%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWW101+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 03:08:45 PM UTC 2026
% Result : Theorem 0.15s 0.48s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWW101+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n010.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Mon Sep 21 09:39:40 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.45 % Drodi V4.1.1
% 0.15/0.48 % Refutation found
% 0.15/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.48 % SZS output start CNFRefutation for theBenchmark
% 0.15/0.48 fof(f1,axiom,(
% 0.15/0.48 (! [X] :( bool(X)<=> ( X = false| X = true ) ) )),
% 0.15/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.48 fof(f3,axiom,(
% 0.15/0.48 ( d(true)& d(false)& d(err) ) ),
% 0.15/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.48 fof(f4,axiom,(
% 0.15/0.48 (! [X,Y] :( forallprefers(X,Y)<=> ( ( ~ d(X)& d(Y) )| ( d(X)& d(Y)& ~ bool(X)& bool(Y) )| ( X = false& Y = true ) ) ) )),
% 0.15/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.48 fof(f6,axiom,(
% 0.15/0.48 (! [X] :( ( d(X)& phi(X) = X )| ( ~ d(X)& phi(X) = err ) ) )),
% 0.15/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.48 fof(f7,axiom,(
% 0.15/0.48 (! [X] :( prop(X) = true<=> bool(X) ) )),
% 0.15/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.48 fof(f8,axiom,(
% 0.15/0.48 (! [X] :( prop(X) = false<=> ~ bool(X) ) )),
% 0.15/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.48 fof(f14,axiom,(
% 0.15/0.48 (! [B] : lazy_impl(false,B) = true )),
% 0.15/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.48 fof(f15,axiom,(
% 0.15/0.48 (! [B] : lazy_impl(true,B) = phi(B) )),
% 0.15/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.48 fof(f38,axiom,(
% 0.15/0.48 false1 = false ),
% 0.15/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.48 fof(f39,axiom,(
% 0.15/0.48 (! [P] : f7(P) = lazy_impl(prop(P),P) )),
% 0.15/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.48 fof(f40,axiom,(
% 0.15/0.48 (? [P] :( false2 = phi(f7(P))& ~ (? [P1] : forallprefers(f7(P1),f7(P)) )) )),
% 0.15/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.48 fof(f45,conjecture,(
% 0.15/0.48 false1 = false2 ),
% 0.15/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.15/0.48 fof(f46,negated_conjecture,(
% 0.15/0.48 ~(false1 = false2 )),
% 0.15/0.48 inference(negated_conjecture,[status(cth)],[f45])).
% 0.15/0.48 fof(f47,plain,(
% 0.15/0.48 ![X]: ((~bool(X)|(X=false|X=true))&(bool(X)|(~X=false&~X=true)))),
% 0.15/0.48 inference(NNF_transformation,[status(thm)],[f1])).
% 0.15/0.48 fof(f48,plain,(
% 0.15/0.48 (![X]: (~bool(X)|(X=false|X=true)))&(![X]: (bool(X)|(~X=false&~X=true)))),
% 0.15/0.48 inference(miniscoping,[status(thm)],[f47])).
% 0.15/0.48 fof(f49,plain,(
% 0.15/0.48 ![X0]: (~bool(X0)|X0=false|X0=true)),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f48])).
% 0.15/0.48 fof(f50,plain,(
% 0.15/0.48 ![X0]: (bool(X0)|~X0=false)),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f48])).
% 0.15/0.48 fof(f51,plain,(
% 0.15/0.48 ![X0]: (bool(X0)|~X0=true)),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f48])).
% 0.15/0.48 fof(f55,plain,(
% 0.15/0.48 d(true)),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f3])).
% 0.15/0.48 fof(f56,plain,(
% 0.15/0.48 d(false)),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f3])).
% 0.15/0.48 fof(f58,definition,(
% 0.15/0.48 ![X,Y]: (sP0_prd(Y,X)<=>((~d(X)&d(Y))|(((d(X)&d(Y))&~bool(X))&bool(Y))))),
% 0.15/0.48 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.15/0.48 fof(f59,plain,(
% 0.15/0.48 ![X,Y]: (forallprefers(X,Y)<=>(sP0_prd(Y,X)|(X=false&Y=true)))),
% 0.15/0.48 inference(formula_renaming,[status(thm)],[f4,f58])).
% 0.15/0.48 fof(f60,plain,(
% 0.15/0.48 ![X,Y]: ((~forallprefers(X,Y)|(sP0_prd(Y,X)|(X=false&Y=true)))&(forallprefers(X,Y)|(~sP0_prd(Y,X)&(~X=false|~Y=true))))),
% 0.15/0.48 inference(NNF_transformation,[status(thm)],[f59])).
% 0.15/0.48 fof(f61,plain,(
% 0.15/0.48 (![X,Y]: (~forallprefers(X,Y)|(sP0_prd(Y,X)|(X=false&Y=true))))&(![X,Y]: (forallprefers(X,Y)|(~sP0_prd(Y,X)&(~X=false|~Y=true))))),
% 0.15/0.48 inference(miniscoping,[status(thm)],[f60])).
% 0.15/0.48 fof(f65,plain,(
% 0.15/0.48 ![X0,X1]: (forallprefers(X0,X1)|~X0=false|~X1=true)),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f61])).
% 0.15/0.48 fof(f74,definition,(
% 0.15/0.48 ![X]: (sP2_prd(X)<=>(d(X)&phi(X)=X))),
% 0.15/0.48 introduced(definition,[new_symbols(definition,[sP2_prd])],[])).
% 0.15/0.48 fof(f75,plain,(
% 0.15/0.48 ![X]: (sP2_prd(X)|(~d(X)&phi(X)=err))),
% 0.15/0.48 inference(formula_renaming,[status(thm)],[f6,f74])).
% 0.15/0.48 fof(f76,plain,(
% 0.15/0.48 ![X0]: (sP2_prd(X0)|~d(X0))),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f75])).
% 0.15/0.48 fof(f78,plain,(
% 0.15/0.48 ![X]: ((~prop(X)=true|bool(X))&(prop(X)=true|~bool(X)))),
% 0.15/0.48 inference(NNF_transformation,[status(thm)],[f7])).
% 0.15/0.48 fof(f79,plain,(
% 0.15/0.48 (![X]: (~prop(X)=true|bool(X)))&(![X]: (prop(X)=true|~bool(X)))),
% 0.15/0.48 inference(miniscoping,[status(thm)],[f78])).
% 0.15/0.48 fof(f81,plain,(
% 0.15/0.48 ![X0]: (prop(X0)=true|~bool(X0))),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f79])).
% 0.15/0.48 fof(f82,plain,(
% 0.15/0.48 ![X]: ((~prop(X)=false|~bool(X))&(prop(X)=false|bool(X)))),
% 0.15/0.48 inference(NNF_transformation,[status(thm)],[f8])).
% 0.15/0.48 fof(f83,plain,(
% 0.15/0.48 (![X]: (~prop(X)=false|~bool(X)))&(![X]: (prop(X)=false|bool(X)))),
% 0.15/0.48 inference(miniscoping,[status(thm)],[f82])).
% 0.15/0.48 fof(f85,plain,(
% 0.15/0.48 ![X0]: (prop(X0)=false|bool(X0))),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f83])).
% 0.15/0.48 fof(f98,plain,(
% 0.15/0.48 ![X0]: (lazy_impl(false,X0)=true)),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f14])).
% 0.15/0.48 fof(f99,plain,(
% 0.15/0.48 ![X0]: (lazy_impl(true,X0)=phi(X0))),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f15])).
% 0.15/0.48 fof(f152,plain,(
% 0.15/0.48 false1=false),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f38])).
% 0.15/0.48 fof(f153,plain,(
% 0.15/0.48 ![X0]: (f7(X0)=lazy_impl(prop(X0),X0))),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f39])).
% 0.15/0.48 fof(f154,plain,(
% 0.15/0.48 ?[P]: (false2=phi(f7(P))&(![P1]: ~forallprefers(f7(P1),f7(P))))),
% 0.15/0.48 inference(pre_NNF_transformation,[status(thm)],[f40])).
% 0.15/0.48 fof(f155,plain,(
% 0.15/0.48 (false2=phi(f7(sK6_skl))&(![P1]: ~forallprefers(f7(P1),f7(sK6_skl))))),
% 0.15/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(P,sK6_skl)],[f154])).
% 0.15/0.48 fof(f156,plain,(
% 0.15/0.48 false2=phi(f7(sK6_skl))),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f155])).
% 0.15/0.48 fof(f157,plain,(
% 0.15/0.48 ![X0]: (~forallprefers(f7(X0),f7(sK6_skl)))),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f155])).
% 0.15/0.48 fof(f163,plain,(
% 0.15/0.48 ~false1=false2),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f46])).
% 0.15/0.48 fof(f184,plain,(
% 0.15/0.48 ![X]: ((~sP2_prd(X)|(d(X)&phi(X)=X))&(sP2_prd(X)|(~d(X)|~phi(X)=X)))),
% 0.15/0.48 inference(NNF_transformation,[status(thm)],[f74])).
% 0.15/0.48 fof(f185,plain,(
% 0.15/0.48 (![X]: (~sP2_prd(X)|(d(X)&phi(X)=X)))&(![X]: (sP2_prd(X)|(~d(X)|~phi(X)=X)))),
% 0.15/0.48 inference(miniscoping,[status(thm)],[f184])).
% 0.15/0.48 fof(f187,plain,(
% 0.15/0.48 ![X0]: (~sP2_prd(X0)|phi(X0)=X0)),
% 0.15/0.48 inference(cnf_transformation,[status(thm)],[f185])).
% 0.15/0.48 fof(f199,plain,(
% 0.15/0.48 bool(false)),
% 0.15/0.48 inference(destructive_equality_resolution,[status(thm)],[f50])).
% 0.15/0.48 fof(f200,plain,(
% 0.15/0.48 bool(true)),
% 0.15/0.48 inference(destructive_equality_resolution,[status(thm)],[f51])).
% 0.15/0.48 fof(f201,plain,(
% 0.15/0.48 forallprefers(false,true)),
% 0.15/0.48 inference(destructive_equality_resolution,[status(thm)],[f65])).
% 0.15/0.48 fof(f203,plain,(
% 0.15/0.48 bool(false1)),
% 0.15/0.48 inference(forward_demodulation,[status(thm)],[f152,f199])).
% 0.15/0.48 fof(f205,plain,(
% 0.15/0.48 ![X0]: (~bool(X0)|X0=false1|X0=true)),
% 0.15/0.48 inference(forward_demodulation,[status(thm)],[f152,f49])).
% 0.15/0.48 fof(f222,plain,(
% 0.15/0.48 d(false1)),
% 0.15/0.48 inference(forward_demodulation,[status(thm)],[f152,f56])).
% 0.15/0.48 fof(f223,plain,(
% 0.15/0.48 forallprefers(false1,true)),
% 0.15/0.48 inference(forward_demodulation,[status(thm)],[f152,f201])).
% 0.15/0.48 fof(f226,plain,(
% 0.15/0.48 sP2_prd(false1)),
% 0.15/0.48 inference(resolution,[status(thm)],[f76,f222])).
% 0.15/0.48 fof(f227,plain,(
% 0.15/0.48 sP2_prd(true)),
% 0.15/0.48 inference(resolution,[status(thm)],[f76,f55])).
% 0.15/0.48 fof(f241,plain,(
% 0.15/0.48 ![X0]: (lazy_impl(false1,X0)=true)),
% 0.15/0.48 inference(forward_demodulation,[status(thm)],[f152,f98])).
% 0.15/0.48 fof(f244,plain,(
% 0.15/0.48 phi(true)=true),
% 0.15/0.48 inference(resolution,[status(thm)],[f187,f227])).
% 0.15/0.48 fof(f246,plain,(
% 0.15/0.48 phi(false1)=false1),
% 0.15/0.48 inference(resolution,[status(thm)],[f187,f226])).
% 0.15/0.48 fof(f257,plain,(
% 0.15/0.48 prop(true)=true),
% 0.15/0.48 inference(resolution,[status(thm)],[f81,f200])).
% 0.15/0.48 fof(f258,plain,(
% 0.15/0.48 prop(false1)=true),
% 0.15/0.48 inference(resolution,[status(thm)],[f81,f203])).
% 0.15/0.48 fof(f276,plain,(
% 0.15/0.48 ![X0]: (prop(X0)=false1|bool(X0))),
% 0.15/0.48 inference(forward_demodulation,[status(thm)],[f152,f85])).
% 0.15/0.48 fof(f278,plain,(
% 0.15/0.48 ![X0]: (prop(X0)=false1|X0=false1|X0=true)),
% 0.15/0.48 inference(resolution,[status(thm)],[f276,f205])).
% 0.15/0.48 fof(f367,plain,(
% 0.15/0.48 f7(true)=lazy_impl(true,true)),
% 0.15/0.48 inference(paramodulation,[status(thm)],[f257,f153])).
% 0.15/0.48 fof(f368,plain,(
% 0.15/0.48 f7(false1)=lazy_impl(true,false1)),
% 0.15/0.48 inference(paramodulation,[status(thm)],[f258,f153])).
% 0.15/0.48 fof(f369,plain,(
% 0.15/0.48 ![X0]: (f7(X0)=lazy_impl(false1,X0)|X0=false1|X0=true)),
% 0.15/0.48 inference(paramodulation,[status(thm)],[f278,f153])).
% 0.15/0.48 fof(f371,plain,(
% 0.15/0.48 f7(true)=phi(true)),
% 0.15/0.48 inference(forward_demodulation,[status(thm)],[f99,f367])).
% 0.15/0.48 fof(f372,plain,(
% 0.15/0.48 f7(true)=true),
% 0.15/0.48 inference(forward_demodulation,[status(thm)],[f244,f371])).
% 0.15/0.48 fof(f373,plain,(
% 0.15/0.48 f7(false1)=phi(false1)),
% 0.15/0.48 inference(forward_demodulation,[status(thm)],[f99,f368])).
% 0.15/0.48 fof(f374,plain,(
% 0.15/0.48 f7(false1)=false1),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f246,f373])).
% 0.15/0.49 fof(f375,plain,(
% 0.15/0.49 ![X0]: (f7(X0)=true|X0=false1|X0=true)),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f241,f369])).
% 0.15/0.49 fof(f377,plain,(
% 0.15/0.49 ~forallprefers(false1,f7(sK6_skl))),
% 0.15/0.49 inference(paramodulation,[status(thm)],[f374,f157])).
% 0.15/0.49 fof(f486,plain,(
% 0.15/0.49 ~forallprefers(false1,true)|sK6_skl=false1|sK6_skl=true),
% 0.15/0.49 inference(paramodulation,[status(thm)],[f375,f377])).
% 0.15/0.49 fof(f497,definition,(
% 0.15/0.49 sQ24_spl <=> (sK6_skl=false1)),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f498,plain,(
% 0.15/0.49 sK6_skl=false1|~sQ24_spl),
% 0.15/0.49 inference(component_clause,[status(thm)],[f497])).
% 0.15/0.49 fof(f500,definition,(
% 0.15/0.49 sQ25_spl <=> (sK6_skl=true)),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f501,plain,(
% 0.15/0.49 sK6_skl=true|~sQ25_spl),
% 0.15/0.49 inference(component_clause,[status(thm)],[f500])).
% 0.15/0.49 fof(f504,definition,(
% 0.15/0.49 sQ26_spl <=> (forallprefers(false1,true))),
% 0.15/0.49 introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 0.15/0.49 fof(f506,plain,(
% 0.15/0.49 ~forallprefers(false1,true)|sQ26_spl),
% 0.15/0.49 inference(component_clause,[status(thm)],[f504])).
% 0.15/0.49 fof(f507,plain,(
% 0.15/0.49 ~sQ26_spl|sQ24_spl|sQ25_spl),
% 0.15/0.49 inference(split_clause,[status(thm)],[f486,f504,f497,f500])).
% 0.15/0.49 fof(f531,plain,(
% 0.15/0.49 f7(true)=sK6_skl|~sQ25_spl),
% 0.15/0.49 inference(backward_demodulation,[status(thm)],[f501,f372])).
% 0.15/0.49 fof(f564,plain,(
% 0.15/0.49 f7(sK6_skl)=sK6_skl|~sQ25_spl),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f501,f531])).
% 0.15/0.49 fof(f587,plain,(
% 0.15/0.49 ~forallprefers(false1,sK6_skl)|~sQ25_spl),
% 0.15/0.49 inference(backward_demodulation,[status(thm)],[f564,f377])).
% 0.15/0.49 fof(f656,plain,(
% 0.15/0.49 $false|sQ26_spl),
% 0.15/0.49 inference(forward_subsumption_resolution,[status(thm)],[f223,f506])).
% 0.15/0.49 fof(f657,plain,(
% 0.15/0.49 sQ26_spl),
% 0.15/0.49 inference(contradiction_clause,[status(thm)],[f656])).
% 0.15/0.49 fof(f681,plain,(
% 0.15/0.49 ~sK6_skl=false2|~sQ24_spl),
% 0.15/0.49 inference(backward_demodulation,[status(thm)],[f498,f163])).
% 0.15/0.49 fof(f719,plain,(
% 0.15/0.49 forallprefers(false1,sK6_skl)|~sQ25_spl),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f501,f223])).
% 0.15/0.49 fof(f742,plain,(
% 0.15/0.49 $false|~sQ25_spl),
% 0.15/0.49 inference(forward_subsumption_resolution,[status(thm)],[f587,f719])).
% 0.15/0.49 fof(f743,plain,(
% 0.15/0.49 ~sQ25_spl),
% 0.15/0.49 inference(contradiction_clause,[status(thm)],[f742])).
% 0.15/0.49 fof(f791,plain,(
% 0.15/0.49 f7(sK6_skl)=false1|~sQ24_spl),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f498,f374])).
% 0.15/0.49 fof(f792,plain,(
% 0.15/0.49 f7(sK6_skl)=sK6_skl|~sQ24_spl),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f498,f791])).
% 0.15/0.49 fof(f793,plain,(
% 0.15/0.49 phi(sK6_skl)=false1|~sQ24_spl),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f498,f246])).
% 0.15/0.49 fof(f794,plain,(
% 0.15/0.49 phi(sK6_skl)=sK6_skl|~sQ24_spl),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f498,f793])).
% 0.15/0.49 fof(f858,plain,(
% 0.15/0.49 false2=phi(sK6_skl)|~sQ24_spl),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f792,f156])).
% 0.15/0.49 fof(f859,plain,(
% 0.15/0.49 false2=sK6_skl|~sQ24_spl),
% 0.15/0.49 inference(forward_demodulation,[status(thm)],[f794,f858])).
% 0.15/0.49 fof(f860,plain,(
% 0.15/0.49 $false|~sQ24_spl),
% 0.15/0.49 inference(forward_subsumption_resolution,[status(thm)],[f859,f681])).
% 0.15/0.49 fof(f861,plain,(
% 0.15/0.49 ~sQ24_spl),
% 0.15/0.49 inference(contradiction_clause,[status(thm)],[f860])).
% 0.15/0.49 fof(f862,plain,(
% 0.15/0.49 $false),
% 0.15/0.49 inference(sat_refutation,[status(thm)],[f507,f657,f743,f861])).
% 0.15/0.49 % SZS output end CNFRefutation for theBenchmark.p
% 0.15/0.53 % Elapsed time: 0.085618 seconds
% 0.15/0.53 % CPU time: 0.206974 seconds
% 0.15/0.53 % Total memory used: 40.405 MB
% 0.15/0.53 % Net memory used: 40.326 MB
%------------------------------------------------------------------------------