TSTP Solution File: KLE010+4 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE010+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n009.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 : Tue Apr 30 13:11:39 EDT 2024
% Result : Theorem 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 27
% Syntax : Number of formulae : 189 ( 61 unt; 0 def)
% Number of atoms : 382 ( 134 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 342 ( 149 ~; 137 |; 30 &)
% ( 18 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 11 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 130 ( 119 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6215,plain,
$false,
inference(avatar_sat_refutation,[],[f153,f162,f829,f1245,f1319,f1334,f1379,f1652,f6190,f6198]) ).
fof(f6198,plain,
spl3_5,
inference(avatar_contradiction_clause,[],[f6197]) ).
fof(f6197,plain,
( $false
| spl3_5 ),
inference(subsumption_resolution,[],[f6196,f98]) ).
fof(f98,plain,
! [X0] : leq(X0,X0),
inference(trivial_inequality_removal,[],[f93]) ).
fof(f93,plain,
! [X0] :
( X0 != X0
| leq(X0,X0) ),
inference(superposition,[],[f69,f56]) ).
fof(f56,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f69,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( addition(X0,X1) = X1
=> leq(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
fof(f6196,plain,
( ~ leq(one,one)
| spl3_5 ),
inference(forward_demodulation,[],[f6195,f1154]) ).
fof(f1154,plain,
one = addition(sK0,c(sK0)),
inference(superposition,[],[f137,f1119]) ).
fof(f1119,plain,
c(sK0) = sK2(sK0),
inference(subsumption_resolution,[],[f1114,f49]) ).
fof(f49,plain,
test(sK0),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
( ( ~ leq(addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))) )
& test(sK0)
& test(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f31,f39]) ).
fof(f39,plain,
( ? [X0,X1] :
( ( ~ leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) )
& test(X0)
& test(X1) )
=> ( ( ~ leq(addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))) )
& test(sK0)
& test(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f31,plain,
? [X0,X1] :
( ( ~ leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) )
& test(X0)
& test(X1) ),
inference(flattening,[],[f30]) ).
fof(f30,plain,
? [X0,X1] :
( ( ~ leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) )
& test(X0)
& test(X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> ( leq(addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
& leq(one,addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) ) ),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ! [X3,X4] :
( ( test(X3)
& test(X4) )
=> ( leq(addition(addition(addition(addition(multiplication(X4,X3),multiplication(c(X4),X3)),multiplication(X3,X4)),multiplication(c(X3),X4)),multiplication(c(X3),c(X4))),one)
& leq(one,addition(addition(addition(addition(multiplication(X4,X3),multiplication(c(X4),X3)),multiplication(X3,X4)),multiplication(c(X3),X4)),multiplication(c(X3),c(X4)))) ) ),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
! [X3,X4] :
( ( test(X3)
& test(X4) )
=> ( leq(addition(addition(addition(addition(multiplication(X4,X3),multiplication(c(X4),X3)),multiplication(X3,X4)),multiplication(c(X3),X4)),multiplication(c(X3),c(X4))),one)
& leq(one,addition(addition(addition(addition(multiplication(X4,X3),multiplication(c(X4),X3)),multiplication(X3,X4)),multiplication(c(X3),X4)),multiplication(c(X3),c(X4)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f1114,plain,
( c(sK0) = sK2(sK0)
| ~ test(sK0) ),
inference(resolution,[],[f1074,f62]) ).
fof(f62,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| c(X0) = X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X3,X4] :
( test(X3)
=> ( c(X3) = X4
<=> complement(X3,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_3) ).
fof(f1074,plain,
complement(sK0,sK2(sK0)),
inference(subsumption_resolution,[],[f1073,f137]) ).
fof(f1073,plain,
( one != addition(sK0,sK2(sK0))
| complement(sK0,sK2(sK0)) ),
inference(forward_demodulation,[],[f1072,f60]) ).
fof(f60,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f1072,plain,
( one != addition(sK2(sK0),sK0)
| complement(sK0,sK2(sK0)) ),
inference(subsumption_resolution,[],[f1008,f112]) ).
fof(f112,plain,
zero = multiplication(sK2(sK0),sK0),
inference(resolution,[],[f87,f49]) ).
fof(f87,plain,
! [X0] :
( ~ test(X0)
| zero = multiplication(sK2(X0),X0) ),
inference(resolution,[],[f66,f58]) ).
fof(f58,plain,
! [X0] :
( complement(sK2(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( complement(sK2(X0),X0)
| ~ test(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f42,f43]) ).
fof(f43,plain,
! [X0] :
( ? [X2] : complement(X2,X0)
=> complement(sK2(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f42,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( ? [X2] : complement(X2,X0)
| ~ test(X0) ) ),
inference(rectify,[],[f41]) ).
fof(f41,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X3] :
( test(X3)
<=> ? [X4] : complement(X4,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_1) ).
fof(f66,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X1,X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X1] :
( ( complement(X1,X0)
| addition(X0,X1) != one
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1) )
& ( ( addition(X0,X1) = one
& zero = multiplication(X1,X0)
& zero = multiplication(X0,X1) )
| ~ complement(X1,X0) ) ),
inference(flattening,[],[f46]) ).
fof(f46,plain,
! [X0,X1] :
( ( complement(X1,X0)
| addition(X0,X1) != one
| zero != multiplication(X1,X0)
| zero != multiplication(X0,X1) )
& ( ( addition(X0,X1) = one
& zero = multiplication(X1,X0)
& zero = multiplication(X0,X1) )
| ~ complement(X1,X0) ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1] :
( complement(X1,X0)
<=> ( addition(X0,X1) = one
& zero = multiplication(X1,X0)
& zero = multiplication(X0,X1) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X3,X4] :
( complement(X4,X3)
<=> ( one = addition(X3,X4)
& zero = multiplication(X4,X3)
& zero = multiplication(X3,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_2) ).
fof(f1008,plain,
( one != addition(sK2(sK0),sK0)
| complement(sK0,sK2(sK0))
| zero != multiplication(sK2(sK0),sK0) ),
inference(trivial_inequality_removal,[],[f985]) ).
fof(f985,plain,
( zero != zero
| one != addition(sK2(sK0),sK0)
| complement(sK0,sK2(sK0))
| zero != multiplication(sK2(sK0),sK0) ),
inference(superposition,[],[f68,f104]) ).
fof(f104,plain,
zero = multiplication(sK0,sK2(sK0)),
inference(resolution,[],[f85,f49]) ).
fof(f85,plain,
! [X0] :
( ~ test(X0)
| zero = multiplication(X0,sK2(X0)) ),
inference(resolution,[],[f65,f58]) ).
fof(f65,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f68,plain,
! [X0,X1] :
( zero != multiplication(X1,X0)
| addition(X0,X1) != one
| complement(X1,X0)
| zero != multiplication(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f137,plain,
one = addition(sK0,sK2(sK0)),
inference(resolution,[],[f89,f49]) ).
fof(f89,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,sK2(X0)) ),
inference(resolution,[],[f67,f58]) ).
fof(f67,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f47]) ).
fof(f6195,plain,
( ~ leq(addition(sK0,c(sK0)),one)
| spl3_5 ),
inference(forward_demodulation,[],[f6194,f54]) ).
fof(f54,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f6194,plain,
( ~ leq(addition(sK0,multiplication(c(sK0),one)),one)
| spl3_5 ),
inference(forward_demodulation,[],[f6193,f1200]) ).
fof(f1200,plain,
one = addition(sK1,c(sK1)),
inference(superposition,[],[f138,f1132]) ).
fof(f1132,plain,
c(sK1) = sK2(sK1),
inference(subsumption_resolution,[],[f1127,f48]) ).
fof(f48,plain,
test(sK1),
inference(cnf_transformation,[],[f40]) ).
fof(f1127,plain,
( c(sK1) = sK2(sK1)
| ~ test(sK1) ),
inference(resolution,[],[f1105,f62]) ).
fof(f1105,plain,
complement(sK1,sK2(sK1)),
inference(subsumption_resolution,[],[f1104,f138]) ).
fof(f1104,plain,
( one != addition(sK1,sK2(sK1))
| complement(sK1,sK2(sK1)) ),
inference(forward_demodulation,[],[f1103,f60]) ).
fof(f1103,plain,
( one != addition(sK2(sK1),sK1)
| complement(sK1,sK2(sK1)) ),
inference(subsumption_resolution,[],[f1004,f113]) ).
fof(f113,plain,
zero = multiplication(sK2(sK1),sK1),
inference(resolution,[],[f87,f48]) ).
fof(f1004,plain,
( one != addition(sK2(sK1),sK1)
| complement(sK1,sK2(sK1))
| zero != multiplication(sK2(sK1),sK1) ),
inference(trivial_inequality_removal,[],[f995]) ).
fof(f995,plain,
( zero != zero
| one != addition(sK2(sK1),sK1)
| complement(sK1,sK2(sK1))
| zero != multiplication(sK2(sK1),sK1) ),
inference(superposition,[],[f68,f105]) ).
fof(f105,plain,
zero = multiplication(sK1,sK2(sK1)),
inference(resolution,[],[f85,f48]) ).
fof(f138,plain,
one = addition(sK1,sK2(sK1)),
inference(resolution,[],[f89,f48]) ).
fof(f6193,plain,
( ~ leq(addition(sK0,multiplication(c(sK0),addition(sK1,c(sK1)))),one)
| spl3_5 ),
inference(forward_demodulation,[],[f6192,f72]) ).
fof(f72,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
fof(f6192,plain,
( ~ leq(addition(sK0,addition(multiplication(c(sK0),sK1),multiplication(c(sK0),c(sK1)))),one)
| spl3_5 ),
inference(forward_demodulation,[],[f6191,f60]) ).
fof(f6191,plain,
( ~ leq(addition(sK0,addition(multiplication(c(sK0),c(sK1)),multiplication(c(sK0),sK1))),one)
| spl3_5 ),
inference(forward_demodulation,[],[f6109,f126]) ).
fof(f126,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(superposition,[],[f70,f60]) ).
fof(f70,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1,X2] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X2,X1,X0] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
fof(f6109,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),sK0)),one)
| spl3_5 ),
inference(superposition,[],[f1300,f5949]) ).
fof(f5949,plain,
! [X0] : addition(X0,multiplication(X0,sK1)) = X0,
inference(forward_demodulation,[],[f5857,f54]) ).
fof(f5857,plain,
! [X0] : multiplication(X0,one) = addition(X0,multiplication(X0,sK1)),
inference(superposition,[],[f285,f1638]) ).
fof(f1638,plain,
one = addition(one,sK1),
inference(superposition,[],[f1607,f60]) ).
fof(f1607,plain,
one = addition(sK1,one),
inference(superposition,[],[f119,f138]) ).
fof(f119,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f70,f56]) ).
fof(f285,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f72,f54]) ).
fof(f1300,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(sK0,multiplication(sK0,sK1)))),one)
| spl3_5 ),
inference(forward_demodulation,[],[f1299,f55]) ).
fof(f55,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f1299,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(one,sK0),multiplication(sK0,sK1)))),one)
| spl3_5 ),
inference(forward_demodulation,[],[f1298,f60]) ).
fof(f1298,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(one,sK0)))),one)
| spl3_5 ),
inference(forward_demodulation,[],[f1240,f1200]) ).
fof(f1240,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)))),one)
| spl3_5 ),
inference(avatar_component_clause,[],[f1238]) ).
fof(f1238,plain,
( spl3_5
<=> leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)))),one) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
fof(f6190,plain,
spl3_6,
inference(avatar_contradiction_clause,[],[f6189]) ).
fof(f6189,plain,
( $false
| spl3_6 ),
inference(subsumption_resolution,[],[f6188,f98]) ).
fof(f6188,plain,
( ~ leq(one,one)
| spl3_6 ),
inference(forward_demodulation,[],[f6187,f1154]) ).
fof(f6187,plain,
( ~ leq(one,addition(sK0,c(sK0)))
| spl3_6 ),
inference(forward_demodulation,[],[f6186,f54]) ).
fof(f6186,plain,
( ~ leq(one,addition(sK0,multiplication(c(sK0),one)))
| spl3_6 ),
inference(forward_demodulation,[],[f6185,f1200]) ).
fof(f6185,plain,
( ~ leq(one,addition(sK0,multiplication(c(sK0),addition(sK1,c(sK1)))))
| spl3_6 ),
inference(forward_demodulation,[],[f6184,f72]) ).
fof(f6184,plain,
( ~ leq(one,addition(sK0,addition(multiplication(c(sK0),sK1),multiplication(c(sK0),c(sK1)))))
| spl3_6 ),
inference(forward_demodulation,[],[f6183,f60]) ).
fof(f6183,plain,
( ~ leq(one,addition(sK0,addition(multiplication(c(sK0),c(sK1)),multiplication(c(sK0),sK1))))
| spl3_6 ),
inference(forward_demodulation,[],[f6108,f126]) ).
fof(f6108,plain,
( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),sK0)))
| spl3_6 ),
inference(superposition,[],[f1337,f5949]) ).
fof(f1337,plain,
( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(sK0,multiplication(sK0,sK1)))))
| spl3_6 ),
inference(forward_demodulation,[],[f1336,f55]) ).
fof(f1336,plain,
( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(one,sK0),multiplication(sK0,sK1)))))
| spl3_6 ),
inference(forward_demodulation,[],[f1335,f60]) ).
fof(f1335,plain,
( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(one,sK0)))))
| spl3_6 ),
inference(forward_demodulation,[],[f1244,f1200]) ).
fof(f1244,plain,
( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)))))
| spl3_6 ),
inference(avatar_component_clause,[],[f1242]) ).
fof(f1242,plain,
( spl3_6
<=> leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
fof(f1652,plain,
spl3_3,
inference(avatar_contradiction_clause,[],[f1651]) ).
fof(f1651,plain,
( $false
| spl3_3 ),
inference(subsumption_resolution,[],[f1649,f156]) ).
fof(f156,plain,
( ~ leq(sK1,one)
| spl3_3 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f155,plain,
( spl3_3
<=> leq(sK1,one) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).
fof(f1649,plain,
leq(sK1,one),
inference(trivial_inequality_removal,[],[f1646]) ).
fof(f1646,plain,
( one != one
| leq(sK1,one) ),
inference(superposition,[],[f69,f1607]) ).
fof(f1379,plain,
( spl3_7
| ~ spl3_9 ),
inference(avatar_contradiction_clause,[],[f1378]) ).
fof(f1378,plain,
( $false
| spl3_7
| ~ spl3_9 ),
inference(subsumption_resolution,[],[f1375,f97]) ).
fof(f97,plain,
! [X0] : leq(zero,X0),
inference(trivial_inequality_removal,[],[f96]) ).
fof(f96,plain,
! [X0] :
( X0 != X0
| leq(zero,X0) ),
inference(superposition,[],[f69,f77]) ).
fof(f77,plain,
! [X0] : addition(zero,X0) = X0,
inference(superposition,[],[f60,f53]) ).
fof(f53,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
fof(f1375,plain,
( ~ leq(zero,one)
| spl3_7
| ~ spl3_9 ),
inference(superposition,[],[f1313,f1374]) ).
fof(f1374,plain,
( zero = c(one)
| ~ spl3_9 ),
inference(subsumption_resolution,[],[f1369,f1353]) ).
fof(f1353,plain,
test(one),
inference(equality_resolution,[],[f1351]) ).
fof(f1351,plain,
! [X0] :
( one != X0
| test(X0) ),
inference(resolution,[],[f1034,f59]) ).
fof(f59,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| test(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f1034,plain,
! [X0] :
( complement(zero,X0)
| one != X0 ),
inference(forward_demodulation,[],[f1033,f53]) ).
fof(f1033,plain,
! [X0] :
( addition(X0,zero) != one
| complement(zero,X0) ),
inference(subsumption_resolution,[],[f1016,f51]) ).
fof(f51,plain,
! [X0] : zero = multiplication(X0,zero),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] : zero = multiplication(X0,zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
fof(f1016,plain,
! [X0] :
( addition(X0,zero) != one
| complement(zero,X0)
| zero != multiplication(X0,zero) ),
inference(trivial_inequality_removal,[],[f969]) ).
fof(f969,plain,
! [X0] :
( zero != zero
| addition(X0,zero) != one
| complement(zero,X0)
| zero != multiplication(X0,zero) ),
inference(superposition,[],[f68,f52]) ).
fof(f52,plain,
! [X0] : zero = multiplication(zero,X0),
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] : zero = multiplication(zero,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
fof(f1369,plain,
( zero = c(one)
| ~ test(one)
| ~ spl3_9 ),
inference(resolution,[],[f1368,f62]) ).
fof(f1368,plain,
( complement(one,zero)
| ~ spl3_9 ),
inference(subsumption_resolution,[],[f1367,f1330]) ).
fof(f1330,plain,
( test(zero)
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f1328]) ).
fof(f1328,plain,
( spl3_9
<=> test(zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).
fof(f1367,plain,
( complement(one,zero)
| ~ test(zero)
| ~ spl3_9 ),
inference(superposition,[],[f58,f1362]) ).
fof(f1362,plain,
( one = sK2(zero)
| ~ spl3_9 ),
inference(superposition,[],[f1344,f77]) ).
fof(f1344,plain,
( one = addition(zero,sK2(zero))
| ~ spl3_9 ),
inference(resolution,[],[f1330,f89]) ).
fof(f1313,plain,
( ~ leq(c(one),one)
| spl3_7 ),
inference(avatar_component_clause,[],[f1312]) ).
fof(f1312,plain,
( spl3_7
<=> leq(c(one),one) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).
fof(f1334,plain,
( spl3_9
| spl3_10 ),
inference(avatar_split_clause,[],[f1325,f1332,f1328]) ).
fof(f1332,plain,
( spl3_10
<=> ! [X0] : one != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_10])]) ).
fof(f1325,plain,
! [X0] :
( one != X0
| test(zero) ),
inference(resolution,[],[f1019,f59]) ).
fof(f1019,plain,
! [X0] :
( complement(X0,zero)
| one != X0 ),
inference(forward_demodulation,[],[f1018,f77]) ).
fof(f1018,plain,
! [X0] :
( one != addition(zero,X0)
| complement(X0,zero) ),
inference(subsumption_resolution,[],[f1017,f52]) ).
fof(f1017,plain,
! [X0] :
( one != addition(zero,X0)
| complement(X0,zero)
| zero != multiplication(zero,X0) ),
inference(trivial_inequality_removal,[],[f959]) ).
fof(f959,plain,
! [X0] :
( zero != zero
| one != addition(zero,X0)
| complement(X0,zero)
| zero != multiplication(zero,X0) ),
inference(superposition,[],[f68,f51]) ).
fof(f1319,plain,
( spl3_7
| ~ spl3_8 ),
inference(avatar_split_clause,[],[f1262,f1316,f1312]) ).
fof(f1316,plain,
( spl3_8
<=> one = sK0 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_8])]) ).
fof(f1262,plain,
( one != sK0
| leq(c(one),one) ),
inference(inner_rewriting,[],[f1256]) ).
fof(f1256,plain,
( one != sK0
| leq(c(sK0),sK0) ),
inference(superposition,[],[f69,f1248]) ).
fof(f1248,plain,
one = addition(c(sK0),sK0),
inference(forward_demodulation,[],[f1115,f1119]) ).
fof(f1115,plain,
one = addition(sK2(sK0),sK0),
inference(resolution,[],[f1074,f67]) ).
fof(f1245,plain,
( ~ spl3_5
| ~ spl3_6 ),
inference(avatar_split_clause,[],[f1197,f1242,f1238]) ).
fof(f1197,plain,
( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)))))
| ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)))),one) ),
inference(forward_demodulation,[],[f1196,f73]) ).
fof(f73,plain,
! [X2,X0,X1] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
fof(f1196,plain,
( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0))))))
| ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)))),one) ),
inference(forward_demodulation,[],[f1195,f60]) ).
fof(f1195,plain,
( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)))))
| ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)))),one) ),
inference(forward_demodulation,[],[f1194,f60]) ).
fof(f1194,plain,
( ~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1))))
| ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)))),one) ),
inference(forward_demodulation,[],[f1193,f60]) ).
fof(f1193,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),multiplication(addition(sK1,c(sK1)),sK0)))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))) ),
inference(forward_demodulation,[],[f1192,f73]) ).
fof(f1192,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(multiplication(sK0,sK1),addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0))))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))) ),
inference(forward_demodulation,[],[f1191,f60]) ).
fof(f1191,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(c(sK0),sK1),addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))) ),
inference(forward_demodulation,[],[f1190,f60]) ).
fof(f1190,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))) ),
inference(forward_demodulation,[],[f50,f60]) ).
fof(f50,plain,
( ~ leq(addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1))),one)
| ~ leq(one,addition(addition(addition(addition(multiplication(sK1,sK0),multiplication(c(sK1),sK0)),multiplication(sK0,sK1)),multiplication(c(sK0),sK1)),multiplication(c(sK0),c(sK1)))) ),
inference(cnf_transformation,[],[f40]) ).
fof(f829,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f828]) ).
fof(f828,plain,
( $false
| spl3_1 ),
inference(subsumption_resolution,[],[f827,f147]) ).
fof(f147,plain,
( ~ leq(sK0,one)
| spl3_1 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f146,plain,
( spl3_1
<=> leq(sK0,one) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f827,plain,
leq(sK0,one),
inference(trivial_inequality_removal,[],[f824]) ).
fof(f824,plain,
( one != one
| leq(sK0,one) ),
inference(superposition,[],[f69,f817]) ).
fof(f817,plain,
one = addition(sK0,one),
inference(forward_demodulation,[],[f811,f56]) ).
fof(f811,plain,
addition(one,one) = addition(sK0,one),
inference(superposition,[],[f165,f170]) ).
fof(f170,plain,
one = addition(one,sK2(sK0)),
inference(forward_demodulation,[],[f164,f137]) ).
fof(f164,plain,
addition(sK0,sK2(sK0)) = addition(one,sK2(sK0)),
inference(superposition,[],[f139,f56]) ).
fof(f139,plain,
! [X0] : addition(sK0,addition(sK2(sK0),X0)) = addition(one,X0),
inference(superposition,[],[f70,f137]) ).
fof(f165,plain,
! [X0] : addition(one,X0) = addition(sK0,addition(X0,sK2(sK0))),
inference(superposition,[],[f139,f60]) ).
fof(f162,plain,
( spl3_3
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f144,f159,f155]) ).
fof(f159,plain,
( spl3_4
<=> one = sK2(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
fof(f144,plain,
( one != sK2(sK1)
| leq(sK1,one) ),
inference(inner_rewriting,[],[f143]) ).
fof(f143,plain,
( one != sK2(sK1)
| leq(sK1,sK2(sK1)) ),
inference(superposition,[],[f69,f138]) ).
fof(f153,plain,
( spl3_1
| ~ spl3_2 ),
inference(avatar_split_clause,[],[f141,f150,f146]) ).
fof(f150,plain,
( spl3_2
<=> one = sK2(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).
fof(f141,plain,
( one != sK2(sK0)
| leq(sK0,one) ),
inference(inner_rewriting,[],[f140]) ).
fof(f140,plain,
( one != sK2(sK0)
| leq(sK0,sK2(sK0)) ),
inference(superposition,[],[f69,f137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : KLE010+4 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n009.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 : 300
% 0.13/0.34 % DateTime : Tue Apr 30 04:57:11 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % (27469)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36 % (27474)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.13/0.36 % (27472)WARNING: value z3 for option sas not known
% 0.13/0.36 % (27470)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.36 % (27471)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.36 % (27472)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.36 % (27473)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36 % (27475)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.13/0.36 % (27476)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.13/0.37 TRYING [1]
% 0.13/0.37 TRYING [2]
% 0.13/0.37 TRYING [3]
% 0.13/0.37 TRYING [1]
% 0.13/0.37 TRYING [2]
% 0.13/0.38 TRYING [4]
% 0.19/0.39 TRYING [3]
% 0.19/0.41 TRYING [5]
% 0.19/0.43 TRYING [4]
% 0.19/0.49 % (27472)First to succeed.
% 0.19/0.49 % (27472)Refutation found. Thanks to Tanya!
% 0.19/0.49 % SZS status Theorem for theBenchmark
% 0.19/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49 % (27472)------------------------------
% 0.19/0.49 % (27472)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.19/0.49 % (27472)Termination reason: Refutation
% 0.19/0.49
% 0.19/0.49 % (27472)Memory used [KB]: 2474
% 0.19/0.49 % (27472)Time elapsed: 0.128 s
% 0.19/0.49 % (27472)Instructions burned: 280 (million)
% 0.19/0.49 % (27472)------------------------------
% 0.19/0.49 % (27472)------------------------------
% 0.19/0.49 % (27469)Success in time 0.144 s
%------------------------------------------------------------------------------