TSTP Solution File: KLE010+4 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE010+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n017.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 : Wed May 31 12:15:28 EDT 2023
% Result : Theorem 1.54s 0.67s
% Output : CNFRefutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 15
% Syntax : Number of formulae : 173 ( 62 unt; 0 def)
% Number of atoms : 324 ( 123 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 272 ( 121 ~; 120 |; 20 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 125 (; 123 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> ( 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))))
& 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) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( ( test(X1)
& test(X0) )
=> ( 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))))
& 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) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f22,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f24,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f26,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f27,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f28,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f29,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f32,plain,
! [A,B] :
( ( ~ leq(A,B)
| addition(A,B) = B )
& ( leq(A,B)
| addition(A,B) != B ) ),
inference(NNF_transformation,[status(esa)],[f12]) ).
fof(f33,plain,
( ! [A,B] :
( ~ leq(A,B)
| addition(A,B) = B )
& ! [A,B] :
( leq(A,B)
| addition(A,B) != B ) ),
inference(miniscoping,[status(esa)],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f41,plain,
! [X0,X1] :
( ( ~ complement(X1,X0)
| ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) )
& ( complement(X1,X0)
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero
| addition(X0,X1) != one ) ),
inference(NNF_transformation,[status(esa)],[f14]) ).
fof(f42,plain,
( ! [X0,X1] :
( ~ complement(X1,X0)
| ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) )
& ! [X0,X1] :
( complement(X1,X0)
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero
| addition(X0,X1) != one ) ),
inference(miniscoping,[status(esa)],[f41]) ).
fof(f45,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| addition(X1,X0) = one ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f47,plain,
! [X0,X1] :
( ~ test(X0)
| ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f48,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) != X1
| complement(X0,X1) )
& ( c(X0) = X1
| ~ complement(X0,X1) ) ) ),
inference(NNF_transformation,[status(esa)],[f47]) ).
fof(f49,plain,
! [X0] :
( ~ test(X0)
| ( ! [X1] :
( c(X0) != X1
| complement(X0,X1) )
& ! [X1] :
( c(X0) = X1
| ~ complement(X0,X1) ) ) ),
inference(miniscoping,[status(esa)],[f48]) ).
fof(f50,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f58,plain,
? [X0,X1] :
( test(X1)
& test(X0)
& ( ~ 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))))
| ~ 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) ) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f59,plain,
( test(sk0_2)
& test(sk0_1)
& ( ~ leq(one,addition(addition(addition(addition(multiplication(sk0_2,sk0_1),multiplication(c(sk0_2),sk0_1)),multiplication(sk0_1,sk0_2)),multiplication(c(sk0_1),sk0_2)),multiplication(c(sk0_1),c(sk0_2))))
| ~ leq(addition(addition(addition(addition(multiplication(sk0_2,sk0_1),multiplication(c(sk0_2),sk0_1)),multiplication(sk0_1,sk0_2)),multiplication(c(sk0_1),sk0_2)),multiplication(c(sk0_1),c(sk0_2))),one) ) ),
inference(skolemization,[status(esa)],[f58]) ).
fof(f60,plain,
test(sk0_2),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f61,plain,
test(sk0_1),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f62,plain,
( ~ leq(one,addition(addition(addition(addition(multiplication(sk0_2,sk0_1),multiplication(c(sk0_2),sk0_1)),multiplication(sk0_1,sk0_2)),multiplication(c(sk0_1),sk0_2)),multiplication(c(sk0_1),c(sk0_2))))
| ~ leq(addition(addition(addition(addition(multiplication(sk0_2,sk0_1),multiplication(c(sk0_2),sk0_1)),multiplication(sk0_1,sk0_2)),multiplication(c(sk0_1),sk0_2)),multiplication(c(sk0_1),c(sk0_2))),one) ),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f63,plain,
( spl0_0
<=> leq(one,addition(addition(addition(addition(multiplication(sk0_2,sk0_1),multiplication(c(sk0_2),sk0_1)),multiplication(sk0_1,sk0_2)),multiplication(c(sk0_1),sk0_2)),multiplication(c(sk0_1),c(sk0_2)))) ),
introduced(split_symbol_definition) ).
fof(f64,plain,
( leq(one,addition(addition(addition(addition(multiplication(sk0_2,sk0_1),multiplication(c(sk0_2),sk0_1)),multiplication(sk0_1,sk0_2)),multiplication(c(sk0_1),sk0_2)),multiplication(c(sk0_1),c(sk0_2))))
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f65,plain,
( ~ leq(one,addition(addition(addition(addition(multiplication(sk0_2,sk0_1),multiplication(c(sk0_2),sk0_1)),multiplication(sk0_1,sk0_2)),multiplication(c(sk0_1),sk0_2)),multiplication(c(sk0_1),c(sk0_2))))
| spl0_0 ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,plain,
( spl0_1
<=> leq(addition(addition(addition(addition(multiplication(sk0_2,sk0_1),multiplication(c(sk0_2),sk0_1)),multiplication(sk0_1,sk0_2)),multiplication(c(sk0_1),sk0_2)),multiplication(c(sk0_1),c(sk0_2))),one) ),
introduced(split_symbol_definition) ).
fof(f68,plain,
( ~ leq(addition(addition(addition(addition(multiplication(sk0_2,sk0_1),multiplication(c(sk0_2),sk0_1)),multiplication(sk0_1,sk0_2)),multiplication(c(sk0_1),sk0_2)),multiplication(c(sk0_1),c(sk0_2))),one)
| spl0_1 ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f69,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f62,f63,f66]) ).
fof(f70,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(destructive_equality_resolution,[status(esa)],[f50]) ).
fof(f71,plain,
( ~ leq(one,addition(addition(addition(multiplication(sk0_2,sk0_1),multiplication(c(sk0_2),sk0_1)),multiplication(sk0_1,sk0_2)),addition(multiplication(c(sk0_1),sk0_2),multiplication(c(sk0_1),c(sk0_2)))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f22,f65]) ).
fof(f72,plain,
( ~ leq(one,addition(addition(multiplication(sk0_2,sk0_1),multiplication(c(sk0_2),sk0_1)),addition(multiplication(sk0_1,sk0_2),addition(multiplication(c(sk0_1),sk0_2),multiplication(c(sk0_1),c(sk0_2))))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f22,f71]) ).
fof(f73,plain,
( ~ leq(one,addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_2),sk0_1),addition(multiplication(sk0_1,sk0_2),addition(multiplication(c(sk0_1),sk0_2),multiplication(c(sk0_1),c(sk0_2)))))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f22,f72]) ).
fof(f74,plain,
( ~ leq(one,addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_2),sk0_1),addition(multiplication(sk0_1,sk0_2),multiplication(c(sk0_1),addition(sk0_2,c(sk0_2)))))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f28,f73]) ).
fof(f76,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X1,X0) != X1 ),
inference(paramodulation,[status(thm)],[f21,f35]) ).
fof(f86,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f21,f22]) ).
fof(f92,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f21,f22]) ).
fof(f93,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f22,f92]) ).
fof(f96,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f102,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f96,f35]) ).
fof(f109,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f21,f96]) ).
fof(f117,plain,
! [X0,X1] :
( leq(addition(X0,X1),X0)
| addition(X0,X1) != X0 ),
inference(paramodulation,[status(thm)],[f96,f76]) ).
fof(f124,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f21,f102]) ).
fof(f129,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f22,f124]) ).
fof(f134,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X1,addition(X2,X0)),
inference(resolution,[status(thm)],[f129,f34]) ).
fof(f137,plain,
! [X0,X1,X2] : leq(X0,addition(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f21,f129]) ).
fof(f138,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f22,f137]) ).
fof(f188,plain,
complement(sk0_1,c(sk0_1)),
inference(resolution,[status(thm)],[f70,f61]) ).
fof(f189,plain,
complement(sk0_2,c(sk0_2)),
inference(resolution,[status(thm)],[f70,f60]) ).
fof(f190,plain,
addition(c(sk0_1),sk0_1) = one,
inference(resolution,[status(thm)],[f188,f45]) ).
fof(f191,plain,
addition(sk0_1,c(sk0_1)) = one,
inference(forward_demodulation,[status(thm)],[f21,f190]) ).
fof(f192,plain,
addition(c(sk0_2),sk0_2) = one,
inference(resolution,[status(thm)],[f189,f45]) ).
fof(f193,plain,
addition(sk0_2,c(sk0_2)) = one,
inference(forward_demodulation,[status(thm)],[f21,f192]) ).
fof(f194,plain,
( ~ leq(one,addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_2),sk0_1),addition(multiplication(sk0_1,sk0_2),multiplication(c(sk0_1),one)))))
| spl0_0 ),
inference(backward_demodulation,[status(thm)],[f193,f74]) ).
fof(f195,plain,
( ~ leq(one,addition(multiplication(sk0_2,sk0_1),addition(multiplication(sk0_1,sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),one)))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f93,f194]) ).
fof(f196,plain,
( ~ leq(one,addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),one)))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f93,f195]) ).
fof(f197,plain,
( ~ leq(one,addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),one),multiplication(c(sk0_2),sk0_1)))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f21,f196]) ).
fof(f198,plain,
( ~ leq(one,addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(c(sk0_1),multiplication(c(sk0_2),sk0_1)))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f26,f197]) ).
fof(f199,plain,
( ~ leq(one,addition(multiplication(sk0_1,sk0_2),addition(c(sk0_1),addition(multiplication(sk0_2,sk0_1),multiplication(c(sk0_2),sk0_1)))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f93,f198]) ).
fof(f200,plain,
( ~ leq(one,addition(c(sk0_1),addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),multiplication(c(sk0_2),sk0_1)))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f93,f199]) ).
fof(f201,plain,
( ~ leq(one,addition(c(sk0_1),addition(multiplication(sk0_1,sk0_2),multiplication(addition(sk0_2,c(sk0_2)),sk0_1))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f29,f200]) ).
fof(f202,plain,
( ~ leq(one,addition(c(sk0_1),addition(multiplication(sk0_1,sk0_2),multiplication(one,sk0_1))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f193,f201]) ).
fof(f203,plain,
( ~ leq(one,addition(c(sk0_1),addition(multiplication(one,sk0_1),multiplication(sk0_1,sk0_2))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f21,f202]) ).
fof(f204,plain,
( ~ leq(one,addition(c(sk0_1),addition(sk0_1,multiplication(sk0_1,sk0_2))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f27,f203]) ).
fof(f205,plain,
( ~ leq(one,addition(sk0_1,addition(c(sk0_1),multiplication(sk0_1,sk0_2))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f93,f204]) ).
fof(f206,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(resolution,[status(thm)],[f138,f34]) ).
fof(f225,plain,
addition(sk0_1,one) = addition(sk0_1,c(sk0_1)),
inference(paramodulation,[status(thm)],[f191,f96]) ).
fof(f226,plain,
addition(one,sk0_1) = addition(sk0_1,c(sk0_1)),
inference(forward_demodulation,[status(thm)],[f21,f225]) ).
fof(f227,plain,
addition(one,sk0_1) = one,
inference(forward_demodulation,[status(thm)],[f191,f226]) ).
fof(f228,plain,
! [X0] : addition(sk0_1,addition(c(sk0_1),X0)) = addition(one,X0),
inference(paramodulation,[status(thm)],[f191,f22]) ).
fof(f245,plain,
( ~ leq(one,addition(one,multiplication(sk0_1,sk0_2)))
| spl0_0 ),
inference(backward_demodulation,[status(thm)],[f228,f205]) ).
fof(f246,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f245,f102]) ).
fof(f247,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f246]) ).
fof(f248,plain,
( ~ leq(addition(addition(addition(multiplication(sk0_2,sk0_1),multiplication(c(sk0_2),sk0_1)),multiplication(sk0_1,sk0_2)),addition(multiplication(c(sk0_1),sk0_2),multiplication(c(sk0_1),c(sk0_2)))),one)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f22,f68]) ).
fof(f249,plain,
( ~ leq(addition(addition(multiplication(sk0_2,sk0_1),multiplication(c(sk0_2),sk0_1)),addition(multiplication(sk0_1,sk0_2),addition(multiplication(c(sk0_1),sk0_2),multiplication(c(sk0_1),c(sk0_2))))),one)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f22,f248]) ).
fof(f250,plain,
( ~ leq(addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_2),sk0_1),addition(multiplication(sk0_1,sk0_2),addition(multiplication(c(sk0_1),sk0_2),multiplication(c(sk0_1),c(sk0_2)))))),one)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f22,f249]) ).
fof(f251,plain,
( ~ leq(addition(multiplication(sk0_2,sk0_1),addition(multiplication(sk0_1,sk0_2),addition(multiplication(c(sk0_2),sk0_1),addition(multiplication(c(sk0_1),sk0_2),multiplication(c(sk0_1),c(sk0_2)))))),one)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f93,f250]) ).
fof(f252,plain,
( ~ leq(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_2),sk0_1),addition(multiplication(c(sk0_1),sk0_2),multiplication(c(sk0_1),c(sk0_2)))))),one)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f93,f251]) ).
fof(f253,plain,
( ~ leq(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f93,f252]) ).
fof(f254,plain,
( leq(one,addition(addition(addition(multiplication(sk0_2,sk0_1),multiplication(c(sk0_2),sk0_1)),multiplication(sk0_1,sk0_2)),addition(multiplication(c(sk0_1),sk0_2),multiplication(c(sk0_1),c(sk0_2)))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f22,f64]) ).
fof(f255,plain,
( leq(one,addition(addition(multiplication(sk0_2,sk0_1),multiplication(c(sk0_2),sk0_1)),addition(multiplication(sk0_1,sk0_2),addition(multiplication(c(sk0_1),sk0_2),multiplication(c(sk0_1),c(sk0_2))))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f22,f254]) ).
fof(f256,plain,
( leq(one,addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_2),sk0_1),addition(multiplication(sk0_1,sk0_2),addition(multiplication(c(sk0_1),sk0_2),multiplication(c(sk0_1),c(sk0_2)))))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f22,f255]) ).
fof(f257,plain,
( leq(one,addition(multiplication(sk0_2,sk0_1),addition(multiplication(sk0_1,sk0_2),addition(multiplication(c(sk0_2),sk0_1),addition(multiplication(c(sk0_1),sk0_2),multiplication(c(sk0_1),c(sk0_2)))))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f93,f256]) ).
fof(f258,plain,
( leq(one,addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_2),sk0_1),addition(multiplication(c(sk0_1),sk0_2),multiplication(c(sk0_1),c(sk0_2)))))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f93,f257]) ).
fof(f259,plain,
( leq(one,addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f93,f258]) ).
fof(f269,plain,
! [X0] : addition(one,addition(sk0_1,X0)) = addition(one,X0),
inference(paramodulation,[status(thm)],[f227,f22]) ).
fof(f273,plain,
( spl0_7
<=> one = one ),
introduced(split_symbol_definition) ).
fof(f275,plain,
( one != one
| spl0_7 ),
inference(component_clause,[status(thm)],[f273]) ).
fof(f283,plain,
( $false
| spl0_7 ),
inference(trivial_equality_resolution,[status(esa)],[f275]) ).
fof(f284,plain,
spl0_7,
inference(contradiction_clause,[status(thm)],[f283]) ).
fof(f303,plain,
addition(sk0_2,one) = addition(sk0_2,c(sk0_2)),
inference(paramodulation,[status(thm)],[f193,f96]) ).
fof(f304,plain,
addition(one,sk0_2) = addition(sk0_2,c(sk0_2)),
inference(forward_demodulation,[status(thm)],[f21,f303]) ).
fof(f305,plain,
addition(one,sk0_2) = one,
inference(forward_demodulation,[status(thm)],[f193,f304]) ).
fof(f306,plain,
! [X0] : addition(sk0_2,addition(c(sk0_2),X0)) = addition(one,X0),
inference(paramodulation,[status(thm)],[f193,f22]) ).
fof(f333,plain,
! [X0] : addition(one,addition(sk0_2,X0)) = addition(one,X0),
inference(paramodulation,[status(thm)],[f305,f22]) ).
fof(f369,plain,
addition(c(sk0_1),one) = addition(c(sk0_1),sk0_1),
inference(paramodulation,[status(thm)],[f191,f109]) ).
fof(f370,plain,
addition(one,c(sk0_1)) = addition(c(sk0_1),sk0_1),
inference(forward_demodulation,[status(thm)],[f21,f369]) ).
fof(f371,plain,
addition(one,c(sk0_1)) = addition(sk0_1,c(sk0_1)),
inference(forward_demodulation,[status(thm)],[f21,f370]) ).
fof(f372,plain,
addition(one,c(sk0_1)) = one,
inference(forward_demodulation,[status(thm)],[f191,f371]) ).
fof(f435,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f21,f29]) ).
fof(f436,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f29,f435]) ).
fof(f456,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f29,f124]) ).
fof(f461,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(X0,X2),X1),X3),
inference(paramodulation,[status(thm)],[f29,f22]) ).
fof(f486,plain,
( addition(one,addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2))))))) = addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2))))))
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f259,f34]) ).
fof(f492,plain,
( addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2))))))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(paramodulation,[status(thm)],[f486,f109]) ).
fof(f493,plain,
( addition(multiplication(sk0_1,sk0_2),addition(addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2))))),addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f22,f492]) ).
fof(f494,plain,
( addition(addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2))))),addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2))))))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f206,f493]) ).
fof(f495,plain,
( addition(multiplication(sk0_2,sk0_1),addition(addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))),addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f22,f494]) ).
fof(f496,plain,
( addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2))),addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2))))))))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f22,f495]) ).
fof(f497,plain,
( addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),addition(multiplication(c(sk0_1),c(sk0_2)),addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))))))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f22,f496]) ).
fof(f498,plain,
( addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),addition(multiplication(sk0_1,sk0_2),addition(multiplication(c(sk0_1),c(sk0_2)),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))))))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f93,f497]) ).
fof(f499,plain,
( addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(sk0_1,sk0_2),addition(multiplication(c(sk0_2),sk0_1),addition(multiplication(c(sk0_1),c(sk0_2)),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))))))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f93,f498]) ).
fof(f500,plain,
( addition(multiplication(sk0_2,sk0_1),addition(multiplication(addition(c(sk0_1),sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),addition(multiplication(c(sk0_1),c(sk0_2)),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2))))))))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f461,f499]) ).
fof(f501,plain,
( addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_2),sk0_1),addition(multiplication(addition(c(sk0_1),sk0_1),sk0_2),addition(multiplication(c(sk0_1),c(sk0_2)),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2))))))))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f93,f500]) ).
fof(f502,plain,
( addition(multiplication(addition(sk0_2,c(sk0_2)),sk0_1),addition(multiplication(addition(c(sk0_1),sk0_1),sk0_2),addition(multiplication(c(sk0_1),c(sk0_2)),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f461,f501]) ).
fof(f503,plain,
( addition(multiplication(one,sk0_1),addition(multiplication(addition(c(sk0_1),sk0_1),sk0_2),addition(multiplication(c(sk0_1),c(sk0_2)),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f193,f502]) ).
fof(f504,plain,
( addition(sk0_1,addition(multiplication(addition(c(sk0_1),sk0_1),sk0_2),addition(multiplication(c(sk0_1),c(sk0_2)),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f27,f503]) ).
fof(f505,plain,
( addition(sk0_1,addition(multiplication(c(sk0_1),c(sk0_2)),addition(multiplication(addition(c(sk0_1),sk0_1),sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f93,f504]) ).
fof(f506,plain,
( addition(sk0_1,addition(multiplication(c(sk0_1),c(sk0_2)),addition(multiplication(sk0_2,sk0_1),addition(multiplication(addition(c(sk0_1),sk0_1),sk0_2),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f93,f505]) ).
fof(f507,plain,
( addition(sk0_1,addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),c(sk0_2)),addition(multiplication(addition(c(sk0_1),sk0_1),sk0_2),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f93,f506]) ).
fof(f508,plain,
( addition(sk0_1,addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),c(sk0_2)),addition(multiplication(addition(addition(c(sk0_1),sk0_1),c(sk0_1)),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2))))))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f461,f507]) ).
fof(f509,plain,
( addition(sk0_1,addition(multiplication(sk0_2,sk0_1),addition(multiplication(addition(addition(c(sk0_1),sk0_1),c(sk0_1)),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f134,f508]) ).
fof(f510,plain,
( addition(sk0_1,addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_2),sk0_1),addition(multiplication(addition(addition(c(sk0_1),sk0_1),c(sk0_1)),sk0_2),multiplication(c(sk0_1),c(sk0_2)))))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f93,f509]) ).
fof(f511,plain,
( addition(sk0_1,addition(multiplication(addition(sk0_2,c(sk0_2)),sk0_1),addition(multiplication(addition(addition(c(sk0_1),sk0_1),c(sk0_1)),sk0_2),multiplication(c(sk0_1),c(sk0_2))))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f461,f510]) ).
fof(f512,plain,
( addition(sk0_1,addition(multiplication(c(sk0_1),c(sk0_2)),addition(multiplication(addition(sk0_2,c(sk0_2)),sk0_1),multiplication(addition(addition(c(sk0_1),sk0_1),c(sk0_1)),sk0_2)))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f86,f511]) ).
fof(f513,plain,
( addition(sk0_1,addition(multiplication(c(sk0_1),c(sk0_2)),addition(multiplication(one,sk0_1),multiplication(addition(addition(c(sk0_1),sk0_1),c(sk0_1)),sk0_2)))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f193,f512]) ).
fof(f514,plain,
( addition(sk0_1,addition(multiplication(one,sk0_1),addition(multiplication(c(sk0_1),c(sk0_2)),multiplication(addition(addition(c(sk0_1),sk0_1),c(sk0_1)),sk0_2)))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f93,f513]) ).
fof(f515,plain,
( addition(sk0_1,addition(sk0_1,addition(multiplication(c(sk0_1),c(sk0_2)),multiplication(addition(addition(c(sk0_1),sk0_1),c(sk0_1)),sk0_2)))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f27,f514]) ).
fof(f516,plain,
( addition(sk0_1,addition(multiplication(c(sk0_1),c(sk0_2)),multiplication(addition(addition(c(sk0_1),sk0_1),c(sk0_1)),sk0_2))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f96,f515]) ).
fof(f517,plain,
( addition(sk0_1,addition(multiplication(c(sk0_1),c(sk0_2)),multiplication(addition(c(sk0_1),addition(c(sk0_1),sk0_1)),sk0_2))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f436,f516]) ).
fof(f518,plain,
( addition(sk0_1,addition(multiplication(c(sk0_1),c(sk0_2)),multiplication(addition(c(sk0_1),sk0_1),sk0_2))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f96,f517]) ).
fof(f519,plain,
( addition(sk0_1,addition(multiplication(c(sk0_1),c(sk0_2)),multiplication(addition(sk0_1,c(sk0_1)),sk0_2))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f436,f518]) ).
fof(f520,plain,
( addition(sk0_1,addition(multiplication(c(sk0_1),c(sk0_2)),multiplication(one,sk0_2))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f191,f519]) ).
fof(f521,plain,
( addition(sk0_1,addition(multiplication(one,sk0_2),multiplication(c(sk0_1),c(sk0_2)))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f21,f520]) ).
fof(f522,plain,
( addition(sk0_1,addition(sk0_2,multiplication(c(sk0_1),c(sk0_2)))) = addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))),one)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f27,f521]) ).
fof(f523,plain,
( addition(sk0_1,addition(sk0_2,multiplication(c(sk0_1),c(sk0_2)))) = addition(multiplication(sk0_1,sk0_2),addition(addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2))))),one))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f22,f522]) ).
fof(f524,plain,
( addition(sk0_1,addition(sk0_2,multiplication(c(sk0_1),c(sk0_2)))) = addition(one,addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f86,f523]) ).
fof(f525,plain,
( addition(sk0_1,addition(sk0_2,multiplication(c(sk0_1),c(sk0_2)))) = addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2))))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f486,f524]) ).
fof(f534,plain,
( leq(one,addition(multiplication(sk0_1,sk0_2),addition(multiplication(sk0_2,sk0_1),addition(multiplication(c(sk0_1),sk0_2),addition(multiplication(c(sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))))))
| ~ spl0_0 ),
inference(paramodulation,[status(thm)],[f486,f102]) ).
fof(f535,plain,
( leq(one,addition(sk0_1,addition(sk0_2,multiplication(c(sk0_1),c(sk0_2)))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f525,f534]) ).
fof(f564,plain,
( ~ leq(addition(sk0_1,addition(sk0_2,multiplication(c(sk0_1),c(sk0_2)))),one)
| ~ spl0_0
| spl0_1 ),
inference(backward_demodulation,[status(thm)],[f525,f253]) ).
fof(f573,plain,
( addition(one,addition(sk0_1,addition(sk0_2,multiplication(c(sk0_1),c(sk0_2))))) = addition(sk0_1,addition(sk0_2,multiplication(c(sk0_1),c(sk0_2))))
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f535,f34]) ).
fof(f574,plain,
( addition(one,addition(sk0_2,multiplication(c(sk0_1),c(sk0_2)))) = addition(sk0_1,addition(sk0_2,multiplication(c(sk0_1),c(sk0_2))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f269,f573]) ).
fof(f575,plain,
( addition(one,multiplication(c(sk0_1),c(sk0_2))) = addition(sk0_1,addition(sk0_2,multiplication(c(sk0_1),c(sk0_2))))
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f333,f574]) ).
fof(f578,plain,
( ~ leq(addition(one,multiplication(c(sk0_1),c(sk0_2))),one)
| ~ spl0_0
| spl0_1 ),
inference(backward_demodulation,[status(thm)],[f575,f564]) ).
fof(f1649,plain,
( spl0_32
<=> addition(one,sk0_1) = one ),
introduced(split_symbol_definition) ).
fof(f1651,plain,
( addition(one,sk0_1) != one
| spl0_32 ),
inference(component_clause,[status(thm)],[f1649]) ).
fof(f1687,plain,
( one != one
| spl0_32 ),
inference(forward_demodulation,[status(thm)],[f227,f1651]) ).
fof(f1688,plain,
( $false
| spl0_32 ),
inference(trivial_equality_resolution,[status(esa)],[f1687]) ).
fof(f1689,plain,
spl0_32,
inference(contradiction_clause,[status(thm)],[f1688]) ).
fof(f1793,plain,
! [X0] : leq(multiplication(c(sk0_1),X0),multiplication(one,X0)),
inference(paramodulation,[status(thm)],[f372,f456]) ).
fof(f1794,plain,
! [X0] : leq(multiplication(c(sk0_1),X0),X0),
inference(forward_demodulation,[status(thm)],[f27,f1793]) ).
fof(f1825,plain,
! [X0] : addition(multiplication(c(sk0_1),X0),X0) = X0,
inference(resolution,[status(thm)],[f1794,f34]) ).
fof(f1826,plain,
! [X0] : addition(X0,multiplication(c(sk0_1),X0)) = X0,
inference(forward_demodulation,[status(thm)],[f21,f1825]) ).
fof(f1886,plain,
addition(sk0_2,c(sk0_2)) = addition(one,multiplication(c(sk0_1),c(sk0_2))),
inference(paramodulation,[status(thm)],[f1826,f306]) ).
fof(f1887,plain,
one = addition(one,multiplication(c(sk0_1),c(sk0_2))),
inference(forward_demodulation,[status(thm)],[f193,f1886]) ).
fof(f1940,plain,
( addition(one,multiplication(c(sk0_1),c(sk0_2))) != one
| ~ spl0_0
| spl0_1 ),
inference(resolution,[status(thm)],[f117,f578]) ).
fof(f1941,plain,
( one != one
| ~ spl0_0
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f1887,f1940]) ).
fof(f1942,plain,
( $false
| ~ spl0_0
| spl0_1 ),
inference(trivial_equality_resolution,[status(esa)],[f1941]) ).
fof(f1943,plain,
( ~ spl0_0
| spl0_1 ),
inference(contradiction_clause,[status(thm)],[f1942]) ).
fof(f1944,plain,
$false,
inference(sat_refutation,[status(thm)],[f69,f247,f284,f1689,f1943]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.19 % Problem : KLE010+4 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.20 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.41 % Computer : n017.cluster.edu
% 0.12/0.41 % Model : x86_64 x86_64
% 0.12/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.41 % Memory : 8042.1875MB
% 0.12/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.41 % CPULimit : 300
% 0.12/0.41 % WCLimit : 300
% 0.12/0.41 % DateTime : Tue May 30 11:15:10 EDT 2023
% 0.12/0.41 % CPUTime :
% 0.12/0.42 % Drodi V3.5.1
% 1.54/0.67 % Refutation found
% 1.54/0.67 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.54/0.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.54/0.69 % Elapsed time: 0.263159 seconds
% 1.54/0.69 % CPU time: 1.940490 seconds
% 1.54/0.69 % Memory used: 85.211 MB
%------------------------------------------------------------------------------