%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET949+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 02:12:54 PM UTC 2026
% Result : Theorem 0.18s 0.44s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET949+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.39 % Computer : n020.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 21 05:45:47 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.18/0.43 % Drodi V4.1.1
% 0.18/0.44 % Refutation found
% 0.18/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.44 % SZS output start CNFRefutation for theBenchmark
% 0.18/0.44 fof(f3,axiom,(
% 0.18/0.44 (! [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) ) )) )) )),
% 0.18/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.44 fof(f8,conjecture,(
% 0.18/0.44 (! [A,B,C] :~ ( in(A,cartesian_product2(B,C))& (! [D,E] : ordered_pair(D,E) != A )) )),
% 0.18/0.44 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/0.44 fof(f9,negated_conjecture,(
% 0.18/0.44 ~((! [A,B,C] :~ ( in(A,cartesian_product2(B,C))& (! [D,E] : ordered_pair(D,E) != A )) ))),
% 0.18/0.44 inference(negated_conjecture,[status(cth)],[f8])).
% 0.18/0.44 fof(f13,definition,(
% 0.18/0.44 ![A,B,D,E,F]: (sP0_prd(F,E,D,B,A)<=>((in(E,A)&in(F,B))&D=ordered_pair(E,F)))),
% 0.18/0.44 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.18/0.44 fof(f14,plain,(
% 0.18/0.44 ![A,B,C]: (C=cartesian_product2(A,B)<=>(![D]: (in(D,C)<=>(?[E,F]: sP0_prd(F,E,D,B,A)))))),
% 0.18/0.44 inference(formula_renaming,[status(thm)],[f3,f13])).
% 0.18/0.44 fof(f15,plain,(
% 0.18/0.44 ![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)))))))),
% 0.18/0.44 inference(NNF_transformation,[status(thm)],[f14])).
% 0.18/0.44 fof(f16,plain,(
% 0.18/0.44 (![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)))))))),
% 0.18/0.44 inference(miniscoping,[status(thm)],[f15])).
% 0.18/0.44 fof(f17,plain,(
% 0.18/0.44 (![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)))))),
% 0.18/0.44 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))],[f16])).
% 0.18/0.44 fof(f18,plain,(
% 0.18/0.44 ![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))),
% 0.18/0.44 inference(cnf_transformation,[status(thm)],[f17])).
% 0.18/0.44 fof(f28,plain,(
% 0.18/0.44 (?[A,B,C]: (in(A,cartesian_product2(B,C))&(![D,E]: ~ordered_pair(D,E)=A)))),
% 0.18/0.44 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.18/0.44 fof(f29,plain,(
% 0.18/0.44 ?[A]: ((?[B,C]: in(A,cartesian_product2(B,C)))&(![D,E]: ~ordered_pair(D,E)=A))),
% 0.18/0.44 inference(miniscoping,[status(thm)],[f28])).
% 0.18/0.44 fof(f30,plain,(
% 0.18/0.44 (in(sK7_skl,cartesian_product2(sK8_skl,sK9_skl))&(![D,E]: ~ordered_pair(D,E)=sK7_skl))),
% 0.18/0.44 inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl,sK9_skl]),skolemize(A,sK7_skl),skolemize(B,sK8_skl),skolemize(C,sK9_skl)],[f29])).
% 0.18/0.44 fof(f31,plain,(
% 0.18/0.44 in(sK7_skl,cartesian_product2(sK8_skl,sK9_skl))),
% 0.18/0.44 inference(cnf_transformation,[status(thm)],[f30])).
% 0.18/0.44 fof(f32,plain,(
% 0.18/0.44 ![X0,X1]: (~ordered_pair(X0,X1)=sK7_skl)),
% 0.18/0.44 inference(cnf_transformation,[status(thm)],[f30])).
% 0.18/0.44 fof(f33,plain,(
% 0.18/0.44 ![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))))),
% 0.18/0.44 inference(NNF_transformation,[status(thm)],[f13])).
% 0.18/0.44 fof(f34,plain,(
% 0.18/0.44 (![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))))),
% 0.18/0.44 inference(miniscoping,[status(thm)],[f33])).
% 0.18/0.44 fof(f37,plain,(
% 0.18/0.44 ![X0,X1,X2,X3,X4]: (~sP0_prd(X0,X1,X2,X3,X4)|X2=ordered_pair(X1,X0))),
% 0.18/0.44 inference(cnf_transformation,[status(thm)],[f34])).
% 0.18/0.44 fof(f39,plain,(
% 0.18/0.44 ![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))),
% 0.18/0.44 inference(destructive_equality_resolution,[status(thm)],[f18])).
% 0.18/0.45 fof(f116,plain,(
% 0.18/0.45 sP0_prd(sK1_skl(sK7_skl,cartesian_product2(sK8_skl,sK9_skl),sK9_skl,sK8_skl),sK0_skl(sK7_skl,cartesian_product2(sK8_skl,sK9_skl),sK9_skl,sK8_skl),sK7_skl,sK9_skl,sK8_skl)),
% 0.18/0.45 inference(resolution,[status(thm)],[f39,f31])).
% 0.18/0.45 fof(f130,plain,(
% 0.18/0.45 sK7_skl=ordered_pair(sK0_skl(sK7_skl,cartesian_product2(sK8_skl,sK9_skl),sK9_skl,sK8_skl),sK1_skl(sK7_skl,cartesian_product2(sK8_skl,sK9_skl),sK9_skl,sK8_skl))),
% 0.18/0.45 inference(resolution,[status(thm)],[f116,f37])).
% 0.18/0.45 fof(f131,plain,(
% 0.18/0.45 $false),
% 0.18/0.45 inference(forward_subsumption_resolution,[status(thm)],[f130,f32])).
% 0.18/0.45 % SZS output end CNFRefutation for theBenchmark.p
% 0.18/0.50 % Elapsed time: 0.093356 seconds
% 0.18/0.50 % CPU time: 0.129812 seconds
% 0.18/0.50 % Total memory used: 16.268 MB
% 0.18/0.50 % Net memory used: 16.210 MB
%------------------------------------------------------------------------------