%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM465+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 0.10s 0.70s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM465+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n026.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 21 02:35:08 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.40 % Drodi V4.1.1
% 0.10/0.70 % Refutation found
% 0.10/0.70 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.70 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.70 fof(f2,axiom,(
% 0.10/0.70 aNaturalNumber0(sz00) ),
% 0.10/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.70 fof(f3,axiom,(
% 0.10/0.70 ( aNaturalNumber0(sz10)& sz10 != sz00 ) ),
% 0.10/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.70 fof(f8,axiom,(
% 0.10/0.70 (! [W0] :( aNaturalNumber0(W0)=> ( sdtpldt0(W0,sz00) = W0& W0 = sdtpldt0(sz00,W0) ) ) )),
% 0.10/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.70 fof(f11,axiom,(
% 0.10/0.70 (! [W0] :( aNaturalNumber0(W0)=> ( sdtasdt0(W0,sz10) = W0& W0 = sdtasdt0(sz10,W0) ) ) )),
% 0.10/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.70 fof(f12,axiom,(
% 0.10/0.70 (! [W0] :( aNaturalNumber0(W0)=> ( sdtasdt0(W0,sz00) = sz00& sz00 = sdtasdt0(sz00,W0) ) ) )),
% 0.10/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.70 fof(f25,axiom,(
% 0.10/0.70 (! [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)) ) ) ) )),
% 0.10/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.70 fof(f27,hypothesis,(
% 0.10/0.70 ( aNaturalNumber0(xm)& aNaturalNumber0(xn) ) ),
% 0.10/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.70 fof(f28,hypothesis,(
% 0.10/0.70 ( xm != sz00=> ( (? [W0] :( aNaturalNumber0(W0)& sdtpldt0(sz10,W0) = xm ))& sdtlseqdt0(sz10,xm) ) ) ),
% 0.10/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.70 fof(f29,conjecture,(
% 0.10/0.70 ( xm != sz00=> ( (? [W0] :( aNaturalNumber0(W0)& sdtpldt0(xn,W0) = sdtasdt0(xn,xm) ))| sdtlseqdt0(xn,sdtasdt0(xn,xm)) ) ) ),
% 0.10/0.70 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.70 fof(f30,negated_conjecture,(
% 0.10/0.70 ~(( xm != sz00=> ( (? [W0] :( aNaturalNumber0(W0)& sdtpldt0(xn,W0) = sdtasdt0(xn,xm) ))| sdtlseqdt0(xn,sdtasdt0(xn,xm)) ) ) )),
% 0.10/0.70 inference(negated_conjecture,[status(cth)],[f29])).
% 0.10/0.70 fof(f34,plain,(
% 0.10/0.70 aNaturalNumber0(sz00)),
% 0.10/0.70 inference(cnf_transformation,[status(thm)],[f2])).
% 0.10/0.70 fof(f35,plain,(
% 0.10/0.70 aNaturalNumber0(sz10)),
% 0.10/0.70 inference(cnf_transformation,[status(thm)],[f3])).
% 0.10/0.70 fof(f45,plain,(
% 0.10/0.70 ![W0]: (~aNaturalNumber0(W0)|(sdtpldt0(W0,sz00)=W0&W0=sdtpldt0(sz00,W0)))),
% 0.10/0.70 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.10/0.70 fof(f46,plain,(
% 0.10/0.70 ![X0]: (~aNaturalNumber0(X0)|sdtpldt0(X0,sz00)=X0)),
% 0.10/0.70 inference(cnf_transformation,[status(thm)],[f45])).
% 0.10/0.70 fof(f52,plain,(
% 0.10/0.70 ![W0]: (~aNaturalNumber0(W0)|(sdtasdt0(W0,sz10)=W0&W0=sdtasdt0(sz10,W0)))),
% 0.10/0.70 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.10/0.70 fof(f53,plain,(
% 0.10/0.70 ![X0]: (~aNaturalNumber0(X0)|sdtasdt0(X0,sz10)=X0)),
% 0.10/0.70 inference(cnf_transformation,[status(thm)],[f52])).
% 0.10/0.70 fof(f55,plain,(
% 0.10/0.70 ![W0]: (~aNaturalNumber0(W0)|(sdtasdt0(W0,sz00)=sz00&sz00=sdtasdt0(sz00,W0)))),
% 0.10/0.70 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.10/0.70 fof(f57,plain,(
% 0.10/0.70 ![X0]: (~aNaturalNumber0(X0)|sz00=sdtasdt0(sz00,X0))),
% 0.10/0.70 inference(cnf_transformation,[status(thm)],[f55])).
% 0.10/0.70 fof(f98,plain,(
% 0.10/0.70 ![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)))))),
% 0.10/0.70 inference(pre_NNF_transformation,[status(thm)],[f25])).
% 0.10/0.70 fof(f100,plain,(
% 0.10/0.70 ![X0,X1,X2]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|~aNaturalNumber0(X2)|X0=sz00|X1=X2|~sdtlseqdt0(X1,X2)|sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)))),
% 0.10/0.70 inference(cnf_transformation,[status(thm)],[f98])).
% 0.10/0.70 fof(f106,plain,(
% 0.10/0.70 aNaturalNumber0(xm)),
% 0.10/0.70 inference(cnf_transformation,[status(thm)],[f27])).
% 0.10/0.70 fof(f107,plain,(
% 0.10/0.70 aNaturalNumber0(xn)),
% 0.10/0.70 inference(cnf_transformation,[status(thm)],[f27])).
% 0.10/0.70 fof(f108,plain,(
% 0.10/0.70 xm=sz00|((?[W0]: (aNaturalNumber0(W0)&sdtpldt0(sz10,W0)=xm))&sdtlseqdt0(sz10,xm))),
% 0.10/0.70 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 0.10/0.70 fof(f109,plain,(
% 0.10/0.70 xm=sz00|((aNaturalNumber0(sK1_skl)&sdtpldt0(sz10,sK1_skl)=xm)&sdtlseqdt0(sz10,xm))),
% 0.10/0.70 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W0,sK1_skl)],[f108])).
% 0.10/0.70 fof(f112,plain,(
% 0.10/0.70 xm=sz00|sdtlseqdt0(sz10,xm)),
% 0.10/0.70 inference(cnf_transformation,[status(thm)],[f109])).
% 0.10/0.70 fof(f113,plain,(
% 0.10/0.70 (~xm=sz00&((![W0]: (~aNaturalNumber0(W0)|~sdtpldt0(xn,W0)=sdtasdt0(xn,xm)))&~sdtlseqdt0(xn,sdtasdt0(xn,xm))))),
% 0.10/0.70 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 0.10/0.70 fof(f114,plain,(
% 0.10/0.70 ~xm=sz00),
% 0.10/0.70 inference(cnf_transformation,[status(thm)],[f113])).
% 0.10/0.70 fof(f115,plain,(
% 0.10/0.70 ![X0]: (~aNaturalNumber0(X0)|~sdtpldt0(xn,X0)=sdtasdt0(xn,xm))),
% 0.10/0.70 inference(cnf_transformation,[status(thm)],[f113])).
% 0.10/0.70 fof(f116,plain,(
% 0.10/0.70 ~sdtlseqdt0(xn,sdtasdt0(xn,xm))),
% 0.10/0.70 inference(cnf_transformation,[status(thm)],[f113])).
% 0.10/0.70 fof(f117,definition,(
% 0.10/0.70 sQ0_spl <=> (xm=sz00)),
% 0.10/0.70 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.10/0.70 fof(f118,plain,(
% 0.10/0.70 xm=sz00|~sQ0_spl),
% 0.10/0.70 inference(component_clause,[status(thm)],[f117])).
% 0.10/0.70 fof(f128,definition,(
% 0.10/0.70 sQ3_spl <=> (sdtlseqdt0(sz10,xm))),
% 0.10/0.70 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.10/0.70 fof(f129,plain,(
% 0.10/0.70 sdtlseqdt0(sz10,xm)|~sQ3_spl),
% 0.10/0.70 inference(component_clause,[status(thm)],[f128])).
% 0.10/0.70 fof(f131,plain,(
% 0.10/0.70 sQ0_spl|sQ3_spl),
% 0.10/0.70 inference(split_clause,[status(thm)],[f112,f117,f128])).
% 0.10/0.70 fof(f140,plain,(
% 0.10/0.70 $false|~sQ0_spl),
% 0.10/0.70 inference(forward_subsumption_resolution,[status(thm)],[f118,f114])).
% 0.10/0.70 fof(f141,plain,(
% 0.10/0.70 ~sQ0_spl),
% 0.10/0.70 inference(contradiction_clause,[status(thm)],[f140])).
% 0.10/0.70 fof(f142,plain,(
% 0.10/0.70 ~sdtpldt0(xn,sz00)=sdtasdt0(xn,xm)),
% 0.10/0.70 inference(resolution,[status(thm)],[f34,f115])).
% 0.10/0.70 fof(f162,plain,(
% 0.10/0.70 sdtpldt0(xn,sz00)=xn),
% 0.10/0.70 inference(resolution,[status(thm)],[f46,f107])).
% 0.10/0.70 fof(f166,plain,(
% 0.10/0.70 ~xn=sdtasdt0(xn,xm)),
% 0.10/0.70 inference(backward_demodulation,[status(thm)],[f162,f142])).
% 0.10/0.70 fof(f179,plain,(
% 0.10/0.70 sdtasdt0(xn,sz10)=xn),
% 0.10/0.70 inference(resolution,[status(thm)],[f53,f107])).
% 0.10/0.70 fof(f261,definition,(
% 0.10/0.70 sQ18_spl <=> (xn=sz00)),
% 0.10/0.70 introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 0.10/0.70 fof(f262,plain,(
% 0.10/0.70 xn=sz00|~sQ18_spl),
% 0.10/0.70 inference(component_clause,[status(thm)],[f261])).
% 0.10/0.70 fof(f301,plain,(
% 0.10/0.70 ~xn=sdtasdt0(sz00,xm)|~sQ18_spl),
% 0.10/0.70 inference(backward_demodulation,[status(thm)],[f262,f166])).
% 0.10/0.70 fof(f319,plain,(
% 0.10/0.70 ~sz00=sdtasdt0(sz00,xm)|~sQ18_spl),
% 0.10/0.70 inference(forward_demodulation,[status(thm)],[f262,f301])).
% 0.10/0.70 fof(f406,definition,(
% 0.10/0.70 sQ39_spl <=> (xm=sz10)),
% 0.10/0.70 introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition])).
% 0.10/0.70 fof(f407,plain,(
% 0.10/0.70 xm=sz10|~sQ39_spl),
% 0.10/0.70 inference(component_clause,[status(thm)],[f406])).
% 0.10/0.70 fof(f421,plain,(
% 0.10/0.70 sz00=sdtasdt0(sz00,xm)),
% 0.10/0.70 inference(resolution,[status(thm)],[f57,f106])).
% 0.10/0.70 fof(f423,plain,(
% 0.10/0.70 $false|~sQ18_spl),
% 0.10/0.70 inference(forward_subsumption_resolution,[status(thm)],[f421,f319])).
% 0.10/0.70 fof(f424,plain,(
% 0.10/0.70 ~sQ18_spl),
% 0.10/0.70 inference(contradiction_clause,[status(thm)],[f423])).
% 0.10/0.70 fof(f474,plain,(
% 0.10/0.70 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|xn=sz00|X0=X1|~sdtlseqdt0(X0,X1)|sdtlseqdt0(sdtasdt0(xn,X0),sdtasdt0(xn,X1)))),
% 0.10/0.70 inference(resolution,[status(thm)],[f107,f100])).
% 0.10/0.70 fof(f505,definition,(
% 0.10/0.70 ![X0,X1]: (sQ46_spl <=> (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|X0=X1|~sdtlseqdt0(X0,X1)|sdtlseqdt0(sdtasdt0(xn,X0),sdtasdt0(xn,X1))))),
% 0.10/0.70 introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition])).
% 0.10/0.70 fof(f506,plain,(
% 0.10/0.70 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|X0=X1|~sdtlseqdt0(X0,X1)|sdtlseqdt0(sdtasdt0(xn,X0),sdtasdt0(xn,X1))|~sQ46_spl)),
% 0.10/0.70 inference(component_clause,[status(thm)],[f505])).
% 0.10/0.70 fof(f508,plain,(
% 0.10/0.70 sQ46_spl|sQ18_spl),
% 0.10/0.70 inference(split_clause,[status(thm)],[f474,f505,f261])).
% 0.10/0.70 fof(f520,plain,(
% 0.10/0.70 ~aNaturalNumber0(sz10)|~aNaturalNumber0(xm)|sz10=xm|sdtlseqdt0(sdtasdt0(xn,sz10),sdtasdt0(xn,xm))|~sQ3_spl|~sQ46_spl),
% 0.10/0.70 inference(resolution,[status(thm)],[f129,f506])).
% 0.10/0.70 fof(f528,definition,(
% 0.10/0.70 sQ49_spl <=> (aNaturalNumber0(sz10))),
% 0.10/0.70 introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition])).
% 0.10/0.70 fof(f530,plain,(
% 0.10/0.70 ~aNaturalNumber0(sz10)|sQ49_spl),
% 0.10/0.70 inference(component_clause,[status(thm)],[f528])).
% 0.10/0.70 fof(f531,definition,(
% 0.10/0.70 sQ50_spl <=> (aNaturalNumber0(xm))),
% 0.10/0.72 introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition])).
% 0.10/0.72 fof(f533,plain,(
% 0.10/0.72 ~aNaturalNumber0(xm)|sQ50_spl),
% 0.10/0.72 inference(component_clause,[status(thm)],[f531])).
% 0.10/0.72 fof(f534,definition,(
% 0.10/0.72 sQ51_spl <=> (sdtlseqdt0(sdtasdt0(xn,sz10),sdtasdt0(xn,xm)))),
% 0.10/0.72 introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition])).
% 0.10/0.72 fof(f535,plain,(
% 0.10/0.72 sdtlseqdt0(sdtasdt0(xn,sz10),sdtasdt0(xn,xm))|~sQ51_spl),
% 0.10/0.72 inference(component_clause,[status(thm)],[f534])).
% 0.10/0.72 fof(f537,plain,(
% 0.10/0.72 ~sQ49_spl|~sQ50_spl|sQ39_spl|sQ51_spl|~sQ3_spl|~sQ46_spl),
% 0.10/0.72 inference(split_clause,[status(thm)],[f520,f528,f531,f406,f534,f128,f505])).
% 0.10/0.72 fof(f570,plain,(
% 0.10/0.72 ~xn=sdtasdt0(xn,sz10)|~sQ39_spl),
% 0.10/0.72 inference(backward_demodulation,[status(thm)],[f407,f166])).
% 0.10/0.72 fof(f606,plain,(
% 0.10/0.72 ~xn=xn|~sQ39_spl),
% 0.10/0.72 inference(forward_demodulation,[status(thm)],[f179,f570])).
% 0.10/0.72 fof(f607,plain,(
% 0.10/0.72 $false|~sQ39_spl),
% 0.10/0.72 inference(trivial_equality_resolution,[status(thm)],[f606])).
% 0.10/0.72 fof(f608,plain,(
% 0.10/0.72 ~sQ39_spl),
% 0.10/0.72 inference(contradiction_clause,[status(thm)],[f607])).
% 0.10/0.72 fof(f609,plain,(
% 0.10/0.72 $false|sQ50_spl),
% 0.10/0.72 inference(forward_subsumption_resolution,[status(thm)],[f106,f533])).
% 0.10/0.72 fof(f610,plain,(
% 0.10/0.72 sQ50_spl),
% 0.10/0.72 inference(contradiction_clause,[status(thm)],[f609])).
% 0.10/0.72 fof(f611,plain,(
% 0.10/0.72 $false|sQ49_spl),
% 0.10/0.72 inference(forward_subsumption_resolution,[status(thm)],[f530,f35])).
% 0.10/0.72 fof(f612,plain,(
% 0.10/0.72 sQ49_spl),
% 0.10/0.72 inference(contradiction_clause,[status(thm)],[f611])).
% 0.10/0.72 fof(f620,plain,(
% 0.10/0.72 sdtlseqdt0(xn,sdtasdt0(xn,xm))|~sQ51_spl),
% 0.10/0.72 inference(forward_demodulation,[status(thm)],[f179,f535])).
% 0.10/0.72 fof(f621,plain,(
% 0.10/0.72 $false|~sQ51_spl),
% 0.10/0.72 inference(forward_subsumption_resolution,[status(thm)],[f620,f116])).
% 0.10/0.72 fof(f622,plain,(
% 0.10/0.72 ~sQ51_spl),
% 0.10/0.72 inference(contradiction_clause,[status(thm)],[f621])).
% 0.10/0.72 fof(f623,plain,(
% 0.10/0.72 $false),
% 0.10/0.72 inference(sat_refutation,[status(thm)],[f131,f141,f424,f508,f537,f608,f610,f612,f622])).
% 0.10/0.72 % SZS output end CNFRefutation for theBenchmark.p
% 0.48/0.72 % Elapsed time: 0.335825 seconds
% 0.48/0.72 % CPU time: 2.392096 seconds
% 0.48/0.72 % Total memory used: 98.482 MB
% 0.48/0.72 % Net memory used: 96.770 MB
%------------------------------------------------------------------------------