TSTP Solution File: KLE011+2 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE011+2 : 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 : n023.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 07:17:00 EDT 2024
% Result : Theorem 38.52s 5.86s
% Output : Refutation 38.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 14
% Syntax : Number of formulae : 149 ( 89 unt; 0 def)
% Number of atoms : 265 ( 102 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 224 ( 108 ~; 70 |; 30 &)
% ( 8 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 150 ( 139 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f545585,plain,
$false,
inference(subsumption_resolution,[],[f545584,f11027]) ).
fof(f11027,plain,
! [X0] : leq(one,addition(sK0,addition(X0,c(sK0)))),
inference(forward_demodulation,[],[f11026,f7206]) ).
fof(f7206,plain,
sK0 = c(c(sK0)),
inference(forward_demodulation,[],[f7198,f7187]) ).
fof(f7187,plain,
c(sK0) = sK2(sK0),
inference(unit_resulting_resolution,[],[f41,f7132,f54]) ).
fof(f54,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| c(X0) = X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0,X1] :
( ( ( c(X0) = X1
| ~ complement(X0,X1) )
& ( complement(X0,X1)
| c(X0) != X1 ) )
| ~ test(X0) ),
inference(nnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( ( c(X0) = X1
<=> complement(X0,X1) )
| ~ test(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,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(f7132,plain,
complement(sK0,sK2(sK0)),
inference(subsumption_resolution,[],[f7131,f186]) ).
fof(f186,plain,
one = addition(sK0,sK2(sK0)),
inference(unit_resulting_resolution,[],[f66,f57]) ).
fof(f57,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,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,[],[f38]) ).
fof(f38,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,[],[f23]) ).
fof(f23,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(f66,plain,
complement(sK2(sK0),sK0),
inference(unit_resulting_resolution,[],[f41,f50]) ).
fof(f50,plain,
! [X0] :
( ~ test(X0)
| complement(sK2(X0),X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( complement(sK2(X0),X0)
| ~ test(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f34,f35]) ).
fof(f35,plain,
! [X0] :
( ? [X2] : complement(X2,X0)
=> complement(sK2(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( ? [X2] : complement(X2,X0)
| ~ test(X0) ) ),
inference(rectify,[],[f33]) ).
fof(f33,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( ? [X1] : complement(X1,X0)
| ~ test(X0) ) ),
inference(nnf_transformation,[],[f21]) ).
fof(f21,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(f7131,plain,
( one != addition(sK0,sK2(sK0))
| complement(sK0,sK2(sK0)) ),
inference(forward_demodulation,[],[f7130,f52]) ).
fof(f52,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(f7130,plain,
( one != addition(sK2(sK0),sK0)
| complement(sK0,sK2(sK0)) ),
inference(subsumption_resolution,[],[f7025,f162]) ).
fof(f162,plain,
zero = multiplication(sK2(sK0),sK0),
inference(unit_resulting_resolution,[],[f66,f56]) ).
fof(f56,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X1,X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f7025,plain,
( one != addition(sK2(sK0),sK0)
| complement(sK0,sK2(sK0))
| zero != multiplication(sK2(sK0),sK0) ),
inference(trivial_inequality_removal,[],[f6978]) ).
fof(f6978,plain,
( zero != zero
| one != addition(sK2(sK0),sK0)
| complement(sK0,sK2(sK0))
| zero != multiplication(sK2(sK0),sK0) ),
inference(superposition,[],[f58,f138]) ).
fof(f138,plain,
zero = multiplication(sK0,sK2(sK0)),
inference(unit_resulting_resolution,[],[f66,f55]) ).
fof(f55,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f58,plain,
! [X0,X1] :
( zero != multiplication(X1,X0)
| addition(X0,X1) != one
| complement(X1,X0)
| zero != multiplication(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
fof(f41,plain,
test(sK0),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
( ( ~ leq(addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1))),one)
| ~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1)))) )
& test(sK0)
& test(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f27,f31]) ).
fof(f31,plain,
( ? [X0,X1] :
( ( ~ leq(addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))),one)
| ~ leq(one,addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1)))) )
& test(X0)
& test(X1) )
=> ( ( ~ leq(addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1))),one)
| ~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1)))) )
& test(sK0)
& test(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f27,plain,
? [X0,X1] :
( ( ~ leq(addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))),one)
| ~ leq(one,addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1)))) )
& test(X0)
& test(X1) ),
inference(flattening,[],[f26]) ).
fof(f26,plain,
? [X0,X1] :
( ( ~ leq(addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))),one)
| ~ leq(one,addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1)))) )
& test(X0)
& test(X1) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
~ ! [X0,X1] :
( ( test(X0)
& test(X1) )
=> ( leq(addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))),one)
& leq(one,addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1)))) ) ),
inference(rectify,[],[f18]) ).
fof(f18,negated_conjecture,
~ ! [X3,X4] :
( ( test(X3)
& test(X4) )
=> ( leq(addition(addition(multiplication(addition(X4,c(X4)),X3),multiplication(addition(X3,c(X3)),X4)),multiplication(c(X3),c(X4))),one)
& leq(one,addition(addition(multiplication(addition(X4,c(X4)),X3),multiplication(addition(X3,c(X3)),X4)),multiplication(c(X3),c(X4)))) ) ),
inference(negated_conjecture,[],[f17]) ).
fof(f17,conjecture,
! [X3,X4] :
( ( test(X3)
& test(X4) )
=> ( leq(addition(addition(multiplication(addition(X4,c(X4)),X3),multiplication(addition(X3,c(X3)),X4)),multiplication(c(X3),c(X4))),one)
& leq(one,addition(addition(multiplication(addition(X4,c(X4)),X3),multiplication(addition(X3,c(X3)),X4)),multiplication(c(X3),c(X4)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f7198,plain,
sK0 = c(sK2(sK0)),
inference(unit_resulting_resolution,[],[f66,f7191,f54]) ).
fof(f7191,plain,
test(sK2(sK0)),
inference(unit_resulting_resolution,[],[f7132,f51]) ).
fof(f51,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| test(X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f11026,plain,
! [X0] : leq(one,addition(c(c(sK0)),addition(X0,c(c(c(sK0)))))),
inference(forward_demodulation,[],[f10884,f1250]) ).
fof(f1250,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(superposition,[],[f61,f52]) ).
fof(f61,plain,
! [X2,X0,X1] : addition(X2,addition(X1,X0)) = addition(addition(X2,X1),X0),
inference(cnf_transformation,[],[f24]) ).
fof(f24,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(f10884,plain,
! [X0] : leq(one,addition(c(c(c(sK0))),addition(c(c(sK0)),X0))),
inference(superposition,[],[f1355,f182]) ).
fof(f182,plain,
one = addition(c(c(c(sK0))),c(c(sK0))),
inference(unit_resulting_resolution,[],[f101,f57]) ).
fof(f101,plain,
complement(c(c(sK0)),c(c(c(sK0)))),
inference(unit_resulting_resolution,[],[f99,f64]) ).
fof(f64,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(equality_resolution,[],[f53]) ).
fof(f53,plain,
! [X0,X1] :
( complement(X0,X1)
| c(X0) != X1
| ~ test(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f99,plain,
test(c(c(sK0))),
inference(unit_resulting_resolution,[],[f87,f51]) ).
fof(f87,plain,
complement(c(sK0),c(c(sK0))),
inference(unit_resulting_resolution,[],[f85,f64]) ).
fof(f85,plain,
test(c(sK0)),
inference(unit_resulting_resolution,[],[f75,f51]) ).
fof(f75,plain,
complement(sK0,c(sK0)),
inference(unit_resulting_resolution,[],[f41,f64]) ).
fof(f1355,plain,
! [X2,X0,X1] : leq(addition(X0,X1),addition(X0,addition(X1,X2))),
inference(superposition,[],[f1266,f61]) ).
fof(f1266,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(unit_resulting_resolution,[],[f1215,f59]) ).
fof(f59,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,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(f1215,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f61,f48]) ).
fof(f48,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(f545584,plain,
~ leq(one,addition(sK0,addition(multiplication(sK0,sK1),c(sK0)))),
inference(forward_demodulation,[],[f545583,f1250]) ).
fof(f545583,plain,
~ leq(one,addition(c(sK0),addition(sK0,multiplication(sK0,sK1)))),
inference(forward_demodulation,[],[f545582,f47]) ).
fof(f47,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(f545582,plain,
~ leq(one,addition(c(sK0),addition(multiplication(one,sK0),multiplication(sK0,sK1)))),
inference(forward_demodulation,[],[f545581,f1250]) ).
fof(f545581,plain,
~ leq(one,addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),c(sK0)))),
inference(forward_demodulation,[],[f545580,f45]) ).
fof(f45,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(f545580,plain,
~ leq(one,addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),multiplication(c(sK0),one)))),
inference(forward_demodulation,[],[f545579,f207]) ).
fof(f207,plain,
one = addition(sK1,c(sK1)),
inference(superposition,[],[f184,f52]) ).
fof(f184,plain,
one = addition(c(sK1),sK1),
inference(unit_resulting_resolution,[],[f74,f57]) ).
fof(f74,plain,
complement(sK1,c(sK1)),
inference(unit_resulting_resolution,[],[f40,f64]) ).
fof(f40,plain,
test(sK1),
inference(cnf_transformation,[],[f32]) ).
fof(f545579,plain,
~ leq(one,addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),multiplication(c(sK0),addition(sK1,c(sK1)))))),
inference(forward_demodulation,[],[f545578,f148993]) ).
fof(f148993,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(superposition,[],[f2240,f62]) ).
fof(f62,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(f2240,plain,
! [X2,X0,X1] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(superposition,[],[f62,f52]) ).
fof(f545578,plain,
~ leq(one,addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),multiplication(c(sK0),addition(c(sK1),sK1))))),
inference(forward_demodulation,[],[f545577,f393985]) ).
fof(f393985,plain,
! [X2,X0,X1] : addition(X1,addition(X0,X2)) = addition(X1,addition(X2,X0)),
inference(superposition,[],[f14623,f1250]) ).
fof(f14623,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(superposition,[],[f1216,f61]) ).
fof(f1216,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(superposition,[],[f61,f52]) ).
fof(f545577,plain,
~ leq(one,addition(multiplication(one,sK0),addition(multiplication(c(sK0),addition(c(sK1),sK1)),multiplication(sK0,sK1)))),
inference(forward_demodulation,[],[f545576,f216529]) ).
fof(f216529,plain,
! [X2,X3,X0,X1] : addition(multiplication(X0,addition(X3,X1)),multiplication(X2,X1)) = addition(multiplication(X0,X3),multiplication(addition(X2,X0),X1)),
inference(superposition,[],[f2246,f4123]) ).
fof(f4123,plain,
! [X2,X0,X1] : multiplication(addition(X0,X2),X1) = addition(multiplication(X2,X1),multiplication(X0,X1)),
inference(superposition,[],[f63,f52]) ).
fof(f63,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(f2246,plain,
! [X2,X3,X0,X1] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3),
inference(superposition,[],[f61,f62]) ).
fof(f545576,plain,
~ leq(one,addition(multiplication(one,sK0),addition(multiplication(c(sK0),c(sK1)),multiplication(addition(sK0,c(sK0)),sK1)))),
inference(forward_demodulation,[],[f545575,f1250]) ).
fof(f545575,plain,
~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(one,sK0)))),
inference(forward_demodulation,[],[f545574,f207]) ).
fof(f545574,plain,
~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK1,c(sK1)),sK0)))),
inference(forward_demodulation,[],[f545573,f393985]) ).
fof(f545573,plain,
~ leq(one,addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)))),
inference(forward_demodulation,[],[f545572,f52]) ).
fof(f545572,plain,
~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1)))),
inference(subsumption_resolution,[],[f545571,f220]) ).
fof(f220,plain,
! [X0] : leq(X0,X0),
inference(unit_resulting_resolution,[],[f48,f59]) ).
fof(f545571,plain,
( ~ leq(one,one)
| ~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1)))) ),
inference(forward_demodulation,[],[f545570,f203]) ).
fof(f203,plain,
one = addition(sK0,c(sK0)),
inference(superposition,[],[f183,f52]) ).
fof(f183,plain,
one = addition(c(sK0),sK0),
inference(unit_resulting_resolution,[],[f75,f57]) ).
fof(f545570,plain,
( ~ leq(addition(sK0,c(sK0)),one)
| ~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1)))) ),
inference(forward_demodulation,[],[f545569,f52]) ).
fof(f545569,plain,
( ~ leq(addition(c(sK0),sK0),one)
| ~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1)))) ),
inference(forward_demodulation,[],[f545568,f54029]) ).
fof(f54029,plain,
! [X0,X1] : addition(X1,X0) = addition(X0,addition(X1,multiplication(X0,sK1))),
inference(superposition,[],[f1250,f53083]) ).
fof(f53083,plain,
! [X0] : addition(multiplication(X0,sK1),X0) = X0,
inference(superposition,[],[f1268,f52787]) ).
fof(f52787,plain,
! [X0] : addition(X0,multiplication(X0,sK1)) = X0,
inference(forward_demodulation,[],[f52786,f45]) ).
fof(f52786,plain,
! [X0] : multiplication(X0,one) = addition(X0,multiplication(X0,sK1)),
inference(forward_demodulation,[],[f52521,f7230]) ).
fof(f7230,plain,
sK1 = c(c(sK1)),
inference(forward_demodulation,[],[f7222,f7211]) ).
fof(f7211,plain,
c(sK1) = sK2(sK1),
inference(unit_resulting_resolution,[],[f40,f7139,f54]) ).
fof(f7139,plain,
complement(sK1,sK2(sK1)),
inference(subsumption_resolution,[],[f7138,f185]) ).
fof(f185,plain,
one = addition(sK1,sK2(sK1)),
inference(unit_resulting_resolution,[],[f65,f57]) ).
fof(f65,plain,
complement(sK2(sK1),sK1),
inference(unit_resulting_resolution,[],[f40,f50]) ).
fof(f7138,plain,
( one != addition(sK1,sK2(sK1))
| complement(sK1,sK2(sK1)) ),
inference(forward_demodulation,[],[f7137,f52]) ).
fof(f7137,plain,
( one != addition(sK2(sK1),sK1)
| complement(sK1,sK2(sK1)) ),
inference(subsumption_resolution,[],[f7021,f161]) ).
fof(f161,plain,
zero = multiplication(sK2(sK1),sK1),
inference(unit_resulting_resolution,[],[f65,f56]) ).
fof(f7021,plain,
( one != addition(sK2(sK1),sK1)
| complement(sK1,sK2(sK1))
| zero != multiplication(sK2(sK1),sK1) ),
inference(trivial_inequality_removal,[],[f6982]) ).
fof(f6982,plain,
( zero != zero
| one != addition(sK2(sK1),sK1)
| complement(sK1,sK2(sK1))
| zero != multiplication(sK2(sK1),sK1) ),
inference(superposition,[],[f58,f137]) ).
fof(f137,plain,
zero = multiplication(sK1,sK2(sK1)),
inference(unit_resulting_resolution,[],[f65,f55]) ).
fof(f7222,plain,
sK1 = c(sK2(sK1)),
inference(unit_resulting_resolution,[],[f65,f7215,f54]) ).
fof(f7215,plain,
test(sK2(sK1)),
inference(unit_resulting_resolution,[],[f7139,f51]) ).
fof(f52521,plain,
! [X0] : multiplication(X0,one) = addition(X0,multiplication(X0,c(c(sK1)))),
inference(superposition,[],[f2106,f1472]) ).
fof(f1472,plain,
one = addition(one,c(c(sK1))),
inference(superposition,[],[f1279,f52]) ).
fof(f1279,plain,
one = addition(c(c(sK1)),one),
inference(superposition,[],[f1215,f179]) ).
fof(f179,plain,
one = addition(c(c(sK1)),c(sK1)),
inference(unit_resulting_resolution,[],[f81,f57]) ).
fof(f81,plain,
complement(c(sK1),c(c(sK1))),
inference(unit_resulting_resolution,[],[f79,f64]) ).
fof(f79,plain,
test(c(sK1)),
inference(unit_resulting_resolution,[],[f74,f51]) ).
fof(f2106,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(superposition,[],[f62,f45]) ).
fof(f1268,plain,
! [X0,X1] : addition(X1,X0) = addition(X0,addition(X1,X0)),
inference(superposition,[],[f1215,f52]) ).
fof(f545568,plain,
( ~ leq(addition(sK0,addition(c(sK0),multiplication(sK0,sK1))),one)
| ~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1)))) ),
inference(forward_demodulation,[],[f545567,f393985]) ).
fof(f545567,plain,
( ~ leq(addition(sK0,addition(multiplication(sK0,sK1),c(sK0))),one)
| ~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1)))) ),
inference(forward_demodulation,[],[f545566,f1250]) ).
fof(f545566,plain,
( ~ leq(addition(c(sK0),addition(sK0,multiplication(sK0,sK1))),one)
| ~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1)))) ),
inference(forward_demodulation,[],[f545565,f47]) ).
fof(f545565,plain,
( ~ leq(addition(c(sK0),addition(multiplication(one,sK0),multiplication(sK0,sK1))),one)
| ~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1)))) ),
inference(forward_demodulation,[],[f545564,f1250]) ).
fof(f545564,plain,
( ~ leq(addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),c(sK0))),one)
| ~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1)))) ),
inference(forward_demodulation,[],[f545563,f45]) ).
fof(f545563,plain,
( ~ leq(addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),multiplication(c(sK0),one))),one)
| ~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1)))) ),
inference(forward_demodulation,[],[f545562,f207]) ).
fof(f545562,plain,
( ~ leq(addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),multiplication(c(sK0),addition(sK1,c(sK1))))),one)
| ~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1)))) ),
inference(forward_demodulation,[],[f545561,f148993]) ).
fof(f545561,plain,
( ~ leq(addition(multiplication(one,sK0),addition(multiplication(sK0,sK1),multiplication(c(sK0),addition(c(sK1),sK1)))),one)
| ~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1)))) ),
inference(forward_demodulation,[],[f545560,f393985]) ).
fof(f545560,plain,
( ~ leq(addition(multiplication(one,sK0),addition(multiplication(c(sK0),addition(c(sK1),sK1)),multiplication(sK0,sK1))),one)
| ~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1)))) ),
inference(forward_demodulation,[],[f545559,f216529]) ).
fof(f545559,plain,
( ~ leq(addition(multiplication(one,sK0),addition(multiplication(c(sK0),c(sK1)),multiplication(addition(sK0,c(sK0)),sK1))),one)
| ~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1)))) ),
inference(forward_demodulation,[],[f545558,f1250]) ).
fof(f545558,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(one,sK0))),one)
| ~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1)))) ),
inference(forward_demodulation,[],[f545557,f207]) ).
fof(f545557,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK0,c(sK0)),sK1),multiplication(addition(sK1,c(sK1)),sK0))),one)
| ~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1)))) ),
inference(forward_demodulation,[],[f545556,f393985]) ).
fof(f545556,plain,
( ~ leq(addition(multiplication(c(sK0),c(sK1)),addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1))),one)
| ~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1)))) ),
inference(forward_demodulation,[],[f543851,f1250]) ).
fof(f543851,plain,
( ~ leq(addition(multiplication(addition(sK0,c(sK0)),sK1),addition(multiplication(c(sK0),c(sK1)),multiplication(addition(sK1,c(sK1)),sK0))),one)
| ~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1)))) ),
inference(superposition,[],[f42,f30425]) ).
fof(f30425,plain,
! [X2,X0,X1] : addition(X2,addition(X0,X1)) = addition(addition(X1,X2),X0),
inference(superposition,[],[f1250,f52]) ).
fof(f42,plain,
( ~ leq(addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1))),one)
| ~ leq(one,addition(addition(multiplication(addition(sK1,c(sK1)),sK0),multiplication(addition(sK0,c(sK0)),sK1)),multiplication(c(sK0),c(sK1)))) ),
inference(cnf_transformation,[],[f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE011+2 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n023.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 : 300
% 0.13/0.35 % DateTime : Fri May 3 21:20:53 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (23508)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36 % (23512)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36 TRYING [1]
% 0.13/0.36 TRYING [2]
% 0.13/0.36 TRYING [3]
% 0.13/0.37 % (23509)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37 % (23511)WARNING: value z3 for option sas not known
% 0.13/0.37 % (23510)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37 % (23511)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)
% 0.13/0.37 TRYING [4]
% 0.13/0.37 % (23513)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)
% 0.13/0.37 % (23515)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 % (23514)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)
% 0.13/0.37 TRYING [1]
% 0.13/0.37 TRYING [2]
% 0.13/0.39 TRYING [3]
% 0.13/0.39 TRYING [5]
% 0.21/0.42 TRYING [4]
% 0.21/0.43 TRYING [6]
% 0.21/0.51 TRYING [5]
% 0.21/0.57 TRYING [7]
% 2.77/0.73 TRYING [6]
% 4.00/0.92 TRYING [8]
% 6.83/1.34 TRYING [7]
% 7.94/1.47 TRYING [1]
% 7.94/1.47 TRYING [2]
% 7.94/1.47 TRYING [3]
% 7.94/1.48 TRYING [4]
% 8.11/1.51 TRYING [5]
% 8.40/1.59 TRYING [9]
% 8.40/1.60 TRYING [6]
% 10.44/1.84 TRYING [7]
% 14.58/2.42 TRYING [8]
% 17.34/2.81 TRYING [8]
% 18.13/2.98 TRYING [10]
% 23.17/3.65 TRYING [9]
% 35.50/5.40 TRYING [11]
% 38.52/5.85 % (23515)First to succeed.
% 38.52/5.85 % (23515)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-23508"
% 38.52/5.86 % (23515)Refutation found. Thanks to Tanya!
% 38.52/5.86 % SZS status Theorem for theBenchmark
% 38.52/5.86 % SZS output start Proof for theBenchmark
% See solution above
% 38.52/5.86 % (23515)------------------------------
% 38.52/5.86 % (23515)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 38.52/5.86 % (23515)Termination reason: Refutation
% 38.52/5.86
% 38.52/5.86 % (23515)Memory used [KB]: 53020
% 38.52/5.86 % (23515)Time elapsed: 5.486 s
% 38.52/5.86 % (23515)Instructions burned: 20242 (million)
% 38.52/5.86 % (23508)Success in time 5.39 s
%------------------------------------------------------------------------------