TSTP Solution File: KLE042+2 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE042+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n032.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 12:15:37 EDT 2023
% Result : Theorem 58.33s 7.73s
% Output : CNFRefutation 60.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 16
% Syntax : Number of formulae : 143 ( 84 unt; 0 def)
% Number of atoms : 206 ( 103 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 121 ( 58 ~; 54 |; 4 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 237 (; 231 !; 6 ?)
% 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(f5,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
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(f13,axiom,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),B)
=> leq(multiplication(star(A),C),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),A)
=> leq(multiplication(C,star(B)),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [X0,X1] :
( leq(multiplication(star(multiplication(X0,X1)),X0),multiplication(X0,star(multiplication(X1,X0))))
& leq(multiplication(X0,star(multiplication(X1,X0))),multiplication(star(multiplication(X0,X1)),X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( leq(multiplication(star(multiplication(X0,X1)),X0),multiplication(X0,star(multiplication(X1,X0))))
& leq(multiplication(X0,star(multiplication(X1,X0))),multiplication(star(multiplication(X0,X1)),X0)) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f20,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f22,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f23,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f24,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f25,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f26,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f27,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f30,plain,
! [A,B] :
( ( ~ leq(A,B)
| addition(A,B) = B )
& ( leq(A,B)
| addition(A,B) != B ) ),
inference(NNF_transformation,[status(esa)],[f12]) ).
fof(f31,plain,
( ! [A,B] :
( ~ leq(A,B)
| addition(A,B) = B )
& ! [A,B] :
( leq(A,B)
| addition(A,B) != B ) ),
inference(miniscoping,[status(esa)],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f34,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f35,plain,
! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f36,plain,
! [A,B,C] :
( ~ leq(addition(multiplication(A,B),C),B)
| leq(multiplication(star(A),C),B) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ leq(addition(multiplication(X0,X1),X2),X1)
| leq(multiplication(star(X0),X2),X1) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f38,plain,
! [A,B,C] :
( ~ leq(addition(multiplication(A,B),C),A)
| leq(multiplication(C,star(B)),A) ),
inference(pre_NNF_transformation,[status(esa)],[f16]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ leq(addition(multiplication(X0,X1),X2),X0)
| leq(multiplication(X2,star(X1)),X0) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f40,plain,
? [X0,X1] :
( ~ leq(multiplication(star(multiplication(X0,X1)),X0),multiplication(X0,star(multiplication(X1,X0))))
| ~ leq(multiplication(X0,star(multiplication(X1,X0))),multiplication(star(multiplication(X0,X1)),X0)) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f41,plain,
( ? [X0,X1] : ~ leq(multiplication(star(multiplication(X0,X1)),X0),multiplication(X0,star(multiplication(X1,X0))))
| ? [X0,X1] : ~ leq(multiplication(X0,star(multiplication(X1,X0))),multiplication(star(multiplication(X0,X1)),X0)) ),
inference(miniscoping,[status(esa)],[f40]) ).
fof(f42,plain,
( ~ leq(multiplication(star(multiplication(sk0_0,sk0_1)),sk0_0),multiplication(sk0_0,star(multiplication(sk0_1,sk0_0))))
| ~ leq(multiplication(sk0_2,star(multiplication(sk0_3,sk0_2))),multiplication(star(multiplication(sk0_2,sk0_3)),sk0_2)) ),
inference(skolemization,[status(esa)],[f41]) ).
fof(f43,plain,
( ~ leq(multiplication(star(multiplication(sk0_0,sk0_1)),sk0_0),multiplication(sk0_0,star(multiplication(sk0_1,sk0_0))))
| ~ leq(multiplication(sk0_2,star(multiplication(sk0_3,sk0_2))),multiplication(star(multiplication(sk0_2,sk0_3)),sk0_2)) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f44,plain,
( spl0_0
<=> leq(multiplication(star(multiplication(sk0_0,sk0_1)),sk0_0),multiplication(sk0_0,star(multiplication(sk0_1,sk0_0)))) ),
introduced(split_symbol_definition) ).
fof(f46,plain,
( ~ leq(multiplication(star(multiplication(sk0_0,sk0_1)),sk0_0),multiplication(sk0_0,star(multiplication(sk0_1,sk0_0))))
| spl0_0 ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f47,plain,
( spl0_1
<=> leq(multiplication(sk0_2,star(multiplication(sk0_3,sk0_2))),multiplication(star(multiplication(sk0_2,sk0_3)),sk0_2)) ),
introduced(split_symbol_definition) ).
fof(f49,plain,
( ~ leq(multiplication(sk0_2,star(multiplication(sk0_3,sk0_2))),multiplication(star(multiplication(sk0_2,sk0_3)),sk0_2))
| spl0_1 ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f43,f44,f47]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ~ leq(addition(multiplication(X0,X1),X2),X1)
| addition(multiplication(star(X0),X2),X1) = X1 ),
inference(resolution,[status(thm)],[f37,f32]) ).
fof(f159,plain,
! [X0] : leq(X0,X0),
inference(resolution,[status(thm)],[f22,f33]) ).
fof(f184,plain,
! [X0,X1] :
( ~ leq(multiplication(X0,X1),X0)
| leq(multiplication(multiplication(X0,X1),star(X1)),X0) ),
inference(paramodulation,[status(thm)],[f22,f39]) ).
fof(f185,plain,
! [X0,X1] :
( ~ leq(multiplication(X0,X1),X0)
| leq(multiplication(X0,multiplication(X1,star(X1))),X0) ),
inference(forward_demodulation,[status(thm)],[f23,f184]) ).
fof(f369,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X0)
| addition(multiplication(star(one),X1),X0) = X0 ),
inference(paramodulation,[status(thm)],[f25,f54]) ).
fof(f667,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X1,X0) != X1 ),
inference(paramodulation,[status(thm)],[f19,f33]) ).
fof(f706,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f714,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f715,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f20,f714]) ).
fof(f718,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f723,plain,
! [X0,X1,X2] :
( leq(addition(X0,X1),X2)
| addition(X0,addition(X1,X2)) != X2 ),
inference(paramodulation,[status(thm)],[f20,f33]) ).
fof(f724,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f718,f33]) ).
fof(f733,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f19,f718]) ).
fof(f762,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f19,f724]) ).
fof(f790,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f24,f26]) ).
fof(f802,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f24,f26]) ).
fof(f803,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19,f802]) ).
fof(f836,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f19,f27]) ).
fof(f837,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f27,f836]) ).
fof(f844,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = addition(multiplication(X0,multiplication(X1,X3)),multiplication(X2,X3)),
inference(paramodulation,[status(thm)],[f23,f27]) ).
fof(f852,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f853,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19,f852]) ).
fof(f854,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),X3) = addition(multiplication(X0,X3),multiplication(X1,multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f23,f27]) ).
fof(f881,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f27,f762]) ).
fof(f893,plain,
! [X0] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f34,f32]) ).
fof(f894,plain,
! [X0] : addition(one,addition(multiplication(X0,star(X0)),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f20,f893]) ).
fof(f895,plain,
! [X0] : addition(one,addition(star(X0),multiplication(X0,star(X0)))) = star(X0),
inference(forward_demodulation,[status(thm)],[f19,f894]) ).
fof(f896,plain,
! [X0] : addition(one,multiplication(addition(X0,one),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f853,f895]) ).
fof(f901,plain,
( ~ leq(addition(multiplication(multiplication(sk0_0,sk0_1),multiplication(sk0_0,star(multiplication(sk0_1,sk0_0)))),sk0_0),multiplication(sk0_0,star(multiplication(sk0_1,sk0_0))))
| spl0_0 ),
inference(resolution,[status(thm)],[f46,f37]) ).
fof(f902,plain,
( ~ leq(addition(sk0_0,multiplication(multiplication(sk0_0,sk0_1),multiplication(sk0_0,star(multiplication(sk0_1,sk0_0))))),multiplication(sk0_0,star(multiplication(sk0_1,sk0_0))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f19,f901]) ).
fof(f903,plain,
( ~ leq(addition(sk0_0,multiplication(sk0_0,multiplication(sk0_1,multiplication(sk0_0,star(multiplication(sk0_1,sk0_0)))))),multiplication(sk0_0,star(multiplication(sk0_1,sk0_0))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f23,f902]) ).
fof(f905,plain,
( addition(multiplication(sk0_0,star(multiplication(sk0_1,sk0_0))),addition(sk0_0,multiplication(sk0_0,multiplication(sk0_1,multiplication(sk0_0,star(multiplication(sk0_1,sk0_0))))))) != multiplication(sk0_0,star(multiplication(sk0_1,sk0_0)))
| spl0_0 ),
inference(resolution,[status(thm)],[f903,f667]) ).
fof(f906,plain,
( addition(sk0_0,addition(multiplication(sk0_0,star(multiplication(sk0_1,sk0_0))),multiplication(sk0_0,multiplication(sk0_1,multiplication(sk0_0,star(multiplication(sk0_1,sk0_0))))))) != multiplication(sk0_0,star(multiplication(sk0_1,sk0_0)))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f715,f905]) ).
fof(f907,plain,
( addition(sk0_0,multiplication(sk0_0,addition(star(multiplication(sk0_1,sk0_0)),multiplication(sk0_1,multiplication(sk0_0,star(multiplication(sk0_1,sk0_0))))))) != multiplication(sk0_0,star(multiplication(sk0_1,sk0_0)))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f26,f906]) ).
fof(f913,plain,
! [X0,X1] : leq(X0,multiplication(addition(X1,one),X0)),
inference(paramodulation,[status(thm)],[f25,f881]) ).
fof(f951,plain,
! [X0] :
( ~ leq(multiplication(X0,one),X0)
| leq(multiplication(X0,star(one)),X0) ),
inference(paramodulation,[status(thm)],[f25,f185]) ).
fof(f952,plain,
! [X0] :
( ~ leq(X0,X0)
| leq(multiplication(X0,star(one)),X0) ),
inference(forward_demodulation,[status(thm)],[f24,f951]) ).
fof(f953,plain,
! [X0] : leq(multiplication(X0,star(one)),X0),
inference(forward_subsumption_resolution,[status(thm)],[f952,f159]) ).
fof(f958,plain,
! [X0] : addition(multiplication(X0,star(one)),X0) = X0,
inference(resolution,[status(thm)],[f953,f32]) ).
fof(f959,plain,
! [X0] : addition(X0,multiplication(X0,star(one))) = X0,
inference(forward_demodulation,[status(thm)],[f19,f958]) ).
fof(f969,plain,
! [X0,X1] : leq(X0,multiplication(addition(one,X1),X0)),
inference(paramodulation,[status(thm)],[f19,f913]) ).
fof(f977,plain,
addition(one,star(one)) = one,
inference(paramodulation,[status(thm)],[f25,f959]) ).
fof(f980,plain,
leq(one,star(one)),
inference(paramodulation,[status(thm)],[f959,f34]) ).
fof(f1033,plain,
addition(one,star(one)) = star(one),
inference(resolution,[status(thm)],[f980,f32]) ).
fof(f1034,plain,
one = star(one),
inference(forward_demodulation,[status(thm)],[f977,f1033]) ).
fof(f1070,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X0)
| addition(multiplication(one,X1),X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f1034,f369]) ).
fof(f1071,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X0)
| addition(X1,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f25,f1070]) ).
fof(f1146,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X0)
| addition(addition(X0,X1),X0) = X0 ),
inference(paramodulation,[status(thm)],[f718,f1071]) ).
fof(f1147,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X0)
| addition(X0,addition(X1,X0)) = X0 ),
inference(forward_demodulation,[status(thm)],[f20,f1146]) ).
fof(f1148,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X0)
| addition(X0,X1) = X0 ),
inference(forward_demodulation,[status(thm)],[f733,f1147]) ).
fof(f1165,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X1)
| addition(X1,X0) = X1 ),
inference(paramodulation,[status(thm)],[f19,f1148]) ).
fof(f1279,plain,
! [X0,X1] : leq(X0,multiplication(star(X1),X0)),
inference(paramodulation,[status(thm)],[f896,f969]) ).
fof(f1282,plain,
! [X0] :
( ~ leq(star(X0),multiplication(addition(X0,one),star(X0)))
| addition(multiplication(addition(X0,one),star(X0)),one) = multiplication(addition(X0,one),star(X0)) ),
inference(paramodulation,[status(thm)],[f896,f1165]) ).
fof(f1283,plain,
! [X0] :
( ~ leq(star(X0),multiplication(addition(X0,one),star(X0)))
| addition(one,multiplication(addition(X0,one),star(X0))) = multiplication(addition(X0,one),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f19,f1282]) ).
fof(f1284,plain,
! [X0] :
( ~ leq(star(X0),multiplication(addition(X0,one),star(X0)))
| star(X0) = multiplication(addition(X0,one),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f896,f1283]) ).
fof(f1285,plain,
! [X0] : star(X0) = multiplication(addition(X0,one),star(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f1284,f913]) ).
fof(f1304,plain,
! [X0] : addition(one,star(X0)) = addition(one,multiplication(addition(X0,one),star(X0))),
inference(paramodulation,[status(thm)],[f896,f718]) ).
fof(f1305,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f896,f1304]) ).
fof(f1306,plain,
! [X0,X1] : addition(one,addition(multiplication(addition(X0,one),star(X0)),X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f896,f20]) ).
fof(f1307,plain,
! [X0,X1] : addition(one,addition(star(X0),X1)) = addition(star(X0),X1),
inference(forward_demodulation,[status(thm)],[f1285,f1306]) ).
fof(f1315,plain,
! [X0,X1] : addition(X0,multiplication(star(X1),X0)) = multiplication(star(X1),X0),
inference(resolution,[status(thm)],[f1279,f32]) ).
fof(f1343,plain,
! [X0] : star(X0) = multiplication(addition(one,X0),star(X0)),
inference(paramodulation,[status(thm)],[f19,f1285]) ).
fof(f1375,plain,
! [X0,X1] : multiplication(addition(X0,addition(X1,one)),star(X1)) = addition(multiplication(X0,star(X1)),star(X1)),
inference(paramodulation,[status(thm)],[f1285,f27]) ).
fof(f1376,plain,
! [X0,X1] : multiplication(addition(X0,addition(X1,one)),star(X1)) = addition(star(X1),multiplication(X0,star(X1))),
inference(forward_demodulation,[status(thm)],[f19,f1375]) ).
fof(f1377,plain,
! [X0,X1] : multiplication(addition(X0,addition(X1,one)),star(X1)) = multiplication(addition(X0,one),star(X1)),
inference(forward_demodulation,[status(thm)],[f853,f1376]) ).
fof(f1504,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(star(X1),X0),X2)) = addition(multiplication(star(X1),X0),X2),
inference(paramodulation,[status(thm)],[f1315,f20]) ).
fof(f1514,plain,
! [X0,X1] : addition(one,addition(X0,star(X1))) = addition(star(X1),X0),
inference(paramodulation,[status(thm)],[f19,f1307]) ).
fof(f1658,plain,
! [X0,X1,X2] :
( leq(addition(X0,X1),X2)
| addition(X1,addition(X0,X2)) != X2 ),
inference(paramodulation,[status(thm)],[f19,f723]) ).
fof(f2314,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),addition(X2,one)),star(X2)) = addition(multiplication(X0,multiplication(X1,star(X2))),star(X2)),
inference(paramodulation,[status(thm)],[f1285,f844]) ).
fof(f2315,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),one),star(X2)) = addition(multiplication(X0,multiplication(X1,star(X2))),star(X2)),
inference(forward_demodulation,[status(thm)],[f1377,f2314]) ).
fof(f2316,plain,
! [X0,X1,X2] : multiplication(addition(one,multiplication(X0,X1)),star(X2)) = addition(multiplication(X0,multiplication(X1,star(X2))),star(X2)),
inference(forward_demodulation,[status(thm)],[f837,f2315]) ).
fof(f2317,plain,
! [X0,X1,X2] : multiplication(addition(one,multiplication(X0,X1)),star(X2)) = addition(star(X2),multiplication(X0,multiplication(X1,star(X2)))),
inference(forward_demodulation,[status(thm)],[f19,f2316]) ).
fof(f2393,plain,
( addition(sk0_0,multiplication(sk0_0,multiplication(addition(one,multiplication(sk0_1,sk0_0)),star(multiplication(sk0_1,sk0_0))))) != multiplication(sk0_0,star(multiplication(sk0_1,sk0_0)))
| spl0_0 ),
inference(backward_demodulation,[status(thm)],[f2317,f907]) ).
fof(f2394,plain,
( addition(sk0_0,multiplication(sk0_0,star(multiplication(sk0_1,sk0_0)))) != multiplication(sk0_0,star(multiplication(sk0_1,sk0_0)))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f1343,f2393]) ).
fof(f2649,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f733,f20]) ).
fof(f2650,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f20,f2649]) ).
fof(f2651,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f20,f2650]) ).
fof(f2833,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f706,f718]) ).
fof(f2834,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f2651,f2833]) ).
fof(f4270,plain,
! [X0] : addition(addition(one,multiplication(star(X0),X0)),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f35,f32]) ).
fof(f4271,plain,
! [X0] : addition(one,addition(multiplication(star(X0),X0),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f20,f4270]) ).
fof(f4272,plain,
! [X0] : addition(star(X0),multiplication(star(X0),X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f1514,f4271]) ).
fof(f4273,plain,
! [X0] : multiplication(star(X0),addition(X0,one)) = star(X0),
inference(forward_demodulation,[status(thm)],[f803,f4272]) ).
fof(f4386,plain,
! [X0,X1] : multiplication(star(X0),multiplication(addition(X0,one),X1)) = multiplication(star(X0),X1),
inference(paramodulation,[status(thm)],[f4273,f23]) ).
fof(f4542,plain,
! [X0,X1] : multiplication(X0,star(X1)) = addition(X0,multiplication(X0,star(X1))),
inference(paramodulation,[status(thm)],[f1305,f790]) ).
fof(f4666,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(one,X1),X2)) = multiplication(addition(X0,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f790,f23]) ).
fof(f4792,plain,
( multiplication(sk0_0,star(multiplication(sk0_1,sk0_0))) != multiplication(sk0_0,star(multiplication(sk0_1,sk0_0)))
| spl0_0 ),
inference(backward_demodulation,[status(thm)],[f4542,f2394]) ).
fof(f4793,plain,
( $false
| spl0_0 ),
inference(trivial_equality_resolution,[status(esa)],[f4792]) ).
fof(f4794,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f4793]) ).
fof(f19688,plain,
! [X0,X1] : multiplication(star(X0),multiplication(addition(one,X0),X1)) = multiplication(star(X0),X1),
inference(paramodulation,[status(thm)],[f837,f4386]) ).
fof(f36248,plain,
! [X0,X1,X2] :
( addition(X0,addition(multiplication(X1,X2),X1)) != X1
| leq(multiplication(X0,star(X2)),X1) ),
inference(resolution,[status(thm)],[f1658,f39]) ).
fof(f36249,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,multiplication(X1,X2))) != X1
| leq(multiplication(X0,star(X2)),X1) ),
inference(forward_demodulation,[status(thm)],[f2834,f36248]) ).
fof(f38983,plain,
( addition(sk0_2,addition(multiplication(star(multiplication(sk0_2,sk0_3)),sk0_2),multiplication(multiplication(star(multiplication(sk0_2,sk0_3)),sk0_2),multiplication(sk0_3,sk0_2)))) != multiplication(star(multiplication(sk0_2,sk0_3)),sk0_2)
| spl0_1 ),
inference(resolution,[status(thm)],[f36249,f49]) ).
fof(f38984,plain,
( addition(multiplication(star(multiplication(sk0_2,sk0_3)),sk0_2),multiplication(multiplication(star(multiplication(sk0_2,sk0_3)),sk0_2),multiplication(sk0_3,sk0_2))) != multiplication(star(multiplication(sk0_2,sk0_3)),sk0_2)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f1504,f38983]) ).
fof(f38985,plain,
( multiplication(addition(star(multiplication(sk0_2,sk0_3)),multiplication(multiplication(star(multiplication(sk0_2,sk0_3)),sk0_2),sk0_3)),sk0_2) != multiplication(star(multiplication(sk0_2,sk0_3)),sk0_2)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f854,f38984]) ).
fof(f38986,plain,
( multiplication(addition(star(multiplication(sk0_2,sk0_3)),multiplication(star(multiplication(sk0_2,sk0_3)),multiplication(sk0_2,sk0_3))),sk0_2) != multiplication(star(multiplication(sk0_2,sk0_3)),sk0_2)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f23,f38985]) ).
fof(f38987,plain,
( multiplication(star(multiplication(sk0_2,sk0_3)),multiplication(addition(one,multiplication(sk0_2,sk0_3)),sk0_2)) != multiplication(star(multiplication(sk0_2,sk0_3)),sk0_2)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f4666,f38986]) ).
fof(f38988,plain,
( multiplication(star(multiplication(sk0_2,sk0_3)),sk0_2) != multiplication(star(multiplication(sk0_2,sk0_3)),sk0_2)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f19688,f38987]) ).
fof(f38989,plain,
( $false
| spl0_1 ),
inference(trivial_equality_resolution,[status(esa)],[f38988]) ).
fof(f38990,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f38989]) ).
fof(f38991,plain,
$false,
inference(sat_refutation,[status(thm)],[f50,f4794,f38990]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : KLE042+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.08 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.08/0.27 % Computer : n032.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 300
% 0.08/0.27 % DateTime : Tue May 30 11:48:46 EDT 2023
% 0.08/0.27 % CPUTime :
% 0.08/0.28 % Drodi V3.5.1
% 58.33/7.73 % Refutation found
% 58.33/7.73 % SZS status Theorem for theBenchmark: Theorem is valid
% 58.33/7.73 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 60.00/7.92 % Elapsed time: 7.622171 seconds
% 60.00/7.92 % CPU time: 59.803158 seconds
% 60.00/7.92 % Memory used: 459.587 MB
%------------------------------------------------------------------------------