TSTP Solution File: NUM004-1 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : NUM004-1 : 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 : n024.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 11:46:18 EDT 2022
% Result : Unsatisfiable 3.07s 3.32s
% Output : CNFRefutation 3.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 20
% Syntax : Number of formulae : 114 ( 74 unt; 6 typ; 0 def)
% Number of atoms : 490 ( 132 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1076 ( 94 ~; 118 |; 0 &; 864 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 313 ( 0 ^ 313 !; 0 ?; 313 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_add,type,
add: $i > $i > $i ).
thf(tp_b,type,
b: $i ).
thf(tp_c,type,
c: $i ).
thf(tp_equalish,type,
equalish: $i > $i > $o ).
thf(tp_subtract,type,
subtract: $i > $i > $i ).
thf(1,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ C @ ( subtract @ D @ A ) )
| ( equalish @ C @ ( subtract @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_substitution2) ).
thf(2,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ C @ ( subtract @ A @ D ) )
| ( equalish @ C @ ( subtract @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subtract_substitution1) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ C @ ( add @ D @ A ) )
| ( equalish @ C @ ( add @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_substitution2) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ C @ ( add @ A @ D ) )
| ( equalish @ C @ ( add @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',add_substitution1) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] : ( equalish @ ( subtract @ ( add @ A @ B ) @ C ) @ ( add @ ( subtract @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity2) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] : ( equalish @ ( add @ ( subtract @ A @ B ) @ C ) @ ( subtract @ ( add @ A @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity1) ).
thf(7,axiom,
! [A: $i,B: $i] : ( equalish @ A @ ( subtract @ ( add @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_inverts_subtraction2) ).
thf(8,axiom,
! [A: $i,B: $i] : ( equalish @ ( subtract @ ( add @ A @ B ) @ B ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',addition_inverts_subtraction1) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] : ( equalish @ ( add @ A @ ( add @ B @ C ) ) @ ( add @ ( add @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_addition) ).
thf(10,axiom,
! [A: $i,B: $i] : ( equalish @ ( add @ A @ B ) @ ( add @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_addition) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ B @ C )
| ( equalish @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(12,axiom,
! [A: $i] : ( equalish @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
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,
~ ( equalish @ ( subtract @ ( add @ a @ b ) @ c ) @ ( add @ a @ ( subtract @ b @ c ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_equation) ).
thf(16,plain,
$false = $false,
inference(unfold_def,[status(thm)],[14]) ).
thf(17,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ C @ ( subtract @ D @ A ) )
| ( equalish @ C @ ( subtract @ D @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(18,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ C @ ( subtract @ A @ D ) )
| ( equalish @ C @ ( subtract @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(19,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ C @ ( add @ D @ A ) )
| ( equalish @ C @ ( add @ D @ B ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ C @ ( add @ A @ D ) )
| ( equalish @ C @ ( add @ B @ D ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(21,plain,
( ( ! [A: $i,B: $i,C: $i] : ( equalish @ ( subtract @ ( add @ A @ B ) @ C ) @ ( add @ ( subtract @ A @ C ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(22,plain,
( ( ! [A: $i,B: $i,C: $i] : ( equalish @ ( add @ ( subtract @ A @ B ) @ C ) @ ( subtract @ ( add @ A @ C ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(23,plain,
( ( ! [A: $i,B: $i] : ( equalish @ A @ ( subtract @ ( add @ A @ B ) @ B ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(24,plain,
( ( ! [A: $i,B: $i] : ( equalish @ ( subtract @ ( add @ A @ B ) @ B ) @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(25,plain,
( ( ! [A: $i,B: $i,C: $i] : ( equalish @ ( add @ A @ ( add @ B @ C ) ) @ ( add @ ( add @ A @ B ) @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(26,plain,
( ( ! [A: $i,B: $i] : ( equalish @ ( add @ A @ B ) @ ( add @ B @ A ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(27,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( equalish @ A @ B )
| ~ ( equalish @ B @ C )
| ( equalish @ A @ C ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(28,plain,
( ( ! [A: $i] : ( equalish @ A @ A ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(29,plain,
( ( ~ ( equalish @ ( subtract @ ( add @ a @ b ) @ c ) @ ( add @ a @ ( subtract @ b @ c ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(30,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[16]) ).
thf(31,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ A @ B )
| ! [C: $i,D: $i] :
( ~ ( equalish @ C @ ( subtract @ D @ A ) )
| ( equalish @ C @ ( subtract @ D @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(32,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ A @ B )
| ! [C: $i,D: $i] :
( ~ ( equalish @ C @ ( subtract @ A @ D ) )
| ( equalish @ C @ ( subtract @ B @ D ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(33,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ A @ B )
| ! [C: $i,D: $i] :
( ~ ( equalish @ C @ ( add @ D @ A ) )
| ( equalish @ C @ ( add @ D @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(34,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ A @ B )
| ! [C: $i,D: $i] :
( ~ ( equalish @ C @ ( add @ A @ D ) )
| ( equalish @ C @ ( add @ B @ D ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(35,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ A @ B )
| ! [C: $i] :
( ~ ( equalish @ B @ C )
| ( equalish @ A @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(36,plain,
( ( ~ ( equalish @ ( subtract @ ( add @ a @ b ) @ c ) @ ( add @ a @ ( subtract @ b @ c ) ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(37,plain,
( ( ! [A: $i] : ( equalish @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ A @ B )
| ! [C: $i] :
( ~ ( equalish @ B @ C )
| ( equalish @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(39,plain,
( ( ! [A: $i,B: $i] : ( equalish @ ( add @ A @ B ) @ ( add @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(40,plain,
( ( ! [A: $i,B: $i,C: $i] : ( equalish @ ( add @ A @ ( add @ B @ C ) ) @ ( add @ ( add @ A @ B ) @ C ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(41,plain,
( ( ! [A: $i,B: $i] : ( equalish @ ( subtract @ ( add @ A @ B ) @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(42,plain,
( ( ! [A: $i,B: $i] : ( equalish @ A @ ( subtract @ ( add @ A @ B ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(43,plain,
( ( ! [A: $i,B: $i,C: $i] : ( equalish @ ( add @ ( subtract @ A @ B ) @ C ) @ ( subtract @ ( add @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(44,plain,
( ( ! [A: $i,B: $i,C: $i] : ( equalish @ ( subtract @ ( add @ A @ B ) @ C ) @ ( add @ ( subtract @ A @ C ) @ B ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(45,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ A @ B )
| ! [C: $i,D: $i] :
( ~ ( equalish @ C @ ( add @ A @ D ) )
| ( equalish @ C @ ( add @ B @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(46,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ A @ B )
| ! [C: $i,D: $i] :
( ~ ( equalish @ C @ ( add @ D @ A ) )
| ( equalish @ C @ ( add @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(47,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ A @ B )
| ! [C: $i,D: $i] :
( ~ ( equalish @ C @ ( subtract @ A @ D ) )
| ( equalish @ C @ ( subtract @ B @ D ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(48,plain,
( ( ! [A: $i,B: $i] :
( ~ ( equalish @ A @ B )
| ! [C: $i,D: $i] :
( ~ ( equalish @ C @ ( subtract @ D @ A ) )
| ( equalish @ C @ ( subtract @ D @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(49,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(50,plain,
( ( equalish @ ( subtract @ ( add @ a @ b ) @ c ) @ ( add @ a @ ( subtract @ b @ c ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(51,plain,
! [SV1: $i] :
( ( equalish @ SV1 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(52,plain,
! [SV2: $i] :
( ( ! [SY35: $i] :
( ~ ( equalish @ SV2 @ SY35 )
| ! [SY36: $i] :
( ~ ( equalish @ SY35 @ SY36 )
| ( equalish @ SV2 @ SY36 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(53,plain,
! [SV3: $i] :
( ( ! [SY37: $i] : ( equalish @ ( add @ SV3 @ SY37 ) @ ( add @ SY37 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(54,plain,
! [SV4: $i] :
( ( ! [SY38: $i,SY39: $i] : ( equalish @ ( add @ SV4 @ ( add @ SY38 @ SY39 ) ) @ ( add @ ( add @ SV4 @ SY38 ) @ SY39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(55,plain,
! [SV5: $i] :
( ( ! [SY40: $i] : ( equalish @ ( subtract @ ( add @ SV5 @ SY40 ) @ SY40 ) @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(56,plain,
! [SV6: $i] :
( ( ! [SY41: $i] : ( equalish @ SV6 @ ( subtract @ ( add @ SV6 @ SY41 ) @ SY41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(57,plain,
! [SV7: $i] :
( ( ! [SY42: $i,SY43: $i] : ( equalish @ ( add @ ( subtract @ SV7 @ SY42 ) @ SY43 ) @ ( subtract @ ( add @ SV7 @ SY43 ) @ SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(58,plain,
! [SV8: $i] :
( ( ! [SY44: $i,SY45: $i] : ( equalish @ ( subtract @ ( add @ SV8 @ SY44 ) @ SY45 ) @ ( add @ ( subtract @ SV8 @ SY45 ) @ SY44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(59,plain,
! [SV9: $i] :
( ( ! [SY46: $i] :
( ~ ( equalish @ SV9 @ SY46 )
| ! [SY47: $i,SY48: $i] :
( ~ ( equalish @ SY47 @ ( add @ SV9 @ SY48 ) )
| ( equalish @ SY47 @ ( add @ SY46 @ SY48 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(60,plain,
! [SV10: $i] :
( ( ! [SY49: $i] :
( ~ ( equalish @ SV10 @ SY49 )
| ! [SY50: $i,SY51: $i] :
( ~ ( equalish @ SY50 @ ( add @ SY51 @ SV10 ) )
| ( equalish @ SY50 @ ( add @ SY51 @ SY49 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(61,plain,
! [SV11: $i] :
( ( ! [SY52: $i] :
( ~ ( equalish @ SV11 @ SY52 )
| ! [SY53: $i,SY54: $i] :
( ~ ( equalish @ SY53 @ ( subtract @ SV11 @ SY54 ) )
| ( equalish @ SY53 @ ( subtract @ SY52 @ SY54 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(62,plain,
! [SV12: $i] :
( ( ! [SY55: $i] :
( ~ ( equalish @ SV12 @ SY55 )
| ! [SY56: $i,SY57: $i] :
( ~ ( equalish @ SY56 @ ( subtract @ SY57 @ SV12 ) )
| ( equalish @ SY56 @ ( subtract @ SY57 @ SY55 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(63,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(64,plain,
! [SV13: $i,SV2: $i] :
( ( ~ ( equalish @ SV2 @ SV13 )
| ! [SY58: $i] :
( ~ ( equalish @ SV13 @ SY58 )
| ( equalish @ SV2 @ SY58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(65,plain,
! [SV14: $i,SV3: $i] :
( ( equalish @ ( add @ SV3 @ SV14 ) @ ( add @ SV14 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(66,plain,
! [SV15: $i,SV4: $i] :
( ( ! [SY59: $i] : ( equalish @ ( add @ SV4 @ ( add @ SV15 @ SY59 ) ) @ ( add @ ( add @ SV4 @ SV15 ) @ SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(67,plain,
! [SV16: $i,SV5: $i] :
( ( equalish @ ( subtract @ ( add @ SV5 @ SV16 ) @ SV16 ) @ SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(68,plain,
! [SV17: $i,SV6: $i] :
( ( equalish @ SV6 @ ( subtract @ ( add @ SV6 @ SV17 ) @ SV17 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(69,plain,
! [SV18: $i,SV7: $i] :
( ( ! [SY60: $i] : ( equalish @ ( add @ ( subtract @ SV7 @ SV18 ) @ SY60 ) @ ( subtract @ ( add @ SV7 @ SY60 ) @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(70,plain,
! [SV19: $i,SV8: $i] :
( ( ! [SY61: $i] : ( equalish @ ( subtract @ ( add @ SV8 @ SV19 ) @ SY61 ) @ ( add @ ( subtract @ SV8 @ SY61 ) @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(71,plain,
! [SV20: $i,SV9: $i] :
( ( ~ ( equalish @ SV9 @ SV20 )
| ! [SY62: $i,SY63: $i] :
( ~ ( equalish @ SY62 @ ( add @ SV9 @ SY63 ) )
| ( equalish @ SY62 @ ( add @ SV20 @ SY63 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(72,plain,
! [SV21: $i,SV10: $i] :
( ( ~ ( equalish @ SV10 @ SV21 )
| ! [SY64: $i,SY65: $i] :
( ~ ( equalish @ SY64 @ ( add @ SY65 @ SV10 ) )
| ( equalish @ SY64 @ ( add @ SY65 @ SV21 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(73,plain,
! [SV22: $i,SV11: $i] :
( ( ~ ( equalish @ SV11 @ SV22 )
| ! [SY66: $i,SY67: $i] :
( ~ ( equalish @ SY66 @ ( subtract @ SV11 @ SY67 ) )
| ( equalish @ SY66 @ ( subtract @ SV22 @ SY67 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(74,plain,
! [SV23: $i,SV12: $i] :
( ( ~ ( equalish @ SV12 @ SV23 )
| ! [SY68: $i,SY69: $i] :
( ~ ( equalish @ SY68 @ ( subtract @ SY69 @ SV12 ) )
| ( equalish @ SY68 @ ( subtract @ SY69 @ SV23 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(75,plain,
! [SV13: $i,SV2: $i] :
( ( ( ~ ( equalish @ SV2 @ SV13 ) )
= $true )
| ( ( ! [SY58: $i] :
( ~ ( equalish @ SV13 @ SY58 )
| ( equalish @ SV2 @ SY58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(76,plain,
! [SV24: $i,SV15: $i,SV4: $i] :
( ( equalish @ ( add @ SV4 @ ( add @ SV15 @ SV24 ) ) @ ( add @ ( add @ SV4 @ SV15 ) @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(77,plain,
! [SV25: $i,SV18: $i,SV7: $i] :
( ( equalish @ ( add @ ( subtract @ SV7 @ SV18 ) @ SV25 ) @ ( subtract @ ( add @ SV7 @ SV25 ) @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(78,plain,
! [SV26: $i,SV19: $i,SV8: $i] :
( ( equalish @ ( subtract @ ( add @ SV8 @ SV19 ) @ SV26 ) @ ( add @ ( subtract @ SV8 @ SV26 ) @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(79,plain,
! [SV20: $i,SV9: $i] :
( ( ( ~ ( equalish @ SV9 @ SV20 ) )
= $true )
| ( ( ! [SY62: $i,SY63: $i] :
( ~ ( equalish @ SY62 @ ( add @ SV9 @ SY63 ) )
| ( equalish @ SY62 @ ( add @ SV20 @ SY63 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(80,plain,
! [SV21: $i,SV10: $i] :
( ( ( ~ ( equalish @ SV10 @ SV21 ) )
= $true )
| ( ( ! [SY64: $i,SY65: $i] :
( ~ ( equalish @ SY64 @ ( add @ SY65 @ SV10 ) )
| ( equalish @ SY64 @ ( add @ SY65 @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(81,plain,
! [SV22: $i,SV11: $i] :
( ( ( ~ ( equalish @ SV11 @ SV22 ) )
= $true )
| ( ( ! [SY66: $i,SY67: $i] :
( ~ ( equalish @ SY66 @ ( subtract @ SV11 @ SY67 ) )
| ( equalish @ SY66 @ ( subtract @ SV22 @ SY67 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(82,plain,
! [SV23: $i,SV12: $i] :
( ( ( ~ ( equalish @ SV12 @ SV23 ) )
= $true )
| ( ( ! [SY68: $i,SY69: $i] :
( ~ ( equalish @ SY68 @ ( subtract @ SY69 @ SV12 ) )
| ( equalish @ SY68 @ ( subtract @ SY69 @ SV23 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(83,plain,
! [SV13: $i,SV2: $i] :
( ( ( equalish @ SV2 @ SV13 )
= $false )
| ( ( ! [SY58: $i] :
( ~ ( equalish @ SV13 @ SY58 )
| ( equalish @ SV2 @ SY58 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(84,plain,
! [SV20: $i,SV9: $i] :
( ( ( equalish @ SV9 @ SV20 )
= $false )
| ( ( ! [SY62: $i,SY63: $i] :
( ~ ( equalish @ SY62 @ ( add @ SV9 @ SY63 ) )
| ( equalish @ SY62 @ ( add @ SV20 @ SY63 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[79]) ).
thf(85,plain,
! [SV21: $i,SV10: $i] :
( ( ( equalish @ SV10 @ SV21 )
= $false )
| ( ( ! [SY64: $i,SY65: $i] :
( ~ ( equalish @ SY64 @ ( add @ SY65 @ SV10 ) )
| ( equalish @ SY64 @ ( add @ SY65 @ SV21 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(86,plain,
! [SV22: $i,SV11: $i] :
( ( ( equalish @ SV11 @ SV22 )
= $false )
| ( ( ! [SY66: $i,SY67: $i] :
( ~ ( equalish @ SY66 @ ( subtract @ SV11 @ SY67 ) )
| ( equalish @ SY66 @ ( subtract @ SV22 @ SY67 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(87,plain,
! [SV23: $i,SV12: $i] :
( ( ( equalish @ SV12 @ SV23 )
= $false )
| ( ( ! [SY68: $i,SY69: $i] :
( ~ ( equalish @ SY68 @ ( subtract @ SY69 @ SV12 ) )
| ( equalish @ SY68 @ ( subtract @ SY69 @ SV23 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(88,plain,
! [SV2: $i,SV27: $i,SV13: $i] :
( ( ( ~ ( equalish @ SV13 @ SV27 )
| ( equalish @ SV2 @ SV27 ) )
= $true )
| ( ( equalish @ SV2 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(89,plain,
! [SV20: $i,SV9: $i,SV28: $i] :
( ( ( ! [SY70: $i] :
( ~ ( equalish @ SV28 @ ( add @ SV9 @ SY70 ) )
| ( equalish @ SV28 @ ( add @ SV20 @ SY70 ) ) ) )
= $true )
| ( ( equalish @ SV9 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(90,plain,
! [SV21: $i,SV10: $i,SV29: $i] :
( ( ( ! [SY71: $i] :
( ~ ( equalish @ SV29 @ ( add @ SY71 @ SV10 ) )
| ( equalish @ SV29 @ ( add @ SY71 @ SV21 ) ) ) )
= $true )
| ( ( equalish @ SV10 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(91,plain,
! [SV22: $i,SV11: $i,SV30: $i] :
( ( ( ! [SY72: $i] :
( ~ ( equalish @ SV30 @ ( subtract @ SV11 @ SY72 ) )
| ( equalish @ SV30 @ ( subtract @ SV22 @ SY72 ) ) ) )
= $true )
| ( ( equalish @ SV11 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(92,plain,
! [SV23: $i,SV12: $i,SV31: $i] :
( ( ( ! [SY73: $i] :
( ~ ( equalish @ SV31 @ ( subtract @ SY73 @ SV12 ) )
| ( equalish @ SV31 @ ( subtract @ SY73 @ SV23 ) ) ) )
= $true )
| ( ( equalish @ SV12 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(93,plain,
! [SV2: $i,SV27: $i,SV13: $i] :
( ( ( ~ ( equalish @ SV13 @ SV27 ) )
= $true )
| ( ( equalish @ SV2 @ SV27 )
= $true )
| ( ( equalish @ SV2 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(94,plain,
! [SV20: $i,SV32: $i,SV9: $i,SV28: $i] :
( ( ( ~ ( equalish @ SV28 @ ( add @ SV9 @ SV32 ) )
| ( equalish @ SV28 @ ( add @ SV20 @ SV32 ) ) )
= $true )
| ( ( equalish @ SV9 @ SV20 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(95,plain,
! [SV21: $i,SV10: $i,SV33: $i,SV29: $i] :
( ( ( ~ ( equalish @ SV29 @ ( add @ SV33 @ SV10 ) )
| ( equalish @ SV29 @ ( add @ SV33 @ SV21 ) ) )
= $true )
| ( ( equalish @ SV10 @ SV21 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(96,plain,
! [SV22: $i,SV34: $i,SV11: $i,SV30: $i] :
( ( ( ~ ( equalish @ SV30 @ ( subtract @ SV11 @ SV34 ) )
| ( equalish @ SV30 @ ( subtract @ SV22 @ SV34 ) ) )
= $true )
| ( ( equalish @ SV11 @ SV22 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(97,plain,
! [SV23: $i,SV12: $i,SV35: $i,SV31: $i] :
( ( ( ~ ( equalish @ SV31 @ ( subtract @ SV35 @ SV12 ) )
| ( equalish @ SV31 @ ( subtract @ SV35 @ SV23 ) ) )
= $true )
| ( ( equalish @ SV12 @ SV23 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(98,plain,
! [SV2: $i,SV27: $i,SV13: $i] :
( ( ( equalish @ SV13 @ SV27 )
= $false )
| ( ( equalish @ SV2 @ SV27 )
= $true )
| ( ( equalish @ SV2 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(99,plain,
! [SV20: $i,SV32: $i,SV9: $i,SV28: $i] :
( ( ( ~ ( equalish @ SV28 @ ( add @ SV9 @ SV32 ) ) )
= $true )
| ( ( equalish @ SV28 @ ( add @ SV20 @ SV32 ) )
= $true )
| ( ( equalish @ SV9 @ SV20 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(100,plain,
! [SV21: $i,SV10: $i,SV33: $i,SV29: $i] :
( ( ( ~ ( equalish @ SV29 @ ( add @ SV33 @ SV10 ) ) )
= $true )
| ( ( equalish @ SV29 @ ( add @ SV33 @ SV21 ) )
= $true )
| ( ( equalish @ SV10 @ SV21 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(101,plain,
! [SV22: $i,SV34: $i,SV11: $i,SV30: $i] :
( ( ( ~ ( equalish @ SV30 @ ( subtract @ SV11 @ SV34 ) ) )
= $true )
| ( ( equalish @ SV30 @ ( subtract @ SV22 @ SV34 ) )
= $true )
| ( ( equalish @ SV11 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[96]) ).
thf(102,plain,
! [SV23: $i,SV12: $i,SV35: $i,SV31: $i] :
( ( ( ~ ( equalish @ SV31 @ ( subtract @ SV35 @ SV12 ) ) )
= $true )
| ( ( equalish @ SV31 @ ( subtract @ SV35 @ SV23 ) )
= $true )
| ( ( equalish @ SV12 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[97]) ).
thf(103,plain,
! [SV20: $i,SV32: $i,SV9: $i,SV28: $i] :
( ( ( equalish @ SV28 @ ( add @ SV9 @ SV32 ) )
= $false )
| ( ( equalish @ SV28 @ ( add @ SV20 @ SV32 ) )
= $true )
| ( ( equalish @ SV9 @ SV20 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(104,plain,
! [SV21: $i,SV10: $i,SV33: $i,SV29: $i] :
( ( ( equalish @ SV29 @ ( add @ SV33 @ SV10 ) )
= $false )
| ( ( equalish @ SV29 @ ( add @ SV33 @ SV21 ) )
= $true )
| ( ( equalish @ SV10 @ SV21 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(105,plain,
! [SV22: $i,SV34: $i,SV11: $i,SV30: $i] :
( ( ( equalish @ SV30 @ ( subtract @ SV11 @ SV34 ) )
= $false )
| ( ( equalish @ SV30 @ ( subtract @ SV22 @ SV34 ) )
= $true )
| ( ( equalish @ SV11 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(106,plain,
! [SV23: $i,SV12: $i,SV35: $i,SV31: $i] :
( ( ( equalish @ SV31 @ ( subtract @ SV35 @ SV12 ) )
= $false )
| ( ( equalish @ SV31 @ ( subtract @ SV35 @ SV23 ) )
= $true )
| ( ( equalish @ SV12 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(107,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[50,106,105,104,103,98,78,77,76,68,67,65,63,51]) ).
thf(108,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM004-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.14/0.32 % Computer : n024.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 600
% 0.14/0.32 % DateTime : Tue Jul 5 22:37:29 EDT 2022
% 0.14/0.32 % CPUTime :
% 0.14/0.34
% 0.14/0.34 No.of.Axioms: 13
% 0.14/0.34
% 0.14/0.34 Length.of.Defs: 0
% 0.14/0.34
% 0.14/0.34 Contains.Choice.Funs: false
% 0.14/0.35 (rf:0,axioms:13,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:15,loop_count:0,foatp_calls:0,translation:fof_full)......
% 3.07/3.32
% 3.07/3.32 ********************************
% 3.07/3.32 * All subproblems solved! *
% 3.07/3.32 ********************************
% 3.07/3.32 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:13,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:107,loop_count:0,foatp_calls:1,translation:fof_full)
% 3.07/3.32
% 3.07/3.32 %**** Beginning of derivation protocol ****
% 3.07/3.32 % SZS output start CNFRefutation
% See solution above
% 3.07/3.33
% 3.07/3.33 %**** End of derivation protocol ****
% 3.07/3.33 %**** no. of clauses in derivation: 108 ****
% 3.07/3.33 %**** clause counter: 107 ****
% 3.07/3.33
% 3.07/3.33 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:13,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:107,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------