TSTP Solution File: FLD040-3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : FLD040-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n006.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 : 300s
% DateTime : Sun May 5 05:08:01 EDT 2024
% Result : Unsatisfiable 6.66s 1.32s
% Output : Refutation 6.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 28
% Syntax : Number of formulae : 118 ( 10 unt; 0 def)
% Number of atoms : 346 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 425 ( 197 ~; 219 |; 0 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 10 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 144 ( 144 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f33719,plain,
$false,
inference(avatar_sat_refutation,[],[f4853,f4857,f6623,f7820,f7825,f8173,f9765,f23238,f32687,f33709]) ).
fof(f33709,plain,
( spl0_23
| ~ spl0_2127 ),
inference(avatar_contradiction_clause,[],[f33708]) ).
fof(f33708,plain,
( $false
| spl0_23
| ~ spl0_2127 ),
inference(subsumption_resolution,[],[f33680,f342]) ).
fof(f342,plain,
( ~ sum(additive_identity,multiplicative_identity,additive_identity)
| spl0_23 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f341,plain,
( spl0_23
<=> sum(additive_identity,multiplicative_identity,additive_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f33680,plain,
( sum(additive_identity,multiplicative_identity,additive_identity)
| ~ spl0_2127 ),
inference(resolution,[],[f33675,f1060]) ).
fof(f1060,plain,
! [X0] :
( ~ sum(multiplicative_identity,X0,multiplicative_identity)
| sum(additive_identity,X0,additive_identity) ),
inference(resolution,[],[f369,f17]) ).
fof(f17,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplicative_identity) ).
fof(f369,plain,
! [X0,X1] :
( ~ defined(X0)
| sum(additive_identity,X1,additive_identity)
| ~ sum(X0,X1,X0) ),
inference(duplicate_literal_removal,[],[f363]) ).
fof(f363,plain,
! [X0,X1] :
( ~ sum(X0,X1,X0)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X0)
| ~ defined(X0) ),
inference(resolution,[],[f118,f4]) ).
fof(f4,axiom,
! [X0] :
( sum(additive_inverse(X0),X0,additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_addition) ).
fof(f118,plain,
! [X2,X3,X0,X1] :
( ~ sum(additive_inverse(X0),X2,X3)
| ~ sum(X0,X1,X2)
| sum(additive_identity,X1,X3)
| ~ defined(X0) ),
inference(resolution,[],[f2,f4]) ).
fof(f2,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X0,X3,X4)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X1,X2)
| sum(X4,X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_addition_2) ).
fof(f33675,plain,
( sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ spl0_2127 ),
inference(subsumption_resolution,[],[f33674,f27]) ).
fof(f27,axiom,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_is_defined) ).
fof(f33674,plain,
( sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| ~ defined(a)
| ~ spl0_2127 ),
inference(subsumption_resolution,[],[f33665,f28]) ).
fof(f28,axiom,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_sum_2) ).
fof(f33665,plain,
( sum(multiplicative_identity,multiplicative_identity,multiplicative_identity)
| sum(additive_identity,a,additive_identity)
| ~ defined(a)
| ~ spl0_2127 ),
inference(resolution,[],[f5091,f33066]) ).
fof(f33066,plain,
( product(additive_identity,a,multiplicative_identity)
| ~ spl0_2127 ),
inference(resolution,[],[f33011,f10]) ).
fof(f10,axiom,
! [X3,X0,X5] :
( ~ product(X0,X3,X5)
| product(X3,X0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_multiplication) ).
fof(f33011,plain,
( product(a,additive_identity,multiplicative_identity)
| ~ spl0_2127 ),
inference(subsumption_resolution,[],[f33010,f28]) ).
fof(f33010,plain,
( product(a,additive_identity,multiplicative_identity)
| sum(additive_identity,a,additive_identity)
| ~ spl0_2127 ),
inference(subsumption_resolution,[],[f33009,f27]) ).
fof(f33009,plain,
( product(a,additive_identity,multiplicative_identity)
| ~ defined(a)
| sum(additive_identity,a,additive_identity)
| ~ spl0_2127 ),
inference(subsumption_resolution,[],[f32980,f17]) ).
fof(f32980,plain,
( product(a,additive_identity,multiplicative_identity)
| ~ defined(multiplicative_identity)
| ~ defined(a)
| sum(additive_identity,a,additive_identity)
| ~ spl0_2127 ),
inference(resolution,[],[f32883,f325]) ).
fof(f325,plain,
! [X2,X0,X1] :
( ~ product(multiplicative_inverse(X0),X1,X2)
| product(X0,X2,X1)
| ~ defined(X1)
| ~ defined(X0)
| sum(additive_identity,X0,additive_identity) ),
inference(resolution,[],[f131,f50]) ).
fof(f50,plain,
! [X0] :
( product(X0,multiplicative_inverse(X0),multiplicative_identity)
| ~ defined(X0)
| sum(additive_identity,X0,additive_identity) ),
inference(resolution,[],[f9,f10]) ).
fof(f9,axiom,
! [X0] :
( product(multiplicative_inverse(X0),X0,multiplicative_identity)
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_inverse_multiplication) ).
fof(f131,plain,
! [X2,X3,X0,X1] :
( ~ product(X3,X0,multiplicative_identity)
| ~ product(X0,X1,X2)
| product(X3,X2,X1)
| ~ defined(X1) ),
inference(resolution,[],[f6,f8]) ).
fof(f8,axiom,
! [X0] :
( product(multiplicative_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_multiplication) ).
fof(f6,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_multiplication_1) ).
fof(f32883,plain,
( product(multiplicative_inverse(a),multiplicative_identity,additive_identity)
| ~ spl0_2127 ),
inference(resolution,[],[f32842,f10]) ).
fof(f32842,plain,
( product(multiplicative_identity,multiplicative_inverse(a),additive_identity)
| ~ spl0_2127 ),
inference(subsumption_resolution,[],[f32819,f14]) ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_identity) ).
fof(f32819,plain,
( product(multiplicative_identity,multiplicative_inverse(a),additive_identity)
| ~ defined(additive_identity)
| ~ spl0_2127 ),
inference(resolution,[],[f32740,f328]) ).
fof(f328,plain,
! [X0,X1] :
( ~ product(multiplicative_identity,X0,X1)
| product(multiplicative_identity,X1,X0)
| ~ defined(X0) ),
inference(subsumption_resolution,[],[f326,f17]) ).
fof(f326,plain,
! [X0,X1] :
( ~ product(multiplicative_identity,X0,X1)
| product(multiplicative_identity,X1,X0)
| ~ defined(X0)
| ~ defined(multiplicative_identity) ),
inference(resolution,[],[f131,f8]) ).
fof(f32740,plain,
( product(multiplicative_identity,additive_identity,multiplicative_inverse(a))
| ~ spl0_2127 ),
inference(resolution,[],[f23233,f10]) ).
fof(f23233,plain,
( product(additive_identity,multiplicative_identity,multiplicative_inverse(a))
| ~ spl0_2127 ),
inference(avatar_component_clause,[],[f23231]) ).
fof(f23231,plain,
( spl0_2127
<=> product(additive_identity,multiplicative_identity,multiplicative_inverse(a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2127])]) ).
fof(f5091,plain,
! [X0,X1] :
( ~ product(additive_identity,X0,X1)
| sum(multiplicative_identity,X1,multiplicative_identity)
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
inference(duplicate_literal_removal,[],[f5090]) ).
fof(f5090,plain,
! [X0,X1] :
( ~ product(additive_identity,X0,X1)
| sum(multiplicative_identity,X1,multiplicative_identity)
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0)
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
inference(resolution,[],[f728,f9]) ).
fof(f728,plain,
! [X2,X0,X1] :
( ~ product(multiplicative_inverse(X0),X0,X2)
| ~ product(additive_identity,X0,X1)
| sum(X2,X1,multiplicative_identity)
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
inference(subsumption_resolution,[],[f724,f18]) ).
fof(f18,axiom,
! [X0] :
( sum(additive_identity,X0,additive_identity)
| defined(multiplicative_inverse(X0))
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_multiplicative_inverse) ).
fof(f724,plain,
! [X2,X0,X1] :
( ~ product(additive_identity,X0,X1)
| ~ product(multiplicative_inverse(X0),X0,X2)
| sum(X2,X1,multiplicative_identity)
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0)
| ~ defined(multiplicative_inverse(X0)) ),
inference(resolution,[],[f145,f31]) ).
fof(f31,plain,
! [X0] :
( sum(X0,additive_identity,X0)
| ~ defined(X0) ),
inference(resolution,[],[f5,f3]) ).
fof(f3,axiom,
! [X0] :
( sum(additive_identity,X0,X0)
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_identity_addition) ).
fof(f5,axiom,
! [X3,X0,X5] :
( ~ sum(X0,X3,X5)
| sum(X3,X0,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_addition) ).
fof(f145,plain,
! [X2,X3,X0,X1,X4] :
( ~ sum(X0,X3,multiplicative_inverse(X1))
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2)
| sum(X2,X4,multiplicative_identity)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
inference(resolution,[],[f11,f9]) ).
fof(f11,axiom,
! [X3,X0,X8,X6,X9,X7,X5] :
( ~ product(X9,X5,X8)
| ~ product(X0,X5,X6)
| ~ product(X3,X5,X7)
| ~ sum(X0,X3,X9)
| sum(X6,X7,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_1) ).
fof(f32687,plain,
( spl0_2128
| ~ spl0_433 ),
inference(avatar_split_clause,[],[f32680,f4747,f23235]) ).
fof(f23235,plain,
( spl0_2128
<=> sum(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(a),multiplicative_identity) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2128])]) ).
fof(f4747,plain,
( spl0_433
<=> product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(multiplicative_identity)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f32680,plain,
( sum(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(a),multiplicative_identity)
| ~ spl0_433 ),
inference(resolution,[],[f10135,f5]) ).
fof(f10135,plain,
( sum(multiplicative_inverse(a),multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ spl0_433 ),
inference(resolution,[],[f9007,f1069]) ).
fof(f1069,plain,
! [X0] :
( ~ sum(additive_identity,X0,multiplicative_identity)
| sum(multiplicative_inverse(a),X0,multiplicative_identity) ),
inference(resolution,[],[f251,f17]) ).
fof(f251,plain,
! [X0,X1] :
( ~ defined(X1)
| sum(multiplicative_inverse(a),X0,X1)
| ~ sum(additive_identity,X0,X1) ),
inference(resolution,[],[f115,f3]) ).
fof(f115,plain,
! [X2,X0,X1] :
( ~ sum(additive_identity,X1,X2)
| ~ sum(additive_identity,X0,X1)
| sum(multiplicative_inverse(a),X0,X2) ),
inference(resolution,[],[f2,f29]) ).
fof(f29,axiom,
sum(additive_identity,additive_identity,multiplicative_inverse(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sum_3) ).
fof(f9007,plain,
( sum(additive_identity,multiplicative_inverse(multiplicative_identity),multiplicative_identity)
| ~ spl0_433 ),
inference(resolution,[],[f2880,f4749]) ).
fof(f4749,plain,
( product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| ~ spl0_433 ),
inference(avatar_component_clause,[],[f4747]) ).
fof(f2880,plain,
! [X0] :
( ~ product(multiplicative_identity,multiplicative_identity,X0)
| sum(additive_identity,X0,multiplicative_identity) ),
inference(subsumption_resolution,[],[f2879,f14]) ).
fof(f2879,plain,
! [X0] :
( ~ product(multiplicative_identity,multiplicative_identity,X0)
| sum(additive_identity,X0,multiplicative_identity)
| ~ defined(additive_identity) ),
inference(subsumption_resolution,[],[f2873,f17]) ).
fof(f2873,plain,
! [X0] :
( ~ product(multiplicative_identity,multiplicative_identity,X0)
| sum(additive_identity,X0,multiplicative_identity)
| ~ defined(multiplicative_identity)
| ~ defined(additive_identity) ),
inference(resolution,[],[f612,f34]) ).
fof(f34,plain,
! [X0] :
( product(X0,multiplicative_identity,X0)
| ~ defined(X0) ),
inference(resolution,[],[f10,f8]) ).
fof(f612,plain,
! [X2,X0,X1] :
( ~ product(additive_identity,X0,X2)
| ~ product(multiplicative_identity,X0,X1)
| sum(X2,X1,X0)
| ~ defined(X0) ),
inference(subsumption_resolution,[],[f608,f17]) ).
fof(f608,plain,
! [X2,X0,X1] :
( ~ product(multiplicative_identity,X0,X1)
| ~ product(additive_identity,X0,X2)
| sum(X2,X1,X0)
| ~ defined(X0)
| ~ defined(multiplicative_identity) ),
inference(resolution,[],[f142,f3]) ).
fof(f142,plain,
! [X2,X3,X0,X1,X4] :
( ~ sum(X0,X3,multiplicative_identity)
| ~ product(X3,X1,X4)
| ~ product(X0,X1,X2)
| sum(X2,X4,X1)
| ~ defined(X1) ),
inference(resolution,[],[f11,f8]) ).
fof(f23238,plain,
( spl0_2127
| ~ spl0_2128
| ~ spl0_25
| ~ spl0_597 ),
inference(avatar_split_clause,[],[f23229,f6621,f402,f23235,f23231]) ).
fof(f402,plain,
( spl0_25
<=> defined(multiplicative_inverse(multiplicative_identity)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f6621,plain,
( spl0_597
<=> ! [X0] :
( ~ sum(additive_inverse(multiplicative_inverse(multiplicative_identity)),multiplicative_identity,X0)
| product(additive_identity,multiplicative_identity,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f23229,plain,
( ~ sum(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(a),multiplicative_identity)
| product(additive_identity,multiplicative_identity,multiplicative_inverse(a))
| ~ spl0_25
| ~ spl0_597 ),
inference(subsumption_resolution,[],[f23214,f404]) ).
fof(f404,plain,
( defined(multiplicative_inverse(multiplicative_identity))
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f23214,plain,
( ~ sum(multiplicative_inverse(multiplicative_identity),multiplicative_inverse(a),multiplicative_identity)
| ~ defined(multiplicative_inverse(multiplicative_identity))
| product(additive_identity,multiplicative_identity,multiplicative_inverse(a))
| ~ spl0_597 ),
inference(resolution,[],[f1769,f6622]) ).
fof(f6622,plain,
( ! [X0] :
( ~ sum(additive_inverse(multiplicative_inverse(multiplicative_identity)),multiplicative_identity,X0)
| product(additive_identity,multiplicative_identity,X0) )
| ~ spl0_597 ),
inference(avatar_component_clause,[],[f6621]) ).
fof(f1769,plain,
! [X0,X1] :
( sum(additive_inverse(X0),X1,multiplicative_inverse(a))
| ~ sum(X0,multiplicative_inverse(a),X1)
| ~ defined(X0) ),
inference(resolution,[],[f310,f4]) ).
fof(f310,plain,
! [X2,X0,X1] :
( ~ sum(X0,X1,additive_identity)
| sum(X0,X2,multiplicative_inverse(a))
| ~ sum(X1,multiplicative_inverse(a),X2) ),
inference(resolution,[],[f100,f39]) ).
fof(f39,plain,
defined(multiplicative_inverse(a)),
inference(subsumption_resolution,[],[f37,f27]) ).
fof(f37,plain,
( defined(multiplicative_inverse(a))
| ~ defined(a) ),
inference(resolution,[],[f18,f28]) ).
fof(f100,plain,
! [X2,X3,X0,X1] :
( ~ defined(X1)
| ~ sum(X3,X0,additive_identity)
| sum(X3,X2,X1)
| ~ sum(X0,X1,X2) ),
inference(resolution,[],[f1,f3]) ).
fof(f1,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_addition_1) ).
fof(f9765,plain,
~ spl0_453,
inference(avatar_contradiction_clause,[],[f9764]) ).
fof(f9764,plain,
( $false
| ~ spl0_453 ),
inference(subsumption_resolution,[],[f9763,f14]) ).
fof(f9763,plain,
( ~ defined(additive_identity)
| ~ spl0_453 ),
inference(subsumption_resolution,[],[f9748,f26]) ).
fof(f26,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',different_identities) ).
fof(f9748,plain,
( sum(additive_identity,additive_identity,multiplicative_identity)
| ~ defined(additive_identity)
| ~ spl0_453 ),
inference(resolution,[],[f4852,f3]) ).
fof(f4852,plain,
( ! [X0] :
( ~ sum(X0,additive_identity,additive_identity)
| sum(X0,additive_identity,multiplicative_identity) )
| ~ spl0_453 ),
inference(avatar_component_clause,[],[f4851]) ).
fof(f4851,plain,
( spl0_453
<=> ! [X0] :
( sum(X0,additive_identity,multiplicative_identity)
| ~ sum(X0,additive_identity,additive_identity) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f8173,plain,
( ~ spl0_25
| spl0_596 ),
inference(avatar_contradiction_clause,[],[f8172]) ).
fof(f8172,plain,
( $false
| ~ spl0_25
| spl0_596 ),
inference(subsumption_resolution,[],[f8171,f404]) ).
fof(f8171,plain,
( ~ defined(multiplicative_inverse(multiplicative_identity))
| spl0_596 ),
inference(resolution,[],[f6619,f15]) ).
fof(f15,axiom,
! [X0] :
( defined(additive_inverse(X0))
| ~ defined(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',well_definedness_of_additive_inverse) ).
fof(f6619,plain,
( ~ defined(additive_inverse(multiplicative_inverse(multiplicative_identity)))
| spl0_596 ),
inference(avatar_component_clause,[],[f6617]) ).
fof(f6617,plain,
( spl0_596
<=> defined(additive_inverse(multiplicative_inverse(multiplicative_identity))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f7825,plain,
( spl0_37
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f6880,f341,f471]) ).
fof(f471,plain,
( spl0_37
<=> ! [X2,X0,X1] :
( ~ sum(additive_identity,X0,X1)
| ~ sum(multiplicative_identity,X2,X0)
| sum(additive_identity,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f6880,plain,
( ! [X2,X0,X1] :
( ~ sum(multiplicative_identity,X0,X1)
| ~ sum(additive_identity,X1,X2)
| sum(additive_identity,X0,X2) )
| ~ spl0_23 ),
inference(resolution,[],[f343,f2]) ).
fof(f343,plain,
( sum(additive_identity,multiplicative_identity,additive_identity)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f7820,plain,
~ spl0_37,
inference(avatar_contradiction_clause,[],[f7819]) ).
fof(f7819,plain,
( $false
| ~ spl0_37 ),
inference(subsumption_resolution,[],[f7818,f17]) ).
fof(f7818,plain,
( ~ defined(multiplicative_identity)
| ~ spl0_37 ),
inference(subsumption_resolution,[],[f7811,f26]) ).
fof(f7811,plain,
( sum(additive_identity,additive_identity,multiplicative_identity)
| ~ defined(multiplicative_identity)
| ~ spl0_37 ),
inference(resolution,[],[f1617,f3]) ).
fof(f1617,plain,
( ! [X0] :
( ~ sum(additive_identity,multiplicative_identity,X0)
| sum(additive_identity,additive_identity,X0) )
| ~ spl0_37 ),
inference(subsumption_resolution,[],[f1612,f17]) ).
fof(f1612,plain,
( ! [X0] :
( ~ sum(additive_identity,multiplicative_identity,X0)
| sum(additive_identity,additive_identity,X0)
| ~ defined(multiplicative_identity) )
| ~ spl0_37 ),
inference(resolution,[],[f472,f31]) ).
fof(f472,plain,
( ! [X2,X0,X1] :
( ~ sum(multiplicative_identity,X2,X0)
| ~ sum(additive_identity,X0,X1)
| sum(additive_identity,X2,X1) )
| ~ spl0_37 ),
inference(avatar_component_clause,[],[f471]) ).
fof(f6623,plain,
( ~ spl0_596
| spl0_23
| spl0_597 ),
inference(avatar_split_clause,[],[f6615,f6621,f341,f6617]) ).
fof(f6615,plain,
! [X0] :
( ~ sum(additive_inverse(multiplicative_inverse(multiplicative_identity)),multiplicative_identity,X0)
| product(additive_identity,multiplicative_identity,X0)
| sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(additive_inverse(multiplicative_inverse(multiplicative_identity))) ),
inference(subsumption_resolution,[],[f5752,f17]) ).
fof(f5752,plain,
! [X0] :
( ~ sum(additive_inverse(multiplicative_inverse(multiplicative_identity)),multiplicative_identity,X0)
| product(additive_identity,multiplicative_identity,X0)
| sum(additive_identity,multiplicative_identity,additive_identity)
| ~ defined(multiplicative_identity)
| ~ defined(additive_inverse(multiplicative_inverse(multiplicative_identity))) ),
inference(resolution,[],[f744,f34]) ).
fof(f744,plain,
! [X2,X0,X1] :
( ~ product(additive_inverse(multiplicative_inverse(X0)),X0,X1)
| ~ sum(X1,multiplicative_identity,X2)
| product(additive_identity,X0,X2)
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
inference(subsumption_resolution,[],[f739,f18]) ).
fof(f739,plain,
! [X2,X0,X1] :
( ~ product(additive_inverse(multiplicative_inverse(X0)),X0,X1)
| ~ sum(X1,multiplicative_identity,X2)
| product(additive_identity,X0,X2)
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0)
| ~ defined(multiplicative_inverse(X0)) ),
inference(resolution,[],[f152,f4]) ).
fof(f152,plain,
! [X2,X3,X0,X1,X4] :
( ~ sum(X0,multiplicative_inverse(X1),X3)
| ~ product(X0,X1,X2)
| ~ sum(X2,multiplicative_identity,X4)
| product(X3,X1,X4)
| sum(additive_identity,X1,additive_identity)
| ~ defined(X1) ),
inference(resolution,[],[f12,f9]) ).
fof(f12,axiom,
! [X3,X0,X8,X6,X9,X7,X5] :
( ~ product(X3,X5,X7)
| ~ product(X0,X5,X6)
| ~ sum(X0,X3,X9)
| ~ sum(X6,X7,X8)
| product(X9,X5,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity_2) ).
fof(f4857,plain,
( spl0_23
| ~ spl0_25
| spl0_433 ),
inference(avatar_split_clause,[],[f4854,f4747,f402,f341]) ).
fof(f4854,plain,
( product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| ~ defined(multiplicative_inverse(multiplicative_identity))
| sum(additive_identity,multiplicative_identity,additive_identity) ),
inference(subsumption_resolution,[],[f1040,f17]) ).
fof(f1040,plain,
( product(multiplicative_identity,multiplicative_identity,multiplicative_inverse(multiplicative_identity))
| ~ defined(multiplicative_inverse(multiplicative_identity))
| ~ defined(multiplicative_identity)
| sum(additive_identity,multiplicative_identity,additive_identity) ),
inference(resolution,[],[f328,f50]) ).
fof(f4853,plain,
( spl0_25
| spl0_453 ),
inference(avatar_split_clause,[],[f4849,f4851,f402]) ).
fof(f4849,plain,
! [X0] :
( sum(X0,additive_identity,multiplicative_identity)
| ~ sum(X0,additive_identity,additive_identity)
| defined(multiplicative_inverse(multiplicative_identity)) ),
inference(subsumption_resolution,[],[f1426,f17]) ).
fof(f1426,plain,
! [X0] :
( sum(X0,additive_identity,multiplicative_identity)
| ~ sum(X0,additive_identity,additive_identity)
| defined(multiplicative_inverse(multiplicative_identity))
| ~ defined(multiplicative_identity) ),
inference(resolution,[],[f309,f18]) ).
fof(f309,plain,
! [X2,X0,X1] :
( ~ sum(X1,multiplicative_identity,X2)
| sum(X0,X2,multiplicative_identity)
| ~ sum(X0,X1,additive_identity) ),
inference(resolution,[],[f100,f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : FLD040-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.12/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.35 % Computer : n006.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Fri May 3 19:44:23 EDT 2024
% 0.19/0.36 % CPUTime :
% 0.19/0.36 % (2823)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.38 % (2827)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.19/0.38 % (2828)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.19/0.38 % (2825)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.19/0.38 % (2830)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.19/0.38 % (2826)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.19/0.38 % (2824)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.19/0.38 % (2829)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.19/0.38 TRYING [1]
% 0.19/0.38 TRYING [2]
% 0.19/0.38 TRYING [1]
% 0.19/0.38 TRYING [1]
% 0.19/0.38 TRYING [2]
% 0.19/0.38 TRYING [1]
% 0.19/0.38 TRYING [2]
% 0.19/0.38 TRYING [2]
% 0.19/0.38 TRYING [3]
% 0.19/0.38 TRYING [3]
% 0.19/0.38 TRYING [3]
% 0.19/0.38 TRYING [3]
% 0.19/0.39 TRYING [4]
% 0.19/0.39 TRYING [4]
% 0.19/0.39 TRYING [4]
% 0.19/0.39 TRYING [4]
% 0.19/0.42 TRYING [5]
% 0.19/0.42 TRYING [5]
% 0.19/0.42 TRYING [5]
% 0.19/0.43 TRYING [5]
% 0.19/0.46 TRYING [6]
% 0.19/0.49 TRYING [6]
% 0.19/0.49 TRYING [6]
% 0.19/0.53 TRYING [6]
% 1.62/0.61 TRYING [7]
% 1.62/0.63 TRYING [7]
% 2.20/0.68 TRYING [7]
% 2.84/0.79 TRYING [7]
% 4.66/1.03 TRYING [8]
% 4.66/1.06 TRYING [8]
% 5.00/1.10 TRYING [8]
% 6.66/1.31 % (2829)First to succeed.
% 6.66/1.31 % (2829)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2823"
% 6.66/1.32 % (2829)Refutation found. Thanks to Tanya!
% 6.66/1.32 % SZS status Unsatisfiable for theBenchmark
% 6.66/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 6.66/1.32 % (2829)------------------------------
% 6.66/1.32 % (2829)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 6.66/1.32 % (2829)Termination reason: Refutation
% 6.66/1.32
% 6.66/1.32 % (2829)Memory used [KB]: 11551
% 6.66/1.32 % (2829)Time elapsed: 0.935 s
% 6.66/1.32 % (2829)Instructions burned: 1868 (million)
% 6.66/1.32 % (2823)Success in time 0.941 s
%------------------------------------------------------------------------------