%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM457+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 : n020.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 01:42:57 PM UTC 2026
% Result : Theorem 0.19s 0.51s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM457+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
% 0.19/0.42 % Computer : n020.cluster.edu
% 0.19/0.42 % Model : x86_64 x86_64
% 0.19/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.42 % Memory : 8046.5625MB
% 0.19/0.42 % OS : Linux 6.8.0-71-generic
% 0.19/0.42 % CPULimit : 300
% 0.19/0.42 % WCLimit : 300
% 0.19/0.42 % DateTime : Mon Sep 21 02:32:32 UTC 2026
% 0.19/0.43 % CPUTime :
% 0.19/0.44 % Drodi V4.1.1
% 0.19/0.51 % Refutation found
% 0.19/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.51 % SZS output start CNFRefutation for theBenchmark
% 0.19/0.51 fof(f2,axiom,(
% 0.19/0.51 aNaturalNumber0(sz00) ),
% 0.19/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f12,axiom,(
% 0.19/0.51 (! [W0] :( aNaturalNumber0(W0)=> ( sdtasdt0(W0,sz00) = sz00& sz00 = sdtasdt0(sz00,W0) ) ) )),
% 0.19/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f15,axiom,(
% 0.19/0.51 (! [W0] :( aNaturalNumber0(W0)=> ( W0 != sz00=> (! [W1,W2] :( ( aNaturalNumber0(W1)& aNaturalNumber0(W2) )=> ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2)| sdtasdt0(W1,W0) = sdtasdt0(W2,W0) )=> W1 = W2 ) ) )) ) )),
% 0.19/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f17,hypothesis,(
% 0.19/0.51 ( aNaturalNumber0(xm)& aNaturalNumber0(xn) ) ),
% 0.19/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f18,conjecture,(
% 0.19/0.51 ( sdtasdt0(xm,xn) = sz00=> ( xm = sz00| xn = sz00 ) ) ),
% 0.19/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.19/0.51 fof(f19,negated_conjecture,(
% 0.19/0.51 ~(( sdtasdt0(xm,xn) = sz00=> ( xm = sz00| xn = sz00 ) ) )),
% 0.19/0.51 inference(negated_conjecture,[status(cth)],[f18])).
% 0.19/0.51 fof(f23,plain,(
% 0.19/0.51 aNaturalNumber0(sz00)),
% 0.19/0.51 inference(cnf_transformation,[status(thm)],[f2])).
% 0.19/0.51 fof(f44,plain,(
% 0.19/0.51 ![W0]: (~aNaturalNumber0(W0)|(sdtasdt0(W0,sz00)=sz00&sz00=sdtasdt0(sz00,W0)))),
% 0.19/0.51 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.19/0.51 fof(f45,plain,(
% 0.19/0.51 ![X0]: (~aNaturalNumber0(X0)|sdtasdt0(X0,sz00)=sz00)),
% 0.19/0.51 inference(cnf_transformation,[status(thm)],[f44])).
% 0.19/0.51 fof(f53,plain,(
% 0.19/0.51 ![W0]: (~aNaturalNumber0(W0)|(W0=sz00|(![W1,W2]: ((~aNaturalNumber0(W1)|~aNaturalNumber0(W2))|((~sdtasdt0(W0,W1)=sdtasdt0(W0,W2)&~sdtasdt0(W1,W0)=sdtasdt0(W2,W0))|W1=W2)))))),
% 0.19/0.51 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.19/0.51 fof(f54,plain,(
% 0.19/0.51 ![X0,X1,X2]: (~aNaturalNumber0(X0)|X0=sz00|~aNaturalNumber0(X1)|~aNaturalNumber0(X2)|~sdtasdt0(X0,X1)=sdtasdt0(X0,X2)|X1=X2)),
% 0.19/0.51 inference(cnf_transformation,[status(thm)],[f53])).
% 0.19/0.51 fof(f59,plain,(
% 0.19/0.51 aNaturalNumber0(xm)),
% 0.19/0.51 inference(cnf_transformation,[status(thm)],[f17])).
% 0.19/0.51 fof(f60,plain,(
% 0.19/0.51 aNaturalNumber0(xn)),
% 0.19/0.51 inference(cnf_transformation,[status(thm)],[f17])).
% 0.19/0.51 fof(f61,plain,(
% 0.19/0.51 (sdtasdt0(xm,xn)=sz00&(~xm=sz00&~xn=sz00))),
% 0.19/0.51 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.19/0.51 fof(f62,plain,(
% 0.19/0.51 sdtasdt0(xm,xn)=sz00),
% 0.19/0.51 inference(cnf_transformation,[status(thm)],[f61])).
% 0.19/0.51 fof(f63,plain,(
% 0.19/0.51 ~xm=sz00),
% 0.19/0.51 inference(cnf_transformation,[status(thm)],[f61])).
% 0.19/0.51 fof(f64,plain,(
% 0.19/0.51 ~xn=sz00),
% 0.19/0.51 inference(cnf_transformation,[status(thm)],[f61])).
% 0.19/0.51 fof(f75,plain,(
% 0.19/0.51 sdtasdt0(xm,sz00)=sz00),
% 0.19/0.51 inference(resolution,[status(thm)],[f45,f59])).
% 0.19/0.51 fof(f169,plain,(
% 0.19/0.51 ![X0]: (~aNaturalNumber0(xm)|xm=sz00|~aNaturalNumber0(xn)|~aNaturalNumber0(X0)|~sz00=sdtasdt0(xm,X0)|xn=X0)),
% 0.19/0.51 inference(paramodulation,[status(thm)],[f62,f54])).
% 0.19/0.51 fof(f190,definition,(
% 0.19/0.51 sQ2_spl <=> (aNaturalNumber0(xm))),
% 0.19/0.51 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.19/0.51 fof(f192,plain,(
% 0.19/0.51 ~aNaturalNumber0(xm)|sQ2_spl),
% 0.19/0.51 inference(component_clause,[status(thm)],[f190])).
% 0.19/0.51 fof(f197,definition,(
% 0.19/0.51 sQ4_spl <=> (aNaturalNumber0(xn))),
% 0.19/0.51 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.19/0.51 fof(f199,plain,(
% 0.19/0.51 ~aNaturalNumber0(xn)|sQ4_spl),
% 0.19/0.51 inference(component_clause,[status(thm)],[f197])).
% 0.19/0.51 fof(f208,definition,(
% 0.19/0.51 sQ7_spl <=> (aNaturalNumber0(sz00))),
% 0.19/0.51 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.19/0.51 fof(f210,plain,(
% 0.19/0.51 ~aNaturalNumber0(sz00)|sQ7_spl),
% 0.19/0.51 inference(component_clause,[status(thm)],[f208])).
% 0.19/0.51 fof(f234,definition,(
% 0.19/0.51 sQ14_spl <=> (xn=sz00)),
% 0.19/0.51 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 0.19/0.51 fof(f235,plain,(
% 0.19/0.51 xn=sz00|~sQ14_spl),
% 0.19/0.51 inference(component_clause,[status(thm)],[f234])).
% 0.19/0.51 fof(f245,definition,(
% 0.19/0.51 sQ17_spl <=> (xm=sz00)),
% 0.19/0.51 introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 0.19/0.51 fof(f246,plain,(
% 0.19/0.51 xm=sz00|~sQ17_spl),
% 0.19/0.51 inference(component_clause,[status(thm)],[f245])).
% 0.19/0.51 fof(f256,definition,(
% 0.19/0.51 ![X0]: (sQ20_spl <=> (~aNaturalNumber0(X0)|~sz00=sdtasdt0(xm,X0)|xn=X0))),
% 0.19/0.51 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.19/0.51 fof(f257,plain,(
% 0.19/0.51 ![X0]: (~aNaturalNumber0(X0)|~sz00=sdtasdt0(xm,X0)|xn=X0|~sQ20_spl)),
% 0.19/0.51 inference(component_clause,[status(thm)],[f256])).
% 0.19/0.51 fof(f259,plain,(
% 0.19/0.51 ~sQ2_spl|sQ17_spl|~sQ4_spl|sQ20_spl),
% 0.19/0.51 inference(split_clause,[status(thm)],[f169,f190,f245,f197,f256])).
% 0.19/0.51 fof(f280,plain,(
% 0.19/0.51 $false|sQ7_spl),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f210,f23])).
% 0.19/0.51 fof(f281,plain,(
% 0.19/0.51 sQ7_spl),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f280])).
% 0.19/0.51 fof(f284,plain,(
% 0.19/0.51 $false|sQ4_spl),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f199,f60])).
% 0.19/0.51 fof(f285,plain,(
% 0.19/0.51 sQ4_spl),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f284])).
% 0.19/0.51 fof(f286,plain,(
% 0.19/0.51 $false|sQ2_spl),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f192,f59])).
% 0.19/0.51 fof(f287,plain,(
% 0.19/0.51 sQ2_spl),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f286])).
% 0.19/0.51 fof(f290,plain,(
% 0.19/0.51 $false|~sQ14_spl),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f235,f64])).
% 0.19/0.51 fof(f291,plain,(
% 0.19/0.51 ~sQ14_spl),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f290])).
% 0.19/0.51 fof(f292,plain,(
% 0.19/0.51 $false|~sQ17_spl),
% 0.19/0.51 inference(forward_subsumption_resolution,[status(thm)],[f246,f63])).
% 0.19/0.51 fof(f293,plain,(
% 0.19/0.51 ~sQ17_spl),
% 0.19/0.51 inference(contradiction_clause,[status(thm)],[f292])).
% 0.19/0.51 fof(f1018,plain,(
% 0.19/0.51 ~aNaturalNumber0(sz00)|xn=sz00|~sQ20_spl),
% 0.19/0.51 inference(resolution,[status(thm)],[f257,f75])).
% 0.19/0.51 fof(f1023,plain,(
% 0.19/0.51 ~sQ7_spl|sQ14_spl|~sQ20_spl),
% 0.19/0.51 inference(split_clause,[status(thm)],[f1018,f208,f234,f256])).
% 0.19/0.51 fof(f1034,plain,(
% 0.19/0.51 $false),
% 0.19/0.51 inference(sat_refutation,[status(thm)],[f259,f281,f285,f287,f291,f293,f1023])).
% 0.19/0.51 % SZS output end CNFRefutation for theBenchmark.p
% 0.19/0.53 % Elapsed time: 0.091020 seconds
% 0.19/0.53 % CPU time: 0.388241 seconds
% 0.19/0.53 % Total memory used: 86.517 MB
% 0.19/0.53 % Net memory used: 86.264 MB
%------------------------------------------------------------------------------