%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM476+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 : n007.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 01:43:00 PM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM476+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n007.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 02:31:35 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.45 % Refutation found
% 0.12/0.45 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.45 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.45 fof(f8,axiom,(
% 0.12/0.45 (! [W0] :( aNaturalNumber0(W0)=> ( sdtpldt0(W0,sz00) = W0& W0 = sdtpldt0(sz00,W0) ) ) )),
% 0.12/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f12,axiom,(
% 0.12/0.45 (! [W0] :( aNaturalNumber0(W0)=> ( sdtasdt0(W0,sz00) = sz00& sz00 = sdtasdt0(sz00,W0) ) ) )),
% 0.12/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f34,hypothesis,(
% 0.12/0.45 ( aNaturalNumber0(xl)& aNaturalNumber0(xm)& aNaturalNumber0(xn) ) ),
% 0.12/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f35,hypothesis,(
% 0.12/0.45 ( (? [W0] :( aNaturalNumber0(W0)& xm = sdtasdt0(xl,W0) ))& doDivides0(xl,xm)& (? [W0] :( aNaturalNumber0(W0)& sdtpldt0(xm,xn) = sdtasdt0(xl,W0) ))& doDivides0(xl,sdtpldt0(xm,xn)) ) ),
% 0.12/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f36,conjecture,(
% 0.12/0.45 ( ( xl != sz00=> (? [W0] :( aNaturalNumber0(W0)& xm = sdtasdt0(xl,W0)& W0 = sdtsldt0(xm,xl)& (? [W1] :( aNaturalNumber0(W1)& sdtpldt0(xm,xn) = sdtasdt0(xl,W1)& W1 = sdtsldt0(sdtpldt0(xm,xn),xl)& (? [W2] :( aNaturalNumber0(W2)& sdtpldt0(W0,W2) = W1 ))& sdtlseqdt0(W0,W1)& (? [W2] :( aNaturalNumber0(W2)& sdtpldt0(W0,W2) = W1& W2 = sdtmndt0(W1,W0)& sdtpldt0(sdtasdt0(xl,W0),sdtasdt0(xl,W2)) = sdtpldt0(sdtasdt0(xl,W0),xn)& xn = sdtasdt0(xl,W2) ) )) )) ))=> ( (? [W0] :( aNaturalNumber0(W0)& xn = sdtasdt0(xl,W0) ))| doDivides0(xl,xn) ) ) ),
% 0.12/0.45 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f37,negated_conjecture,(
% 0.12/0.45 ~(( ( xl != sz00=> (? [W0] :( aNaturalNumber0(W0)& xm = sdtasdt0(xl,W0)& W0 = sdtsldt0(xm,xl)& (? [W1] :( aNaturalNumber0(W1)& sdtpldt0(xm,xn) = sdtasdt0(xl,W1)& W1 = sdtsldt0(sdtpldt0(xm,xn),xl)& (? [W2] :( aNaturalNumber0(W2)& sdtpldt0(W0,W2) = W1 ))& sdtlseqdt0(W0,W1)& (? [W2] :( aNaturalNumber0(W2)& sdtpldt0(W0,W2) = W1& W2 = sdtmndt0(W1,W0)& sdtpldt0(sdtasdt0(xl,W0),sdtasdt0(xl,W2)) = sdtpldt0(sdtasdt0(xl,W0),xn)& xn = sdtasdt0(xl,W2) ) )) )) ))=> ( (? [W0] :( aNaturalNumber0(W0)& xn = sdtasdt0(xl,W0) ))| doDivides0(xl,xn) ) ) )),
% 0.12/0.45 inference(negated_conjecture,[status(cth)],[f36])).
% 0.12/0.45 fof(f52,plain,(
% 0.12/0.45 ![W0]: (~aNaturalNumber0(W0)|(sdtpldt0(W0,sz00)=W0&W0=sdtpldt0(sz00,W0)))),
% 0.12/0.45 inference(pre_NNF_transformation,[status(thm)],[f8])).
% 0.12/0.45 fof(f54,plain,(
% 0.12/0.45 ![X0]: (~aNaturalNumber0(X0)|X0=sdtpldt0(sz00,X0))),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f52])).
% 0.12/0.45 fof(f62,plain,(
% 0.12/0.45 ![W0]: (~aNaturalNumber0(W0)|(sdtasdt0(W0,sz00)=sz00&sz00=sdtasdt0(sz00,W0)))),
% 0.12/0.45 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.12/0.45 fof(f64,plain,(
% 0.12/0.45 ![X0]: (~aNaturalNumber0(X0)|sz00=sdtasdt0(sz00,X0))),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f62])).
% 0.12/0.45 fof(f137,plain,(
% 0.12/0.45 aNaturalNumber0(xn)),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f34])).
% 0.12/0.45 fof(f138,plain,(
% 0.12/0.45 (((aNaturalNumber0(sK2_skl)&xm=sdtasdt0(xl,sK2_skl))&doDivides0(xl,xm))&(aNaturalNumber0(sK3_skl)&sdtpldt0(xm,xn)=sdtasdt0(xl,sK3_skl)))&doDivides0(xl,sdtpldt0(xm,xn))),
% 0.12/0.45 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(W0,sK2_skl),skolemize(W0,sK3_skl)],[f35])).
% 0.12/0.45 fof(f139,plain,(
% 0.12/0.45 aNaturalNumber0(sK2_skl)),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f138])).
% 0.12/0.45 fof(f140,plain,(
% 0.12/0.45 xm=sdtasdt0(xl,sK2_skl)),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f138])).
% 0.12/0.45 fof(f144,plain,(
% 0.12/0.45 doDivides0(xl,sdtpldt0(xm,xn))),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f138])).
% 0.12/0.45 fof(f145,plain,(
% 0.12/0.45 ((xl=sz00|(?[W0]: (((aNaturalNumber0(W0)&xm=sdtasdt0(xl,W0))&W0=sdtsldt0(xm,xl))&(?[W1]: (((((aNaturalNumber0(W1)&sdtpldt0(xm,xn)=sdtasdt0(xl,W1))&W1=sdtsldt0(sdtpldt0(xm,xn),xl))&(?[W2]: (aNaturalNumber0(W2)&sdtpldt0(W0,W2)=W1)))&sdtlseqdt0(W0,W1))&(?[W2]: ((((aNaturalNumber0(W2)&sdtpldt0(W0,W2)=W1)&W2=sdtmndt0(W1,W0))&sdtpldt0(sdtasdt0(xl,W0),sdtasdt0(xl,W2))=sdtpldt0(sdtasdt0(xl,W0),xn))&xn=sdtasdt0(xl,W2))))))))&((![W0]: (~aNaturalNumber0(W0)|~xn=sdtasdt0(xl,W0)))&~doDivides0(xl,xn)))),
% 0.12/0.45 inference(pre_NNF_transformation,[status(thm)],[f37])).
% 0.12/0.45 fof(f146,plain,(
% 0.12/0.45 (xl=sz00|(((aNaturalNumber0(sK4_skl)&xm=sdtasdt0(xl,sK4_skl))&sK4_skl=sdtsldt0(xm,xl))&(((((aNaturalNumber0(sK5_skl)&sdtpldt0(xm,xn)=sdtasdt0(xl,sK5_skl))&sK5_skl=sdtsldt0(sdtpldt0(xm,xn),xl))&(aNaturalNumber0(sK6_skl)&sdtpldt0(sK4_skl,sK6_skl)=sK5_skl))&sdtlseqdt0(sK4_skl,sK5_skl))&((((aNaturalNumber0(sK7_skl)&sdtpldt0(sK4_skl,sK7_skl)=sK5_skl)&sK7_skl=sdtmndt0(sK5_skl,sK4_skl))&sdtpldt0(sdtasdt0(xl,sK4_skl),sdtasdt0(xl,sK7_skl))=sdtpldt0(sdtasdt0(xl,sK4_skl),xn))&xn=sdtasdt0(xl,sK7_skl)))))&((![W0]: (~aNaturalNumber0(W0)|~xn=sdtasdt0(xl,W0)))&~doDivides0(xl,xn))),
% 0.12/0.46 inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl,sK6_skl,sK7_skl]),skolemize(W0,sK4_skl),skolemize(W1,sK5_skl),skolemize(W2,sK6_skl),skolemize(W2,sK7_skl)],[f145])).
% 0.12/0.46 fof(f156,plain,(
% 0.12/0.46 xl=sz00|aNaturalNumber0(sK7_skl)),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f146])).
% 0.12/0.46 fof(f160,plain,(
% 0.12/0.46 xl=sz00|xn=sdtasdt0(xl,sK7_skl)),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f146])).
% 0.12/0.46 fof(f161,plain,(
% 0.12/0.46 ![X0]: (~aNaturalNumber0(X0)|~xn=sdtasdt0(xl,X0))),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f146])).
% 0.12/0.46 fof(f162,plain,(
% 0.12/0.46 ~doDivides0(xl,xn)),
% 0.12/0.46 inference(cnf_transformation,[status(thm)],[f146])).
% 0.12/0.46 fof(f163,definition,(
% 0.12/0.46 sQ0_spl <=> (xl=sz00)),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f164,plain,(
% 0.12/0.46 xl=sz00|~sQ0_spl),
% 0.12/0.46 inference(component_clause,[status(thm)],[f163])).
% 0.12/0.46 fof(f202,definition,(
% 0.12/0.46 sQ10_spl <=> (aNaturalNumber0(sK7_skl))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f203,plain,(
% 0.12/0.46 aNaturalNumber0(sK7_skl)|~sQ10_spl),
% 0.12/0.46 inference(component_clause,[status(thm)],[f202])).
% 0.12/0.46 fof(f205,plain,(
% 0.12/0.46 sQ0_spl|sQ10_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f156,f163,f202])).
% 0.12/0.46 fof(f218,definition,(
% 0.12/0.46 sQ14_spl <=> (xn=sdtasdt0(xl,sK7_skl))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f219,plain,(
% 0.12/0.46 xn=sdtasdt0(xl,sK7_skl)|~sQ14_spl),
% 0.12/0.46 inference(component_clause,[status(thm)],[f218])).
% 0.12/0.46 fof(f221,plain,(
% 0.12/0.46 sQ0_spl|sQ14_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f160,f163,f218])).
% 0.12/0.46 fof(f346,plain,(
% 0.12/0.46 ~xn=sdtasdt0(xl,sK7_skl)|~sQ10_spl),
% 0.12/0.46 inference(resolution,[status(thm)],[f203,f161])).
% 0.12/0.46 fof(f358,plain,(
% 0.12/0.46 xn=sdtpldt0(sz00,xn)),
% 0.12/0.46 inference(resolution,[status(thm)],[f54,f137])).
% 0.12/0.46 fof(f465,plain,(
% 0.12/0.46 ~xn=xn|~sQ14_spl|~sQ10_spl),
% 0.12/0.46 inference(forward_demodulation,[status(thm)],[f219,f346])).
% 0.12/0.46 fof(f466,plain,(
% 0.12/0.46 $false|~sQ14_spl|~sQ10_spl),
% 0.12/0.46 inference(trivial_equality_resolution,[status(thm)],[f465])).
% 0.12/0.46 fof(f467,plain,(
% 0.12/0.46 ~sQ14_spl|~sQ10_spl),
% 0.12/0.46 inference(contradiction_clause,[status(thm)],[f466])).
% 0.12/0.46 fof(f482,plain,(
% 0.12/0.46 ![X0]: (~aNaturalNumber0(X0)|xl=sdtasdt0(sz00,X0)|~sQ0_spl)),
% 0.12/0.46 inference(forward_demodulation,[status(thm)],[f164,f64])).
% 0.12/0.46 fof(f483,plain,(
% 0.12/0.46 ![X0]: (~aNaturalNumber0(X0)|xl=sdtasdt0(xl,X0)|~sQ0_spl)),
% 0.12/0.46 inference(forward_demodulation,[status(thm)],[f164,f482])).
% 0.12/0.46 fof(f486,plain,(
% 0.12/0.46 xl=sdtasdt0(xl,sK2_skl)|~sQ0_spl),
% 0.12/0.46 inference(resolution,[status(thm)],[f483,f139])).
% 0.12/0.46 fof(f492,plain,(
% 0.12/0.46 xl=xm|~sQ0_spl),
% 0.12/0.46 inference(forward_demodulation,[status(thm)],[f140,f486])).
% 0.12/0.46 fof(f496,plain,(
% 0.12/0.46 xm=sz00|~sQ0_spl),
% 0.12/0.46 inference(backward_demodulation,[status(thm)],[f492,f164])).
% 0.12/0.46 fof(f508,plain,(
% 0.12/0.46 ~doDivides0(xm,xn)|~sQ0_spl),
% 0.12/0.46 inference(backward_demodulation,[status(thm)],[f492,f162])).
% 0.12/0.46 fof(f713,plain,(
% 0.12/0.46 xn=sdtpldt0(xm,xn)|~sQ0_spl),
% 0.12/0.46 inference(forward_demodulation,[status(thm)],[f496,f358])).
% 0.12/0.46 fof(f1269,plain,(
% 0.12/0.46 doDivides0(xm,sdtpldt0(xm,xn))|~sQ0_spl),
% 0.12/0.46 inference(forward_demodulation,[status(thm)],[f492,f144])).
% 0.12/0.46 fof(f1368,plain,(
% 0.12/0.46 doDivides0(xm,xn)|~sQ0_spl),
% 0.12/0.46 inference(backward_demodulation,[status(thm)],[f713,f1269])).
% 0.12/0.46 fof(f1369,plain,(
% 0.12/0.46 $false|~sQ0_spl),
% 0.12/0.46 inference(forward_subsumption_resolution,[status(thm)],[f1368,f508])).
% 0.12/0.46 fof(f1370,plain,(
% 0.12/0.46 ~sQ0_spl),
% 0.12/0.46 inference(contradiction_clause,[status(thm)],[f1369])).
% 0.12/0.46 fof(f1371,plain,(
% 0.12/0.46 $false),
% 0.12/0.46 inference(sat_refutation,[status(thm)],[f205,f221,f467,f1370])).
% 0.12/0.46 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.47 % Elapsed time: 0.100092 seconds
% 0.12/0.47 % CPU time: 0.546869 seconds
% 0.12/0.47 % Total memory used: 111.724 MB
% 0.12/0.47 % Net memory used: 110.960 MB
%------------------------------------------------------------------------------