%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : ALG227+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 11:49:53 AM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG227+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n003.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Mon Sep 21 13:08:31 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.17/0.47 % Refutation found
% 0.17/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.47 % SZS output start CNFRefutation for theBenchmark
% 0.17/0.47 fof(f1,conjecture,(
% 0.17/0.47 (! [A] :( ~ v1_xboole_0(A)=> (! [B] :( m1_pboole(B,A)=> (! [C] :( m1_subset_1(C,A)=> ( ~ r2_hidden(C,k1_closure3(A,B))=> k1_funct_1(B,C) = k1_xboole_0 ) ) )) )) )),
% 0.17/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.47 fof(f2,negated_conjecture,(
% 0.17/0.47 ~((! [A] :( ~ v1_xboole_0(A)=> (! [B] :( m1_pboole(B,A)=> (! [C] :( m1_subset_1(C,A)=> ( ~ r2_hidden(C,k1_closure3(A,B))=> k1_funct_1(B,C) = k1_xboole_0 ) ) )) )) ))),
% 0.17/0.47 inference(negated_conjecture,[status(cth)],[f1])).
% 0.17/0.47 fof(f8,axiom,(
% 0.17/0.47 (! [A] :( ~ v1_xboole_0(A)=> (! [B] :( m1_pboole(B,A)=> (! [C] :( C = k1_closure3(A,B)<=> C = a_2_0_closure3(A,B) ) )) )) )),
% 0.17/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.47 fof(f17,axiom,(
% 0.17/0.47 (! [A,B,C] :( ( ~ v1_xboole_0(B)& m1_pboole(C,B) )=> ( r2_hidden(A,a_2_0_closure3(B,C))<=> (? [D] :( m1_subset_1(D,B)& A = D& k1_funct_1(C,D) != k1_xboole_0 ) )) ) )),
% 0.17/0.47 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.47 fof(f31,plain,(
% 0.17/0.47 (?[A]: (~v1_xboole_0(A)&(?[B]: (m1_pboole(B,A)&(?[C]: (m1_subset_1(C,A)&(~r2_hidden(C,k1_closure3(A,B))&~k1_funct_1(B,C)=k1_xboole_0)))))))),
% 0.17/0.47 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.17/0.47 fof(f32,plain,(
% 0.17/0.47 (~v1_xboole_0(sK0_skl)&(m1_pboole(sK1_skl,sK0_skl)&(m1_subset_1(sK2_skl,sK0_skl)&(~r2_hidden(sK2_skl,k1_closure3(sK0_skl,sK1_skl))&~k1_funct_1(sK1_skl,sK2_skl)=k1_xboole_0))))),
% 0.17/0.47 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl),skolemize(C,sK2_skl)],[f31])).
% 0.17/0.47 fof(f33,plain,(
% 0.17/0.47 ~v1_xboole_0(sK0_skl)),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f32])).
% 0.17/0.47 fof(f34,plain,(
% 0.17/0.47 m1_pboole(sK1_skl,sK0_skl)),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f32])).
% 0.17/0.47 fof(f35,plain,(
% 0.17/0.47 m1_subset_1(sK2_skl,sK0_skl)),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f32])).
% 0.17/0.47 fof(f36,plain,(
% 0.17/0.47 ~r2_hidden(sK2_skl,k1_closure3(sK0_skl,sK1_skl))),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f32])).
% 0.17/0.47 fof(f37,plain,(
% 0.17/0.47 ~k1_funct_1(sK1_skl,sK2_skl)=k1_xboole_0),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f32])).
% 0.17/0.47 fof(f50,plain,(
% 0.17/0.47 ![A]: (v1_xboole_0(A)|(![B]: (~m1_pboole(B,A)|(![C]: (C=k1_closure3(A,B)<=>C=a_2_0_closure3(A,B))))))),
% 0.17/0.47 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.17/0.47 fof(f51,plain,(
% 0.17/0.47 ![A]: (v1_xboole_0(A)|(![B]: (~m1_pboole(B,A)|(![C]: ((~C=k1_closure3(A,B)|C=a_2_0_closure3(A,B))&(C=k1_closure3(A,B)|~C=a_2_0_closure3(A,B)))))))),
% 0.17/0.47 inference(NNF_transformation,[status(thm)],[f50])).
% 0.17/0.47 fof(f52,plain,(
% 0.17/0.47 ![A]: (v1_xboole_0(A)|(![B]: (~m1_pboole(B,A)|((![C]: (~C=k1_closure3(A,B)|C=a_2_0_closure3(A,B)))&(![C]: (C=k1_closure3(A,B)|~C=a_2_0_closure3(A,B)))))))),
% 0.17/0.47 inference(miniscoping,[status(thm)],[f51])).
% 0.17/0.47 fof(f53,plain,(
% 0.17/0.47 ![X0,X1,X2]: (v1_xboole_0(X0)|~m1_pboole(X1,X0)|~X2=k1_closure3(X0,X1)|X2=a_2_0_closure3(X0,X1))),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f52])).
% 0.17/0.47 fof(f64,plain,(
% 0.17/0.47 ![A,B,C]: ((v1_xboole_0(B)|~m1_pboole(C,B))|(r2_hidden(A,a_2_0_closure3(B,C))<=>(?[D]: ((m1_subset_1(D,B)&A=D)&~k1_funct_1(C,D)=k1_xboole_0))))),
% 0.17/0.47 inference(pre_NNF_transformation,[status(thm)],[f17])).
% 0.17/0.47 fof(f65,plain,(
% 0.17/0.47 ![A,B,C]: ((v1_xboole_0(B)|~m1_pboole(C,B))|((~r2_hidden(A,a_2_0_closure3(B,C))|(?[D]: ((m1_subset_1(D,B)&A=D)&~k1_funct_1(C,D)=k1_xboole_0)))&(r2_hidden(A,a_2_0_closure3(B,C))|(![D]: ((~m1_subset_1(D,B)|~A=D)|k1_funct_1(C,D)=k1_xboole_0)))))),
% 0.17/0.47 inference(NNF_transformation,[status(thm)],[f64])).
% 0.17/0.47 fof(f66,plain,(
% 0.17/0.47 ![B,C]: ((v1_xboole_0(B)|~m1_pboole(C,B))|((![A]: (~r2_hidden(A,a_2_0_closure3(B,C))|(?[D]: ((m1_subset_1(D,B)&A=D)&~k1_funct_1(C,D)=k1_xboole_0))))&(![A]: (r2_hidden(A,a_2_0_closure3(B,C))|(![D]: ((~m1_subset_1(D,B)|~A=D)|k1_funct_1(C,D)=k1_xboole_0))))))),
% 0.17/0.47 inference(miniscoping,[status(thm)],[f65])).
% 0.17/0.47 fof(f67,plain,(
% 0.17/0.47 ![B,C]: ((v1_xboole_0(B)|~m1_pboole(C,B))|((![A]: (~r2_hidden(A,a_2_0_closure3(B,C))|((m1_subset_1(sK5_skl(A,C,B),B)&A=sK5_skl(A,C,B))&~k1_funct_1(C,sK5_skl(A,C,B))=k1_xboole_0)))&(![A]: (r2_hidden(A,a_2_0_closure3(B,C))|(![D]: ((~m1_subset_1(D,B)|~A=D)|k1_funct_1(C,D)=k1_xboole_0))))))),
% 0.17/0.47 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(D,sK5_skl(A,C,B))],[f66])).
% 0.17/0.47 fof(f71,plain,(
% 0.17/0.47 ![X0,X1,X2,X3]: (v1_xboole_0(X0)|~m1_pboole(X1,X0)|r2_hidden(X2,a_2_0_closure3(X0,X1))|~m1_subset_1(X3,X0)|~X2=X3|k1_funct_1(X1,X3)=k1_xboole_0)),
% 0.17/0.47 inference(cnf_transformation,[status(thm)],[f67])).
% 0.17/0.47 fof(f115,plain,(
% 0.17/0.47 ![X0,X1]: (v1_xboole_0(X0)|~m1_pboole(X1,X0)|k1_closure3(X0,X1)=a_2_0_closure3(X0,X1))),
% 0.17/0.47 inference(destructive_equality_resolution,[status(thm)],[f53])).
% 0.17/0.47 fof(f117,plain,(
% 0.17/0.47 ![X0,X1,X2]: (v1_xboole_0(X0)|~m1_pboole(X1,X0)|r2_hidden(X2,a_2_0_closure3(X0,X1))|~m1_subset_1(X2,X0)|k1_funct_1(X1,X2)=k1_xboole_0)),
% 0.17/0.47 inference(destructive_equality_resolution,[status(thm)],[f71])).
% 0.17/0.47 fof(f123,definition,(
% 0.17/0.47 sQ0_spl <=> (v1_xboole_0(sK0_skl))),
% 0.17/0.47 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.17/0.47 fof(f124,plain,(
% 0.17/0.47 v1_xboole_0(sK0_skl)|~sQ0_spl),
% 0.17/0.47 inference(component_clause,[status(thm)],[f123])).
% 0.17/0.47 fof(f130,plain,(
% 0.17/0.47 $false|~sQ0_spl),
% 0.17/0.47 inference(forward_subsumption_resolution,[status(thm)],[f124,f33])).
% 0.17/0.47 fof(f131,plain,(
% 0.17/0.47 ~sQ0_spl),
% 0.17/0.47 inference(contradiction_clause,[status(thm)],[f130])).
% 0.17/0.47 fof(f132,plain,(
% 0.17/0.47 v1_xboole_0(sK0_skl)|k1_closure3(sK0_skl,sK1_skl)=a_2_0_closure3(sK0_skl,sK1_skl)),
% 0.17/0.47 inference(resolution,[status(thm)],[f115,f34])).
% 0.17/0.47 fof(f133,definition,(
% 0.17/0.47 sQ2_spl <=> (k1_closure3(sK0_skl,sK1_skl)=a_2_0_closure3(sK0_skl,sK1_skl))),
% 0.17/0.47 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.17/0.47 fof(f134,plain,(
% 0.17/0.47 k1_closure3(sK0_skl,sK1_skl)=a_2_0_closure3(sK0_skl,sK1_skl)|~sQ2_spl),
% 0.17/0.47 inference(component_clause,[status(thm)],[f133])).
% 0.17/0.47 fof(f136,plain,(
% 0.17/0.47 sQ0_spl|sQ2_spl),
% 0.17/0.47 inference(split_clause,[status(thm)],[f132,f123,f133])).
% 0.17/0.47 fof(f137,plain,(
% 0.17/0.47 ~r2_hidden(sK2_skl,a_2_0_closure3(sK0_skl,sK1_skl))|~sQ2_spl),
% 0.17/0.47 inference(backward_demodulation,[status(thm)],[f134,f36])).
% 0.17/0.47 fof(f138,plain,(
% 0.17/0.47 ![X0]: (v1_xboole_0(sK0_skl)|r2_hidden(X0,a_2_0_closure3(sK0_skl,sK1_skl))|~m1_subset_1(X0,sK0_skl)|k1_funct_1(sK1_skl,X0)=k1_xboole_0)),
% 0.17/0.47 inference(resolution,[status(thm)],[f117,f34])).
% 0.17/0.47 fof(f139,definition,(
% 0.17/0.47 ![X0]: (sQ3_spl <=> (r2_hidden(X0,a_2_0_closure3(sK0_skl,sK1_skl))|~m1_subset_1(X0,sK0_skl)|k1_funct_1(sK1_skl,X0)=k1_xboole_0))),
% 0.17/0.47 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.17/0.47 fof(f140,plain,(
% 0.17/0.47 ![X0]: (r2_hidden(X0,a_2_0_closure3(sK0_skl,sK1_skl))|~m1_subset_1(X0,sK0_skl)|k1_funct_1(sK1_skl,X0)=k1_xboole_0|~sQ3_spl)),
% 0.17/0.47 inference(component_clause,[status(thm)],[f139])).
% 0.17/0.47 fof(f142,plain,(
% 0.17/0.47 sQ0_spl|sQ3_spl),
% 0.17/0.47 inference(split_clause,[status(thm)],[f138,f123,f139])).
% 0.17/0.47 fof(f143,plain,(
% 0.17/0.47 r2_hidden(sK2_skl,a_2_0_closure3(sK0_skl,sK1_skl))|k1_funct_1(sK1_skl,sK2_skl)=k1_xboole_0|~sQ3_spl),
% 0.17/0.47 inference(resolution,[status(thm)],[f140,f35])).
% 0.17/0.47 fof(f144,definition,(
% 0.17/0.47 sQ4_spl <=> (r2_hidden(sK2_skl,a_2_0_closure3(sK0_skl,sK1_skl)))),
% 0.17/0.47 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.17/0.47 fof(f145,plain,(
% 0.17/0.47 r2_hidden(sK2_skl,a_2_0_closure3(sK0_skl,sK1_skl))|~sQ4_spl),
% 0.17/0.47 inference(component_clause,[status(thm)],[f144])).
% 0.17/0.47 fof(f147,definition,(
% 0.17/0.47 sQ5_spl <=> (k1_funct_1(sK1_skl,sK2_skl)=k1_xboole_0)),
% 0.17/0.47 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.17/0.47 fof(f148,plain,(
% 0.17/0.47 k1_funct_1(sK1_skl,sK2_skl)=k1_xboole_0|~sQ5_spl),
% 0.17/0.47 inference(component_clause,[status(thm)],[f147])).
% 0.17/0.47 fof(f150,plain,(
% 0.17/0.47 sQ4_spl|sQ5_spl|~sQ3_spl),
% 0.17/0.47 inference(split_clause,[status(thm)],[f143,f144,f147,f139])).
% 0.17/0.47 fof(f151,plain,(
% 0.17/0.47 $false|~sQ2_spl|~sQ4_spl),
% 0.17/0.47 inference(forward_subsumption_resolution,[status(thm)],[f145,f137])).
% 0.17/0.47 fof(f152,plain,(
% 0.17/0.47 ~sQ2_spl|~sQ4_spl),
% 0.17/0.47 inference(contradiction_clause,[status(thm)],[f151])).
% 0.17/0.47 fof(f153,plain,(
% 0.17/0.47 $false|~sQ5_spl),
% 0.17/0.47 inference(forward_subsumption_resolution,[status(thm)],[f148,f37])).
% 0.17/0.47 fof(f154,plain,(
% 0.17/0.47 ~sQ5_spl),
% 0.17/0.47 inference(contradiction_clause,[status(thm)],[f153])).
% 0.17/0.47 fof(f155,plain,(
% 0.17/0.47 $false),
% 0.17/0.47 inference(sat_refutation,[status(thm)],[f131,f136,f142,f150,f152,f154])).
% 0.17/0.47 % SZS output end CNFRefutation for theBenchmark.p
% 0.23/0.52 % Elapsed time: 0.062331 seconds
% 0.23/0.52 % CPU time: 0.162394 seconds
% 0.23/0.52 % Total memory used: 78.636 MB
% 0.23/0.52 % Net memory used: 78.605 MB
%------------------------------------------------------------------------------