%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET950+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 : n006.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 0.13s 15.52s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET950+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/15.38 % Computer : n006.cluster.edu
% 0.10/15.38 % Model : x86_64 x86_64
% 0.10/15.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.38 % Memory : 8046.5625MB
% 0.10/15.38 % OS : Linux 6.8.0-71-generic
% 0.10/15.38 % CPULimit : 300
% 0.10/15.38 % WCLimit : 300
% 0.10/15.38 % DateTime : Mon Sep 21 05:44:58 UTC 2026
% 0.10/15.38 % CPUTime :
% 0.13/15.40 % Drodi V4.1.1
% 0.13/15.52 % Refutation found
% 0.13/15.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/15.52 % SZS output start CNFRefutation for theBenchmark
% 0.13/15.52 fof(f3,axiom,(
% 0.13/15.52 (! [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) ) )) )) )),
% 0.13/15.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/15.52 fof(f4,axiom,(
% 0.13/15.52 (! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
% 0.13/15.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/15.52 fof(f10,conjecture,(
% 0.13/15.52 (! [A,B,C,D] :~ ( subset(A,cartesian_product2(B,C))& in(D,A)& (! [E,F] :~ ( in(E,B)& in(F,C)& D = ordered_pair(E,F) ) )) )),
% 0.13/15.52 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/15.52 fof(f11,negated_conjecture,(
% 0.13/15.52 ~((! [A,B,C,D] :~ ( subset(A,cartesian_product2(B,C))& in(D,A)& (! [E,F] :~ ( in(E,B)& in(F,C)& D = ordered_pair(E,F) ) )) ))),
% 0.13/15.52 inference(negated_conjecture,[status(cth)],[f10])).
% 0.13/15.52 fof(f15,definition,(
% 0.13/15.52 ![A,B,D,E,F]: (sP0_prd(F,E,D,B,A)<=>((in(E,A)&in(F,B))&D=ordered_pair(E,F)))),
% 0.13/15.52 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.13/15.52 fof(f16,plain,(
% 0.13/15.52 ![A,B,C]: (C=cartesian_product2(A,B)<=>(![D]: (in(D,C)<=>(?[E,F]: sP0_prd(F,E,D,B,A)))))),
% 0.13/15.52 inference(formula_renaming,[status(thm)],[f3,f15])).
% 0.13/15.52 fof(f17,plain,(
% 0.13/15.52 ![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)))))))),
% 0.13/15.52 inference(NNF_transformation,[status(thm)],[f16])).
% 0.13/15.52 fof(f18,plain,(
% 0.13/15.52 (![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)))))))),
% 0.13/15.52 inference(miniscoping,[status(thm)],[f17])).
% 0.13/15.52 fof(f19,plain,(
% 0.13/15.52 (![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)))))),
% 0.13/15.52 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))],[f18])).
% 0.13/15.52 fof(f20,plain,(
% 0.13/15.52 ![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))),
% 0.13/15.52 inference(cnf_transformation,[status(thm)],[f19])).
% 0.13/15.52 fof(f24,plain,(
% 0.13/15.52 ![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
% 0.13/15.52 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 0.13/15.52 fof(f25,plain,(
% 0.13/15.52 ![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.13/15.52 inference(NNF_transformation,[status(thm)],[f24])).
% 0.13/15.52 fof(f26,plain,(
% 0.13/15.52 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.13/15.52 inference(miniscoping,[status(thm)],[f25])).
% 0.13/15.52 fof(f27,plain,(
% 0.13/15.52 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(in(sK5_skl(B,A),A)&~in(sK5_skl(B,A),B))))),
% 0.13/15.52 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(C,sK5_skl(B,A))],[f26])).
% 0.13/15.52 fof(f28,plain,(
% 0.13/15.52 ![X0,X1,X2]: (~subset(X0,X1)|~in(X2,X0)|in(X2,X1))),
% 0.13/15.52 inference(cnf_transformation,[status(thm)],[f27])).
% 0.13/15.52 fof(f39,plain,(
% 0.13/15.52 (?[A,B,C,D]: ((subset(A,cartesian_product2(B,C))&in(D,A))&(![E,F]: ((~in(E,B)|~in(F,C))|~D=ordered_pair(E,F)))))),
% 0.13/15.52 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.13/15.52 fof(f40,plain,(
% 0.13/15.52 ?[B,C,D]: ((?[A]: (subset(A,cartesian_product2(B,C))&in(D,A)))&(![E,F]: ((~in(E,B)|~in(F,C))|~D=ordered_pair(E,F))))),
% 0.13/15.52 inference(miniscoping,[status(thm)],[f39])).
% 0.13/15.52 fof(f41,plain,(
% 0.13/15.52 ((subset(sK11_skl,cartesian_product2(sK8_skl,sK9_skl))&in(sK10_skl,sK11_skl))&(![E,F]: ((~in(E,sK8_skl)|~in(F,sK9_skl))|~sK10_skl=ordered_pair(E,F))))),
% 0.13/15.52 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl,sK9_skl,sK10_skl,sK11_skl]),skolemize(B,sK8_skl),skolemize(C,sK9_skl),skolemize(D,sK10_skl),skolemize(A,sK11_skl)],[f40])).
% 0.13/15.52 fof(f42,plain,(
% 0.13/15.52 subset(sK11_skl,cartesian_product2(sK8_skl,sK9_skl))),
% 0.13/15.52 inference(cnf_transformation,[status(thm)],[f41])).
% 0.13/15.52 fof(f43,plain,(
% 0.13/15.52 in(sK10_skl,sK11_skl)),
% 0.13/15.52 inference(cnf_transformation,[status(thm)],[f41])).
% 0.13/15.52 fof(f44,plain,(
% 0.13/15.52 ![X0,X1]: (~in(X0,sK8_skl)|~in(X1,sK9_skl)|~sK10_skl=ordered_pair(X0,X1))),
% 0.13/15.52 inference(cnf_transformation,[status(thm)],[f41])).
% 0.13/15.52 fof(f45,plain,(
% 0.13/15.52 ![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))))),
% 0.13/15.52 inference(NNF_transformation,[status(thm)],[f15])).
% 0.13/15.52 fof(f46,plain,(
% 0.13/15.52 (![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))))),
% 0.13/15.52 inference(miniscoping,[status(thm)],[f45])).
% 0.13/15.52 fof(f47,plain,(
% 0.13/15.52 ![X0,X1,X2,X3,X4]: (~sP0_prd(X0,X1,X2,X3,X4)|in(X1,X4))),
% 0.13/15.52 inference(cnf_transformation,[status(thm)],[f46])).
% 0.13/15.52 fof(f48,plain,(
% 0.13/15.52 ![X0,X1,X2,X3,X4]: (~sP0_prd(X0,X1,X2,X3,X4)|in(X0,X3))),
% 0.13/15.52 inference(cnf_transformation,[status(thm)],[f46])).
% 0.13/15.52 fof(f49,plain,(
% 0.13/15.52 ![X0,X1,X2,X3,X4]: (~sP0_prd(X0,X1,X2,X3,X4)|X2=ordered_pair(X1,X0))),
% 0.13/15.52 inference(cnf_transformation,[status(thm)],[f46])).
% 0.13/15.52 fof(f51,plain,(
% 0.13/15.52 ![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))),
% 0.13/15.52 inference(destructive_equality_resolution,[status(thm)],[f20])).
% 0.13/15.52 fof(f55,plain,(
% 0.13/15.52 ![X0]: (~subset(sK11_skl,X0)|in(sK10_skl,X0))),
% 0.13/15.52 inference(resolution,[status(thm)],[f28,f43])).
% 0.13/15.52 fof(f60,plain,(
% 0.13/15.52 in(sK10_skl,cartesian_product2(sK8_skl,sK9_skl))),
% 0.13/15.52 inference(resolution,[status(thm)],[f55,f42])).
% 0.13/15.52 fof(f64,plain,(
% 0.13/15.52 sP0_prd(sK1_skl(sK10_skl,cartesian_product2(sK8_skl,sK9_skl),sK9_skl,sK8_skl),sK0_skl(sK10_skl,cartesian_product2(sK8_skl,sK9_skl),sK9_skl,sK8_skl),sK10_skl,sK9_skl,sK8_skl)),
% 0.13/15.52 inference(resolution,[status(thm)],[f51,f60])).
% 0.13/15.52 fof(f68,plain,(
% 0.13/15.52 sK10_skl=ordered_pair(sK0_skl(sK10_skl,cartesian_product2(sK8_skl,sK9_skl),sK9_skl,sK8_skl),sK1_skl(sK10_skl,cartesian_product2(sK8_skl,sK9_skl),sK9_skl,sK8_skl))),
% 0.13/15.52 inference(resolution,[status(thm)],[f64,f49])).
% 0.13/15.52 fof(f118,plain,(
% 0.13/15.52 in(sK0_skl(sK10_skl,cartesian_product2(sK8_skl,sK9_skl),sK9_skl,sK8_skl),sK8_skl)),
% 0.13/15.52 inference(resolution,[status(thm)],[f47,f64])).
% 0.13/15.52 fof(f121,plain,(
% 0.13/15.52 in(sK1_skl(sK10_skl,cartesian_product2(sK8_skl,sK9_skl),sK9_skl,sK8_skl),sK9_skl)),
% 0.13/15.52 inference(resolution,[status(thm)],[f48,f64])).
% 0.13/15.52 fof(f156,plain,(
% 0.13/15.52 ![X0]: (~in(X0,sK8_skl)|~sK10_skl=ordered_pair(X0,sK1_skl(sK10_skl,cartesian_product2(sK8_skl,sK9_skl),sK9_skl,sK8_skl)))),
% 0.13/15.52 inference(resolution,[status(thm)],[f121,f44])).
% 0.13/15.52 fof(f932,plain,(
% 0.13/15.52 ~sK10_skl=ordered_pair(sK0_skl(sK10_skl,cartesian_product2(sK8_skl,sK9_skl),sK9_skl,sK8_skl),sK1_skl(sK10_skl,cartesian_product2(sK8_skl,sK9_skl),sK9_skl,sK8_skl))),
% 0.13/15.52 inference(resolution,[status(thm)],[f156,f118])).
% 0.13/15.52 fof(f938,plain,(
% 0.13/15.52 ~sK10_skl=sK10_skl),
% 0.13/15.52 inference(forward_demodulation,[status(thm)],[f68,f932])).
% 0.13/15.52 fof(f939,plain,(
% 0.13/15.52 $false),
% 0.13/15.52 inference(trivial_equality_resolution,[status(thm)],[f938])).
% 0.13/15.52 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/15.55 % Elapsed time: 0.149479 seconds
% 0.13/15.55 % CPU time: 0.913893 seconds
% 0.13/15.55 % Total memory used: 122.169 MB
% 0.13/15.55 % Net memory used: 120.744 MB
%------------------------------------------------------------------------------