%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : NUM480+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 : 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 01:43:00 PM UTC 2026
% Result : Theorem 5.33s 1.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM480+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
% 0.08/0.58 % Computer : n020.cluster.edu
% 0.08/0.58 % Model : x86_64 x86_64
% 0.08/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.58 % Memory : 8046.5625MB
% 0.08/0.58 % OS : Linux 6.8.0-71-generic
% 0.08/0.58 % CPULimit : 300
% 0.08/0.58 % WCLimit : 300
% 0.08/0.58 % DateTime : Mon Sep 21 02:34:33 UTC 2026
% 0.08/0.58 % CPUTime :
% 0.08/0.60 % Drodi V4.1.1
% 5.33/1.40 % Refutation found
% 5.33/1.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 5.33/1.40 % SZS output start CNFRefutation for theBenchmark
% 5.33/1.40 fof(f10,axiom,(
% 5.33/1.40 (! [W0,W1,W2] :( ( aNaturalNumber0(W0)& aNaturalNumber0(W1)& aNaturalNumber0(W2) )=> sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ) )),
% 5.33/1.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.33/1.40 fof(f15,axiom,(
% 5.33/1.40 (! [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 ) ) )) ) )),
% 5.33/1.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.33/1.40 fof(f36,hypothesis,(
% 5.33/1.40 ( aNaturalNumber0(xl)& aNaturalNumber0(xm) ) ),
% 5.33/1.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.33/1.40 fof(f37,hypothesis,(
% 5.33/1.40 ( xl != sz00& (? [W0] :( aNaturalNumber0(W0)& xm = sdtasdt0(xl,W0) ))& doDivides0(xl,xm) ) ),
% 5.33/1.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.33/1.40 fof(f38,hypothesis,(
% 5.33/1.40 aNaturalNumber0(xn) ),
% 5.33/1.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.33/1.40 fof(f39,hypothesis,(
% 5.33/1.40 ( aNaturalNumber0(sdtsldt0(xm,xl))& xm = sdtasdt0(xl,sdtsldt0(xm,xl))& aNaturalNumber0(sdtsldt0(sdtasdt0(xn,xm),xl))& sdtasdt0(xn,xm) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl))& sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl)) = sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl)) ) ),
% 5.33/1.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.33/1.40 fof(f40,conjecture,(
% 5.33/1.40 ( ( aNaturalNumber0(sdtsldt0(xm,xl))& xm = sdtasdt0(xl,sdtsldt0(xm,xl)) )=> ( sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))| sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl) ) ) ),
% 5.33/1.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 5.33/1.40 fof(f41,negated_conjecture,(
% 5.33/1.40 ~(( ( aNaturalNumber0(sdtsldt0(xm,xl))& xm = sdtasdt0(xl,sdtsldt0(xm,xl)) )=> ( sdtasdt0(xn,xm) = sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))| sdtasdt0(xn,sdtsldt0(xm,xl)) = sdtsldt0(sdtasdt0(xn,xm),xl) ) ) )),
% 5.33/1.40 inference(negated_conjecture,[status(cth)],[f40])).
% 5.33/1.40 fof(f61,plain,(
% 5.33/1.40 ![W0,W1,W2]: (((~aNaturalNumber0(W0)|~aNaturalNumber0(W1))|~aNaturalNumber0(W2))|sdtasdt0(sdtasdt0(W0,W1),W2)=sdtasdt0(W0,sdtasdt0(W1,W2)))),
% 5.33/1.40 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 5.33/1.40 fof(f62,plain,(
% 5.33/1.40 ![X0,X1,X2]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|~aNaturalNumber0(X2)|sdtasdt0(sdtasdt0(X0,X1),X2)=sdtasdt0(X0,sdtasdt0(X1,X2)))),
% 5.33/1.40 inference(cnf_transformation,[status(thm)],[f61])).
% 5.33/1.40 fof(f75,plain,(
% 5.33/1.40 ![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)))))),
% 5.33/1.40 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 5.33/1.40 fof(f76,plain,(
% 5.33/1.40 ![X0,X1,X2]: (~aNaturalNumber0(X0)|X0=sz00|~aNaturalNumber0(X1)|~aNaturalNumber0(X2)|~sdtasdt0(X0,X1)=sdtasdt0(X0,X2)|X1=X2)),
% 5.33/1.40 inference(cnf_transformation,[status(thm)],[f75])).
% 5.33/1.40 fof(f143,plain,(
% 5.33/1.40 aNaturalNumber0(xl)),
% 5.33/1.40 inference(cnf_transformation,[status(thm)],[f36])).
% 5.33/1.40 fof(f145,plain,(
% 5.33/1.40 (~xl=sz00&(aNaturalNumber0(sK2_skl)&xm=sdtasdt0(xl,sK2_skl)))&doDivides0(xl,xm)),
% 5.33/1.40 inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(W0,sK2_skl)],[f37])).
% 5.33/1.40 fof(f146,plain,(
% 5.33/1.40 ~xl=sz00),
% 5.33/1.40 inference(cnf_transformation,[status(thm)],[f145])).
% 5.33/1.40 fof(f147,plain,(
% 5.33/1.40 aNaturalNumber0(sK2_skl)),
% 5.33/1.40 inference(cnf_transformation,[status(thm)],[f145])).
% 5.33/1.40 fof(f148,plain,(
% 5.33/1.40 xm=sdtasdt0(xl,sK2_skl)),
% 5.33/1.40 inference(cnf_transformation,[status(thm)],[f145])).
% 5.33/1.40 fof(f150,plain,(
% 5.33/1.40 aNaturalNumber0(xn)),
% 5.33/1.40 inference(cnf_transformation,[status(thm)],[f38])).
% 5.33/1.40 fof(f154,plain,(
% 5.33/1.40 sdtasdt0(xn,xm)=sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl))),
% 5.33/1.40 inference(cnf_transformation,[status(thm)],[f39])).
% 5.33/1.40 fof(f155,plain,(
% 5.33/1.40 sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl))=sdtasdt0(xl,sdtsldt0(sdtasdt0(xn,xm),xl))),
% 5.33/1.40 inference(cnf_transformation,[status(thm)],[f39])).
% 5.33/1.40 fof(f156,plain,(
% 5.33/1.40 ((aNaturalNumber0(sdtsldt0(xm,xl))&xm=sdtasdt0(xl,sdtsldt0(xm,xl)))&(~sdtasdt0(xn,xm)=sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))&~sdtasdt0(xn,sdtsldt0(xm,xl))=sdtsldt0(sdtasdt0(xn,xm),xl)))),
% 5.33/1.40 inference(pre_NNF_transformation,[status(thm)],[f41])).
% 5.33/1.40 fof(f157,plain,(
% 5.33/1.40 aNaturalNumber0(sdtsldt0(xm,xl))),
% 5.33/1.40 inference(cnf_transformation,[status(thm)],[f156])).
% 5.33/1.40 fof(f158,plain,(
% 5.33/1.40 xm=sdtasdt0(xl,sdtsldt0(xm,xl))),
% 5.33/1.40 inference(cnf_transformation,[status(thm)],[f156])).
% 5.33/1.40 fof(f159,plain,(
% 5.33/1.40 ~sdtasdt0(xn,xm)=sdtasdt0(xl,sdtasdt0(xn,sdtsldt0(xm,xl)))),
% 5.33/1.40 inference(cnf_transformation,[status(thm)],[f156])).
% 5.33/1.40 fof(f172,plain,(
% 5.33/1.40 sdtasdt0(sdtasdt0(xl,xn),sdtsldt0(xm,xl))=sdtasdt0(xn,xm)),
% 5.33/1.40 inference(forward_demodulation,[status(thm)],[f154,f155])).
% 5.33/1.40 fof(f195,definition,(
% 5.33/1.40 sQ4_spl <=> (aNaturalNumber0(sdtsldt0(xm,xl)))),
% 5.33/1.40 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 5.33/1.40 fof(f197,plain,(
% 5.33/1.40 ~aNaturalNumber0(sdtsldt0(xm,xl))|sQ4_spl),
% 5.33/1.40 inference(component_clause,[status(thm)],[f195])).
% 5.33/1.40 fof(f199,definition,(
% 5.33/1.40 sQ5_spl <=> (aNaturalNumber0(xl))),
% 5.33/1.40 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 5.33/1.40 fof(f201,plain,(
% 5.33/1.40 ~aNaturalNumber0(xl)|sQ5_spl),
% 5.33/1.40 inference(component_clause,[status(thm)],[f199])).
% 5.33/1.40 fof(f202,definition,(
% 5.33/1.40 sQ6_spl <=> (xl=sz00)),
% 5.33/1.40 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 5.33/1.40 fof(f203,plain,(
% 5.33/1.40 xl=sz00|~sQ6_spl),
% 5.33/1.40 inference(component_clause,[status(thm)],[f202])).
% 5.33/1.40 fof(f222,plain,(
% 5.33/1.40 $false|sQ4_spl),
% 5.33/1.40 inference(forward_subsumption_resolution,[status(thm)],[f197,f157])).
% 5.33/1.40 fof(f223,plain,(
% 5.33/1.40 sQ4_spl),
% 5.33/1.40 inference(contradiction_clause,[status(thm)],[f222])).
% 5.33/1.40 fof(f230,plain,(
% 5.33/1.40 ![X0,X1]: (~aNaturalNumber0(X0)|~aNaturalNumber0(X1)|sdtasdt0(sdtasdt0(X0,X1),sK2_skl)=sdtasdt0(X0,sdtasdt0(X1,sK2_skl)))),
% 5.33/1.40 inference(resolution,[status(thm)],[f147,f62])).
% 5.33/1.40 fof(f847,plain,(
% 5.33/1.40 $false|~sQ6_spl),
% 5.33/1.40 inference(forward_subsumption_resolution,[status(thm)],[f203,f146])).
% 5.33/1.40 fof(f848,plain,(
% 5.33/1.40 ~sQ6_spl),
% 5.33/1.40 inference(contradiction_clause,[status(thm)],[f847])).
% 5.33/1.40 fof(f1039,plain,(
% 5.33/1.40 $false|sQ5_spl),
% 5.33/1.40 inference(forward_subsumption_resolution,[status(thm)],[f201,f143])).
% 5.33/1.40 fof(f1040,plain,(
% 5.33/1.40 sQ5_spl),
% 5.33/1.40 inference(contradiction_clause,[status(thm)],[f1039])).
% 5.33/1.40 fof(f1161,plain,(
% 5.33/1.40 ![X0]: (~aNaturalNumber0(xl)|xl=sz00|~aNaturalNumber0(sdtsldt0(xm,xl))|~aNaturalNumber0(X0)|~xm=sdtasdt0(xl,X0)|sdtsldt0(xm,xl)=X0)),
% 5.33/1.40 inference(paramodulation,[status(thm)],[f158,f76])).
% 5.33/1.40 fof(f1281,definition,(
% 5.33/1.40 ![X0]: (sQ142_spl <=> (~aNaturalNumber0(X0)|~xm=sdtasdt0(xl,X0)|sdtsldt0(xm,xl)=X0))),
% 5.33/1.40 introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition])).
% 5.33/1.40 fof(f1282,plain,(
% 5.33/1.40 ![X0]: (~aNaturalNumber0(X0)|~xm=sdtasdt0(xl,X0)|sdtsldt0(xm,xl)=X0|~sQ142_spl)),
% 5.33/1.40 inference(component_clause,[status(thm)],[f1281])).
% 5.33/1.40 fof(f1284,plain,(
% 5.33/1.40 ~sQ5_spl|sQ6_spl|~sQ4_spl|sQ142_spl),
% 5.33/1.40 inference(split_clause,[status(thm)],[f1161,f199,f202,f195,f1281])).
% 5.33/1.40 fof(f2172,plain,(
% 5.33/1.40 ![X0]: (~aNaturalNumber0(X0)|sdtasdt0(sdtasdt0(X0,xn),sK2_skl)=sdtasdt0(X0,sdtasdt0(xn,sK2_skl)))),
% 5.33/1.40 inference(resolution,[status(thm)],[f230,f150])).
% 5.33/1.40 fof(f2649,plain,(
% 5.33/1.40 ~xm=sdtasdt0(xl,sK2_skl)|sdtsldt0(xm,xl)=sK2_skl|~sQ142_spl),
% 5.33/1.40 inference(resolution,[status(thm)],[f1282,f147])).
% 5.33/1.40 fof(f2689,definition,(
% 5.33/1.40 sQ361_spl <=> (xm=sdtasdt0(xl,sK2_skl))),
% 5.33/1.40 introduced(definition,[new_symbols(definition,[sQ361_spl])],[split_symbol_definition])).
% 5.33/1.40 fof(f2691,plain,(
% 5.33/1.40 ~xm=sdtasdt0(xl,sK2_skl)|sQ361_spl),
% 5.33/1.40 inference(component_clause,[status(thm)],[f2689])).
% 5.33/1.40 fof(f2692,definition,(
% 5.33/1.40 sQ362_spl <=> (sdtsldt0(xm,xl)=sK2_skl)),
% 5.33/1.40 introduced(definition,[new_symbols(definition,[sQ362_spl])],[split_symbol_definition])).
% 5.33/1.40 fof(f2693,plain,(
% 5.33/1.40 sdtsldt0(xm,xl)=sK2_skl|~sQ362_spl),
% 5.33/1.40 inference(component_clause,[status(thm)],[f2692])).
% 5.33/1.40 fof(f2695,plain,(
% 5.33/1.40 ~sQ361_spl|sQ362_spl|~sQ142_spl),
% 5.33/1.40 inference(split_clause,[status(thm)],[f2649,f2689,f2692,f1281])).
% 5.33/1.40 fof(f2700,plain,(
% 5.33/1.40 ~xm=xm|sQ361_spl),
% 5.33/1.40 inference(forward_demodulation,[status(thm)],[f148,f2691])).
% 5.33/1.40 fof(f2701,plain,(
% 5.33/1.40 $false|sQ361_spl),
% 5.33/1.40 inference(trivial_equality_resolution,[status(thm)],[f2700])).
% 5.33/1.40 fof(f2702,plain,(
% 5.33/1.40 sQ361_spl),
% 5.33/1.40 inference(contradiction_clause,[status(thm)],[f2701])).
% 5.33/1.40 fof(f3217,plain,(
% 5.33/1.40 sdtasdt0(sdtasdt0(xl,xn),sK2_skl)=sdtasdt0(xl,sdtasdt0(xn,sK2_skl))),
% 5.33/1.40 inference(resolution,[status(thm)],[f2172,f143])).
% 5.33/1.40 fof(f3680,plain,(
% 5.33/1.40 ~sdtasdt0(xn,xm)=sdtasdt0(xl,sdtasdt0(xn,sK2_skl))|~sQ362_spl),
% 5.33/1.40 inference(backward_demodulation,[status(thm)],[f2693,f159])).
% 5.33/1.40 fof(f3683,plain,(
% 5.33/1.40 sdtasdt0(sdtasdt0(xl,xn),sK2_skl)=sdtasdt0(xn,xm)|~sQ362_spl),
% 5.33/1.40 inference(backward_demodulation,[status(thm)],[f2693,f172])).
% 5.33/1.40 fof(f5153,plain,(
% 5.33/1.40 sdtasdt0(xn,xm)=sdtasdt0(xl,sdtasdt0(xn,sK2_skl))|~sQ362_spl),
% 5.33/1.40 inference(forward_demodulation,[status(thm)],[f3683,f3217])).
% 5.33/1.40 fof(f5154,plain,(
% 5.33/1.40 $false|~sQ362_spl),
% 5.33/1.40 inference(forward_subsumption_resolution,[status(thm)],[f5153,f3680])).
% 5.33/1.40 fof(f5155,plain,(
% 5.33/1.40 ~sQ362_spl),
% 5.33/1.40 inference(contradiction_clause,[status(thm)],[f5154])).
% 5.33/1.40 fof(f5156,plain,(
% 5.33/1.40 $false),
% 5.33/1.40 inference(sat_refutation,[status(thm)],[f223,f848,f1040,f1284,f2695,f2702,f5155])).
% 5.33/1.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.29/1.42 % Elapsed time: 0.821598 seconds
% 0.29/1.42 % CPU time: 6.218621 seconds
% 0.29/1.42 % Total memory used: 175.076 MB
% 0.29/1.42 % Net memory used: 169.112 MB
%------------------------------------------------------------------------------