TSTP Solution File: KLE131+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE131+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n004.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 12:15:50 EDT 2023
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 11
% Syntax : Number of formulae : 60 ( 56 unt; 0 def)
% Number of atoms : 64 ( 63 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 0 |; 2 &)
% ( 0 <=>; 0 =>; 2 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 58 (; 57 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : multiplication(A,zero) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [X0] : forward_diamond(X0,divergence(X0)) = divergence(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [X0] :
( divergence(X0) = zero
<= ! [X1] : addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [X0] :
( divergence(X0) = zero
<= ! [X1] : addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f33,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f36,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f40,plain,
! [X0] : multiplication(X0,zero) = zero,
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f46,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f48,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f49,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f55,plain,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f56,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f60,plain,
! [X0] : forward_diamond(X0,divergence(X0)) = divergence(X0),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f63,plain,
? [X0] :
( divergence(X0) != zero
& ! [X1] : addition(domain(X1),forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1))))) = forward_diamond(star(X0),domain_difference(domain(X1),forward_diamond(X0,domain(X1)))) ),
inference(pre_NNF_transformation,[status(esa)],[f30]) ).
fof(f64,plain,
( divergence(sk0_0) != zero
& ! [X1] : addition(domain(X1),forward_diamond(star(sk0_0),domain_difference(domain(X1),forward_diamond(sk0_0,domain(X1))))) = forward_diamond(star(sk0_0),domain_difference(domain(X1),forward_diamond(sk0_0,domain(X1)))) ),
inference(skolemization,[status(esa)],[f63]) ).
fof(f65,plain,
divergence(sk0_0) != zero,
inference(cnf_transformation,[status(esa)],[f64]) ).
fof(f66,plain,
! [X0] : addition(domain(X0),forward_diamond(star(sk0_0),domain_difference(domain(X0),forward_diamond(sk0_0,domain(X0))))) = forward_diamond(star(sk0_0),domain_difference(domain(X0),forward_diamond(sk0_0,domain(X0)))),
inference(cnf_transformation,[status(esa)],[f64]) ).
fof(f71,plain,
! [X0] : addition(domain(X0),antidomain(X0)) = one,
inference(backward_demodulation,[status(thm)],[f49,f48]) ).
fof(f72,plain,
! [X0] : addition(antidomain(X0),domain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f31,f71]) ).
fof(f79,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f33,f31]) ).
fof(f93,plain,
! [X0,X1] : addition(domain(multiplication(X0,domain(X1))),forward_diamond(star(sk0_0),domain_difference(domain(multiplication(X0,domain(X1))),forward_diamond(sk0_0,forward_diamond(X0,X1))))) = forward_diamond(star(sk0_0),domain_difference(domain(multiplication(X0,domain(X1))),forward_diamond(sk0_0,domain(multiplication(X0,domain(X1)))))),
inference(paramodulation,[status(thm)],[f56,f66]) ).
fof(f94,plain,
! [X0,X1] : addition(forward_diamond(X0,X1),forward_diamond(star(sk0_0),domain_difference(domain(multiplication(X0,domain(X1))),forward_diamond(sk0_0,forward_diamond(X0,X1))))) = forward_diamond(star(sk0_0),domain_difference(domain(multiplication(X0,domain(X1))),forward_diamond(sk0_0,domain(multiplication(X0,domain(X1)))))),
inference(forward_demodulation,[status(thm)],[f56,f93]) ).
fof(f95,plain,
! [X0,X1] : addition(forward_diamond(X0,X1),forward_diamond(star(sk0_0),domain_difference(forward_diamond(X0,X1),forward_diamond(sk0_0,forward_diamond(X0,X1))))) = forward_diamond(star(sk0_0),domain_difference(domain(multiplication(X0,domain(X1))),forward_diamond(sk0_0,domain(multiplication(X0,domain(X1)))))),
inference(forward_demodulation,[status(thm)],[f56,f94]) ).
fof(f96,plain,
! [X0,X1] : addition(forward_diamond(X0,X1),forward_diamond(star(sk0_0),domain_difference(forward_diamond(X0,X1),forward_diamond(sk0_0,forward_diamond(X0,X1))))) = forward_diamond(star(sk0_0),domain_difference(forward_diamond(X0,X1),forward_diamond(sk0_0,domain(multiplication(X0,domain(X1)))))),
inference(forward_demodulation,[status(thm)],[f56,f95]) ).
fof(f97,plain,
! [X0,X1] : addition(forward_diamond(X0,X1),forward_diamond(star(sk0_0),domain_difference(forward_diamond(X0,X1),forward_diamond(sk0_0,forward_diamond(X0,X1))))) = forward_diamond(star(sk0_0),domain_difference(forward_diamond(X0,X1),forward_diamond(sk0_0,forward_diamond(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f56,f96]) ).
fof(f162,plain,
zero = antidomain(one),
inference(paramodulation,[status(thm)],[f46,f36]) ).
fof(f173,plain,
addition(zero,domain(one)) = one,
inference(paramodulation,[status(thm)],[f162,f72]) ).
fof(f174,plain,
domain(one) = one,
inference(forward_demodulation,[status(thm)],[f79,f173]) ).
fof(f218,plain,
domain(one) = antidomain(zero),
inference(paramodulation,[status(thm)],[f162,f49]) ).
fof(f219,plain,
one = antidomain(zero),
inference(forward_demodulation,[status(thm)],[f174,f218]) ).
fof(f223,plain,
! [X0] : multiplication(domain(X0),antidomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f49,f46]) ).
fof(f224,plain,
! [X0] : domain_difference(X0,X0) = zero,
inference(forward_demodulation,[status(thm)],[f55,f223]) ).
fof(f225,plain,
domain(zero) = antidomain(one),
inference(paramodulation,[status(thm)],[f219,f49]) ).
fof(f226,plain,
domain(zero) = zero,
inference(forward_demodulation,[status(thm)],[f162,f225]) ).
fof(f238,plain,
! [X0] : forward_diamond(X0,zero) = domain(multiplication(X0,zero)),
inference(paramodulation,[status(thm)],[f226,f56]) ).
fof(f239,plain,
! [X0] : forward_diamond(X0,zero) = domain(zero),
inference(forward_demodulation,[status(thm)],[f40,f238]) ).
fof(f240,plain,
! [X0] : forward_diamond(X0,zero) = zero,
inference(forward_demodulation,[status(thm)],[f226,f239]) ).
fof(f350,plain,
! [X0] : addition(divergence(X0),forward_diamond(star(sk0_0),domain_difference(forward_diamond(X0,divergence(X0)),forward_diamond(sk0_0,forward_diamond(X0,divergence(X0)))))) = forward_diamond(star(sk0_0),domain_difference(forward_diamond(X0,divergence(X0)),forward_diamond(sk0_0,forward_diamond(X0,divergence(X0))))),
inference(paramodulation,[status(thm)],[f60,f97]) ).
fof(f351,plain,
! [X0] : addition(forward_diamond(star(sk0_0),domain_difference(forward_diamond(X0,divergence(X0)),forward_diamond(sk0_0,forward_diamond(X0,divergence(X0))))),divergence(X0)) = forward_diamond(star(sk0_0),domain_difference(forward_diamond(X0,divergence(X0)),forward_diamond(sk0_0,forward_diamond(X0,divergence(X0))))),
inference(forward_demodulation,[status(thm)],[f31,f350]) ).
fof(f352,plain,
! [X0] : addition(forward_diamond(star(sk0_0),domain_difference(divergence(X0),forward_diamond(sk0_0,forward_diamond(X0,divergence(X0))))),divergence(X0)) = forward_diamond(star(sk0_0),domain_difference(forward_diamond(X0,divergence(X0)),forward_diamond(sk0_0,forward_diamond(X0,divergence(X0))))),
inference(forward_demodulation,[status(thm)],[f60,f351]) ).
fof(f353,plain,
! [X0] : addition(forward_diamond(star(sk0_0),domain_difference(divergence(X0),forward_diamond(sk0_0,divergence(X0)))),divergence(X0)) = forward_diamond(star(sk0_0),domain_difference(forward_diamond(X0,divergence(X0)),forward_diamond(sk0_0,forward_diamond(X0,divergence(X0))))),
inference(forward_demodulation,[status(thm)],[f60,f352]) ).
fof(f354,plain,
! [X0] : addition(forward_diamond(star(sk0_0),domain_difference(divergence(X0),forward_diamond(sk0_0,divergence(X0)))),divergence(X0)) = forward_diamond(star(sk0_0),domain_difference(divergence(X0),forward_diamond(sk0_0,forward_diamond(X0,divergence(X0))))),
inference(forward_demodulation,[status(thm)],[f60,f353]) ).
fof(f355,plain,
! [X0] : addition(forward_diamond(star(sk0_0),domain_difference(divergence(X0),forward_diamond(sk0_0,divergence(X0)))),divergence(X0)) = forward_diamond(star(sk0_0),domain_difference(divergence(X0),forward_diamond(sk0_0,divergence(X0)))),
inference(forward_demodulation,[status(thm)],[f60,f354]) ).
fof(f389,plain,
addition(forward_diamond(star(sk0_0),domain_difference(divergence(sk0_0),divergence(sk0_0))),divergence(sk0_0)) = forward_diamond(star(sk0_0),domain_difference(divergence(sk0_0),forward_diamond(sk0_0,divergence(sk0_0)))),
inference(paramodulation,[status(thm)],[f60,f355]) ).
fof(f390,plain,
addition(forward_diamond(star(sk0_0),zero),divergence(sk0_0)) = forward_diamond(star(sk0_0),domain_difference(divergence(sk0_0),forward_diamond(sk0_0,divergence(sk0_0)))),
inference(forward_demodulation,[status(thm)],[f224,f389]) ).
fof(f391,plain,
addition(zero,divergence(sk0_0)) = forward_diamond(star(sk0_0),domain_difference(divergence(sk0_0),forward_diamond(sk0_0,divergence(sk0_0)))),
inference(forward_demodulation,[status(thm)],[f240,f390]) ).
fof(f392,plain,
divergence(sk0_0) = forward_diamond(star(sk0_0),domain_difference(divergence(sk0_0),forward_diamond(sk0_0,divergence(sk0_0)))),
inference(forward_demodulation,[status(thm)],[f79,f391]) ).
fof(f393,plain,
divergence(sk0_0) = forward_diamond(star(sk0_0),domain_difference(divergence(sk0_0),divergence(sk0_0))),
inference(forward_demodulation,[status(thm)],[f60,f392]) ).
fof(f394,plain,
divergence(sk0_0) = forward_diamond(star(sk0_0),zero),
inference(forward_demodulation,[status(thm)],[f224,f393]) ).
fof(f395,plain,
divergence(sk0_0) = zero,
inference(forward_demodulation,[status(thm)],[f240,f394]) ).
fof(f396,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f395,f65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : KLE131+1 : TPTP v8.1.2. Released v4.0.0.
% 0.05/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.29 % Computer : n004.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Tue May 30 11:41:52 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.09/0.30 % Drodi V3.5.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.131912 seconds
% 0.14/0.43 % CPU time: 0.364428 seconds
% 0.14/0.43 % Memory used: 26.897 MB
%------------------------------------------------------------------------------