TSTP Solution File: KLE082+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE082+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n011.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 12:15:44 EDT 2023
% Result : Theorem 5.08s 1.08s
% Output : CNFRefutation 5.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 15
% Syntax : Number of formulae : 104 ( 99 unt; 0 def)
% Number of atoms : 114 ( 113 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 7 ~; 0 |; 8 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 172 (; 168 !; 4 ?)
% 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] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,conjecture,
! [X0,X1] :
( ! [X2] :
( addition(domain(X2),antidomain(X2)) = one
& multiplication(domain(X2),antidomain(X2)) = zero )
=> addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) = antidomain(multiplication(X0,domain(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ! [X0,X1] :
( ! [X2] :
( addition(domain(X2),antidomain(X2)) = one
& multiplication(domain(X2),antidomain(X2)) = zero )
=> addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) = antidomain(multiplication(X0,domain(X1))) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f21,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,zero) = X0,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f23,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f24,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f25,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f26,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f27,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f28,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,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f35,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f36,plain,
! [X0,X1] : domain(multiplication(X0,X1)) = domain(multiplication(X0,domain(X1))),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f37,plain,
! [X0] : addition(domain(X0),one) = one,
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f39,plain,
! [X0,X1] : domain(addition(X0,X1)) = addition(domain(X0),domain(X1)),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f40,plain,
? [X0,X1] :
( ! [X2] :
( addition(domain(X2),antidomain(X2)) = one
& multiplication(domain(X2),antidomain(X2)) = zero )
& addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) != antidomain(multiplication(X0,domain(X1))) ),
inference(pre_NNF_transformation,[status(esa)],[f19]) ).
fof(f41,plain,
( ! [X2] : addition(domain(X2),antidomain(X2)) = one
& ! [X2] : multiplication(domain(X2),antidomain(X2)) = zero
& ? [X0,X1] : addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) != antidomain(multiplication(X0,domain(X1))) ),
inference(miniscoping,[status(esa)],[f40]) ).
fof(f42,plain,
( ! [X2] : addition(domain(X2),antidomain(X2)) = one
& ! [X2] : multiplication(domain(X2),antidomain(X2)) = zero
& addition(antidomain(multiplication(sk0_0,sk0_1)),antidomain(multiplication(sk0_0,domain(sk0_1)))) != antidomain(multiplication(sk0_0,domain(sk0_1))) ),
inference(skolemization,[status(esa)],[f41]) ).
fof(f43,plain,
! [X0] : addition(domain(X0),antidomain(X0)) = one,
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f44,plain,
! [X0] : multiplication(domain(X0),antidomain(X0)) = zero,
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f45,plain,
addition(antidomain(multiplication(sk0_0,sk0_1)),antidomain(multiplication(sk0_0,domain(sk0_1)))) != antidomain(multiplication(sk0_0,domain(sk0_1))),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f46,plain,
! [X0] : addition(one,domain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f20,f37]) ).
fof(f47,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f78,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f23,f21]) ).
fof(f96,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f20,f78]) ).
fof(f114,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X0),X1)) = multiplication(zero,X1),
inference(paramodulation,[status(thm)],[f44,f24]) ).
fof(f115,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X0),X1)) = zero,
inference(forward_demodulation,[status(thm)],[f30,f114]) ).
fof(f141,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f176,plain,
! [X0] : addition(antidomain(X0),one) = addition(antidomain(X0),domain(X0)),
inference(paramodulation,[status(thm)],[f43,f96]) ).
fof(f177,plain,
! [X0] : addition(one,antidomain(X0)) = addition(antidomain(X0),domain(X0)),
inference(forward_demodulation,[status(thm)],[f20,f176]) ).
fof(f178,plain,
! [X0] : addition(one,antidomain(X0)) = addition(domain(X0),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f20,f177]) ).
fof(f179,plain,
! [X0] : addition(one,antidomain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f43,f178]) ).
fof(f210,plain,
! [X0] : domain(multiplication(one,X0)) = domain(domain(X0)),
inference(paramodulation,[status(thm)],[f26,f36]) ).
fof(f211,plain,
! [X0] : domain(X0) = domain(domain(X0)),
inference(forward_demodulation,[status(thm)],[f26,f210]) ).
fof(f216,plain,
! [X0,X1] : addition(domain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))) = one,
inference(paramodulation,[status(thm)],[f36,f43]) ).
fof(f221,plain,
! [X0] : addition(domain(X0),antidomain(domain(X0))) = one,
inference(paramodulation,[status(thm)],[f211,f43]) ).
fof(f269,plain,
! [X0,X1,X2] : domain(addition(X0,multiplication(X1,domain(X2)))) = addition(domain(X0),domain(multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f36,f39]) ).
fof(f270,plain,
! [X0,X1,X2] : domain(addition(X0,multiplication(X1,domain(X2)))) = domain(addition(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f39,f269]) ).
fof(f860,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f863,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),antidomain(X0)) = addition(zero,multiplication(X1,antidomain(X0))),
inference(paramodulation,[status(thm)],[f44,f28]) ).
fof(f864,plain,
! [X0,X1] : multiplication(addition(domain(X0),X1),antidomain(X0)) = multiplication(X1,antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f47,f863]) ).
fof(f942,plain,
addition(one,domain(one)) = multiplication(domain(one),one),
inference(paramodulation,[status(thm)],[f25,f35]) ).
fof(f943,plain,
one = multiplication(domain(one),one),
inference(forward_demodulation,[status(thm)],[f46,f942]) ).
fof(f944,plain,
one = domain(one),
inference(forward_demodulation,[status(thm)],[f25,f943]) ).
fof(f1092,plain,
! [X0] : multiplication(one,antidomain(X0)) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(paramodulation,[status(thm)],[f221,f864]) ).
fof(f1093,plain,
! [X0] : antidomain(X0) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f26,f1092]) ).
fof(f1252,plain,
! [X0] : domain(addition(one,X0)) = addition(one,domain(X0)),
inference(paramodulation,[status(thm)],[f944,f39]) ).
fof(f1253,plain,
! [X0] : domain(addition(one,X0)) = one,
inference(forward_demodulation,[status(thm)],[f46,f1252]) ).
fof(f1914,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(antidomain(X1),X0)),
inference(paramodulation,[status(thm)],[f179,f860]) ).
fof(f1915,plain,
! [X0,X1] : X0 = addition(X0,multiplication(antidomain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f26,f1914]) ).
fof(f1916,plain,
! [X0,X1] : multiplication(one,X0) = addition(X0,multiplication(domain(X1),X0)),
inference(paramodulation,[status(thm)],[f46,f860]) ).
fof(f1917,plain,
! [X0,X1] : X0 = addition(X0,multiplication(domain(X1),X0)),
inference(forward_demodulation,[status(thm)],[f26,f1916]) ).
fof(f1947,plain,
! [X0] : multiplication(addition(one,domain(X0)),X0) = multiplication(domain(X0),X0),
inference(paramodulation,[status(thm)],[f35,f860]) ).
fof(f1948,plain,
! [X0] : multiplication(one,X0) = multiplication(domain(X0),X0),
inference(forward_demodulation,[status(thm)],[f46,f1947]) ).
fof(f1949,plain,
! [X0] : X0 = multiplication(domain(X0),X0),
inference(forward_demodulation,[status(thm)],[f26,f1948]) ).
fof(f2089,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f1949,f28]) ).
fof(f2090,plain,
! [X0,X1] : multiplication(addition(X0,domain(X1)),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f20,f2089]) ).
fof(f3212,plain,
! [X0,X1] : multiplication(domain(addition(X0,X1)),X1) = addition(X1,multiplication(domain(X0),X1)),
inference(paramodulation,[status(thm)],[f39,f2090]) ).
fof(f3213,plain,
! [X0,X1] : multiplication(domain(addition(X0,X1)),X1) = X1,
inference(forward_demodulation,[status(thm)],[f1917,f3212]) ).
fof(f3319,plain,
! [X0,X1] : multiplication(domain(X0),multiplication(antidomain(X1),X0)) = multiplication(antidomain(X1),X0),
inference(paramodulation,[status(thm)],[f1915,f3213]) ).
fof(f3979,plain,
! [X0,X1] : multiplication(X0,one) = addition(X0,multiplication(X0,antidomain(X1))),
inference(paramodulation,[status(thm)],[f179,f141]) ).
fof(f3980,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,antidomain(X1))),
inference(forward_demodulation,[status(thm)],[f25,f3979]) ).
fof(f3981,plain,
! [X0,X1] : multiplication(X0,one) = addition(X0,multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f46,f141]) ).
fof(f3982,plain,
! [X0,X1] : X0 = addition(X0,multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f25,f3981]) ).
fof(f4803,plain,
! [X0] : antidomain(domain(X0)) = addition(antidomain(domain(X0)),antidomain(X0)),
inference(paramodulation,[status(thm)],[f1093,f3980]) ).
fof(f4804,plain,
! [X0] : antidomain(domain(X0)) = addition(antidomain(X0),antidomain(domain(X0))),
inference(forward_demodulation,[status(thm)],[f20,f4803]) ).
fof(f4938,plain,
! [X0,X1] : antidomain(domain(multiplication(X0,domain(X1)))) = addition(antidomain(multiplication(X0,domain(X1))),antidomain(domain(multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f36,f4804]) ).
fof(f4939,plain,
! [X0,X1] : antidomain(domain(multiplication(X0,X1))) = addition(antidomain(multiplication(X0,domain(X1))),antidomain(domain(multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f36,f4938]) ).
fof(f7171,plain,
! [X0,X1] : addition(domain(addition(X0,multiplication(X0,X1))),antidomain(multiplication(X0,domain(addition(one,X1))))) = one,
inference(paramodulation,[status(thm)],[f141,f216]) ).
fof(f7172,plain,
! [X0,X1] : addition(domain(addition(X0,multiplication(X0,X1))),antidomain(multiplication(X0,one))) = one,
inference(forward_demodulation,[status(thm)],[f1253,f7171]) ).
fof(f7173,plain,
! [X0,X1] : addition(antidomain(multiplication(X0,one)),domain(addition(X0,multiplication(X0,X1)))) = one,
inference(forward_demodulation,[status(thm)],[f20,f7172]) ).
fof(f7174,plain,
! [X0,X1] : addition(antidomain(X0),domain(addition(X0,multiplication(X0,X1)))) = one,
inference(forward_demodulation,[status(thm)],[f25,f7173]) ).
fof(f8424,plain,
! [X0] : zero = multiplication(antidomain(X0),X0),
inference(paramodulation,[status(thm)],[f115,f3319]) ).
fof(f8590,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = addition(multiplication(antidomain(X0),X1),zero),
inference(paramodulation,[status(thm)],[f8424,f27]) ).
fof(f8591,plain,
! [X0,X1] : multiplication(antidomain(X0),addition(X1,X0)) = multiplication(antidomain(X0),X1),
inference(forward_demodulation,[status(thm)],[f22,f8590]) ).
fof(f9136,plain,
! [X0,X1] : multiplication(antidomain(domain(addition(X0,multiplication(X0,X1)))),one) = multiplication(antidomain(domain(addition(X0,multiplication(X0,X1)))),antidomain(X0)),
inference(paramodulation,[status(thm)],[f7174,f8591]) ).
fof(f9137,plain,
! [X0,X1] : antidomain(domain(addition(X0,multiplication(X0,X1)))) = multiplication(antidomain(domain(addition(X0,multiplication(X0,X1)))),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f25,f9136]) ).
fof(f9559,plain,
! [X0,X1] : domain(X0) = domain(addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f3982,f270]) ).
fof(f9784,plain,
! [X0,X1] : antidomain(domain(addition(X0,multiplication(X0,X1)))) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(backward_demodulation,[status(thm)],[f9559,f9137]) ).
fof(f9785,plain,
! [X0] : antidomain(domain(X0)) = multiplication(antidomain(domain(X0)),antidomain(X0)),
inference(forward_demodulation,[status(thm)],[f9559,f9784]) ).
fof(f9786,plain,
! [X0] : antidomain(domain(X0)) = antidomain(X0),
inference(forward_demodulation,[status(thm)],[f1093,f9785]) ).
fof(f9843,plain,
! [X0,X1] : antidomain(domain(multiplication(X0,X1))) = addition(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(X0,X1))),
inference(backward_demodulation,[status(thm)],[f9786,f4939]) ).
fof(f9844,plain,
! [X0,X1] : antidomain(multiplication(X0,X1)) = addition(antidomain(multiplication(X0,domain(X1))),antidomain(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f9786,f9843]) ).
fof(f9845,plain,
! [X0,X1] : antidomain(multiplication(X0,X1)) = addition(antidomain(multiplication(X0,X1)),antidomain(multiplication(X0,domain(X1)))),
inference(forward_demodulation,[status(thm)],[f20,f9844]) ).
fof(f9990,plain,
antidomain(multiplication(sk0_0,sk0_1)) != antidomain(multiplication(sk0_0,domain(sk0_1))),
inference(backward_demodulation,[status(thm)],[f9845,f45]) ).
fof(f10009,plain,
! [X0,X1] : antidomain(domain(multiplication(X0,X1))) = antidomain(multiplication(X0,domain(X1))),
inference(paramodulation,[status(thm)],[f36,f9786]) ).
fof(f10010,plain,
! [X0,X1] : antidomain(multiplication(X0,X1)) = antidomain(multiplication(X0,domain(X1))),
inference(forward_demodulation,[status(thm)],[f9786,f10009]) ).
fof(f10169,plain,
antidomain(multiplication(sk0_0,sk0_1)) != antidomain(multiplication(sk0_0,sk0_1)),
inference(backward_demodulation,[status(thm)],[f10010,f9990]) ).
fof(f10170,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f10169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : KLE082+1 : TPTP v8.1.2. Released v4.0.0.
% 0.08/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n011.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue May 30 11:46:57 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.5.1
% 5.08/1.08 % Refutation found
% 5.08/1.08 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.08/1.08 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.18/1.12 % Elapsed time: 0.759647 seconds
% 5.18/1.12 % CPU time: 5.454864 seconds
% 5.18/1.12 % Memory used: 109.762 MB
%------------------------------------------------------------------------------