TSTP Solution File: KLE132+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE132+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n026.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 12:15:51 EDT 2023
% Result : Theorem 2.01s 0.62s
% Output : CNFRefutation 2.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 13
% Syntax : Number of formulae : 72 ( 65 unt; 0 def)
% Number of atoms : 83 ( 82 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 6 ~; 2 |; 4 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-2 aty)
% Number of variables : 77 (; 75 !; 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(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : multiplication(A,zero) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [X0] : forward_diamond(X0,divergence(X0)) = divergence(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [X0,X1,X2] :
( addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2))) = addition(forward_diamond(X1,domain(X0)),domain(X2))
=> addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [X0] :
( ! [X1] : addition(forward_diamond(X0,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))))
=> ! [X2] :
( addition(domain(X2),forward_diamond(X0,domain(X2))) = forward_diamond(X0,domain(X2))
=> domain(X2) = zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [X0] :
( ! [X1] : addition(forward_diamond(X0,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))))
=> ! [X2] :
( addition(domain(X2),forward_diamond(X0,domain(X2))) = forward_diamond(X0,domain(X2))
=> domain(X2) = zero ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f32,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f2]) ).
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(f61,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2))) != addition(forward_diamond(X1,domain(X0)),domain(X2))
| addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2))) ),
inference(pre_NNF_transformation,[status(esa)],[f28]) ).
fof(f62,plain,
! [X0,X1,X2] :
( addition(domain(X0),addition(forward_diamond(X1,domain(X0)),domain(X2))) != addition(forward_diamond(X1,domain(X0)),domain(X2))
| addition(domain(X0),addition(divergence(X1),forward_diamond(star(X1),domain(X2)))) = addition(divergence(X1),forward_diamond(star(X1),domain(X2))) ),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f63,plain,
? [X0] :
( ! [X1] : addition(forward_diamond(X0,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))))
& ? [X2] :
( addition(domain(X2),forward_diamond(X0,domain(X2))) = forward_diamond(X0,domain(X2))
& domain(X2) != zero ) ),
inference(pre_NNF_transformation,[status(esa)],[f30]) ).
fof(f64,plain,
( ! [X1] : addition(forward_diamond(sk0_0,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))))
& addition(domain(sk0_1),forward_diamond(sk0_0,domain(sk0_1))) = forward_diamond(sk0_0,domain(sk0_1))
& domain(sk0_1) != zero ),
inference(skolemization,[status(esa)],[f63]) ).
fof(f65,plain,
! [X0] : addition(forward_diamond(sk0_0,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(f66,plain,
addition(domain(sk0_1),forward_diamond(sk0_0,domain(sk0_1))) = forward_diamond(sk0_0,domain(sk0_1)),
inference(cnf_transformation,[status(esa)],[f64]) ).
fof(f67,plain,
domain(sk0_1) != zero,
inference(cnf_transformation,[status(esa)],[f64]) ).
fof(f68,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f33,f31]) ).
fof(f80,plain,
! [X0,X1] : addition(forward_diamond(sk0_0,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,f65]) ).
fof(f81,plain,
! [X0,X1] : addition(forward_diamond(sk0_0,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,f80]) ).
fof(f82,plain,
! [X0,X1] : addition(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))))) = 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,f81]) ).
fof(f83,plain,
! [X0,X1] : addition(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))))) = 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,f82]) ).
fof(f84,plain,
! [X0,X1] : addition(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))))) = 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,f83]) ).
fof(f104,plain,
! [X0] : addition(domain(sk0_1),addition(forward_diamond(sk0_0,domain(sk0_1)),X0)) = addition(forward_diamond(sk0_0,domain(sk0_1)),X0),
inference(paramodulation,[status(thm)],[f66,f32]) ).
fof(f129,plain,
zero = antidomain(one),
inference(paramodulation,[status(thm)],[f46,f36]) ).
fof(f139,plain,
domain(one) = antidomain(zero),
inference(paramodulation,[status(thm)],[f129,f49]) ).
fof(f141,plain,
! [X0] : multiplication(domain(X0),antidomain(X0)) = zero,
inference(paramodulation,[status(thm)],[f49,f46]) ).
fof(f142,plain,
! [X0] : domain_difference(X0,X0) = zero,
inference(forward_demodulation,[status(thm)],[f55,f141]) ).
fof(f302,plain,
! [X0] : addition(forward_diamond(sk0_0,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,f84]) ).
fof(f303,plain,
! [X0] : addition(forward_diamond(sk0_0,divergence(X0)),forward_diamond(star(sk0_0),domain_difference(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(forward_demodulation,[status(thm)],[f60,f302]) ).
fof(f304,plain,
! [X0] : addition(forward_diamond(sk0_0,divergence(X0)),forward_diamond(star(sk0_0),domain_difference(divergence(X0),forward_diamond(sk0_0,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,f303]) ).
fof(f305,plain,
! [X0] : addition(forward_diamond(sk0_0,divergence(X0)),forward_diamond(star(sk0_0),domain_difference(divergence(X0),forward_diamond(sk0_0,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,f304]) ).
fof(f306,plain,
! [X0] : addition(forward_diamond(sk0_0,divergence(X0)),forward_diamond(star(sk0_0),domain_difference(divergence(X0),forward_diamond(sk0_0,divergence(X0))))) = forward_diamond(star(sk0_0),domain_difference(divergence(X0),forward_diamond(sk0_0,divergence(X0)))),
inference(forward_demodulation,[status(thm)],[f60,f305]) ).
fof(f410,plain,
! [X0] : addition(domain(sk0_1),addition(divergence(sk0_0),forward_diamond(star(sk0_0),domain(X0)))) = addition(divergence(sk0_0),forward_diamond(star(sk0_0),domain(X0))),
inference(resolution,[status(thm)],[f104,f62]) ).
fof(f500,plain,
addition(divergence(sk0_0),forward_diamond(star(sk0_0),domain_difference(divergence(sk0_0),forward_diamond(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,f306]) ).
fof(f501,plain,
addition(divergence(sk0_0),forward_diamond(star(sk0_0),domain_difference(divergence(sk0_0),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)],[f60,f500]) ).
fof(f502,plain,
addition(divergence(sk0_0),forward_diamond(star(sk0_0),zero)) = forward_diamond(star(sk0_0),domain_difference(divergence(sk0_0),forward_diamond(sk0_0,divergence(sk0_0)))),
inference(forward_demodulation,[status(thm)],[f142,f501]) ).
fof(f503,plain,
addition(divergence(sk0_0),forward_diamond(star(sk0_0),zero)) = forward_diamond(star(sk0_0),domain_difference(divergence(sk0_0),divergence(sk0_0))),
inference(forward_demodulation,[status(thm)],[f60,f502]) ).
fof(f504,plain,
addition(divergence(sk0_0),forward_diamond(star(sk0_0),zero)) = forward_diamond(star(sk0_0),zero),
inference(forward_demodulation,[status(thm)],[f142,f503]) ).
fof(f1784,plain,
! [X0] : addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(forward_demodulation,[status(thm)],[f31,f48]) ).
fof(f1785,plain,
! [X0] : addition(antidomain(X0),domain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f49,f1784]) ).
fof(f1787,plain,
addition(zero,domain(one)) = one,
inference(paramodulation,[status(thm)],[f129,f1785]) ).
fof(f1788,plain,
domain(one) = one,
inference(forward_demodulation,[status(thm)],[f68,f1787]) ).
fof(f1789,plain,
antidomain(zero) = one,
inference(forward_demodulation,[status(thm)],[f139,f1788]) ).
fof(f1819,plain,
domain(zero) = antidomain(one),
inference(paramodulation,[status(thm)],[f1789,f49]) ).
fof(f1820,plain,
domain(zero) = zero,
inference(forward_demodulation,[status(thm)],[f129,f1819]) ).
fof(f1903,plain,
addition(domain(sk0_1),addition(divergence(sk0_0),forward_diamond(star(sk0_0),zero))) = addition(divergence(sk0_0),forward_diamond(star(sk0_0),domain(zero))),
inference(paramodulation,[status(thm)],[f1820,f410]) ).
fof(f1904,plain,
addition(domain(sk0_1),forward_diamond(star(sk0_0),zero)) = addition(divergence(sk0_0),forward_diamond(star(sk0_0),domain(zero))),
inference(forward_demodulation,[status(thm)],[f504,f1903]) ).
fof(f1905,plain,
addition(domain(sk0_1),forward_diamond(star(sk0_0),zero)) = addition(divergence(sk0_0),forward_diamond(star(sk0_0),zero)),
inference(forward_demodulation,[status(thm)],[f1820,f1904]) ).
fof(f1906,plain,
addition(domain(sk0_1),forward_diamond(star(sk0_0),zero)) = forward_diamond(star(sk0_0),zero),
inference(forward_demodulation,[status(thm)],[f504,f1905]) ).
fof(f1955,plain,
! [X0] : forward_diamond(X0,zero) = domain(multiplication(X0,zero)),
inference(paramodulation,[status(thm)],[f1820,f56]) ).
fof(f1956,plain,
! [X0] : forward_diamond(X0,zero) = domain(zero),
inference(forward_demodulation,[status(thm)],[f40,f1955]) ).
fof(f1957,plain,
! [X0] : forward_diamond(X0,zero) = zero,
inference(forward_demodulation,[status(thm)],[f1820,f1956]) ).
fof(f2458,plain,
addition(domain(sk0_1),zero) = forward_diamond(star(sk0_0),zero),
inference(forward_demodulation,[status(thm)],[f1957,f1906]) ).
fof(f2459,plain,
domain(sk0_1) = forward_diamond(star(sk0_0),zero),
inference(forward_demodulation,[status(thm)],[f33,f2458]) ).
fof(f2460,plain,
domain(sk0_1) = zero,
inference(forward_demodulation,[status(thm)],[f1957,f2459]) ).
fof(f2461,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f2460,f67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE132+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue May 30 12:03:43 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.5.1
% 2.01/0.62 % Refutation found
% 2.01/0.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.01/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.01/0.64 % Elapsed time: 0.297021 seconds
% 2.01/0.64 % CPU time: 2.218961 seconds
% 2.01/0.64 % Memory used: 75.102 MB
%------------------------------------------------------------------------------