%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SET930+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 : n008.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 02:12:53 PM UTC 2026
% Result : Theorem 13.84s 2.27s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET930+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n008.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Mon Sep 21 05:44:54 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.44 % Drodi V4.1.1
% 13.84/2.27 % Refutation found
% 13.84/2.27 % SZS status Theorem for theBenchmark: Theorem is valid
% 13.84/2.27 % SZS output start CNFRefutation for theBenchmark
% 13.84/2.27 fof(f2,axiom,(
% 13.84/2.27 (! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) )),
% 13.84/2.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.84/2.27 fof(f4,axiom,(
% 13.84/2.27 (! [A,B,C] :( set_difference(unordered_pair(A,B),C) = singleton(A)<=> ( ~ in(A,C)& ( in(B,C)| A = B ) ) ) )),
% 13.84/2.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.84/2.27 fof(f7,axiom,(
% 13.84/2.27 (! [A,B,C] :( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)<=> ( ~ in(A,C)& ~ in(B,C) ) ) )),
% 13.84/2.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.84/2.27 fof(f8,axiom,(
% 13.84/2.27 (! [A,B,C] :( set_difference(unordered_pair(A,B),C) = empty_set<=> ( in(A,C)& in(B,C) ) ) )),
% 13.84/2.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.84/2.27 fof(f9,conjecture,(
% 13.84/2.27 (! [A,B,C] :~ ( set_difference(unordered_pair(A,B),C) != empty_set& set_difference(unordered_pair(A,B),C) != singleton(A)& set_difference(unordered_pair(A,B),C) != singleton(B)& set_difference(unordered_pair(A,B),C) != unordered_pair(A,B) ) )),
% 13.84/2.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 13.84/2.27 fof(f10,negated_conjecture,(
% 13.84/2.27 ~((! [A,B,C] :~ ( set_difference(unordered_pair(A,B),C) != empty_set& set_difference(unordered_pair(A,B),C) != singleton(A)& set_difference(unordered_pair(A,B),C) != singleton(B)& set_difference(unordered_pair(A,B),C) != unordered_pair(A,B) ) ))),
% 13.84/2.27 inference(negated_conjecture,[status(cth)],[f9])).
% 13.84/2.27 fof(f13,plain,(
% 13.84/2.27 ![X0,X1]: (unordered_pair(X0,X1)=unordered_pair(X1,X0))),
% 13.84/2.27 inference(cnf_transformation,[status(thm)],[f2])).
% 13.84/2.27 fof(f15,plain,(
% 13.84/2.27 ![A,B,C]: ((~set_difference(unordered_pair(A,B),C)=singleton(A)|(~in(A,C)&(in(B,C)|A=B)))&(set_difference(unordered_pair(A,B),C)=singleton(A)|(in(A,C)|(~in(B,C)&~A=B))))),
% 13.84/2.27 inference(NNF_transformation,[status(thm)],[f4])).
% 13.84/2.27 fof(f16,plain,(
% 13.84/2.27 (![A,B,C]: (~set_difference(unordered_pair(A,B),C)=singleton(A)|(~in(A,C)&(in(B,C)|A=B))))&(![A,B,C]: (set_difference(unordered_pair(A,B),C)=singleton(A)|(in(A,C)|(~in(B,C)&~A=B))))),
% 13.84/2.27 inference(miniscoping,[status(thm)],[f15])).
% 13.84/2.27 fof(f17,plain,(
% 13.84/2.27 ![X0,X1,X2]: (~set_difference(unordered_pair(X0,X1),X2)=singleton(X0)|~in(X0,X2))),
% 13.84/2.27 inference(cnf_transformation,[status(thm)],[f16])).
% 13.84/2.27 fof(f19,plain,(
% 13.84/2.27 ![X0,X1,X2]: (set_difference(unordered_pair(X0,X1),X2)=singleton(X0)|in(X0,X2)|~in(X1,X2))),
% 13.84/2.27 inference(cnf_transformation,[status(thm)],[f16])).
% 13.84/2.27 fof(f20,plain,(
% 13.84/2.27 ![X0,X1,X2]: (set_difference(unordered_pair(X0,X1),X2)=singleton(X0)|in(X0,X2)|~X0=X1)),
% 13.84/2.27 inference(cnf_transformation,[status(thm)],[f16])).
% 13.84/2.27 fof(f25,plain,(
% 13.84/2.27 ![A,B,C]: ((~set_difference(unordered_pair(A,B),C)=unordered_pair(A,B)|(~in(A,C)&~in(B,C)))&(set_difference(unordered_pair(A,B),C)=unordered_pair(A,B)|(in(A,C)|in(B,C))))),
% 13.84/2.27 inference(NNF_transformation,[status(thm)],[f7])).
% 13.84/2.27 fof(f26,plain,(
% 13.84/2.27 (![A,B,C]: (~set_difference(unordered_pair(A,B),C)=unordered_pair(A,B)|(~in(A,C)&~in(B,C))))&(![A,B,C]: (set_difference(unordered_pair(A,B),C)=unordered_pair(A,B)|(in(A,C)|in(B,C))))),
% 13.84/2.27 inference(miniscoping,[status(thm)],[f25])).
% 13.84/2.27 fof(f29,plain,(
% 13.84/2.27 ![X0,X1,X2]: (set_difference(unordered_pair(X0,X1),X2)=unordered_pair(X0,X1)|in(X0,X2)|in(X1,X2))),
% 13.84/2.27 inference(cnf_transformation,[status(thm)],[f26])).
% 13.84/2.27 fof(f30,plain,(
% 13.84/2.27 ![A,B,C]: ((~set_difference(unordered_pair(A,B),C)=empty_set|(in(A,C)&in(B,C)))&(set_difference(unordered_pair(A,B),C)=empty_set|(~in(A,C)|~in(B,C))))),
% 13.84/2.27 inference(NNF_transformation,[status(thm)],[f8])).
% 13.84/2.27 fof(f31,plain,(
% 13.84/2.27 (![A,B,C]: (~set_difference(unordered_pair(A,B),C)=empty_set|(in(A,C)&in(B,C))))&(![A,B,C]: (set_difference(unordered_pair(A,B),C)=empty_set|(~in(A,C)|~in(B,C))))),
% 13.84/2.27 inference(miniscoping,[status(thm)],[f30])).
% 13.84/2.27 fof(f34,plain,(
% 13.84/2.27 ![X0,X1,X2]: (set_difference(unordered_pair(X0,X1),X2)=empty_set|~in(X0,X2)|~in(X1,X2))),
% 13.84/2.27 inference(cnf_transformation,[status(thm)],[f31])).
% 13.84/2.27 fof(f35,plain,(
% 13.84/2.27 (?[A,B,C]: (((~set_difference(unordered_pair(A,B),C)=empty_set&~set_difference(unordered_pair(A,B),C)=singleton(A))&~set_difference(unordered_pair(A,B),C)=singleton(B))&~set_difference(unordered_pair(A,B),C)=unordered_pair(A,B)))),
% 13.84/2.27 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 13.84/2.27 fof(f36,plain,(
% 13.84/2.27 (((~set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=empty_set&~set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=singleton(sK2_skl))&~set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=singleton(sK3_skl))&~set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=unordered_pair(sK2_skl,sK3_skl))),
% 13.84/2.27 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)],[f35])).
% 13.84/2.27 fof(f37,plain,(
% 13.84/2.27 ~set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=empty_set),
% 13.84/2.27 inference(cnf_transformation,[status(thm)],[f36])).
% 13.84/2.27 fof(f38,plain,(
% 13.84/2.27 ~set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=singleton(sK2_skl)),
% 13.84/2.27 inference(cnf_transformation,[status(thm)],[f36])).
% 13.84/2.27 fof(f39,plain,(
% 13.84/2.27 ~set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=singleton(sK3_skl)),
% 13.84/2.27 inference(cnf_transformation,[status(thm)],[f36])).
% 13.84/2.27 fof(f40,plain,(
% 13.84/2.27 ~set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=unordered_pair(sK2_skl,sK3_skl)),
% 13.84/2.27 inference(cnf_transformation,[status(thm)],[f36])).
% 13.84/2.27 fof(f41,plain,(
% 13.84/2.27 ![X0,X1]: (set_difference(unordered_pair(X0,X0),X1)=singleton(X0)|in(X0,X1))),
% 13.84/2.27 inference(destructive_equality_resolution,[status(thm)],[f20])).
% 13.84/2.27 fof(f46,plain,(
% 13.84/2.27 ![X0,X1,X2]: (~set_difference(unordered_pair(X0,X1),X2)=singleton(X1)|~in(X1,X2))),
% 13.84/2.27 inference(paramodulation,[status(thm)],[f13,f17])).
% 13.84/2.27 fof(f50,plain,(
% 13.84/2.27 ![X0,X1,X2]: (set_difference(unordered_pair(X0,X0),X1)=singleton(X0)|set_difference(unordered_pair(X2,X0),X1)=singleton(X2)|in(X2,X1))),
% 13.84/2.27 inference(resolution,[status(thm)],[f41,f19])).
% 13.84/2.27 fof(f57,plain,(
% 13.84/2.27 ![X0,X1,X2,X3]: (set_difference(unordered_pair(X0,X1),X2)=unordered_pair(X0,X1)|in(X0,X2)|set_difference(unordered_pair(X3,X1),X2)=singleton(X3)|in(X3,X2))),
% 13.84/2.27 inference(resolution,[status(thm)],[f29,f19])).
% 13.84/2.27 fof(f66,plain,(
% 13.84/2.27 ![X0,X1,X2]: (set_difference(unordered_pair(X0,X1),X2)=empty_set|~in(X0,X2)|set_difference(unordered_pair(X1,X1),X2)=singleton(X1))),
% 13.84/2.27 inference(resolution,[status(thm)],[f34,f41])).
% 13.84/2.27 fof(f99,plain,(
% 13.84/2.27 ![X0,X1,X2,X3]: (set_difference(unordered_pair(X0,X1),X2)=unordered_pair(X0,X1)|set_difference(unordered_pair(X0,X1),X2)=singleton(X0)|set_difference(unordered_pair(X3,X0),X2)=singleton(X3)|in(X3,X2))),
% 13.84/2.27 inference(resolution,[status(thm)],[f57,f19])).
% 13.84/2.27 fof(f158,plain,(
% 13.84/2.27 ![X0,X1,X2,X3]: (set_difference(unordered_pair(X0,X1),X2)=empty_set|set_difference(unordered_pair(X1,X1),X2)=singleton(X1)|set_difference(unordered_pair(X3,X3),X2)=singleton(X3)|set_difference(unordered_pair(X0,X3),X2)=singleton(X0))),
% 13.84/2.27 inference(resolution,[status(thm)],[f66,f50])).
% 13.84/2.27 fof(f164,plain,(
% 13.84/2.27 ![X0]: (set_difference(unordered_pair(sK3_skl,sK3_skl),sK4_skl)=singleton(sK3_skl)|set_difference(unordered_pair(X0,X0),sK4_skl)=singleton(X0)|set_difference(unordered_pair(sK2_skl,X0),sK4_skl)=singleton(sK2_skl))),
% 13.84/2.27 inference(resolution,[status(thm)],[f158,f37])).
% 13.84/2.27 fof(f207,definition,(
% 13.84/2.27 sQ0_spl <=> (set_difference(unordered_pair(sK3_skl,sK3_skl),sK4_skl)=singleton(sK3_skl))),
% 13.84/2.27 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 13.84/2.27 fof(f208,plain,(
% 13.84/2.27 set_difference(unordered_pair(sK3_skl,sK3_skl),sK4_skl)=singleton(sK3_skl)|~sQ0_spl),
% 13.84/2.27 inference(component_clause,[status(thm)],[f207])).
% 13.84/2.27 fof(f210,definition,(
% 13.84/2.27 ![X0]: (sQ1_spl <=> (set_difference(unordered_pair(X0,X0),sK4_skl)=singleton(X0)|set_difference(unordered_pair(sK2_skl,X0),sK4_skl)=singleton(sK2_skl)))),
% 13.84/2.27 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 13.84/2.27 fof(f211,plain,(
% 13.84/2.27 ![X0]: (set_difference(unordered_pair(X0,X0),sK4_skl)=singleton(X0)|set_difference(unordered_pair(sK2_skl,X0),sK4_skl)=singleton(sK2_skl)|~sQ1_spl)),
% 13.84/2.27 inference(component_clause,[status(thm)],[f210])).
% 13.84/2.27 fof(f213,plain,(
% 13.84/2.27 sQ0_spl|sQ1_spl),
% 13.84/2.27 inference(split_clause,[status(thm)],[f164,f207,f210])).
% 13.84/2.27 fof(f420,plain,(
% 13.84/2.27 ~in(sK3_skl,sK4_skl)|~sQ0_spl),
% 13.84/2.27 inference(resolution,[status(thm)],[f208,f46])).
% 13.84/2.27 fof(f775,plain,(
% 13.84/2.27 set_difference(unordered_pair(sK3_skl,sK3_skl),sK4_skl)=singleton(sK3_skl)|~sQ1_spl),
% 13.84/2.28 inference(resolution,[status(thm)],[f211,f38])).
% 13.84/2.28 fof(f808,definition,(
% 13.84/2.28 sQ35_spl <=> (set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=singleton(sK2_skl))),
% 13.84/2.28 introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition])).
% 13.84/2.28 fof(f809,plain,(
% 13.84/2.28 set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=singleton(sK2_skl)|~sQ35_spl),
% 13.84/2.28 inference(component_clause,[status(thm)],[f808])).
% 13.84/2.28 fof(f4814,plain,(
% 13.84/2.28 ![X0,X1]: (set_difference(unordered_pair(X0,X1),sK4_skl)=unordered_pair(X0,X1)|set_difference(unordered_pair(X0,X1),sK4_skl)=singleton(X0)|set_difference(unordered_pair(sK3_skl,X0),sK4_skl)=singleton(sK3_skl)|~sQ0_spl)),
% 13.84/2.28 inference(resolution,[status(thm)],[f420,f99])).
% 13.84/2.28 fof(f5086,plain,(
% 13.84/2.28 set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=singleton(sK2_skl)|set_difference(unordered_pair(sK3_skl,sK2_skl),sK4_skl)=singleton(sK3_skl)|~sQ0_spl),
% 13.84/2.28 inference(resolution,[status(thm)],[f4814,f40])).
% 13.84/2.28 fof(f5156,definition,(
% 13.84/2.28 sQ140_spl <=> (set_difference(unordered_pair(sK3_skl,sK2_skl),sK4_skl)=singleton(sK3_skl))),
% 13.84/2.28 introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition])).
% 13.84/2.28 fof(f5157,plain,(
% 13.84/2.28 set_difference(unordered_pair(sK3_skl,sK2_skl),sK4_skl)=singleton(sK3_skl)|~sQ140_spl),
% 13.84/2.28 inference(component_clause,[status(thm)],[f5156])).
% 13.84/2.28 fof(f5159,plain,(
% 13.84/2.28 sQ35_spl|sQ140_spl|~sQ0_spl),
% 13.84/2.28 inference(split_clause,[status(thm)],[f5086,f808,f5156,f207])).
% 13.84/2.28 fof(f5217,plain,(
% 13.84/2.28 $false|~sQ35_spl),
% 13.84/2.28 inference(forward_subsumption_resolution,[status(thm)],[f809,f38])).
% 13.84/2.28 fof(f5218,plain,(
% 13.84/2.28 ~sQ35_spl),
% 13.84/2.28 inference(contradiction_clause,[status(thm)],[f5217])).
% 13.84/2.28 fof(f7110,plain,(
% 13.84/2.28 set_difference(unordered_pair(sK2_skl,sK3_skl),sK4_skl)=singleton(sK3_skl)|~sQ140_spl),
% 13.84/2.28 inference(paramodulation,[status(thm)],[f13,f5157])).
% 13.84/2.28 fof(f7155,plain,(
% 13.84/2.28 $false|~sQ140_spl),
% 13.84/2.28 inference(forward_subsumption_resolution,[status(thm)],[f7110,f39])).
% 13.84/2.28 fof(f7156,plain,(
% 13.84/2.28 ~sQ140_spl),
% 13.84/2.28 inference(contradiction_clause,[status(thm)],[f7155])).
% 13.84/2.28 fof(f7157,plain,(
% 13.84/2.28 sQ0_spl|~sQ1_spl),
% 13.84/2.28 inference(split_clause,[status(thm)],[f775,f207,f210])).
% 13.84/2.28 fof(f7161,plain,(
% 13.84/2.28 $false),
% 13.84/2.28 inference(sat_refutation,[status(thm)],[f213,f5159,f5218,f7156,f7157])).
% 13.84/2.28 % SZS output end CNFRefutation for theBenchmark.p
% 13.84/2.30 % Elapsed time: 1.863841 seconds
% 13.84/2.30 % CPU time: 14.366990 seconds
% 13.84/2.30 % Total memory used: 147.998 MB
% 13.84/2.30 % Net memory used: 137.990 MB
%------------------------------------------------------------------------------