%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SYN724+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 03:20:25 PM UTC 2026
% Result : Theorem 0.12s 5.56s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN724+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/5.53 % Computer : n020.cluster.edu
% 0.12/5.53 % Model : x86_64 x86_64
% 0.12/5.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.53 % Memory : 8046.5625MB
% 0.12/5.53 % OS : Linux 6.8.0-71-generic
% 0.12/5.53 % CPULimit : 300
% 0.12/5.53 % WCLimit : 300
% 0.12/5.53 % DateTime : Mon Sep 21 11:14:08 UTC 2026
% 0.12/5.53 % CPUTime :
% 0.12/5.54 % Drodi V4.1.1
% 0.12/5.56 % Refutation found
% 0.12/5.56 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/5.56 % SZS output start CNFRefutation for theBenchmark
% 0.12/5.56 fof(f1,conjecture,(
% 0.12/5.56 ( (! [X] :( r(X)=> s(X) ))<=> (! [X] :( ( r(X)& s(X) )<=> r(X) ) )) ),
% 0.12/5.56 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/5.56 fof(f2,negated_conjecture,(
% 0.12/5.56 ~(( (! [X] :( r(X)=> s(X) ))<=> (! [X] :( ( r(X)& s(X) )<=> r(X) ) )) )),
% 0.12/5.56 inference(negated_conjecture,[status(cth)],[f1])).
% 0.12/5.56 fof(f3,plain,(
% 0.12/5.56 ((![X]: (~r(X)|s(X)))<~>(![X]: ((r(X)&s(X))<=>r(X))))),
% 0.12/5.56 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.12/5.56 fof(f4,definition,(
% 0.12/5.56 ![X]: (sP0_prd(X)<=>(~r(X)|s(X)))),
% 0.12/5.56 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.12/5.56 fof(f5,plain,(
% 0.12/5.56 (![X]: sP0_prd(X))<~>(![X]: ((r(X)&s(X))<=>r(X)))),
% 0.12/5.56 inference(formula_renaming,[status(thm)],[f3,f4])).
% 0.12/5.56 fof(f6,plain,(
% 0.12/5.56 ((![X]: sP0_prd(X))|(![X]: (((~r(X)|~s(X))|r(X))&((r(X)&s(X))|~r(X)))))&((?[X]: ~sP0_prd(X))|(?[X]: (((~r(X)|~s(X))|~r(X))&((r(X)&s(X))|r(X)))))),
% 0.12/5.56 inference(NNF_transformation,[status(thm)],[f5])).
% 0.12/5.56 fof(f7,plain,(
% 0.12/5.56 ((![X]: sP0_prd(X))|((![X]: ((~r(X)|~s(X))|r(X)))&(![X]: ((r(X)&s(X))|~r(X)))))&((?[X]: ~sP0_prd(X))|(?[X]: (((~r(X)|~s(X))|~r(X))&((r(X)&s(X))|r(X)))))),
% 0.12/5.56 inference(miniscoping,[status(thm)],[f6])).
% 0.12/5.56 fof(f8,plain,(
% 0.12/5.56 ((![X]: sP0_prd(X))|((![X]: ((~r(X)|~s(X))|r(X)))&(![X]: ((r(X)&s(X))|~r(X)))))&(~sP0_prd(sK0_skl)|(((~r(sK1_skl)|~s(sK1_skl))|~r(sK1_skl))&((r(sK1_skl)&s(sK1_skl))|r(sK1_skl))))),
% 0.12/5.56 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(X,sK1_skl)],[f7])).
% 0.12/5.56 fof(f11,plain,(
% 0.12/5.56 ![X0,X1]: (sP0_prd(X0)|s(X1)|~r(X1))),
% 0.12/5.56 inference(cnf_transformation,[status(thm)],[f8])).
% 0.12/5.56 fof(f12,plain,(
% 0.12/5.56 ~sP0_prd(sK0_skl)|~r(sK1_skl)|~s(sK1_skl)|~r(sK1_skl)),
% 0.12/5.56 inference(cnf_transformation,[status(thm)],[f8])).
% 0.12/5.56 fof(f13,plain,(
% 0.12/5.56 ~sP0_prd(sK0_skl)|r(sK1_skl)|r(sK1_skl)),
% 0.12/5.56 inference(cnf_transformation,[status(thm)],[f8])).
% 0.12/5.56 fof(f15,plain,(
% 0.12/5.56 ![X]: ((~sP0_prd(X)|(~r(X)|s(X)))&(sP0_prd(X)|(r(X)&~s(X))))),
% 0.12/5.56 inference(NNF_transformation,[status(thm)],[f4])).
% 0.12/5.56 fof(f16,plain,(
% 0.12/5.56 (![X]: (~sP0_prd(X)|(~r(X)|s(X))))&(![X]: (sP0_prd(X)|(r(X)&~s(X))))),
% 0.12/5.56 inference(miniscoping,[status(thm)],[f15])).
% 0.12/5.56 fof(f17,plain,(
% 0.12/5.56 ![X0]: (~sP0_prd(X0)|~r(X0)|s(X0))),
% 0.12/5.56 inference(cnf_transformation,[status(thm)],[f16])).
% 0.12/5.56 fof(f18,plain,(
% 0.12/5.56 ![X0]: (sP0_prd(X0)|r(X0))),
% 0.12/5.56 inference(cnf_transformation,[status(thm)],[f16])).
% 0.12/5.56 fof(f19,plain,(
% 0.12/5.56 ![X0]: (sP0_prd(X0)|~s(X0))),
% 0.12/5.56 inference(cnf_transformation,[status(thm)],[f16])).
% 0.12/5.56 fof(f20,definition,(
% 0.12/5.56 ![X0]: (sQ0_spl <=> (sP0_prd(X0)))),
% 0.12/5.56 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.12/5.56 fof(f21,plain,(
% 0.12/5.56 ![X0]: (sP0_prd(X0)|~sQ0_spl)),
% 0.12/5.56 inference(component_clause,[status(thm)],[f20])).
% 0.12/5.56 fof(f31,definition,(
% 0.12/5.56 ![X1]: (sQ3_spl <=> (s(X1)|~r(X1)))),
% 0.12/5.56 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.12/5.56 fof(f32,plain,(
% 0.12/5.56 ![X0]: (s(X0)|~r(X0)|~sQ3_spl)),
% 0.12/5.56 inference(component_clause,[status(thm)],[f31])).
% 0.12/5.56 fof(f34,plain,(
% 0.12/5.56 sQ0_spl|sQ3_spl),
% 0.12/5.56 inference(split_clause,[status(thm)],[f11,f20,f31])).
% 0.12/5.56 fof(f35,definition,(
% 0.12/5.56 sQ4_spl <=> (sP0_prd(sK0_skl))),
% 0.12/5.56 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.12/5.56 fof(f37,plain,(
% 0.12/5.56 ~sP0_prd(sK0_skl)|sQ4_spl),
% 0.12/5.56 inference(component_clause,[status(thm)],[f35])).
% 0.12/5.56 fof(f38,definition,(
% 0.12/5.56 sQ5_spl <=> (r(sK1_skl))),
% 0.12/5.56 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.12/5.56 fof(f39,plain,(
% 0.12/5.56 r(sK1_skl)|~sQ5_spl),
% 0.12/5.56 inference(component_clause,[status(thm)],[f38])).
% 0.12/5.56 fof(f41,definition,(
% 0.12/5.56 sQ6_spl <=> (s(sK1_skl))),
% 0.12/5.56 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.12/5.56 fof(f43,plain,(
% 0.12/5.56 ~s(sK1_skl)|sQ6_spl),
% 0.12/5.56 inference(component_clause,[status(thm)],[f41])).
% 0.12/5.56 fof(f44,plain,(
% 0.12/5.56 ~sQ4_spl|~sQ5_spl|~sQ6_spl),
% 0.12/5.56 inference(split_clause,[status(thm)],[f12,f35,f38,f41])).
% 0.12/5.56 fof(f45,plain,(
% 0.12/5.56 ~sQ4_spl|sQ5_spl),
% 0.12/5.56 inference(split_clause,[status(thm)],[f13,f35,f38])).
% 0.12/5.56 fof(f47,plain,(
% 0.12/5.56 $false|~sQ0_spl|sQ4_spl),
% 0.12/5.56 inference(forward_subsumption_resolution,[status(thm)],[f37,f21])).
% 0.12/5.56 fof(f48,plain,(
% 0.12/5.56 ~sQ0_spl|sQ4_spl),
% 0.12/5.56 inference(contradiction_clause,[status(thm)],[f47])).
% 0.12/5.56 fof(f51,plain,(
% 0.12/5.56 ![X0]: (~r(X0)|sP0_prd(X0)|~sQ3_spl)),
% 0.12/5.56 inference(resolution,[status(thm)],[f32,f19])).
% 0.12/5.56 fof(f52,plain,(
% 0.12/5.56 ![X0]: (sP0_prd(X0)|~sQ3_spl)),
% 0.12/5.56 inference(forward_subsumption_resolution,[status(thm)],[f51,f18])).
% 0.12/5.56 fof(f55,plain,(
% 0.12/5.56 ![X0]: (~r(X0)|s(X0)|~sQ0_spl)),
% 0.12/5.56 inference(forward_subsumption_resolution,[status(thm)],[f17,f21])).
% 0.12/5.56 fof(f56,plain,(
% 0.12/5.56 ~r(sK1_skl)|~sQ0_spl|sQ6_spl),
% 0.12/5.56 inference(resolution,[status(thm)],[f55,f43])).
% 0.12/5.56 fof(f57,plain,(
% 0.12/5.56 $false|~sQ5_spl|~sQ0_spl|sQ6_spl),
% 0.12/5.56 inference(forward_subsumption_resolution,[status(thm)],[f56,f39])).
% 0.12/5.56 fof(f58,plain,(
% 0.12/5.56 ~sQ5_spl|~sQ0_spl|sQ6_spl),
% 0.12/5.56 inference(contradiction_clause,[status(thm)],[f57])).
% 0.12/5.56 fof(f59,plain,(
% 0.12/5.56 sQ0_spl|~sQ3_spl),
% 0.12/5.56 inference(split_clause,[status(thm)],[f52,f20,f31])).
% 0.12/5.56 fof(f60,plain,(
% 0.12/5.56 $false),
% 0.12/5.56 inference(sat_refutation,[status(thm)],[f34,f44,f45,f48,f58,f59])).
% 0.12/5.56 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/5.59 % Elapsed time: 0.038024 seconds
% 0.12/5.59 % CPU time: 0.110744 seconds
% 0.12/5.59 % Total memory used: 16.605 MB
% 0.12/5.59 % Net memory used: 16.096 MB
%------------------------------------------------------------------------------