TSTP Solution File: KLE099+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------