%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM463+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 : n008.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 01:42:58 PM UTC 2026
% Result : Theorem 0.18s 5.55s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM463+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/5.42 % Computer : n008.cluster.edu
% 0.12/5.42 % Model : x86_64 x86_64
% 0.12/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.42 % Memory : 8046.5625MB
% 0.12/5.42 % OS : Linux 6.8.0-71-generic
% 0.12/5.42 % CPULimit : 300
% 0.12/5.42 % WCLimit : 300
% 0.12/5.42 % DateTime : Mon Sep 21 02:32:46 UTC 2026
% 0.12/5.43 % CPUTime :
% 0.12/5.44 % Drodi V4.1.1
% 0.18/5.55 % Refutation found
% 0.18/5.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/5.55 % SZS output start CNFRefutation for theBenchmark
% 0.18/5.55 fof(f2,axiom,(
% 0.18/5.55 aNaturalNumber0(sz00) ),
% 0.18/5.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/5.55 fof(f3,axiom,(
% 0.18/5.55 ( aNaturalNumber0(sz10)& sz10 != sz00 ) ),
% 0.18/5.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/5.55 fof(f11,axiom,(
% 0.18/5.55 (! [W0] :( aNaturalNumber0(W0)=> ( sdtasdt0(W0,sz10) = W0& W0 = sdtasdt0(sz10,W0) ) ) )),
% 0.18/5.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/5.55 fof(f12,axiom,(
% 0.18/5.55 (! [W0] :( aNaturalNumber0(W0)=> ( sdtasdt0(W0,sz00) = sz00& sz00 = sdtasdt0(sz00,W0) ) ) )),
% 0.18/5.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/5.55 fof(f20,axiom,(
% 0.18/5.55 (! [W0] :( aNaturalNumber0(W0)=> sdtlseqdt0(W0,W0) ) )),
% 0.18/5.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/5.55 fof(f25,axiom,(
% 0.18/5.55 (! [W0,W1,W2] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1)& aNaturalNumber0(W2) )=> ( ( W0 != sz00& W1 != W2& sdtlseqdt0(W1,W2) )=> ( sdtasdt0(W0,W1) != sdtasdt0(W0,W2)& sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2))& sdtasdt0(W1,W0) != sdtasdt0(W2,W0)& sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
% 0.18/5.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/5.55 fof(f26,axiom,(
% 0.18/5.55 (! [W0] :( aNaturalNumber0(W0)=> ( W0 = sz00| W0 = sz10| ( sz10 != W0& sdtlseqdt0(sz10,W0) ) ) ) )),
% 0.18/5.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/5.55 fof(f27,hypothesis,(
% 0.18/5.55 ( aNaturalNumber0(xm)& aNaturalNumber0(xn) ) ),
% 0.18/5.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/5.55 fof(f28,conjecture,(
% 0.18/5.55 ( xm != sz00=> sdtlseqdt0(xn,sdtasdt0(xn,xm)) ) ),
% 0.18/5.55 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.18/5.55 fof(f29,negated_conjecture,(
% 0.18/5.55 ~(( xm != sz00=> sdtlseqdt0(xn,sdtasdt0(xn,xm)) ) )),
% 0.18/5.55 inference(negated_conjecture,[status(cth)],[f28])).
% 0.18/5.55 fof(f33,plain,(
% 0.18/5.55 aNaturalNumber0(sz00)),
% 0.18/5.55 inference(cnf_transformation,[status(thm)],[f2])).
% 0.18/5.55 fof(f34,plain,(
% 0.18/5.55 aNaturalNumber0(sz10)),
% 0.18/5.55 inference(cnf_transformation,[status(thm)],[f3])).
% 0.18/5.55 fof(f51,plain,(
% 0.18/5.55 ![W0]: (~aNaturalNumber0(W0)|(sdtasdt0(W0,sz10)=W0&W0=sdtasdt0(sz10,W0)))),
% 0.18/5.55 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.18/5.55 fof(f52,plain,(
% 0.18/5.55 ![X0]: (~aNaturalNumber0(X0)|sdtasdt0(X0,sz10)=X0)),
% 0.18/5.55 inference(cnf_transformation,[status(thm)],[f51])).
% 0.18/5.55 fof(f54,plain,(
% 0.18/5.55 ![W0]: (~aNaturalNumber0(W0)|(sdtasdt0(W0,sz00)=sz00&sz00=sdtasdt0(sz00,W0)))),
% 0.18/5.55 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.18/5.55 fof(f56,plain,(
% 0.18/5.55 ![X0]: (~aNaturalNumber0(X0)|sz00=sdtasdt0(sz00,X0))),
% 0.18/5.55 inference(cnf_transformation,[status(thm)],[f54])).
% 0.18/5.55 fof(f83,plain,(
% 0.18/5.55 ![W0]: (~aNaturalNumber0(W0)|sdtlseqdt0(W0,W0))),
% 0.18/5.55 inference(pre_NNF_transformation,[status(thm)],[f20])).
% 0.18/5.55 fof(f84,plain,(
% 0.18/5.55 ![X0]: (~aNaturalNumber0(X0)|sdtlseqdt0(X0,X0))),
% 0.18/5.55 inference(cnf_transformation,[status(thm)],[f83])).
% 0.18/5.55 fof(f97,plain,(
% 0.18/5.55 ![W0,W1,W2]: (((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|~aNaturalNumber0(W2))|(((W0=sz00|W1=W2)|~sdtlseqdt0(W1,W2))|(((~sdtasdt0(W0,W1)=sdtasdt0(W0,W2)&sdtlseqdt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)))&~sdtasdt0(W1,W0)=sdtasdt0(W2,W0))&sdtlseqdt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)))))),
% 0.18/5.55 inference(pre_NNF_transformation,[status(thm)],[f25])).
% 0.18/5.55 fof(f99,plain,(
% 0.18/5.55 ![X0,X1,X2]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|~aNaturalNumber0(X2)|X0=sz00|X1=X2|~sdtlseqdt0(X1,X2)|sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)))),
% 0.18/5.55 inference(cnf_transformation,[status(thm)],[f97])).
% 0.18/5.55 fof(f102,plain,(
% 0.18/5.55 ![W0]: (~aNaturalNumber0(W0)|((W0=sz00|W0=sz10)|(~sz10=W0&sdtlseqdt0(sz10,W0))))),
% 0.18/5.55 inference(pre_NNF_transformation,[status(thm)],[f26])).
% 0.18/5.55 fof(f104,plain,(
% 0.18/5.55 ![X0]: (~aNaturalNumber0(X0)|X0=sz00|X0=sz10|sdtlseqdt0(sz10,X0))),
% 0.18/5.55 inference(cnf_transformation,[status(thm)],[f102])).
% 0.18/5.55 fof(f105,plain,(
% 0.18/5.55 aNaturalNumber0(xm)),
% 0.18/5.55 inference(cnf_transformation,[status(thm)],[f27])).
% 0.18/5.55 fof(f106,plain,(
% 0.18/5.55 aNaturalNumber0(xn)),
% 0.18/5.55 inference(cnf_transformation,[status(thm)],[f27])).
% 0.18/5.55 fof(f107,plain,(
% 0.18/5.55 (~xm=sz00&~sdtlseqdt0(xn,sdtasdt0(xn,xm)))),
% 0.18/5.55 inference(pre_NNF_transformation,[status(thm)],[f29])).
% 0.18/5.55 fof(f108,plain,(
% 0.18/5.55 ~xm=sz00),
% 0.18/5.55 inference(cnf_transformation,[status(thm)],[f107])).
% 0.18/5.55 fof(f109,plain,(
% 0.18/5.55 ~sdtlseqdt0(xn,sdtasdt0(xn,xm))),
% 0.18/5.55 inference(cnf_transformation,[status(thm)],[f107])).
% 0.18/5.55 fof(f135,plain,(
% 0.18/5.55 sdtlseqdt0(xn,xn)),
% 0.18/5.55 inference(resolution,[status(thm)],[f84,f106])).
% 0.18/5.55 fof(f137,plain,(
% 0.18/5.55 sdtlseqdt0(sz00,sz00)),
% 0.18/5.55 inference(resolution,[status(thm)],[f84,f33])).
% 0.18/5.55 fof(f155,plain,(
% 0.18/5.55 sdtasdt0(xn,sz10)=xn),
% 0.18/5.55 inference(resolution,[status(thm)],[f52,f106])).
% 0.18/5.55 fof(f181,definition,(
% 0.18/5.55 sQ3_spl <=> (sdtlseqdt0(sz10,xm))),
% 0.18/5.55 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.18/5.55 fof(f182,plain,(
% 0.18/5.55 sdtlseqdt0(sz10,xm)|~sQ3_spl),
% 0.18/5.55 inference(component_clause,[status(thm)],[f181])).
% 0.18/5.55 fof(f246,definition,(
% 0.18/5.55 sQ17_spl <=> (xn=sz00)),
% 0.18/5.55 introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 0.18/5.55 fof(f247,plain,(
% 0.18/5.55 xn=sz00|~sQ17_spl),
% 0.18/5.55 inference(component_clause,[status(thm)],[f246])).
% 0.18/5.55 fof(f253,definition,(
% 0.18/5.55 sQ19_spl <=> (xm=sz00)),
% 0.18/5.55 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.18/5.55 fof(f254,plain,(
% 0.18/5.55 xm=sz00|~sQ19_spl),
% 0.18/5.55 inference(component_clause,[status(thm)],[f253])).
% 0.18/5.55 fof(f267,plain,(
% 0.18/5.55 $false|~sQ19_spl),
% 0.18/5.55 inference(forward_subsumption_resolution,[status(thm)],[f254,f108])).
% 0.18/5.55 fof(f268,plain,(
% 0.18/5.55 ~sQ19_spl),
% 0.18/5.55 inference(contradiction_clause,[status(thm)],[f267])).
% 0.18/5.55 fof(f271,plain,(
% 0.18/5.55 ~sdtlseqdt0(xn,sdtasdt0(sz00,xm))|~sQ17_spl),
% 0.18/5.55 inference(backward_demodulation,[status(thm)],[f247,f109])).
% 0.18/5.55 fof(f289,plain,(
% 0.18/5.55 ~sdtlseqdt0(sz00,sdtasdt0(sz00,xm))|~sQ17_spl),
% 0.18/5.55 inference(forward_demodulation,[status(thm)],[f247,f271])).
% 0.18/5.55 fof(f369,plain,(
% 0.18/5.55 xm=sz00|xm=sz10|sdtlseqdt0(sz10,xm)),
% 0.18/5.55 inference(resolution,[status(thm)],[f104,f105])).
% 0.18/5.55 fof(f375,definition,(
% 0.18/5.55 sQ37_spl <=> (xm=sz10)),
% 0.18/5.55 introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition])).
% 0.18/5.55 fof(f376,plain,(
% 0.18/5.55 xm=sz10|~sQ37_spl),
% 0.18/5.55 inference(component_clause,[status(thm)],[f375])).
% 0.18/5.55 fof(f378,plain,(
% 0.18/5.55 sQ19_spl|sQ37_spl|sQ3_spl),
% 0.18/5.55 inference(split_clause,[status(thm)],[f369,f253,f375,f181])).
% 0.18/5.55 fof(f386,definition,(
% 0.18/5.55 sQ38_spl <=> (aNaturalNumber0(sz10))),
% 0.18/5.55 introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition])).
% 0.18/5.55 fof(f388,plain,(
% 0.18/5.55 ~aNaturalNumber0(sz10)|sQ38_spl),
% 0.18/5.55 inference(component_clause,[status(thm)],[f386])).
% 0.18/5.55 fof(f414,plain,(
% 0.18/5.55 sz00=sdtasdt0(sz00,xm)),
% 0.18/5.55 inference(resolution,[status(thm)],[f56,f105])).
% 0.18/5.55 fof(f416,plain,(
% 0.18/5.55 ~sdtlseqdt0(sz00,sz00)|~sQ17_spl),
% 0.18/5.55 inference(backward_demodulation,[status(thm)],[f414,f289])).
% 0.18/5.55 fof(f417,plain,(
% 0.18/5.55 $false|~sQ17_spl),
% 0.18/5.55 inference(forward_subsumption_resolution,[status(thm)],[f416,f137])).
% 0.18/5.55 fof(f418,plain,(
% 0.18/5.55 ~sQ17_spl),
% 0.18/5.55 inference(contradiction_clause,[status(thm)],[f417])).
% 0.18/5.55 fof(f459,plain,(
% 0.18/5.55 $false|sQ38_spl),
% 0.18/5.55 inference(forward_subsumption_resolution,[status(thm)],[f388,f34])).
% 0.18/5.55 fof(f460,plain,(
% 0.18/5.55 sQ38_spl),
% 0.18/5.55 inference(contradiction_clause,[status(thm)],[f459])).
% 0.18/5.55 fof(f472,plain,(
% 0.18/5.55 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|xn=sz00|X0=X1|~sdtlseqdt0(X0,X1)|sdtlseqdt0(sdtasdt0(xn,X0),sdtasdt0(xn,X1)))),
% 0.18/5.55 inference(resolution,[status(thm)],[f106,f99])).
% 0.18/5.55 fof(f504,definition,(
% 0.18/5.55 ![X0,X1]: (sQ51_spl <=> (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|X0=X1|~sdtlseqdt0(X0,X1)|sdtlseqdt0(sdtasdt0(xn,X0),sdtasdt0(xn,X1))))),
% 0.18/5.55 introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition])).
% 0.18/5.55 fof(f505,plain,(
% 0.18/5.55 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|X0=X1|~sdtlseqdt0(X0,X1)|sdtlseqdt0(sdtasdt0(xn,X0),sdtasdt0(xn,X1))|~sQ51_spl)),
% 0.18/5.55 inference(component_clause,[status(thm)],[f504])).
% 0.18/5.55 fof(f507,plain,(
% 0.18/5.55 sQ51_spl|sQ17_spl),
% 0.18/5.55 inference(split_clause,[status(thm)],[f472,f504,f246])).
% 0.18/5.55 fof(f553,definition,(
% 0.18/5.55 sQ56_spl <=> (aNaturalNumber0(xm))),
% 0.18/5.55 introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition])).
% 0.18/5.55 fof(f555,plain,(
% 0.18/5.55 ~aNaturalNumber0(xm)|sQ56_spl),
% 0.18/5.55 inference(component_clause,[status(thm)],[f553])).
% 0.18/5.55 fof(f587,plain,(
% 0.18/5.55 $false|sQ56_spl),
% 0.18/5.55 inference(forward_subsumption_resolution,[status(thm)],[f555,f105])).
% 0.18/5.55 fof(f588,plain,(
% 0.18/5.55 sQ56_spl),
% 0.18/5.55 inference(contradiction_clause,[status(thm)],[f587])).
% 0.18/5.55 fof(f688,plain,(
% 0.18/5.58 ~aNaturalNumber0(sz10)|~aNaturalNumber0(xm)|sz10=xm|sdtlseqdt0(sdtasdt0(xn,sz10),sdtasdt0(xn,xm))|~sQ3_spl|~sQ51_spl),
% 0.18/5.58 inference(resolution,[status(thm)],[f182,f505])).
% 0.18/5.58 fof(f698,definition,(
% 0.18/5.58 sQ83_spl <=> (sdtlseqdt0(sdtasdt0(xn,sz10),sdtasdt0(xn,xm)))),
% 0.18/5.58 introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition])).
% 0.18/5.58 fof(f699,plain,(
% 0.18/5.58 sdtlseqdt0(sdtasdt0(xn,sz10),sdtasdt0(xn,xm))|~sQ83_spl),
% 0.18/5.58 inference(component_clause,[status(thm)],[f698])).
% 0.18/5.58 fof(f701,plain,(
% 0.18/5.58 ~sQ38_spl|~sQ56_spl|sQ37_spl|sQ83_spl|~sQ3_spl|~sQ51_spl),
% 0.18/5.58 inference(split_clause,[status(thm)],[f688,f386,f553,f375,f698,f181,f504])).
% 0.18/5.58 fof(f737,plain,(
% 0.18/5.58 ~sdtlseqdt0(xn,sdtasdt0(xn,sz10))|~sQ37_spl),
% 0.18/5.58 inference(backward_demodulation,[status(thm)],[f376,f109])).
% 0.18/5.58 fof(f769,plain,(
% 0.18/5.58 ~sdtlseqdt0(xn,xn)|~sQ37_spl),
% 0.18/5.58 inference(forward_demodulation,[status(thm)],[f155,f737])).
% 0.18/5.58 fof(f770,plain,(
% 0.18/5.58 $false|~sQ37_spl),
% 0.18/5.58 inference(forward_subsumption_resolution,[status(thm)],[f769,f135])).
% 0.18/5.58 fof(f771,plain,(
% 0.18/5.58 ~sQ37_spl),
% 0.18/5.58 inference(contradiction_clause,[status(thm)],[f770])).
% 0.18/5.58 fof(f775,plain,(
% 0.18/5.58 sdtlseqdt0(xn,sdtasdt0(xn,xm))|~sQ83_spl),
% 0.18/5.58 inference(forward_demodulation,[status(thm)],[f155,f699])).
% 0.18/5.58 fof(f776,plain,(
% 0.18/5.58 $false|~sQ83_spl),
% 0.18/5.58 inference(forward_subsumption_resolution,[status(thm)],[f109,f775])).
% 0.18/5.58 fof(f777,plain,(
% 0.18/5.58 ~sQ83_spl),
% 0.18/5.58 inference(contradiction_clause,[status(thm)],[f776])).
% 0.18/5.58 fof(f778,plain,(
% 0.18/5.58 $false),
% 0.18/5.58 inference(sat_refutation,[status(thm)],[f268,f378,f418,f460,f507,f588,f701,f771,f777])).
% 0.18/5.58 % SZS output end CNFRefutation for theBenchmark.p
% 0.18/5.58 % Elapsed time: 0.136703 seconds
% 0.18/5.58 % CPU time: 0.848582 seconds
% 0.18/5.58 % Total memory used: 92.214 MB
% 0.18/5.58 % Net memory used: 90.932 MB
%------------------------------------------------------------------------------