%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SWV487+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 : n016.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 26.61s 4.01s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV487+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.51 % Computer : n016.cluster.edu
% 0.19/0.51 % Model : x86_64 x86_64
% 0.19/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.51 % Memory : 8046.5625MB
% 0.19/0.51 % OS : Linux 6.8.0-71-generic
% 0.19/0.52 % CPULimit : 300
% 0.19/0.52 % WCLimit : 300
% 0.19/0.52 % DateTime : Mon Sep 21 08:59:23 UTC 2026
% 0.19/0.52 % CPUTime :
% 0.19/0.54 % Drodi V4.1.1
% 26.61/4.01 % Refutation found
% 26.61/4.01 % SZS status Theorem for theBenchmark: Theorem is valid
% 26.61/4.01 % SZS output start CNFRefutation for theBenchmark
% 26.61/4.01 fof(f1,axiom,(
% 26.61/4.01 (! [I,J] :( int_leq(I,J)<=> ( int_less(I,J)| I = J ) ) )),
% 26.61/4.01 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.61/4.01 fof(f2,axiom,(
% 26.61/4.01 (! [I,J,K] :( ( int_less(I,J)& int_less(J,K) )=> int_less(I,K) ) )),
% 26.61/4.01 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.61/4.01 fof(f3,axiom,(
% 26.61/4.01 (! [I,J] :( int_less(I,J)=> I != J ) )),
% 26.61/4.01 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.61/4.01 fof(f4,axiom,(
% 26.61/4.01 (! [I,J] :( int_less(I,J)| int_leq(J,I) ) )),
% 26.61/4.01 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.61/4.01 fof(f9,axiom,(
% 26.61/4.01 (! [I,J] :( int_less(I,J)<=> (? [K] :( plus(I,K) = J& int_less(int_zero,K) ) )) )),
% 26.61/4.01 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.61/4.01 fof(f10,axiom,(
% 26.61/4.01 (! [I] :( int_less(int_zero,I)<=> int_leq(int_one,I) ) )),
% 26.61/4.01 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.61/4.01 fof(f12,hypothesis,(
% 26.61/4.01 (! [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 ) )))& (! [C] :( ( int_leq(int_zero,C)& J = plus(I,C) )=> (! [K] :( ( int_leq(int_one,K)& int_leq(K,I) )=> a(K,plus(K,C)) = lu(K,plus(K,C)) ) )) )) ) )),
% 26.61/4.01 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.61/4.01 fof(f13,conjecture,(
% 26.61/4.01 (! [I,J] :( ( int_leq(int_one,J)& int_less(J,I)& int_leq(I,n) )=> a(I,J) = real_zero ) )),
% 26.61/4.01 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 26.61/4.01 fof(f14,negated_conjecture,(
% 26.61/4.01 ~((! [I,J] :( ( int_leq(int_one,J)& int_less(J,I)& int_leq(I,n) )=> a(I,J) = real_zero ) ))),
% 26.61/4.01 inference(negated_conjecture,[status(cth)],[f13])).
% 26.61/4.01 fof(f15,plain,(
% 26.61/4.01 ![I,J]: ((~int_leq(I,J)|(int_less(I,J)|I=J))&(int_leq(I,J)|(~int_less(I,J)&~I=J)))),
% 26.61/4.01 inference(NNF_transformation,[status(thm)],[f1])).
% 26.61/4.01 fof(f16,plain,(
% 26.61/4.01 (![I,J]: (~int_leq(I,J)|(int_less(I,J)|I=J)))&(![I,J]: (int_leq(I,J)|(~int_less(I,J)&~I=J)))),
% 26.61/4.01 inference(miniscoping,[status(thm)],[f15])).
% 26.61/4.02 fof(f17,plain,(
% 26.61/4.02 ![X0,X1]: (~int_leq(X0,X1)|int_less(X0,X1)|X0=X1)),
% 26.61/4.02 inference(cnf_transformation,[status(thm)],[f16])).
% 26.61/4.02 fof(f18,plain,(
% 26.61/4.02 ![X0,X1]: (int_leq(X0,X1)|~int_less(X0,X1))),
% 26.61/4.02 inference(cnf_transformation,[status(thm)],[f16])).
% 26.61/4.02 fof(f19,plain,(
% 26.61/4.02 ![X0,X1]: (int_leq(X0,X1)|~X0=X1)),
% 26.61/4.02 inference(cnf_transformation,[status(thm)],[f16])).
% 26.61/4.02 fof(f20,plain,(
% 26.61/4.02 ![I,J,K]: ((~int_less(I,J)|~int_less(J,K))|int_less(I,K))),
% 26.61/4.02 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 26.61/4.02 fof(f21,plain,(
% 26.61/4.02 ![I,K]: ((![J]: (~int_less(I,J)|~int_less(J,K)))|int_less(I,K))),
% 26.61/4.02 inference(miniscoping,[status(thm)],[f20])).
% 26.61/4.02 fof(f22,plain,(
% 26.61/4.02 ![X0,X1,X2]: (~int_less(X0,X1)|~int_less(X1,X2)|int_less(X0,X2))),
% 26.61/4.02 inference(cnf_transformation,[status(thm)],[f21])).
% 26.61/4.02 fof(f23,plain,(
% 26.61/4.02 ![I,J]: (~int_less(I,J)|~I=J)),
% 26.61/4.02 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 26.61/4.02 fof(f24,plain,(
% 26.61/4.02 ![X0,X1]: (~int_less(X0,X1)|~X0=X1)),
% 26.61/4.02 inference(cnf_transformation,[status(thm)],[f23])).
% 26.61/4.02 fof(f25,plain,(
% 26.61/4.02 ![X0,X1]: (int_less(X0,X1)|int_leq(X1,X0))),
% 26.61/4.02 inference(cnf_transformation,[status(thm)],[f4])).
% 26.61/4.02 fof(f31,plain,(
% 26.61/4.02 ![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)))))),
% 26.61/4.02 inference(NNF_transformation,[status(thm)],[f9])).
% 26.61/4.02 fof(f32,plain,(
% 26.61/4.02 (![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)))))),
% 26.61/4.02 inference(miniscoping,[status(thm)],[f31])).
% 26.61/4.02 fof(f33,plain,(
% 26.61/4.02 (![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)))))),
% 26.61/4.02 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(K,sK0_skl(J,I))],[f32])).
% 26.61/4.02 fof(f34,plain,(
% 26.61/4.02 ![X0,X1]: (~int_less(X0,X1)|plus(X0,sK0_skl(X1,X0))=X1)),
% 26.61/4.02 inference(cnf_transformation,[status(thm)],[f33])).
% 26.61/4.02 fof(f35,plain,(
% 26.61/4.02 ![X0,X1]: (~int_less(X0,X1)|int_less(int_zero,sK0_skl(X1,X0)))),
% 26.61/4.02 inference(cnf_transformation,[status(thm)],[f33])).
% 26.61/4.02 fof(f37,plain,(
% 26.61/4.02 ![I]: ((~int_less(int_zero,I)|int_leq(int_one,I))&(int_less(int_zero,I)|~int_leq(int_one,I)))),
% 26.61/4.02 inference(NNF_transformation,[status(thm)],[f10])).
% 26.61/4.02 fof(f38,plain,(
% 26.61/4.02 (![I]: (~int_less(int_zero,I)|int_leq(int_one,I)))&(![I]: (int_less(int_zero,I)|~int_leq(int_one,I)))),
% 26.61/4.02 inference(miniscoping,[status(thm)],[f37])).
% 26.61/4.02 fof(f39,plain,(
% 26.61/4.02 ![X0]: (~int_less(int_zero,X0)|int_leq(int_one,X0))),
% 26.61/4.02 inference(cnf_transformation,[status(thm)],[f38])).
% 26.61/4.02 fof(f40,plain,(
% 26.61/4.02 ![X0]: (int_less(int_zero,X0)|~int_leq(int_one,X0))),
% 26.61/4.02 inference(cnf_transformation,[status(thm)],[f38])).
% 26.61/4.02 fof(f42,plain,(
% 26.61/4.02 ![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))))&(![C]: ((~int_leq(int_zero,C)|~J=plus(I,C))|(![K]: ((~int_leq(int_one,K)|~int_leq(K,I))|a(K,plus(K,C))=lu(K,plus(K,C))))))))),
% 26.61/4.02 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 26.61/4.02 fof(f43,plain,(
% 26.61/4.02 ![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)),
% 26.61/4.02 inference(cnf_transformation,[status(thm)],[f42])).
% 26.61/4.02 fof(f45,plain,(
% 26.61/4.02 (?[I,J]: (((int_leq(int_one,J)&int_less(J,I))&int_leq(I,n))&~a(I,J)=real_zero))),
% 26.61/4.02 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 26.61/4.02 fof(f46,plain,(
% 26.61/4.02 (((int_leq(int_one,sK2_skl)&int_less(sK2_skl,sK1_skl))&int_leq(sK1_skl,n))&~a(sK1_skl,sK2_skl)=real_zero)),
% 26.61/4.02 inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(I,sK1_skl),skolemize(J,sK2_skl)],[f45])).
% 26.61/4.02 fof(f47,plain,(
% 26.61/4.02 int_leq(int_one,sK2_skl)),
% 26.61/4.02 inference(cnf_transformation,[status(thm)],[f46])).
% 26.61/4.02 fof(f48,plain,(
% 26.61/4.02 int_less(sK2_skl,sK1_skl)),
% 26.61/4.02 inference(cnf_transformation,[status(thm)],[f46])).
% 26.61/4.02 fof(f49,plain,(
% 26.61/4.02 int_leq(sK1_skl,n)),
% 26.61/4.02 inference(cnf_transformation,[status(thm)],[f46])).
% 26.61/4.02 fof(f50,plain,(
% 26.61/4.02 ~a(sK1_skl,sK2_skl)=real_zero),
% 26.61/4.02 inference(cnf_transformation,[status(thm)],[f46])).
% 26.61/4.02 fof(f51,plain,(
% 26.61/4.02 ![X0]: (int_leq(X0,X0))),
% 26.61/4.02 inference(destructive_equality_resolution,[status(thm)],[f19])).
% 26.61/4.02 fof(f52,plain,(
% 26.61/4.02 ![X0]: (~int_less(X0,X0))),
% 26.61/4.02 inference(destructive_equality_resolution,[status(thm)],[f24])).
% 26.61/4.02 fof(f54,plain,(
% 26.61/4.02 ![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)),
% 26.61/4.02 inference(destructive_equality_resolution,[status(thm)],[f43])).
% 26.61/4.02 fof(f56,plain,(
% 26.61/4.02 int_less(sK1_skl,n)|sK1_skl=n),
% 26.61/4.02 inference(resolution,[status(thm)],[f17,f49])).
% 26.61/4.02 fof(f58,plain,(
% 26.61/4.02 ![X0,X1]: (int_less(X0,X1)|X0=X1|int_less(X1,X0))),
% 26.61/4.02 inference(resolution,[status(thm)],[f17,f25])).
% 26.61/4.02 fof(f61,definition,(
% 26.61/4.02 sQ0_spl <=> (int_less(sK1_skl,n))),
% 26.61/4.02 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 26.61/4.02 fof(f62,plain,(
% 26.61/4.02 int_less(sK1_skl,n)|~sQ0_spl),
% 26.61/4.02 inference(component_clause,[status(thm)],[f61])).
% 26.61/4.02 fof(f64,definition,(
% 26.61/4.02 sQ1_spl <=> (sK1_skl=n)),
% 26.61/4.02 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 26.61/4.02 fof(f65,plain,(
% 26.61/4.02 sK1_skl=n|~sQ1_spl),
% 26.61/4.02 inference(component_clause,[status(thm)],[f64])).
% 26.61/4.02 fof(f67,plain,(
% 26.61/4.02 sQ0_spl|sQ1_spl),
% 26.61/4.02 inference(split_clause,[status(thm)],[f56,f61,f64])).
% 26.61/4.02 fof(f75,plain,(
% 26.61/4.02 ![X0,X1]: (~int_less(X0,X1)|~int_less(X1,X0))),
% 26.61/4.02 inference(resolution,[status(thm)],[f22,f52])).
% 26.61/4.02 fof(f100,plain,(
% 26.61/4.02 plus(sK2_skl,sK0_skl(sK1_skl,sK2_skl))=sK1_skl),
% 26.61/4.02 inference(resolution,[status(thm)],[f34,f48])).
% 26.61/4.02 fof(f114,plain,(
% 26.61/4.02 ~int_less(n,sK1_skl)|~sQ0_spl),
% 26.61/4.02 inference(resolution,[status(thm)],[f75,f62])).
% 26.61/4.02 fof(f118,plain,(
% 26.61/4.02 ~int_less(sK1_skl,sK2_skl)),
% 26.61/4.02 inference(resolution,[status(thm)],[f75,f48])).
% 26.61/4.02 fof(f120,plain,(
% 26.61/4.02 ![X0]: (~int_less(n,X0)|~int_less(X0,sK1_skl)|~sQ0_spl)),
% 26.61/4.02 inference(resolution,[status(thm)],[f114,f22])).
% 26.61/4.02 fof(f124,plain,(
% 26.61/4.02 sK1_skl=sK2_skl|int_less(sK2_skl,sK1_skl)),
% 26.61/4.02 inference(resolution,[status(thm)],[f58,f118])).
% 26.61/4.02 fof(f147,definition,(
% 26.61/4.02 sQ4_spl <=> (sK1_skl=sK2_skl)),
% 26.61/4.02 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 26.61/4.02 fof(f148,plain,(
% 26.61/4.02 sK1_skl=sK2_skl|~sQ4_spl),
% 26.61/4.02 inference(component_clause,[status(thm)],[f147])).
% 26.61/4.02 fof(f149,plain,(
% 26.61/4.02 ~sK1_skl=sK2_skl|sQ4_spl),
% 26.61/4.02 inference(component_clause,[status(thm)],[f147])).
% 26.61/4.02 fof(f150,definition,(
% 26.61/4.02 sQ5_spl <=> (int_less(sK2_skl,sK1_skl))),
% 26.61/4.02 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 26.61/4.02 fof(f151,plain,(
% 26.61/4.02 int_less(sK2_skl,sK1_skl)|~sQ5_spl),
% 26.61/4.02 inference(component_clause,[status(thm)],[f150])).
% 26.61/4.02 fof(f153,plain,(
% 26.61/4.02 sQ4_spl|sQ5_spl),
% 26.61/4.02 inference(split_clause,[status(thm)],[f124,f147,f150])).
% 26.61/4.02 fof(f225,plain,(
% 26.61/4.02 int_less(sK1_skl,sK1_skl)|~sQ4_spl),
% 26.61/4.02 inference(backward_demodulation,[status(thm)],[f148,f48])).
% 26.61/4.02 fof(f227,plain,(
% 26.61/4.02 $false|~sQ4_spl),
% 26.61/4.02 inference(forward_subsumption_resolution,[status(thm)],[f225,f52])).
% 26.61/4.02 fof(f228,plain,(
% 26.61/4.02 ~sQ4_spl),
% 26.61/4.02 inference(contradiction_clause,[status(thm)],[f227])).
% 26.61/4.02 fof(f265,plain,(
% 26.61/4.02 int_less(int_zero,sK2_skl)),
% 26.61/4.02 inference(resolution,[status(thm)],[f47,f40])).
% 26.61/4.02 fof(f278,plain,(
% 26.61/4.02 ~int_less(sK2_skl,int_zero)),
% 26.61/4.02 inference(resolution,[status(thm)],[f265,f75])).
% 26.61/4.02 fof(f417,plain,(
% 26.61/4.02 ~int_less(n,sK2_skl)|~sQ0_spl|~sQ5_spl),
% 26.61/4.02 inference(resolution,[status(thm)],[f120,f151])).
% 26.61/4.02 fof(f462,plain,(
% 26.61/4.02 ~int_less(n,sK2_skl)|~sQ1_spl),
% 26.61/4.02 inference(backward_demodulation,[status(thm)],[f65,f118])).
% 26.61/4.02 fof(f468,plain,(
% 26.61/4.02 int_less(sK2_skl,n)|sK2_skl=n|~sQ1_spl),
% 26.61/4.02 inference(resolution,[status(thm)],[f462,f58])).
% 26.61/4.02 fof(f471,definition,(
% 26.61/4.02 sQ21_spl <=> (int_less(sK2_skl,n))),
% 26.61/4.02 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 26.61/4.02 fof(f474,definition,(
% 26.61/4.02 sQ22_spl <=> (sK2_skl=n)),
% 26.61/4.02 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 26.61/4.02 fof(f477,plain,(
% 26.61/4.02 sQ21_spl|sQ22_spl|~sQ1_spl),
% 26.61/4.02 inference(split_clause,[status(thm)],[f468,f471,f474,f64])).
% 26.61/4.02 fof(f535,plain,(
% 26.61/4.02 ![X0]: (~int_less(sK1_skl,X0)|~int_less(X0,sK2_skl))),
% 26.61/4.02 inference(resolution,[status(thm)],[f118,f22])).
% 26.61/4.02 fof(f550,plain,(
% 26.61/4.02 ![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)),
% 26.61/4.02 inference(resolution,[status(thm)],[f54,f47])).
% 26.61/4.02 fof(f903,definition,(
% 26.61/4.02 sQ38_spl <=> (int_leq(int_one,sK2_skl))),
% 26.61/4.02 introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition])).
% 26.61/4.02 fof(f905,plain,(
% 26.61/4.02 ~int_leq(int_one,sK2_skl)|sQ38_spl),
% 26.61/4.02 inference(component_clause,[status(thm)],[f903])).
% 26.61/4.02 fof(f906,definition,(
% 26.61/4.02 sQ39_spl <=> (int_leq(sK2_skl,n))),
% 26.61/4.02 introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition])).
% 26.61/4.02 fof(f908,plain,(
% 26.61/4.02 ~int_leq(sK2_skl,n)|sQ39_spl),
% 26.61/4.02 inference(component_clause,[status(thm)],[f906])).
% 26.61/4.02 fof(f910,plain,(
% 26.61/4.02 $false|sQ38_spl),
% 26.61/4.02 inference(forward_subsumption_resolution,[status(thm)],[f905,f47])).
% 26.61/4.02 fof(f911,plain,(
% 26.61/4.02 sQ38_spl),
% 26.61/4.02 inference(contradiction_clause,[status(thm)],[f910])).
% 26.61/4.02 fof(f912,plain,(
% 26.61/4.02 int_less(n,sK2_skl)|sQ39_spl),
% 26.61/4.02 inference(resolution,[status(thm)],[f908,f25])).
% 26.61/4.02 fof(f913,plain,(
% 26.61/4.02 ~int_less(sK2_skl,n)|sQ39_spl),
% 26.61/4.02 inference(resolution,[status(thm)],[f908,f18])).
% 26.61/4.02 fof(f914,plain,(
% 26.61/4.02 $false|~sQ0_spl|~sQ5_spl|sQ39_spl),
% 26.61/4.02 inference(forward_subsumption_resolution,[status(thm)],[f912,f417])).
% 26.61/4.02 fof(f915,plain,(
% 26.61/4.02 ~sQ0_spl|~sQ5_spl|sQ39_spl),
% 26.61/4.02 inference(contradiction_clause,[status(thm)],[f914])).
% 26.61/4.02 fof(f919,plain,(
% 26.61/4.02 ~n=sK2_skl|~sQ1_spl|sQ4_spl),
% 26.61/4.02 inference(backward_demodulation,[status(thm)],[f65,f149])).
% 26.61/4.02 fof(f1612,definition,(
% 26.61/4.02 sQ75_spl <=> (int_leq(int_one,sK1_skl))),
% 26.61/4.02 introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition])).
% 26.61/4.02 fof(f1613,plain,(
% 26.61/4.02 int_leq(int_one,sK1_skl)|~sQ75_spl),
% 26.61/4.02 inference(component_clause,[status(thm)],[f1612])).
% 26.61/4.02 fof(f1614,plain,(
% 26.61/4.02 ~int_leq(int_one,sK1_skl)|sQ75_spl),
% 26.61/4.02 inference(component_clause,[status(thm)],[f1612])).
% 26.61/4.02 fof(f1708,plain,(
% 26.61/4.02 ~int_less(int_zero,sK1_skl)|sQ75_spl),
% 26.61/4.02 inference(resolution,[status(thm)],[f1614,f39])).
% 26.61/4.02 fof(f1712,plain,(
% 26.61/4.02 int_less(sK1_skl,int_zero)|sK1_skl=int_zero|sQ75_spl),
% 26.61/4.02 inference(resolution,[status(thm)],[f1708,f58])).
% 26.61/4.02 fof(f1715,definition,(
% 26.61/4.02 sQ83_spl <=> (int_less(sK1_skl,int_zero))),
% 26.61/4.02 introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition])).
% 26.61/4.02 fof(f1716,plain,(
% 26.61/4.02 int_less(sK1_skl,int_zero)|~sQ83_spl),
% 26.61/4.02 inference(component_clause,[status(thm)],[f1715])).
% 26.61/4.02 fof(f1718,definition,(
% 26.61/4.02 sQ84_spl <=> (sK1_skl=int_zero)),
% 26.61/4.02 introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition])).
% 26.61/4.02 fof(f1719,plain,(
% 26.61/4.02 sK1_skl=int_zero|~sQ84_spl),
% 26.61/4.02 inference(component_clause,[status(thm)],[f1718])).
% 26.61/4.02 fof(f1721,plain,(
% 26.61/4.02 sQ83_spl|sQ84_spl|sQ75_spl),
% 26.61/4.02 inference(split_clause,[status(thm)],[f1712,f1715,f1718,f1612])).
% 26.61/4.02 fof(f1727,plain,(
% 26.61/4.02 int_less(sK2_skl,int_zero)|~sQ84_spl|~sQ5_spl),
% 26.61/4.02 inference(backward_demodulation,[status(thm)],[f1719,f151])).
% 26.61/4.02 fof(f1733,plain,(
% 26.61/4.02 $false|~sQ84_spl|~sQ5_spl),
% 26.61/4.02 inference(forward_subsumption_resolution,[status(thm)],[f1727,f278])).
% 26.61/4.02 fof(f1734,plain,(
% 26.61/4.02 ~sQ84_spl|~sQ5_spl),
% 26.61/4.02 inference(contradiction_clause,[status(thm)],[f1733])).
% 26.61/4.02 fof(f1759,definition,(
% 26.61/4.02 sQ86_spl <=> (int_leq(sK1_skl,n))),
% 26.61/4.02 introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition])).
% 26.61/4.02 fof(f1761,plain,(
% 26.61/4.02 ~int_leq(sK1_skl,n)|sQ86_spl),
% 26.61/4.02 inference(component_clause,[status(thm)],[f1759])).
% 26.61/4.02 fof(f1777,plain,(
% 26.61/4.02 $false|sQ86_spl),
% 26.61/4.02 inference(forward_subsumption_resolution,[status(thm)],[f1761,f49])).
% 26.61/4.02 fof(f1778,plain,(
% 26.61/4.02 sQ86_spl),
% 26.61/4.02 inference(contradiction_clause,[status(thm)],[f1777])).
% 26.61/4.02 fof(f2303,plain,(
% 26.61/4.02 ~int_less(sK1_skl,int_zero)),
% 26.61/4.02 inference(resolution,[status(thm)],[f535,f265])).
% 26.61/4.02 fof(f4160,plain,(
% 26.61/4.02 ~sQ21_spl|sQ39_spl),
% 26.61/4.02 inference(split_clause,[status(thm)],[f913,f471,f906])).
% 26.61/4.02 fof(f4161,plain,(
% 26.61/4.02 $false|~sQ83_spl),
% 26.61/4.02 inference(forward_subsumption_resolution,[status(thm)],[f1716,f2303])).
% 26.61/4.02 fof(f4162,plain,(
% 26.61/4.02 ~sQ83_spl),
% 26.61/4.02 inference(contradiction_clause,[status(thm)],[f4161])).
% 26.61/4.02 fof(f4788,definition,(
% 26.61/4.02 sQ241_spl <=> (int_leq(int_one,plus(sK2_skl,sK0_skl(sK1_skl,sK2_skl))))),
% 26.61/4.02 introduced(definition,[new_symbols(definition,[sQ241_spl])],[split_symbol_definition])).
% 26.61/4.02 fof(f4790,plain,(
% 26.61/4.02 ~int_leq(int_one,plus(sK2_skl,sK0_skl(sK1_skl,sK2_skl)))|sQ241_spl),
% 26.61/4.02 inference(component_clause,[status(thm)],[f4788])).
% 26.61/4.02 fof(f4798,definition,(
% 26.61/4.02 sQ244_spl <=> (int_less(int_zero,sK0_skl(sK1_skl,sK2_skl)))),
% 26.61/4.02 introduced(definition,[new_symbols(definition,[sQ244_spl])],[split_symbol_definition])).
% 26.61/4.02 fof(f4800,plain,(
% 26.61/4.02 ~int_less(int_zero,sK0_skl(sK1_skl,sK2_skl))|sQ244_spl),
% 26.61/4.02 inference(component_clause,[status(thm)],[f4798])).
% 26.61/4.02 fof(f4826,plain,(
% 26.61/4.02 ~int_leq(int_one,sK1_skl)|sQ241_spl),
% 26.61/4.02 inference(forward_demodulation,[status(thm)],[f100,f4790])).
% 26.61/4.02 fof(f4997,plain,(
% 26.61/4.02 $false|~sQ75_spl|sQ241_spl),
% 26.61/4.02 inference(forward_subsumption_resolution,[status(thm)],[f4826,f1613])).
% 26.61/4.02 fof(f4998,plain,(
% 26.61/4.02 ~sQ75_spl|sQ241_spl),
% 26.61/4.02 inference(contradiction_clause,[status(thm)],[f4997])).
% 26.61/4.02 fof(f6797,plain,(
% 26.61/4.02 ~int_less(sK2_skl,sK1_skl)|sQ244_spl),
% 26.61/4.02 inference(resolution,[status(thm)],[f4800,f35])).
% 26.61/4.02 fof(f6803,plain,(
% 26.61/4.02 $false|~sQ5_spl|sQ244_spl),
% 26.61/4.02 inference(forward_subsumption_resolution,[status(thm)],[f6797,f151])).
% 26.61/4.02 fof(f6804,plain,(
% 26.61/4.02 ~sQ5_spl|sQ244_spl),
% 26.61/4.02 inference(contradiction_clause,[status(thm)],[f6803])).
% 26.61/4.02 fof(f6865,plain,(
% 26.61/4.02 ~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),
% 26.61/4.02 inference(paramodulation,[status(thm)],[f100,f550])).
% 26.61/4.02 fof(f6870,definition,(
% 26.61/4.02 sQ314_spl <=> (int_leq(sK2_skl,sK2_skl))),
% 26.61/4.02 introduced(definition,[new_symbols(definition,[sQ314_spl])],[split_symbol_definition])).
% 26.61/4.02 fof(f6872,plain,(
% 26.61/4.02 ~int_leq(sK2_skl,sK2_skl)|sQ314_spl),
% 26.61/4.02 inference(component_clause,[status(thm)],[f6870])).
% 26.61/4.02 fof(f6873,definition,(
% 26.61/4.02 sQ315_spl <=> (a(plus(sK2_skl,sK0_skl(sK1_skl,sK2_skl)),sK2_skl)=real_zero)),
% 26.61/4.02 introduced(definition,[new_symbols(definition,[sQ315_spl])],[split_symbol_definition])).
% 26.61/4.02 fof(f6874,plain,(
% 26.61/4.02 a(plus(sK2_skl,sK0_skl(sK1_skl,sK2_skl)),sK2_skl)=real_zero|~sQ315_spl),
% 26.61/4.05 inference(component_clause,[status(thm)],[f6873])).
% 26.61/4.05 fof(f6876,plain,(
% 26.61/4.05 ~sQ241_spl|~sQ86_spl|~sQ38_spl|~sQ39_spl|~sQ244_spl|~sQ314_spl|sQ315_spl),
% 26.61/4.05 inference(split_clause,[status(thm)],[f6865,f4788,f1759,f903,f906,f4798,f6870,f6873])).
% 26.61/4.05 fof(f6891,plain,(
% 26.61/4.05 $false|sQ314_spl),
% 26.61/4.05 inference(forward_subsumption_resolution,[status(thm)],[f6872,f51])).
% 26.61/4.05 fof(f6892,plain,(
% 26.61/4.05 sQ314_spl),
% 26.61/4.05 inference(contradiction_clause,[status(thm)],[f6891])).
% 26.61/4.05 fof(f6898,plain,(
% 26.61/4.05 a(sK1_skl,sK2_skl)=real_zero|~sQ315_spl),
% 26.61/4.05 inference(forward_demodulation,[status(thm)],[f100,f6874])).
% 26.61/4.05 fof(f6899,plain,(
% 26.61/4.05 $false|~sQ315_spl),
% 26.61/4.05 inference(forward_subsumption_resolution,[status(thm)],[f6898,f50])).
% 26.61/4.05 fof(f6900,plain,(
% 26.61/4.05 ~sQ315_spl),
% 26.61/4.05 inference(contradiction_clause,[status(thm)],[f6899])).
% 26.61/4.05 fof(f6902,plain,(
% 26.61/4.05 ~sQ22_spl|~sQ1_spl|sQ4_spl),
% 26.61/4.05 inference(split_clause,[status(thm)],[f919,f474,f64,f147])).
% 26.61/4.05 fof(f6906,plain,(
% 26.61/4.05 $false),
% 26.61/4.05 inference(sat_refutation,[status(thm)],[f67,f153,f228,f477,f911,f915,f1721,f1734,f1778,f4160,f4162,f4998,f6804,f6876,f6892,f6900,f6902])).
% 26.61/4.05 % SZS output end CNFRefutation for theBenchmark.p
% 12.09/4.06 % Elapsed time: 3.525943 seconds
% 12.09/4.06 % CPU time: 27.398718 seconds
% 12.09/4.06 % Total memory used: 199.711 MB
% 12.09/4.06 % Net memory used: 177.952 MB
%------------------------------------------------------------------------------