TSTP Solution File: KLE147+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE147+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n028.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 12:15:54 EDT 2023
% Result : Theorem 110.60s 14.32s
% Output : CNFRefutation 112.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 17
% Syntax : Number of formulae : 133 ( 60 unt; 0 def)
% Number of atoms : 211 ( 67 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 154 ( 76 ~; 71 |; 2 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 18 ( 3 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 501 (; 499 !; 2 ?)
% 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(f3,axiom,
! [A] : addition(A,zero) = A,
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(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(f10,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] : addition(one,multiplication(A,star(A))) = star(A),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C] :
( leq(C,addition(multiplication(A,C),B))
=> leq(C,multiplication(strong_iteration(A),B)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
! [X0,X1] : strong_iteration(multiplication(star(X0),X1)) = multiplication(star(X1),strong_iteration(multiplication(star(X0),X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0,X1] : strong_iteration(multiplication(star(X0),X1)) = multiplication(star(X1),strong_iteration(multiplication(star(X0),X1))),
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(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(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(f37,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f38,plain,
! [A,B,C] :
( ~ leq(C,addition(multiplication(A,C),B))
| leq(C,multiplication(strong_iteration(A),B)) ),
inference(pre_NNF_transformation,[status(esa)],[f16]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ leq(X0,addition(multiplication(X1,X0),X2))
| leq(X0,multiplication(strong_iteration(X1),X2)) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
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] : strong_iteration(multiplication(star(X0),X1)) != multiplication(star(X1),strong_iteration(multiplication(star(X0),X1))),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f46,plain,
strong_iteration(multiplication(star(sk0_0),sk0_1)) != multiplication(star(sk0_1),strong_iteration(multiplication(star(sk0_0),sk0_1))),
inference(skolemization,[status(esa)],[f45]) ).
fof(f47,plain,
strong_iteration(multiplication(star(sk0_0),sk0_1)) != multiplication(star(sk0_1),strong_iteration(multiplication(star(sk0_0),sk0_1))),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f48,plain,
! [X0] : strong_iteration(X0) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(forward_demodulation,[status(thm)],[f21,f37]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,X0)),X3))
| leq(X0,multiplication(strong_iteration(multiplication(X1,X2)),X3)) ),
inference(paramodulation,[status(thm)],[f25,f39]) ).
fof(f53,plain,
! [X0,X1,X2,X3,X4] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,X0))),X4))
| leq(X0,multiplication(strong_iteration(multiplication(multiplication(X1,X2),X3)),X4)) ),
inference(paramodulation,[status(thm)],[f25,f52]) ).
fof(f54,plain,
! [X0,X1,X2,X3,X4] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,X0))),X4))
| leq(X0,multiplication(strong_iteration(multiplication(X1,multiplication(X2,X3))),X4)) ),
inference(forward_demodulation,[status(thm)],[f25,f53]) ).
fof(f58,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,X0)))),X5))
| leq(X0,multiplication(strong_iteration(multiplication(multiplication(X1,X2),multiplication(X3,X4))),X5)) ),
inference(paramodulation,[status(thm)],[f25,f54]) ).
fof(f59,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,X0)))),X5))
| leq(X0,multiplication(strong_iteration(multiplication(X1,multiplication(X2,multiplication(X3,X4)))),X5)) ),
inference(forward_demodulation,[status(thm)],[f25,f58]) ).
fof(f67,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,X0))))),X6))
| leq(X0,multiplication(strong_iteration(multiplication(multiplication(X1,X2),multiplication(X3,multiplication(X4,X5)))),X6)) ),
inference(paramodulation,[status(thm)],[f25,f59]) ).
fof(f68,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,X0))))),X6))
| leq(X0,multiplication(strong_iteration(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,X5))))),X6)) ),
inference(forward_demodulation,[status(thm)],[f25,f67]) ).
fof(f80,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,X0)))))),X7))
| leq(X0,multiplication(strong_iteration(multiplication(multiplication(X1,X2),multiplication(X3,multiplication(X4,multiplication(X5,X6))))),X7)) ),
inference(paramodulation,[status(thm)],[f25,f68]) ).
fof(f81,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,X0)))))),X7))
| leq(X0,multiplication(strong_iteration(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,X6)))))),X7)) ),
inference(forward_demodulation,[status(thm)],[f25,f80]) ).
fof(f97,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,X0))))))),X8))
| leq(X0,multiplication(strong_iteration(multiplication(multiplication(X1,X2),multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,X7)))))),X8)) ),
inference(paramodulation,[status(thm)],[f25,f81]) ).
fof(f98,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,X0))))))),X8))
| leq(X0,multiplication(strong_iteration(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,X7))))))),X8)) ),
inference(forward_demodulation,[status(thm)],[f25,f97]) ).
fof(f118,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,X0)))))))),X9))
| leq(X0,multiplication(strong_iteration(multiplication(multiplication(X1,X2),multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,X8))))))),X9)) ),
inference(paramodulation,[status(thm)],[f25,f98]) ).
fof(f119,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,X0)))))))),X9))
| leq(X0,multiplication(strong_iteration(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,X8)))))))),X9)) ),
inference(forward_demodulation,[status(thm)],[f25,f118]) ).
fof(f143,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,X0))))))))),X10))
| leq(X0,multiplication(strong_iteration(multiplication(multiplication(X1,X2),multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,X9)))))))),X10)) ),
inference(paramodulation,[status(thm)],[f25,f119]) ).
fof(f144,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,X0))))))))),X10))
| leq(X0,multiplication(strong_iteration(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,X9))))))))),X10)) ),
inference(forward_demodulation,[status(thm)],[f25,f143]) ).
fof(f172,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,X0)))))))))),X11))
| leq(X0,multiplication(strong_iteration(multiplication(multiplication(X1,X2),multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,X10))))))))),X11)) ),
inference(paramodulation,[status(thm)],[f25,f144]) ).
fof(f173,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,X0)))))))))),X11))
| leq(X0,multiplication(strong_iteration(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,X10)))))))))),X11)) ),
inference(forward_demodulation,[status(thm)],[f25,f172]) ).
fof(f205,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,multiplication(X11,X0))))))))))),X12))
| leq(X0,multiplication(strong_iteration(multiplication(multiplication(X1,X2),multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,X11)))))))))),X12)) ),
inference(paramodulation,[status(thm)],[f25,f173]) ).
fof(f206,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,multiplication(X11,X0))))))))))),X12))
| leq(X0,multiplication(strong_iteration(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,X11))))))))))),X12)) ),
inference(forward_demodulation,[status(thm)],[f25,f205]) ).
fof(f242,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,multiplication(X11,multiplication(X12,X0)))))))))))),X13))
| leq(X0,multiplication(strong_iteration(multiplication(multiplication(X1,X2),multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,multiplication(X11,X12))))))))))),X13)) ),
inference(paramodulation,[status(thm)],[f25,f206]) ).
fof(f243,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,multiplication(X11,multiplication(X12,X0)))))))))))),X13))
| leq(X0,multiplication(strong_iteration(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,multiplication(X11,X12)))))))))))),X13)) ),
inference(forward_demodulation,[status(thm)],[f25,f242]) ).
fof(f283,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,multiplication(X11,multiplication(X12,multiplication(X13,X0))))))))))))),X14))
| leq(X0,multiplication(strong_iteration(multiplication(multiplication(X1,X2),multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,multiplication(X11,multiplication(X12,X13)))))))))))),X14)) ),
inference(paramodulation,[status(thm)],[f25,f243]) ).
fof(f284,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,multiplication(X11,multiplication(X12,multiplication(X13,X0))))))))))))),X14))
| leq(X0,multiplication(strong_iteration(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,multiplication(X11,multiplication(X12,X13))))))))))))),X14)) ),
inference(forward_demodulation,[status(thm)],[f25,f283]) ).
fof(f328,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,multiplication(X11,multiplication(X12,multiplication(X13,multiplication(X14,X0)))))))))))))),X15))
| leq(X0,multiplication(strong_iteration(multiplication(multiplication(X1,X2),multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,multiplication(X11,multiplication(X12,multiplication(X13,X14))))))))))))),X15)) ),
inference(paramodulation,[status(thm)],[f25,f284]) ).
fof(f329,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,multiplication(X11,multiplication(X12,multiplication(X13,multiplication(X14,X0)))))))))))))),X15))
| leq(X0,multiplication(strong_iteration(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,multiplication(X11,multiplication(X12,multiplication(X13,X14)))))))))))))),X15)) ),
inference(forward_demodulation,[status(thm)],[f25,f328]) ).
fof(f377,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,multiplication(X11,multiplication(X12,multiplication(X13,multiplication(X14,multiplication(X15,X0))))))))))))))),X16))
| leq(X0,multiplication(strong_iteration(multiplication(multiplication(X1,X2),multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,multiplication(X11,multiplication(X12,multiplication(X13,multiplication(X14,X15)))))))))))))),X16)) ),
inference(paramodulation,[status(thm)],[f25,f329]) ).
fof(f378,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,multiplication(X11,multiplication(X12,multiplication(X13,multiplication(X14,multiplication(X15,X0))))))))))))))),X16))
| leq(X0,multiplication(strong_iteration(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,multiplication(X11,multiplication(X12,multiplication(X13,multiplication(X14,X15))))))))))))))),X16)) ),
inference(forward_demodulation,[status(thm)],[f25,f377]) ).
fof(f430,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,X17] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,multiplication(X11,multiplication(X12,multiplication(X13,multiplication(X14,multiplication(X15,multiplication(X16,X0)))))))))))))))),X17))
| leq(X0,multiplication(strong_iteration(multiplication(multiplication(X1,X2),multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,multiplication(X11,multiplication(X12,multiplication(X13,multiplication(X14,multiplication(X15,X16))))))))))))))),X17)) ),
inference(paramodulation,[status(thm)],[f25,f378]) ).
fof(f431,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16,X17] :
( ~ leq(X0,addition(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,multiplication(X11,multiplication(X12,multiplication(X13,multiplication(X14,multiplication(X15,multiplication(X16,X0)))))))))))))))),X17))
| leq(X0,multiplication(strong_iteration(multiplication(X1,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,multiplication(X11,multiplication(X12,multiplication(X13,multiplication(X14,multiplication(X15,X16)))))))))))))))),X17)) ),
inference(forward_demodulation,[status(thm)],[f25,f430]) ).
fof(f611,plain,
! [X0,X1] :
( ~ leq(X0,addition(multiplication(X1,X0),one))
| leq(X0,strong_iteration(X1)) ),
inference(paramodulation,[status(thm)],[f26,f39]) ).
fof(f612,plain,
! [X0,X1] :
( ~ leq(X0,addition(one,multiplication(X1,X0)))
| leq(X0,strong_iteration(X1)) ),
inference(forward_demodulation,[status(thm)],[f21,f611]) ).
fof(f1173,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8,X9,X10,X11,X12,X13,X14,X15,X16] :
( ~ leq(X0,addition(zero,X1))
| leq(X0,multiplication(strong_iteration(multiplication(zero,multiplication(X2,multiplication(X3,multiplication(X4,multiplication(X5,multiplication(X6,multiplication(X7,multiplication(X8,multiplication(X9,multiplication(X10,multiplication(X11,multiplication(X12,multiplication(X13,multiplication(X14,multiplication(X15,X16)))))))))))))))),X1)) ),
inference(paramodulation,[status(thm)],[f30,f431]) ).
fof(f1174,plain,
! [X0,X1] :
( ~ leq(X0,addition(zero,X1))
| leq(X0,multiplication(strong_iteration(zero),X1)) ),
inference(forward_demodulation,[status(thm)],[f30,f1173]) ).
fof(f1671,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f23,f21]) ).
fof(f1707,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| leq(X0,multiplication(strong_iteration(zero),X1)) ),
inference(backward_demodulation,[status(thm)],[f1671,f1174]) ).
fof(f1729,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X1,X0) = X1 ),
inference(paramodulation,[status(thm)],[f21,f43]) ).
fof(f1749,plain,
! [X0] : leq(X0,X0),
inference(resolution,[status(thm)],[f44,f24]) ).
fof(f1756,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X1,X0) != X1 ),
inference(paramodulation,[status(thm)],[f21,f44]) ).
fof(f1875,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f1951,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f27,f29]) ).
fof(f2013,plain,
! [X0] : leq(X0,multiplication(strong_iteration(zero),X0)),
inference(resolution,[status(thm)],[f1707,f1749]) ).
fof(f2023,plain,
leq(one,strong_iteration(zero)),
inference(paramodulation,[status(thm)],[f26,f2013]) ).
fof(f2025,plain,
addition(strong_iteration(zero),one) = strong_iteration(zero),
inference(resolution,[status(thm)],[f2023,f1729]) ).
fof(f2026,plain,
addition(one,strong_iteration(zero)) = strong_iteration(zero),
inference(forward_demodulation,[status(thm)],[f21,f2025]) ).
fof(f2047,plain,
( spl0_2
<=> strong_iteration(zero) = one ),
introduced(split_symbol_definition) ).
fof(f2049,plain,
( strong_iteration(zero) != one
| spl0_2 ),
inference(component_clause,[status(thm)],[f2047]) ).
fof(f2050,plain,
( spl0_3
<=> addition(strong_iteration(zero),one) = one ),
introduced(split_symbol_definition) ).
fof(f2051,plain,
( addition(strong_iteration(zero),one) = one
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f2050]) ).
fof(f2052,plain,
( addition(strong_iteration(zero),one) != one
| spl0_3 ),
inference(component_clause,[status(thm)],[f2050]) ).
fof(f2250,plain,
( addition(one,strong_iteration(zero)) != one
| spl0_3 ),
inference(forward_demodulation,[status(thm)],[f21,f2052]) ).
fof(f2332,plain,
! [X0] :
( ~ leq(one,addition(one,X0))
| leq(one,strong_iteration(X0)) ),
inference(paramodulation,[status(thm)],[f26,f612]) ).
fof(f2365,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f1875,f44]) ).
fof(f2410,plain,
! [X0,X1] :
( leq(addition(X0,X1),X0)
| addition(X0,X1) != X0 ),
inference(paramodulation,[status(thm)],[f1875,f1756]) ).
fof(f2415,plain,
! [X0] : leq(one,strong_iteration(X0)),
inference(backward_subsumption_resolution,[status(thm)],[f2332,f2365]) ).
fof(f2460,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f21,f2365]) ).
fof(f2464,plain,
! [X0] : addition(strong_iteration(X0),one) = strong_iteration(X0),
inference(resolution,[status(thm)],[f2415,f1729]) ).
fof(f2465,plain,
! [X0] : addition(one,strong_iteration(X0)) = strong_iteration(X0),
inference(forward_demodulation,[status(thm)],[f21,f2464]) ).
fof(f2482,plain,
! [X0,X1] : leq(X0,multiplication(strong_iteration(X1),X0)),
inference(resolution,[status(thm)],[f2460,f39]) ).
fof(f2489,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f22,f2460]) ).
fof(f2502,plain,
! [X0,X1] : addition(multiplication(strong_iteration(X0),X1),X1) = multiplication(strong_iteration(X0),X1),
inference(resolution,[status(thm)],[f2482,f1729]) ).
fof(f2503,plain,
! [X0,X1] : addition(X0,multiplication(strong_iteration(X1),X0)) = multiplication(strong_iteration(X1),X0),
inference(forward_demodulation,[status(thm)],[f21,f2502]) ).
fof(f2550,plain,
! [X0,X1,X2] : leq(X0,addition(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f21,f2489]) ).
fof(f2551,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f22,f2550]) ).
fof(f2799,plain,
! [X0] : addition(one,star(X0)) = addition(one,multiplication(X0,star(X0))),
inference(paramodulation,[status(thm)],[f31,f1875]) ).
fof(f2800,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f31,f2799]) ).
fof(f2926,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(f3019,plain,
( strong_iteration(zero) != one
| spl0_3 ),
inference(backward_demodulation,[status(thm)],[f2026,f2250]) ).
fof(f3020,plain,
( ~ spl0_2
| spl0_3 ),
inference(split_clause,[status(thm)],[f3019,f2047,f2050]) ).
fof(f3236,plain,
( addition(one,strong_iteration(zero)) = one
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f21,f2051]) ).
fof(f3771,plain,
( strong_iteration(zero) = one
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f2465,f3236]) ).
fof(f6044,plain,
! [X0,X1] :
( leq(addition(X0,X1),X0)
| ~ leq(X1,X0) ),
inference(resolution,[status(thm)],[f2410,f1729]) ).
fof(f6265,plain,
! [X0,X1] :
( leq(addition(X0,X1),X1)
| ~ leq(X0,X1) ),
inference(paramodulation,[status(thm)],[f21,f6044]) ).
fof(f6532,plain,
strong_iteration(zero) = addition(one,zero),
inference(paramodulation,[status(thm)],[f30,f48]) ).
fof(f6533,plain,
strong_iteration(zero) = one,
inference(forward_demodulation,[status(thm)],[f23,f6532]) ).
fof(f6534,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f6533,f2049]) ).
fof(f6535,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f6534]) ).
fof(f6537,plain,
! [X0,X1] : strong_iteration(multiplication(X0,X1)) = addition(one,multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1))))),
inference(paramodulation,[status(thm)],[f25,f48]) ).
fof(f7341,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(strong_iteration(X2),X0))),
inference(paramodulation,[status(thm)],[f2503,f2551]) ).
fof(f7378,plain,
! [X0,X1,X2] : leq(X0,multiplication(addition(X1,strong_iteration(X2)),X0)),
inference(paramodulation,[status(thm)],[f29,f7341]) ).
fof(f7422,plain,
! [X0,X1] :
( leq(X0,multiplication(addition(X1,one),X0))
| ~ spl0_3 ),
inference(paramodulation,[status(thm)],[f3771,f7378]) ).
fof(f7440,plain,
! [X0,X1] :
( leq(X0,multiplication(addition(one,X1),X0))
| ~ spl0_3 ),
inference(paramodulation,[status(thm)],[f21,f7422]) ).
fof(f7453,plain,
! [X0,X1] :
( leq(X0,multiplication(star(X1),X0))
| ~ spl0_3 ),
inference(paramodulation,[status(thm)],[f2800,f7440]) ).
fof(f7477,plain,
! [X0,X1] :
( addition(multiplication(star(X0),X1),X1) = multiplication(star(X0),X1)
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f7453,f1729]) ).
fof(f7478,plain,
! [X0,X1] :
( addition(X0,multiplication(star(X1),X0)) = multiplication(star(X1),X0)
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f21,f7477]) ).
fof(f11625,plain,
! [X0,X1] :
( addition(multiplication(star(X0),X1),X1) = X1
| ~ leq(multiplication(X0,X1),X1) ),
inference(resolution,[status(thm)],[f2926,f6265]) ).
fof(f11626,plain,
! [X0,X1] :
( addition(X0,multiplication(star(X1),X0)) = X0
| ~ leq(multiplication(X1,X0),X0) ),
inference(forward_demodulation,[status(thm)],[f21,f11625]) ).
fof(f11627,plain,
! [X0,X1] :
( multiplication(star(X0),X1) = X1
| ~ leq(multiplication(X0,X1),X1)
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f7478,f11626]) ).
fof(f31487,plain,
( ~ leq(multiplication(sk0_1,strong_iteration(multiplication(star(sk0_0),sk0_1))),strong_iteration(multiplication(star(sk0_0),sk0_1)))
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f11627,f47]) ).
fof(f37730,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(addition(one,X2),X0))),
inference(paramodulation,[status(thm)],[f1951,f2551]) ).
fof(f78696,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(star(X2),X0))),
inference(paramodulation,[status(thm)],[f2800,f37730]) ).
fof(f78774,plain,
! [X0,X1] : leq(multiplication(X0,strong_iteration(multiplication(star(X1),X0))),strong_iteration(multiplication(star(X1),X0))),
inference(paramodulation,[status(thm)],[f6537,f78696]) ).
fof(f78814,plain,
( $false
| ~ spl0_3 ),
inference(backward_subsumption_resolution,[status(thm)],[f31487,f78774]) ).
fof(f78815,plain,
~ spl0_3,
inference(contradiction_clause,[status(thm)],[f78814]) ).
fof(f78816,plain,
$false,
inference(sat_refutation,[status(thm)],[f3020,f6535,f78815]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : KLE147+1 : TPTP v8.1.2. Released v4.0.0.
% 0.02/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n028.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Tue May 30 12:00:17 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.10/0.32 % Drodi V3.5.1
% 110.60/14.32 % Refutation found
% 110.60/14.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 110.60/14.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 115.27/15.84 % Elapsed time: 15.288474 seconds
% 115.27/15.84 % CPU time: 109.403403 seconds
% 115.27/15.84 % Memory used: 1.059 GB
%------------------------------------------------------------------------------