%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET873+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/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 02:12:47 PM UTC 2026
% Result : Theorem 0.20s 10.51s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET873+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/10.48 % Computer : n015.cluster.edu
% 0.15/10.48 % Model : x86_64 x86_64
% 0.15/10.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/10.48 % Memory : 8046.5625MB
% 0.15/10.48 % OS : Linux 6.8.0-71-generic
% 0.15/10.48 % CPULimit : 300
% 0.15/10.48 % WCLimit : 300
% 0.15/10.48 % DateTime : Mon Sep 21 05:46:01 UTC 2026
% 0.15/10.49 % CPUTime :
% 0.20/10.50 % Drodi V4.1.1
% 0.20/10.51 % Refutation found
% 0.20/10.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/10.51 % SZS output start CNFRefutation for theBenchmark
% 0.20/10.51 fof(f2,axiom,(
% 0.20/10.51 (! [A,B] : set_union2(A,B) = set_union2(B,A) )),
% 0.20/10.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/10.51 fof(f3,axiom,(
% 0.20/10.51 (! [A,B] :( B = singleton(A)<=> (! [C] :( in(C,B)<=> C = A ) )) )),
% 0.20/10.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/10.51 fof(f7,axiom,(
% 0.20/10.51 (! [A,B] :( subset(set_union2(singleton(A),B),B)=> in(A,B) ) )),
% 0.20/10.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/10.51 fof(f10,axiom,(
% 0.20/10.51 (! [A,B] : subset(A,A) )),
% 0.20/10.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/10.51 fof(f11,conjecture,(
% 0.20/10.51 (! [A,B] :( set_union2(singleton(A),singleton(B)) = singleton(A)=> A = B ) )),
% 0.20/10.51 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/10.51 fof(f12,negated_conjecture,(
% 0.20/10.51 ~((! [A,B] :( set_union2(singleton(A),singleton(B)) = singleton(A)=> A = B ) ))),
% 0.20/10.51 inference(negated_conjecture,[status(cth)],[f11])).
% 0.20/10.51 fof(f15,plain,(
% 0.20/10.51 ![X0,X1]: (set_union2(X0,X1)=set_union2(X1,X0))),
% 0.20/10.52 inference(cnf_transformation,[status(thm)],[f2])).
% 0.20/10.52 fof(f16,plain,(
% 0.20/10.52 ![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)))))),
% 0.20/10.52 inference(NNF_transformation,[status(thm)],[f3])).
% 0.20/10.52 fof(f17,plain,(
% 0.20/10.52 (![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)))))),
% 0.20/10.52 inference(miniscoping,[status(thm)],[f16])).
% 0.20/10.52 fof(f18,plain,(
% 0.20/10.52 (![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))))),
% 0.20/10.52 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f17])).
% 0.20/10.52 fof(f19,plain,(
% 0.20/10.52 ![X0,X1,X2]: (~X0=singleton(X1)|~in(X2,X0)|X2=X1)),
% 0.20/10.52 inference(cnf_transformation,[status(thm)],[f18])).
% 0.20/10.52 fof(f31,plain,(
% 0.20/10.52 ![A,B]: (~subset(set_union2(singleton(A),B),B)|in(A,B))),
% 0.20/10.52 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.20/10.52 fof(f32,plain,(
% 0.20/10.52 ![X0,X1]: (~subset(set_union2(singleton(X0),X1),X1)|in(X0,X1))),
% 0.20/10.52 inference(cnf_transformation,[status(thm)],[f31])).
% 0.20/10.52 fof(f37,plain,(
% 0.20/10.52 ![A]: subset(A,A)),
% 0.20/10.52 inference(miniscoping,[status(thm)],[f10])).
% 0.20/10.52 fof(f38,plain,(
% 0.20/10.52 ![X0]: (subset(X0,X0))),
% 0.20/10.52 inference(cnf_transformation,[status(thm)],[f37])).
% 0.20/10.52 fof(f39,plain,(
% 0.20/10.52 (?[A,B]: (set_union2(singleton(A),singleton(B))=singleton(A)&~A=B))),
% 0.20/10.52 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.20/10.52 fof(f40,plain,(
% 0.20/10.52 (set_union2(singleton(sK3_skl),singleton(sK4_skl))=singleton(sK3_skl)&~sK3_skl=sK4_skl)),
% 0.20/10.52 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl)],[f39])).
% 0.20/10.52 fof(f41,plain,(
% 0.20/10.52 set_union2(singleton(sK3_skl),singleton(sK4_skl))=singleton(sK3_skl)),
% 0.20/10.52 inference(cnf_transformation,[status(thm)],[f40])).
% 0.20/10.52 fof(f42,plain,(
% 0.20/10.52 ~sK3_skl=sK4_skl),
% 0.20/10.52 inference(cnf_transformation,[status(thm)],[f40])).
% 0.20/10.52 fof(f43,plain,(
% 0.20/10.52 ![X0,X1]: (~in(X0,singleton(X1))|X0=X1)),
% 0.20/10.52 inference(destructive_equality_resolution,[status(thm)],[f19])).
% 0.20/10.52 fof(f64,plain,(
% 0.20/10.52 ![X0,X1]: (~subset(set_union2(X0,singleton(X1)),X0)|in(X1,X0))),
% 0.20/10.52 inference(paramodulation,[status(thm)],[f15,f32])).
% 0.20/10.52 fof(f74,plain,(
% 0.20/10.52 ~subset(singleton(sK3_skl),singleton(sK3_skl))|in(sK4_skl,singleton(sK3_skl))),
% 0.20/10.52 inference(paramodulation,[status(thm)],[f41,f64])).
% 0.20/10.52 fof(f78,plain,(
% 0.20/10.52 in(sK4_skl,singleton(sK3_skl))),
% 0.20/10.52 inference(forward_subsumption_resolution,[status(thm)],[f74,f38])).
% 0.20/10.52 fof(f79,plain,(
% 0.20/10.52 sK4_skl=sK3_skl),
% 0.20/10.52 inference(resolution,[status(thm)],[f78,f43])).
% 0.20/10.52 fof(f81,plain,(
% 0.20/10.52 $false),
% 0.20/10.52 inference(forward_subsumption_resolution,[status(thm)],[f79,f42])).
% 0.20/10.52 % SZS output end CNFRefutation for theBenchmark.p
% 0.20/10.54 % Elapsed time: 0.044783 seconds
% 0.20/10.54 % CPU time: 0.131130 seconds
% 0.20/10.54 % Total memory used: 69.751 MB
% 0.20/10.54 % Net memory used: 69.479 MB
%------------------------------------------------------------------------------