%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM500+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 : n001.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 01:43:03 PM UTC 2026
% Result : Theorem 106.18s 13.93s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM500+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 02:40:44 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 106.18/13.93 % Refutation found
% 106.18/13.93 % SZS status Theorem for theBenchmark: Theorem is valid
% 106.18/13.93 % SZS output start CNFRefutation for theBenchmark
% 106.18/13.93 fof(f2,axiom,(
% 106.18/13.93 aNaturalNumber0(sz00) ),
% 106.18/13.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.18/13.93 fof(f5,axiom,(
% 106.18/13.93 (! [W0,W1] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1) )=> aNaturalNumber0(sdtasdt0(W0,W1)) ) )),
% 106.18/13.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.18/13.93 fof(f11,axiom,(
% 106.18/13.93 (! [W0] :( aNaturalNumber0(W0)=> ( sdtasdt0(W0,sz10) = W0& W0 = sdtasdt0(sz10,W0) ) ) )),
% 106.18/13.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.18/13.93 fof(f31,definition,(
% 106.18/13.93 (! [W0,W1] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1) )=> ( ( W0 != sz00& doDivides0(W0,W1) )=> (! [W2] :( W2 = sdtsldt0(W1,W0)<=> ( aNaturalNumber0(W2)& W1 = sdtasdt0(W0,W2) ) ) )) ) )),
% 106.18/13.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.18/13.93 fof(f37,definition,(
% 106.18/13.93 (! [W0] :( aNaturalNumber0(W0)=> ( isPrime0(W0)<=> ( W0 != sz00& W0 != sz10& (! [W1] :( ( aNaturalNumber0(W1)& doDivides0(W1,W0) )=> ( W1 = sz10| W1 = W0 ) ) )) ) ) )),
% 106.18/13.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.18/13.93 fof(f38,axiom,(
% 106.18/13.93 (! [W0] :( ( aNaturalNumber0(W0)& W0 != sz00& W0 != sz10 )=> (? [W1] :( aNaturalNumber0(W1)& doDivides0(W1,W0)& isPrime0(W1) ) )) )),
% 106.18/13.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.18/13.93 fof(f39,hypothesis,(
% 106.18/13.93 ( aNaturalNumber0(xn)& aNaturalNumber0(xm)& aNaturalNumber0(xp) ) ),
% 106.18/13.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.18/13.93 fof(f41,hypothesis,(
% 106.18/13.93 ( isPrime0(xp)& doDivides0(xp,sdtasdt0(xn,xm)) ) ),
% 106.18/13.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.18/13.93 fof(f45,hypothesis,(
% 106.18/13.93 xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
% 106.18/13.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.18/13.93 fof(f46,hypothesis,(
% 106.18/13.93 ~ ( xk = sz00| xk = sz10 ) ),
% 106.18/13.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.18/13.93 fof(f48,conjecture,(
% 106.18/13.93 (? [W0] :( aNaturalNumber0(W0)& doDivides0(W0,xk)& isPrime0(W0) ) )),
% 106.18/13.93 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 106.18/13.93 fof(f49,negated_conjecture,(
% 106.18/13.93 ~((? [W0] :( aNaturalNumber0(W0)& doDivides0(W0,xk)& isPrime0(W0) ) ))),
% 106.18/13.93 inference(negated_conjecture,[status(cth)],[f48])).
% 106.18/13.93 fof(f53,plain,(
% 106.18/13.93 aNaturalNumber0(sz00)),
% 106.18/13.93 inference(cnf_transformation,[status(thm)],[f2])).
% 106.18/13.93 fof(f58,plain,(
% 106.18/13.93 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|aNaturalNumber0(sdtasdt0(W0,W1)))),
% 106.18/13.93 inference(pre_NNF_transformation,[status(thm)],[f5])).
% 106.18/13.93 fof(f59,plain,(
% 106.18/13.93 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|aNaturalNumber0(sdtasdt0(X0,X1)))),
% 106.18/13.93 inference(cnf_transformation,[status(thm)],[f58])).
% 106.18/13.93 fof(f71,plain,(
% 106.18/13.93 ![W0]: (~aNaturalNumber0(W0)|(sdtasdt0(W0,sz10)=W0&W0=sdtasdt0(sz10,W0)))),
% 106.18/13.93 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 106.18/13.93 fof(f72,plain,(
% 106.18/13.93 ![X0]: (~aNaturalNumber0(X0)|sdtasdt0(X0,sz10)=X0)),
% 106.18/13.93 inference(cnf_transformation,[status(thm)],[f71])).
% 106.18/13.93 fof(f137,plain,(
% 106.18/13.93 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|((W0=sz00|~doDivides0(W0,W1))|(![W2]: (W2=sdtsldt0(W1,W0)<=>(aNaturalNumber0(W2)&W1=sdtasdt0(W0,W2))))))),
% 106.18/13.93 inference(pre_NNF_transformation,[status(thm)],[f31])).
% 106.18/13.93 fof(f138,plain,(
% 106.18/13.93 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|((W0=sz00|~doDivides0(W0,W1))|(![W2]: ((~W2=sdtsldt0(W1,W0)|(aNaturalNumber0(W2)&W1=sdtasdt0(W0,W2)))&(W2=sdtsldt0(W1,W0)|(~aNaturalNumber0(W2)|~W1=sdtasdt0(W0,W2)))))))),
% 106.18/13.93 inference(NNF_transformation,[status(thm)],[f137])).
% 106.18/13.93 fof(f139,plain,(
% 106.18/13.93 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|((W0=sz00|~doDivides0(W0,W1))|((![W2]: (~W2=sdtsldt0(W1,W0)|(aNaturalNumber0(W2)&W1=sdtasdt0(W0,W2))))&(![W2]: (W2=sdtsldt0(W1,W0)|(~aNaturalNumber0(W2)|~W1=sdtasdt0(W0,W2)))))))),
% 106.18/13.93 inference(miniscoping,[status(thm)],[f138])).
% 106.18/13.93 fof(f140,plain,(
% 106.18/13.93 ![X0,X1,X2]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|X0=sz00|~doDivides0(X0,X1)|~X2=sdtsldt0(X1,X0)|aNaturalNumber0(X2))),
% 106.18/13.93 inference(cnf_transformation,[status(thm)],[f139])).
% 106.18/13.93 fof(f153,plain,(
% 106.18/13.93 ![W0]: (~aNaturalNumber0(W0)|(isPrime0(W0)<=>((~W0=sz00&~W0=sz10)&(![W1]: ((~aNaturalNumber0(W1)|~doDivides0(W1,W0))|(W1=sz10|W1=W0))))))),
% 106.18/13.93 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 106.18/13.95 fof(f154,plain,(
% 106.18/13.95 ![W0]: (~aNaturalNumber0(W0)|((~isPrime0(W0)|((~W0=sz00&~W0=sz10)&(![W1]: ((~aNaturalNumber0(W1)|~doDivides0(W1,W0))|(W1=sz10|W1=W0)))))&(isPrime0(W0)|((W0=sz00|W0=sz10)|(?[W1]: ((aNaturalNumber0(W1)&doDivides0(W1,W0))&(~W1=sz10&~W1=W0)))))))),
% 106.18/13.95 inference(NNF_transformation,[status(thm)],[f153])).
% 106.18/13.95 fof(f155,plain,(
% 106.18/13.95 ![W0]: (~aNaturalNumber0(W0)|((~isPrime0(W0)|((~W0=sz00&~W0=sz10)&(![W1]: ((~aNaturalNumber0(W1)|~doDivides0(W1,W0))|(W1=sz10|W1=W0)))))&(isPrime0(W0)|((W0=sz00|W0=sz10)|((aNaturalNumber0(sK2_skl(W0))&doDivides0(sK2_skl(W0),W0))&(~sK2_skl(W0)=sz10&~sK2_skl(W0)=W0))))))),
% 106.18/13.95 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(W1,sK2_skl(W0))],[f154])).
% 106.18/13.95 fof(f156,plain,(
% 106.18/13.95 ![X0]: (~aNaturalNumber0(X0)|~isPrime0(X0)|~X0=sz00)),
% 106.18/13.95 inference(cnf_transformation,[status(thm)],[f155])).
% 106.18/13.95 fof(f163,plain,(
% 106.18/13.95 ![W0]: (((~aNaturalNumber0(W0)|W0=sz00)|W0=sz10)|(?[W1]: ((aNaturalNumber0(W1)&doDivides0(W1,W0))&isPrime0(W1))))),
% 106.18/13.95 inference(pre_NNF_transformation,[status(thm)],[f38])).
% 106.18/13.95 fof(f164,plain,(
% 106.18/13.95 ![W0]: (((~aNaturalNumber0(W0)|W0=sz00)|W0=sz10)|((aNaturalNumber0(sK3_skl(W0))&doDivides0(sK3_skl(W0),W0))&isPrime0(sK3_skl(W0))))),
% 106.18/13.95 inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(W1,sK3_skl(W0))],[f163])).
% 106.18/13.95 fof(f165,plain,(
% 106.18/13.95 ![X0]: (~aNaturalNumber0(X0)|X0=sz00|X0=sz10|aNaturalNumber0(sK3_skl(X0)))),
% 106.18/13.95 inference(cnf_transformation,[status(thm)],[f164])).
% 106.18/13.95 fof(f166,plain,(
% 106.18/13.95 ![X0]: (~aNaturalNumber0(X0)|X0=sz00|X0=sz10|doDivides0(sK3_skl(X0),X0))),
% 106.18/13.95 inference(cnf_transformation,[status(thm)],[f164])).
% 106.18/13.95 fof(f167,plain,(
% 106.18/13.95 ![X0]: (~aNaturalNumber0(X0)|X0=sz00|X0=sz10|isPrime0(sK3_skl(X0)))),
% 106.18/13.95 inference(cnf_transformation,[status(thm)],[f164])).
% 106.18/13.95 fof(f168,plain,(
% 106.18/13.95 aNaturalNumber0(xn)),
% 106.18/13.95 inference(cnf_transformation,[status(thm)],[f39])).
% 106.18/13.95 fof(f169,plain,(
% 106.18/13.95 aNaturalNumber0(xm)),
% 106.18/13.95 inference(cnf_transformation,[status(thm)],[f39])).
% 106.18/13.95 fof(f170,plain,(
% 106.18/13.95 aNaturalNumber0(xp)),
% 106.18/13.95 inference(cnf_transformation,[status(thm)],[f39])).
% 106.18/13.95 fof(f173,plain,(
% 106.18/13.95 isPrime0(xp)),
% 106.18/13.95 inference(cnf_transformation,[status(thm)],[f41])).
% 106.18/13.95 fof(f174,plain,(
% 106.18/13.95 doDivides0(xp,sdtasdt0(xn,xm))),
% 106.18/13.95 inference(cnf_transformation,[status(thm)],[f41])).
% 106.18/13.95 fof(f181,plain,(
% 106.18/13.95 xk=sdtsldt0(sdtasdt0(xn,xm),xp)),
% 106.18/13.95 inference(cnf_transformation,[status(thm)],[f45])).
% 106.18/13.95 fof(f182,plain,(
% 106.18/13.95 (~xk=sz00&~xk=sz10)),
% 106.18/13.95 inference(pre_NNF_transformation,[status(thm)],[f46])).
% 106.18/13.95 fof(f183,plain,(
% 106.18/13.95 ~xk=sz00),
% 106.18/13.95 inference(cnf_transformation,[status(thm)],[f182])).
% 106.18/13.95 fof(f184,plain,(
% 106.18/13.95 ~xk=sz10),
% 106.18/13.95 inference(cnf_transformation,[status(thm)],[f182])).
% 106.18/13.95 fof(f187,plain,(
% 106.18/13.95 (![W0]: ((~aNaturalNumber0(W0)|~doDivides0(W0,xk))|~isPrime0(W0)))),
% 106.18/13.95 inference(pre_NNF_transformation,[status(thm)],[f49])).
% 106.18/13.95 fof(f188,plain,(
% 106.18/13.95 ![X0]: (~aNaturalNumber0(X0)|~doDivides0(X0,xk)|~isPrime0(X0))),
% 106.18/13.95 inference(cnf_transformation,[status(thm)],[f187])).
% 106.18/13.95 fof(f196,plain,(
% 106.18/13.95 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|X0=sz00|~doDivides0(X0,X1)|aNaturalNumber0(sdtsldt0(X1,X0)))),
% 106.18/13.95 inference(destructive_equality_resolution,[status(thm)],[f140])).
% 106.18/13.95 fof(f199,plain,(
% 106.18/13.95 ~aNaturalNumber0(sz00)|~isPrime0(sz00)),
% 106.18/13.95 inference(destructive_equality_resolution,[status(thm)],[f156])).
% 106.18/13.95 fof(f210,definition,(
% 106.18/13.95 sQ1_spl <=> (aNaturalNumber0(xk))),
% 106.18/13.95 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 106.18/13.95 fof(f211,plain,(
% 106.18/13.95 aNaturalNumber0(xk)|~sQ1_spl),
% 106.18/13.95 inference(component_clause,[status(thm)],[f210])).
% 106.18/13.95 fof(f212,plain,(
% 106.18/13.95 ~aNaturalNumber0(xk)|sQ1_spl),
% 106.18/13.95 inference(component_clause,[status(thm)],[f210])).
% 106.18/13.95 fof(f232,plain,(
% 106.18/13.95 ~isPrime0(sz00)),
% 106.18/13.95 inference(backward_subsumption_resolution,[status(thm)],[f199,f53])).
% 106.18/13.95 fof(f247,plain,(
% 106.18/13.95 ![X0]: (~aNaturalNumber0(X0)|aNaturalNumber0(sdtasdt0(xn,X0)))),
% 106.18/13.95 inference(resolution,[status(thm)],[f59,f168])).
% 106.18/13.95 fof(f277,definition,(
% 106.18/13.95 sQ5_spl <=> (aNaturalNumber0(xp))),
% 106.18/13.95 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 106.18/13.95 fof(f279,plain,(
% 106.18/13.95 ~aNaturalNumber0(xp)|sQ5_spl),
% 106.18/13.95 inference(component_clause,[status(thm)],[f277])).
% 106.18/13.95 fof(f349,plain,(
% 106.18/13.95 $false|sQ5_spl),
% 106.18/13.95 inference(forward_subsumption_resolution,[status(thm)],[f279,f170])).
% 106.18/13.95 fof(f350,plain,(
% 106.18/13.95 sQ5_spl),
% 106.18/13.95 inference(contradiction_clause,[status(thm)],[f349])).
% 106.18/13.95 fof(f422,definition,(
% 106.18/13.95 sQ39_spl <=> (sdtasdt0(xp,sz10)=sz00)),
% 106.18/13.95 introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition])).
% 106.18/13.95 fof(f423,plain,(
% 106.18/13.95 sdtasdt0(xp,sz10)=sz00|~sQ39_spl),
% 106.18/13.95 inference(component_clause,[status(thm)],[f422])).
% 106.18/13.95 fof(f424,plain,(
% 106.18/13.95 ~sdtasdt0(xp,sz10)=sz00|sQ39_spl),
% 106.18/13.95 inference(component_clause,[status(thm)],[f422])).
% 106.18/13.95 fof(f920,plain,(
% 106.18/13.95 sdtasdt0(xp,sz10)=xp),
% 106.18/13.95 inference(resolution,[status(thm)],[f72,f170])).
% 106.18/13.95 fof(f928,plain,(
% 106.18/13.95 xp=sz00|~sQ39_spl),
% 106.18/13.95 inference(forward_demodulation,[status(thm)],[f920,f423])).
% 106.18/13.95 fof(f945,plain,(
% 106.18/13.95 ~isPrime0(xp)|~sQ39_spl),
% 106.18/13.95 inference(backward_demodulation,[status(thm)],[f928,f232])).
% 106.18/13.95 fof(f948,plain,(
% 106.18/13.95 $false|~sQ39_spl),
% 106.18/13.95 inference(forward_subsumption_resolution,[status(thm)],[f945,f173])).
% 106.18/13.95 fof(f949,plain,(
% 106.18/13.95 ~sQ39_spl),
% 106.18/13.95 inference(contradiction_clause,[status(thm)],[f948])).
% 106.18/13.95 fof(f952,plain,(
% 106.18/13.95 ~xp=sz00|sQ39_spl),
% 106.18/13.95 inference(forward_demodulation,[status(thm)],[f920,f424])).
% 106.18/13.95 fof(f1052,definition,(
% 106.18/13.95 sQ136_spl <=> (xp=sz00)),
% 106.18/13.95 introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition])).
% 106.18/13.95 fof(f1053,plain,(
% 106.18/13.95 xp=sz00|~sQ136_spl),
% 106.18/13.95 inference(component_clause,[status(thm)],[f1052])).
% 106.18/13.95 fof(f1062,plain,(
% 106.18/13.95 $false|sQ39_spl|~sQ136_spl),
% 106.18/13.95 inference(forward_subsumption_resolution,[status(thm)],[f1053,f952])).
% 106.18/13.95 fof(f1063,plain,(
% 106.18/13.95 sQ39_spl|~sQ136_spl),
% 106.18/13.95 inference(contradiction_clause,[status(thm)],[f1062])).
% 106.18/13.95 fof(f1508,definition,(
% 106.18/13.95 sQ191_spl <=> (aNaturalNumber0(sdtasdt0(xn,xm)))),
% 106.18/13.95 introduced(definition,[new_symbols(definition,[sQ191_spl])],[split_symbol_definition])).
% 106.18/13.95 fof(f1510,plain,(
% 106.18/13.95 ~aNaturalNumber0(sdtasdt0(xn,xm))|sQ191_spl),
% 106.18/13.95 inference(component_clause,[status(thm)],[f1508])).
% 106.18/13.95 fof(f13852,plain,(
% 106.18/13.95 ~aNaturalNumber0(xp)|~aNaturalNumber0(sdtasdt0(xn,xm))|xp=sz00|aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))),
% 106.18/13.95 inference(resolution,[status(thm)],[f196,f174])).
% 106.18/13.95 fof(f13865,definition,(
% 106.18/13.95 sQ1203_spl <=> (aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp)))),
% 106.18/13.95 introduced(definition,[new_symbols(definition,[sQ1203_spl])],[split_symbol_definition])).
% 106.18/13.95 fof(f13866,plain,(
% 106.18/13.95 aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xp))|~sQ1203_spl),
% 106.18/13.95 inference(component_clause,[status(thm)],[f13865])).
% 106.18/13.95 fof(f13868,plain,(
% 106.18/13.95 ~sQ5_spl|~sQ191_spl|sQ136_spl|sQ1203_spl),
% 106.18/13.95 inference(split_clause,[status(thm)],[f13852,f277,f1508,f1052,f13865])).
% 106.18/13.95 fof(f13871,plain,(
% 106.18/13.95 aNaturalNumber0(xk)|~sQ1203_spl),
% 106.18/13.95 inference(forward_demodulation,[status(thm)],[f181,f13866])).
% 106.18/13.95 fof(f13872,plain,(
% 106.18/13.95 $false|sQ1_spl|~sQ1203_spl),
% 106.18/13.95 inference(forward_subsumption_resolution,[status(thm)],[f13871,f212])).
% 106.18/13.95 fof(f13873,plain,(
% 106.18/13.95 sQ1_spl|~sQ1203_spl),
% 106.18/13.95 inference(contradiction_clause,[status(thm)],[f13872])).
% 106.18/13.95 fof(f18915,plain,(
% 106.18/13.95 aNaturalNumber0(sdtasdt0(xn,xm))),
% 106.18/13.95 inference(resolution,[status(thm)],[f247,f169])).
% 106.18/13.95 fof(f18918,plain,(
% 106.18/13.95 $false|sQ191_spl),
% 106.18/13.95 inference(forward_subsumption_resolution,[status(thm)],[f18915,f1510])).
% 106.18/13.95 fof(f18919,plain,(
% 106.18/13.95 sQ191_spl),
% 106.18/13.95 inference(contradiction_clause,[status(thm)],[f18918])).
% 106.18/13.95 fof(f19032,plain,(
% 106.18/13.95 xk=sz00|xk=sz10|isPrime0(sK3_skl(xk))|~sQ1_spl),
% 106.18/13.95 inference(resolution,[status(thm)],[f211,f167])).
% 106.18/13.95 fof(f19076,definition,(
% 106.18/13.95 sQ1555_spl <=> (xk=sz00)),
% 106.18/13.95 introduced(definition,[new_symbols(definition,[sQ1555_spl])],[split_symbol_definition])).
% 106.18/13.95 fof(f19077,plain,(
% 106.18/13.95 xk=sz00|~sQ1555_spl),
% 106.18/13.95 inference(component_clause,[status(thm)],[f19076])).
% 106.18/13.95 fof(f19079,definition,(
% 106.18/13.95 sQ1556_spl <=> (xk=sz10)),
% 106.18/13.95 introduced(definition,[new_symbols(definition,[sQ1556_spl])],[split_symbol_definition])).
% 106.18/13.95 fof(f19080,plain,(
% 106.18/13.95 xk=sz10|~sQ1556_spl),
% 106.18/13.95 inference(component_clause,[status(thm)],[f19079])).
% 106.18/13.95 fof(f19082,definition,(
% 106.18/13.95 sQ1557_spl <=> (isPrime0(sK3_skl(xk)))),
% 106.18/13.95 introduced(definition,[new_symbols(definition,[sQ1557_spl])],[split_symbol_definition])).
% 106.18/13.95 fof(f19085,plain,(
% 106.18/13.95 sQ1555_spl|sQ1556_spl|sQ1557_spl|~sQ1_spl),
% 106.18/13.95 inference(split_clause,[status(thm)],[f19032,f19076,f19079,f19082,f210])).
% 106.18/13.99 fof(f19102,plain,(
% 106.18/13.99 $false|~sQ1555_spl),
% 106.18/13.99 inference(forward_subsumption_resolution,[status(thm)],[f19077,f183])).
% 106.18/13.99 fof(f19103,plain,(
% 106.18/13.99 ~sQ1555_spl),
% 106.18/13.99 inference(contradiction_clause,[status(thm)],[f19102])).
% 106.18/13.99 fof(f19189,plain,(
% 106.18/13.99 ~xk=xk|~sQ1556_spl),
% 106.18/13.99 inference(forward_demodulation,[status(thm)],[f19080,f184])).
% 106.18/13.99 fof(f19190,plain,(
% 106.18/13.99 $false|~sQ1556_spl),
% 106.18/13.99 inference(trivial_equality_resolution,[status(thm)],[f19189])).
% 106.18/13.99 fof(f19191,plain,(
% 106.18/13.99 ~sQ1556_spl),
% 106.18/13.99 inference(contradiction_clause,[status(thm)],[f19190])).
% 106.18/13.99 fof(f19373,plain,(
% 106.18/13.99 xk=sz00|xk=sz10|doDivides0(sK3_skl(xk),xk)|~sQ1_spl),
% 106.18/13.99 inference(resolution,[status(thm)],[f166,f211])).
% 106.18/13.99 fof(f19381,definition,(
% 106.18/13.99 sQ1577_spl <=> (doDivides0(sK3_skl(xk),xk))),
% 106.18/13.99 introduced(definition,[new_symbols(definition,[sQ1577_spl])],[split_symbol_definition])).
% 106.18/13.99 fof(f19382,plain,(
% 106.18/13.99 doDivides0(sK3_skl(xk),xk)|~sQ1577_spl),
% 106.18/13.99 inference(component_clause,[status(thm)],[f19381])).
% 106.18/13.99 fof(f19384,plain,(
% 106.18/13.99 sQ1555_spl|sQ1556_spl|sQ1577_spl|~sQ1_spl),
% 106.18/13.99 inference(split_clause,[status(thm)],[f19373,f19076,f19079,f19381,f210])).
% 106.18/14.00 fof(f20351,plain,(
% 106.18/14.00 xk=sz00|xk=sz10|aNaturalNumber0(sK3_skl(xk))|~sQ1_spl),
% 106.18/14.00 inference(resolution,[status(thm)],[f165,f211])).
% 106.18/14.00 fof(f20364,definition,(
% 106.18/14.00 sQ1654_spl <=> (aNaturalNumber0(sK3_skl(xk)))),
% 106.18/14.00 introduced(definition,[new_symbols(definition,[sQ1654_spl])],[split_symbol_definition])).
% 106.18/14.00 fof(f20367,plain,(
% 106.18/14.00 sQ1555_spl|sQ1556_spl|sQ1654_spl|~sQ1_spl),
% 106.18/14.00 inference(split_clause,[status(thm)],[f20351,f19076,f19079,f20364,f210])).
% 106.18/14.00 fof(f26332,plain,(
% 106.18/14.00 ~aNaturalNumber0(sK3_skl(xk))|~isPrime0(sK3_skl(xk))|~sQ1577_spl),
% 106.18/14.00 inference(resolution,[status(thm)],[f19382,f188])).
% 106.18/14.00 fof(f26353,plain,(
% 106.18/14.00 ~sQ1654_spl|~sQ1557_spl|~sQ1577_spl),
% 106.18/14.00 inference(split_clause,[status(thm)],[f26332,f20364,f19082,f19381])).
% 106.18/14.00 fof(f26418,plain,(
% 106.18/14.00 $false),
% 106.18/14.00 inference(sat_refutation,[status(thm)],[f350,f949,f1063,f13868,f13873,f18919,f19085,f19103,f19191,f19384,f20367,f26353])).
% 106.18/14.00 % SZS output end CNFRefutation for theBenchmark.p
% 106.18/14.01 % Elapsed time: 13.648874 seconds
% 106.18/14.01 % CPU time: 107.604789 seconds
% 106.18/14.01 % Total memory used: 448.549 MB
% 106.18/14.01 % Net memory used: 414.952 MB
%------------------------------------------------------------------------------