TSTP Solution File: KLE160+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE160+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n031.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 12:15:57 EDT 2023
% Result : Theorem 164.37s 21.13s
% Output : CNFRefutation 167.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 17
% Syntax : Number of formulae : 152 ( 103 unt; 0 def)
% Number of atoms : 205 ( 118 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 113 ( 60 ~; 43 |; 4 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 230 (; 227 !; 3 ?)
% 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(f3,axiom,
! [A] : addition(A,zero) = A,
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(f10,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] : addition(one,multiplication(A,star(A))) = star(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A] : addition(one,multiplication(star(A),A)) = star(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,C),B),C)
=> leq(multiplication(star(A),B),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A,B,C] :
( leq(addition(multiplication(C,A),B),C)
=> leq(multiplication(B,star(A)),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
! [X0,X1,X2] :
( leq(multiplication(X0,X1),multiplication(X1,X2))
=> leq(multiplication(star(X0),X1),multiplication(X1,star(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0,X1,X2] :
( leq(multiplication(X0,X1),multiplication(X1,X2))
=> leq(multiplication(star(X0),X1),multiplication(X1,star(X2))) ),
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(f23,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f24,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f25,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f5]) ).
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(f30,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f31,plain,
! [X0] : addition(one,multiplication(X0,star(X0))) = star(X0),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f32,plain,
! [X0] : addition(one,multiplication(star(X0),X0)) = star(X0),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f33,plain,
! [A,B,C] :
( ~ leq(addition(multiplication(A,C),B),C)
| leq(multiplication(star(A),B),C) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ leq(addition(multiplication(X0,X1),X2),X1)
| leq(multiplication(star(X0),X2),X1) ),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f35,plain,
! [A,B,C] :
( ~ leq(addition(multiplication(C,A),B),C)
| leq(multiplication(B,star(A)),C) ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ~ leq(addition(multiplication(X0,X1),X2),X0)
| leq(multiplication(X2,star(X1)),X0) ),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f41,plain,
! [A,B] :
( ( ~ leq(A,B)
| addition(A,B) = B )
& ( leq(A,B)
| addition(A,B) != B ) ),
inference(NNF_transformation,[status(esa)],[f18]) ).
fof(f42,plain,
( ! [A,B] :
( ~ leq(A,B)
| addition(A,B) = B )
& ! [A,B] :
( leq(A,B)
| addition(A,B) != B ) ),
inference(miniscoping,[status(esa)],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f45,plain,
? [X0,X1,X2] :
( leq(multiplication(X0,X1),multiplication(X1,X2))
& ~ leq(multiplication(star(X0),X1),multiplication(X1,star(X2))) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f46,plain,
( leq(multiplication(sk0_0,sk0_1),multiplication(sk0_1,sk0_2))
& ~ leq(multiplication(star(sk0_0),sk0_1),multiplication(sk0_1,star(sk0_2))) ),
inference(skolemization,[status(esa)],[f45]) ).
fof(f47,plain,
leq(multiplication(sk0_0,sk0_1),multiplication(sk0_1,sk0_2)),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f48,plain,
~ leq(multiplication(star(sk0_0),sk0_1),multiplication(sk0_1,star(sk0_2))),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f49,plain,
addition(multiplication(sk0_0,sk0_1),multiplication(sk0_1,sk0_2)) = multiplication(sk0_1,sk0_2),
inference(resolution,[status(thm)],[f43,f47]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ~ leq(addition(multiplication(X0,X1),X2),X1)
| addition(multiplication(star(X0),X2),X1) = X1 ),
inference(resolution,[status(thm)],[f34,f43]) ).
fof(f197,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f23,f21]) ).
fof(f214,plain,
! [X0,X1,X2] :
( ~ leq(addition(X0,multiplication(X1,X2)),X2)
| addition(multiplication(star(X1),X0),X2) = X2 ),
inference(paramodulation,[status(thm)],[f21,f55]) ).
fof(f238,plain,
addition(one,zero) = star(zero),
inference(paramodulation,[status(thm)],[f30,f31]) ).
fof(f239,plain,
one = star(zero),
inference(forward_demodulation,[status(thm)],[f23,f238]) ).
fof(f258,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f21,f22]) ).
fof(f267,plain,
! [X0] : addition(multiplication(sk0_0,sk0_1),addition(multiplication(sk0_1,sk0_2),X0)) = addition(multiplication(sk0_1,sk0_2),X0),
inference(paramodulation,[status(thm)],[f49,f22]) ).
fof(f269,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f21,f22]) ).
fof(f270,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f22,f269]) ).
fof(f273,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f278,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f21,f28]) ).
fof(f279,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f28,f278]) ).
fof(f292,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f302,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f303,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f21,f302]) ).
fof(f320,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f21,f29]) ).
fof(f321,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f29,f320]) ).
fof(f327,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f27,f29]) ).
fof(f328,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)],[f25,f29]) ).
fof(f347,plain,
! [X0,X1,X2] :
( ~ leq(multiplication(addition(X0,X1),X2),X2)
| addition(multiplication(star(X0),multiplication(X1,X2)),X2) = X2 ),
inference(paramodulation,[status(thm)],[f29,f55]) ).
fof(f348,plain,
! [X0,X1,X2] :
( ~ leq(multiplication(addition(X0,X1),X2),X2)
| addition(X2,multiplication(star(X0),multiplication(X1,X2))) = X2 ),
inference(forward_demodulation,[status(thm)],[f21,f347]) ).
fof(f366,plain,
! [X0] : addition(multiplication(sk0_0,sk0_1),multiplication(sk0_1,addition(sk0_2,X0))) = addition(multiplication(sk0_1,sk0_2),multiplication(sk0_1,X0)),
inference(paramodulation,[status(thm)],[f28,f267]) ).
fof(f367,plain,
! [X0] : addition(multiplication(sk0_0,sk0_1),multiplication(sk0_1,addition(sk0_2,X0))) = multiplication(sk0_1,addition(sk0_2,X0)),
inference(forward_demodulation,[status(thm)],[f28,f366]) ).
fof(f1146,plain,
! [X0] : addition(one,star(X0)) = addition(one,multiplication(X0,star(X0))),
inference(paramodulation,[status(thm)],[f31,f273]) ).
fof(f1147,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f31,f1146]) ).
fof(f1162,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f21,f273]) ).
fof(f1243,plain,
! [X0] : addition(multiplication(X0,star(X0)),star(X0)) = addition(multiplication(X0,star(X0)),one),
inference(paramodulation,[status(thm)],[f31,f1162]) ).
fof(f1244,plain,
! [X0] : addition(star(X0),multiplication(X0,star(X0))) = addition(multiplication(X0,star(X0)),one),
inference(forward_demodulation,[status(thm)],[f21,f1243]) ).
fof(f1245,plain,
! [X0] : addition(star(X0),multiplication(X0,star(X0))) = addition(one,multiplication(X0,star(X0))),
inference(forward_demodulation,[status(thm)],[f21,f1244]) ).
fof(f1246,plain,
! [X0] : addition(star(X0),multiplication(X0,star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f31,f1245]) ).
fof(f1368,plain,
! [X0] : addition(multiplication(star(X0),X0),star(X0)) = addition(multiplication(star(X0),X0),one),
inference(paramodulation,[status(thm)],[f32,f1162]) ).
fof(f1369,plain,
! [X0] : addition(star(X0),multiplication(star(X0),X0)) = addition(multiplication(star(X0),X0),one),
inference(forward_demodulation,[status(thm)],[f21,f1368]) ).
fof(f1370,plain,
! [X0] : addition(star(X0),multiplication(star(X0),X0)) = addition(one,multiplication(star(X0),X0)),
inference(forward_demodulation,[status(thm)],[f21,f1369]) ).
fof(f1371,plain,
! [X0] : addition(star(X0),multiplication(star(X0),X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f32,f1370]) ).
fof(f1434,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f1162,f258]) ).
fof(f1435,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f22,f1434]) ).
fof(f1436,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f1162,f1435]) ).
fof(f1791,plain,
! [X0] :
( ~ leq(star(X0),star(X0))
| addition(multiplication(star(X0),star(X0)),star(X0)) = star(X0) ),
inference(paramodulation,[status(thm)],[f1246,f214]) ).
fof(f1792,plain,
! [X0] :
( ~ leq(star(X0),star(X0))
| addition(star(X0),multiplication(star(X0),star(X0))) = star(X0) ),
inference(forward_demodulation,[status(thm)],[f21,f1791]) ).
fof(f3188,plain,
! [X0,X1] :
( ~ leq(multiplication(X0,X1),X1)
| addition(X1,multiplication(star(zero),multiplication(X0,X1))) = X1 ),
inference(paramodulation,[status(thm)],[f197,f348]) ).
fof(f3189,plain,
! [X0,X1] :
( ~ leq(multiplication(X0,X1),X1)
| addition(X1,multiplication(one,multiplication(X0,X1))) = X1 ),
inference(forward_demodulation,[status(thm)],[f239,f3188]) ).
fof(f3190,plain,
! [X0,X1] :
( ~ leq(multiplication(X0,X1),X1)
| addition(X1,multiplication(X0,X1)) = X1 ),
inference(forward_demodulation,[status(thm)],[f27,f3189]) ).
fof(f3228,plain,
! [X0,X1] :
( addition(X0,multiplication(star(X1),X0)) = X0
| ~ leq(addition(multiplication(X1,X0),X0),X0) ),
inference(resolution,[status(thm)],[f3190,f34]) ).
fof(f3229,plain,
! [X0,X1] :
( addition(X0,multiplication(star(X1),X0)) = X0
| ~ leq(addition(X0,multiplication(X1,X0)),X0) ),
inference(forward_demodulation,[status(thm)],[f21,f3228]) ).
fof(f5088,plain,
! [X0] :
( addition(star(X0),multiplication(star(X0),star(X0))) = star(X0)
| addition(star(X0),star(X0)) != star(X0) ),
inference(resolution,[status(thm)],[f1792,f44]) ).
fof(f5089,plain,
! [X0] :
( addition(star(X0),multiplication(star(X0),star(X0))) = star(X0)
| star(X0) != star(X0) ),
inference(forward_demodulation,[status(thm)],[f24,f5088]) ).
fof(f5090,plain,
! [X0] : addition(star(X0),multiplication(star(X0),star(X0))) = star(X0),
inference(trivial_equality_resolution,[status(esa)],[f5089]) ).
fof(f5556,plain,
! [X0] : multiplication(star(X0),addition(star(X0),one)) = star(X0),
inference(paramodulation,[status(thm)],[f5090,f303]) ).
fof(f5557,plain,
! [X0] : multiplication(star(X0),addition(one,star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f21,f5556]) ).
fof(f5558,plain,
! [X0] : multiplication(star(X0),star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f1147,f5557]) ).
fof(f5559,plain,
! [X0] : multiplication(star(X0),addition(X0,one)) = star(X0),
inference(paramodulation,[status(thm)],[f1371,f303]) ).
fof(f5934,plain,
! [X0,X1] : multiplication(star(X0),multiplication(star(X0),X1)) = multiplication(star(X0),X1),
inference(paramodulation,[status(thm)],[f5558,f25]) ).
fof(f5940,plain,
! [X0] : multiplication(star(X0),addition(one,X0)) = star(X0),
inference(paramodulation,[status(thm)],[f21,f5559]) ).
fof(f8533,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(X1,multiplication(multiplication(star(X0),X0),X1)),
inference(paramodulation,[status(thm)],[f32,f327]) ).
fof(f8534,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(X1,multiplication(star(X0),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f25,f8533]) ).
fof(f8577,plain,
! [X0] : multiplication(addition(one,star(X0)),addition(X0,one)) = addition(addition(X0,one),star(X0)),
inference(paramodulation,[status(thm)],[f5559,f327]) ).
fof(f8578,plain,
! [X0] : multiplication(star(X0),addition(X0,one)) = addition(addition(X0,one),star(X0)),
inference(forward_demodulation,[status(thm)],[f1147,f8577]) ).
fof(f8579,plain,
! [X0] : star(X0) = addition(addition(X0,one),star(X0)),
inference(forward_demodulation,[status(thm)],[f5559,f8578]) ).
fof(f8580,plain,
! [X0] : star(X0) = addition(X0,addition(one,star(X0))),
inference(forward_demodulation,[status(thm)],[f22,f8579]) ).
fof(f8581,plain,
! [X0] : star(X0) = addition(X0,star(X0)),
inference(forward_demodulation,[status(thm)],[f1147,f8580]) ).
fof(f8766,plain,
addition(multiplication(sk0_0,sk0_1),multiplication(sk0_1,star(sk0_2))) = multiplication(sk0_1,addition(sk0_2,star(sk0_2))),
inference(paramodulation,[status(thm)],[f8581,f367]) ).
fof(f8767,plain,
addition(multiplication(sk0_0,sk0_1),multiplication(sk0_1,star(sk0_2))) = multiplication(sk0_1,star(sk0_2)),
inference(forward_demodulation,[status(thm)],[f8581,f8766]) ).
fof(f10602,plain,
( spl0_173
<=> leq(multiplication(sk0_1,star(sk0_2)),multiplication(sk0_1,star(sk0_2))) ),
introduced(split_symbol_definition) ).
fof(f10603,plain,
( leq(multiplication(sk0_1,star(sk0_2)),multiplication(sk0_1,star(sk0_2)))
| ~ spl0_173 ),
inference(component_clause,[status(thm)],[f10602]) ).
fof(f10604,plain,
( ~ leq(multiplication(sk0_1,star(sk0_2)),multiplication(sk0_1,star(sk0_2)))
| spl0_173 ),
inference(component_clause,[status(thm)],[f10602]) ).
fof(f11104,plain,
! [X0,X1] : addition(X0,multiplication(star(X1),X0)) = addition(X0,multiplication(star(X1),multiplication(X1,X0))),
inference(paramodulation,[status(thm)],[f8534,f273]) ).
fof(f11105,plain,
! [X0,X1] : addition(X0,multiplication(star(X1),X0)) = multiplication(star(X1),X0),
inference(forward_demodulation,[status(thm)],[f8534,f11104]) ).
fof(f11150,plain,
! [X0,X1] :
( multiplication(star(X0),X1) = X1
| ~ leq(addition(X1,multiplication(X0,X1)),X1) ),
inference(backward_demodulation,[status(thm)],[f11105,f3229]) ).
fof(f11245,plain,
! [X0] : multiplication(star(multiplication(star(X0),one)),multiplication(star(X0),one)) = star(multiplication(star(X0),one)),
inference(paramodulation,[status(thm)],[f11105,f5940]) ).
fof(f11246,plain,
! [X0] : multiplication(star(star(X0)),multiplication(star(X0),one)) = star(multiplication(star(X0),one)),
inference(forward_demodulation,[status(thm)],[f26,f11245]) ).
fof(f11247,plain,
! [X0] : multiplication(star(star(X0)),star(X0)) = star(multiplication(star(X0),one)),
inference(forward_demodulation,[status(thm)],[f26,f11246]) ).
fof(f11248,plain,
! [X0] : multiplication(star(star(X0)),star(X0)) = star(star(X0)),
inference(forward_demodulation,[status(thm)],[f26,f11247]) ).
fof(f11249,plain,
! [X0,X1] : multiplication(X0,multiplication(star(X1),one)) = addition(X0,multiplication(X0,multiplication(star(X1),one))),
inference(paramodulation,[status(thm)],[f11105,f292]) ).
fof(f11250,plain,
! [X0,X1] : multiplication(X0,star(X1)) = addition(X0,multiplication(X0,multiplication(star(X1),one))),
inference(forward_demodulation,[status(thm)],[f26,f11249]) ).
fof(f11251,plain,
! [X0,X1] : multiplication(X0,star(X1)) = addition(X0,multiplication(X0,star(X1))),
inference(forward_demodulation,[status(thm)],[f26,f11250]) ).
fof(f11790,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,star(X2)))) = addition(X1,multiplication(X0,star(X2))),
inference(paramodulation,[status(thm)],[f11251,f270]) ).
fof(f11827,plain,
! [X0] :
( multiplication(star(star(X0)),star(X0)) = star(X0)
| ~ leq(multiplication(star(X0),star(X0)),star(X0)) ),
inference(paramodulation,[status(thm)],[f11251,f11150]) ).
fof(f11828,plain,
! [X0] :
( star(star(X0)) = star(X0)
| ~ leq(multiplication(star(X0),star(X0)),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f11248,f11827]) ).
fof(f11829,plain,
! [X0] :
( star(star(X0)) = star(X0)
| ~ leq(star(X0),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f5558,f11828]) ).
fof(f11901,plain,
! [X0] :
( star(star(X0)) = star(X0)
| addition(star(X0),star(X0)) != star(X0) ),
inference(resolution,[status(thm)],[f11829,f44]) ).
fof(f11902,plain,
! [X0] :
( star(star(X0)) = star(X0)
| star(X0) != star(X0) ),
inference(forward_demodulation,[status(thm)],[f24,f11901]) ).
fof(f11903,plain,
! [X0] : star(star(X0)) = star(X0),
inference(trivial_equality_resolution,[status(esa)],[f11902]) ).
fof(f12150,plain,
! [X0,X1,X2] :
( ~ leq(addition(multiplication(X0,star(X1)),X2),X0)
| leq(multiplication(X2,star(X1)),X0) ),
inference(paramodulation,[status(thm)],[f11903,f36]) ).
fof(f12151,plain,
! [X0,X1,X2] :
( ~ leq(addition(multiplication(star(X0),X1),X2),X1)
| leq(multiplication(star(X0),X2),X1) ),
inference(paramodulation,[status(thm)],[f11903,f34]) ).
fof(f13686,plain,
( addition(multiplication(sk0_1,star(sk0_2)),multiplication(sk0_1,star(sk0_2))) != multiplication(sk0_1,star(sk0_2))
| spl0_173 ),
inference(resolution,[status(thm)],[f10604,f44]) ).
fof(f13687,plain,
( multiplication(addition(sk0_1,sk0_1),star(sk0_2)) != multiplication(sk0_1,star(sk0_2))
| spl0_173 ),
inference(forward_demodulation,[status(thm)],[f29,f13686]) ).
fof(f13688,plain,
( multiplication(sk0_1,star(sk0_2)) != multiplication(sk0_1,star(sk0_2))
| spl0_173 ),
inference(forward_demodulation,[status(thm)],[f24,f13687]) ).
fof(f13689,plain,
( $false
| spl0_173 ),
inference(trivial_equality_resolution,[status(esa)],[f13688]) ).
fof(f13690,plain,
spl0_173,
inference(contradiction_clause,[status(thm)],[f13689]) ).
fof(f52273,plain,
! [X0,X1,X2] :
( ~ leq(multiplication(addition(X0,X1),star(X2)),X0)
| leq(multiplication(multiplication(X1,star(X2)),star(X2)),X0) ),
inference(paramodulation,[status(thm)],[f29,f12150]) ).
fof(f52274,plain,
! [X0,X1,X2] :
( ~ leq(multiplication(addition(X0,X1),star(X2)),X0)
| leq(multiplication(X1,multiplication(star(X2),star(X2))),X0) ),
inference(forward_demodulation,[status(thm)],[f25,f52273]) ).
fof(f52275,plain,
! [X0,X1,X2] :
( ~ leq(multiplication(addition(X0,X1),star(X2)),X0)
| leq(multiplication(X1,star(X2)),X0) ),
inference(forward_demodulation,[status(thm)],[f5558,f52274]) ).
fof(f52384,plain,
! [X0,X1,X2] :
( ~ leq(multiplication(star(X0),addition(X1,X2)),X1)
| leq(multiplication(star(X0),multiplication(star(X0),X2)),X1) ),
inference(paramodulation,[status(thm)],[f28,f12151]) ).
fof(f52385,plain,
! [X0,X1,X2] :
( ~ leq(multiplication(star(X0),addition(X1,X2)),X1)
| leq(multiplication(star(X0),X2),X1) ),
inference(forward_demodulation,[status(thm)],[f5934,f52384]) ).
fof(f70853,plain,
~ leq(multiplication(star(sk0_0),addition(multiplication(sk0_1,star(sk0_2)),sk0_1)),multiplication(sk0_1,star(sk0_2))),
inference(resolution,[status(thm)],[f52385,f48]) ).
fof(f70854,plain,
~ leq(multiplication(star(sk0_0),addition(sk0_1,multiplication(sk0_1,star(sk0_2)))),multiplication(sk0_1,star(sk0_2))),
inference(forward_demodulation,[status(thm)],[f279,f70853]) ).
fof(f70855,plain,
~ leq(multiplication(star(sk0_0),multiplication(sk0_1,star(sk0_2))),multiplication(sk0_1,star(sk0_2))),
inference(forward_demodulation,[status(thm)],[f11251,f70854]) ).
fof(f74852,plain,
~ leq(addition(multiplication(sk0_0,multiplication(sk0_1,star(sk0_2))),multiplication(sk0_1,star(sk0_2))),multiplication(sk0_1,star(sk0_2))),
inference(resolution,[status(thm)],[f70855,f34]) ).
fof(f74853,plain,
~ leq(multiplication(addition(multiplication(sk0_0,sk0_1),sk0_1),star(sk0_2)),multiplication(sk0_1,star(sk0_2))),
inference(forward_demodulation,[status(thm)],[f328,f74852]) ).
fof(f74854,plain,
~ leq(multiplication(addition(sk0_1,multiplication(sk0_0,sk0_1)),star(sk0_2)),multiplication(sk0_1,star(sk0_2))),
inference(forward_demodulation,[status(thm)],[f321,f74853]) ).
fof(f74867,plain,
~ leq(multiplication(addition(multiplication(sk0_1,star(sk0_2)),addition(sk0_1,multiplication(sk0_0,sk0_1))),star(sk0_2)),multiplication(sk0_1,star(sk0_2))),
inference(resolution,[status(thm)],[f74854,f52275]) ).
fof(f74868,plain,
~ leq(multiplication(addition(multiplication(sk0_0,sk0_1),addition(sk0_1,multiplication(sk0_1,star(sk0_2)))),star(sk0_2)),multiplication(sk0_1,star(sk0_2))),
inference(forward_demodulation,[status(thm)],[f1436,f74867]) ).
fof(f74869,plain,
~ leq(multiplication(addition(sk0_1,addition(multiplication(sk0_0,sk0_1),multiplication(sk0_1,star(sk0_2)))),star(sk0_2)),multiplication(sk0_1,star(sk0_2))),
inference(forward_demodulation,[status(thm)],[f270,f74868]) ).
fof(f74870,plain,
~ leq(multiplication(addition(multiplication(sk0_0,sk0_1),multiplication(sk0_1,star(sk0_2))),star(sk0_2)),multiplication(sk0_1,star(sk0_2))),
inference(forward_demodulation,[status(thm)],[f11790,f74869]) ).
fof(f74871,plain,
~ leq(multiplication(multiplication(sk0_1,star(sk0_2)),star(sk0_2)),multiplication(sk0_1,star(sk0_2))),
inference(forward_demodulation,[status(thm)],[f8767,f74870]) ).
fof(f74872,plain,
~ leq(multiplication(sk0_1,multiplication(star(sk0_2),star(sk0_2))),multiplication(sk0_1,star(sk0_2))),
inference(forward_demodulation,[status(thm)],[f25,f74871]) ).
fof(f74873,plain,
~ leq(multiplication(sk0_1,star(sk0_2)),multiplication(sk0_1,star(sk0_2))),
inference(forward_demodulation,[status(thm)],[f5558,f74872]) ).
fof(f74874,plain,
( $false
| ~ spl0_173 ),
inference(forward_subsumption_resolution,[status(thm)],[f74873,f10603]) ).
fof(f74875,plain,
~ spl0_173,
inference(contradiction_clause,[status(thm)],[f74874]) ).
fof(f74876,plain,
$false,
inference(sat_refutation,[status(thm)],[f13690,f74875]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE160+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33 % Computer : n031.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Tue May 30 12:09:37 EDT 2023
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % Drodi V3.5.1
% 164.37/21.13 % Refutation found
% 164.37/21.13 % SZS status Theorem for theBenchmark: Theorem is valid
% 164.37/21.13 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 168.96/22.68 % Elapsed time: 22.101039 seconds
% 168.96/22.68 % CPU time: 161.456237 seconds
% 168.96/22.68 % Memory used: 1.324 GB
%------------------------------------------------------------------------------