TSTP Solution File: KLE133+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : KLE133+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 0.15s 0.34s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   62 (  58 unt;   0 def)
%            Number of atoms       :   70 (  69 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   18 (  10   ~;   0   |;   6   &)
%                                         (   0 <=>;   2  =>;   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    :   11 (  11 usr;   4 con; 0-2 aty)
%            Number of variables   :   68 (;  66   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [A,B] : addition(A,B) = addition(B,A),
    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(f29,conjecture,
    ! [X0] :
      ( ( ! [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))))
        & ! [X2] : forward_diamond(X0,forward_diamond(X0,domain(X2))) = forward_diamond(X0,domain(X2)) )
     => ! [X3] : addition(forward_diamond(X0,domain(X3)),forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3))))) = forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3)))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f30,negated_conjecture,
    ~ ! [X0] :
        ( ( ! [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))))
          & ! [X2] : forward_diamond(X0,forward_diamond(X0,domain(X2))) = forward_diamond(X0,domain(X2)) )
       => ! [X3] : addition(forward_diamond(X0,domain(X3)),forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3))))) = forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3)))) ),
    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(f63,plain,
    ? [X0] :
      ( ! [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))))
      & ! [X2] : forward_diamond(X0,forward_diamond(X0,domain(X2))) = forward_diamond(X0,domain(X2))
      & ? [X3] : addition(forward_diamond(X0,domain(X3)),forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3))))) != forward_diamond(star(X0),domain_difference(domain(X3),forward_diamond(X0,domain(X3)))) ),
    inference(pre_NNF_transformation,[status(esa)],[f30]) ).

fof(f64,plain,
    ( ! [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))))
    & ! [X2] : forward_diamond(sk0_0,forward_diamond(sk0_0,domain(X2))) = forward_diamond(sk0_0,domain(X2))
    & addition(forward_diamond(sk0_0,domain(sk0_1)),forward_diamond(star(sk0_0),domain_difference(domain(sk0_1),forward_diamond(sk0_0,domain(sk0_1))))) != forward_diamond(star(sk0_0),domain_difference(domain(sk0_1),forward_diamond(sk0_0,domain(sk0_1)))) ),
    inference(skolemization,[status(esa)],[f63]) ).

fof(f65,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(f66,plain,
    ! [X0] : forward_diamond(sk0_0,forward_diamond(sk0_0,domain(X0))) = forward_diamond(sk0_0,domain(X0)),
    inference(cnf_transformation,[status(esa)],[f64]) ).

fof(f67,plain,
    addition(forward_diamond(sk0_0,domain(sk0_1)),forward_diamond(star(sk0_0),domain_difference(domain(sk0_1),forward_diamond(sk0_0,domain(sk0_1))))) != forward_diamond(star(sk0_0),domain_difference(domain(sk0_1),forward_diamond(sk0_0,domain(sk0_1)))),
    inference(cnf_transformation,[status(esa)],[f64]) ).

fof(f124,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,f65]) ).

fof(f125,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,f124]) ).

fof(f126,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,f125]) ).

fof(f127,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,f126]) ).

fof(f128,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,f127]) ).

fof(f389,plain,
    ! [X0] : addition(zero,X0) = X0,
    inference(paramodulation,[status(thm)],[f31,f33]) ).

fof(f434,plain,
    antidomain(one) = zero,
    inference(paramodulation,[status(thm)],[f36,f46]) ).

fof(f441,plain,
    domain(one) = antidomain(zero),
    inference(paramodulation,[status(thm)],[f434,f49]) ).

fof(f442,plain,
    ! [X0] : multiplication(domain(X0),antidomain(X0)) = zero,
    inference(paramodulation,[status(thm)],[f49,f46]) ).

fof(f443,plain,
    ! [X0] : domain_difference(X0,X0) = zero,
    inference(forward_demodulation,[status(thm)],[f55,f442]) ).

fof(f608,plain,
    ! [X0] : addition(forward_diamond(sk0_0,domain(X0)),forward_diamond(star(sk0_0),domain_difference(forward_diamond(sk0_0,domain(X0)),forward_diamond(sk0_0,domain(X0))))) = forward_diamond(star(sk0_0),domain_difference(forward_diamond(sk0_0,domain(X0)),forward_diamond(sk0_0,forward_diamond(sk0_0,domain(X0))))),
    inference(paramodulation,[status(thm)],[f66,f128]) ).

fof(f609,plain,
    ! [X0] : addition(forward_diamond(sk0_0,domain(X0)),forward_diamond(star(sk0_0),zero)) = forward_diamond(star(sk0_0),domain_difference(forward_diamond(sk0_0,domain(X0)),forward_diamond(sk0_0,forward_diamond(sk0_0,domain(X0))))),
    inference(forward_demodulation,[status(thm)],[f443,f608]) ).

fof(f610,plain,
    ! [X0] : addition(forward_diamond(sk0_0,domain(X0)),forward_diamond(star(sk0_0),zero)) = forward_diamond(star(sk0_0),domain_difference(forward_diamond(sk0_0,domain(X0)),forward_diamond(sk0_0,domain(X0)))),
    inference(forward_demodulation,[status(thm)],[f66,f609]) ).

fof(f611,plain,
    ! [X0] : addition(forward_diamond(sk0_0,domain(X0)),forward_diamond(star(sk0_0),zero)) = forward_diamond(star(sk0_0),zero),
    inference(forward_demodulation,[status(thm)],[f443,f610]) ).

fof(f638,plain,
    ! [X0] : addition(forward_diamond(star(sk0_0),zero),forward_diamond(sk0_0,domain(X0))) = forward_diamond(star(sk0_0),zero),
    inference(paramodulation,[status(thm)],[f31,f611]) ).

fof(f960,plain,
    ! [X0] : addition(antidomain(X0),antidomain(antidomain(X0))) = one,
    inference(forward_demodulation,[status(thm)],[f31,f48]) ).

fof(f961,plain,
    ! [X0] : addition(antidomain(X0),domain(X0)) = one,
    inference(forward_demodulation,[status(thm)],[f49,f960]) ).

fof(f964,plain,
    addition(zero,domain(one)) = one,
    inference(paramodulation,[status(thm)],[f434,f961]) ).

fof(f965,plain,
    domain(one) = one,
    inference(forward_demodulation,[status(thm)],[f389,f964]) ).

fof(f966,plain,
    antidomain(zero) = one,
    inference(forward_demodulation,[status(thm)],[f441,f965]) ).

fof(f1089,plain,
    domain(zero) = antidomain(one),
    inference(paramodulation,[status(thm)],[f966,f49]) ).

fof(f1090,plain,
    domain(zero) = zero,
    inference(forward_demodulation,[status(thm)],[f434,f1089]) ).

fof(f1092,plain,
    ! [X0] : domain_difference(X0,zero) = multiplication(domain(X0),one),
    inference(paramodulation,[status(thm)],[f966,f55]) ).

fof(f1093,plain,
    ! [X0] : domain_difference(X0,zero) = domain(X0),
    inference(forward_demodulation,[status(thm)],[f36,f1092]) ).

fof(f1171,plain,
    ! [X0] : forward_diamond(X0,zero) = domain(multiplication(X0,zero)),
    inference(paramodulation,[status(thm)],[f1090,f56]) ).

fof(f1172,plain,
    ! [X0] : forward_diamond(X0,zero) = domain(zero),
    inference(forward_demodulation,[status(thm)],[f40,f1171]) ).

fof(f1173,plain,
    ! [X0] : forward_diamond(X0,zero) = zero,
    inference(forward_demodulation,[status(thm)],[f1090,f1172]) ).

fof(f1344,plain,
    ! [X0] : addition(forward_diamond(star(sk0_0),zero),forward_diamond(sk0_0,domain(X0))) = zero,
    inference(backward_demodulation,[status(thm)],[f1173,f638]) ).

fof(f1345,plain,
    ! [X0] : addition(zero,forward_diamond(sk0_0,domain(X0))) = zero,
    inference(forward_demodulation,[status(thm)],[f1173,f1344]) ).

fof(f1346,plain,
    ! [X0] : forward_diamond(sk0_0,domain(X0)) = zero,
    inference(forward_demodulation,[status(thm)],[f389,f1345]) ).

fof(f1484,plain,
    addition(forward_diamond(sk0_0,domain(sk0_1)),forward_diamond(star(sk0_0),domain_difference(domain(sk0_1),forward_diamond(sk0_0,domain(sk0_1))))) != forward_diamond(star(sk0_0),domain_difference(domain(sk0_1),zero)),
    inference(backward_demodulation,[status(thm)],[f1346,f67]) ).

fof(f1485,plain,
    addition(zero,forward_diamond(star(sk0_0),domain_difference(domain(sk0_1),forward_diamond(sk0_0,domain(sk0_1))))) != forward_diamond(star(sk0_0),domain_difference(domain(sk0_1),zero)),
    inference(forward_demodulation,[status(thm)],[f1346,f1484]) ).

fof(f1486,plain,
    forward_diamond(star(sk0_0),domain_difference(domain(sk0_1),forward_diamond(sk0_0,domain(sk0_1)))) != forward_diamond(star(sk0_0),domain_difference(domain(sk0_1),zero)),
    inference(forward_demodulation,[status(thm)],[f389,f1485]) ).

fof(f1487,plain,
    forward_diamond(star(sk0_0),domain_difference(domain(sk0_1),zero)) != forward_diamond(star(sk0_0),domain_difference(domain(sk0_1),zero)),
    inference(forward_demodulation,[status(thm)],[f1346,f1486]) ).

fof(f1488,plain,
    forward_diamond(star(sk0_0),domain(domain(sk0_1))) != forward_diamond(star(sk0_0),domain_difference(domain(sk0_1),zero)),
    inference(forward_demodulation,[status(thm)],[f1093,f1487]) ).

fof(f1489,plain,
    forward_diamond(star(sk0_0),domain(domain(sk0_1))) != forward_diamond(star(sk0_0),domain(domain(sk0_1))),
    inference(forward_demodulation,[status(thm)],[f1093,f1488]) ).

fof(f1490,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f1489]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09  % Problem  : KLE133+1 : TPTP v8.1.2. Released v4.0.0.
% 0.04/0.09  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30  % Computer : n026.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit : 300
% 0.09/0.30  % WCLimit  : 300
% 0.09/0.30  % DateTime : Tue May 30 12:02:43 EDT 2023
% 0.09/0.30  % CPUTime  : 
% 0.09/0.30  % Drodi V3.5.1
% 0.15/0.34  % Refutation found
% 0.15/0.34  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.34  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.29/0.57  % Elapsed time: 0.055846 seconds
% 0.29/0.57  % CPU time: 0.127841 seconds
% 0.29/0.57  % Memory used: 12.769 MB
%------------------------------------------------------------------------------