TSTP Solution File: ALG002-1 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : ALG002-1 : 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 : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 14 17:22:37 EDT 2022
% Result : Unsatisfiable 0.21s 0.44s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 22
% Syntax : Number of formulae : 110 ( 66 unt; 7 typ; 0 def)
% Number of atoms : 470 ( 123 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 785 ( 101 ~; 121 |; 0 &; 563 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-3 aty)
% Number of variables : 192 ( 0 ^ 192 !; 0 ?; 192 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_additive_identity,type,
additive_identity: $i ).
thf(tp_additive_inverse,type,
additive_inverse: $i > $i ).
thf(tp_greater_than_0,type,
greater_than_0: $i > $o ).
thf(tp_multiplicative_identity,type,
multiplicative_identity: $i ).
thf(tp_multiplicative_inverse,type,
multiplicative_inverse: $i > $i ).
thf(tp_product,type,
product: $i > $i > $i > $o ).
thf(1,axiom,
! [Y: $i,Z: $i,X: $i] :
( ~ ( product @ Y @ Z @ X )
| ~ ( greater_than_0 @ Y )
| ~ ( greater_than_0 @ Z )
| ( greater_than_0 @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_and_greater_than_0) ).
thf(2,axiom,
! [Y: $i,Z: $i,X: $i] :
( ~ ( product @ Y @ Z @ X )
| ~ ( product @ Y @ Y @ additive_identity )
| ( product @ X @ X @ additive_identity ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',square_to_0) ).
thf(3,axiom,
! [X: $i] :
( ( greater_than_0 @ X )
| ( product @ X @ X @ additive_identity )
| ( greater_than_0 @ ( additive_inverse @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_and_inverse) ).
thf(4,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ( product @ Y @ X @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_product) ).
thf(5,axiom,
! [X: $i] :
( ~ ( greater_than_0 @ X )
| ~ ( product @ X @ X @ additive_identity ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',greater_than_0_square) ).
thf(6,axiom,
! [X: $i] :
( ~ ( greater_than_0 @ X )
| ~ ( greater_than_0 @ ( additive_inverse @ X ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_greater_than_0) ).
thf(7,axiom,
! [X: $i] :
( ( product @ X @ ( multiplicative_inverse @ X ) @ multiplicative_identity )
| ( product @ X @ X @ additive_identity ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_and_identity) ).
thf(8,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ( product @ X @ ( additive_inverse @ Y ) @ ( additive_inverse @ Z ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_to_inverse) ).
thf(9,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( product @ X @ Y @ Z )
| ~ ( product @ ( additive_inverse @ X ) @ ( additive_inverse @ Y ) @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_of_inverses2) ).
thf(10,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ( product @ ( additive_inverse @ X ) @ ( additive_inverse @ Y ) @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_of_inverses1) ).
thf(11,axiom,
~ ( product @ multiplicative_identity @ multiplicative_identity @ additive_identity ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_abelian) ).
thf(12,axiom,
! [X: $i] : ( product @ X @ multiplicative_identity @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
thf(13,axiom,
greater_than_0 @ a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_greater_than_0) ).
thf(14,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(15,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[14]) ).
thf(16,negated_conjecture,
~ ( greater_than_0 @ ( multiplicative_inverse @ a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_inverse_greater_than_0) ).
thf(17,plain,
$false = $false,
inference(unfold_def,[status(thm)],[15]) ).
thf(18,plain,
( ( ! [Y: $i,Z: $i,X: $i] :
( ~ ( product @ Y @ Z @ X )
| ~ ( greater_than_0 @ Y )
| ~ ( greater_than_0 @ Z )
| ( greater_than_0 @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(19,plain,
( ( ! [Y: $i,Z: $i,X: $i] :
( ~ ( product @ Y @ Z @ X )
| ~ ( product @ Y @ Y @ additive_identity )
| ( product @ X @ X @ additive_identity ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(20,plain,
( ( ! [X: $i] :
( ( greater_than_0 @ X )
| ( product @ X @ X @ additive_identity )
| ( greater_than_0 @ ( additive_inverse @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(21,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ( product @ Y @ X @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(22,plain,
( ( ! [X: $i] :
( ~ ( greater_than_0 @ X )
| ~ ( product @ X @ X @ additive_identity ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(23,plain,
( ( ! [X: $i] :
( ~ ( greater_than_0 @ X )
| ~ ( greater_than_0 @ ( additive_inverse @ X ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(24,plain,
( ( ! [X: $i] :
( ( product @ X @ ( multiplicative_inverse @ X ) @ multiplicative_identity )
| ( product @ X @ X @ additive_identity ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(25,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ( product @ X @ ( additive_inverse @ Y ) @ ( additive_inverse @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(26,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( product @ X @ Y @ Z )
| ~ ( product @ ( additive_inverse @ X ) @ ( additive_inverse @ Y ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(27,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ( product @ ( additive_inverse @ X ) @ ( additive_inverse @ Y ) @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(28,plain,
( ( ~ ( product @ multiplicative_identity @ multiplicative_identity @ additive_identity ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(29,plain,
( ( ! [X: $i] : ( product @ X @ multiplicative_identity @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(30,plain,
( ( greater_than_0 @ a )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(31,plain,
( ( ~ ( greater_than_0 @ ( multiplicative_inverse @ a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(32,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[17]) ).
thf(33,plain,
( ( ! [X: $i] :
( ( greater_than_0 @ X )
| ( greater_than_0 @ ( additive_inverse @ X ) )
| ( product @ X @ X @ additive_identity ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(34,plain,
( ( ~ ( greater_than_0 @ ( multiplicative_inverse @ a ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(35,plain,
( ( greater_than_0 @ a )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(36,plain,
( ( ! [X: $i] : ( product @ X @ multiplicative_identity @ X ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(37,plain,
( ( ~ ( product @ multiplicative_identity @ multiplicative_identity @ additive_identity ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(38,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ( product @ ( additive_inverse @ X ) @ ( additive_inverse @ Y ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( product @ X @ Y @ Z )
| ~ ( product @ ( additive_inverse @ X ) @ ( additive_inverse @ Y ) @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(40,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ( product @ X @ ( additive_inverse @ Y ) @ ( additive_inverse @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(41,plain,
( ( ! [X: $i] :
( ( product @ X @ ( multiplicative_inverse @ X ) @ multiplicative_identity )
| ( product @ X @ X @ additive_identity ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(42,plain,
( ( ! [X: $i] :
( ~ ( greater_than_0 @ X )
| ~ ( greater_than_0 @ ( additive_inverse @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(43,plain,
( ( ! [X: $i] :
( ~ ( greater_than_0 @ X )
| ~ ( product @ X @ X @ additive_identity ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(44,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( product @ X @ Y @ Z )
| ( product @ Y @ X @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(45,plain,
( ( ! [X: $i] :
( ( greater_than_0 @ X )
| ( greater_than_0 @ ( additive_inverse @ X ) )
| ( product @ X @ X @ additive_identity ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(46,plain,
( ( ! [Y: $i,Z: $i,X: $i] :
( ~ ( product @ Y @ Z @ X )
| ~ ( product @ Y @ Y @ additive_identity )
| ( product @ X @ X @ additive_identity ) ) )
= $true ),
inference(copy,[status(thm)],[19]) ).
thf(47,plain,
( ( ! [Y: $i,Z: $i,X: $i] :
( ~ ( product @ Y @ Z @ X )
| ~ ( greater_than_0 @ Y )
| ~ ( greater_than_0 @ Z )
| ( greater_than_0 @ X ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(48,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(49,plain,
( ( greater_than_0 @ ( multiplicative_inverse @ a ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(50,plain,
! [SV1: $i] :
( ( product @ SV1 @ multiplicative_identity @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(51,plain,
( ( product @ multiplicative_identity @ multiplicative_identity @ additive_identity )
= $false ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(52,plain,
! [SV2: $i] :
( ( ! [SY23: $i,SY24: $i] :
( ~ ( product @ SV2 @ SY23 @ SY24 )
| ( product @ ( additive_inverse @ SV2 ) @ ( additive_inverse @ SY23 ) @ SY24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(53,plain,
! [SV3: $i] :
( ( ! [SY25: $i,SY26: $i] :
( ( product @ SV3 @ SY25 @ SY26 )
| ~ ( product @ ( additive_inverse @ SV3 ) @ ( additive_inverse @ SY25 ) @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(54,plain,
! [SV4: $i] :
( ( ! [SY27: $i,SY28: $i] :
( ~ ( product @ SV4 @ SY27 @ SY28 )
| ( product @ SV4 @ ( additive_inverse @ SY27 ) @ ( additive_inverse @ SY28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(55,plain,
! [SV5: $i] :
( ( ( product @ SV5 @ ( multiplicative_inverse @ SV5 ) @ multiplicative_identity )
| ( product @ SV5 @ SV5 @ additive_identity ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(56,plain,
! [SV6: $i] :
( ( ~ ( greater_than_0 @ SV6 )
| ~ ( greater_than_0 @ ( additive_inverse @ SV6 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(57,plain,
! [SV7: $i] :
( ( ~ ( greater_than_0 @ SV7 )
| ~ ( product @ SV7 @ SV7 @ additive_identity ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(58,plain,
! [SV8: $i] :
( ( ! [SY29: $i,SY30: $i] :
( ~ ( product @ SV8 @ SY29 @ SY30 )
| ( product @ SY29 @ SV8 @ SY30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(59,plain,
! [SV9: $i] :
( ( ( greater_than_0 @ SV9 )
| ( greater_than_0 @ ( additive_inverse @ SV9 ) )
| ( product @ SV9 @ SV9 @ additive_identity ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(60,plain,
! [SV10: $i] :
( ( ! [SY31: $i,SY32: $i] :
( ~ ( product @ SV10 @ SY31 @ SY32 )
| ~ ( product @ SV10 @ SV10 @ additive_identity )
| ( product @ SY32 @ SY32 @ additive_identity ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(61,plain,
! [SV11: $i] :
( ( ! [SY33: $i,SY34: $i] :
( ~ ( product @ SV11 @ SY33 @ SY34 )
| ~ ( greater_than_0 @ SV11 )
| ~ ( greater_than_0 @ SY33 )
| ( greater_than_0 @ SY34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(62,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(63,plain,
! [SV12: $i,SV2: $i] :
( ( ! [SY35: $i] :
( ~ ( product @ SV2 @ SV12 @ SY35 )
| ( product @ ( additive_inverse @ SV2 ) @ ( additive_inverse @ SV12 ) @ SY35 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(64,plain,
! [SV13: $i,SV3: $i] :
( ( ! [SY36: $i] :
( ( product @ SV3 @ SV13 @ SY36 )
| ~ ( product @ ( additive_inverse @ SV3 ) @ ( additive_inverse @ SV13 ) @ SY36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(65,plain,
! [SV14: $i,SV4: $i] :
( ( ! [SY37: $i] :
( ~ ( product @ SV4 @ SV14 @ SY37 )
| ( product @ SV4 @ ( additive_inverse @ SV14 ) @ ( additive_inverse @ SY37 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(66,plain,
! [SV5: $i] :
( ( ( product @ SV5 @ ( multiplicative_inverse @ SV5 ) @ multiplicative_identity )
= $true )
| ( ( product @ SV5 @ SV5 @ additive_identity )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(67,plain,
! [SV6: $i] :
( ( ( ~ ( greater_than_0 @ SV6 ) )
= $true )
| ( ( ~ ( greater_than_0 @ ( additive_inverse @ SV6 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[56]) ).
thf(68,plain,
! [SV7: $i] :
( ( ( ~ ( greater_than_0 @ SV7 ) )
= $true )
| ( ( ~ ( product @ SV7 @ SV7 @ additive_identity ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[57]) ).
thf(69,plain,
! [SV15: $i,SV8: $i] :
( ( ! [SY38: $i] :
( ~ ( product @ SV8 @ SV15 @ SY38 )
| ( product @ SV15 @ SV8 @ SY38 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(70,plain,
! [SV9: $i] :
( ( ( greater_than_0 @ SV9 )
= $true )
| ( ( ( greater_than_0 @ ( additive_inverse @ SV9 ) )
| ( product @ SV9 @ SV9 @ additive_identity ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[59]) ).
thf(71,plain,
! [SV16: $i,SV10: $i] :
( ( ! [SY39: $i] :
( ~ ( product @ SV10 @ SV16 @ SY39 )
| ~ ( product @ SV10 @ SV10 @ additive_identity )
| ( product @ SY39 @ SY39 @ additive_identity ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(72,plain,
! [SV17: $i,SV11: $i] :
( ( ! [SY40: $i] :
( ~ ( product @ SV11 @ SV17 @ SY40 )
| ~ ( greater_than_0 @ SV11 )
| ~ ( greater_than_0 @ SV17 )
| ( greater_than_0 @ SY40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(73,plain,
! [SV18: $i,SV12: $i,SV2: $i] :
( ( ~ ( product @ SV2 @ SV12 @ SV18 )
| ( product @ ( additive_inverse @ SV2 ) @ ( additive_inverse @ SV12 ) @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(74,plain,
! [SV19: $i,SV13: $i,SV3: $i] :
( ( ( product @ SV3 @ SV13 @ SV19 )
| ~ ( product @ ( additive_inverse @ SV3 ) @ ( additive_inverse @ SV13 ) @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(75,plain,
! [SV20: $i,SV14: $i,SV4: $i] :
( ( ~ ( product @ SV4 @ SV14 @ SV20 )
| ( product @ SV4 @ ( additive_inverse @ SV14 ) @ ( additive_inverse @ SV20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(76,plain,
! [SV6: $i] :
( ( ( greater_than_0 @ SV6 )
= $false )
| ( ( ~ ( greater_than_0 @ ( additive_inverse @ SV6 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(77,plain,
! [SV7: $i] :
( ( ( greater_than_0 @ SV7 )
= $false )
| ( ( ~ ( product @ SV7 @ SV7 @ additive_identity ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(78,plain,
! [SV21: $i,SV15: $i,SV8: $i] :
( ( ~ ( product @ SV8 @ SV15 @ SV21 )
| ( product @ SV15 @ SV8 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(79,plain,
! [SV9: $i] :
( ( ( greater_than_0 @ ( additive_inverse @ SV9 ) )
= $true )
| ( ( product @ SV9 @ SV9 @ additive_identity )
= $true )
| ( ( greater_than_0 @ SV9 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[70]) ).
thf(80,plain,
! [SV22: $i,SV16: $i,SV10: $i] :
( ( ~ ( product @ SV10 @ SV16 @ SV22 )
| ~ ( product @ SV10 @ SV10 @ additive_identity )
| ( product @ SV22 @ SV22 @ additive_identity ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(81,plain,
! [SV23: $i,SV17: $i,SV11: $i] :
( ( ~ ( product @ SV11 @ SV17 @ SV23 )
| ~ ( greater_than_0 @ SV11 )
| ~ ( greater_than_0 @ SV17 )
| ( greater_than_0 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(82,plain,
! [SV18: $i,SV12: $i,SV2: $i] :
( ( ( ~ ( product @ SV2 @ SV12 @ SV18 ) )
= $true )
| ( ( product @ ( additive_inverse @ SV2 ) @ ( additive_inverse @ SV12 ) @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(83,plain,
! [SV19: $i,SV13: $i,SV3: $i] :
( ( ( product @ SV3 @ SV13 @ SV19 )
= $true )
| ( ( ~ ( product @ ( additive_inverse @ SV3 ) @ ( additive_inverse @ SV13 ) @ SV19 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(84,plain,
! [SV20: $i,SV14: $i,SV4: $i] :
( ( ( ~ ( product @ SV4 @ SV14 @ SV20 ) )
= $true )
| ( ( product @ SV4 @ ( additive_inverse @ SV14 ) @ ( additive_inverse @ SV20 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(85,plain,
! [SV6: $i] :
( ( ( greater_than_0 @ ( additive_inverse @ SV6 ) )
= $false )
| ( ( greater_than_0 @ SV6 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(86,plain,
! [SV7: $i] :
( ( ( product @ SV7 @ SV7 @ additive_identity )
= $false )
| ( ( greater_than_0 @ SV7 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(87,plain,
! [SV21: $i,SV15: $i,SV8: $i] :
( ( ( ~ ( product @ SV8 @ SV15 @ SV21 ) )
= $true )
| ( ( product @ SV15 @ SV8 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(88,plain,
! [SV22: $i,SV16: $i,SV10: $i] :
( ( ( ~ ( product @ SV10 @ SV16 @ SV22 ) )
= $true )
| ( ( ~ ( product @ SV10 @ SV10 @ additive_identity )
| ( product @ SV22 @ SV22 @ additive_identity ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[80]) ).
thf(89,plain,
! [SV23: $i,SV17: $i,SV11: $i] :
( ( ( ~ ( product @ SV11 @ SV17 @ SV23 ) )
= $true )
| ( ( ~ ( greater_than_0 @ SV11 )
| ~ ( greater_than_0 @ SV17 )
| ( greater_than_0 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[81]) ).
thf(90,plain,
! [SV18: $i,SV12: $i,SV2: $i] :
( ( ( product @ SV2 @ SV12 @ SV18 )
= $false )
| ( ( product @ ( additive_inverse @ SV2 ) @ ( additive_inverse @ SV12 ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(91,plain,
! [SV19: $i,SV13: $i,SV3: $i] :
( ( ( product @ ( additive_inverse @ SV3 ) @ ( additive_inverse @ SV13 ) @ SV19 )
= $false )
| ( ( product @ SV3 @ SV13 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(92,plain,
! [SV20: $i,SV14: $i,SV4: $i] :
( ( ( product @ SV4 @ SV14 @ SV20 )
= $false )
| ( ( product @ SV4 @ ( additive_inverse @ SV14 ) @ ( additive_inverse @ SV20 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[84]) ).
thf(93,plain,
! [SV21: $i,SV15: $i,SV8: $i] :
( ( ( product @ SV8 @ SV15 @ SV21 )
= $false )
| ( ( product @ SV15 @ SV8 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(94,plain,
! [SV22: $i,SV16: $i,SV10: $i] :
( ( ( product @ SV10 @ SV16 @ SV22 )
= $false )
| ( ( ~ ( product @ SV10 @ SV10 @ additive_identity )
| ( product @ SV22 @ SV22 @ additive_identity ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(95,plain,
! [SV23: $i,SV17: $i,SV11: $i] :
( ( ( product @ SV11 @ SV17 @ SV23 )
= $false )
| ( ( ~ ( greater_than_0 @ SV11 )
| ~ ( greater_than_0 @ SV17 )
| ( greater_than_0 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(96,plain,
! [SV16: $i,SV22: $i,SV10: $i] :
( ( ( ~ ( product @ SV10 @ SV10 @ additive_identity ) )
= $true )
| ( ( product @ SV22 @ SV22 @ additive_identity )
= $true )
| ( ( product @ SV10 @ SV16 @ SV22 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[94]) ).
thf(97,plain,
! [SV23: $i,SV17: $i,SV11: $i] :
( ( ( ~ ( greater_than_0 @ SV11 ) )
= $true )
| ( ( ~ ( greater_than_0 @ SV17 )
| ( greater_than_0 @ SV23 ) )
= $true )
| ( ( product @ SV11 @ SV17 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[95]) ).
thf(98,plain,
! [SV16: $i,SV22: $i,SV10: $i] :
( ( ( product @ SV10 @ SV10 @ additive_identity )
= $false )
| ( ( product @ SV22 @ SV22 @ additive_identity )
= $true )
| ( ( product @ SV10 @ SV16 @ SV22 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[96]) ).
thf(99,plain,
! [SV23: $i,SV17: $i,SV11: $i] :
( ( ( greater_than_0 @ SV11 )
= $false )
| ( ( ~ ( greater_than_0 @ SV17 )
| ( greater_than_0 @ SV23 ) )
= $true )
| ( ( product @ SV11 @ SV17 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(100,plain,
! [SV11: $i,SV23: $i,SV17: $i] :
( ( ( ~ ( greater_than_0 @ SV17 ) )
= $true )
| ( ( greater_than_0 @ SV23 )
= $true )
| ( ( greater_than_0 @ SV11 )
= $false )
| ( ( product @ SV11 @ SV17 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(101,plain,
! [SV11: $i,SV23: $i,SV17: $i] :
( ( ( greater_than_0 @ SV17 )
= $false )
| ( ( greater_than_0 @ SV23 )
= $true )
| ( ( greater_than_0 @ SV11 )
= $false )
| ( ( product @ SV11 @ SV17 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(102,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[35,101,98,93,92,91,90,86,85,79,66,62,51,50,49]) ).
thf(103,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ALG002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Wed Jun 8 11:19:51 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36
% 0.13/0.36 No.of.Axioms: 14
% 0.13/0.36
% 0.13/0.36 Length.of.Defs: 0
% 0.13/0.36
% 0.13/0.36 Contains.Choice.Funs: false
% 0.13/0.37 (rf:0,axioms:14,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:16,loop_count:0,foatp_calls:0,translation:fof_full)....
% 0.21/0.44
% 0.21/0.44 ********************************
% 0.21/0.44 * All subproblems solved! *
% 0.21/0.44 ********************************
% 0.21/0.44 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:14,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:102,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.21/0.44
% 0.21/0.44 %**** Beginning of derivation protocol ****
% 0.21/0.44 % SZS output start CNFRefutation
% See solution above
% 0.21/0.44
% 0.21/0.44 %**** End of derivation protocol ****
% 0.21/0.44 %**** no. of clauses in derivation: 103 ****
% 0.21/0.44 %**** clause counter: 102 ****
% 0.21/0.44
% 0.21/0.44 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:14,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:102,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------