TSTP Solution File: SET601+3 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET601+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n009.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 : Tue Apr 30 20:39:56 EDT 2024

% Result   : Theorem 14.94s 2.31s
% Output   : CNFRefutation 15.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   74 (  74 unt;   0 def)
%            Number of atoms       :   74 (  73 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :   19 (  19   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :  146 ( 143   !;   3   ?)

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

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

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

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

fof(f5,axiom,
    ! [B,C,D] : union(B,intersection(C,D)) = intersection(union(B,C),union(B,D)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

fof(f10,axiom,
    ! [B,C] : intersection(B,C) = intersection(C,B),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

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

fof(f16,plain,
    ! [X0,X1,X2] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f1]) ).

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

fof(f18,plain,
    ! [X0,X1,X2] : intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
    inference(cnf_transformation,[status(esa)],[f3]) ).

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

fof(f20,plain,
    ! [X0,X1,X2] : union(X0,intersection(X1,X2)) = intersection(union(X0,X1),union(X0,X2)),
    inference(cnf_transformation,[status(esa)],[f5]) ).

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

fof(f37,plain,
    ! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
    inference(cnf_transformation,[status(esa)],[f10]) ).

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

fof(f54,plain,
    union(union(intersection(sk0_2,sk0_3),intersection(sk0_3,sk0_4)),intersection(sk0_4,sk0_2)) != intersection(intersection(union(sk0_2,sk0_3),union(sk0_3,sk0_4)),union(sk0_4,sk0_2)),
    inference(skolemization,[status(esa)],[f53]) ).

fof(f55,plain,
    union(union(intersection(sk0_2,sk0_3),intersection(sk0_3,sk0_4)),intersection(sk0_4,sk0_2)) != intersection(intersection(union(sk0_2,sk0_3),union(sk0_3,sk0_4)),union(sk0_4,sk0_2)),
    inference(cnf_transformation,[status(esa)],[f54]) ).

fof(f58,plain,
    union(union(intersection(sk0_2,sk0_3),intersection(sk0_3,sk0_4)),intersection(sk0_2,sk0_4)) != intersection(intersection(union(sk0_2,sk0_3),union(sk0_3,sk0_4)),union(sk0_4,sk0_2)),
    inference(forward_demodulation,[status(thm)],[f37,f55]) ).

fof(f59,plain,
    union(union(intersection(sk0_2,sk0_3),intersection(sk0_3,sk0_4)),intersection(sk0_2,sk0_4)) != intersection(union(sk0_2,sk0_3),intersection(union(sk0_3,sk0_4),union(sk0_4,sk0_2))),
    inference(forward_demodulation,[status(thm)],[f18,f58]) ).

fof(f60,plain,
    union(union(intersection(sk0_2,sk0_3),intersection(sk0_3,sk0_4)),intersection(sk0_2,sk0_4)) != intersection(union(sk0_2,sk0_3),intersection(union(sk0_3,sk0_4),union(sk0_2,sk0_4))),
    inference(forward_demodulation,[status(thm)],[f36,f59]) ).

fof(f61,plain,
    union(union(intersection(sk0_2,sk0_3),intersection(sk0_3,sk0_4)),intersection(sk0_2,sk0_4)) != intersection(union(sk0_2,sk0_3),intersection(union(sk0_2,sk0_4),union(sk0_3,sk0_4))),
    inference(forward_demodulation,[status(thm)],[f37,f60]) ).

fof(f62,plain,
    ! [X0] : union(X0,X0) = X0,
    inference(paramodulation,[status(thm)],[f17,f19]) ).

fof(f71,plain,
    ! [X0,X1] : union(X0,X1) = union(X0,union(X0,X1)),
    inference(paramodulation,[status(thm)],[f62,f16]) ).

fof(f76,plain,
    ! [X0,X1] : union(X0,intersection(X1,X0)) = X0,
    inference(paramodulation,[status(thm)],[f37,f19]) ).

fof(f85,plain,
    ! [X0,X1,X2] : union(union(X0,X1),X2) = union(union(X0,X1),union(X0,union(X1,X2))),
    inference(paramodulation,[status(thm)],[f16,f71]) ).

fof(f90,plain,
    ! [X0,X1] : union(X0,X1) = union(X0,union(X1,X0)),
    inference(paramodulation,[status(thm)],[f36,f71]) ).

fof(f98,plain,
    ! [X0,X1] : union(union(X0,X1),X0) = union(union(X0,X1),union(X0,X1)),
    inference(paramodulation,[status(thm)],[f71,f90]) ).

fof(f99,plain,
    ! [X0,X1] : union(union(X0,X1),X0) = union(X0,X1),
    inference(forward_demodulation,[status(thm)],[f62,f98]) ).

fof(f123,plain,
    ! [X0,X1] : union(union(X0,X1),X1) = union(X1,X0),
    inference(paramodulation,[status(thm)],[f36,f99]) ).

fof(f128,plain,
    ! [X0,X1,X2] : union(union(X0,X1),X2) = union(union(X0,X1),union(X0,X2)),
    inference(paramodulation,[status(thm)],[f99,f16]) ).

fof(f134,plain,
    ! [X0,X1,X2] : union(union(X0,X1),X2) = union(union(X0,X1),union(X1,X2)),
    inference(backward_demodulation,[status(thm)],[f128,f85]) ).

fof(f151,plain,
    ! [X0,X1] : union(X0,intersection(X0,X1)) = union(intersection(X0,X1),X0),
    inference(paramodulation,[status(thm)],[f19,f123]) ).

fof(f152,plain,
    ! [X0,X1] : X0 = union(intersection(X0,X1),X0),
    inference(forward_demodulation,[status(thm)],[f19,f151]) ).

fof(f166,plain,
    ! [X0,X1,X2] : union(union(X0,X1),X2) = union(union(X1,X0),union(X0,X2)),
    inference(paramodulation,[status(thm)],[f123,f16]) ).

fof(f167,plain,
    ! [X0,X1,X2] : union(union(X0,X1),X2) = union(union(X1,X0),X2),
    inference(forward_demodulation,[status(thm)],[f134,f166]) ).

fof(f209,plain,
    ! [X0,X1,X2] : union(X0,intersection(X1,intersection(X2,X0))) = X0,
    inference(paramodulation,[status(thm)],[f18,f76]) ).

fof(f225,plain,
    ! [X0,X1,X2] : union(X0,intersection(X1,X2)) = intersection(union(X0,X2),union(X0,X1)),
    inference(paramodulation,[status(thm)],[f37,f20]) ).

fof(f226,plain,
    ! [X0,X1,X2] : union(X0,intersection(X1,X2)) = union(X0,intersection(X2,X1)),
    inference(forward_demodulation,[status(thm)],[f20,f225]) ).

fof(f243,plain,
    ! [X0,X1] : union(X0,intersection(X0,X1)) = intersection(X0,union(X0,X1)),
    inference(paramodulation,[status(thm)],[f62,f20]) ).

fof(f244,plain,
    ! [X0,X1] : X0 = intersection(X0,union(X0,X1)),
    inference(forward_demodulation,[status(thm)],[f19,f243]) ).

fof(f254,plain,
    ! [X0,X1,X2] : union(X0,intersection(X1,intersection(X2,X0))) = intersection(union(X0,X1),X0),
    inference(paramodulation,[status(thm)],[f76,f20]) ).

fof(f255,plain,
    ! [X0,X1] : X0 = intersection(union(X0,X1),X0),
    inference(forward_demodulation,[status(thm)],[f209,f254]) ).

fof(f258,plain,
    ! [X0,X1,X2] : union(X0,intersection(X1,X2)) = intersection(union(X0,X1),union(X2,X0)),
    inference(paramodulation,[status(thm)],[f36,f20]) ).

fof(f265,plain,
    ! [X0,X1,X2,X3] : intersection(union(X0,intersection(X1,X2)),X3) = intersection(union(X0,X1),intersection(union(X0,X2),X3)),
    inference(paramodulation,[status(thm)],[f20,f18]) ).

fof(f270,plain,
    ! [X0,X1,X2] : union(union(X0,X1),union(X0,intersection(X2,X1))) = union(X0,X1),
    inference(paramodulation,[status(thm)],[f20,f76]) ).

fof(f271,plain,
    ! [X0,X1,X2] : union(union(X0,X1),intersection(X2,X1)) = union(X0,X1),
    inference(forward_demodulation,[status(thm)],[f128,f270]) ).

fof(f287,plain,
    union(union(intersection(sk0_2,sk0_3),intersection(sk0_3,sk0_4)),intersection(sk0_2,sk0_4)) != intersection(union(sk0_2,intersection(sk0_3,sk0_4)),union(sk0_3,sk0_4)),
    inference(backward_demodulation,[status(thm)],[f265,f61]) ).

fof(f288,plain,
    union(union(intersection(sk0_2,sk0_3),intersection(sk0_3,sk0_4)),intersection(sk0_2,sk0_4)) != intersection(union(intersection(sk0_3,sk0_4),sk0_2),union(sk0_3,sk0_4)),
    inference(forward_demodulation,[status(thm)],[f36,f287]) ).

fof(f314,plain,
    ! [X0,X1] : X0 = intersection(X0,union(X1,X0)),
    inference(paramodulation,[status(thm)],[f36,f244]) ).

fof(f322,plain,
    ! [X0,X1,X2] : intersection(X0,X1) = intersection(X0,intersection(union(X0,X2),X1)),
    inference(paramodulation,[status(thm)],[f244,f18]) ).

fof(f346,plain,
    ! [X0,X1,X2] : intersection(X0,X1) = intersection(union(X0,X2),intersection(X0,X1)),
    inference(paramodulation,[status(thm)],[f255,f18]) ).

fof(f375,plain,
    ! [X0,X1,X2] : intersection(X0,X1) = intersection(X0,intersection(union(X2,X0),X1)),
    inference(paramodulation,[status(thm)],[f314,f18]) ).

fof(f862,plain,
    union(intersection(sk0_2,sk0_4),union(intersection(sk0_2,sk0_3),intersection(sk0_3,sk0_4))) != intersection(union(intersection(sk0_3,sk0_4),sk0_2),union(sk0_3,sk0_4)),
    inference(paramodulation,[status(thm)],[f36,f288]) ).

fof(f863,plain,
    union(union(intersection(sk0_2,sk0_4),intersection(sk0_2,sk0_3)),intersection(sk0_3,sk0_4)) != intersection(union(intersection(sk0_3,sk0_4),sk0_2),union(sk0_3,sk0_4)),
    inference(forward_demodulation,[status(thm)],[f16,f862]) ).

fof(f864,plain,
    union(union(intersection(sk0_2,sk0_3),intersection(sk0_2,sk0_4)),intersection(sk0_3,sk0_4)) != intersection(union(intersection(sk0_3,sk0_4),sk0_2),union(sk0_3,sk0_4)),
    inference(forward_demodulation,[status(thm)],[f167,f863]) ).

fof(f2764,plain,
    ! [X0,X1,X2] : union(intersection(X0,X1),X2) = union(union(X2,intersection(X0,X1)),intersection(X1,X0)),
    inference(paramodulation,[status(thm)],[f123,f226]) ).

fof(f2889,plain,
    ! [X0,X1,X2] : union(union(X0,intersection(X1,X2)),intersection(X2,X1)) = union(intersection(X2,X1),X0),
    inference(paramodulation,[status(thm)],[f226,f123]) ).

fof(f2890,plain,
    ! [X0,X1,X2] : union(intersection(X0,X1),X2) = union(intersection(X1,X0),X2),
    inference(forward_demodulation,[status(thm)],[f2764,f2889]) ).

fof(f4433,plain,
    ! [X0,X1,X2] : intersection(union(X0,X1),X2) = intersection(union(X0,X1),intersection(union(X1,X0),X2)),
    inference(paramodulation,[status(thm)],[f123,f322]) ).

fof(f4555,plain,
    ! [X0,X1,X2] : intersection(union(X0,X1),X2) = intersection(union(X1,X0),intersection(union(X0,X1),X2)),
    inference(paramodulation,[status(thm)],[f123,f346]) ).

fof(f4556,plain,
    ! [X0,X1,X2] : intersection(union(X0,X1),X2) = intersection(union(X1,X0),X2),
    inference(forward_demodulation,[status(thm)],[f4433,f4555]) ).

fof(f5499,plain,
    ! [X0,X1,X2] : intersection(X0,union(X1,X2)) = intersection(X0,union(X1,intersection(X0,X2))),
    inference(paramodulation,[status(thm)],[f20,f375]) ).

fof(f9635,plain,
    ! [X0,X1,X2] : union(intersection(X0,X1),intersection(X0,X2)) = intersection(X0,union(X2,intersection(X0,X1))),
    inference(paramodulation,[status(thm)],[f152,f258]) ).

fof(f9636,plain,
    ! [X0,X1,X2] : union(intersection(X0,X1),intersection(X0,X2)) = intersection(X0,union(X2,X1)),
    inference(forward_demodulation,[status(thm)],[f5499,f9635]) ).

fof(f9748,plain,
    ! [X0,X1,X2,X3] : union(intersection(X0,X1),intersection(X2,union(X3,X1))) = intersection(union(intersection(X0,X1),X2),union(X3,X1)),
    inference(paramodulation,[status(thm)],[f271,f258]) ).

fof(f9950,plain,
    union(intersection(sk0_2,union(sk0_4,sk0_3)),intersection(sk0_3,sk0_4)) != intersection(union(intersection(sk0_3,sk0_4),sk0_2),union(sk0_3,sk0_4)),
    inference(backward_demodulation,[status(thm)],[f9636,f864]) ).

fof(f9951,plain,
    union(intersection(union(sk0_4,sk0_3),sk0_2),intersection(sk0_3,sk0_4)) != intersection(union(intersection(sk0_3,sk0_4),sk0_2),union(sk0_3,sk0_4)),
    inference(forward_demodulation,[status(thm)],[f2890,f9950]) ).

fof(f9952,plain,
    union(intersection(union(sk0_3,sk0_4),sk0_2),intersection(sk0_3,sk0_4)) != intersection(union(intersection(sk0_3,sk0_4),sk0_2),union(sk0_3,sk0_4)),
    inference(forward_demodulation,[status(thm)],[f4556,f9951]) ).

fof(f9953,plain,
    union(intersection(union(sk0_3,sk0_4),sk0_2),intersection(sk0_3,sk0_4)) != union(intersection(sk0_3,sk0_4),intersection(sk0_2,union(sk0_3,sk0_4))),
    inference(forward_demodulation,[status(thm)],[f9748,f9952]) ).

fof(f9954,plain,
    union(intersection(union(sk0_3,sk0_4),sk0_2),intersection(sk0_3,sk0_4)) != union(intersection(sk0_3,sk0_4),intersection(union(sk0_3,sk0_4),sk0_2)),
    inference(forward_demodulation,[status(thm)],[f226,f9953]) ).

fof(f9955,plain,
    union(intersection(union(sk0_3,sk0_4),sk0_2),intersection(sk0_3,sk0_4)) != union(intersection(union(sk0_3,sk0_4),sk0_2),intersection(sk0_3,sk0_4)),
    inference(forward_demodulation,[status(thm)],[f36,f9954]) ).

fof(f9956,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f9955]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : SET601+3 : TPTP v8.1.2. Released v2.2.0.
% 0.02/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30  % Computer : n009.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 : Mon Apr 29 21:38:56 EDT 2024
% 0.09/0.30  % CPUTime  : 
% 0.09/0.31  % Drodi V3.6.0
% 14.94/2.31  % Refutation found
% 14.94/2.31  % SZS status Theorem for theBenchmark: Theorem is valid
% 14.94/2.31  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 15.71/2.36  % Elapsed time: 2.048961 seconds
% 15.71/2.36  % CPU time: 16.049494 seconds
% 15.71/2.36  % Total memory used: 194.114 MB
% 15.71/2.36  % Net memory used: 192.114 MB
%------------------------------------------------------------------------------