%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWV487+3 : 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 : n012.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 02:51:00 PM UTC 2026
% Result : Theorem 2.56s 1.02s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV487+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n012.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 08:54:22 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 2.56/1.02 % Refutation found
% 2.56/1.02 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.56/1.02 % SZS output start CNFRefutation for theBenchmark
% 2.56/1.02 fof(f1,axiom,(
% 2.56/1.02 (! [I,J] :( int_leq(I,J)<=> ( int_less(I,J)| I = J ) ) )),
% 2.56/1.02 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.56/1.02 fof(f2,axiom,(
% 2.56/1.02 (! [I,J,K] :( ( int_less(I,J)& int_less(J,K) )=> int_less(I,K) ) )),
% 2.56/1.02 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.56/1.02 fof(f9,axiom,(
% 2.56/1.02 (! [I,J] :( int_less(I,J)<=> (? [K] :( plus(I,K) = J& int_less(int_zero,K) ) )) )),
% 2.56/1.02 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.56/1.02 fof(f10,axiom,(
% 2.56/1.02 (! [I] :( int_less(int_zero,I)<=> int_leq(int_one,I) ) )),
% 2.56/1.02 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.56/1.02 fof(f12,hypothesis,(
% 2.56/1.02 (! [I,J] :( ( int_leq(int_one,I)& int_leq(I,n)& int_leq(int_one,J)& int_leq(J,n) )=> ( (! [C] :( ( int_less(int_zero,C)& I = plus(J,C) )=> (! [K] :( ( int_leq(int_one,K)& int_leq(K,J) )=> a(plus(K,C),K) = real_zero ) )))& (! [K] :( ( int_leq(int_one,K)& int_leq(K,J) )=> a(K,K) = real_one ))& (! [C] :( ( int_less(int_zero,C)& J = plus(I,C) )=> (! [K] :( ( int_leq(int_one,K)& int_leq(K,I) )=> a(K,plus(K,C)) = real_zero ) )) )) ) )),
% 2.56/1.02 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.56/1.02 fof(f13,conjecture,(
% 2.56/1.02 (! [I,J] :( ( int_leq(int_one,J)& int_less(J,I)& int_leq(I,n) )=> a(I,J) = real_zero ) )),
% 2.56/1.02 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 2.56/1.02 fof(f14,negated_conjecture,(
% 2.56/1.02 ~((! [I,J] :( ( int_leq(int_one,J)& int_less(J,I)& int_leq(I,n) )=> a(I,J) = real_zero ) ))),
% 2.56/1.02 inference(negated_conjecture,[status(cth)],[f13])).
% 2.56/1.02 fof(f15,plain,(
% 2.56/1.02 ![I,J]: ((~int_leq(I,J)|(int_less(I,J)|I=J))&(int_leq(I,J)|(~int_less(I,J)&~I=J)))),
% 2.56/1.02 inference(NNF_transformation,[status(thm)],[f1])).
% 2.56/1.02 fof(f16,plain,(
% 2.56/1.02 (![I,J]: (~int_leq(I,J)|(int_less(I,J)|I=J)))&(![I,J]: (int_leq(I,J)|(~int_less(I,J)&~I=J)))),
% 2.56/1.02 inference(miniscoping,[status(thm)],[f15])).
% 2.56/1.02 fof(f17,plain,(
% 2.56/1.02 ![X0,X1]: (~int_leq(X0,X1)|int_less(X0,X1)|X0=X1)),
% 2.56/1.02 inference(cnf_transformation,[status(thm)],[f16])).
% 2.56/1.02 fof(f18,plain,(
% 2.56/1.02 ![X0,X1]: (int_leq(X0,X1)|~int_less(X0,X1))),
% 2.56/1.02 inference(cnf_transformation,[status(thm)],[f16])).
% 2.56/1.02 fof(f19,plain,(
% 2.56/1.02 ![X0,X1]: (int_leq(X0,X1)|~X0=X1)),
% 2.56/1.02 inference(cnf_transformation,[status(thm)],[f16])).
% 2.56/1.02 fof(f20,plain,(
% 2.56/1.02 ![I,J,K]: ((~int_less(I,J)|~int_less(J,K))|int_less(I,K))),
% 2.56/1.02 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 2.56/1.02 fof(f21,plain,(
% 2.56/1.02 ![I,K]: ((![J]: (~int_less(I,J)|~int_less(J,K)))|int_less(I,K))),
% 2.56/1.02 inference(miniscoping,[status(thm)],[f20])).
% 2.56/1.02 fof(f22,plain,(
% 2.56/1.02 ![X0,X1,X2]: (~int_less(X0,X1)|~int_less(X1,X2)|int_less(X0,X2))),
% 2.56/1.02 inference(cnf_transformation,[status(thm)],[f21])).
% 2.56/1.02 fof(f31,plain,(
% 2.56/1.02 ![I,J]: ((~int_less(I,J)|(?[K]: (plus(I,K)=J&int_less(int_zero,K))))&(int_less(I,J)|(![K]: (~plus(I,K)=J|~int_less(int_zero,K)))))),
% 2.56/1.02 inference(NNF_transformation,[status(thm)],[f9])).
% 2.56/1.02 fof(f32,plain,(
% 2.56/1.02 (![I,J]: (~int_less(I,J)|(?[K]: (plus(I,K)=J&int_less(int_zero,K)))))&(![I,J]: (int_less(I,J)|(![K]: (~plus(I,K)=J|~int_less(int_zero,K)))))),
% 2.56/1.02 inference(miniscoping,[status(thm)],[f31])).
% 2.56/1.02 fof(f33,plain,(
% 2.56/1.02 (![I,J]: (~int_less(I,J)|(plus(I,sK0_skl(J,I))=J&int_less(int_zero,sK0_skl(J,I)))))&(![I,J]: (int_less(I,J)|(![K]: (~plus(I,K)=J|~int_less(int_zero,K)))))),
% 2.56/1.02 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(K,sK0_skl(J,I))],[f32])).
% 2.56/1.02 fof(f34,plain,(
% 2.56/1.02 ![X0,X1]: (~int_less(X0,X1)|plus(X0,sK0_skl(X1,X0))=X1)),
% 2.56/1.02 inference(cnf_transformation,[status(thm)],[f33])).
% 2.56/1.02 fof(f35,plain,(
% 2.56/1.02 ![X0,X1]: (~int_less(X0,X1)|int_less(int_zero,sK0_skl(X1,X0)))),
% 2.56/1.02 inference(cnf_transformation,[status(thm)],[f33])).
% 2.56/1.02 fof(f37,plain,(
% 2.56/1.02 ![I]: ((~int_less(int_zero,I)|int_leq(int_one,I))&(int_less(int_zero,I)|~int_leq(int_one,I)))),
% 2.56/1.02 inference(NNF_transformation,[status(thm)],[f10])).
% 2.56/1.02 fof(f38,plain,(
% 2.56/1.02 (![I]: (~int_less(int_zero,I)|int_leq(int_one,I)))&(![I]: (int_less(int_zero,I)|~int_leq(int_one,I)))),
% 2.56/1.02 inference(miniscoping,[status(thm)],[f37])).
% 2.56/1.02 fof(f39,plain,(
% 2.56/1.02 ![X0]: (~int_less(int_zero,X0)|int_leq(int_one,X0))),
% 2.56/1.02 inference(cnf_transformation,[status(thm)],[f38])).
% 2.56/1.02 fof(f40,plain,(
% 2.56/1.02 ![X0]: (int_less(int_zero,X0)|~int_leq(int_one,X0))),
% 2.56/1.02 inference(cnf_transformation,[status(thm)],[f38])).
% 2.56/1.02 fof(f42,plain,(
% 2.56/1.02 ![I,J]: ((((~int_leq(int_one,I)|~int_leq(I,n))|~int_leq(int_one,J))|~int_leq(J,n))|(((![C]: ((~int_less(int_zero,C)|~I=plus(J,C))|(![K]: ((~int_leq(int_one,K)|~int_leq(K,J))|a(plus(K,C),K)=real_zero))))&(![K]: ((~int_leq(int_one,K)|~int_leq(K,J))|a(K,K)=real_one)))&(![C]: ((~int_less(int_zero,C)|~J=plus(I,C))|(![K]: ((~int_leq(int_one,K)|~int_leq(K,I))|a(K,plus(K,C))=real_zero))))))),
% 2.56/1.02 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 2.56/1.02 fof(f43,plain,(
% 2.56/1.02 ![X0,X1,X2,X3]: (~int_leq(int_one,X0)|~int_leq(X0,n)|~int_leq(int_one,X1)|~int_leq(X1,n)|~int_less(int_zero,X2)|~X0=plus(X1,X2)|~int_leq(int_one,X3)|~int_leq(X3,X1)|a(plus(X3,X2),X3)=real_zero)),
% 2.56/1.02 inference(cnf_transformation,[status(thm)],[f42])).
% 2.56/1.02 fof(f46,plain,(
% 2.56/1.02 (?[I,J]: (((int_leq(int_one,J)&int_less(J,I))&int_leq(I,n))&~a(I,J)=real_zero))),
% 2.56/1.02 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 2.56/1.02 fof(f47,plain,(
% 2.56/1.02 (((int_leq(int_one,sK2_skl)&int_less(sK2_skl,sK1_skl))&int_leq(sK1_skl,n))&~a(sK1_skl,sK2_skl)=real_zero)),
% 2.56/1.02 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(I,sK1_skl),skolemize(J,sK2_skl)],[f46])).
% 2.56/1.02 fof(f48,plain,(
% 2.56/1.02 int_leq(int_one,sK2_skl)),
% 2.56/1.02 inference(cnf_transformation,[status(thm)],[f47])).
% 2.56/1.02 fof(f49,plain,(
% 2.56/1.02 int_less(sK2_skl,sK1_skl)),
% 2.56/1.02 inference(cnf_transformation,[status(thm)],[f47])).
% 2.56/1.02 fof(f50,plain,(
% 2.56/1.02 int_leq(sK1_skl,n)),
% 2.56/1.02 inference(cnf_transformation,[status(thm)],[f47])).
% 2.56/1.02 fof(f51,plain,(
% 2.56/1.02 ~a(sK1_skl,sK2_skl)=real_zero),
% 2.56/1.02 inference(cnf_transformation,[status(thm)],[f47])).
% 2.56/1.02 fof(f59,plain,(
% 2.56/1.02 ![X0]: (int_leq(X0,X0))),
% 2.56/1.02 inference(destructive_equality_resolution,[status(thm)],[f19])).
% 2.56/1.02 fof(f62,plain,(
% 2.56/1.02 ![X0,X1,X2]: (~int_leq(int_one,plus(X0,X1))|~int_leq(plus(X0,X1),n)|~int_leq(int_one,X0)|~int_leq(X0,n)|~int_less(int_zero,X1)|~int_leq(int_one,X2)|~int_leq(X2,X0)|a(plus(X2,X1),X2)=real_zero)),
% 2.56/1.02 inference(destructive_equality_resolution,[status(thm)],[f43])).
% 2.56/1.02 fof(f73,plain,(
% 2.56/1.02 int_leq(sK2_skl,sK1_skl)),
% 2.56/1.02 inference(resolution,[status(thm)],[f18,f49])).
% 2.56/1.02 fof(f76,plain,(
% 2.56/1.02 ![X0]: (~int_less(sK1_skl,X0)|int_less(sK2_skl,X0))),
% 2.56/1.02 inference(resolution,[status(thm)],[f22,f49])).
% 2.56/1.02 fof(f78,plain,(
% 2.56/1.02 ![X0]: (~int_less(X0,sK2_skl)|int_less(X0,sK1_skl))),
% 2.56/1.02 inference(resolution,[status(thm)],[f22,f49])).
% 2.56/1.02 fof(f93,plain,(
% 2.56/1.02 int_less(sK1_skl,n)|sK1_skl=n),
% 2.56/1.02 inference(resolution,[status(thm)],[f50,f17])).
% 2.56/1.02 fof(f94,definition,(
% 2.56/1.02 sQ4_spl <=> (int_less(sK1_skl,n))),
% 2.56/1.02 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 2.56/1.02 fof(f95,plain,(
% 2.56/1.02 int_less(sK1_skl,n)|~sQ4_spl),
% 2.56/1.02 inference(component_clause,[status(thm)],[f94])).
% 2.56/1.02 fof(f97,definition,(
% 2.56/1.02 sQ5_spl <=> (sK1_skl=n)),
% 2.56/1.02 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 2.56/1.02 fof(f98,plain,(
% 2.56/1.02 sK1_skl=n|~sQ5_spl),
% 2.56/1.02 inference(component_clause,[status(thm)],[f97])).
% 2.56/1.02 fof(f100,plain,(
% 2.56/1.02 sQ4_spl|sQ5_spl),
% 2.56/1.02 inference(split_clause,[status(thm)],[f93,f94,f97])).
% 2.56/1.02 fof(f152,plain,(
% 2.56/1.02 plus(sK2_skl,sK0_skl(sK1_skl,sK2_skl))=sK1_skl),
% 2.56/1.02 inference(resolution,[status(thm)],[f34,f49])).
% 2.56/1.02 fof(f160,plain,(
% 2.56/1.02 int_less(int_zero,sK0_skl(sK1_skl,sK2_skl))),
% 2.56/1.02 inference(resolution,[status(thm)],[f35,f49])).
% 2.56/1.02 fof(f167,definition,(
% 2.56/1.02 sQ10_spl <=> (int_less(int_zero,sK2_skl))),
% 2.56/1.02 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 2.56/1.02 fof(f168,plain,(
% 2.56/1.02 int_less(int_zero,sK2_skl)|~sQ10_spl),
% 2.56/1.02 inference(component_clause,[status(thm)],[f167])).
% 2.56/1.02 fof(f169,plain,(
% 2.56/1.02 ~int_less(int_zero,sK2_skl)|sQ10_spl),
% 2.56/1.02 inference(component_clause,[status(thm)],[f167])).
% 2.56/1.02 fof(f208,plain,(
% 2.56/1.02 int_less(sK2_skl,n)|~sQ4_spl),
% 2.56/1.02 inference(resolution,[status(thm)],[f76,f95])).
% 2.56/1.02 fof(f210,plain,(
% 2.56/1.02 int_less(int_zero,sK1_skl)|~sQ10_spl),
% 2.56/1.02 inference(resolution,[status(thm)],[f78,f168])).
% 2.56/1.02 fof(f267,plain,(
% 2.56/1.02 int_leq(sK2_skl,n)|~sQ4_spl),
% 2.56/1.02 inference(resolution,[status(thm)],[f208,f18])).
% 2.56/1.02 fof(f358,plain,(
% 2.56/1.02 int_leq(int_one,sK1_skl)|~sQ10_spl),
% 2.56/1.02 inference(resolution,[status(thm)],[f39,f210])).
% 2.56/1.02 fof(f497,definition,(
% 2.56/1.02 sQ18_spl <=> (int_leq(sK2_skl,sK2_skl))),
% 2.56/1.02 introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 2.56/1.02 fof(f499,plain,(
% 2.56/1.02 ~int_leq(sK2_skl,sK2_skl)|sQ18_spl),
% 2.56/1.02 inference(component_clause,[status(thm)],[f497])).
% 2.56/1.02 fof(f537,plain,(
% 2.56/1.02 $false|sQ18_spl),
% 2.56/1.02 inference(forward_subsumption_resolution,[status(thm)],[f499,f59])).
% 2.56/1.02 fof(f538,plain,(
% 2.56/1.02 sQ18_spl),
% 2.56/1.02 inference(contradiction_clause,[status(thm)],[f537])).
% 2.56/1.02 fof(f705,definition,(
% 2.56/1.02 sQ51_spl <=> (int_leq(int_one,sK2_skl))),
% 2.56/1.02 introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition])).
% 2.56/1.02 fof(f707,plain,(
% 2.56/1.02 ~int_leq(int_one,sK2_skl)|sQ51_spl),
% 2.56/1.02 inference(component_clause,[status(thm)],[f705])).
% 2.56/1.02 fof(f777,definition,(
% 2.56/1.02 sQ61_spl <=> (int_leq(sK2_skl,n))),
% 2.56/1.02 introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition])).
% 2.56/1.02 fof(f779,plain,(
% 2.56/1.02 ~int_leq(sK2_skl,n)|sQ61_spl),
% 2.56/1.02 inference(component_clause,[status(thm)],[f777])).
% 2.56/1.02 fof(f784,definition,(
% 2.56/1.02 sQ63_spl <=> (int_leq(sK1_skl,n))),
% 2.56/1.02 introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition])).
% 2.56/1.02 fof(f786,plain,(
% 2.56/1.02 ~int_leq(sK1_skl,n)|sQ63_spl),
% 2.56/1.02 inference(component_clause,[status(thm)],[f784])).
% 2.56/1.02 fof(f807,plain,(
% 2.56/1.02 $false|sQ51_spl),
% 2.56/1.02 inference(forward_subsumption_resolution,[status(thm)],[f707,f48])).
% 2.56/1.02 fof(f808,plain,(
% 2.56/1.02 sQ51_spl),
% 2.56/1.02 inference(contradiction_clause,[status(thm)],[f807])).
% 2.56/1.02 fof(f809,plain,(
% 2.56/1.02 $false|sQ63_spl),
% 2.56/1.02 inference(forward_subsumption_resolution,[status(thm)],[f786,f50])).
% 2.56/1.02 fof(f810,plain,(
% 2.56/1.02 sQ63_spl),
% 2.56/1.02 inference(contradiction_clause,[status(thm)],[f809])).
% 2.56/1.02 fof(f811,plain,(
% 2.56/1.02 $false|~sQ4_spl|sQ61_spl),
% 2.56/1.02 inference(forward_subsumption_resolution,[status(thm)],[f779,f267])).
% 2.56/1.02 fof(f812,plain,(
% 2.56/1.02 ~sQ4_spl|sQ61_spl),
% 2.56/1.02 inference(contradiction_clause,[status(thm)],[f811])).
% 2.56/1.02 fof(f813,plain,(
% 2.56/1.02 ![X0,X1]: (~int_leq(int_one,plus(X0,X1))|~int_leq(plus(X0,X1),n)|~int_leq(int_one,X0)|~int_leq(X0,n)|~int_less(int_zero,X1)|~int_leq(sK2_skl,X0)|a(plus(sK2_skl,X1),sK2_skl)=real_zero)),
% 2.56/1.02 inference(resolution,[status(thm)],[f62,f48])).
% 2.56/1.02 fof(f904,plain,(
% 2.56/1.02 int_less(int_zero,sK2_skl)),
% 2.56/1.02 inference(resolution,[status(thm)],[f40,f48])).
% 2.56/1.02 fof(f1181,plain,(
% 2.56/1.02 ~int_leq(sK2_skl,sK1_skl)|~sQ5_spl|sQ61_spl),
% 2.56/1.02 inference(forward_demodulation,[status(thm)],[f98,f779])).
% 2.56/1.02 fof(f1182,plain,(
% 2.56/1.02 $false|~sQ5_spl|sQ61_spl),
% 2.56/1.02 inference(forward_subsumption_resolution,[status(thm)],[f1181,f73])).
% 2.56/1.02 fof(f1183,plain,(
% 2.56/1.02 ~sQ5_spl|sQ61_spl),
% 2.56/1.02 inference(contradiction_clause,[status(thm)],[f1182])).
% 2.56/1.02 fof(f1671,definition,(
% 2.56/1.02 sQ121_spl <=> (int_leq(int_one,plus(sK2_skl,sK0_skl(sK1_skl,sK2_skl))))),
% 2.56/1.02 introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition])).
% 2.56/1.02 fof(f1673,plain,(
% 2.56/1.02 ~int_leq(int_one,plus(sK2_skl,sK0_skl(sK1_skl,sK2_skl)))|sQ121_spl),
% 2.56/1.02 inference(component_clause,[status(thm)],[f1671])).
% 2.56/1.02 fof(f1674,definition,(
% 2.56/1.02 sQ122_spl <=> (int_less(int_zero,sK0_skl(sK1_skl,sK2_skl)))),
% 2.56/1.02 introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition])).
% 2.56/1.02 fof(f1676,plain,(
% 2.56/1.02 ~int_less(int_zero,sK0_skl(sK1_skl,sK2_skl))|sQ122_spl),
% 2.56/1.02 inference(component_clause,[status(thm)],[f1674])).
% 2.56/1.02 fof(f1685,plain,(
% 2.56/1.02 $false|sQ122_spl),
% 2.56/1.02 inference(forward_subsumption_resolution,[status(thm)],[f1676,f160])).
% 2.56/1.02 fof(f1686,plain,(
% 2.56/1.02 sQ122_spl),
% 2.56/1.02 inference(contradiction_clause,[status(thm)],[f1685])).
% 2.56/1.02 fof(f1687,plain,(
% 2.56/1.02 ~int_leq(int_one,sK1_skl)|sQ121_spl),
% 2.56/1.02 inference(forward_demodulation,[status(thm)],[f152,f1673])).
% 2.56/1.02 fof(f1688,plain,(
% 2.56/1.02 $false|~sQ10_spl|sQ121_spl),
% 2.56/1.02 inference(forward_subsumption_resolution,[status(thm)],[f1687,f358])).
% 2.56/1.02 fof(f1689,plain,(
% 2.56/1.02 ~sQ10_spl|sQ121_spl),
% 2.56/1.02 inference(contradiction_clause,[status(thm)],[f1688])).
% 2.56/1.02 fof(f2339,plain,(
% 2.56/1.02 ~int_leq(int_one,plus(sK2_skl,sK0_skl(sK1_skl,sK2_skl)))|~int_leq(sK1_skl,n)|~int_leq(int_one,sK2_skl)|~int_leq(sK2_skl,n)|~int_less(int_zero,sK0_skl(sK1_skl,sK2_skl))|~int_leq(sK2_skl,sK2_skl)|a(plus(sK2_skl,sK0_skl(sK1_skl,sK2_skl)),sK2_skl)=real_zero),
% 2.56/1.02 inference(paramodulation,[status(thm)],[f152,f813])).
% 2.56/1.02 fof(f2344,definition,(
% 2.56/1.02 sQ168_spl <=> (a(plus(sK2_skl,sK0_skl(sK1_skl,sK2_skl)),sK2_skl)=real_zero)),
% 2.56/1.03 introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition])).
% 2.56/1.03 fof(f2345,plain,(
% 2.56/1.03 a(plus(sK2_skl,sK0_skl(sK1_skl,sK2_skl)),sK2_skl)=real_zero|~sQ168_spl),
% 2.56/1.03 inference(component_clause,[status(thm)],[f2344])).
% 2.56/1.03 fof(f2347,plain,(
% 2.56/1.03 ~sQ121_spl|~sQ63_spl|~sQ51_spl|~sQ61_spl|~sQ122_spl|~sQ18_spl|sQ168_spl),
% 2.56/1.03 inference(split_clause,[status(thm)],[f2339,f1671,f784,f705,f777,f1674,f497,f2344])).
% 2.56/1.03 fof(f2356,plain,(
% 2.56/1.03 a(sK1_skl,sK2_skl)=real_zero|~sQ168_spl),
% 2.56/1.03 inference(forward_demodulation,[status(thm)],[f152,f2345])).
% 2.56/1.03 fof(f2357,plain,(
% 2.56/1.03 $false|~sQ168_spl),
% 2.56/1.03 inference(forward_subsumption_resolution,[status(thm)],[f2356,f51])).
% 2.56/1.03 fof(f2358,plain,(
% 2.56/1.03 ~sQ168_spl),
% 2.56/1.03 inference(contradiction_clause,[status(thm)],[f2357])).
% 2.56/1.03 fof(f2363,plain,(
% 2.56/1.03 $false|sQ10_spl),
% 2.56/1.03 inference(forward_subsumption_resolution,[status(thm)],[f169,f904])).
% 2.56/1.03 fof(f2364,plain,(
% 2.56/1.03 sQ10_spl),
% 2.56/1.03 inference(contradiction_clause,[status(thm)],[f2363])).
% 2.56/1.03 fof(f2365,plain,(
% 2.56/1.03 $false),
% 2.56/1.03 inference(sat_refutation,[status(thm)],[f100,f538,f808,f810,f812,f1183,f1686,f1689,f2347,f2358,f2364])).
% 2.56/1.03 % SZS output end CNFRefutation for theBenchmark.p
% 2.56/1.04 % Elapsed time: 0.674660 seconds
% 2.56/1.04 % CPU time: 5.090782 seconds
% 2.56/1.04 % Total memory used: 147.036 MB
% 2.56/1.04 % Net memory used: 138.132 MB
%------------------------------------------------------------------------------