TSTP Solution File: KLE099+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE099+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n019.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 12:15:47 EDT 2023
% Result : Theorem 10.32s 1.72s
% Output : CNFRefutation 10.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 17
% Syntax : Number of formulae : 97 ( 93 unt; 0 def)
% Number of atoms : 101 ( 100 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 120 (; 117 !; 3 ?)
% 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(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(f11,axiom,
! [A] : multiplication(zero,A) = 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(f21,axiom,
! [X0] : c(X0) = antidomain(domain(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,conjecture,
! [X0,X1,X2] :
( addition(forward_diamond(X0,domain(X1)),domain(X2)) = domain(X2)
=> multiplication(antidomain(X2),multiplication(X0,domain(X1))) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ ! [X0,X1,X2] :
( addition(forward_diamond(X0,domain(X1)),domain(X2)) = domain(X2)
=> multiplication(antidomain(X2),multiplication(X0,domain(X1))) = zero ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f29,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f30,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f31,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f32,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f33,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f34,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f35,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f36,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f37,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f39,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f44,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f46,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f47,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f52,plain,
! [X0] : c(X0) = antidomain(domain(X0)),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f53,plain,
! [X0,X1] : domain_difference(X0,X1) = multiplication(domain(X0),antidomain(X1)),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f54,plain,
! [X0,X1] : forward_diamond(X0,X1) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f58,plain,
? [X0,X1,X2] :
( addition(forward_diamond(X0,domain(X1)),domain(X2)) = domain(X2)
& multiplication(antidomain(X2),multiplication(X0,domain(X1))) != zero ),
inference(pre_NNF_transformation,[status(esa)],[f28]) ).
fof(f59,plain,
( addition(forward_diamond(sk0_0,domain(sk0_1)),domain(sk0_2)) = domain(sk0_2)
& multiplication(antidomain(sk0_2),multiplication(sk0_0,domain(sk0_1))) != zero ),
inference(skolemization,[status(esa)],[f58]) ).
fof(f60,plain,
addition(forward_diamond(sk0_0,domain(sk0_1)),domain(sk0_2)) = domain(sk0_2),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f61,plain,
multiplication(antidomain(sk0_2),multiplication(sk0_0,domain(sk0_1))) != zero,
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f62,plain,
! [X0] : addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(forward_demodulation,[status(thm)],[f29,f46]) ).
fof(f64,plain,
addition(domain(sk0_2),forward_diamond(sk0_0,domain(sk0_1))) = domain(sk0_2),
inference(forward_demodulation,[status(thm)],[f29,f60]) ).
fof(f65,plain,
! [X0] : addition(antidomain(X0),domain(X0)) = one,
inference(backward_demodulation,[status(thm)],[f47,f62]) ).
fof(f71,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f31,f29]) ).
fof(f79,plain,
! [X0] : domain(antidomain(X0)) = antidomain(domain(X0)),
inference(paramodulation,[status(thm)],[f47,f47]) ).
fof(f80,plain,
! [X0] : domain(antidomain(X0)) = c(X0),
inference(forward_demodulation,[status(thm)],[f52,f79]) ).
fof(f83,plain,
! [X0] : addition(domain(X0),domain(antidomain(X0))) = one,
inference(paramodulation,[status(thm)],[f47,f65]) ).
fof(f84,plain,
! [X0] : addition(domain(X0),c(X0)) = one,
inference(forward_demodulation,[status(thm)],[f80,f83]) ).
fof(f90,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,domain(X1))),forward_diamond(X0,X1)) = one,
inference(paramodulation,[status(thm)],[f54,f65]) ).
fof(f91,plain,
! [X0,X1] : addition(forward_diamond(X0,X1),antidomain(multiplication(X0,domain(X1)))) = one,
inference(forward_demodulation,[status(thm)],[f29,f90]) ).
fof(f102,plain,
! [X0] : addition(domain(sk0_2),addition(forward_diamond(sk0_0,domain(sk0_1)),X0)) = addition(domain(sk0_2),X0),
inference(paramodulation,[status(thm)],[f64,f30]) ).
fof(f109,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f32,f30]) ).
fof(f120,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(X0,X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f44,f33]) ).
fof(f121,plain,
! [X0,X1] : multiplication(antidomain(X0),multiplication(X0,X1)) = zero,
inference(forward_demodulation,[status(thm)],[f39,f120]) ).
fof(f134,plain,
zero = antidomain(one),
inference(paramodulation,[status(thm)],[f44,f34]) ).
fof(f142,plain,
addition(zero,domain(one)) = one,
inference(paramodulation,[status(thm)],[f134,f65]) ).
fof(f143,plain,
domain(one) = one,
inference(forward_demodulation,[status(thm)],[f71,f142]) ).
fof(f247,plain,
! [X0] : addition(domain(X0),one) = addition(domain(X0),c(X0)),
inference(paramodulation,[status(thm)],[f84,f109]) ).
fof(f248,plain,
! [X0] : addition(one,domain(X0)) = addition(domain(X0),c(X0)),
inference(forward_demodulation,[status(thm)],[f29,f247]) ).
fof(f249,plain,
! [X0] : addition(one,domain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f84,f248]) ).
fof(f291,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = addition(multiplication(antidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f44,f36]) ).
fof(f292,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f31,f291]) ).
fof(f322,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),X0) = addition(zero,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f44,f37]) ).
fof(f323,plain,
! [X0,X1] : multiplication(addition(antidomain(X0),X1),X0) = multiplication(X1,X0),
inference(forward_demodulation,[status(thm)],[f71,f322]) ).
fof(f336,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = addition(multiplication(X0,X1),zero),
inference(paramodulation,[status(thm)],[f44,f37]) ).
fof(f337,plain,
! [X0,X1] : multiplication(addition(X0,antidomain(X1)),X1) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f31,f336]) ).
fof(f584,plain,
! [X0] : domain(domain(X0)) = c(antidomain(X0)),
inference(paramodulation,[status(thm)],[f47,f80]) ).
fof(f711,plain,
! [X0,X1] : domain_difference(antidomain(X0),X1) = multiplication(c(X0),antidomain(X1)),
inference(paramodulation,[status(thm)],[f80,f53]) ).
fof(f714,plain,
! [X0] : domain_difference(one,X0) = multiplication(one,antidomain(X0)),
inference(paramodulation,[status(thm)],[f143,f53]) ).
fof(f715,plain,
! [X0] : domain_difference(one,X0) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f35,f714]) ).
fof(f1107,plain,
! [X0] : c(antidomain(X0)) = antidomain(c(X0)),
inference(paramodulation,[status(thm)],[f80,f52]) ).
fof(f1108,plain,
! [X0] : domain(domain(X0)) = antidomain(c(X0)),
inference(forward_demodulation,[status(thm)],[f584,f1107]) ).
fof(f1114,plain,
! [X0,X1] : domain_difference(X0,domain(X1)) = multiplication(domain(X0),c(X1)),
inference(paramodulation,[status(thm)],[f52,f53]) ).
fof(f1613,plain,
addition(domain(sk0_2),one) = addition(domain(sk0_2),antidomain(multiplication(sk0_0,domain(domain(sk0_1))))),
inference(paramodulation,[status(thm)],[f91,f102]) ).
fof(f1614,plain,
addition(one,domain(sk0_2)) = addition(domain(sk0_2),antidomain(multiplication(sk0_0,domain(domain(sk0_1))))),
inference(forward_demodulation,[status(thm)],[f29,f1613]) ).
fof(f1615,plain,
one = addition(domain(sk0_2),antidomain(multiplication(sk0_0,domain(domain(sk0_1))))),
inference(forward_demodulation,[status(thm)],[f249,f1614]) ).
fof(f1616,plain,
one = addition(domain(sk0_2),antidomain(multiplication(sk0_0,antidomain(c(sk0_1))))),
inference(forward_demodulation,[status(thm)],[f1108,f1615]) ).
fof(f1988,plain,
! [X0] : multiplication(one,X0) = multiplication(domain(X0),X0),
inference(paramodulation,[status(thm)],[f65,f323]) ).
fof(f1989,plain,
! [X0] : X0 = multiplication(domain(X0),X0),
inference(forward_demodulation,[status(thm)],[f35,f1988]) ).
fof(f2033,plain,
! [X0] : antidomain(X0) = domain_difference(antidomain(X0),X0),
inference(paramodulation,[status(thm)],[f53,f1989]) ).
fof(f2917,plain,
multiplication(one,multiplication(sk0_0,antidomain(c(sk0_1)))) = multiplication(domain(sk0_2),multiplication(sk0_0,antidomain(c(sk0_1)))),
inference(paramodulation,[status(thm)],[f1616,f337]) ).
fof(f2918,plain,
multiplication(sk0_0,antidomain(c(sk0_1))) = multiplication(domain(sk0_2),multiplication(sk0_0,antidomain(c(sk0_1)))),
inference(forward_demodulation,[status(thm)],[f35,f2917]) ).
fof(f8073,plain,
! [X0] : multiplication(antidomain(domain(X0)),one) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(paramodulation,[status(thm)],[f65,f292]) ).
fof(f8074,plain,
! [X0] : antidomain(domain(X0)) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f34,f8073]) ).
fof(f8075,plain,
! [X0] : c(X0) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f52,f8074]) ).
fof(f8076,plain,
! [X0] : c(X0) = multiplication(c(X0),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f52,f8075]) ).
fof(f8077,plain,
! [X0] : c(X0) = domain_difference(antidomain(X0),X0),
inference(forward_demodulation,[status(thm)],[f711,f8076]) ).
fof(f8078,plain,
! [X0] : c(X0) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f2033,f8077]) ).
fof(f8180,plain,
! [X0,X1] : domain_difference(X0,domain(X1)) = multiplication(domain(X0),antidomain(X1)),
inference(backward_demodulation,[status(thm)],[f8078,f1114]) ).
fof(f8181,plain,
! [X0,X1] : domain_difference(X0,domain(X1)) = domain_difference(X0,X1),
inference(forward_demodulation,[status(thm)],[f53,f8180]) ).
fof(f8304,plain,
multiplication(sk0_0,antidomain(c(sk0_1))) = multiplication(domain(sk0_2),multiplication(sk0_0,antidomain(antidomain(sk0_1)))),
inference(backward_demodulation,[status(thm)],[f8078,f2918]) ).
fof(f8305,plain,
multiplication(sk0_0,antidomain(antidomain(sk0_1))) = multiplication(domain(sk0_2),multiplication(sk0_0,antidomain(antidomain(sk0_1)))),
inference(forward_demodulation,[status(thm)],[f8078,f8304]) ).
fof(f8306,plain,
multiplication(sk0_0,domain(sk0_1)) = multiplication(domain(sk0_2),multiplication(sk0_0,antidomain(antidomain(sk0_1)))),
inference(forward_demodulation,[status(thm)],[f47,f8305]) ).
fof(f8307,plain,
multiplication(sk0_0,domain(sk0_1)) = multiplication(domain(sk0_2),multiplication(sk0_0,domain(sk0_1))),
inference(forward_demodulation,[status(thm)],[f47,f8306]) ).
fof(f9197,plain,
! [X0] : antidomain(domain(X0)) = domain_difference(one,X0),
inference(paramodulation,[status(thm)],[f715,f8181]) ).
fof(f9198,plain,
! [X0] : antidomain(domain(X0)) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f715,f9197]) ).
fof(f10895,plain,
multiplication(antidomain(domain(sk0_2)),multiplication(sk0_0,domain(sk0_1))) = zero,
inference(paramodulation,[status(thm)],[f8307,f121]) ).
fof(f10896,plain,
multiplication(antidomain(sk0_2),multiplication(sk0_0,domain(sk0_1))) = zero,
inference(forward_demodulation,[status(thm)],[f9198,f10895]) ).
fof(f10897,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f10896,f61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : KLE099+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 : n019.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 11:48:25 EDT 2023
% 0.10/0.32 % CPUTime :
% 0.10/0.32 % Drodi V3.5.1
% 10.32/1.72 % Refutation found
% 10.32/1.72 % SZS status Theorem for theBenchmark: Theorem is valid
% 10.32/1.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 10.83/1.79 % Elapsed time: 1.454319 seconds
% 10.83/1.79 % CPU time: 10.872320 seconds
% 10.83/1.79 % Memory used: 166.451 MB
%------------------------------------------------------------------------------