%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM436+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 01:42:53 PM UTC 2026
% Result : Theorem 0.08s 6.80s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM436+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/6.70 % Computer : n012.cluster.edu
% 0.04/6.70 % Model : x86_64 x86_64
% 0.04/6.70 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/6.70 % Memory : 8046.5625MB
% 0.04/6.70 % OS : Linux 6.8.0-71-generic
% 0.04/6.70 % CPULimit : 300
% 0.04/6.70 % WCLimit : 300
% 0.04/6.70 % DateTime : Mon Sep 21 02:29:55 UTC 2026
% 0.04/6.70 % CPUTime :
% 0.04/6.71 % Drodi V4.1.1
% 0.08/6.80 % Refutation found
% 0.08/6.80 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/6.80 % SZS output start CNFRefutation for theBenchmark
% 0.08/6.80 fof(f6,axiom,(
% 0.08/6.80 (! [W0,W1] :( ( aInteger0(W0)& aInteger0(W1) )=> aInteger0(sdtasdt0(W0,W1)) ) )),
% 0.08/6.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/6.80 fof(f23,hypothesis,(
% 0.08/6.80 ( aInteger0(xa)& aInteger0(xb)& aInteger0(xp)& xp != sz00& aInteger0(xq)& xq != sz00 ) ),
% 0.08/6.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/6.80 fof(f25,hypothesis,(
% 0.08/6.80 ( aInteger0(xm)& sdtasdt0(sdtasdt0(xp,xq),xm) = sdtpldt0(xa,smndt0(xb)) ) ),
% 0.08/6.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/6.80 fof(f26,hypothesis,(
% 0.08/6.80 ( sdtasdt0(xp,sdtasdt0(xq,xm)) = sdtpldt0(xa,smndt0(xb))& sdtpldt0(xa,smndt0(xb)) = sdtasdt0(xq,sdtasdt0(xp,xm)) ) ),
% 0.08/6.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/6.80 fof(f27,conjecture,(
% 0.08/6.80 ( ( (? [W0] :( aInteger0(W0)& sdtasdt0(xp,W0) = sdtpldt0(xa,smndt0(xb)) ))| aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))| sdteqdtlpzmzozddtrp0(xa,xb,xp) )& ( (? [W0] :( aInteger0(W0)& sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb)) ))| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))| sdteqdtlpzmzozddtrp0(xa,xb,xq) ) ) ),
% 0.08/6.80 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.08/6.80 fof(f28,negated_conjecture,(
% 0.08/6.80 ~(( ( (? [W0] :( aInteger0(W0)& sdtasdt0(xp,W0) = sdtpldt0(xa,smndt0(xb)) ))| aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb)))| sdteqdtlpzmzozddtrp0(xa,xb,xp) )& ( (? [W0] :( aInteger0(W0)& sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb)) ))| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))| sdteqdtlpzmzozddtrp0(xa,xb,xq) ) ) )),
% 0.08/6.80 inference(negated_conjecture,[status(cth)],[f27])).
% 0.08/6.80 fof(f38,plain,(
% 0.08/6.80 ![W0,W1]: ((~aInteger0(W0)|~aInteger0(W1))|aInteger0(sdtasdt0(W0,W1)))),
% 0.08/6.80 inference(pre_NNF_transformation,[status(thm)],[f6])).
% 0.08/6.80 fof(f39,plain,(
% 0.08/6.80 ![X0,X1]: (~aInteger0(X0)|~aInteger0(X1)|aInteger0(sdtasdt0(X0,X1)))),
% 0.08/6.80 inference(cnf_transformation,[status(thm)],[f38])).
% 0.08/6.80 fof(f89,plain,(
% 0.08/6.80 aInteger0(xp)),
% 0.08/6.80 inference(cnf_transformation,[status(thm)],[f23])).
% 0.08/6.80 fof(f91,plain,(
% 0.08/6.80 aInteger0(xq)),
% 0.08/6.80 inference(cnf_transformation,[status(thm)],[f23])).
% 0.08/6.80 fof(f99,plain,(
% 0.08/6.80 aInteger0(xm)),
% 0.08/6.80 inference(cnf_transformation,[status(thm)],[f25])).
% 0.08/6.80 fof(f101,plain,(
% 0.08/6.80 sdtasdt0(xp,sdtasdt0(xq,xm))=sdtpldt0(xa,smndt0(xb))),
% 0.08/6.80 inference(cnf_transformation,[status(thm)],[f26])).
% 0.08/6.80 fof(f102,plain,(
% 0.08/6.80 sdtpldt0(xa,smndt0(xb))=sdtasdt0(xq,sdtasdt0(xp,xm))),
% 0.08/6.80 inference(cnf_transformation,[status(thm)],[f26])).
% 0.08/6.80 fof(f103,plain,(
% 0.08/6.80 ((((![W0]: (~aInteger0(W0)|~sdtasdt0(xp,W0)=sdtpldt0(xa,smndt0(xb))))&~aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb))))&~sdteqdtlpzmzozddtrp0(xa,xb,xp))|(((![W0]: (~aInteger0(W0)|~sdtasdt0(xq,W0)=sdtpldt0(xa,smndt0(xb))))&~aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))))&~sdteqdtlpzmzozddtrp0(xa,xb,xq)))),
% 0.08/6.80 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 0.08/6.80 fof(f104,definition,(
% 0.08/6.80 sP0_prd<=>(((![W0]: (~aInteger0(W0)|~sdtasdt0(xp,W0)=sdtpldt0(xa,smndt0(xb))))&~aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb))))&~sdteqdtlpzmzozddtrp0(xa,xb,xp))),
% 0.08/6.80 introduced(definition,[new_symbols(definition,[sP0_prd])],[])).
% 0.08/6.80 fof(f105,plain,(
% 0.08/6.80 sP0_prd|(((![W0]: (~aInteger0(W0)|~sdtasdt0(xq,W0)=sdtpldt0(xa,smndt0(xb))))&~aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb))))&~sdteqdtlpzmzozddtrp0(xa,xb,xq))),
% 0.08/6.80 inference(formula_renaming,[status(thm)],[f103,f104])).
% 0.08/6.80 fof(f106,plain,(
% 0.08/6.80 ![X0]: (sP0_prd|~aInteger0(X0)|~sdtasdt0(xq,X0)=sdtpldt0(xa,smndt0(xb)))),
% 0.08/6.80 inference(cnf_transformation,[status(thm)],[f105])).
% 0.08/6.80 fof(f109,plain,(
% 0.08/6.80 (~sP0_prd|(((![W0]: (~aInteger0(W0)|~sdtasdt0(xp,W0)=sdtpldt0(xa,smndt0(xb))))&~aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb))))&~sdteqdtlpzmzozddtrp0(xa,xb,xp)))&(sP0_prd|(((?[W0]: (aInteger0(W0)&sdtasdt0(xp,W0)=sdtpldt0(xa,smndt0(xb))))|aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb))))|sdteqdtlpzmzozddtrp0(xa,xb,xp)))),
% 0.08/6.80 inference(NNF_transformation,[status(thm)],[f104])).
% 0.08/6.80 fof(f110,plain,(
% 0.08/6.80 (~sP0_prd|(((![W0]: (~aInteger0(W0)|~sdtasdt0(xp,W0)=sdtpldt0(xa,smndt0(xb))))&~aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb))))&~sdteqdtlpzmzozddtrp0(xa,xb,xp)))&(sP0_prd|(((aInteger0(sK2_skl)&sdtasdt0(xp,sK2_skl)=sdtpldt0(xa,smndt0(xb)))|aDivisorOf0(xp,sdtpldt0(xa,smndt0(xb))))|sdteqdtlpzmzozddtrp0(xa,xb,xp)))),
% 0.08/6.81 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(W0,sK2_skl)],[f109])).
% 0.08/6.81 fof(f111,plain,(
% 0.08/6.81 ![X0]: (~sP0_prd|~aInteger0(X0)|~sdtasdt0(xp,X0)=sdtpldt0(xa,smndt0(xb)))),
% 0.08/6.81 inference(cnf_transformation,[status(thm)],[f110])).
% 0.08/6.81 fof(f116,definition,(
% 0.08/6.81 sQ0_spl <=> (sP0_prd)),
% 0.08/6.81 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.08/6.81 fof(f119,definition,(
% 0.08/6.81 ![X0]: (sQ1_spl <=> (~aInteger0(X0)|~sdtasdt0(xq,X0)=sdtpldt0(xa,smndt0(xb))))),
% 0.08/6.81 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.08/6.81 fof(f120,plain,(
% 0.08/6.81 ![X0]: (~aInteger0(X0)|~sdtasdt0(xq,X0)=sdtpldt0(xa,smndt0(xb))|~sQ1_spl)),
% 0.08/6.81 inference(component_clause,[status(thm)],[f119])).
% 0.08/6.81 fof(f122,plain,(
% 0.08/6.81 sQ0_spl|sQ1_spl),
% 0.08/6.81 inference(split_clause,[status(thm)],[f106,f116,f119])).
% 0.08/6.81 fof(f131,definition,(
% 0.08/6.81 ![X0]: (sQ4_spl <=> (~aInteger0(X0)|~sdtasdt0(xp,X0)=sdtpldt0(xa,smndt0(xb))))),
% 0.08/6.81 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.08/6.81 fof(f132,plain,(
% 0.08/6.81 ![X0]: (~aInteger0(X0)|~sdtasdt0(xp,X0)=sdtpldt0(xa,smndt0(xb))|~sQ4_spl)),
% 0.08/6.81 inference(component_clause,[status(thm)],[f131])).
% 0.08/6.81 fof(f134,plain,(
% 0.08/6.81 ~sQ0_spl|sQ4_spl),
% 0.08/6.81 inference(split_clause,[status(thm)],[f111,f116,f131])).
% 0.08/6.81 fof(f165,definition,(
% 0.08/6.81 sQ9_spl <=> (aInteger0(xm))),
% 0.08/6.81 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.08/6.81 fof(f167,plain,(
% 0.08/6.81 ~aInteger0(xm)|sQ9_spl),
% 0.08/6.81 inference(component_clause,[status(thm)],[f165])).
% 0.08/6.81 fof(f229,definition,(
% 0.08/6.81 sQ11_spl <=> (aInteger0(xq))),
% 0.08/6.81 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.08/6.81 fof(f231,plain,(
% 0.08/6.81 ~aInteger0(xq)|sQ11_spl),
% 0.08/6.81 inference(component_clause,[status(thm)],[f229])).
% 0.08/6.81 fof(f234,definition,(
% 0.08/6.81 sQ12_spl <=> (aInteger0(xp))),
% 0.08/6.81 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.08/6.81 fof(f236,plain,(
% 0.08/6.81 ~aInteger0(xp)|sQ12_spl),
% 0.08/6.81 inference(component_clause,[status(thm)],[f234])).
% 0.08/6.81 fof(f510,plain,(
% 0.08/6.81 $false|sQ11_spl),
% 0.08/6.81 inference(forward_subsumption_resolution,[status(thm)],[f231,f91])).
% 0.08/6.81 fof(f511,plain,(
% 0.08/6.81 sQ11_spl),
% 0.08/6.81 inference(contradiction_clause,[status(thm)],[f510])).
% 0.08/6.81 fof(f512,plain,(
% 0.08/6.81 $false|sQ12_spl),
% 0.08/6.81 inference(forward_subsumption_resolution,[status(thm)],[f236,f89])).
% 0.08/6.81 fof(f513,plain,(
% 0.08/6.81 sQ12_spl),
% 0.08/6.81 inference(contradiction_clause,[status(thm)],[f512])).
% 0.08/6.81 fof(f613,plain,(
% 0.08/6.81 $false|sQ9_spl),
% 0.08/6.81 inference(forward_subsumption_resolution,[status(thm)],[f167,f99])).
% 0.08/6.81 fof(f614,plain,(
% 0.08/6.81 sQ9_spl),
% 0.08/6.81 inference(contradiction_clause,[status(thm)],[f613])).
% 0.08/6.81 fof(f994,definition,(
% 0.08/6.81 sQ64_spl <=> (aInteger0(sdtasdt0(xq,xm)))),
% 0.08/6.81 introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition])).
% 0.08/6.81 fof(f996,plain,(
% 0.08/6.81 ~aInteger0(sdtasdt0(xq,xm))|sQ64_spl),
% 0.08/6.81 inference(component_clause,[status(thm)],[f994])).
% 0.08/6.81 fof(f1670,plain,(
% 0.08/6.81 ~aInteger0(sdtasdt0(xq,xm))|~sdtpldt0(xa,smndt0(xb))=sdtpldt0(xa,smndt0(xb))|~sQ4_spl),
% 0.08/6.81 inference(paramodulation,[status(thm)],[f101,f132])).
% 0.08/6.81 fof(f1671,definition,(
% 0.08/6.81 sQ108_spl <=> (sdtpldt0(xa,smndt0(xb))=sdtpldt0(xa,smndt0(xb)))),
% 0.08/6.81 introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition])).
% 0.08/6.81 fof(f1673,plain,(
% 0.08/6.81 ~sdtpldt0(xa,smndt0(xb))=sdtpldt0(xa,smndt0(xb))|sQ108_spl),
% 0.08/6.81 inference(component_clause,[status(thm)],[f1671])).
% 0.08/6.81 fof(f1674,plain,(
% 0.08/6.81 ~sQ64_spl|~sQ108_spl|~sQ4_spl),
% 0.08/6.81 inference(split_clause,[status(thm)],[f1670,f994,f1671,f131])).
% 0.08/6.81 fof(f1908,plain,(
% 0.08/6.81 ~aInteger0(xq)|~aInteger0(xm)|sQ64_spl),
% 0.08/6.81 inference(resolution,[status(thm)],[f996,f39])).
% 0.08/6.81 fof(f1909,plain,(
% 0.08/6.81 ~sQ11_spl|~sQ9_spl|sQ64_spl),
% 0.08/6.81 inference(split_clause,[status(thm)],[f1908,f229,f165,f994])).
% 0.08/6.81 fof(f1910,plain,(
% 0.08/6.81 $false|sQ108_spl),
% 0.08/6.81 inference(trivial_equality_resolution,[status(thm)],[f1673])).
% 0.08/6.81 fof(f1911,plain,(
% 0.08/6.81 sQ108_spl),
% 0.08/6.81 inference(contradiction_clause,[status(thm)],[f1910])).
% 0.08/6.81 fof(f2143,plain,(
% 0.08/6.81 ~aInteger0(sdtasdt0(xp,xm))|~sQ1_spl),
% 0.08/6.81 inference(resolution,[status(thm)],[f120,f102])).
% 0.08/6.81 fof(f2288,plain,(
% 0.08/6.81 ~aInteger0(xp)|~aInteger0(xm)|~sQ1_spl),
% 0.08/6.81 inference(resolution,[status(thm)],[f2143,f39])).
% 0.08/6.81 fof(f2289,plain,(
% 0.08/6.81 ~sQ12_spl|~sQ9_spl|~sQ1_spl),
% 0.08/6.81 inference(split_clause,[status(thm)],[f2288,f234,f165,f119])).
% 0.08/6.81 fof(f2290,plain,(
% 0.08/6.81 $false),
% 0.08/6.81 inference(sat_refutation,[status(thm)],[f122,f134,f511,f513,f614,f1674,f1909,f1911,f2289])).
% 0.08/6.81 % SZS output end CNFRefutation for theBenchmark.p
% 0.08/6.81 % Elapsed time: 0.107536 seconds
% 0.08/6.81 % CPU time: 0.683923 seconds
% 0.08/6.81 % Total memory used: 123.282 MB
% 0.08/6.81 % Net memory used: 121.797 MB
%------------------------------------------------------------------------------