TSTP Solution File: KLE151+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE151+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n013.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 12:15:56 EDT 2023
% Result : Theorem 3.42s 0.85s
% Output : CNFRefutation 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 11
% Syntax : Number of formulae : 76 ( 49 unt; 0 def)
% Number of atoms : 107 ( 77 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 71 ( 40 ~; 27 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 153 (; 151 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(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(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(f15,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
file('/export/starexec/sandbox/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/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] : leq(multiplication(X0,strong_iteration(multiplication(X1,X0))),multiplication(strong_iteration(multiplication(X0,X1)),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0,X1] : leq(multiplication(X0,strong_iteration(multiplication(X1,X0))),multiplication(strong_iteration(multiplication(X0,X1)),X0)),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f22,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f24,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(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(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(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] : ~ leq(multiplication(X0,strong_iteration(multiplication(X1,X0))),multiplication(strong_iteration(multiplication(X0,X1)),X0)),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f46,plain,
~ leq(multiplication(sk0_0,strong_iteration(multiplication(sk0_1,sk0_0))),multiplication(strong_iteration(multiplication(sk0_0,sk0_1)),sk0_0)),
inference(skolemization,[status(esa)],[f45]) ).
fof(f47,plain,
~ leq(multiplication(sk0_0,strong_iteration(multiplication(sk0_1,sk0_0))),multiplication(strong_iteration(multiplication(sk0_0,sk0_1)),sk0_0)),
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(f255,plain,
! [X0,X1] :
( ~ leq(one,addition(X0,X1))
| leq(one,multiplication(strong_iteration(X0),X1)) ),
inference(paramodulation,[status(thm)],[f26,f39]) ).
fof(f557,plain,
! [X0,X1,X2] :
( ~ leq(X0,addition(X1,multiplication(X2,X0)))
| leq(X0,multiplication(strong_iteration(X2),X1)) ),
inference(paramodulation,[status(thm)],[f21,f39]) ).
fof(f559,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X1,X0) != X1 ),
inference(paramodulation,[status(thm)],[f21,f44]) ).
fof(f602,plain,
! [X0,X1] :
( addition(X0,X1) != X0
| addition(X1,X0) = X0 ),
inference(resolution,[status(thm)],[f559,f43]) ).
fof(f619,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(f643,plain,
! [X0,X1] : addition(X0,addition(X1,addition(X0,X1))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f657,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f663,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f21,f28]) ).
fof(f664,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f28,f663]) ).
fof(f677,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f748,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X0
| addition(X1,addition(X2,X0)) = X0 ),
inference(paramodulation,[status(thm)],[f22,f602]) ).
fof(f793,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X0
| addition(X1,addition(X0,X2)) = X0 ),
inference(paramodulation,[status(thm)],[f21,f748]) ).
fof(f928,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X0
| addition(addition(X0,X2),X1) = X0 ),
inference(paramodulation,[status(thm)],[f21,f793]) ).
fof(f929,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X0
| addition(X0,addition(X2,X1)) = X0 ),
inference(forward_demodulation,[status(thm)],[f22,f928]) ).
fof(f998,plain,
! [X0,X1,X2,X3] :
( addition(X0,addition(multiplication(X1,X2),multiplication(X3,X2))) != X0
| addition(X0,multiplication(addition(X3,X1),X2)) = X0 ),
inference(paramodulation,[status(thm)],[f29,f929]) ).
fof(f999,plain,
! [X0,X1,X2,X3] :
( addition(X0,multiplication(addition(X1,X2),X3)) != X0
| addition(X0,multiplication(addition(X2,X1),X3)) = X0 ),
inference(forward_demodulation,[status(thm)],[f29,f998]) ).
fof(f1102,plain,
! [X0] :
( ~ leq(one,addition(X0,one))
| leq(one,strong_iteration(X0)) ),
inference(paramodulation,[status(thm)],[f26,f255]) ).
fof(f1606,plain,
! [X0,X1,X2,X3] :
( addition(X0,multiplication(addition(X1,X2),X3)) != X0
| addition(multiplication(addition(X2,X1),X3),X0) = X0 ),
inference(paramodulation,[status(thm)],[f21,f999]) ).
fof(f1645,plain,
! [X0,X1,X2] :
( addition(multiplication(addition(X0,X1),X2),multiplication(addition(X1,X0),X2)) = multiplication(addition(X1,X0),X2)
| addition(multiplication(addition(X1,X0),X2),multiplication(addition(X1,X0),X2)) != multiplication(addition(X1,X0),X2) ),
inference(resolution,[status(thm)],[f1606,f602]) ).
fof(f1646,plain,
! [X0,X1,X2] :
( multiplication(addition(addition(X0,X1),addition(X1,X0)),X2) = multiplication(addition(X1,X0),X2)
| addition(multiplication(addition(X1,X0),X2),multiplication(addition(X1,X0),X2)) != multiplication(addition(X1,X0),X2) ),
inference(forward_demodulation,[status(thm)],[f29,f1645]) ).
fof(f1647,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,addition(X1,addition(X1,X0))),X2) = multiplication(addition(X1,X0),X2)
| addition(multiplication(addition(X1,X0),X2),multiplication(addition(X1,X0),X2)) != multiplication(addition(X1,X0),X2) ),
inference(forward_demodulation,[status(thm)],[f22,f1646]) ).
fof(f1648,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,addition(X1,X0)),X2) = multiplication(addition(X1,X0),X2)
| addition(multiplication(addition(X1,X0),X2),multiplication(addition(X1,X0),X2)) != multiplication(addition(X1,X0),X2) ),
inference(forward_demodulation,[status(thm)],[f657,f1647]) ).
fof(f1649,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,addition(X1,X0)),X2) = multiplication(addition(X1,X0),X2)
| multiplication(addition(addition(X1,X0),addition(X1,X0)),X2) != multiplication(addition(X1,X0),X2) ),
inference(forward_demodulation,[status(thm)],[f29,f1648]) ).
fof(f1650,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,addition(X1,X0)),X2) = multiplication(addition(X1,X0),X2)
| multiplication(addition(X1,addition(X0,addition(X1,X0))),X2) != multiplication(addition(X1,X0),X2) ),
inference(forward_demodulation,[status(thm)],[f22,f1649]) ).
fof(f1651,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,addition(X1,X0)),X2) = multiplication(addition(X1,X0),X2)
| multiplication(addition(X1,X0),X2) != multiplication(addition(X1,X0),X2) ),
inference(forward_demodulation,[status(thm)],[f643,f1650]) ).
fof(f1652,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,X0)),X2) = multiplication(addition(X1,X0),X2),
inference(trivial_equality_resolution,[status(esa)],[f1651]) ).
fof(f1706,plain,
~ leq(multiplication(sk0_0,strong_iteration(multiplication(sk0_1,sk0_0))),addition(sk0_0,multiplication(multiplication(sk0_0,sk0_1),multiplication(sk0_0,strong_iteration(multiplication(sk0_1,sk0_0)))))),
inference(resolution,[status(thm)],[f557,f47]) ).
fof(f1707,plain,
~ leq(multiplication(sk0_0,strong_iteration(multiplication(sk0_1,sk0_0))),addition(sk0_0,multiplication(sk0_0,multiplication(sk0_1,multiplication(sk0_0,strong_iteration(multiplication(sk0_1,sk0_0))))))),
inference(forward_demodulation,[status(thm)],[f25,f1706]) ).
fof(f1713,plain,
addition(addition(sk0_0,multiplication(sk0_0,multiplication(sk0_1,multiplication(sk0_0,strong_iteration(multiplication(sk0_1,sk0_0)))))),multiplication(sk0_0,strong_iteration(multiplication(sk0_1,sk0_0)))) != addition(sk0_0,multiplication(sk0_0,multiplication(sk0_1,multiplication(sk0_0,strong_iteration(multiplication(sk0_1,sk0_0)))))),
inference(resolution,[status(thm)],[f1707,f559]) ).
fof(f1714,plain,
addition(sk0_0,addition(multiplication(sk0_0,multiplication(sk0_1,multiplication(sk0_0,strong_iteration(multiplication(sk0_1,sk0_0))))),multiplication(sk0_0,strong_iteration(multiplication(sk0_1,sk0_0))))) != addition(sk0_0,multiplication(sk0_0,multiplication(sk0_1,multiplication(sk0_0,strong_iteration(multiplication(sk0_1,sk0_0)))))),
inference(forward_demodulation,[status(thm)],[f22,f1713]) ).
fof(f1715,plain,
addition(sk0_0,multiplication(sk0_0,addition(multiplication(sk0_1,multiplication(sk0_0,strong_iteration(multiplication(sk0_1,sk0_0)))),strong_iteration(multiplication(sk0_1,sk0_0))))) != addition(sk0_0,multiplication(sk0_0,multiplication(sk0_1,multiplication(sk0_0,strong_iteration(multiplication(sk0_1,sk0_0)))))),
inference(forward_demodulation,[status(thm)],[f28,f1714]) ).
fof(f1716,plain,
addition(sk0_0,multiplication(sk0_0,addition(strong_iteration(multiplication(sk0_1,sk0_0)),multiplication(sk0_1,multiplication(sk0_0,strong_iteration(multiplication(sk0_1,sk0_0))))))) != addition(sk0_0,multiplication(sk0_0,multiplication(sk0_1,multiplication(sk0_0,strong_iteration(multiplication(sk0_1,sk0_0)))))),
inference(forward_demodulation,[status(thm)],[f664,f1715]) ).
fof(f1718,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = multiplication(addition(X1,X0),one),
inference(paramodulation,[status(thm)],[f26,f1652]) ).
fof(f1719,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X1,X0),
inference(forward_demodulation,[status(thm)],[f26,f1718]) ).
fof(f1944,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(resolution,[status(thm)],[f1719,f44]) ).
fof(f2072,plain,
! [X0] : leq(one,strong_iteration(X0)),
inference(backward_subsumption_resolution,[status(thm)],[f1102,f1944]) ).
fof(f2123,plain,
! [X0] : addition(one,strong_iteration(X0)) = strong_iteration(X0),
inference(resolution,[status(thm)],[f2072,f43]) ).
fof(f2407,plain,
! [X0,X1] : addition(multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1)))),strong_iteration(multiplication(X0,X1))) = addition(one,multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1))))),
inference(paramodulation,[status(thm)],[f619,f1719]) ).
fof(f2408,plain,
! [X0,X1] : addition(strong_iteration(multiplication(X0,X1)),multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1))))) = addition(one,multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f21,f2407]) ).
fof(f2409,plain,
! [X0,X1] : addition(strong_iteration(multiplication(X0,X1)),multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1))))) = strong_iteration(multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f619,f2408]) ).
fof(f2445,plain,
addition(sk0_0,multiplication(sk0_0,strong_iteration(multiplication(sk0_1,sk0_0)))) != addition(sk0_0,multiplication(sk0_0,multiplication(sk0_1,multiplication(sk0_0,strong_iteration(multiplication(sk0_1,sk0_0)))))),
inference(backward_demodulation,[status(thm)],[f2409,f1716]) ).
fof(f12192,plain,
! [X0,X1] : multiplication(X0,strong_iteration(X1)) = addition(X0,multiplication(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f2123,f677]) ).
fof(f12518,plain,
multiplication(sk0_0,strong_iteration(multiplication(sk0_1,sk0_0))) != addition(sk0_0,multiplication(sk0_0,multiplication(sk0_1,multiplication(sk0_0,strong_iteration(multiplication(sk0_1,sk0_0)))))),
inference(backward_demodulation,[status(thm)],[f12192,f2445]) ).
fof(f15181,plain,
! [X0,X1,X2] : multiplication(X0,strong_iteration(multiplication(X1,X2))) = addition(X0,multiplication(X0,multiplication(X1,multiplication(X2,strong_iteration(multiplication(X1,X2)))))),
inference(paramodulation,[status(thm)],[f619,f677]) ).
fof(f15274,plain,
multiplication(sk0_0,strong_iteration(multiplication(sk0_1,sk0_0))) != multiplication(sk0_0,strong_iteration(multiplication(sk0_1,sk0_0))),
inference(backward_demodulation,[status(thm)],[f15181,f12518]) ).
fof(f15275,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f15274]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : KLE151+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 11:41:20 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 3.42/0.85 % Refutation found
% 3.42/0.85 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.42/0.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.93/0.89 % Elapsed time: 0.526267 seconds
% 3.93/0.89 % CPU time: 4.011327 seconds
% 3.93/0.89 % Memory used: 96.448 MB
%------------------------------------------------------------------------------