TSTP Solution File: KLE040+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE040+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:15:37 EDT 2023
% Result : Theorem 9.19s 1.62s
% Output : CNFRefutation 9.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 12
% Syntax : Number of formulae : 75 ( 64 unt; 0 def)
% Number of atoms : 90 ( 62 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 31 ( 16 ~; 11 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 135 (; 134 !; 1 ?)
% 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(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(f17,conjecture,
! [X0] : multiplication(star(X0),star(X0)) = star(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0] : multiplication(star(X0),star(X0)) = star(X0),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f20,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f22,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f23,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f24,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f25,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f26,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f27,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f30,plain,
! [A,B] :
( ( ~ leq(A,B)
| addition(A,B) = B )
& ( leq(A,B)
| addition(A,B) != B ) ),
inference(NNF_transformation,[status(esa)],[f12]) ).
fof(f31,plain,
( ! [A,B] :
( ~ leq(A,B)
| addition(A,B) = B )
& ! [A,B] :
( leq(A,B)
| addition(A,B) != B ) ),
inference(miniscoping,[status(esa)],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f34,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(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(f40,plain,
? [X0] : multiplication(star(X0),star(X0)) != star(X0),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f41,plain,
multiplication(star(sk0_0),star(sk0_0)) != star(sk0_0),
inference(skolemization,[status(esa)],[f40]) ).
fof(f42,plain,
multiplication(star(sk0_0),star(sk0_0)) != star(sk0_0),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f100,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f142,plain,
! [X0] : leq(X0,X0),
inference(resolution,[status(thm)],[f33,f22]) ).
fof(f169,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f100,f33]) ).
fof(f181,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f19,f100]) ).
fof(f237,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = addition(multiplication(X0,multiplication(X1,X3)),multiplication(X2,X3)),
inference(paramodulation,[status(thm)],[f23,f27]) ).
fof(f245,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f246,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19,f245]) ).
fof(f247,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(f269,plain,
! [X0] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f34,f32]) ).
fof(f270,plain,
! [X0] : addition(one,addition(multiplication(X0,star(X0)),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f20,f269]) ).
fof(f271,plain,
! [X0] : addition(one,addition(star(X0),multiplication(X0,star(X0)))) = star(X0),
inference(forward_demodulation,[status(thm)],[f19,f270]) ).
fof(f282,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X0),X2) = multiplication(X0,addition(multiplication(X1,X2),X2)),
inference(paramodulation,[status(thm)],[f26,f237]) ).
fof(f283,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,X1)),X2) = multiplication(X0,addition(multiplication(X1,X2),X2)),
inference(forward_demodulation,[status(thm)],[f19,f282]) ).
fof(f284,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,X1)),X2) = multiplication(X0,addition(X2,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f19,f283]) ).
fof(f285,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3))),
inference(paramodulation,[status(thm)],[f19,f237]) ).
fof(f619,plain,
! [X0,X1] : addition(X0,multiplication(X0,X1)) = multiplication(X0,addition(one,multiplication(X1,one))),
inference(paramodulation,[status(thm)],[f24,f284]) ).
fof(f620,plain,
! [X0,X1] : addition(X0,multiplication(X0,X1)) = multiplication(X0,addition(one,X1)),
inference(forward_demodulation,[status(thm)],[f24,f619]) ).
fof(f884,plain,
! [X0,X1,X2] :
( ~ leq(multiplication(addition(X0,X1),X2),X2)
| leq(multiplication(star(X0),multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f27,f37]) ).
fof(f1197,plain,
! [X0,X1] : leq(X0,multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f620,f169]) ).
fof(f2348,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = multiplication(addition(X2,multiplication(X0,X1)),X3),
inference(forward_demodulation,[status(thm)],[f247,f285]) ).
fof(f2386,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,multiplication(one,X0)),X2),
inference(paramodulation,[status(thm)],[f25,f2348]) ).
fof(f2387,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f25,f2386]) ).
fof(f7524,plain,
! [X0] : addition(one,multiplication(addition(X0,one),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f246,f271]) ).
fof(f7556,plain,
! [X0,X1] : leq(X0,multiplication(X0,star(X1))),
inference(paramodulation,[status(thm)],[f7524,f1197]) ).
fof(f7628,plain,
! [X0] : addition(multiplication(addition(X0,one),star(X0)),star(X0)) = addition(multiplication(addition(X0,one),star(X0)),one),
inference(paramodulation,[status(thm)],[f7524,f181]) ).
fof(f7629,plain,
! [X0] : addition(star(X0),multiplication(addition(X0,one),star(X0))) = addition(multiplication(addition(X0,one),star(X0)),one),
inference(forward_demodulation,[status(thm)],[f19,f7628]) ).
fof(f7630,plain,
! [X0] : multiplication(addition(addition(X0,one),one),star(X0)) = addition(multiplication(addition(X0,one),star(X0)),one),
inference(forward_demodulation,[status(thm)],[f246,f7629]) ).
fof(f7631,plain,
! [X0] : multiplication(addition(one,addition(X0,one)),star(X0)) = addition(multiplication(addition(X0,one),star(X0)),one),
inference(forward_demodulation,[status(thm)],[f2387,f7630]) ).
fof(f7632,plain,
! [X0] : multiplication(addition(one,X0),star(X0)) = addition(multiplication(addition(X0,one),star(X0)),one),
inference(forward_demodulation,[status(thm)],[f181,f7631]) ).
fof(f7633,plain,
! [X0] : multiplication(addition(one,X0),star(X0)) = addition(one,multiplication(addition(X0,one),star(X0))),
inference(forward_demodulation,[status(thm)],[f19,f7632]) ).
fof(f7634,plain,
! [X0] : multiplication(addition(one,X0),star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f7524,f7633]) ).
fof(f7871,plain,
! [X0] : leq(one,star(X0)),
inference(paramodulation,[status(thm)],[f25,f7556]) ).
fof(f7877,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(resolution,[status(thm)],[f7871,f32]) ).
fof(f11183,plain,
! [X0] : multiplication(addition(X0,one),star(X0)) = star(X0),
inference(paramodulation,[status(thm)],[f2387,f7634]) ).
fof(f13258,plain,
! [X0] :
( ~ leq(star(X0),star(X0))
| leq(multiplication(star(X0),multiplication(one,star(X0))),star(X0)) ),
inference(paramodulation,[status(thm)],[f11183,f884]) ).
fof(f13259,plain,
! [X0] :
( ~ leq(star(X0),star(X0))
| leq(multiplication(star(X0),star(X0)),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f25,f13258]) ).
fof(f13260,plain,
! [X0] : leq(multiplication(star(X0),star(X0)),star(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f13259,f142]) ).
fof(f15685,plain,
! [X0] : addition(multiplication(star(X0),star(X0)),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f13260,f32]) ).
fof(f15686,plain,
! [X0] : addition(star(X0),multiplication(star(X0),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f19,f15685]) ).
fof(f15687,plain,
! [X0] : multiplication(addition(star(X0),one),star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f246,f15686]) ).
fof(f15688,plain,
! [X0] : multiplication(addition(one,star(X0)),star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f2387,f15687]) ).
fof(f15689,plain,
! [X0] : multiplication(star(X0),star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f7877,f15688]) ).
fof(f15835,plain,
star(sk0_0) != star(sk0_0),
inference(backward_demodulation,[status(thm)],[f15689,f42]) ).
fof(f15836,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f15835]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE040+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.32 % Computer : n007.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue May 30 11:34:47 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % Drodi V3.5.1
% 9.19/1.62 % Refutation found
% 9.19/1.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 9.19/1.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.82/1.67 % Elapsed time: 1.328694 seconds
% 9.82/1.67 % CPU time: 9.980261 seconds
% 9.82/1.67 % Memory used: 161.498 MB
%------------------------------------------------------------------------------