%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM427+1 : 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 : n017.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 01:42:52 PM UTC 2026
% Result : Theorem 29.35s 4.17s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM427+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n017.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 02:23:41 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.37 % Drodi V4.1.1
% 29.35/4.17 % Refutation found
% 29.35/4.17 % SZS status Theorem for theBenchmark: Theorem is valid
% 29.35/4.17 % SZS output start CNFRefutation for theBenchmark
% 29.35/4.17 fof(f4,axiom,(
% 29.35/4.17 (! [W0] :( aInteger0(W0)=> aInteger0(smndt0(W0)) ) )),
% 29.35/4.17 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 29.35/4.17 fof(f5,axiom,(
% 29.35/4.17 (! [W0,W1] :( ( aInteger0(W0)& aInteger0(W1) )=> aInteger0(sdtpldt0(W0,W1)) ) )),
% 29.35/4.17 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 29.35/4.17 fof(f18,definition,(
% 29.35/4.17 (! [W0] :( aInteger0(W0)=> (! [W1] :( aDivisorOf0(W1,W0)<=> ( aInteger0(W1)& W1 != sz00& (? [W2] :( aInteger0(W2)& sdtasdt0(W1,W2) = W0 ) )) ) )) )),
% 29.35/4.17 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 29.35/4.17 fof(f19,definition,(
% 29.35/4.17 (! [W0,W1,W2] :( ( aInteger0(W0)& aInteger0(W1)& aInteger0(W2)& W2 != sz00 )=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ) )),
% 29.35/4.17 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 29.35/4.17 fof(f21,hypothesis,(
% 29.35/4.17 ( aInteger0(xa)& aInteger0(xb)& aInteger0(xq)& xq != sz00 ) ),
% 29.35/4.17 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 29.35/4.17 fof(f23,hypothesis,(
% 29.35/4.17 ( aInteger0(xn)& sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ) ),
% 29.35/4.17 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 29.35/4.17 fof(f24,hypothesis,(
% 29.35/4.17 sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)) ),
% 29.35/4.17 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 29.35/4.17 fof(f25,conjecture,(
% 29.35/4.17 sdteqdtlpzmzozddtrp0(xb,xa,xq) ),
% 29.35/4.17 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 29.35/4.17 fof(f26,negated_conjecture,(
% 29.35/4.17 ~(sdteqdtlpzmzozddtrp0(xb,xa,xq) )),
% 29.35/4.17 inference(negated_conjecture,[status(cth)],[f25])).
% 29.35/4.17 fof(f32,plain,(
% 29.35/4.17 ![W0]: (~aInteger0(W0)|aInteger0(smndt0(W0)))),
% 29.35/4.17 inference(pre_NNF_transformation,[status(thm)],[f4])).
% 29.35/4.17 fof(f33,plain,(
% 29.35/4.17 ![X0]: (~aInteger0(X0)|aInteger0(smndt0(X0)))),
% 29.35/4.17 inference(cnf_transformation,[status(thm)],[f32])).
% 29.35/4.17 fof(f34,plain,(
% 29.35/4.17 ![W0,W1]: ((~aInteger0(W0)|~aInteger0(W1))|aInteger0(sdtpldt0(W0,W1)))),
% 29.35/4.17 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 29.35/4.17 fof(f35,plain,(
% 29.35/4.17 ![X0,X1]: (~aInteger0(X0)|~aInteger0(X1)|aInteger0(sdtpldt0(X0,X1)))),
% 29.35/4.17 inference(cnf_transformation,[status(thm)],[f34])).
% 29.35/4.17 fof(f66,plain,(
% 29.35/4.17 ![W0]: (~aInteger0(W0)|(![W1]: (aDivisorOf0(W1,W0)<=>((aInteger0(W1)&~W1=sz00)&(?[W2]: (aInteger0(W2)&sdtasdt0(W1,W2)=W0))))))),
% 29.35/4.17 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 29.35/4.17 fof(f67,plain,(
% 29.35/4.17 ![W0]: (~aInteger0(W0)|(![W1]: ((~aDivisorOf0(W1,W0)|((aInteger0(W1)&~W1=sz00)&(?[W2]: (aInteger0(W2)&sdtasdt0(W1,W2)=W0))))&(aDivisorOf0(W1,W0)|((~aInteger0(W1)|W1=sz00)|(![W2]: (~aInteger0(W2)|~sdtasdt0(W1,W2)=W0)))))))),
% 29.35/4.17 inference(NNF_transformation,[status(thm)],[f66])).
% 29.35/4.17 fof(f68,plain,(
% 29.35/4.17 ![W0]: (~aInteger0(W0)|((![W1]: (~aDivisorOf0(W1,W0)|((aInteger0(W1)&~W1=sz00)&(?[W2]: (aInteger0(W2)&sdtasdt0(W1,W2)=W0)))))&(![W1]: (aDivisorOf0(W1,W0)|((~aInteger0(W1)|W1=sz00)|(![W2]: (~aInteger0(W2)|~sdtasdt0(W1,W2)=W0)))))))),
% 29.35/4.17 inference(miniscoping,[status(thm)],[f67])).
% 29.35/4.17 fof(f69,plain,(
% 29.35/4.17 ![W0]: (~aInteger0(W0)|((![W1]: (~aDivisorOf0(W1,W0)|((aInteger0(W1)&~W1=sz00)&(aInteger0(sK0_skl(W1,W0))&sdtasdt0(W1,sK0_skl(W1,W0))=W0))))&(![W1]: (aDivisorOf0(W1,W0)|((~aInteger0(W1)|W1=sz00)|(![W2]: (~aInteger0(W2)|~sdtasdt0(W1,W2)=W0)))))))),
% 29.35/4.17 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(W2,sK0_skl(W1,W0))],[f68])).
% 29.35/4.17 fof(f74,plain,(
% 29.35/4.17 ![X0,X1,X2]: (~aInteger0(X0)|aDivisorOf0(X1,X0)|~aInteger0(X1)|X1=sz00|~aInteger0(X2)|~sdtasdt0(X1,X2)=X0)),
% 29.35/4.17 inference(cnf_transformation,[status(thm)],[f69])).
% 29.35/4.17 fof(f75,plain,(
% 29.35/4.17 ![W0,W1,W2]: ((((~aInteger0(W0)|~aInteger0(W1))|~aInteger0(W2))|W2=sz00)|(sdteqdtlpzmzozddtrp0(W0,W1,W2)<=>aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1)))))),
% 29.35/4.17 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 29.35/4.17 fof(f76,plain,(
% 29.35/4.17 ![W0,W1,W2]: ((((~aInteger0(W0)|~aInteger0(W1))|~aInteger0(W2))|W2=sz00)|((~sdteqdtlpzmzozddtrp0(W0,W1,W2)|aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))))&(sdteqdtlpzmzozddtrp0(W0,W1,W2)|~aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))))))),
% 29.35/4.17 inference(NNF_transformation,[status(thm)],[f75])).
% 29.35/4.17 fof(f78,plain,(
% 29.35/4.17 ![X0,X1,X2]: (~aInteger0(X0)|~aInteger0(X1)|~aInteger0(X2)|X2=sz00|sdteqdtlpzmzozddtrp0(X0,X1,X2)|~aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))))),
% 29.35/4.17 inference(cnf_transformation,[status(thm)],[f76])).
% 29.35/4.17 fof(f81,plain,(
% 29.35/4.17 aInteger0(xa)),
% 29.35/4.17 inference(cnf_transformation,[status(thm)],[f21])).
% 29.35/4.17 fof(f82,plain,(
% 29.35/4.17 aInteger0(xb)),
% 29.35/4.17 inference(cnf_transformation,[status(thm)],[f21])).
% 29.35/4.17 fof(f83,plain,(
% 29.35/4.17 aInteger0(xq)),
% 29.35/4.17 inference(cnf_transformation,[status(thm)],[f21])).
% 29.35/4.17 fof(f84,plain,(
% 29.35/4.17 ~xq=sz00),
% 29.35/4.17 inference(cnf_transformation,[status(thm)],[f21])).
% 29.35/4.17 fof(f86,plain,(
% 29.35/4.17 aInteger0(xn)),
% 29.35/4.17 inference(cnf_transformation,[status(thm)],[f23])).
% 29.35/4.17 fof(f88,plain,(
% 29.35/4.17 sdtasdt0(xq,smndt0(xn))=sdtpldt0(xb,smndt0(xa))),
% 29.35/4.17 inference(cnf_transformation,[status(thm)],[f24])).
% 29.35/4.17 fof(f89,plain,(
% 29.35/4.17 ~sdteqdtlpzmzozddtrp0(xb,xa,xq)),
% 29.35/4.17 inference(cnf_transformation,[status(thm)],[f26])).
% 29.35/4.17 fof(f115,plain,(
% 29.35/4.17 ![X0,X1]: (~aInteger0(X0)|aInteger0(sdtpldt0(X0,smndt0(X1)))|~aInteger0(X1))),
% 29.35/4.17 inference(resolution,[status(thm)],[f35,f33])).
% 29.35/4.17 fof(f222,definition,(
% 29.35/4.17 sQ0_spl <=> (aInteger0(xq))),
% 29.35/4.17 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 29.35/4.17 fof(f224,plain,(
% 29.35/4.17 ~aInteger0(xq)|sQ0_spl),
% 29.35/4.17 inference(component_clause,[status(thm)],[f222])).
% 29.35/4.17 fof(f233,plain,(
% 29.35/4.17 $false|sQ0_spl),
% 29.35/4.17 inference(forward_subsumption_resolution,[status(thm)],[f224,f83])).
% 29.35/4.17 fof(f234,plain,(
% 29.35/4.17 sQ0_spl),
% 29.35/4.17 inference(contradiction_clause,[status(thm)],[f233])).
% 29.35/4.17 fof(f237,definition,(
% 29.35/4.17 sQ3_spl <=> (aInteger0(xb))),
% 29.35/4.17 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 29.35/4.17 fof(f239,plain,(
% 29.35/4.17 ~aInteger0(xb)|sQ3_spl),
% 29.35/4.17 inference(component_clause,[status(thm)],[f237])).
% 29.35/4.17 fof(f248,plain,(
% 29.35/4.17 $false|sQ3_spl),
% 29.35/4.17 inference(forward_subsumption_resolution,[status(thm)],[f239,f82])).
% 29.35/4.17 fof(f249,plain,(
% 29.35/4.17 sQ3_spl),
% 29.35/4.17 inference(contradiction_clause,[status(thm)],[f248])).
% 29.35/4.17 fof(f262,definition,(
% 29.35/4.17 sQ6_spl <=> (aInteger0(xa))),
% 29.35/4.17 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 29.35/4.17 fof(f264,plain,(
% 29.35/4.17 ~aInteger0(xa)|sQ6_spl),
% 29.35/4.17 inference(component_clause,[status(thm)],[f262])).
% 29.35/4.17 fof(f273,plain,(
% 29.35/4.17 $false|sQ6_spl),
% 29.35/4.17 inference(forward_subsumption_resolution,[status(thm)],[f264,f81])).
% 29.35/4.17 fof(f274,plain,(
% 29.35/4.17 sQ6_spl),
% 29.35/4.17 inference(contradiction_clause,[status(thm)],[f273])).
% 29.35/4.17 fof(f429,definition,(
% 29.35/4.17 sQ15_spl <=> (xq=sz00)),
% 29.35/4.17 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 29.35/4.17 fof(f430,plain,(
% 29.35/4.17 xq=sz00|~sQ15_spl),
% 29.35/4.17 inference(component_clause,[status(thm)],[f429])).
% 29.35/4.17 fof(f663,plain,(
% 29.35/4.17 ![X0,X1,X2,X3]: (~aInteger0(sdtpldt0(X0,smndt0(X1)))|~aInteger0(X2)|X2=sz00|~aInteger0(X3)|~sdtasdt0(X2,X3)=sdtpldt0(X0,smndt0(X1))|~aInteger0(X0)|~aInteger0(X1)|~aInteger0(X2)|X2=sz00|sdteqdtlpzmzozddtrp0(X0,X1,X2))),
% 29.35/4.17 inference(resolution,[status(thm)],[f74,f78])).
% 29.35/4.17 fof(f668,plain,(
% 29.35/4.17 ![X0,X1,X2,X3]: (~aInteger0(sdtpldt0(X0,smndt0(X1)))|~aInteger0(X2)|X2=sz00|~aInteger0(X3)|~sdtasdt0(X2,X3)=sdtpldt0(X0,smndt0(X1))|~aInteger0(X0)|~aInteger0(X1)|sdteqdtlpzmzozddtrp0(X0,X1,X2))),
% 29.35/4.17 inference(duplicate_literals_removal,[status(thm)],[f663])).
% 29.35/4.17 fof(f5183,plain,(
% 29.35/4.17 $false|~sQ15_spl),
% 29.35/4.17 inference(forward_subsumption_resolution,[status(thm)],[f430,f84])).
% 29.35/4.17 fof(f5184,plain,(
% 29.35/4.17 ~sQ15_spl),
% 29.35/4.17 inference(contradiction_clause,[status(thm)],[f5183])).
% 29.35/4.17 fof(f5420,plain,(
% 29.35/4.17 ![X0,X1,X2,X3]: (~aInteger0(X0)|X0=sz00|~aInteger0(X1)|~sdtasdt0(X0,X1)=sdtpldt0(X2,smndt0(X3))|~aInteger0(X2)|~aInteger0(X3)|sdteqdtlpzmzozddtrp0(X2,X3,X0))),
% 29.35/4.17 inference(forward_subsumption_resolution,[status(thm)],[f668,f115])).
% 29.35/4.17 fof(f5424,plain,(
% 29.35/4.17 ![X0]: (~aInteger0(xq)|xq=sz00|~aInteger0(X0)|~sdtasdt0(xq,X0)=sdtpldt0(xb,smndt0(xa))|~aInteger0(xb)|~aInteger0(xa))),
% 29.35/4.17 inference(resolution,[status(thm)],[f5420,f89])).
% 29.35/4.17 fof(f5439,definition,(
% 29.35/4.17 ![X0]: (sQ119_spl <=> (~aInteger0(X0)|~sdtasdt0(xq,X0)=sdtpldt0(xb,smndt0(xa))))),
% 29.35/4.17 introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition])).
% 29.35/4.17 fof(f5440,plain,(
% 29.35/4.17 ![X0]: (~aInteger0(X0)|~sdtasdt0(xq,X0)=sdtpldt0(xb,smndt0(xa))|~sQ119_spl)),
% 29.35/4.17 inference(component_clause,[status(thm)],[f5439])).
% 29.35/4.17 fof(f5442,plain,(
% 29.35/4.17 ~sQ0_spl|sQ15_spl|sQ119_spl|~sQ3_spl|~sQ6_spl),
% 29.35/4.17 inference(split_clause,[status(thm)],[f5424,f222,f429,f5439,f237,f262])).
% 29.35/4.18 fof(f5447,plain,(
% 29.35/4.18 ![X0]: (~aInteger0(X0)|~sdtasdt0(xq,X0)=sdtasdt0(xq,smndt0(xn))|~sQ119_spl)),
% 29.35/4.18 inference(forward_demodulation,[status(thm)],[f88,f5440])).
% 29.35/4.18 fof(f5577,plain,(
% 29.35/4.18 ![X0]: (~sdtasdt0(xq,smndt0(X0))=sdtasdt0(xq,smndt0(xn))|~aInteger0(X0)|~sQ119_spl)),
% 29.35/4.18 inference(resolution,[status(thm)],[f5447,f33])).
% 29.35/4.18 fof(f7148,plain,(
% 29.35/4.18 ~aInteger0(xn)|~sQ119_spl),
% 29.35/4.18 inference(equality_resolution,[status(thm)],[f5577])).
% 29.35/4.18 fof(f7153,plain,(
% 29.35/4.18 $false|~sQ119_spl),
% 29.35/4.18 inference(forward_subsumption_resolution,[status(thm)],[f7148,f86])).
% 29.35/4.18 fof(f7154,plain,(
% 29.35/4.18 ~sQ119_spl),
% 29.35/4.18 inference(contradiction_clause,[status(thm)],[f7153])).
% 29.35/4.18 fof(f7155,plain,(
% 29.35/4.18 $false),
% 29.35/4.18 inference(sat_refutation,[status(thm)],[f234,f249,f274,f5184,f5442,f7154])).
% 29.35/4.18 % SZS output end CNFRefutation for theBenchmark.p
% 3.97/4.22 % Elapsed time: 3.846590 seconds
% 3.97/4.22 % CPU time: 30.155173 seconds
% 3.97/4.22 % Total memory used: 418.564 MB
% 3.97/4.22 % Net memory used: 391.609 MB
%------------------------------------------------------------------------------