%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET903+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 : n002.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 02:12:50 PM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET903+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.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 05:46:03 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.40 fof(f1,axiom,(
% 0.09/0.40 (! [A,B] : set_union2(A,B) = set_union2(B,A) )),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f8,axiom,(
% 0.09/0.40 (! [A,B,C] :~ ( singleton(A) = set_union2(B,C)& ~ ( B = singleton(A)& C = singleton(A) )& ~ ( B = empty_set& C = singleton(A) )& ~ ( B = singleton(A)& C = empty_set ) ) )),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f9,conjecture,(
% 0.09/0.40 (! [A,B,C] :~ ( singleton(A) = set_union2(B,C)& B != C& B != empty_set& C != empty_set ) )),
% 0.09/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.40 fof(f10,negated_conjecture,(
% 0.09/0.40 ~((! [A,B,C] :~ ( singleton(A) = set_union2(B,C)& B != C& B != empty_set& C != empty_set ) ))),
% 0.09/0.40 inference(negated_conjecture,[status(cth)],[f9])).
% 0.09/0.40 fof(f11,plain,(
% 0.09/0.40 ![X0,X1]: (set_union2(X0,X1)=set_union2(X1,X0))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f1])).
% 0.09/0.40 fof(f25,plain,(
% 0.09/0.40 ![A,B,C]: (((~singleton(A)=set_union2(B,C)|(B=singleton(A)&C=singleton(A)))|(B=empty_set&C=singleton(A)))|(B=singleton(A)&C=empty_set))),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.09/0.40 fof(f26,definition,(
% 0.09/0.40 ![A,B,C]: (sP0_prd(C,B,A)<=>(B=singleton(A)&C=singleton(A)))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.09/0.40 fof(f27,definition,(
% 0.09/0.40 ![A,B,C]: (sP1_prd(C,B,A)<=>(B=empty_set&C=singleton(A)))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sP1_prd])],[])).
% 0.09/0.40 fof(f28,plain,(
% 0.09/0.40 ![A,B,C]: (((~singleton(A)=set_union2(B,C)|sP0_prd(C,B,A))|sP1_prd(C,B,A))|(B=singleton(A)&C=empty_set))),
% 0.09/0.40 inference(formula_renaming,[status(thm)],[f25,f27,f26])).
% 0.09/0.40 fof(f30,plain,(
% 0.09/0.40 ![X0,X1,X2]: (~singleton(X0)=set_union2(X1,X2)|sP0_prd(X2,X1,X0)|sP1_prd(X2,X1,X0)|X2=empty_set)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f28])).
% 0.09/0.40 fof(f31,plain,(
% 0.09/0.40 (?[A,B,C]: (((singleton(A)=set_union2(B,C)&~B=C)&~B=empty_set)&~C=empty_set))),
% 0.09/0.40 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.09/0.40 fof(f32,plain,(
% 0.09/0.40 ?[C]: ((?[B]: (((?[A]: singleton(A)=set_union2(B,C))&~B=C)&~B=empty_set))&~C=empty_set)),
% 0.09/0.40 inference(miniscoping,[status(thm)],[f31])).
% 0.09/0.40 fof(f33,plain,(
% 0.09/0.40 (((singleton(sK4_skl)=set_union2(sK3_skl,sK2_skl)&~sK3_skl=sK2_skl)&~sK3_skl=empty_set)&~sK2_skl=empty_set)),
% 0.09/0.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(C,sK2_skl),skolemize(B,sK3_skl),skolemize(A,sK4_skl)],[f32])).
% 0.09/0.40 fof(f34,plain,(
% 0.09/0.40 singleton(sK4_skl)=set_union2(sK3_skl,sK2_skl)),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f33])).
% 0.09/0.40 fof(f35,plain,(
% 0.09/0.40 ~sK3_skl=sK2_skl),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f33])).
% 0.09/0.40 fof(f36,plain,(
% 0.09/0.40 ~sK3_skl=empty_set),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f33])).
% 0.09/0.40 fof(f37,plain,(
% 0.09/0.40 ~sK2_skl=empty_set),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f33])).
% 0.09/0.40 fof(f38,plain,(
% 0.09/0.40 ![A,B,C]: ((~sP0_prd(C,B,A)|(B=singleton(A)&C=singleton(A)))&(sP0_prd(C,B,A)|(~B=singleton(A)|~C=singleton(A))))),
% 0.09/0.40 inference(NNF_transformation,[status(thm)],[f26])).
% 0.09/0.40 fof(f39,plain,(
% 0.09/0.40 (![A,B,C]: (~sP0_prd(C,B,A)|(B=singleton(A)&C=singleton(A))))&(![A,B,C]: (sP0_prd(C,B,A)|(~B=singleton(A)|~C=singleton(A))))),
% 0.09/0.40 inference(miniscoping,[status(thm)],[f38])).
% 0.09/0.40 fof(f41,plain,(
% 0.09/0.40 ![X0,X1,X2]: (~sP0_prd(X0,X1,X2)|X0=singleton(X2))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f39])).
% 0.09/0.40 fof(f43,plain,(
% 0.09/0.40 ![A,B,C]: ((~sP1_prd(C,B,A)|(B=empty_set&C=singleton(A)))&(sP1_prd(C,B,A)|(~B=empty_set|~C=singleton(A))))),
% 0.09/0.40 inference(NNF_transformation,[status(thm)],[f27])).
% 0.09/0.40 fof(f44,plain,(
% 0.09/0.40 (![A,B,C]: (~sP1_prd(C,B,A)|(B=empty_set&C=singleton(A))))&(![A,B,C]: (sP1_prd(C,B,A)|(~B=empty_set|~C=singleton(A))))),
% 0.09/0.40 inference(miniscoping,[status(thm)],[f43])).
% 0.09/0.40 fof(f46,plain,(
% 0.09/0.40 ![X0,X1,X2]: (~sP1_prd(X0,X1,X2)|X0=singleton(X2))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f44])).
% 0.09/0.40 fof(f51,plain,(
% 0.09/0.40 singleton(sK4_skl)=set_union2(sK2_skl,sK3_skl)),
% 0.09/0.40 inference(paramodulation,[status(thm)],[f34,f11])).
% 0.09/0.40 fof(f74,plain,(
% 0.09/0.40 ![X0,X1,X2]: (X0=singleton(X1)|~singleton(X1)=set_union2(X2,X0)|sP0_prd(X0,X2,X1)|X0=empty_set)),
% 0.09/0.40 inference(resolution,[status(thm)],[f46,f30])).
% 0.09/0.41 fof(f75,plain,(
% 0.09/0.41 ![X0,X1,X2]: (X0=singleton(X1)|~singleton(X1)=set_union2(X2,X0)|X0=empty_set)),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f74,f41])).
% 0.09/0.41 fof(f76,plain,(
% 0.09/0.41 sK3_skl=singleton(sK4_skl)|sK3_skl=empty_set),
% 0.09/0.41 inference(resolution,[status(thm)],[f75,f51])).
% 0.09/0.41 fof(f77,plain,(
% 0.09/0.41 sK2_skl=singleton(sK4_skl)|sK2_skl=empty_set),
% 0.09/0.41 inference(resolution,[status(thm)],[f75,f34])).
% 0.09/0.41 fof(f88,plain,(
% 0.09/0.41 sK3_skl=singleton(sK4_skl)),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f76,f36])).
% 0.09/0.41 fof(f89,plain,(
% 0.09/0.41 sK2_skl=sK3_skl|sK2_skl=empty_set),
% 0.09/0.41 inference(forward_demodulation,[status(thm)],[f88,f77])).
% 0.09/0.41 fof(f90,plain,(
% 0.09/0.41 ~empty_set=empty_set),
% 0.09/0.41 inference(backward_demodulation,[status(thm)],[f92,f37])).
% 0.09/0.41 fof(f92,plain,(
% 0.09/0.41 sK2_skl=empty_set),
% 0.09/0.41 inference(forward_subsumption_resolution,[status(thm)],[f89,f35])).
% 0.09/0.41 fof(f98,plain,(
% 0.09/0.41 $false),
% 0.09/0.41 inference(trivial_equality_resolution,[status(thm)],[f90])).
% 0.09/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.42 % Elapsed time: 0.049092 seconds
% 0.09/0.42 % CPU time: 0.149575 seconds
% 0.09/0.42 % Total memory used: 101.734 MB
% 0.09/0.42 % Net memory used: 101.324 MB
%------------------------------------------------------------------------------