TSTP Solution File: KLE017+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : KLE017+1 : 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 : n027.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 13:11:40 EDT 2024
% Result : Theorem 113.36s 16.61s
% Output : Refutation 113.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 14
% Syntax : Number of formulae : 124 ( 70 unt; 0 def)
% Number of atoms : 260 ( 108 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 192 ( 56 ~; 65 |; 56 &)
% ( 8 <=>; 5 =>; 0 <=; 2 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 146 ( 126 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f208815,plain,
$false,
inference(resolution,[],[f208814,f164246]) ).
fof(f164246,plain,
leq(sK2,sK0),
inference(trivial_inequality_removal,[],[f164123]) ).
fof(f164123,plain,
( sK0 != sK0
| leq(sK2,sK0) ),
inference(superposition,[],[f64,f163128]) ).
fof(f163128,plain,
sK0 = addition(sK2,sK0),
inference(duplicate_literal_removal,[],[f163127]) ).
fof(f163127,plain,
( sK0 = addition(sK2,sK0)
| sK0 = addition(sK2,sK0) ),
inference(forward_demodulation,[],[f163126,f4523]) ).
fof(f4523,plain,
! [X0] : addition(X0,multiplication(X0,sK1)) = X0,
inference(superposition,[],[f4401,f56]) ).
fof(f56,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/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
fof(f4401,plain,
! [X0] : addition(multiplication(X0,sK1),X0) = X0,
inference(resolution,[],[f4370,f63]) ).
fof(f63,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0,X1] :
( ( leq(X0,X1)
| addition(X0,X1) != X1 )
& ( addition(X0,X1) = X1
| ~ leq(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
fof(f4370,plain,
! [X0] : leq(multiplication(X0,sK1),X0),
inference(forward_demodulation,[],[f4326,f50]) ).
fof(f50,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] : multiplication(X0,one) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
fof(f4326,plain,
! [X0] : leq(multiplication(X0,sK1),multiplication(X0,one)),
inference(trivial_inequality_removal,[],[f4310]) ).
fof(f4310,plain,
! [X0] :
( multiplication(X0,one) != multiplication(X0,one)
| leq(multiplication(X0,sK1),multiplication(X0,one)) ),
inference(superposition,[],[f286,f1342]) ).
fof(f1342,plain,
one = addition(sK1,one),
inference(superposition,[],[f117,f1130]) ).
fof(f1130,plain,
one = addition(sK1,sK3(sK1)),
inference(resolution,[],[f86,f42]) ).
fof(f42,plain,
test(sK1),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
( ( ~ leq(sK2,sK1)
| ~ leq(sK2,sK0)
| ~ leq(sK2,multiplication(sK0,sK1)) )
& ( ( leq(sK2,sK1)
& leq(sK2,sK0) )
| leq(sK2,multiplication(sK0,sK1)) )
& test(sK2)
& test(sK1)
& test(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f30,f31]) ).
fof(f31,plain,
( ? [X0,X1,X2] :
( ( ~ leq(X2,X1)
| ~ leq(X2,X0)
| ~ leq(X2,multiplication(X0,X1)) )
& ( ( leq(X2,X1)
& leq(X2,X0) )
| leq(X2,multiplication(X0,X1)) )
& test(X2)
& test(X1)
& test(X0) )
=> ( ( ~ leq(sK2,sK1)
| ~ leq(sK2,sK0)
| ~ leq(sK2,multiplication(sK0,sK1)) )
& ( ( leq(sK2,sK1)
& leq(sK2,sK0) )
| leq(sK2,multiplication(sK0,sK1)) )
& test(sK2)
& test(sK1)
& test(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f30,plain,
? [X0,X1,X2] :
( ( ~ leq(X2,X1)
| ~ leq(X2,X0)
| ~ leq(X2,multiplication(X0,X1)) )
& ( ( leq(X2,X1)
& leq(X2,X0) )
| leq(X2,multiplication(X0,X1)) )
& test(X2)
& test(X1)
& test(X0) ),
inference(flattening,[],[f29]) ).
fof(f29,plain,
? [X0,X1,X2] :
( ( ~ leq(X2,X1)
| ~ leq(X2,X0)
| ~ leq(X2,multiplication(X0,X1)) )
& ( ( leq(X2,X1)
& leq(X2,X0) )
| leq(X2,multiplication(X0,X1)) )
& test(X2)
& test(X1)
& test(X0) ),
inference(nnf_transformation,[],[f26]) ).
fof(f26,plain,
? [X0,X1,X2] :
( ( leq(X2,multiplication(X0,X1))
<~> ( leq(X2,X1)
& leq(X2,X0) ) )
& test(X2)
& test(X1)
& test(X0) ),
inference(flattening,[],[f25]) ).
fof(f25,plain,
? [X0,X1,X2] :
( ( leq(X2,multiplication(X0,X1))
<~> ( leq(X2,X1)
& leq(X2,X0) ) )
& test(X2)
& test(X1)
& test(X0) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
~ ! [X0,X1,X2] :
( ( test(X2)
& test(X1)
& test(X0) )
=> ( leq(X2,multiplication(X0,X1))
<=> ( leq(X2,X1)
& leq(X2,X0) ) ) ),
inference(rectify,[],[f18]) ).
fof(f18,negated_conjecture,
~ ! [X3,X4,X5] :
( ( test(X5)
& test(X4)
& test(X3) )
=> ( leq(X5,multiplication(X3,X4))
<=> ( leq(X5,X4)
& leq(X5,X3) ) ) ),
inference(negated_conjecture,[],[f17]) ).
fof(f17,conjecture,
! [X3,X4,X5] :
( ( test(X5)
& test(X4)
& test(X3) )
=> ( leq(X5,multiplication(X3,X4))
<=> ( leq(X5,X4)
& leq(X5,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f86,plain,
! [X0] :
( ~ test(X0)
| one = addition(X0,sK3(X0)) ),
inference(resolution,[],[f61,f54]) ).
fof(f54,plain,
! [X0] :
( complement(sK3(X0),X0)
| ~ test(X0) ),
inference(cnf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0] :
( ( test(X0)
| ! [X1] : ~ complement(X1,X0) )
& ( complement(sK3(X0),X0)
| ~ test(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f34,f35]) ).
fof(f35,plain,
! [X0] :
( ? [X2] : complement(X2,X0)
=> complement(sK3(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/sandbox2/benchmark/theBenchmark.p',test_1) ).
fof(f61,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/sandbox2/benchmark/theBenchmark.p',test_2) ).
fof(f117,plain,
! [X0,X1] : addition(X0,X1) = addition(X0,addition(X0,X1)),
inference(superposition,[],[f65,f52]) ).
fof(f52,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] : addition(X0,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
fof(f65,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/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
fof(f286,plain,
! [X2,X0,X1] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(superposition,[],[f64,f67]) ).
fof(f67,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/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
fof(f163126,plain,
( addition(sK2,sK0) = addition(sK0,multiplication(sK0,sK1))
| sK0 = addition(sK2,sK0) ),
inference(forward_demodulation,[],[f163125,f50]) ).
fof(f163125,plain,
( addition(sK0,multiplication(sK0,sK1)) = addition(sK2,multiplication(sK0,one))
| sK0 = addition(sK2,sK0) ),
inference(forward_demodulation,[],[f161806,f1342]) ).
fof(f161806,plain,
( addition(sK0,multiplication(sK0,sK1)) = addition(sK2,multiplication(sK0,addition(sK1,one)))
| sK0 = addition(sK2,sK0) ),
inference(superposition,[],[f2209,f92]) ).
fof(f92,plain,
( multiplication(sK0,sK1) = addition(sK2,multiplication(sK0,sK1))
| sK0 = addition(sK2,sK0) ),
inference(resolution,[],[f90,f63]) ).
fof(f90,plain,
( leq(sK2,sK0)
| multiplication(sK0,sK1) = addition(sK2,multiplication(sK0,sK1)) ),
inference(resolution,[],[f63,f44]) ).
fof(f44,plain,
( leq(sK2,multiplication(sK0,sK1))
| leq(sK2,sK0) ),
inference(cnf_transformation,[],[f32]) ).
fof(f2209,plain,
! [X2,X0,X1] : addition(X0,addition(X2,multiplication(X0,X1))) = addition(X2,multiplication(X0,addition(X1,one))),
inference(superposition,[],[f124,f258]) ).
fof(f258,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(superposition,[],[f67,f50]) ).
fof(f124,plain,
! [X2,X0,X1] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(superposition,[],[f65,f56]) ).
fof(f64,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f208814,plain,
~ leq(sK2,sK0),
inference(resolution,[],[f208631,f205368]) ).
fof(f205368,plain,
leq(sK2,sK1),
inference(trivial_inequality_removal,[],[f205243]) ).
fof(f205243,plain,
( sK1 != sK1
| leq(sK2,sK1) ),
inference(superposition,[],[f64,f204401]) ).
fof(f204401,plain,
sK1 = addition(sK2,sK1),
inference(duplicate_literal_removal,[],[f204400]) ).
fof(f204400,plain,
( sK1 = addition(sK2,sK1)
| sK1 = addition(sK2,sK1) ),
inference(forward_demodulation,[],[f204399,f4870]) ).
fof(f4870,plain,
! [X0] : addition(X0,multiplication(sK0,X0)) = X0,
inference(superposition,[],[f4737,f56]) ).
fof(f4737,plain,
! [X0] : addition(multiplication(sK0,X0),X0) = X0,
inference(resolution,[],[f4714,f63]) ).
fof(f4714,plain,
! [X0] : leq(multiplication(sK0,X0),X0),
inference(forward_demodulation,[],[f4645,f51]) ).
fof(f51,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] : multiplication(one,X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
fof(f4645,plain,
! [X0] : leq(multiplication(sK0,X0),multiplication(one,X0)),
inference(trivial_inequality_removal,[],[f4625]) ).
fof(f4625,plain,
! [X0] :
( multiplication(one,X0) != multiplication(one,X0)
| leq(multiplication(sK0,X0),multiplication(one,X0)) ),
inference(superposition,[],[f514,f1341]) ).
fof(f1341,plain,
one = addition(sK0,one),
inference(superposition,[],[f117,f1129]) ).
fof(f1129,plain,
one = addition(sK0,sK3(sK0)),
inference(resolution,[],[f86,f41]) ).
fof(f41,plain,
test(sK0),
inference(cnf_transformation,[],[f32]) ).
fof(f514,plain,
! [X2,X0,X1] :
( multiplication(X2,X1) != multiplication(addition(X0,X2),X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(superposition,[],[f64,f68]) ).
fof(f68,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/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
fof(f204399,plain,
( addition(sK2,sK1) = addition(sK1,multiplication(sK0,sK1))
| sK1 = addition(sK2,sK1) ),
inference(forward_demodulation,[],[f204398,f51]) ).
fof(f204398,plain,
( addition(sK1,multiplication(sK0,sK1)) = addition(sK2,multiplication(one,sK1))
| sK1 = addition(sK2,sK1) ),
inference(forward_demodulation,[],[f202940,f1341]) ).
fof(f202940,plain,
( addition(sK1,multiplication(sK0,sK1)) = addition(sK2,multiplication(addition(sK0,one),sK1))
| sK1 = addition(sK2,sK1) ),
inference(superposition,[],[f2814,f91]) ).
fof(f91,plain,
( multiplication(sK0,sK1) = addition(sK2,multiplication(sK0,sK1))
| sK1 = addition(sK2,sK1) ),
inference(resolution,[],[f89,f63]) ).
fof(f89,plain,
( leq(sK2,sK1)
| multiplication(sK0,sK1) = addition(sK2,multiplication(sK0,sK1)) ),
inference(resolution,[],[f63,f45]) ).
fof(f45,plain,
( leq(sK2,multiplication(sK0,sK1))
| leq(sK2,sK1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f2814,plain,
! [X2,X0,X1] : addition(X2,multiplication(addition(X0,one),X1)) = addition(X1,addition(X2,multiplication(X0,X1))),
inference(superposition,[],[f124,f479]) ).
fof(f479,plain,
! [X0,X1] : multiplication(addition(X1,one),X0) = addition(multiplication(X1,X0),X0),
inference(superposition,[],[f68,f51]) ).
fof(f208631,plain,
( ~ leq(sK2,sK1)
| ~ leq(sK2,sK0) ),
inference(resolution,[],[f206793,f46]) ).
fof(f46,plain,
( ~ leq(sK2,multiplication(sK0,sK1))
| ~ leq(sK2,sK0)
| ~ leq(sK2,sK1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f206793,plain,
leq(sK2,multiplication(sK0,sK1)),
inference(superposition,[],[f164244,f206013]) ).
fof(f206013,plain,
sK2 = multiplication(sK2,sK1),
inference(forward_demodulation,[],[f206012,f4523]) ).
fof(f206012,plain,
multiplication(sK2,sK1) = addition(sK2,multiplication(sK2,sK1)),
inference(resolution,[],[f205219,f63]) ).
fof(f205219,plain,
leq(sK2,multiplication(sK2,sK1)),
inference(superposition,[],[f189778,f204401]) ).
fof(f189778,plain,
! [X0] : leq(sK2,multiplication(sK2,addition(sK2,X0))),
inference(forward_demodulation,[],[f189662,f168053]) ).
fof(f168053,plain,
! [X0] : multiplication(sK2,addition(sK2,X0)) = multiplication(sK2,addition(sK0,X0)),
inference(forward_demodulation,[],[f167870,f1327]) ).
fof(f1327,plain,
! [X0] : multiplication(sK2,addition(sK2,X0)) = addition(sK2,multiplication(sK2,X0)),
inference(superposition,[],[f67,f1316]) ).
fof(f1316,plain,
sK2 = multiplication(sK2,sK2),
inference(forward_demodulation,[],[f1311,f51]) ).
fof(f1311,plain,
multiplication(sK2,sK2) = multiplication(one,sK2),
inference(superposition,[],[f572,f1131]) ).
fof(f1131,plain,
one = addition(sK2,sK3(sK2)),
inference(resolution,[],[f86,f43]) ).
fof(f43,plain,
test(sK2),
inference(cnf_transformation,[],[f32]) ).
fof(f572,plain,
! [X0] : multiplication(X0,sK2) = multiplication(addition(X0,sK3(sK2)),sK2),
inference(forward_demodulation,[],[f506,f49]) ).
fof(f49,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : addition(X0,zero) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
fof(f506,plain,
! [X0] : addition(multiplication(X0,sK2),zero) = multiplication(addition(X0,sK3(sK2)),sK2),
inference(superposition,[],[f68,f137]) ).
fof(f137,plain,
zero = multiplication(sK3(sK2),sK2),
inference(resolution,[],[f84,f43]) ).
fof(f84,plain,
! [X0] :
( ~ test(X0)
| zero = multiplication(sK3(X0),X0) ),
inference(resolution,[],[f60,f54]) ).
fof(f60,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| zero = multiplication(X1,X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f167870,plain,
! [X0] : addition(sK2,multiplication(sK2,X0)) = multiplication(sK2,addition(sK0,X0)),
inference(superposition,[],[f67,f167557]) ).
fof(f167557,plain,
sK2 = multiplication(sK2,sK0),
inference(forward_demodulation,[],[f167556,f4443]) ).
fof(f4443,plain,
! [X0] : addition(X0,multiplication(X0,sK0)) = X0,
inference(superposition,[],[f4393,f56]) ).
fof(f4393,plain,
! [X0] : addition(multiplication(X0,sK0),X0) = X0,
inference(resolution,[],[f4367,f63]) ).
fof(f4367,plain,
! [X0] : leq(multiplication(X0,sK0),X0),
inference(forward_demodulation,[],[f4328,f50]) ).
fof(f4328,plain,
! [X0] : leq(multiplication(X0,sK0),multiplication(X0,one)),
inference(trivial_inequality_removal,[],[f4307]) ).
fof(f4307,plain,
! [X0] :
( multiplication(X0,one) != multiplication(X0,one)
| leq(multiplication(X0,sK0),multiplication(X0,one)) ),
inference(superposition,[],[f286,f1341]) ).
fof(f167556,plain,
multiplication(sK2,sK0) = addition(sK2,multiplication(sK2,sK0)),
inference(resolution,[],[f167468,f63]) ).
fof(f167468,plain,
leq(sK2,multiplication(sK2,sK0)),
inference(superposition,[],[f164245,f1316]) ).
fof(f164245,plain,
! [X0] : leq(multiplication(X0,sK2),multiplication(X0,sK0)),
inference(trivial_inequality_removal,[],[f164131]) ).
fof(f164131,plain,
! [X0] :
( multiplication(X0,sK0) != multiplication(X0,sK0)
| leq(multiplication(X0,sK2),multiplication(X0,sK0)) ),
inference(superposition,[],[f286,f163128]) ).
fof(f189662,plain,
! [X0] : leq(sK2,multiplication(sK2,addition(sK0,X0))),
inference(superposition,[],[f181218,f1316]) ).
fof(f181218,plain,
! [X0,X1] : leq(multiplication(X1,sK2),multiplication(X1,addition(sK0,X0))),
inference(trivial_inequality_removal,[],[f181104]) ).
fof(f181104,plain,
! [X0,X1] :
( multiplication(X1,addition(sK0,X0)) != multiplication(X1,addition(sK0,X0))
| leq(multiplication(X1,sK2),multiplication(X1,addition(sK0,X0))) ),
inference(superposition,[],[f286,f164124]) ).
fof(f164124,plain,
! [X0] : addition(sK0,X0) = addition(sK2,addition(sK0,X0)),
inference(superposition,[],[f65,f163128]) ).
fof(f164244,plain,
! [X0] : leq(multiplication(sK2,X0),multiplication(sK0,X0)),
inference(trivial_inequality_removal,[],[f164132]) ).
fof(f164132,plain,
! [X0] :
( multiplication(sK0,X0) != multiplication(sK0,X0)
| leq(multiplication(sK2,X0),multiplication(sK0,X0)) ),
inference(superposition,[],[f514,f163128]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : KLE017+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.36 % Computer : n027.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Tue Apr 30 05:29:32 EDT 2024
% 0.13/0.36 % CPUTime :
% 0.13/0.37 % (12498)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.38 % (12501)WARNING: value z3 for option sas not known
% 0.13/0.38 % (12502)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.38 % (12504)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)
% 0.13/0.38 % (12505)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)
% 0.13/0.38 % (12500)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.38 % (12501)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)
% 0.13/0.38 % (12503)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)
% 0.13/0.38 TRYING [1]
% 0.13/0.38 TRYING [2]
% 0.13/0.38 % (12499)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.38 TRYING [3]
% 0.13/0.39 TRYING [4]
% 0.13/0.39 TRYING [1]
% 0.13/0.39 TRYING [2]
% 0.13/0.41 TRYING [3]
% 0.13/0.41 TRYING [5]
% 0.21/0.45 TRYING [4]
% 0.21/0.48 TRYING [6]
% 0.21/0.53 TRYING [5]
% 2.17/0.67 TRYING [7]
% 3.41/0.85 TRYING [6]
% 4.70/1.07 TRYING [8]
% 7.68/1.48 TRYING [1]
% 7.68/1.48 TRYING [2]
% 7.68/1.49 TRYING [3]
% 7.97/1.50 TRYING [4]
% 8.30/1.54 TRYING [5]
% 8.86/1.67 TRYING [6]
% 10.21/1.89 TRYING [7]
% 11.40/2.00 TRYING [7]
% 12.05/2.08 TRYING [9]
% 17.36/2.89 TRYING [8]
% 26.31/4.16 TRYING [10]
% 31.89/4.93 TRYING [9]
% 41.07/6.28 TRYING [8]
% 51.63/7.79 TRYING [11]
% 61.43/9.22 TRYING [10]
% 102.70/15.11 TRYING [11]
% 113.07/16.59 % (12504)First to succeed.
% 113.36/16.61 % (12504)Refutation found. Thanks to Tanya!
% 113.36/16.61 % SZS status Theorem for theBenchmark
% 113.36/16.61 % SZS output start Proof for theBenchmark
% See solution above
% 113.36/16.61 % (12504)------------------------------
% 113.36/16.61 % (12504)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 113.36/16.61 % (12504)Termination reason: Refutation
% 113.36/16.61
% 113.36/16.61 % (12504)Memory used [KB]: 96959
% 113.36/16.61 % (12504)Time elapsed: 16.206 s
% 113.36/16.61 % (12504)Instructions burned: 38490 (million)
% 113.36/16.61 % (12504)------------------------------
% 113.36/16.61 % (12504)------------------------------
% 113.36/16.61 % (12498)Success in time 16.127 s
%------------------------------------------------------------------------------