV9: $i] :
( ( ~ ( equalish @ ( add @ ( successor @ SV9 ) @ SV21 ) @ SV27 )
| ( less @ SV21 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(88,plain,
! [SV22: $i,SV10: $i] :
( ( ( ~ ( less @ SV10 @ SV22 ) )
= $true )
| ( ( equalish @ ( add @ ( successor @ ( predecessor_of_1st_minus_2nd @ SV22 @ SV10 ) ) @ SV10 ) @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(89,plain,
! [SV23: $i,SV12: $i] :
( ( ( ~ ( equalish @ SV12 @ SV23 ) )
= $true )
| ( ( equalish @ SV23 @ SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(90,plain,
! [SV24: $i,SV13: $i] :
( ( ( ~ ( equalish @ SV13 @ SV24 ) )
= $true )
| ( ( ! [SY47: $i] :
( ~ ( equalish @ SV24 @ SY47 )
| ( equalish @ SV13 @ SY47 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(91,plain,
! [SV28: $i,SV25: $i,SV14: $i] :
( ( ~ ( equalish @ ( add @ SV14 @ SV25 ) @ ( add @ SV28 @ SV25 ) )
| ( equalish @ SV14 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(92,plain,
! [SV18: $i,SV6: $i] :
( ( ( equalish @ ( successor @ SV6 ) @ ( successor @ SV18 ) )
= $false )
| ( ( equalish @ SV6 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(93,plain,
! [SV19: $i,SV7: $i] :
( ( ( equalish @ SV7 @ SV19 )
= $false )
| ( ( equalish @ ( successor @ SV7 ) @ ( successor @ SV19 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(94,plain,
! [SV20: $i,SV8: $i] :
( ( ( less @ SV8 @ SV20 )
= $false )
| ( ( ! [SY45: $i] :
( ~ ( less @ SY45 @ SV8 )
| ( less @ SY45 @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[86]) ).
thf(95,plain,
! [SV27: $i,SV21: $i,SV9: $i] :
( ( ( ~ ( equalish @ ( add @ ( successor @ SV9 ) @ SV21 ) @ SV27 ) )
= $true )
| ( ( less @ SV21 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(96,plain,
! [SV22: $i,SV10: $i] :
( ( ( less @ SV10 @ SV22 )
= $false )
| ( ( equalish @ ( add @ ( successor @ ( predecessor_of_1st_minus_2nd @ SV22 @ SV10 ) ) @ SV10 ) @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(97,plain,
! [SV23: $i,SV12: $i] :
( ( ( equalish @ SV12 @ SV23 )
= $false )
| ( ( equalish @ SV23 @ SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(98,plain,
! [SV24: $i,SV13: $i] :
( ( ( equalish @ SV13 @ SV24 )
= $false )
| ( ( ! [SY47: $i] :
( ~ ( equalish @ SV24 @ SY47 )
| ( equalish @ SV13 @ SY47 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(99,plain,
! [SV28: $i,SV25: $i,SV14: $i] :
( ( ( ~ ( equalish @ ( add @ SV14 @ SV25 ) @ ( add @ SV28 @ SV25 ) ) )
= $true )
| ( ( equalish @ SV14 @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(100,plain,
! [SV20: $i,SV8: $i,SV29: $i] :
( ( ( ~ ( less @ SV29 @ SV8 )
| ( less @ SV29 @ SV20 ) )
= $true )
| ( ( less @ SV8 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(101,plain,
! [SV27: $i,SV21: $i,SV9: $i] :
( ( ( equalish @ ( add @ ( successor @ SV9 ) @ SV21 ) @ SV27 )
= $false )
| ( ( less @ SV21 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[95]) ).
thf(102,plain,
! [SV13: $i,SV30: $i,SV24: $i] :
( ( ( ~ ( equalish @ SV24 @ SV30 )
| ( equalish @ SV13 @ SV30 ) )
= $true )
| ( ( equalish @ SV13 @ SV24 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(103,plain,
! [SV28: $i,SV25: $i,SV14: $i] :
( ( ( equalish @ ( add @ SV14 @ SV25 ) @ ( add @ SV28 @ SV25 ) )
= $false )
| ( ( equalish @ SV14 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(104,plain,
! [SV20: $i,SV8: $i,SV29: $i] :
( ( ( ~ ( less @ SV29 @ SV8 ) )
= $true )
| ( ( less @ SV29 @ SV20 )
= $true )
| ( ( less @ SV8 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[100]) ).
thf(105,plain,
! [SV13: $i,SV30: $i,SV24: $i] :
( ( ( ~ ( equalish @ SV24 @ SV30 ) )
= $true )
| ( ( equalish @ SV13 @ SV30 )
= $true )
| ( ( equalish @ SV13 @ SV24 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(106,plain,
! [SV20: $i,SV8: $i,SV29: $i] :
( ( ( less @ SV29 @ SV8 )
= $false )
| ( ( less @ SV29 @ SV20 )
= $true )
| ( ( less @ SV8 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(107,plain,
! [SV13: $i,SV30: $i,SV24: $i] :
( ( ( equalish @ SV24 @ SV30 )
= $false )
| ( ( equalish @ SV13 @ SV30 )
= $true )
| ( ( equalish @ SV13 @ SV24 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(108,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[40,107,106,103,101,97,96,93,92,83,74,73,72,71,66,59,57]) ).
thf(109,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM024-1 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n027.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 Jul 6 08:31:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 16
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.36 (rf:0,axioms:16,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:18,loop_count:0,foatp_calls:0,translation:fof_full).....
% 0.19/0.46
% 0.19/0.46 ********************************
% 0.19/0.46 * All subproblems solved! *
% 0.19/0.46 ********************************
% 0.19/0.46 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:16,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:108,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.19/0.46
% 0.19/0.46 %**** Beginning of derivation protocol ****
% 0.19/0.46 % SZS output start CNFRefutation
% See solution above
% 0.19/0.46
% 0.19/0.46 %**** End of derivation protocol ****
% 0.19/0.46 %**** no. of clauses in derivation: 109 ****
% 0.19/0.46 %**** clause counter: 108 ****
% 0.19/0.46
% 0.19/0.46 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:16,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:108,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------