%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET956+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 : n015.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 0.17s 0.50s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET956+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n015.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
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 05:47:50 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.17/0.50 % Refutation found
% 0.17/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.50 % SZS output start CNFRefutation for theBenchmark
% 0.17/0.50 fof(f3,axiom,(
% 0.17/0.50 (! [A,B] :( subset(A,B)<=> (! [C] :( in(C,A)=> in(C,B) ) )) )),
% 0.17/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.50 fof(f9,axiom,(
% 0.17/0.50 (! [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) ) )) )),
% 0.17/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.50 fof(f10,conjecture,(
% 0.17/0.50 (! [A,B,C,D] :( ( subset(A,cartesian_product2(B,C))& (! [E,F] :( in(ordered_pair(E,F),A)=> in(ordered_pair(E,F),D) ) ))=> subset(A,D) ) )),
% 0.17/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.50 fof(f11,negated_conjecture,(
% 0.17/0.50 ~((! [A,B,C,D] :( ( subset(A,cartesian_product2(B,C))& (! [E,F] :( in(ordered_pair(E,F),A)=> in(ordered_pair(E,F),D) ) ))=> subset(A,D) ) ))),
% 0.17/0.50 inference(negated_conjecture,[status(cth)],[f10])).
% 0.17/0.50 fof(f15,plain,(
% 0.17/0.50 ![A,B]: (subset(A,B)<=>(![C]: (~in(C,A)|in(C,B))))),
% 0.17/0.50 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 0.17/0.50 fof(f16,plain,(
% 0.17/0.50 ![A,B]: ((~subset(A,B)|(![C]: (~in(C,A)|in(C,B))))&(subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.17/0.50 inference(NNF_transformation,[status(thm)],[f15])).
% 0.17/0.50 fof(f17,plain,(
% 0.17/0.50 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(?[C]: (in(C,A)&~in(C,B)))))),
% 0.17/0.50 inference(miniscoping,[status(thm)],[f16])).
% 0.17/0.50 fof(f18,plain,(
% 0.17/0.50 (![A,B]: (~subset(A,B)|(![C]: (~in(C,A)|in(C,B)))))&(![A,B]: (subset(A,B)|(in(sK0_skl(B,A),A)&~in(sK0_skl(B,A),B))))),
% 0.17/0.50 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f17])).
% 0.17/0.50 fof(f20,plain,(
% 0.17/0.50 ![X0,X1]: (subset(X0,X1)|in(sK0_skl(X1,X0),X0))),
% 0.17/0.50 inference(cnf_transformation,[status(thm)],[f18])).
% 0.17/0.50 fof(f21,plain,(
% 0.17/0.50 ![X0,X1]: (subset(X0,X1)|~in(sK0_skl(X1,X0),X1))),
% 0.17/0.50 inference(cnf_transformation,[status(thm)],[f18])).
% 0.17/0.50 fof(f30,plain,(
% 0.17/0.50 ![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))))),
% 0.17/0.50 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.17/0.50 fof(f31,plain,(
% 0.17/0.50 ![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))))),
% 0.17/0.50 inference(miniscoping,[status(thm)],[f30])).
% 0.17/0.50 fof(f32,plain,(
% 0.17/0.50 ![B,C,D]: ((![A]: (~subset(A,cartesian_product2(B,C))|~in(D,A)))|((in(sK3_skl(D,C,B),B)&in(sK4_skl(D,C,B),C))&D=ordered_pair(sK3_skl(D,C,B),sK4_skl(D,C,B))))),
% 0.17/0.50 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(E,sK3_skl(D,C,B)),skolemize(F,sK4_skl(D,C,B))],[f31])).
% 0.17/0.50 fof(f35,plain,(
% 0.17/0.50 ![X0,X1,X2,X3]: (~subset(X0,cartesian_product2(X1,X2))|~in(X3,X0)|X3=ordered_pair(sK3_skl(X3,X2,X1),sK4_skl(X3,X2,X1)))),
% 0.17/0.50 inference(cnf_transformation,[status(thm)],[f32])).
% 0.17/0.50 fof(f36,plain,(
% 0.17/0.50 (?[A,B,C,D]: ((subset(A,cartesian_product2(B,C))&(![E,F]: (~in(ordered_pair(E,F),A)|in(ordered_pair(E,F),D))))&~subset(A,D)))),
% 0.17/0.50 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.17/0.50 fof(f37,plain,(
% 0.17/0.50 ?[A,D]: (((?[B,C]: subset(A,cartesian_product2(B,C)))&(![E,F]: (~in(ordered_pair(E,F),A)|in(ordered_pair(E,F),D))))&~subset(A,D))),
% 0.17/0.50 inference(miniscoping,[status(thm)],[f36])).
% 0.17/0.50 fof(f38,plain,(
% 0.17/0.50 ((subset(sK5_skl,cartesian_product2(sK7_skl,sK8_skl))&(![E,F]: (~in(ordered_pair(E,F),sK5_skl)|in(ordered_pair(E,F),sK6_skl))))&~subset(sK5_skl,sK6_skl))),
% 0.17/0.50 inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl,sK7_skl,sK8_skl]),skolemize(A,sK5_skl),skolemize(D,sK6_skl),skolemize(B,sK7_skl),skolemize(C,sK8_skl)],[f37])).
% 0.17/0.50 fof(f39,plain,(
% 0.17/0.50 subset(sK5_skl,cartesian_product2(sK7_skl,sK8_skl))),
% 0.17/0.50 inference(cnf_transformation,[status(thm)],[f38])).
% 0.17/0.50 fof(f40,plain,(
% 0.17/0.50 ![X0,X1]: (~in(ordered_pair(X0,X1),sK5_skl)|in(ordered_pair(X0,X1),sK6_skl))),
% 0.17/0.50 inference(cnf_transformation,[status(thm)],[f38])).
% 0.17/0.50 fof(f41,plain,(
% 0.17/0.50 ~subset(sK5_skl,sK6_skl)),
% 0.17/0.50 inference(cnf_transformation,[status(thm)],[f38])).
% 0.17/0.50 fof(f83,plain,(
% 0.17/0.50 ![X0]: (~in(X0,sK5_skl)|X0=ordered_pair(sK3_skl(X0,sK8_skl,sK7_skl),sK4_skl(X0,sK8_skl,sK7_skl)))),
% 0.17/0.50 inference(resolution,[status(thm)],[f35,f39])).
% 0.17/0.50 fof(f88,plain,(
% 0.17/0.50 ![X0]: (sK0_skl(X0,sK5_skl)=ordered_pair(sK3_skl(sK0_skl(X0,sK5_skl),sK8_skl,sK7_skl),sK4_skl(sK0_skl(X0,sK5_skl),sK8_skl,sK7_skl))|subset(sK5_skl,X0))),
% 0.17/0.50 inference(resolution,[status(thm)],[f83,f20])).
% 0.17/0.50 fof(f89,plain,(
% 0.17/0.50 sK0_skl(sK6_skl,sK5_skl)=ordered_pair(sK3_skl(sK0_skl(sK6_skl,sK5_skl),sK8_skl,sK7_skl),sK4_skl(sK0_skl(sK6_skl,sK5_skl),sK8_skl,sK7_skl))),
% 0.17/0.50 inference(resolution,[status(thm)],[f88,f41])).
% 0.17/0.50 fof(f92,plain,(
% 0.17/0.50 ~in(sK0_skl(sK6_skl,sK5_skl),sK5_skl)|in(ordered_pair(sK3_skl(sK0_skl(sK6_skl,sK5_skl),sK8_skl,sK7_skl),sK4_skl(sK0_skl(sK6_skl,sK5_skl),sK8_skl,sK7_skl)),sK6_skl)),
% 0.17/0.50 inference(paramodulation,[status(thm)],[f89,f40])).
% 0.17/0.50 fof(f93,definition,(
% 0.17/0.50 sQ0_spl <=> (in(sK0_skl(sK6_skl,sK5_skl),sK5_skl))),
% 0.17/0.50 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.17/0.50 fof(f95,plain,(
% 0.17/0.50 ~in(sK0_skl(sK6_skl,sK5_skl),sK5_skl)|sQ0_spl),
% 0.17/0.50 inference(component_clause,[status(thm)],[f93])).
% 0.17/0.50 fof(f96,definition,(
% 0.17/0.50 sQ1_spl <=> (in(ordered_pair(sK3_skl(sK0_skl(sK6_skl,sK5_skl),sK8_skl,sK7_skl),sK4_skl(sK0_skl(sK6_skl,sK5_skl),sK8_skl,sK7_skl)),sK6_skl))),
% 0.17/0.50 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.17/0.50 fof(f97,plain,(
% 0.17/0.50 in(ordered_pair(sK3_skl(sK0_skl(sK6_skl,sK5_skl),sK8_skl,sK7_skl),sK4_skl(sK0_skl(sK6_skl,sK5_skl),sK8_skl,sK7_skl)),sK6_skl)|~sQ1_spl),
% 0.17/0.50 inference(component_clause,[status(thm)],[f96])).
% 0.17/0.50 fof(f99,plain,(
% 0.17/0.50 ~sQ0_spl|sQ1_spl),
% 0.17/0.50 inference(split_clause,[status(thm)],[f92,f93,f96])).
% 0.17/0.50 fof(f103,plain,(
% 0.17/0.50 subset(sK5_skl,sK6_skl)|sQ0_spl),
% 0.17/0.50 inference(resolution,[status(thm)],[f95,f20])).
% 0.17/0.50 fof(f111,plain,(
% 0.17/0.50 $false|sQ0_spl),
% 0.17/0.50 inference(forward_subsumption_resolution,[status(thm)],[f103,f41])).
% 0.17/0.50 fof(f112,plain,(
% 0.17/0.50 sQ0_spl),
% 0.17/0.50 inference(contradiction_clause,[status(thm)],[f111])).
% 0.17/0.50 fof(f113,plain,(
% 0.17/0.50 in(sK0_skl(sK6_skl,sK5_skl),sK6_skl)|~sQ1_spl),
% 0.17/0.50 inference(forward_demodulation,[status(thm)],[f89,f97])).
% 0.17/0.50 fof(f114,plain,(
% 0.17/0.50 subset(sK5_skl,sK6_skl)|~sQ1_spl),
% 0.17/0.50 inference(resolution,[status(thm)],[f113,f21])).
% 0.17/0.50 fof(f117,plain,(
% 0.17/0.50 $false|~sQ1_spl),
% 0.17/0.50 inference(forward_subsumption_resolution,[status(thm)],[f114,f41])).
% 0.17/0.51 fof(f118,plain,(
% 0.17/0.51 ~sQ1_spl),
% 0.17/0.51 inference(contradiction_clause,[status(thm)],[f117])).
% 0.17/0.51 fof(f119,plain,(
% 0.17/0.51 $false),
% 0.17/0.51 inference(sat_refutation,[status(thm)],[f99,f112,f118])).
% 0.17/0.51 % SZS output end CNFRefutation for theBenchmark.p
% 0.24/0.54 % Elapsed time: 0.101136 seconds
% 0.24/0.54 % CPU time: 0.231892 seconds
% 0.24/0.54 % Total memory used: 43.597 MB
% 0.24/0.54 % Net memory used: 43.417 MB
%------------------------------------------------------------------------------