TSTP Solution File: SEU132+1 by Drodi---3.5.1

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU132+1 : TPTP v8.1.2. Released v3.3.0.
% 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 12:35:55 EDT 2023

% Result   : Theorem 0.13s 0.31s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08  % Problem  : SEU132+1 : TPTP v8.1.2. Released v3.3.0.
% 0.02/0.09  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.08/0.28  % Computer : n019.cluster.edu
% 0.08/0.28  % Model    : x86_64 x86_64
% 0.08/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28  % Memory   : 8042.1875MB
% 0.08/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28  % CPULimit : 300
% 0.08/0.28  % WCLimit  : 300
% 0.08/0.28  % DateTime : Tue May 30 09:09:40 EDT 2023
% 0.08/0.28  % CPUTime  : 
% 0.08/0.29  % Drodi V3.5.1
% 0.13/0.31  % Refutation found
% 0.13/0.31  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.31  % SZS output start CNFRefutation for theBenchmark
% 0.13/0.31  fof(f2,axiom,(
% 0.13/0.31    (! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
% 0.13/0.31    file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.31  fof(f3,axiom,(
% 0.13/0.31    (! [A,B,C] :( C = set_difference(A,B)<=> (! [D] :( in(D,C)<=> ( in(D,A)& ~ in(D,B) ) ) )) )),
% 0.13/0.31    file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.31  fof(f6,axiom,(
% 0.13/0.31    empty(empty_set) ),
% 0.13/0.31    file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.31  fof(f10,conjecture,(
% 0.13/0.31    (! [A,B,C] :( subset(A,B)=> subset(set_difference(A,C),set_difference(B,C)) ) )),
% 0.13/0.31    file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.31  fof(f11,negated_conjecture,(
% 0.13/0.31    ~((! [A,B,C] :( subset(A,B)=> subset(set_difference(A,C),set_difference(B,C)) ) ))),
% 0.13/0.31    inference(negated_conjecture,[status(cth)],[f10])).
% 0.13/0.31  fof(f12,axiom,(
% 0.13/0.31    (! [A] : set_difference(A,empty_set) = A )),
% 0.13/0.31    file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.31  fof(f15,axiom,(
% 0.13/0.31    (! [A,B] :~ ( in(A,B)& empty(B) ) )),
% 0.13/0.31    file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.31  fof(f19,plain,(
% 0.13/0.31    ![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
% 0.13/0.31    inference(pre_NNF_transformation,[status(esa)],[f2])).
% 0.13/0.31  fof(f20,plain,(
% 0.13/0.31    ![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.13/0.31    inference(NNF_transformation,[status(esa)],[f19])).
% 0.13/0.31  fof(f21,plain,(
% 0.13/0.31    (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.13/0.31    inference(miniscoping,[status(esa)],[f20])).
% 0.13/0.31  fof(f22,plain,(
% 0.13/0.31    (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(in(sk0_0(B,A),A)&~in(sk0_0(B,A),B))))),
% 0.13/0.31    inference(skolemization,[status(esa)],[f21])).
% 0.13/0.31  fof(f23,plain,(
% 0.13/0.31    ![X0,X1,X2]: (~subset(X0,X1)|~in(X2,X0)|in(X2,X1))),
% 0.13/0.31    inference(cnf_transformation,[status(esa)],[f22])).
% 0.13/0.31  fof(f24,plain,(
% 0.13/0.31    ![X0,X1]: (subset(X0,X1)|in(sk0_0(X1,X0),X0))),
% 0.13/0.31    inference(cnf_transformation,[status(esa)],[f22])).
% 0.13/0.31  fof(f25,plain,(
% 0.13/0.31    ![X0,X1]: (subset(X0,X1)|~in(sk0_0(X1,X0),X1))),
% 0.13/0.31    inference(cnf_transformation,[status(esa)],[f22])).
% 0.13/0.31  fof(f26,plain,(
% 0.13/0.31    ![A,B,C]: ((~C=set_difference(A,B)|(![D]: ((~in(D,C)|(in(D,A)&~in(D,B)))&(in(D,C)|(~in(D,A)|in(D,B))))))&(C=set_difference(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)|in(D,B)))&(in(D,C)|(in(D,A)&~in(D,B)))))))),
% 0.13/0.31    inference(NNF_transformation,[status(esa)],[f3])).
% 0.13/0.31  fof(f27,plain,(
% 0.13/0.31    (![A,B,C]: (~C=set_difference(A,B)|((![D]: (~in(D,C)|(in(D,A)&~in(D,B))))&(![D]: (in(D,C)|(~in(D,A)|in(D,B)))))))&(![A,B,C]: (C=set_difference(A,B)|(?[D]: ((~in(D,C)|(~in(D,A)|in(D,B)))&(in(D,C)|(in(D,A)&~in(D,B)))))))),
% 0.13/0.31    inference(miniscoping,[status(esa)],[f26])).
% 0.13/0.31  fof(f28,plain,(
% 0.13/0.31    (![A,B,C]: (~C=set_difference(A,B)|((![D]: (~in(D,C)|(in(D,A)&~in(D,B))))&(![D]: (in(D,C)|(~in(D,A)|in(D,B)))))))&(![A,B,C]: (C=set_difference(A,B)|((~in(sk0_1(C,B,A),C)|(~in(sk0_1(C,B,A),A)|in(sk0_1(C,B,A),B)))&(in(sk0_1(C,B,A),C)|(in(sk0_1(C,B,A),A)&~in(sk0_1(C,B,A),B))))))),
% 0.13/0.31    inference(skolemization,[status(esa)],[f27])).
% 0.13/0.31  fof(f29,plain,(
% 0.13/0.31    ![X0,X1,X2,X3]: (~X0=set_difference(X1,X2)|~in(X3,X0)|in(X3,X1))),
% 0.13/0.31    inference(cnf_transformation,[status(esa)],[f28])).
% 0.13/0.31  fof(f30,plain,(
% 0.13/0.31    ![X0,X1,X2,X3]: (~X0=set_difference(X1,X2)|~in(X3,X0)|~in(X3,X2))),
% 0.13/0.31    inference(cnf_transformation,[status(esa)],[f28])).
% 0.13/0.31  fof(f31,plain,(
% 0.13/0.31    ![X0,X1,X2,X3]: (~X0=set_difference(X1,X2)|in(X3,X0)|~in(X3,X1)|in(X3,X2))),
% 0.13/0.31    inference(cnf_transformation,[status(esa)],[f28])).
% 0.13/0.31  fof(f33,plain,(
% 0.13/0.31    ![X0,X1,X2]: (X0=set_difference(X1,X2)|in(sk0_1(X0,X2,X1),X0)|in(sk0_1(X0,X2,X1),X1))),
% 0.13/0.31    inference(cnf_transformation,[status(esa)],[f28])).
% 0.13/0.31  fof(f34,plain,(
% 0.13/0.31    ![X0,X1,X2]: (X0=set_difference(X1,X2)|in(sk0_1(X0,X2,X1),X0)|~in(sk0_1(X0,X2,X1),X2))),
% 0.13/0.31    inference(cnf_transformation,[status(esa)],[f28])).
% 0.13/0.31  fof(f35,plain,(
% 0.13/0.31    empty(empty_set)),
% 0.13/0.31    inference(cnf_transformation,[status(esa)],[f6])).
% 0.13/0.31  fof(f42,plain,(
% 0.13/0.31    (?[A,B,C]: (subset(A,B)&~subset(set_difference(A,C),set_difference(B,C))))),
% 0.13/0.31    inference(pre_NNF_transformation,[status(esa)],[f11])).
% 0.13/0.31  fof(f43,plain,(
% 0.13/0.31    ?[A,B]: (subset(A,B)&(?[C]: ~subset(set_difference(A,C),set_difference(B,C))))),
% 0.13/0.31    inference(miniscoping,[status(esa)],[f42])).
% 0.13/0.31  fof(f44,plain,(
% 0.13/0.31    (subset(sk0_4,sk0_5)&~subset(set_difference(sk0_4,sk0_6),set_difference(sk0_5,sk0_6)))),
% 0.13/0.31    inference(skolemization,[status(esa)],[f43])).
% 0.13/0.31  fof(f45,plain,(
% 0.13/0.31    subset(sk0_4,sk0_5)),
% 0.13/0.31    inference(cnf_transformation,[status(esa)],[f44])).
% 0.13/0.31  fof(f46,plain,(
% 0.13/0.31    ~subset(set_difference(sk0_4,sk0_6),set_difference(sk0_5,sk0_6))),
% 0.13/0.31    inference(cnf_transformation,[status(esa)],[f44])).
% 0.13/0.31  fof(f47,plain,(
% 0.13/0.31    ![X0]: (set_difference(X0,empty_set)=X0)),
% 0.13/0.31    inference(cnf_transformation,[status(esa)],[f12])).
% 0.13/0.31  fof(f51,plain,(
% 0.13/0.31    ![A,B]: (~in(A,B)|~empty(B))),
% 0.13/0.31    inference(pre_NNF_transformation,[status(esa)],[f15])).
% 0.13/0.31  fof(f52,plain,(
% 0.13/0.31    ![B]: ((![A]: ~in(A,B))|~empty(B))),
% 0.13/0.31    inference(miniscoping,[status(esa)],[f51])).
% 0.13/0.31  fof(f53,plain,(
% 0.13/0.31    ![X0,X1]: (~in(X0,X1)|~empty(X1))),
% 0.13/0.31    inference(cnf_transformation,[status(esa)],[f52])).
% 0.13/0.31  fof(f57,plain,(
% 0.13/0.31    ![X0,X1,X2]: (~in(X0,set_difference(X1,X2))|in(X0,X1))),
% 0.13/0.31    inference(destructive_equality_resolution,[status(esa)],[f29])).
% 0.13/0.31  fof(f58,plain,(
% 0.13/0.31    ![X0,X1,X2]: (~in(X0,set_difference(X1,X2))|~in(X0,X2))),
% 0.13/0.31    inference(destructive_equality_resolution,[status(esa)],[f30])).
% 0.13/0.31  fof(f59,plain,(
% 0.13/0.31    ![X0,X1,X2]: (in(X0,set_difference(X1,X2))|~in(X0,X1)|in(X0,X2))),
% 0.13/0.31    inference(destructive_equality_resolution,[status(esa)],[f31])).
% 0.13/0.31  fof(f60,plain,(
% 0.13/0.31    ![X0]: (~in(X0,sk0_4)|in(X0,sk0_5))),
% 0.13/0.31    inference(resolution,[status(thm)],[f23,f45])).
% 0.13/0.31  fof(f61,plain,(
% 0.13/0.31    ![X0,X1]: (~in(X0,X1)|~in(X0,empty_set))),
% 0.13/0.31    inference(paramodulation,[status(thm)],[f47,f58])).
% 0.13/0.31  fof(f69,plain,(
% 0.13/0.31    ![X0,X1,X2]: (~empty(set_difference(X0,X1))|~in(X2,X0)|in(X2,X1))),
% 0.13/0.31    inference(resolution,[status(thm)],[f53,f59])).
% 0.13/0.31  fof(f71,plain,(
% 0.13/0.31    ![X0,X1]: (subset(empty_set,X0)|~in(sk0_0(X0,empty_set),X1))),
% 0.13/0.31    inference(resolution,[status(thm)],[f24,f61])).
% 0.13/0.31  fof(f73,plain,(
% 0.13/0.31    ![X0,X1,X2]: (subset(set_difference(X0,X1),X2)|~in(sk0_0(X2,set_difference(X0,X1)),X1))),
% 0.13/0.31    inference(resolution,[status(thm)],[f24,f58])).
% 0.13/0.31  fof(f74,plain,(
% 0.13/0.31    ![X0,X1,X2]: (subset(set_difference(X0,X1),X2)|in(sk0_0(X2,set_difference(X0,X1)),X0))),
% 0.13/0.31    inference(resolution,[status(thm)],[f24,f57])).
% 0.13/0.31  fof(f81,plain,(
% 0.13/0.31    ![X0,X1,X2]: (subset(X0,set_difference(X1,X2))|~in(sk0_0(set_difference(X1,X2),X0),X1)|in(sk0_0(set_difference(X1,X2),X0),X2))),
% 0.13/0.31    inference(resolution,[status(thm)],[f25,f59])).
% 0.13/0.31  fof(f82,plain,(
% 0.13/0.31    ![X0]: (subset(empty_set,X0)|subset(empty_set,X0))),
% 0.13/0.31    inference(resolution,[status(thm)],[f71,f24])).
% 0.13/0.31  fof(f83,plain,(
% 0.13/0.31    ![X0]: (subset(empty_set,X0))),
% 0.13/0.31    inference(duplicate_literals_removal,[status(esa)],[f82])).
% 0.13/0.31  fof(f85,plain,(
% 0.13/0.31    ![X0,X1]: (~in(X0,empty_set)|in(X0,X1))),
% 0.13/0.31    inference(resolution,[status(thm)],[f83,f23])).
% 0.13/0.31  fof(f86,plain,(
% 0.13/0.31    ![X0]: (~in(X0,empty_set))),
% 0.13/0.31    inference(forward_subsumption_resolution,[status(thm)],[f85,f61])).
% 0.13/0.31  fof(f88,plain,(
% 0.13/0.31    spl0_0 <=> empty(empty_set)),
% 0.13/0.31    introduced(split_symbol_definition)).
% 0.13/0.31  fof(f90,plain,(
% 0.13/0.31    ~empty(empty_set)|spl0_0),
% 0.13/0.31    inference(component_clause,[status(thm)],[f88])).
% 0.13/0.31  fof(f97,plain,(
% 0.13/0.31    $false|spl0_0),
% 0.13/0.31    inference(forward_subsumption_resolution,[status(thm)],[f90,f35])).
% 0.13/0.31  fof(f98,plain,(
% 0.13/0.31    spl0_0),
% 0.13/0.31    inference(contradiction_clause,[status(thm)],[f97])).
% 0.13/0.31  fof(f136,plain,(
% 0.13/0.31    ![X0,X1]: (X0=set_difference(sk0_4,X1)|in(sk0_1(X0,X1,sk0_4),X0)|in(sk0_1(X0,X1,sk0_4),sk0_5))),
% 0.13/0.31    inference(resolution,[status(thm)],[f33,f60])).
% 0.13/0.31  fof(f163,plain,(
% 0.13/0.31    ![X0]: (X0=set_difference(sk0_4,sk0_5)|in(sk0_1(X0,sk0_5,sk0_4),X0)|X0=set_difference(sk0_4,sk0_5)|in(sk0_1(X0,sk0_5,sk0_4),X0))),
% 0.13/0.31    inference(resolution,[status(thm)],[f136,f34])).
% 0.13/0.31  fof(f164,plain,(
% 0.13/0.31    ![X0]: (X0=set_difference(sk0_4,sk0_5)|in(sk0_1(X0,sk0_5,sk0_4),X0))),
% 0.13/0.31    inference(duplicate_literals_removal,[status(esa)],[f163])).
% 0.13/0.31  fof(f195,plain,(
% 0.13/0.31    empty_set=set_difference(sk0_4,sk0_5)),
% 0.13/0.31    inference(resolution,[status(thm)],[f164,f86])).
% 0.13/0.31  fof(f226,plain,(
% 0.13/0.31    spl0_15 <=> ~in(X0,sk0_4)|in(X0,sk0_5)),
% 0.13/0.31    introduced(split_symbol_definition)).
% 0.13/0.31  fof(f227,plain,(
% 0.13/0.31    ![X0]: (~in(X0,sk0_4)|in(X0,sk0_5)|~spl0_15)),
% 0.13/0.31    inference(component_clause,[status(thm)],[f226])).
% 0.13/0.31  fof(f329,plain,(
% 0.13/0.31    ![X0]: (~empty(empty_set)|~in(X0,sk0_4)|in(X0,sk0_5))),
% 0.13/0.31    inference(paramodulation,[status(thm)],[f195,f69])).
% 0.13/0.32  fof(f330,plain,(
% 0.13/0.32    ~spl0_0|spl0_15),
% 0.13/0.32    inference(split_clause,[status(thm)],[f329,f88,f226])).
% 0.13/0.32  fof(f337,plain,(
% 0.13/0.32    ![X0,X1]: (in(sk0_0(X0,set_difference(sk0_4,X1)),sk0_5)|subset(set_difference(sk0_4,X1),X0)|~spl0_15)),
% 0.13/0.32    inference(resolution,[status(thm)],[f227,f74])).
% 0.13/0.32  fof(f424,plain,(
% 0.13/0.32    ![X0,X1]: (subset(set_difference(sk0_4,X0),set_difference(sk0_5,X1))|in(sk0_0(set_difference(sk0_5,X1),set_difference(sk0_4,X0)),X1)|subset(set_difference(sk0_4,X0),set_difference(sk0_5,X1))|~spl0_15)),
% 0.13/0.32    inference(resolution,[status(thm)],[f81,f337])).
% 0.13/0.32  fof(f425,plain,(
% 0.13/0.32    ![X0,X1]: (subset(set_difference(sk0_4,X0),set_difference(sk0_5,X1))|in(sk0_0(set_difference(sk0_5,X1),set_difference(sk0_4,X0)),X1)|~spl0_15)),
% 0.13/0.32    inference(duplicate_literals_removal,[status(esa)],[f424])).
% 0.13/0.32  fof(f879,plain,(
% 0.13/0.32    ![X0]: (subset(set_difference(sk0_4,X0),set_difference(sk0_5,X0))|subset(set_difference(sk0_4,X0),set_difference(sk0_5,X0))|~spl0_15)),
% 0.13/0.32    inference(resolution,[status(thm)],[f425,f73])).
% 0.13/0.32  fof(f880,plain,(
% 0.13/0.32    ![X0]: (subset(set_difference(sk0_4,X0),set_difference(sk0_5,X0))|~spl0_15)),
% 0.13/0.32    inference(duplicate_literals_removal,[status(esa)],[f879])).
% 0.13/0.32  fof(f1718,plain,(
% 0.13/0.32    $false|~spl0_15),
% 0.13/0.32    inference(backward_subsumption_resolution,[status(thm)],[f46,f880])).
% 0.13/0.32  fof(f1719,plain,(
% 0.13/0.32    ~spl0_15),
% 0.13/0.32    inference(contradiction_clause,[status(thm)],[f1718])).
% 0.13/0.32  fof(f1720,plain,(
% 0.13/0.32    $false),
% 0.13/0.32    inference(sat_refutation,[status(thm)],[f98,f330,f1719])).
% 0.13/0.32  % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.32  % Elapsed time: 0.029868 seconds
% 0.13/0.32  % CPU time: 0.132966 seconds
% 0.13/0.32  % Memory used: 18.003 MB
%------------------------------------------------------------------------------