TSTP Solution File: SET619+3 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SET619+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n022.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 12:34:50 EDT 2023

% Result   : Theorem 0.19s 0.59s
% Output   : CNFRefutation 1.90s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   29 (  29 unt;   0 def)
%            Number of atoms       :   29 (  28 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    6 (   6   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   53 (;  51   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [B,C,D] : union(union(B,C),D) = union(B,union(C,D)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [B,C] : union(B,intersection(B,C)) = B,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [B,C] : union(intersection(B,C),difference(B,C)) = B,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [B,C] : union(B,C) = union(C,B),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [B,C] : intersection(B,C) = intersection(C,B),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f14,conjecture,
    ! [B,C] : union(B,C) = union(symmetric_difference(B,C),intersection(B,C)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f15,negated_conjecture,
    ~ ! [B,C] : union(B,C) = union(symmetric_difference(B,C),intersection(B,C)),
    inference(negated_conjecture,[status(cth)],[f14]) ).

fof(f16,plain,
    ! [X0,X1] : symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
    inference(cnf_transformation,[status(esa)],[f1]) ).

fof(f17,plain,
    ! [X0,X1,X2] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f18,plain,
    ! [X0,X1] : union(X0,intersection(X0,X1)) = X0,
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f19,plain,
    ! [X0,X1] : union(intersection(X0,X1),difference(X0,X1)) = X0,
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f35,plain,
    ! [X0,X1] : union(X0,X1) = union(X1,X0),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f36,plain,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f53,plain,
    ? [B,C] : union(B,C) != union(symmetric_difference(B,C),intersection(B,C)),
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f54,plain,
    union(sk0_2,sk0_3) != union(symmetric_difference(sk0_2,sk0_3),intersection(sk0_2,sk0_3)),
    inference(skolemization,[status(esa)],[f53]) ).

fof(f55,plain,
    union(sk0_2,sk0_3) != union(symmetric_difference(sk0_2,sk0_3),intersection(sk0_2,sk0_3)),
    inference(cnf_transformation,[status(esa)],[f54]) ).

fof(f66,plain,
    ! [X0,X1,X2] : union(X0,X1) = union(X0,union(intersection(X0,X2),X1)),
    inference(paramodulation,[status(thm)],[f18,f17]) ).

fof(f137,plain,
    ! [X0,X1] : union(difference(X0,X1),intersection(X0,X1)) = X0,
    inference(forward_demodulation,[status(thm)],[f35,f19]) ).

fof(f138,plain,
    ! [X0,X1] : union(difference(X0,X1),intersection(X1,X0)) = X0,
    inference(paramodulation,[status(thm)],[f36,f137]) ).

fof(f160,plain,
    ! [X0,X1,X2] : union(symmetric_difference(X0,X1),X2) = union(difference(X0,X1),union(difference(X1,X0),X2)),
    inference(paramodulation,[status(thm)],[f16,f17]) ).

fof(f177,plain,
    ! [X0,X1,X2] : union(X0,X1) = union(X0,union(X1,intersection(X0,X2))),
    inference(paramodulation,[status(thm)],[f35,f66]) ).

fof(f661,plain,
    ! [X0,X1] : union(X0,difference(X1,X0)) = union(X0,X1),
    inference(paramodulation,[status(thm)],[f138,f177]) ).

fof(f1344,plain,
    ! [X0,X1] : union(symmetric_difference(X0,X1),intersection(X0,X1)) = union(difference(X0,X1),X1),
    inference(paramodulation,[status(thm)],[f138,f160]) ).

fof(f1345,plain,
    ! [X0,X1] : union(symmetric_difference(X0,X1),intersection(X0,X1)) = union(X1,difference(X0,X1)),
    inference(forward_demodulation,[status(thm)],[f35,f1344]) ).

fof(f1346,plain,
    ! [X0,X1] : union(symmetric_difference(X0,X1),intersection(X0,X1)) = union(X1,X0),
    inference(forward_demodulation,[status(thm)],[f661,f1345]) ).

fof(f3490,plain,
    union(sk0_2,sk0_3) != union(sk0_3,sk0_2),
    inference(backward_demodulation,[status(thm)],[f1346,f55]) ).

fof(f3491,plain,
    union(sk0_2,sk0_3) != union(sk0_2,sk0_3),
    inference(forward_demodulation,[status(thm)],[f35,f3490]) ).

fof(f3492,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f3491]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET619+3 : TPTP v8.1.2. Released v2.2.0.
% 0.11/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n022.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue May 30 10:16:42 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 0.19/0.59  % Refutation found
% 0.19/0.59  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.59  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.90/0.60  % Elapsed time: 0.258627 seconds
% 1.90/0.60  % CPU time: 1.925323 seconds
% 1.90/0.60  % Memory used: 77.859 MB
%------------------------------------------------------------------------------