%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET977+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 02:12:56 PM UTC 2026
% Result : Theorem 0.10s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET977+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:49:06 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.39 % Refutation found
% 0.10/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.39 fof(f3,axiom,(
% 0.10/0.39 (! [A] :( A = empty_set<=> (! [B] : ~ in(B,A) )) )),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f9,axiom,(
% 0.10/0.39 (! [A,B,C,D] :( in(ordered_pair(A,B),cartesian_product2(singleton(C),D))<=> ( A = C& in(B,D) ) ) )),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f10,axiom,(
% 0.10/0.39 (! [A,B,C,D] :( in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))<=> ( in(A,C)& B = D ) ) )),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f11,conjecture,(
% 0.10/0.39 (! [A,B] :( A != empty_set=> ( cartesian_product2(singleton(B),A) != empty_set& cartesian_product2(A,singleton(B)) != empty_set ) ) )),
% 0.10/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f12,negated_conjecture,(
% 0.10/0.39 ~((! [A,B] :( A != empty_set=> ( cartesian_product2(singleton(B),A) != empty_set& cartesian_product2(A,singleton(B)) != empty_set ) ) ))),
% 0.10/0.39 inference(negated_conjecture,[status(cth)],[f11])).
% 0.10/0.39 fof(f16,plain,(
% 0.10/0.39 ![A]: ((~A=empty_set|(![B]: ~in(B,A)))&(A=empty_set|(?[B]: in(B,A))))),
% 0.10/0.39 inference(NNF_transformation,[status(thm)],[f3])).
% 0.10/0.39 fof(f17,plain,(
% 0.10/0.39 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|(?[B]: in(B,A))))),
% 0.10/0.39 inference(miniscoping,[status(thm)],[f16])).
% 0.10/0.39 fof(f18,plain,(
% 0.10/0.39 (![A]: (~A=empty_set|(![B]: ~in(B,A))))&(![A]: (A=empty_set|in(sK0_skl(A),A)))),
% 0.10/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl(A))],[f17])).
% 0.10/0.39 fof(f19,plain,(
% 0.10/0.39 ![X0,X1]: (~X0=empty_set|~in(X1,X0))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f18])).
% 0.10/0.39 fof(f20,plain,(
% 0.10/0.39 ![X0]: (X0=empty_set|in(sK0_skl(X0),X0))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f18])).
% 0.10/0.39 fof(f28,plain,(
% 0.10/0.39 ![A,B,C,D]: ((~in(ordered_pair(A,B),cartesian_product2(singleton(C),D))|(A=C&in(B,D)))&(in(ordered_pair(A,B),cartesian_product2(singleton(C),D))|(~A=C|~in(B,D))))),
% 0.10/0.39 inference(NNF_transformation,[status(thm)],[f9])).
% 0.10/0.39 fof(f29,plain,(
% 0.10/0.39 (![A,B,C,D]: (~in(ordered_pair(A,B),cartesian_product2(singleton(C),D))|(A=C&in(B,D))))&(![A,B,C,D]: (in(ordered_pair(A,B),cartesian_product2(singleton(C),D))|(~A=C|~in(B,D))))),
% 0.10/0.39 inference(miniscoping,[status(thm)],[f28])).
% 0.10/0.39 fof(f32,plain,(
% 0.10/0.39 ![X0,X1,X2,X3]: (in(ordered_pair(X0,X1),cartesian_product2(singleton(X2),X3))|~X0=X2|~in(X1,X3))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f29])).
% 0.10/0.39 fof(f33,plain,(
% 0.10/0.39 ![A,B,C,D]: ((~in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))|(in(A,C)&B=D))&(in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))|(~in(A,C)|~B=D)))),
% 0.10/0.39 inference(NNF_transformation,[status(thm)],[f10])).
% 0.10/0.39 fof(f34,plain,(
% 0.10/0.39 (![A,B,C,D]: (~in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))|(in(A,C)&B=D)))&(![A,B,C,D]: (in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))|(~in(A,C)|~B=D)))),
% 0.10/0.39 inference(miniscoping,[status(thm)],[f33])).
% 0.10/0.39 fof(f37,plain,(
% 0.10/0.39 ![X0,X1,X2,X3]: (in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X3)))|~in(X0,X2)|~X1=X3)),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f34])).
% 0.10/0.39 fof(f38,plain,(
% 0.10/0.39 (?[A,B]: (~A=empty_set&(cartesian_product2(singleton(B),A)=empty_set|cartesian_product2(A,singleton(B))=empty_set)))),
% 0.10/0.39 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.10/0.39 fof(f39,plain,(
% 0.10/0.39 ?[A]: (~A=empty_set&((?[B]: cartesian_product2(singleton(B),A)=empty_set)|(?[B]: cartesian_product2(A,singleton(B))=empty_set)))),
% 0.10/0.39 inference(miniscoping,[status(thm)],[f38])).
% 0.10/0.39 fof(f40,plain,(
% 0.10/0.39 (~sK3_skl=empty_set&(cartesian_product2(singleton(sK4_skl),sK3_skl)=empty_set|cartesian_product2(sK3_skl,singleton(sK5_skl))=empty_set))),
% 0.10/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl),skolemize(B,sK5_skl)],[f39])).
% 0.10/0.39 fof(f41,plain,(
% 0.10/0.39 ~sK3_skl=empty_set),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f40])).
% 0.10/0.39 fof(f42,plain,(
% 0.10/0.39 cartesian_product2(singleton(sK4_skl),sK3_skl)=empty_set|cartesian_product2(sK3_skl,singleton(sK5_skl))=empty_set),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f40])).
% 0.10/0.39 fof(f43,plain,(
% 0.10/0.39 ![X0]: (~in(X0,empty_set))),
% 0.10/0.39 inference(destructive_equality_resolution,[status(thm)],[f19])).
% 0.10/0.39 fof(f44,plain,(
% 0.10/0.39 ![X0,X1,X2]: (in(ordered_pair(X0,X1),cartesian_product2(singleton(X0),X2))|~in(X1,X2))),
% 0.10/0.39 inference(destructive_equality_resolution,[status(thm)],[f32])).
% 0.10/0.39 fof(f45,plain,(
% 0.10/0.39 ![X0,X1,X2]: (in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X1)))|~in(X0,X2))),
% 0.10/0.39 inference(destructive_equality_resolution,[status(thm)],[f37])).
% 0.10/0.39 fof(f54,plain,(
% 0.10/0.39 ![X0,X1]: (X0=empty_set|in(ordered_pair(sK0_skl(X0),X1),cartesian_product2(X0,singleton(X1))))),
% 0.10/0.39 inference(resolution,[status(thm)],[f20,f45])).
% 0.10/0.39 fof(f55,plain,(
% 0.10/0.39 ![X0,X1]: (X0=empty_set|in(ordered_pair(X1,sK0_skl(X0)),cartesian_product2(singleton(X1),X0)))),
% 0.10/0.39 inference(resolution,[status(thm)],[f20,f44])).
% 0.10/0.39 fof(f77,plain,(
% 0.10/0.39 sK3_skl=empty_set|in(ordered_pair(sK4_skl,sK0_skl(sK3_skl)),empty_set)|cartesian_product2(sK3_skl,singleton(sK5_skl))=empty_set),
% 0.10/0.39 inference(paramodulation,[status(thm)],[f42,f55])).
% 0.10/0.39 fof(f78,plain,(
% 0.10/0.39 in(ordered_pair(sK4_skl,sK0_skl(sK3_skl)),empty_set)|cartesian_product2(sK3_skl,singleton(sK5_skl))=empty_set),
% 0.10/0.39 inference(forward_subsumption_resolution,[status(thm)],[f77,f41])).
% 0.10/0.39 fof(f80,plain,(
% 0.10/0.39 cartesian_product2(sK3_skl,singleton(sK5_skl))=empty_set),
% 0.10/0.39 inference(forward_subsumption_resolution,[status(thm)],[f78,f43])).
% 0.10/0.39 fof(f81,plain,(
% 0.10/0.39 sK3_skl=empty_set|in(ordered_pair(sK0_skl(sK3_skl),sK5_skl),empty_set)),
% 0.10/0.39 inference(paramodulation,[status(thm)],[f80,f54])).
% 0.10/0.39 fof(f84,plain,(
% 0.10/0.39 in(ordered_pair(sK0_skl(sK3_skl),sK5_skl),empty_set)),
% 0.10/0.39 inference(forward_subsumption_resolution,[status(thm)],[f81,f41])).
% 0.10/0.39 fof(f149,plain,(
% 0.10/0.39 $false),
% 0.10/0.39 inference(forward_subsumption_resolution,[status(thm)],[f84,f43])).
% 0.10/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.42 % Elapsed time: 0.050602 seconds
% 0.10/0.42 % CPU time: 0.155504 seconds
% 0.10/0.42 % Total memory used: 95.877 MB
% 0.10/0.42 % Net memory used: 95.473 MB
%------------------------------------------------------------------------------