%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU157+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 02:21:50 PM UTC 2026
% Result : Theorem 0.11s 0.42s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU157+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n008.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 05:54:24 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.42 % Refutation found
% 0.11/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.42 % SZS output start CNFRefutation for theBenchmark
% 0.11/0.42 fof(f3,axiom,(
% 0.11/0.42 (! [A,B,C] :( C = cartesian_product2(A,B)<=> (! [D] :( in(D,C)<=> (? [E,F] :( in(E,A)& in(F,B)& D = ordered_pair(E,F) ) )) )) )),
% 0.11/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.42 fof(f10,conjecture,(
% 0.11/0.42 (! [A,B,C,D] :( in(ordered_pair(A,B),cartesian_product2(C,D))<=> ( in(A,C)& in(B,D) ) ) )),
% 0.11/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.42 fof(f11,negated_conjecture,(
% 0.11/0.42 ~((! [A,B,C,D] :( in(ordered_pair(A,B),cartesian_product2(C,D))<=> ( in(A,C)& in(B,D) ) ) ))),
% 0.11/0.42 inference(negated_conjecture,[status(cth)],[f10])).
% 0.11/0.42 fof(f14,axiom,(
% 0.11/0.42 (! [A,B,C,D] :( ordered_pair(A,B) = ordered_pair(C,D)=> ( A = C& B = D ) ) )),
% 0.11/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.42 fof(f18,definition,(
% 0.11/0.42 ![A,B,D,E,F]: (sP0_prd(F,E,D,B,A)<=>((in(E,A)&in(F,B))&D=ordered_pair(E,F)))),
% 0.11/0.42 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.11/0.42 fof(f19,plain,(
% 0.11/0.42 ![A,B,C]: (C=cartesian_product2(A,B)<=>(![D]: (in(D,C)<=>(?[E,F]: sP0_prd(F,E,D,B,A)))))),
% 0.11/0.42 inference(formula_renaming,[status(thm)],[f3,f18])).
% 0.11/0.42 fof(f20,plain,(
% 0.11/0.42 ![A,B,C]: ((~C=cartesian_product2(A,B)|(![D]: ((~in(D,C)|(?[E,F]: sP0_prd(F,E,D,B,A)))&(in(D,C)|(![E,F]: ~sP0_prd(F,E,D,B,A))))))&(C=cartesian_product2(A,B)|(?[D]: ((~in(D,C)|(![E,F]: ~sP0_prd(F,E,D,B,A)))&(in(D,C)|(?[E,F]: sP0_prd(F,E,D,B,A)))))))),
% 0.11/0.42 inference(NNF_transformation,[status(thm)],[f19])).
% 0.11/0.42 fof(f21,plain,(
% 0.11/0.42 (![A,B,C]: (~C=cartesian_product2(A,B)|((![D]: (~in(D,C)|(?[E,F]: sP0_prd(F,E,D,B,A))))&(![D]: (in(D,C)|(![E,F]: ~sP0_prd(F,E,D,B,A)))))))&(![A,B,C]: (C=cartesian_product2(A,B)|(?[D]: ((~in(D,C)|(![E,F]: ~sP0_prd(F,E,D,B,A)))&(in(D,C)|(?[E,F]: sP0_prd(F,E,D,B,A)))))))),
% 0.11/0.42 inference(miniscoping,[status(thm)],[f20])).
% 0.11/0.42 fof(f22,plain,(
% 0.11/0.42 (![A,B,C]: (~C=cartesian_product2(A,B)|((![D]: (~in(D,C)|sP0_prd(sK1_skl(D,C,B,A),sK0_skl(D,C,B,A),D,B,A)))&(![D]: (in(D,C)|(![E,F]: ~sP0_prd(F,E,D,B,A)))))))&(![A,B,C]: (C=cartesian_product2(A,B)|((~in(sK2_skl(C,B,A),C)|(![E,F]: ~sP0_prd(F,E,sK2_skl(C,B,A),B,A)))&(in(sK2_skl(C,B,A),C)|sP0_prd(sK4_skl(C,B,A),sK3_skl(C,B,A),sK2_skl(C,B,A),B,A)))))),
% 0.11/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl]),skolemize(E,sK0_skl(D,C,B,A)),skolemize(F,sK1_skl(D,C,B,A)),skolemize(D,sK2_skl(C,B,A)),skolemize(E,sK3_skl(C,B,A)),skolemize(F,sK4_skl(C,B,A))],[f21])).
% 0.11/0.42 fof(f23,plain,(
% 0.11/0.42 ![X0,X1,X2,X3]: (~X0=cartesian_product2(X1,X2)|~in(X3,X0)|sP0_prd(sK1_skl(X3,X0,X2,X1),sK0_skl(X3,X0,X2,X1),X3,X2,X1))),
% 0.11/0.42 inference(cnf_transformation,[status(thm)],[f22])).
% 0.11/0.42 fof(f24,plain,(
% 0.11/0.42 ![X0,X1,X2,X3,X4,X5]: (~X0=cartesian_product2(X1,X2)|in(X3,X0)|~sP0_prd(X4,X5,X3,X2,X1))),
% 0.11/0.42 inference(cnf_transformation,[status(thm)],[f22])).
% 0.11/0.42 fof(f29,plain,(
% 0.11/0.42 (?[A,B,C,D]: (in(ordered_pair(A,B),cartesian_product2(C,D))<~>(in(A,C)&in(B,D))))),
% 0.11/0.42 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.11/0.42 fof(f30,plain,(
% 0.11/0.42 ?[A,B,C,D]: ((in(ordered_pair(A,B),cartesian_product2(C,D))|(in(A,C)&in(B,D)))&(~in(ordered_pair(A,B),cartesian_product2(C,D))|(~in(A,C)|~in(B,D))))),
% 0.11/0.42 inference(NNF_transformation,[status(thm)],[f29])).
% 0.11/0.42 fof(f31,plain,(
% 0.11/0.42 ((in(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl))|(in(sK5_skl,sK7_skl)&in(sK6_skl,sK8_skl)))&(~in(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl))|(~in(sK5_skl,sK7_skl)|~in(sK6_skl,sK8_skl))))),
% 0.11/0.42 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl,sK7_skl,sK8_skl]),skolemize(A,sK5_skl),skolemize(B,sK6_skl),skolemize(C,sK7_skl),skolemize(D,sK8_skl)],[f30])).
% 0.11/0.42 fof(f32,plain,(
% 0.11/0.42 in(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl))|in(sK5_skl,sK7_skl)),
% 0.11/0.42 inference(cnf_transformation,[status(thm)],[f31])).
% 0.11/0.42 fof(f33,plain,(
% 0.11/0.42 in(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl))|in(sK6_skl,sK8_skl)),
% 0.11/0.42 inference(cnf_transformation,[status(thm)],[f31])).
% 0.11/0.42 fof(f34,plain,(
% 0.11/0.42 ~in(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl))|~in(sK5_skl,sK7_skl)|~in(sK6_skl,sK8_skl)),
% 0.11/0.42 inference(cnf_transformation,[status(thm)],[f31])).
% 0.11/0.42 fof(f39,plain,(
% 0.11/0.42 ![A,B,C,D]: (~ordered_pair(A,B)=ordered_pair(C,D)|(A=C&B=D))),
% 0.11/0.42 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.11/0.42 fof(f40,plain,(
% 0.11/0.42 ![X0,X1,X2,X3]: (~ordered_pair(X0,X1)=ordered_pair(X2,X3)|X0=X2)),
% 0.11/0.42 inference(cnf_transformation,[status(thm)],[f39])).
% 0.11/0.42 fof(f41,plain,(
% 0.11/0.42 ![X0,X1,X2,X3]: (~ordered_pair(X0,X1)=ordered_pair(X2,X3)|X1=X3)),
% 0.11/0.42 inference(cnf_transformation,[status(thm)],[f39])).
% 0.11/0.42 fof(f42,plain,(
% 0.11/0.42 ![A,B,D,E,F]: ((~sP0_prd(F,E,D,B,A)|((in(E,A)&in(F,B))&D=ordered_pair(E,F)))&(sP0_prd(F,E,D,B,A)|((~in(E,A)|~in(F,B))|~D=ordered_pair(E,F))))),
% 0.11/0.42 inference(NNF_transformation,[status(thm)],[f18])).
% 0.11/0.42 fof(f43,plain,(
% 0.11/0.42 (![A,B,D,E,F]: (~sP0_prd(F,E,D,B,A)|((in(E,A)&in(F,B))&D=ordered_pair(E,F))))&(![A,B,D,E,F]: (sP0_prd(F,E,D,B,A)|((~in(E,A)|~in(F,B))|~D=ordered_pair(E,F))))),
% 0.11/0.42 inference(miniscoping,[status(thm)],[f42])).
% 0.11/0.42 fof(f44,plain,(
% 0.11/0.42 ![X0,X1,X2,X3,X4]: (~sP0_prd(X0,X1,X2,X3,X4)|in(X1,X4))),
% 0.11/0.42 inference(cnf_transformation,[status(thm)],[f43])).
% 0.11/0.42 fof(f45,plain,(
% 0.11/0.42 ![X0,X1,X2,X3,X4]: (~sP0_prd(X0,X1,X2,X3,X4)|in(X0,X3))),
% 0.11/0.42 inference(cnf_transformation,[status(thm)],[f43])).
% 0.11/0.42 fof(f46,plain,(
% 0.11/0.42 ![X0,X1,X2,X3,X4]: (~sP0_prd(X0,X1,X2,X3,X4)|X2=ordered_pair(X1,X0))),
% 0.11/0.42 inference(cnf_transformation,[status(thm)],[f43])).
% 0.11/0.42 fof(f47,plain,(
% 0.11/0.42 ![X0,X1,X2,X3,X4]: (sP0_prd(X0,X1,X2,X3,X4)|~in(X1,X4)|~in(X0,X3)|~X2=ordered_pair(X1,X0))),
% 0.11/0.42 inference(cnf_transformation,[status(thm)],[f43])).
% 0.11/0.42 fof(f48,definition,(
% 0.11/0.42 sQ0_spl <=> (in(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl)))),
% 0.11/0.42 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.11/0.42 fof(f49,plain,(
% 0.11/0.42 in(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl))|~sQ0_spl),
% 0.11/0.42 inference(component_clause,[status(thm)],[f48])).
% 0.11/0.42 fof(f51,definition,(
% 0.11/0.42 sQ1_spl <=> (in(sK5_skl,sK7_skl))),
% 0.11/0.42 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.11/0.42 fof(f52,plain,(
% 0.11/0.42 in(sK5_skl,sK7_skl)|~sQ1_spl),
% 0.11/0.42 inference(component_clause,[status(thm)],[f51])).
% 0.11/0.42 fof(f53,plain,(
% 0.11/0.42 ~in(sK5_skl,sK7_skl)|sQ1_spl),
% 0.11/0.42 inference(component_clause,[status(thm)],[f51])).
% 0.11/0.42 fof(f54,plain,(
% 0.11/0.42 sQ0_spl|sQ1_spl),
% 0.11/0.42 inference(split_clause,[status(thm)],[f32,f48,f51])).
% 0.11/0.42 fof(f55,definition,(
% 0.11/0.42 sQ2_spl <=> (in(sK6_skl,sK8_skl))),
% 0.11/0.42 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.11/0.42 fof(f56,plain,(
% 0.11/0.42 in(sK6_skl,sK8_skl)|~sQ2_spl),
% 0.11/0.42 inference(component_clause,[status(thm)],[f55])).
% 0.11/0.42 fof(f58,plain,(
% 0.11/0.42 sQ0_spl|sQ2_spl),
% 0.11/0.42 inference(split_clause,[status(thm)],[f33,f48,f55])).
% 0.11/0.42 fof(f59,plain,(
% 0.11/0.42 ~sQ0_spl|~sQ1_spl|~sQ2_spl),
% 0.11/0.42 inference(split_clause,[status(thm)],[f34,f48,f51,f55])).
% 0.11/0.42 fof(f60,plain,(
% 0.11/0.42 ![X0,X1,X2]: (~in(X0,cartesian_product2(X1,X2))|sP0_prd(sK1_skl(X0,cartesian_product2(X1,X2),X2,X1),sK0_skl(X0,cartesian_product2(X1,X2),X2,X1),X0,X2,X1))),
% 0.11/0.42 inference(destructive_equality_resolution,[status(thm)],[f23])).
% 0.11/0.42 fof(f61,plain,(
% 0.11/0.42 ![X0,X1,X2,X3,X4]: (in(X0,cartesian_product2(X1,X2))|~sP0_prd(X3,X4,X0,X2,X1))),
% 0.11/0.42 inference(destructive_equality_resolution,[status(thm)],[f24])).
% 0.11/0.42 fof(f62,plain,(
% 0.11/0.42 ![X0,X1,X2,X3]: (sP0_prd(X0,X1,ordered_pair(X1,X0),X2,X3)|~in(X1,X3)|~in(X0,X2))),
% 0.11/0.42 inference(destructive_equality_resolution,[status(thm)],[f47])).
% 0.11/0.42 fof(f82,plain,(
% 0.11/0.42 sP0_prd(sK1_skl(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl),sK8_skl,sK7_skl),sK0_skl(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl),sK8_skl,sK7_skl),ordered_pair(sK5_skl,sK6_skl),sK8_skl,sK7_skl)|~sQ0_spl),
% 0.11/0.42 inference(resolution,[status(thm)],[f60,f49])).
% 0.11/0.42 fof(f83,plain,(
% 0.11/0.42 ordered_pair(sK5_skl,sK6_skl)=ordered_pair(sK0_skl(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl),sK8_skl,sK7_skl),sK1_skl(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl),sK8_skl,sK7_skl))|~sQ0_spl),
% 0.11/0.42 inference(resolution,[status(thm)],[f82,f46])).
% 0.11/0.42 fof(f84,plain,(
% 0.11/0.42 in(sK1_skl(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl),sK8_skl,sK7_skl),sK8_skl)|~sQ0_spl),
% 0.11/0.42 inference(resolution,[status(thm)],[f82,f45])).
% 0.11/0.42 fof(f85,plain,(
% 0.11/0.42 in(sK0_skl(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl),sK8_skl,sK7_skl),sK7_skl)|~sQ0_spl),
% 0.11/0.42 inference(resolution,[status(thm)],[f82,f44])).
% 0.11/0.42 fof(f175,plain,(
% 0.11/0.42 sK6_skl=sK1_skl(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl),sK8_skl,sK7_skl)|~sQ0_spl),
% 0.11/0.42 inference(resolution,[status(thm)],[f83,f41])).
% 0.11/0.42 fof(f176,plain,(
% 0.11/0.42 sK5_skl=sK0_skl(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl),sK8_skl,sK7_skl)|~sQ0_spl),
% 0.11/0.42 inference(resolution,[status(thm)],[f83,f40])).
% 0.11/0.42 fof(f190,plain,(
% 0.11/0.42 in(sK6_skl,sK8_skl)|~sQ0_spl),
% 0.11/0.42 inference(backward_demodulation,[status(thm)],[f175,f84])).
% 0.11/0.42 fof(f208,plain,(
% 0.11/0.42 in(sK5_skl,sK7_skl)|~sQ0_spl),
% 0.11/0.42 inference(backward_demodulation,[status(thm)],[f176,f85])).
% 0.11/0.42 fof(f209,plain,(
% 0.11/0.42 $false|sQ1_spl|~sQ0_spl),
% 0.11/0.42 inference(forward_subsumption_resolution,[status(thm)],[f208,f53])).
% 0.11/0.42 fof(f210,plain,(
% 0.11/0.42 sQ1_spl|~sQ0_spl),
% 0.11/0.42 inference(contradiction_clause,[status(thm)],[f209])).
% 0.11/0.42 fof(f211,plain,(
% 0.11/0.42 ![X0,X1]: (sP0_prd(X0,sK5_skl,ordered_pair(sK5_skl,X0),X1,sK7_skl)|~in(X0,X1)|~sQ1_spl)),
% 0.11/0.42 inference(resolution,[status(thm)],[f52,f62])).
% 0.11/0.42 fof(f228,plain,(
% 0.11/0.42 sP0_prd(sK6_skl,sK5_skl,ordered_pair(sK5_skl,sK6_skl),sK8_skl,sK7_skl)|~sQ1_spl|~sQ2_spl),
% 0.11/0.42 inference(resolution,[status(thm)],[f211,f56])).
% 0.11/0.42 fof(f233,plain,(
% 0.11/0.42 in(ordered_pair(sK5_skl,sK6_skl),cartesian_product2(sK7_skl,sK8_skl))|~sQ1_spl|~sQ2_spl),
% 0.11/0.42 inference(resolution,[status(thm)],[f228,f61])).
% 0.11/0.42 fof(f234,plain,(
% 0.11/0.42 sQ0_spl|~sQ1_spl|~sQ2_spl),
% 0.11/0.42 inference(split_clause,[status(thm)],[f233,f48,f51,f55])).
% 0.11/0.42 fof(f235,plain,(
% 0.11/0.42 sQ2_spl|~sQ0_spl),
% 0.11/0.42 inference(split_clause,[status(thm)],[f190,f55,f48])).
% 0.11/0.42 fof(f236,plain,(
% 0.11/0.42 $false),
% 0.11/0.42 inference(sat_refutation,[status(thm)],[f54,f58,f59,f210,f234,f235])).
% 0.11/0.42 % SZS output end CNFRefutation for theBenchmark.p
% 0.11/0.44 % Elapsed time: 0.068397 seconds
% 0.11/0.44 % CPU time: 0.195093 seconds
% 0.11/0.44 % Total memory used: 103.140 MB
% 0.11/0.44 % Net memory used: 102.704 MB
%------------------------------------------------------------------------------