%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM465+1 : 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 : n003.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 0.24s 0.60s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM465+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.45 % Computer : n003.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Mon Sep 21 02:34:01 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.47 % Drodi V4.1.1
% 0.24/0.60 % Refutation found
% 0.24/0.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.24/0.60 % SZS output start CNFRefutation for theBenchmark
% 0.24/0.60 fof(f2,axiom,(
% 0.24/0.60 aNaturalNumber0(sz00) ),
% 0.24/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.60 fof(f3,axiom,(
% 0.24/0.60 ( aNaturalNumber0(sz10)& sz10 != sz00 ) ),
% 0.24/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.60 fof(f11,axiom,(
% 0.24/0.60 (! [W0] :( aNaturalNumber0(W0)=> ( sdtasdt0(W0,sz10) = W0& W0 = sdtasdt0(sz10,W0) ) ) )),
% 0.24/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.60 fof(f12,axiom,(
% 0.24/0.60 (! [W0] :( aNaturalNumber0(W0)=> ( sdtasdt0(W0,sz00) = sz00& sz00 = sdtasdt0(sz00,W0) ) ) )),
% 0.24/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.60 fof(f23,axiom,(
% 0.24/0.60 (! [W0,W1] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1) )=> ( sdtlseqdt0(W0,W1)| ( W1 != W0& sdtlseqdt0(W1,W0) ) ) ) )),
% 0.24/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.60 fof(f25,axiom,(
% 0.24/0.60 (! [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)) ) ) ) )),
% 0.24/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.60 fof(f27,hypothesis,(
% 0.24/0.60 ( aNaturalNumber0(xm)& aNaturalNumber0(xn) ) ),
% 0.24/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.60 fof(f28,hypothesis,(
% 0.24/0.60 ( xm != sz00=> sdtlseqdt0(sz10,xm) ) ),
% 0.24/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.60 fof(f29,conjecture,(
% 0.24/0.60 ( xm != sz00=> sdtlseqdt0(xn,sdtasdt0(xn,xm)) ) ),
% 0.24/0.60 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.24/0.60 fof(f30,negated_conjecture,(
% 0.24/0.60 ~(( xm != sz00=> sdtlseqdt0(xn,sdtasdt0(xn,xm)) ) )),
% 0.24/0.60 inference(negated_conjecture,[status(cth)],[f29])).
% 0.24/0.60 fof(f34,plain,(
% 0.24/0.60 aNaturalNumber0(sz00)),
% 0.24/0.60 inference(cnf_transformation,[status(thm)],[f2])).
% 0.24/0.60 fof(f35,plain,(
% 0.24/0.60 aNaturalNumber0(sz10)),
% 0.24/0.60 inference(cnf_transformation,[status(thm)],[f3])).
% 0.24/0.60 fof(f52,plain,(
% 0.24/0.60 ![W0]: (~aNaturalNumber0(W0)|(sdtasdt0(W0,sz10)=W0&W0=sdtasdt0(sz10,W0)))),
% 0.24/0.60 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.24/0.60 fof(f53,plain,(
% 0.24/0.60 ![X0]: (~aNaturalNumber0(X0)|sdtasdt0(X0,sz10)=X0)),
% 0.24/0.60 inference(cnf_transformation,[status(thm)],[f52])).
% 0.24/0.60 fof(f55,plain,(
% 0.24/0.60 ![W0]: (~aNaturalNumber0(W0)|(sdtasdt0(W0,sz00)=sz00&sz00=sdtasdt0(sz00,W0)))),
% 0.24/0.60 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.24/0.60 fof(f57,plain,(
% 0.24/0.60 ![X0]: (~aNaturalNumber0(X0)|sz00=sdtasdt0(sz00,X0))),
% 0.24/0.60 inference(cnf_transformation,[status(thm)],[f55])).
% 0.24/0.60 fof(f90,plain,(
% 0.24/0.60 ![W0,W1]: ((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|(sdtlseqdt0(W0,W1)|(~W1=W0&sdtlseqdt0(W1,W0))))),
% 0.24/0.60 inference(pre_NNF_transformation,[status(thm)],[f23])).
% 0.24/0.60 fof(f92,plain,(
% 0.24/0.60 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|sdtlseqdt0(X0,X1)|sdtlseqdt0(X1,X0))),
% 0.24/0.60 inference(cnf_transformation,[status(thm)],[f90])).
% 0.24/0.60 fof(f98,plain,(
% 0.24/0.60 ![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)))))),
% 0.24/0.60 inference(pre_NNF_transformation,[status(thm)],[f25])).
% 0.24/0.60 fof(f100,plain,(
% 0.24/0.60 ![X0,X1,X2]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|~aNaturalNumber0(X2)|X0=sz00|X1=X2|~sdtlseqdt0(X1,X2)|sdtlseqdt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)))),
% 0.24/0.60 inference(cnf_transformation,[status(thm)],[f98])).
% 0.24/0.60 fof(f106,plain,(
% 0.24/0.60 aNaturalNumber0(xm)),
% 0.24/0.60 inference(cnf_transformation,[status(thm)],[f27])).
% 0.24/0.60 fof(f107,plain,(
% 0.24/0.60 aNaturalNumber0(xn)),
% 0.24/0.60 inference(cnf_transformation,[status(thm)],[f27])).
% 0.24/0.60 fof(f108,plain,(
% 0.24/0.60 xm=sz00|sdtlseqdt0(sz10,xm)),
% 0.24/0.60 inference(pre_NNF_transformation,[status(thm)],[f28])).
% 0.24/0.60 fof(f109,plain,(
% 0.24/0.60 xm=sz00|sdtlseqdt0(sz10,xm)),
% 0.24/0.60 inference(cnf_transformation,[status(thm)],[f108])).
% 0.24/0.60 fof(f110,plain,(
% 0.24/0.60 (~xm=sz00&~sdtlseqdt0(xn,sdtasdt0(xn,xm)))),
% 0.24/0.60 inference(pre_NNF_transformation,[status(thm)],[f30])).
% 0.24/0.60 fof(f111,plain,(
% 0.24/0.60 ~xm=sz00),
% 0.24/0.60 inference(cnf_transformation,[status(thm)],[f110])).
% 0.24/0.60 fof(f112,plain,(
% 0.24/0.60 ~sdtlseqdt0(xn,sdtasdt0(xn,xm))),
% 0.24/0.60 inference(cnf_transformation,[status(thm)],[f110])).
% 0.24/0.60 fof(f113,definition,(
% 0.24/0.60 sQ0_spl <=> (xm=sz00)),
% 0.24/0.60 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.24/0.60 fof(f114,plain,(
% 0.24/0.60 xm=sz00|~sQ0_spl),
% 0.24/0.60 inference(component_clause,[status(thm)],[f113])).
% 0.24/0.60 fof(f116,definition,(
% 0.24/0.60 sQ1_spl <=> (sdtlseqdt0(sz10,xm))),
% 0.24/0.60 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.24/0.60 fof(f117,plain,(
% 0.24/0.60 sdtlseqdt0(sz10,xm)|~sQ1_spl),
% 0.24/0.60 inference(component_clause,[status(thm)],[f116])).
% 0.24/0.60 fof(f119,plain,(
% 0.24/0.60 sQ0_spl|sQ1_spl),
% 0.24/0.60 inference(split_clause,[status(thm)],[f109,f113,f116])).
% 0.24/0.60 fof(f128,plain,(
% 0.24/0.60 $false|~sQ0_spl),
% 0.24/0.60 inference(forward_subsumption_resolution,[status(thm)],[f114,f111])).
% 0.24/0.60 fof(f129,plain,(
% 0.24/0.60 ~sQ0_spl),
% 0.24/0.60 inference(contradiction_clause,[status(thm)],[f128])).
% 0.24/0.60 fof(f163,plain,(
% 0.24/0.60 sdtasdt0(xn,sz10)=xn),
% 0.24/0.60 inference(resolution,[status(thm)],[f53,f107])).
% 0.24/0.60 fof(f171,plain,(
% 0.24/0.60 ![X0]: (~aNaturalNumber0(X0)|sdtlseqdt0(xn,X0)|sdtlseqdt0(X0,xn))),
% 0.24/0.60 inference(resolution,[status(thm)],[f92,f107])).
% 0.24/0.60 fof(f173,plain,(
% 0.24/0.60 ![X0]: (~aNaturalNumber0(X0)|sdtlseqdt0(sz00,X0)|sdtlseqdt0(X0,sz00))),
% 0.24/0.60 inference(resolution,[status(thm)],[f92,f34])).
% 0.24/0.60 fof(f201,plain,(
% 0.24/0.60 sdtlseqdt0(xn,xn)|sdtlseqdt0(xn,xn)),
% 0.24/0.60 inference(resolution,[status(thm)],[f171,f107])).
% 0.24/0.60 fof(f205,definition,(
% 0.24/0.60 sQ8_spl <=> (sdtlseqdt0(xn,xn))),
% 0.24/0.60 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.24/0.60 fof(f206,plain,(
% 0.24/0.60 sdtlseqdt0(xn,xn)|~sQ8_spl),
% 0.24/0.60 inference(component_clause,[status(thm)],[f205])).
% 0.24/0.60 fof(f208,plain,(
% 0.24/0.60 sQ8_spl),
% 0.24/0.60 inference(split_clause,[status(thm)],[f201,f205])).
% 0.24/0.60 fof(f251,definition,(
% 0.24/0.60 sQ18_spl <=> (xn=sz00)),
% 0.24/0.60 introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 0.24/0.60 fof(f252,plain,(
% 0.24/0.60 xn=sz00|~sQ18_spl),
% 0.24/0.60 inference(component_clause,[status(thm)],[f251])).
% 0.24/0.60 fof(f271,plain,(
% 0.24/0.60 ~sdtlseqdt0(xn,sdtasdt0(sz00,xm))|~sQ18_spl),
% 0.24/0.60 inference(backward_demodulation,[status(thm)],[f252,f112])).
% 0.24/0.60 fof(f289,plain,(
% 0.24/0.60 ~sdtlseqdt0(sz00,sdtasdt0(sz00,xm))|~sQ18_spl),
% 0.24/0.60 inference(forward_demodulation,[status(thm)],[f252,f271])).
% 0.24/0.60 fof(f330,definition,(
% 0.24/0.60 sQ29_spl <=> (aNaturalNumber0(sz10))),
% 0.24/0.60 introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 0.24/0.60 fof(f332,plain,(
% 0.24/0.60 ~aNaturalNumber0(sz10)|sQ29_spl),
% 0.24/0.60 inference(component_clause,[status(thm)],[f330])).
% 0.24/0.60 fof(f333,definition,(
% 0.24/0.60 sQ30_spl <=> (aNaturalNumber0(xm))),
% 0.24/0.60 introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition])).
% 0.24/0.60 fof(f335,plain,(
% 0.24/0.60 ~aNaturalNumber0(xm)|sQ30_spl),
% 0.24/0.60 inference(component_clause,[status(thm)],[f333])).
% 0.24/0.60 fof(f336,definition,(
% 0.24/0.60 sQ31_spl <=> (sz10=xm)),
% 0.24/0.60 introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition])).
% 0.24/0.60 fof(f337,plain,(
% 0.24/0.60 sz10=xm|~sQ31_spl),
% 0.24/0.60 inference(component_clause,[status(thm)],[f336])).
% 0.24/0.60 fof(f387,plain,(
% 0.24/0.60 $false|sQ29_spl),
% 0.24/0.60 inference(forward_subsumption_resolution,[status(thm)],[f332,f35])).
% 0.24/0.60 fof(f388,plain,(
% 0.24/0.60 sQ29_spl),
% 0.24/0.60 inference(contradiction_clause,[status(thm)],[f387])).
% 0.24/0.60 fof(f395,plain,(
% 0.24/0.60 ~sdtlseqdt0(xn,sdtasdt0(xn,sz10))|~sQ31_spl),
% 0.24/0.60 inference(forward_demodulation,[status(thm)],[f337,f112])).
% 0.24/0.60 fof(f397,plain,(
% 0.24/0.60 ~sdtlseqdt0(xn,xn)|~sQ31_spl),
% 0.24/0.60 inference(backward_demodulation,[status(thm)],[f163,f395])).
% 0.24/0.60 fof(f399,plain,(
% 0.24/0.60 $false|~sQ8_spl|~sQ31_spl),
% 0.24/0.60 inference(forward_subsumption_resolution,[status(thm)],[f397,f206])).
% 0.24/0.60 fof(f400,plain,(
% 0.24/0.60 ~sQ8_spl|~sQ31_spl),
% 0.24/0.60 inference(contradiction_clause,[status(thm)],[f399])).
% 0.24/0.60 fof(f401,plain,(
% 0.24/0.60 $false|sQ30_spl),
% 0.24/0.60 inference(forward_subsumption_resolution,[status(thm)],[f106,f335])).
% 0.24/0.60 fof(f402,plain,(
% 0.24/0.60 sQ30_spl),
% 0.24/0.60 inference(contradiction_clause,[status(thm)],[f401])).
% 0.24/0.60 fof(f416,plain,(
% 0.24/0.60 sdtlseqdt0(sz00,sz00)|sdtlseqdt0(sz00,sz00)),
% 0.24/0.60 inference(resolution,[status(thm)],[f173,f34])).
% 0.24/0.60 fof(f418,definition,(
% 0.24/0.60 sQ34_spl <=> (sdtlseqdt0(sz00,sz00))),
% 0.24/0.60 introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition])).
% 0.24/0.60 fof(f419,plain,(
% 0.24/0.60 sdtlseqdt0(sz00,sz00)|~sQ34_spl),
% 0.24/0.60 inference(component_clause,[status(thm)],[f418])).
% 0.24/0.60 fof(f421,plain,(
% 0.24/0.60 sQ34_spl),
% 0.24/0.60 inference(split_clause,[status(thm)],[f416,f418])).
% 0.24/0.60 fof(f476,plain,(
% 0.24/0.60 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|xn=sz00|X0=X1|~sdtlseqdt0(X0,X1)|sdtlseqdt0(sdtasdt0(xn,X0),sdtasdt0(xn,X1)))),
% 0.24/0.60 inference(resolution,[status(thm)],[f107,f100])).
% 0.24/0.60 fof(f500,definition,(
% 0.24/0.60 ![X0,X1]: (sQ41_spl <=> (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|X0=X1|~sdtlseqdt0(X0,X1)|sdtlseqdt0(sdtasdt0(xn,X0),sdtasdt0(xn,X1))))),
% 0.24/0.60 introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition])).
% 0.24/0.60 fof(f501,plain,(
% 0.24/0.60 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|X0=X1|~sdtlseqdt0(X0,X1)|sdtlseqdt0(sdtasdt0(xn,X0),sdtasdt0(xn,X1))|~sQ41_spl)),
% 0.24/0.60 inference(component_clause,[status(thm)],[f500])).
% 0.24/0.60 fof(f503,plain,(
% 0.24/0.60 sQ41_spl|sQ18_spl),
% 0.24/0.60 inference(split_clause,[status(thm)],[f476,f500,f251])).
% 0.24/0.60 fof(f602,plain,(
% 0.24/0.60 sz00=sdtasdt0(sz00,xm)),
% 0.24/0.60 inference(resolution,[status(thm)],[f106,f57])).
% 0.24/0.60 fof(f628,plain,(
% 0.24/0.60 ~sdtlseqdt0(sz00,sz00)|~sQ18_spl),
% 0.24/0.60 inference(backward_demodulation,[status(thm)],[f602,f289])).
% 0.24/0.60 fof(f644,plain,(
% 0.24/0.60 $false|~sQ34_spl|~sQ18_spl),
% 0.24/0.60 inference(forward_subsumption_resolution,[status(thm)],[f628,f419])).
% 0.24/0.60 fof(f645,plain,(
% 0.24/0.60 ~sQ34_spl|~sQ18_spl),
% 0.24/0.60 inference(contradiction_clause,[status(thm)],[f644])).
% 0.24/0.60 fof(f664,plain,(
% 0.24/0.60 ~aNaturalNumber0(sz10)|~aNaturalNumber0(xm)|sz10=xm|sdtlseqdt0(sdtasdt0(xn,sz10),sdtasdt0(xn,xm))|~sQ41_spl|~sQ1_spl),
% 0.24/0.60 inference(resolution,[status(thm)],[f501,f117])).
% 0.24/0.60 fof(f665,definition,(
% 0.24/0.60 sQ55_spl <=> (sdtlseqdt0(sdtasdt0(xn,sz10),sdtasdt0(xn,xm)))),
% 0.24/0.60 introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition])).
% 0.24/0.60 fof(f666,plain,(
% 0.24/0.60 sdtlseqdt0(sdtasdt0(xn,sz10),sdtasdt0(xn,xm))|~sQ55_spl),
% 0.24/0.60 inference(component_clause,[status(thm)],[f665])).
% 0.24/0.60 fof(f668,plain,(
% 0.24/0.60 ~sQ29_spl|~sQ30_spl|sQ31_spl|sQ55_spl|~sQ41_spl|~sQ1_spl),
% 0.24/0.60 inference(split_clause,[status(thm)],[f664,f330,f333,f336,f665,f500,f116])).
% 0.24/0.60 fof(f669,plain,(
% 0.24/0.60 sdtlseqdt0(xn,sdtasdt0(xn,xm))|~sQ55_spl),
% 0.24/0.60 inference(forward_demodulation,[status(thm)],[f163,f666])).
% 0.24/0.60 fof(f670,plain,(
% 0.24/0.60 $false|~sQ55_spl),
% 0.24/0.60 inference(forward_subsumption_resolution,[status(thm)],[f669,f112])).
% 0.24/0.60 fof(f671,plain,(
% 0.24/0.60 ~sQ55_spl),
% 0.24/0.60 inference(contradiction_clause,[status(thm)],[f670])).
% 0.24/0.60 fof(f672,plain,(
% 0.24/0.60 $false),
% 0.24/0.60 inference(sat_refutation,[status(thm)],[f119,f129,f208,f388,f400,f402,f421,f503,f645,f668,f671])).
% 0.24/0.60 % SZS output end CNFRefutation for theBenchmark.p
% 0.24/0.63 % Elapsed time: 0.163303 seconds
% 0.24/0.63 % CPU time: 0.857919 seconds
% 0.24/0.63 % Total memory used: 78.560 MB
% 0.24/0.63 % Net memory used: 77.740 MB
%------------------------------------------------------------------------------