%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET902+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 : n011.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 0.08s 0.37s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET902+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 05:43:26 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.08/0.37 % Refutation found
% 0.08/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.37 % SZS output start CNFRefutation for theBenchmark
% 0.08/0.37 fof(f1,axiom,(
% 0.08/0.37 (! [A,B] : set_union2(A,B) = set_union2(B,A) )),
% 0.08/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.37 fof(f5,axiom,(
% 0.08/0.37 (! [A,B] : set_union2(A,A) = A )),
% 0.08/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.37 fof(f6,axiom,(
% 0.08/0.37 (! [A] : singleton(A) != empty_set )),
% 0.08/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.37 fof(f7,axiom,(
% 0.08/0.37 (! [A,B] :( subset(A,singleton(B))<=> ( A = empty_set| A = singleton(B) ) ) )),
% 0.08/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.37 fof(f11,conjecture,(
% 0.08/0.37 (! [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 ) ) )),
% 0.08/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.37 fof(f12,negated_conjecture,(
% 0.08/0.37 ~((! [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 ) ) ))),
% 0.08/0.37 inference(negated_conjecture,[status(cth)],[f11])).
% 0.08/0.37 fof(f13,axiom,(
% 0.08/0.37 (! [A,B] : subset(A,set_union2(A,B)) )),
% 0.08/0.37 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/0.37 fof(f14,plain,(
% 0.08/0.37 ![X0,X1]: (set_union2(X0,X1)=set_union2(X1,X0))),
% 0.08/0.37 inference(cnf_transformation,[status(thm)],[f1])).
% 0.08/0.37 fof(f22,plain,(
% 0.08/0.37 ![A]: set_union2(A,A)=A),
% 0.08/0.37 inference(miniscoping,[status(thm)],[f5])).
% 0.08/0.37 fof(f23,plain,(
% 0.08/0.37 ![X0]: (set_union2(X0,X0)=X0)),
% 0.08/0.37 inference(cnf_transformation,[status(thm)],[f22])).
% 0.08/0.37 fof(f24,plain,(
% 0.08/0.37 ![X0]: (~singleton(X0)=empty_set)),
% 0.08/0.37 inference(cnf_transformation,[status(thm)],[f6])).
% 0.08/0.37 fof(f25,plain,(
% 0.08/0.37 ![A,B]: ((~subset(A,singleton(B))|(A=empty_set|A=singleton(B)))&(subset(A,singleton(B))|(~A=empty_set&~A=singleton(B))))),
% 0.08/0.37 inference(NNF_transformation,[status(thm)],[f7])).
% 0.08/0.37 fof(f26,plain,(
% 0.08/0.37 (![A,B]: (~subset(A,singleton(B))|(A=empty_set|A=singleton(B))))&(![A,B]: (subset(A,singleton(B))|(~A=empty_set&~A=singleton(B))))),
% 0.08/0.37 inference(miniscoping,[status(thm)],[f25])).
% 0.08/0.37 fof(f27,plain,(
% 0.08/0.37 ![X0,X1]: (~subset(X0,singleton(X1))|X0=empty_set|X0=singleton(X1))),
% 0.08/0.37 inference(cnf_transformation,[status(thm)],[f26])).
% 0.08/0.37 fof(f36,plain,(
% 0.08/0.37 (?[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)))),
% 0.08/0.37 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.08/0.37 fof(f37,plain,(
% 0.08/0.37 (((singleton(sK2_skl)=set_union2(sK3_skl,sK4_skl)&(~sK3_skl=singleton(sK2_skl)|~sK4_skl=singleton(sK2_skl)))&(~sK3_skl=empty_set|~sK4_skl=singleton(sK2_skl)))&(~sK3_skl=singleton(sK2_skl)|~sK4_skl=empty_set))),
% 0.08/0.37 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(A,sK2_skl),skolemize(B,sK3_skl),skolemize(C,sK4_skl)],[f36])).
% 0.08/0.37 fof(f38,plain,(
% 0.08/0.37 singleton(sK2_skl)=set_union2(sK3_skl,sK4_skl)),
% 0.08/0.37 inference(cnf_transformation,[status(thm)],[f37])).
% 0.08/0.37 fof(f39,plain,(
% 0.08/0.37 ~sK3_skl=singleton(sK2_skl)|~sK4_skl=singleton(sK2_skl)),
% 0.08/0.37 inference(cnf_transformation,[status(thm)],[f37])).
% 0.08/0.37 fof(f40,plain,(
% 0.08/0.37 ~sK3_skl=empty_set|~sK4_skl=singleton(sK2_skl)),
% 0.08/0.37 inference(cnf_transformation,[status(thm)],[f37])).
% 0.08/0.37 fof(f41,plain,(
% 0.08/0.37 ~sK3_skl=singleton(sK2_skl)|~sK4_skl=empty_set),
% 0.08/0.37 inference(cnf_transformation,[status(thm)],[f37])).
% 0.08/0.37 fof(f42,plain,(
% 0.08/0.37 ![X0,X1]: (subset(X0,set_union2(X0,X1)))),
% 0.08/0.37 inference(cnf_transformation,[status(thm)],[f13])).
% 0.08/0.37 fof(f43,definition,(
% 0.08/0.37 sQ0_spl <=> (sK3_skl=singleton(sK2_skl))),
% 0.08/0.37 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.08/0.37 fof(f44,plain,(
% 0.08/0.37 sK3_skl=singleton(sK2_skl)|~sQ0_spl),
% 0.08/0.37 inference(component_clause,[status(thm)],[f43])).
% 0.08/0.37 fof(f46,definition,(
% 0.08/0.37 sQ1_spl <=> (sK4_skl=singleton(sK2_skl))),
% 0.08/0.37 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.08/0.37 fof(f48,plain,(
% 0.08/0.37 ~sK4_skl=singleton(sK2_skl)|sQ1_spl),
% 0.08/0.37 inference(component_clause,[status(thm)],[f46])).
% 0.08/0.37 fof(f49,plain,(
% 0.08/0.37 ~sQ0_spl|~sQ1_spl),
% 0.08/0.37 inference(split_clause,[status(thm)],[f39,f43,f46])).
% 0.08/0.37 fof(f50,definition,(
% 0.08/0.37 sQ2_spl <=> (sK3_skl=empty_set)),
% 0.08/0.37 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.08/0.37 fof(f51,plain,(
% 0.08/0.37 sK3_skl=empty_set|~sQ2_spl),
% 0.08/0.37 inference(component_clause,[status(thm)],[f50])).
% 0.08/0.37 fof(f53,plain,(
% 0.08/0.37 ~sQ2_spl|~sQ1_spl),
% 0.08/0.37 inference(split_clause,[status(thm)],[f40,f50,f46])).
% 0.08/0.37 fof(f54,definition,(
% 0.08/0.37 sQ3_spl <=> (sK4_skl=empty_set)),
% 0.08/0.37 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.08/0.37 fof(f57,plain,(
% 0.08/0.37 ~sQ0_spl|~sQ3_spl),
% 0.08/0.37 inference(split_clause,[status(thm)],[f41,f43,f54])).
% 0.08/0.37 fof(f83,plain,(
% 0.08/0.37 subset(sK3_skl,singleton(sK2_skl))),
% 0.08/0.37 inference(paramodulation,[status(thm)],[f38,f42])).
% 0.08/0.37 fof(f84,plain,(
% 0.08/0.37 ![X0,X1]: (subset(X0,set_union2(X1,X0)))),
% 0.08/0.37 inference(paramodulation,[status(thm)],[f14,f42])).
% 0.08/0.37 fof(f96,plain,(
% 0.08/0.37 sK3_skl=empty_set|sK3_skl=singleton(sK2_skl)),
% 0.08/0.37 inference(resolution,[status(thm)],[f83,f27])).
% 0.08/0.37 fof(f97,plain,(
% 0.08/0.37 sQ2_spl|sQ0_spl),
% 0.08/0.37 inference(split_clause,[status(thm)],[f96,f50,f43])).
% 0.08/0.37 fof(f102,plain,(
% 0.08/0.37 ![X0]: (~subset(X0,sK3_skl)|X0=empty_set|X0=singleton(sK2_skl)|~sQ0_spl)),
% 0.08/0.37 inference(paramodulation,[status(thm)],[f44,f27])).
% 0.08/0.37 fof(f105,plain,(
% 0.08/0.37 ![X0]: (~subset(X0,sK3_skl)|X0=empty_set|X0=sK3_skl|~sQ0_spl)),
% 0.08/0.37 inference(forward_demodulation,[status(thm)],[f44,f102])).
% 0.08/0.37 fof(f116,plain,(
% 0.08/0.37 ![X0,X1]: (~subset(X0,singleton(X1))|X0=sK3_skl|X0=singleton(X1)|~sQ2_spl)),
% 0.08/0.37 inference(backward_demodulation,[status(thm)],[f51,f27])).
% 0.08/0.37 fof(f118,plain,(
% 0.08/0.37 ![X0]: (~singleton(X0)=sK3_skl|~sQ2_spl)),
% 0.08/0.37 inference(backward_demodulation,[status(thm)],[f51,f24])).
% 0.08/0.37 fof(f126,plain,(
% 0.08/0.37 subset(sK4_skl,singleton(sK2_skl))),
% 0.08/0.37 inference(paramodulation,[status(thm)],[f38,f84])).
% 0.08/0.37 fof(f130,plain,(
% 0.08/0.37 sK4_skl=sK3_skl|sK4_skl=singleton(sK2_skl)|~sQ2_spl),
% 0.08/0.37 inference(resolution,[status(thm)],[f126,f116])).
% 0.08/0.37 fof(f131,definition,(
% 0.08/0.37 sQ11_spl <=> (sK4_skl=sK3_skl)),
% 0.08/0.37 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.08/0.37 fof(f132,plain,(
% 0.08/0.37 sK4_skl=sK3_skl|~sQ11_spl),
% 0.08/0.37 inference(component_clause,[status(thm)],[f131])).
% 0.08/0.37 fof(f134,plain,(
% 0.08/0.37 sQ11_spl|sQ1_spl|~sQ2_spl),
% 0.08/0.37 inference(split_clause,[status(thm)],[f130,f131,f46,f50])).
% 0.08/0.37 fof(f136,plain,(
% 0.08/0.37 singleton(sK2_skl)=set_union2(sK3_skl,sK3_skl)|~sQ11_spl),
% 0.08/0.37 inference(backward_demodulation,[status(thm)],[f132,f38])).
% 0.08/0.37 fof(f137,plain,(
% 0.08/0.37 ~sK3_skl=singleton(sK2_skl)|~sQ11_spl|sQ1_spl),
% 0.08/0.37 inference(backward_demodulation,[status(thm)],[f132,f48])).
% 0.08/0.37 fof(f138,plain,(
% 0.08/0.37 singleton(sK2_skl)=sK3_skl|~sQ11_spl),
% 0.08/0.37 inference(forward_demodulation,[status(thm)],[f23,f136])).
% 0.08/0.37 fof(f139,plain,(
% 0.08/0.37 $false|~sQ2_spl|~sQ11_spl),
% 0.08/0.37 inference(forward_subsumption_resolution,[status(thm)],[f138,f118])).
% 0.08/0.37 fof(f140,plain,(
% 0.08/0.37 ~sQ2_spl|~sQ11_spl),
% 0.08/0.37 inference(contradiction_clause,[status(thm)],[f139])).
% 0.08/0.37 fof(f159,plain,(
% 0.08/0.37 subset(sK4_skl,sK3_skl)|~sQ0_spl),
% 0.08/0.37 inference(forward_demodulation,[status(thm)],[f44,f126])).
% 0.08/0.37 fof(f160,plain,(
% 0.08/0.37 sK4_skl=empty_set|sK4_skl=sK3_skl|~sQ0_spl),
% 0.08/0.37 inference(resolution,[status(thm)],[f159,f105])).
% 0.08/0.37 fof(f161,plain,(
% 0.08/0.37 sQ3_spl|sQ11_spl|~sQ0_spl),
% 0.08/0.37 inference(split_clause,[status(thm)],[f160,f54,f131,f43])).
% 0.08/0.37 fof(f162,plain,(
% 0.08/0.37 ~sQ0_spl|~sQ11_spl|sQ1_spl),
% 0.08/0.37 inference(split_clause,[status(thm)],[f137,f43,f131,f46])).
% 0.08/0.37 fof(f165,plain,(
% 0.08/0.37 $false),
% 0.08/0.37 inference(sat_refutation,[status(thm)],[f49,f53,f57,f97,f134,f140,f161,f162])).
% 0.08/0.37 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.40 % Elapsed time: 0.040551 seconds
% 0.12/0.40 % CPU time: 0.089188 seconds
% 0.12/0.40 % Total memory used: 15.982 MB
% 0.12/0.40 % Net memory used: 15.954 MB
%------------------------------------------------------------------------------