TSTP Solution File: KLE045+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE045+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n006.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 12:15:38 EDT 2023
% Result : Theorem 46.63s 6.23s
% Output : CNFRefutation 47.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 15
% Syntax : Number of formulae : 150 ( 99 unt; 0 def)
% Number of atoms : 205 ( 111 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 118 ( 63 ~; 45 |; 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 217 (; 214 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A] : leq(addition(one,multiplication(star(A),A)),star(A)),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [X0,X1,X2] :
( leq(multiplication(X0,X2),multiplication(X2,X1))
=> leq(multiplication(star(X0),X2),multiplication(X2,star(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( leq(multiplication(X0,X2),multiplication(X2,X1))
=> leq(multiplication(star(X0),X2),multiplication(X2,star(X1))) ),
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,X2] :
( leq(multiplication(X0,X2),multiplication(X2,X1))
& ~ leq(multiplication(star(X0),X2),multiplication(X2,star(X1))) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f41,plain,
( leq(multiplication(sk0_0,sk0_2),multiplication(sk0_2,sk0_1))
& ~ leq(multiplication(star(sk0_0),sk0_2),multiplication(sk0_2,star(sk0_1))) ),
inference(skolemization,[status(esa)],[f40]) ).
fof(f42,plain,
leq(multiplication(sk0_0,sk0_2),multiplication(sk0_2,sk0_1)),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f43,plain,
~ leq(multiplication(star(sk0_0),sk0_2),multiplication(sk0_2,star(sk0_1))),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f44,plain,
addition(multiplication(sk0_0,sk0_2),multiplication(sk0_2,sk0_1)) = multiplication(sk0_2,sk0_1),
inference(resolution,[status(thm)],[f32,f42]) ).
fof(f49,plain,
~ leq(addition(multiplication(sk0_0,multiplication(sk0_2,star(sk0_1))),sk0_2),multiplication(sk0_2,star(sk0_1))),
inference(resolution,[status(thm)],[f37,f43]) ).
fof(f50,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(f113,plain,
! [X0,X1] :
( ~ leq(multiplication(X0,X1),X1)
| addition(multiplication(star(X0),multiplication(X0,X1)),X1) = X1 ),
inference(paramodulation,[status(thm)],[f22,f50]) ).
fof(f147,plain,
! [X0,X1] :
( ~ leq(addition(multiplication(X0,X1),one),X0)
| leq(star(X1),X0) ),
inference(paramodulation,[status(thm)],[f25,f39]) ).
fof(f234,plain,
~ leq(addition(sk0_2,multiplication(sk0_0,multiplication(sk0_2,star(sk0_1)))),multiplication(sk0_2,star(sk0_1))),
inference(paramodulation,[status(thm)],[f19,f49]) ).
fof(f273,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f280,plain,
! [X0] : addition(multiplication(sk0_0,sk0_2),addition(multiplication(sk0_2,sk0_1),X0)) = addition(multiplication(sk0_2,sk0_1),X0),
inference(paramodulation,[status(thm)],[f44,f20]) ).
fof(f282,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f283,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f20,f282]) ).
fof(f286,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f307,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f24,f26]) ).
fof(f337,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f19,f27]) ).
fof(f338,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f27,f337]) ).
fof(f344,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f355,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(f389,plain,
! [X0] : addition(multiplication(sk0_0,sk0_2),multiplication(sk0_2,addition(sk0_1,X0))) = addition(multiplication(sk0_2,sk0_1),multiplication(sk0_2,X0)),
inference(paramodulation,[status(thm)],[f26,f280]) ).
fof(f390,plain,
! [X0] : addition(multiplication(sk0_0,sk0_2),multiplication(sk0_2,addition(sk0_1,X0))) = multiplication(sk0_2,addition(sk0_1,X0)),
inference(forward_demodulation,[status(thm)],[f26,f389]) ).
fof(f936,plain,
! [X0,X1] :
( ~ leq(addition(one,multiplication(X0,X1)),X0)
| leq(star(X1),X0) ),
inference(forward_demodulation,[status(thm)],[f19,f147]) ).
fof(f938,plain,
! [X0,X1] :
( ~ leq(multiplication(X0,X1),X1)
| addition(X1,multiplication(star(X0),multiplication(X0,X1))) = X1 ),
inference(forward_demodulation,[status(thm)],[f19,f113]) ).
fof(f961,plain,
! [X0] :
( ~ leq(X0,X0)
| addition(X0,multiplication(star(one),multiplication(one,X0))) = X0 ),
inference(paramodulation,[status(thm)],[f25,f938]) ).
fof(f962,plain,
! [X0] :
( ~ leq(X0,X0)
| addition(X0,multiplication(star(one),X0)) = X0 ),
inference(forward_demodulation,[status(thm)],[f25,f961]) ).
fof(f1236,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f19,f286]) ).
fof(f1460,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(addition(X1,X2),X3)) = addition(multiplication(X2,X3),addition(X0,multiplication(X1,X3))),
inference(paramodulation,[status(thm)],[f27,f273]) ).
fof(f1466,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f1236,f273]) ).
fof(f1467,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f20,f1466]) ).
fof(f1468,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f1236,f1467]) ).
fof(f1620,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f273,f283]) ).
fof(f2268,plain,
! [X0] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f34,f32]) ).
fof(f2269,plain,
! [X0] : addition(one,addition(multiplication(X0,star(X0)),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f20,f2268]) ).
fof(f2270,plain,
! [X0] : addition(one,addition(star(X0),multiplication(X0,star(X0)))) = star(X0),
inference(forward_demodulation,[status(thm)],[f1620,f2269]) ).
fof(f2282,plain,
! [X0] : addition(addition(one,multiplication(star(X0),X0)),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f35,f32]) ).
fof(f2283,plain,
! [X0] : addition(one,addition(multiplication(star(X0),X0),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f20,f2282]) ).
fof(f2284,plain,
! [X0] : addition(one,addition(star(X0),multiplication(star(X0),X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f1620,f2283]) ).
fof(f3721,plain,
! [X0] : addition(addition(star(X0),multiplication(X0,star(X0))),star(X0)) = addition(addition(star(X0),multiplication(X0,star(X0))),one),
inference(paramodulation,[status(thm)],[f2270,f1236]) ).
fof(f3722,plain,
! [X0] : addition(star(X0),addition(multiplication(X0,star(X0)),star(X0))) = addition(addition(star(X0),multiplication(X0,star(X0))),one),
inference(forward_demodulation,[status(thm)],[f20,f3721]) ).
fof(f3723,plain,
! [X0] : addition(star(X0),addition(star(X0),multiplication(X0,star(X0)))) = addition(addition(star(X0),multiplication(X0,star(X0))),one),
inference(forward_demodulation,[status(thm)],[f1620,f3722]) ).
fof(f3724,plain,
! [X0] : addition(star(X0),multiplication(X0,star(X0))) = addition(addition(star(X0),multiplication(X0,star(X0))),one),
inference(forward_demodulation,[status(thm)],[f286,f3723]) ).
fof(f3725,plain,
! [X0] : addition(star(X0),multiplication(X0,star(X0))) = addition(star(X0),addition(multiplication(X0,star(X0)),one)),
inference(forward_demodulation,[status(thm)],[f20,f3724]) ).
fof(f3726,plain,
! [X0] : addition(star(X0),multiplication(X0,star(X0))) = addition(star(X0),addition(one,multiplication(X0,star(X0)))),
inference(forward_demodulation,[status(thm)],[f1620,f3725]) ).
fof(f3727,plain,
! [X0] : addition(star(X0),multiplication(X0,star(X0))) = addition(one,addition(star(X0),multiplication(X0,star(X0)))),
inference(forward_demodulation,[status(thm)],[f283,f3726]) ).
fof(f3728,plain,
! [X0] : addition(star(X0),multiplication(X0,star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f2270,f3727]) ).
fof(f3729,plain,
! [X0] : addition(one,star(X0)) = addition(one,addition(star(X0),multiplication(X0,star(X0)))),
inference(paramodulation,[status(thm)],[f2270,f286]) ).
fof(f3730,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f2270,f3729]) ).
fof(f3737,plain,
! [X0,X1] : addition(star(X0),addition(one,X1)) = addition(X1,star(X0)),
inference(paramodulation,[status(thm)],[f3730,f1468]) ).
fof(f3738,plain,
! [X0,X1] : addition(one,addition(star(X0),X1)) = addition(X1,star(X0)),
inference(forward_demodulation,[status(thm)],[f283,f3737]) ).
fof(f3741,plain,
! [X0,X1] : addition(one,addition(X0,star(X1))) = addition(X0,star(X1)),
inference(paramodulation,[status(thm)],[f3730,f283]) ).
fof(f5204,plain,
! [X0] : addition(multiplication(star(X0),X0),star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f3738,f2284]) ).
fof(f5205,plain,
! [X0] : addition(star(X0),multiplication(star(X0),X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f19,f5204]) ).
fof(f5658,plain,
! [X0,X1] : multiplication(X0,star(X1)) = addition(X0,multiplication(X0,star(X1))),
inference(paramodulation,[status(thm)],[f3730,f307]) ).
fof(f5677,plain,
! [X0] : multiplication(star(X0),addition(one,X0)) = star(X0),
inference(paramodulation,[status(thm)],[f5205,f307]) ).
fof(f7239,plain,
! [X0] : multiplication(star(star(X0)),star(X0)) = star(star(X0)),
inference(paramodulation,[status(thm)],[f3730,f5677]) ).
fof(f7379,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(X1,multiplication(star(X0),X1)),
inference(paramodulation,[status(thm)],[f3730,f344]) ).
fof(f7398,plain,
! [X0] : multiplication(addition(one,X0),star(X0)) = star(X0),
inference(paramodulation,[status(thm)],[f3728,f344]) ).
fof(f7404,plain,
! [X0] : multiplication(addition(one,star(X0)),addition(one,X0)) = addition(addition(one,X0),star(X0)),
inference(paramodulation,[status(thm)],[f5677,f344]) ).
fof(f7405,plain,
! [X0] : multiplication(star(X0),addition(one,X0)) = addition(addition(one,X0),star(X0)),
inference(forward_demodulation,[status(thm)],[f3730,f7404]) ).
fof(f7406,plain,
! [X0] : star(X0) = addition(addition(one,X0),star(X0)),
inference(forward_demodulation,[status(thm)],[f5677,f7405]) ).
fof(f7407,plain,
! [X0] : star(X0) = addition(one,addition(X0,star(X0))),
inference(forward_demodulation,[status(thm)],[f20,f7406]) ).
fof(f7408,plain,
! [X0] : star(X0) = addition(X0,star(X0)),
inference(forward_demodulation,[status(thm)],[f3741,f7407]) ).
fof(f7599,plain,
addition(multiplication(sk0_0,sk0_2),multiplication(sk0_2,star(sk0_1))) = multiplication(sk0_2,addition(sk0_1,star(sk0_1))),
inference(paramodulation,[status(thm)],[f7408,f390]) ).
fof(f7600,plain,
addition(multiplication(sk0_0,sk0_2),multiplication(sk0_2,star(sk0_1))) = multiplication(sk0_2,star(sk0_1)),
inference(forward_demodulation,[status(thm)],[f7408,f7599]) ).
fof(f7699,plain,
! [X0] : multiplication(star(X0),star(star(X0))) = star(star(X0)),
inference(paramodulation,[status(thm)],[f3730,f7398]) ).
fof(f8347,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X0,star(X2)))) = addition(X1,multiplication(X0,star(X2))),
inference(paramodulation,[status(thm)],[f5658,f283]) ).
fof(f8453,plain,
! [X0] :
( ~ leq(X0,X0)
| multiplication(star(one),X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f7379,f962]) ).
fof(f8664,plain,
! [X0] :
( multiplication(star(one),X0) = X0
| addition(X0,X0) != X0 ),
inference(resolution,[status(thm)],[f8453,f33]) ).
fof(f8665,plain,
! [X0] :
( multiplication(star(one),X0) = X0
| X0 != X0 ),
inference(forward_demodulation,[status(thm)],[f22,f8664]) ).
fof(f8666,plain,
! [X0] : multiplication(star(one),X0) = X0,
inference(trivial_equality_resolution,[status(esa)],[f8665]) ).
fof(f8701,plain,
! [X0,X1] :
( ~ leq(addition(multiplication(one,X0),X1),X0)
| leq(X1,X0) ),
inference(paramodulation,[status(thm)],[f8666,f37]) ).
fof(f8702,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X0)
| leq(X1,X0) ),
inference(forward_demodulation,[status(thm)],[f25,f8701]) ).
fof(f9831,plain,
~ leq(addition(multiplication(sk0_2,star(sk0_1)),addition(sk0_2,multiplication(sk0_0,multiplication(sk0_2,star(sk0_1))))),multiplication(sk0_2,star(sk0_1))),
inference(resolution,[status(thm)],[f8702,f234]) ).
fof(f9832,plain,
~ leq(addition(sk0_2,addition(multiplication(sk0_2,star(sk0_1)),multiplication(sk0_0,multiplication(sk0_2,star(sk0_1))))),multiplication(sk0_2,star(sk0_1))),
inference(forward_demodulation,[status(thm)],[f283,f9831]) ).
fof(f9833,plain,
~ leq(addition(sk0_2,multiplication(addition(sk0_2,multiplication(sk0_0,sk0_2)),star(sk0_1))),multiplication(sk0_2,star(sk0_1))),
inference(forward_demodulation,[status(thm)],[f355,f9832]) ).
fof(f9874,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X0)
| addition(X1,X0) = X0 ),
inference(resolution,[status(thm)],[f8702,f32]) ).
fof(f9970,plain,
! [X0,X1] :
( ~ leq(multiplication(star(X0),X1),X1)
| addition(multiplication(star(X0),X1),X1) = X1 ),
inference(paramodulation,[status(thm)],[f7379,f9874]) ).
fof(f9971,plain,
! [X0,X1] :
( ~ leq(multiplication(star(X0),X1),X1)
| addition(X1,multiplication(star(X0),X1)) = X1 ),
inference(forward_demodulation,[status(thm)],[f19,f9970]) ).
fof(f9972,plain,
! [X0,X1] :
( ~ leq(multiplication(star(X0),X1),X1)
| multiplication(star(X0),X1) = X1 ),
inference(forward_demodulation,[status(thm)],[f7379,f9971]) ).
fof(f10779,plain,
( spl0_252
<=> leq(multiplication(sk0_2,star(sk0_1)),multiplication(sk0_2,star(sk0_1))) ),
introduced(split_symbol_definition) ).
fof(f10780,plain,
( leq(multiplication(sk0_2,star(sk0_1)),multiplication(sk0_2,star(sk0_1)))
| ~ spl0_252 ),
inference(component_clause,[status(thm)],[f10779]) ).
fof(f10781,plain,
( ~ leq(multiplication(sk0_2,star(sk0_1)),multiplication(sk0_2,star(sk0_1)))
| spl0_252 ),
inference(component_clause,[status(thm)],[f10779]) ).
fof(f11767,plain,
( addition(multiplication(sk0_2,star(sk0_1)),multiplication(sk0_2,star(sk0_1))) != multiplication(sk0_2,star(sk0_1))
| spl0_252 ),
inference(resolution,[status(thm)],[f10781,f33]) ).
fof(f11768,plain,
( multiplication(addition(sk0_2,sk0_2),star(sk0_1)) != multiplication(sk0_2,star(sk0_1))
| spl0_252 ),
inference(forward_demodulation,[status(thm)],[f27,f11767]) ).
fof(f11769,plain,
( multiplication(sk0_2,star(sk0_1)) != multiplication(sk0_2,star(sk0_1))
| spl0_252 ),
inference(forward_demodulation,[status(thm)],[f22,f11768]) ).
fof(f11770,plain,
( $false
| spl0_252 ),
inference(trivial_equality_resolution,[status(esa)],[f11769]) ).
fof(f11771,plain,
spl0_252,
inference(contradiction_clause,[status(thm)],[f11770]) ).
fof(f12139,plain,
! [X0,X1] :
( multiplication(star(X0),X1) = X1
| ~ leq(addition(multiplication(X0,X1),X1),X1) ),
inference(resolution,[status(thm)],[f9972,f37]) ).
fof(f12140,plain,
! [X0,X1] :
( multiplication(star(X0),X1) = X1
| ~ leq(addition(X1,multiplication(X0,X1)),X1) ),
inference(forward_demodulation,[status(thm)],[f19,f12139]) ).
fof(f12260,plain,
! [X0] :
( multiplication(star(X0),X0) = X0
| ~ leq(multiplication(X0,addition(one,X0)),X0) ),
inference(paramodulation,[status(thm)],[f307,f12140]) ).
fof(f12902,plain,
! [X0] :
( multiplication(star(star(X0)),star(X0)) = star(X0)
| ~ leq(addition(multiplication(X0,star(X0)),addition(one,star(X0))),star(X0)) ),
inference(resolution,[status(thm)],[f12260,f37]) ).
fof(f12903,plain,
! [X0] :
( star(star(X0)) = star(X0)
| ~ leq(addition(multiplication(X0,star(X0)),addition(one,star(X0))),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f7239,f12902]) ).
fof(f12904,plain,
! [X0] :
( star(star(X0)) = star(X0)
| ~ leq(addition(star(X0),addition(one,multiplication(X0,star(X0)))),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f1468,f12903]) ).
fof(f12905,plain,
! [X0] :
( star(star(X0)) = star(X0)
| ~ leq(addition(one,addition(star(X0),multiplication(X0,star(X0)))),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f283,f12904]) ).
fof(f12906,plain,
! [X0] :
( star(star(X0)) = star(X0)
| ~ leq(addition(multiplication(X0,star(X0)),star(X0)),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f3738,f12905]) ).
fof(f12907,plain,
! [X0] :
( star(star(X0)) = star(X0)
| ~ leq(addition(star(X0),multiplication(X0,star(X0))),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f19,f12906]) ).
fof(f12908,plain,
! [X0] :
( star(star(X0)) = star(X0)
| ~ leq(star(X0),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f3728,f12907]) ).
fof(f13042,plain,
! [X0] :
( star(star(X0)) = star(X0)
| ~ leq(addition(one,multiplication(star(X0),X0)),star(X0)) ),
inference(resolution,[status(thm)],[f12908,f936]) ).
fof(f13043,plain,
! [X0] : star(star(X0)) = star(X0),
inference(forward_subsumption_resolution,[status(thm)],[f13042,f35]) ).
fof(f13084,plain,
! [X0] : multiplication(star(X0),star(star(X0))) = star(X0),
inference(backward_demodulation,[status(thm)],[f13043,f7699]) ).
fof(f13085,plain,
! [X0] : multiplication(star(X0),star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f13043,f13084]) ).
fof(f13163,plain,
! [X0,X1,X2] :
( ~ leq(addition(multiplication(X0,star(X1)),X2),X0)
| leq(multiplication(X2,star(X1)),X0) ),
inference(paramodulation,[status(thm)],[f13043,f39]) ).
fof(f25359,plain,
! [X0,X1,X2] : addition(X0,multiplication(addition(X0,X1),star(X2))) = addition(multiplication(X1,star(X2)),multiplication(X0,star(X2))),
inference(paramodulation,[status(thm)],[f5658,f1460]) ).
fof(f25360,plain,
! [X0,X1,X2] : addition(X0,multiplication(addition(X0,X1),star(X2))) = multiplication(addition(X1,X0),star(X2)),
inference(forward_demodulation,[status(thm)],[f27,f25359]) ).
fof(f41974,plain,
~ leq(multiplication(addition(multiplication(sk0_0,sk0_2),sk0_2),star(sk0_1)),multiplication(sk0_2,star(sk0_1))),
inference(backward_demodulation,[status(thm)],[f25360,f9833]) ).
fof(f41975,plain,
~ leq(multiplication(addition(sk0_2,multiplication(sk0_0,sk0_2)),star(sk0_1)),multiplication(sk0_2,star(sk0_1))),
inference(forward_demodulation,[status(thm)],[f338,f41974]) ).
fof(f45898,plain,
~ leq(addition(multiplication(multiplication(sk0_2,star(sk0_1)),star(sk0_1)),addition(sk0_2,multiplication(sk0_0,sk0_2))),multiplication(sk0_2,star(sk0_1))),
inference(resolution,[status(thm)],[f41975,f13163]) ).
fof(f45899,plain,
~ leq(addition(multiplication(sk0_0,sk0_2),addition(sk0_2,multiplication(multiplication(sk0_2,star(sk0_1)),star(sk0_1)))),multiplication(sk0_2,star(sk0_1))),
inference(forward_demodulation,[status(thm)],[f1468,f45898]) ).
fof(f45900,plain,
~ leq(addition(sk0_2,addition(multiplication(sk0_0,sk0_2),multiplication(multiplication(sk0_2,star(sk0_1)),star(sk0_1)))),multiplication(sk0_2,star(sk0_1))),
inference(forward_demodulation,[status(thm)],[f283,f45899]) ).
fof(f45901,plain,
~ leq(addition(sk0_2,addition(multiplication(sk0_0,sk0_2),multiplication(sk0_2,multiplication(star(sk0_1),star(sk0_1))))),multiplication(sk0_2,star(sk0_1))),
inference(forward_demodulation,[status(thm)],[f23,f45900]) ).
fof(f45902,plain,
~ leq(addition(sk0_2,addition(multiplication(sk0_0,sk0_2),multiplication(sk0_2,star(sk0_1)))),multiplication(sk0_2,star(sk0_1))),
inference(forward_demodulation,[status(thm)],[f13085,f45901]) ).
fof(f45903,plain,
~ leq(addition(multiplication(sk0_0,sk0_2),multiplication(sk0_2,star(sk0_1))),multiplication(sk0_2,star(sk0_1))),
inference(forward_demodulation,[status(thm)],[f8347,f45902]) ).
fof(f45904,plain,
~ leq(multiplication(sk0_2,star(sk0_1)),multiplication(sk0_2,star(sk0_1))),
inference(forward_demodulation,[status(thm)],[f7600,f45903]) ).
fof(f45905,plain,
( $false
| ~ spl0_252 ),
inference(forward_subsumption_resolution,[status(thm)],[f45904,f10780]) ).
fof(f45906,plain,
~ spl0_252,
inference(contradiction_clause,[status(thm)],[f45905]) ).
fof(f45907,plain,
$false,
inference(sat_refutation,[status(thm)],[f11771,f45906]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : KLE045+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue May 30 11:42:47 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Drodi V3.5.1
% 46.63/6.23 % Refutation found
% 46.63/6.23 % SZS status Theorem for theBenchmark: Theorem is valid
% 46.63/6.23 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 48.20/6.39 % Elapsed time: 6.039019 seconds
% 48.20/6.39 % CPU time: 47.535809 seconds
% 48.20/6.39 % Memory used: 587.448 MB
%------------------------------------------------------------------------------