%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET976+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 : n003.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 0.14s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET976+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
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:46:31 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.40 fof(f3,axiom,(
% 0.14/0.40 (! [A,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = A ) )) )),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f6,axiom,(
% 0.14/0.40 (! [A,B,C,D] :( in(ordered_pair(A,B),cartesian_product2(C,D))<=> ( in(A,C)& in(B,D) ) ) )),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f9,conjecture,(
% 0.14/0.40 (! [A,B,C,D] :( in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))<=> ( in(A,C)& B = D ) ) )),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.40 fof(f10,negated_conjecture,(
% 0.14/0.40 ~((! [A,B,C,D] :( in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))<=> ( in(A,C)& B = D ) ) ))),
% 0.14/0.40 inference(negated_conjecture,[status(cth)],[f9])).
% 0.14/0.40 fof(f14,plain,(
% 0.14/0.40 ![A,B]: ((~B=singleton(A)|(![C]: ((~in(C,B)|C=A)&(in(C,B)|~C=A))))&(B=singleton(A)|(?[C]: ((~in(C,B)|~C=A)&(in(C,B)|C=A)))))),
% 0.14/0.40 inference(NNF_transformation,[status(thm)],[f3])).
% 0.14/0.40 fof(f15,plain,(
% 0.14/0.40 (![A,B]: (~B=singleton(A)|((![C]: (~in(C,B)|C=A))&(![C]: (in(C,B)|~C=A)))))&(![A,B]: (B=singleton(A)|(?[C]: ((~in(C,B)|~C=A)&(in(C,B)|C=A)))))),
% 0.14/0.40 inference(miniscoping,[status(thm)],[f14])).
% 0.14/0.40 fof(f16,plain,(
% 0.14/0.40 (![A,B]: (~B=singleton(A)|((![C]: (~in(C,B)|C=A))&(![C]: (in(C,B)|~C=A)))))&(![A,B]: (B=singleton(A)|((~in(sK0_skl(B,A),B)|~sK0_skl(B,A)=A)&(in(sK0_skl(B,A),B)|sK0_skl(B,A)=A))))),
% 0.14/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f15])).
% 0.14/0.40 fof(f17,plain,(
% 0.14/0.40 ![X0,X1,X2]: (~X0=singleton(X1)|~in(X2,X0)|X2=X1)),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f16])).
% 0.14/0.40 fof(f18,plain,(
% 0.14/0.40 ![X0,X1,X2]: (~X0=singleton(X1)|in(X2,X0)|~X2=X1)),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f16])).
% 0.14/0.40 fof(f23,plain,(
% 0.14/0.40 ![A,B,C,D]: ((~in(ordered_pair(A,B),cartesian_product2(C,D))|(in(A,C)&in(B,D)))&(in(ordered_pair(A,B),cartesian_product2(C,D))|(~in(A,C)|~in(B,D))))),
% 0.14/0.40 inference(NNF_transformation,[status(thm)],[f6])).
% 0.14/0.40 fof(f24,plain,(
% 0.14/0.40 (![A,B,C,D]: (~in(ordered_pair(A,B),cartesian_product2(C,D))|(in(A,C)&in(B,D))))&(![A,B,C,D]: (in(ordered_pair(A,B),cartesian_product2(C,D))|(~in(A,C)|~in(B,D))))),
% 0.14/0.40 inference(miniscoping,[status(thm)],[f23])).
% 0.14/0.40 fof(f25,plain,(
% 0.14/0.40 ![X0,X1,X2,X3]: (~in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|in(X0,X2))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f24])).
% 0.14/0.40 fof(f26,plain,(
% 0.14/0.40 ![X0,X1,X2,X3]: (~in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|in(X1,X3))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f24])).
% 0.14/0.40 fof(f27,plain,(
% 0.14/0.40 ![X0,X1,X2,X3]: (in(ordered_pair(X0,X1),cartesian_product2(X2,X3))|~in(X0,X2)|~in(X1,X3))),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f24])).
% 0.14/0.40 fof(f32,plain,(
% 0.14/0.40 (?[A,B,C,D]: (in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))<~>(in(A,C)&B=D)))),
% 0.14/0.40 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.14/0.40 fof(f33,plain,(
% 0.14/0.40 ?[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)))),
% 0.14/0.40 inference(NNF_transformation,[status(thm)],[f32])).
% 0.14/0.40 fof(f34,plain,(
% 0.14/0.40 ((in(ordered_pair(sK3_skl,sK4_skl),cartesian_product2(sK5_skl,singleton(sK6_skl)))|(in(sK3_skl,sK5_skl)&sK4_skl=sK6_skl))&(~in(ordered_pair(sK3_skl,sK4_skl),cartesian_product2(sK5_skl,singleton(sK6_skl)))|(~in(sK3_skl,sK5_skl)|~sK4_skl=sK6_skl)))),
% 0.14/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl,sK6_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl),skolemize(C,sK5_skl),skolemize(D,sK6_skl)],[f33])).
% 0.14/0.40 fof(f35,plain,(
% 0.14/0.40 in(ordered_pair(sK3_skl,sK4_skl),cartesian_product2(sK5_skl,singleton(sK6_skl)))|in(sK3_skl,sK5_skl)),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f34])).
% 0.14/0.40 fof(f36,plain,(
% 0.14/0.40 in(ordered_pair(sK3_skl,sK4_skl),cartesian_product2(sK5_skl,singleton(sK6_skl)))|sK4_skl=sK6_skl),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f34])).
% 0.14/0.40 fof(f37,plain,(
% 0.14/0.40 ~in(ordered_pair(sK3_skl,sK4_skl),cartesian_product2(sK5_skl,singleton(sK6_skl)))|~in(sK3_skl,sK5_skl)|~sK4_skl=sK6_skl),
% 0.14/0.40 inference(cnf_transformation,[status(thm)],[f34])).
% 0.14/0.40 fof(f38,plain,(
% 0.14/0.40 ![X0,X1]: (~in(X0,singleton(X1))|X0=X1)),
% 0.14/0.40 inference(destructive_equality_resolution,[status(thm)],[f17])).
% 0.14/0.40 fof(f39,plain,(
% 0.14/0.40 ![X0]: (in(X0,singleton(X0)))),
% 0.14/0.40 inference(destructive_equality_resolution,[status(thm)],[f18])).
% 0.14/0.40 fof(f40,plain,(
% 0.14/0.40 in(sK3_skl,sK5_skl)),
% 0.14/0.40 inference(forward_subsumption_resolution,[status(thm)],[f35,f25])).
% 0.14/0.40 fof(f41,plain,(
% 0.14/0.40 ~in(ordered_pair(sK3_skl,sK4_skl),cartesian_product2(sK5_skl,singleton(sK6_skl)))|~sK4_skl=sK6_skl),
% 0.14/0.40 inference(forward_subsumption_resolution,[status(thm)],[f37,f25])).
% 0.14/0.40 fof(f48,plain,(
% 0.14/0.40 in(sK4_skl,singleton(sK6_skl))|sK4_skl=sK6_skl),
% 0.14/0.40 inference(resolution,[status(thm)],[f26,f36])).
% 0.14/0.40 fof(f49,plain,(
% 0.14/0.40 ~in(ordered_pair(sK3_skl,sK4_skl),cartesian_product2(sK5_skl,singleton(sK6_skl)))|~sK6_skl=sK6_skl),
% 0.14/0.40 inference(backward_demodulation,[status(thm)],[f52,f41])).
% 0.14/0.40 fof(f52,plain,(
% 0.14/0.40 sK4_skl=sK6_skl),
% 0.14/0.40 inference(forward_subsumption_resolution,[status(thm)],[f48,f38])).
% 0.14/0.40 fof(f53,plain,(
% 0.14/0.40 ~in(ordered_pair(sK3_skl,sK6_skl),cartesian_product2(sK5_skl,singleton(sK6_skl)))|~sK6_skl=sK6_skl),
% 0.14/0.40 inference(forward_demodulation,[status(thm)],[f52,f49])).
% 0.14/0.40 fof(f54,plain,(
% 0.14/0.40 ~in(ordered_pair(sK3_skl,sK6_skl),cartesian_product2(sK5_skl,singleton(sK6_skl)))),
% 0.14/0.40 inference(trivial_equality_resolution,[status(thm)],[f53])).
% 0.14/0.40 fof(f56,plain,(
% 0.14/0.40 ![X0,X1,X2]: (in(ordered_pair(X0,X1),cartesian_product2(X2,singleton(X1)))|~in(X0,X2))),
% 0.14/0.40 inference(resolution,[status(thm)],[f27,f39])).
% 0.14/0.40 fof(f59,plain,(
% 0.14/0.40 ![X0]: (in(ordered_pair(sK3_skl,X0),cartesian_product2(sK5_skl,singleton(X0))))),
% 0.14/0.40 inference(resolution,[status(thm)],[f56,f40])).
% 0.14/0.40 fof(f62,plain,(
% 0.14/0.40 $false),
% 0.14/0.40 inference(backward_subsumption_resolution,[status(thm)],[f54,f59])).
% 0.14/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.43 % Elapsed time: 0.053345 seconds
% 0.14/0.43 % CPU time: 0.158069 seconds
% 0.14/0.43 % Total memory used: 101.704 MB
% 0.14/0.43 % Net memory used: 101.273 MB
%------------------------------------------------------------------------------