%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET960+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 02:12:55 PM UTC 2026
% Result : Theorem 0.16s 0.51s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET960+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n010.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 21 05:45:55 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.44 % Drodi V4.1.1
% 0.16/0.51 % Refutation found
% 0.16/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.51 % SZS output start CNFRefutation for theBenchmark
% 0.16/0.51 fof(f3,axiom,(
% 0.16/0.51 (! [A] :( A = empty_set<=> (! [B] : ~ in(B,A) )) )),
% 0.16/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.51 fof(f4,axiom,(
% 0.16/0.51 (! [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) ) )) )) )),
% 0.16/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.51 fof(f10,conjecture,(
% 0.16/0.51 (! [A,B] :( cartesian_product2(A,B) = empty_set<=> ( A = empty_set| B = empty_set ) ) )),
% 0.16/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.16/0.51 fof(f11,negated_conjecture,(
% 0.16/0.51 ~((! [A,B] :( cartesian_product2(A,B) = empty_set<=> ( A = empty_set| B = empty_set ) ) ))),
% 0.16/0.51 inference(negated_conjecture,[status(cth)],[f10])).
% 0.16/0.51 fof(f15,plain,(
% 0.16/0.51 ![A]: ((~A=empty_set|(![B]: ~in(B,A)))&(A=empty_set|(?[B]: in(B,A))))),
% 0.16/0.51 inference(NNF_transformation,[status(thm)],[f3])).
% 0.16/0.51 fof(f16,plain,(
% 0.16/0.51 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|(?[B]: in(B,A))))),
% 0.16/0.51 inference(miniscoping,[status(thm)],[f15])).
% 0.16/0.51 fof(f17,plain,(
% 0.16/0.51 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|in(sK0_skl(A),A)))),
% 0.16/0.51 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(A))],[f16])).
% 0.16/0.51 fof(f18,plain,(
% 0.16/0.51 ![X0,X1]: (~X0=empty_set|~in(X1,X0))),
% 0.16/0.51 inference(cnf_transformation,[status(thm)],[f17])).
% 0.16/0.51 fof(f20,definition,(
% 0.16/0.51 ![A,B,D,E,F]: (sP0_prd(F,E,D,B,A)<=>((in(E,A)&in(F,B))&D=ordered_pair(E,F)))),
% 0.16/0.51 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.16/0.51 fof(f21,plain,(
% 0.16/0.51 ![A,B,C]: (C=cartesian_product2(A,B)<=>(![D]: (in(D,C)<=>(?[E,F]: sP0_prd(F,E,D,B,A)))))),
% 0.16/0.51 inference(formula_renaming,[status(thm)],[f4,f20])).
% 0.16/0.51 fof(f22,plain,(
% 0.16/0.51 ![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)))))))),
% 0.16/0.51 inference(NNF_transformation,[status(thm)],[f21])).
% 0.16/0.51 fof(f23,plain,(
% 0.16/0.51 (![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)))))))),
% 0.16/0.51 inference(miniscoping,[status(thm)],[f22])).
% 0.16/0.51 fof(f24,plain,(
% 0.16/0.51 (![A,B,C]: (~C=cartesian_product2(A,B)|((![D]: (~in(D,C)|sP0_prd(sK2_skl(D,C,B,A),sK1_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(sK3_skl(C,B,A),C)|(![E,F]: ~sP0_prd(F,E,sK3_skl(C,B,A),B,A)))&(in(sK3_skl(C,B,A),C)|sP0_prd(sK5_skl(C,B,A),sK4_skl(C,B,A),sK3_skl(C,B,A),B,A)))))),
% 0.16/0.51 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(E,sK1_skl(D,C,B,A)),skolemize(F,sK2_skl(D,C,B,A)),skolemize(D,sK3_skl(C,B,A)),skolemize(E,sK4_skl(C,B,A)),skolemize(F,sK5_skl(C,B,A))],[f23])).
% 0.16/0.51 fof(f26,plain,(
% 0.16/0.51 ![X0,X1,X2,X3,X4,X5]: (~X0=cartesian_product2(X1,X2)|in(X3,X0)|~sP0_prd(X4,X5,X3,X2,X1))),
% 0.16/0.51 inference(cnf_transformation,[status(thm)],[f24])).
% 0.16/0.51 fof(f28,plain,(
% 0.16/0.51 ![X0,X1,X2]: (X0=cartesian_product2(X1,X2)|in(sK3_skl(X0,X2,X1),X0)|sP0_prd(sK5_skl(X0,X2,X1),sK4_skl(X0,X2,X1),sK3_skl(X0,X2,X1),X2,X1))),
% 0.16/0.51 inference(cnf_transformation,[status(thm)],[f24])).
% 0.16/0.51 fof(f36,plain,(
% 0.16/0.51 (?[A,B]: (cartesian_product2(A,B)=empty_set<~>(A=empty_set|B=empty_set)))),
% 0.16/0.51 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.16/0.51 fof(f37,plain,(
% 0.16/0.51 ?[A,B]: ((cartesian_product2(A,B)=empty_set|(A=empty_set|B=empty_set))&(~cartesian_product2(A,B)=empty_set|(~A=empty_set&~B=empty_set)))),
% 0.16/0.51 inference(NNF_transformation,[status(thm)],[f36])).
% 0.16/0.51 fof(f38,plain,(
% 0.16/0.51 ((cartesian_product2(sK8_skl,sK9_skl)=empty_set|(sK8_skl=empty_set|sK9_skl=empty_set))&(~cartesian_product2(sK8_skl,sK9_skl)=empty_set|(~sK8_skl=empty_set&~sK9_skl=empty_set)))),
% 0.16/0.51 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl]),skolemize(A,sK8_skl),skolemize(B,sK9_skl)],[f37])).
% 0.16/0.51 fof(f39,plain,(
% 0.16/0.51 cartesian_product2(sK8_skl,sK9_skl)=empty_set|sK8_skl=empty_set|sK9_skl=empty_set),
% 0.16/0.51 inference(cnf_transformation,[status(thm)],[f38])).
% 0.16/0.51 fof(f40,plain,(
% 0.16/0.51 ~cartesian_product2(sK8_skl,sK9_skl)=empty_set|~sK8_skl=empty_set),
% 0.16/0.51 inference(cnf_transformation,[status(thm)],[f38])).
% 0.16/0.51 fof(f41,plain,(
% 0.16/0.51 ~cartesian_product2(sK8_skl,sK9_skl)=empty_set|~sK9_skl=empty_set),
% 0.16/0.51 inference(cnf_transformation,[status(thm)],[f38])).
% 0.16/0.51 fof(f42,plain,(
% 0.16/0.51 ![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))))),
% 0.16/0.51 inference(NNF_transformation,[status(thm)],[f20])).
% 0.16/0.51 fof(f43,plain,(
% 0.16/0.51 (![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))))),
% 0.16/0.51 inference(miniscoping,[status(thm)],[f42])).
% 0.16/0.51 fof(f44,plain,(
% 0.16/0.51 ![X0,X1,X2,X3,X4]: (~sP0_prd(X0,X1,X2,X3,X4)|in(X1,X4))),
% 0.16/0.51 inference(cnf_transformation,[status(thm)],[f43])).
% 0.16/0.51 fof(f45,plain,(
% 0.16/0.51 ![X0,X1,X2,X3,X4]: (~sP0_prd(X0,X1,X2,X3,X4)|in(X0,X3))),
% 0.16/0.51 inference(cnf_transformation,[status(thm)],[f43])).
% 0.16/0.51 fof(f47,plain,(
% 0.16/0.51 ![X0,X1,X2,X3,X4]: (sP0_prd(X0,X1,X2,X3,X4)|~in(X1,X4)|~in(X0,X3)|~X2=ordered_pair(X1,X0))),
% 0.16/0.51 inference(cnf_transformation,[status(thm)],[f43])).
% 0.16/0.51 fof(f48,plain,(
% 0.16/0.51 ![X0]: (~in(X0,empty_set))),
% 0.16/0.51 inference(destructive_equality_resolution,[status(thm)],[f18])).
% 0.16/0.51 fof(f50,plain,(
% 0.16/0.51 ![X0,X1,X2,X3,X4]: (in(X0,cartesian_product2(X1,X2))|~sP0_prd(X3,X4,X0,X2,X1))),
% 0.16/0.51 inference(destructive_equality_resolution,[status(thm)],[f26])).
% 0.16/0.51 fof(f51,plain,(
% 0.16/0.51 ![X0,X1,X2,X3]: (sP0_prd(X0,X1,ordered_pair(X1,X0),X2,X3)|~in(X1,X3)|~in(X0,X2))),
% 0.16/0.51 inference(destructive_equality_resolution,[status(thm)],[f47])).
% 0.16/0.51 fof(f60,plain,(
% 0.16/0.51 ![X0,X1,X2]: (X0=cartesian_product2(X1,X2)|in(sK3_skl(X0,X2,X1),X0)|in(sK5_skl(X0,X2,X1),X2))),
% 0.16/0.51 inference(resolution,[status(thm)],[f28,f45])).
% 0.16/0.51 fof(f61,plain,(
% 0.16/0.51 ![X0,X1,X2]: (X0=cartesian_product2(X1,X2)|in(sK3_skl(X0,X2,X1),X0)|in(sK4_skl(X0,X2,X1),X1))),
% 0.16/0.51 inference(resolution,[status(thm)],[f28,f44])).
% 0.16/0.51 fof(f147,plain,(
% 0.16/0.51 ![X0,X1,X2,X3]: (~in(X0,X1)|~in(X2,X3)|in(ordered_pair(X0,X2),cartesian_product2(X1,X3)))),
% 0.16/0.51 inference(resolution,[status(thm)],[f51,f50])).
% 0.16/0.51 fof(f159,plain,(
% 0.16/0.51 ![X0,X1]: (empty_set=cartesian_product2(X0,X1)|in(sK5_skl(empty_set,X1,X0),X1))),
% 0.16/0.51 inference(resolution,[status(thm)],[f60,f48])).
% 0.16/0.51 fof(f162,plain,(
% 0.16/0.51 ![X0,X1]: (X0=cartesian_product2(X1,empty_set)|in(sK3_skl(X0,empty_set,X1),X0))),
% 0.16/0.51 inference(resolution,[status(thm)],[f60,f48])).
% 0.16/0.51 fof(f167,plain,(
% 0.16/0.51 ![X0,X1]: (empty_set=cartesian_product2(X0,X1)|in(sK4_skl(empty_set,X1,X0),X0))),
% 0.16/0.51 inference(resolution,[status(thm)],[f61,f48])).
% 0.16/0.51 fof(f197,plain,(
% 0.16/0.51 ![X0]: (empty_set=cartesian_product2(X0,empty_set))),
% 0.16/0.51 inference(resolution,[status(thm)],[f159,f48])).
% 0.16/0.51 fof(f199,plain,(
% 0.16/0.51 ![X0,X1]: (X0=empty_set|in(sK3_skl(X0,empty_set,X1),X0))),
% 0.16/0.51 inference(backward_demodulation,[status(thm)],[f197,f162])).
% 0.16/0.51 fof(f313,plain,(
% 0.16/0.51 ![X0,X1]: (~in(X0,sK8_skl)|~in(X1,sK9_skl)|in(ordered_pair(X0,X1),empty_set)|sK8_skl=empty_set|sK9_skl=empty_set)),
% 0.16/0.51 inference(paramodulation,[status(thm)],[f39,f147])).
% 0.16/0.51 fof(f315,plain,(
% 0.16/0.51 ![X0,X1]: (~in(X0,sK8_skl)|~in(X1,sK9_skl)|sK8_skl=empty_set|sK9_skl=empty_set)),
% 0.16/0.51 inference(forward_subsumption_resolution,[status(thm)],[f313,f48])).
% 0.16/0.51 fof(f317,plain,(
% 0.16/0.51 ![X0]: (empty_set=cartesian_product2(empty_set,X0))),
% 0.16/0.51 inference(resolution,[status(thm)],[f167,f48])).
% 0.16/0.51 fof(f480,plain,(
% 0.16/0.51 ![X0]: (~in(X0,sK8_skl)|sK8_skl=empty_set|sK9_skl=empty_set|sK9_skl=empty_set)),
% 0.16/0.51 inference(resolution,[status(thm)],[f315,f199])).
% 0.16/0.51 fof(f488,plain,(
% 0.16/0.51 ![X0]: (~in(X0,sK8_skl)|sK8_skl=empty_set|sK9_skl=empty_set)),
% 0.16/0.51 inference(duplicate_literals_removal,[status(thm)],[f480])).
% 0.16/0.51 fof(f496,plain,(
% 0.16/0.51 sK8_skl=empty_set|sK9_skl=empty_set|sK8_skl=empty_set),
% 0.16/0.51 inference(resolution,[status(thm)],[f488,f199])).
% 0.16/0.51 fof(f504,plain,(
% 0.16/0.51 sK8_skl=empty_set|sK9_skl=empty_set),
% 0.16/0.51 inference(duplicate_literals_removal,[status(thm)],[f496])).
% 0.16/0.51 fof(f508,plain,(
% 0.16/0.51 sK8_skl=empty_set|~cartesian_product2(sK8_skl,sK9_skl)=empty_set),
% 0.16/0.51 inference(resolution,[status(thm)],[f504,f41])).
% 0.16/0.52 fof(f510,plain,(
% 0.16/0.52 ~cartesian_product2(sK8_skl,sK9_skl)=empty_set),
% 0.16/0.52 inference(forward_subsumption_resolution,[status(thm)],[f508,f40])).
% 0.16/0.52 fof(f512,plain,(
% 0.16/0.52 ~cartesian_product2(sK8_skl,empty_set)=empty_set|sK8_skl=empty_set),
% 0.16/0.52 inference(paramodulation,[status(thm)],[f504,f510])).
% 0.16/0.52 fof(f513,plain,(
% 0.16/0.52 ~empty_set=empty_set|sK8_skl=empty_set),
% 0.16/0.52 inference(forward_demodulation,[status(thm)],[f197,f512])).
% 0.16/0.52 fof(f514,plain,(
% 0.16/0.52 ~cartesian_product2(empty_set,sK9_skl)=empty_set),
% 0.16/0.52 inference(backward_demodulation,[status(thm)],[f516,f510])).
% 0.16/0.52 fof(f516,plain,(
% 0.16/0.52 sK8_skl=empty_set),
% 0.16/0.52 inference(trivial_equality_resolution,[status(thm)],[f513])).
% 0.16/0.52 fof(f517,plain,(
% 0.16/0.52 ~empty_set=empty_set),
% 0.16/0.52 inference(forward_demodulation,[status(thm)],[f317,f514])).
% 0.16/0.52 fof(f518,plain,(
% 0.16/0.52 $false),
% 0.16/0.52 inference(trivial_equality_resolution,[status(thm)],[f517])).
% 0.16/0.52 % SZS output end CNFRefutation for theBenchmark.p
% 0.16/0.55 % Elapsed time: 0.118386 seconds
% 0.16/0.55 % CPU time: 0.536071 seconds
% 0.16/0.55 % Total memory used: 106.041 MB
% 0.16/0.55 % Net memory used: 105.207 MB
%------------------------------------------------------------------------------