TSTP Solution File: HAL001+2 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : HAL001+2 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:12:43 EDT 2023
% Result : Theorem 124.25s 15.94s
% Output : CNFRefutation 124.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08 % Problem : HAL001+2 : TPTP v8.1.2. Released v2.6.0.
% 0.04/0.08 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.27 % Computer : n004.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 300
% 0.07/0.27 % DateTime : Tue May 30 10:58:52 EDT 2023
% 0.07/0.27 % CPUTime :
% 0.07/0.28 % Drodi V3.5.1
% 124.25/15.94 % Refutation found
% 124.25/15.94 % SZS status Theorem for theBenchmark: Theorem is valid
% 124.25/15.94 % SZS output start CNFRefutation for theBenchmark
% 124.25/15.94 fof(f1,axiom,(
% 124.25/15.94 (! [Morphism,Dom,Cod] :( morphism(Morphism,Dom,Cod)=> ( (! [El] :( element(El,Dom)=> element(apply(Morphism,El),Cod) ))& apply(Morphism,zero(Dom)) = zero(Cod) ) ) )),
% 124.25/15.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 124.25/15.94 fof(f6,axiom,(
% 124.25/15.94 (! [Morphism1,Morphism2,Dom,CodDom,Cod] :( ( exact(Morphism1,Morphism2)& morphism(Morphism1,Dom,CodDom)& morphism(Morphism2,CodDom,Cod) )=> (! [ElCodDom] :( ( element(ElCodDom,CodDom)& apply(Morphism2,ElCodDom) = zero(Cod) )<=> (? [ElDom] :( element(ElDom,Dom)& apply(Morphism1,ElDom) = ElCodDom ) )) )) )),
% 124.25/15.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 124.25/15.94 fof(f8,axiom,(
% 124.25/15.94 (! [M1,M2,M3,M4,Dom,DomCod1,DomCod2,Cod] :( ( commute(M1,M2,M3,M4)& morphism(M1,Dom,DomCod1)& morphism(M2,DomCod1,Cod)& morphism(M3,Dom,DomCod2)& morphism(M4,DomCod2,Cod) )=> (! [ElDom] :( element(ElDom,Dom)=> apply(M2,apply(M1,ElDom)) = apply(M4,apply(M3,ElDom)) ) )) )),
% 124.25/15.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 124.25/15.94 fof(f14,axiom,(
% 124.25/15.94 (! [Morphism,Dom,Cod] :( ( injection(Morphism)& morphism(Morphism,Dom,Cod) )=> (! [El] :( ( element(El,Dom)& apply(Morphism,El) = zero(Cod) )=> El = zero(Dom) ) )) )),
% 124.25/15.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 124.25/15.94 fof(f15,axiom,(
% 124.25/15.94 (! [Morphism,Dom,Cod] :( ( morphism(Morphism,Dom,Cod)& (! [El] :( ( element(El,Dom)& apply(Morphism,El) = zero(Cod) )=> El = zero(Dom) ) ))=> injection(Morphism) ) )),
% 124.25/15.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 124.25/15.94 fof(f16,axiom,(
% 124.25/15.94 morphism(alpha,a,b) ),
% 124.25/15.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 124.25/15.94 fof(f17,axiom,(
% 124.25/15.94 morphism(beta,b,c) ),
% 124.25/15.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 124.25/15.94 fof(f18,axiom,(
% 124.25/15.94 morphism(gamma,d,e) ),
% 124.25/15.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 124.25/15.94 fof(f19,axiom,(
% 124.25/15.94 morphism(delta,e,r) ),
% 124.25/15.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 124.25/15.94 fof(f20,axiom,(
% 124.25/15.94 morphism(f,a,d) ),
% 124.25/15.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 124.25/15.94 fof(f21,axiom,(
% 124.25/15.94 morphism(g,b,e) ),
% 124.25/15.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 124.25/15.94 fof(f22,axiom,(
% 124.25/15.94 morphism(h,c,r) ),
% 124.25/15.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 124.25/15.94 fof(f24,axiom,(
% 124.25/15.94 injection(gamma) ),
% 124.25/15.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 124.25/15.94 fof(f27,axiom,(
% 124.25/15.94 exact(alpha,beta) ),
% 124.25/15.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 124.25/15.94 fof(f29,axiom,(
% 124.25/15.94 commute(alpha,g,f,gamma) ),
% 124.25/15.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 124.25/15.94 fof(f30,axiom,(
% 124.25/15.94 commute(beta,h,g,delta) ),
% 124.25/15.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 124.25/15.94 fof(f31,hypothesis,(
% 124.25/15.94 injection(f) ),
% 124.25/15.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 124.25/15.94 fof(f32,hypothesis,(
% 124.25/15.94 injection(h) ),
% 124.25/15.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 124.25/15.94 fof(f33,conjecture,(
% 124.25/15.94 injection(g) ),
% 124.25/15.94 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 124.25/15.94 fof(f34,negated_conjecture,(
% 124.25/15.94 ~(injection(g) )),
% 124.25/15.94 inference(negated_conjecture,[status(cth)],[f33])).
% 124.25/15.94 fof(f35,plain,(
% 124.25/15.94 ![Morphism,Dom,Cod]: (~morphism(Morphism,Dom,Cod)|((![El]: (~element(El,Dom)|element(apply(Morphism,El),Cod)))&apply(Morphism,zero(Dom))=zero(Cod)))),
% 124.25/15.94 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 124.25/15.94 fof(f36,plain,(
% 124.25/15.94 ![X0,X1,X2,X3]: (~morphism(X0,X1,X2)|~element(X3,X1)|element(apply(X0,X3),X2))),
% 124.25/15.94 inference(cnf_transformation,[status(esa)],[f35])).
% 124.25/15.94 fof(f37,plain,(
% 124.25/15.94 ![X0,X1,X2]: (~morphism(X0,X1,X2)|apply(X0,zero(X1))=zero(X2))),
% 124.25/15.94 inference(cnf_transformation,[status(esa)],[f35])).
% 124.25/15.94 fof(f57,plain,(
% 124.25/15.94 ![Morphism1,Morphism2,Dom,CodDom,Cod]: (((~exact(Morphism1,Morphism2)|~morphism(Morphism1,Dom,CodDom))|~morphism(Morphism2,CodDom,Cod))|(![ElCodDom]: ((element(ElCodDom,CodDom)&apply(Morphism2,ElCodDom)=zero(Cod))<=>(?[ElDom]: (element(ElDom,Dom)&apply(Morphism1,ElDom)=ElCodDom)))))),
% 124.25/15.94 inference(pre_NNF_transformation,[status(esa)],[f6])).
% 124.25/15.94 fof(f58,plain,(
% 124.25/15.94 ![Morphism1,Morphism2,Dom,CodDom,Cod]: (((~exact(Morphism1,Morphism2)|~morphism(Morphism1,Dom,CodDom))|~morphism(Morphism2,CodDom,Cod))|(![ElCodDom]: (((~element(ElCodDom,CodDom)|~apply(Morphism2,ElCodDom)=zero(Cod))|(?[ElDom]: (element(ElDom,Dom)&apply(Morphism1,ElDom)=ElCodDom)))&((element(ElCodDom,CodDom)&apply(Morphism2,ElCodDom)=zero(Cod))|(![ElDom]: (~element(ElDom,Dom)|~apply(Morphism1,ElDom)=ElCodDom))))))),
% 124.55/15.95 inference(NNF_transformation,[status(esa)],[f57])).
% 124.55/15.95 fof(f59,plain,(
% 124.55/15.95 ![Morphism1,Morphism2,Dom,CodDom,Cod]: (((~exact(Morphism1,Morphism2)|~morphism(Morphism1,Dom,CodDom))|~morphism(Morphism2,CodDom,Cod))|((![ElCodDom]: ((~element(ElCodDom,CodDom)|~apply(Morphism2,ElCodDom)=zero(Cod))|(?[ElDom]: (element(ElDom,Dom)&apply(Morphism1,ElDom)=ElCodDom))))&(![ElCodDom]: ((element(ElCodDom,CodDom)&apply(Morphism2,ElCodDom)=zero(Cod))|(![ElDom]: (~element(ElDom,Dom)|~apply(Morphism1,ElDom)=ElCodDom))))))),
% 124.55/15.95 inference(miniscoping,[status(esa)],[f58])).
% 124.55/15.95 fof(f60,plain,(
% 124.55/15.95 ![Morphism1,Morphism2,Dom,CodDom,Cod]: (((~exact(Morphism1,Morphism2)|~morphism(Morphism1,Dom,CodDom))|~morphism(Morphism2,CodDom,Cod))|((![ElCodDom]: ((~element(ElCodDom,CodDom)|~apply(Morphism2,ElCodDom)=zero(Cod))|(element(sk0_4(ElCodDom,Cod,CodDom,Dom,Morphism2,Morphism1),Dom)&apply(Morphism1,sk0_4(ElCodDom,Cod,CodDom,Dom,Morphism2,Morphism1))=ElCodDom)))&(![ElCodDom]: ((element(ElCodDom,CodDom)&apply(Morphism2,ElCodDom)=zero(Cod))|(![ElDom]: (~element(ElDom,Dom)|~apply(Morphism1,ElDom)=ElCodDom))))))),
% 124.55/15.95 inference(skolemization,[status(esa)],[f59])).
% 124.55/15.95 fof(f61,plain,(
% 124.55/15.95 ![X0,X1,X2,X3,X4,X5]: (~exact(X0,X1)|~morphism(X0,X2,X3)|~morphism(X1,X3,X4)|~element(X5,X3)|~apply(X1,X5)=zero(X4)|element(sk0_4(X5,X4,X3,X2,X1,X0),X2))),
% 124.55/15.95 inference(cnf_transformation,[status(esa)],[f60])).
% 124.55/15.95 fof(f62,plain,(
% 124.55/15.95 ![X0,X1,X2,X3,X4,X5]: (~exact(X0,X1)|~morphism(X0,X2,X3)|~morphism(X1,X3,X4)|~element(X5,X3)|~apply(X1,X5)=zero(X4)|apply(X0,sk0_4(X5,X4,X3,X2,X1,X0))=X5)),
% 124.55/15.95 inference(cnf_transformation,[status(esa)],[f60])).
% 124.55/15.95 fof(f74,plain,(
% 124.55/15.95 ![M1,M2,M3,M4,Dom,DomCod1,DomCod2,Cod]: (((((~commute(M1,M2,M3,M4)|~morphism(M1,Dom,DomCod1))|~morphism(M2,DomCod1,Cod))|~morphism(M3,Dom,DomCod2))|~morphism(M4,DomCod2,Cod))|(![ElDom]: (~element(ElDom,Dom)|apply(M2,apply(M1,ElDom))=apply(M4,apply(M3,ElDom)))))),
% 124.55/15.95 inference(pre_NNF_transformation,[status(esa)],[f8])).
% 124.55/15.95 fof(f75,plain,(
% 124.55/15.95 ![M1,M2,M3,M4,Dom]: ((![DomCod2,Cod]: (((![DomCod1]: ((~commute(M1,M2,M3,M4)|~morphism(M1,Dom,DomCod1))|~morphism(M2,DomCod1,Cod)))|~morphism(M3,Dom,DomCod2))|~morphism(M4,DomCod2,Cod)))|(![ElDom]: (~element(ElDom,Dom)|apply(M2,apply(M1,ElDom))=apply(M4,apply(M3,ElDom)))))),
% 124.55/15.95 inference(miniscoping,[status(esa)],[f74])).
% 124.55/15.95 fof(f76,plain,(
% 124.55/15.95 ![X0,X1,X2,X3,X4,X5,X6,X7,X8]: (~commute(X0,X1,X2,X3)|~morphism(X0,X4,X5)|~morphism(X1,X5,X6)|~morphism(X2,X4,X7)|~morphism(X3,X7,X6)|~element(X8,X4)|apply(X1,apply(X0,X8))=apply(X3,apply(X2,X8)))),
% 124.55/15.95 inference(cnf_transformation,[status(esa)],[f75])).
% 124.55/15.95 fof(f90,plain,(
% 124.55/15.95 ![Morphism,Dom,Cod]: ((~injection(Morphism)|~morphism(Morphism,Dom,Cod))|(![El]: ((~element(El,Dom)|~apply(Morphism,El)=zero(Cod))|El=zero(Dom))))),
% 124.55/15.95 inference(pre_NNF_transformation,[status(esa)],[f14])).
% 124.55/15.95 fof(f91,plain,(
% 124.55/15.95 ![X0,X1,X2,X3]: (~injection(X0)|~morphism(X0,X1,X2)|~element(X3,X1)|~apply(X0,X3)=zero(X2)|X3=zero(X1))),
% 124.55/15.95 inference(cnf_transformation,[status(esa)],[f90])).
% 124.55/15.95 fof(f92,plain,(
% 124.55/15.95 ![Morphism,Dom,Cod]: ((~morphism(Morphism,Dom,Cod)|(?[El]: ((element(El,Dom)&apply(Morphism,El)=zero(Cod))&~El=zero(Dom))))|injection(Morphism))),
% 124.55/15.95 inference(pre_NNF_transformation,[status(esa)],[f15])).
% 124.55/15.95 fof(f93,plain,(
% 124.55/15.95 ![Morphism]: ((![Dom,Cod]: (~morphism(Morphism,Dom,Cod)|(?[El]: ((element(El,Dom)&apply(Morphism,El)=zero(Cod))&~El=zero(Dom)))))|injection(Morphism))),
% 124.55/15.95 inference(miniscoping,[status(esa)],[f92])).
% 124.55/15.95 fof(f94,plain,(
% 124.55/15.95 ![Morphism]: ((![Dom,Cod]: (~morphism(Morphism,Dom,Cod)|((element(sk0_8(Cod,Dom,Morphism),Dom)&apply(Morphism,sk0_8(Cod,Dom,Morphism))=zero(Cod))&~sk0_8(Cod,Dom,Morphism)=zero(Dom))))|injection(Morphism))),
% 124.55/15.95 inference(skolemization,[status(esa)],[f93])).
% 124.55/15.95 fof(f95,plain,(
% 124.55/15.95 ![X0,X1,X2]: (~morphism(X0,X1,X2)|element(sk0_8(X2,X1,X0),X1)|injection(X0))),
% 124.55/15.95 inference(cnf_transformation,[status(esa)],[f94])).
% 124.55/15.95 fof(f96,plain,(
% 124.55/15.95 ![X0,X1,X2]: (~morphism(X0,X1,X2)|apply(X0,sk0_8(X2,X1,X0))=zero(X2)|injection(X0))),
% 124.55/15.95 inference(cnf_transformation,[status(esa)],[f94])).
% 124.55/15.95 fof(f97,plain,(
% 124.55/15.95 ![X0,X1,X2]: (~morphism(X0,X1,X2)|~sk0_8(X2,X1,X0)=zero(X1)|injection(X0))),
% 124.55/15.95 inference(cnf_transformation,[status(esa)],[f94])).
% 124.55/15.95 fof(f98,plain,(
% 124.55/15.95 morphism(alpha,a,b)),
% 124.55/15.95 inference(cnf_transformation,[status(esa)],[f16])).
% 124.55/15.95 fof(f99,plain,(
% 124.55/15.95 morphism(beta,b,c)),
% 124.55/15.95 inference(cnf_transformation,[status(esa)],[f17])).
% 124.55/15.95 fof(f100,plain,(
% 124.55/15.95 morphism(gamma,d,e)),
% 124.55/15.95 inference(cnf_transformation,[status(esa)],[f18])).
% 124.55/15.95 fof(f101,plain,(
% 124.55/15.95 morphism(delta,e,r)),
% 124.55/15.95 inference(cnf_transformation,[status(esa)],[f19])).
% 124.55/15.95 fof(f102,plain,(
% 124.55/15.95 morphism(f,a,d)),
% 124.55/15.95 inference(cnf_transformation,[status(esa)],[f20])).
% 124.55/15.95 fof(f103,plain,(
% 124.55/15.95 morphism(g,b,e)),
% 124.55/15.95 inference(cnf_transformation,[status(esa)],[f21])).
% 124.55/15.95 fof(f104,plain,(
% 124.55/15.95 morphism(h,c,r)),
% 124.55/15.95 inference(cnf_transformation,[status(esa)],[f22])).
% 124.55/15.95 fof(f106,plain,(
% 124.55/15.95 injection(gamma)),
% 124.55/15.95 inference(cnf_transformation,[status(esa)],[f24])).
% 124.55/15.95 fof(f109,plain,(
% 124.55/15.95 exact(alpha,beta)),
% 124.55/15.95 inference(cnf_transformation,[status(esa)],[f27])).
% 124.55/15.95 fof(f111,plain,(
% 124.55/15.95 commute(alpha,g,f,gamma)),
% 124.55/15.95 inference(cnf_transformation,[status(esa)],[f29])).
% 124.55/15.95 fof(f112,plain,(
% 124.55/15.95 commute(beta,h,g,delta)),
% 124.55/15.95 inference(cnf_transformation,[status(esa)],[f30])).
% 124.55/15.95 fof(f113,plain,(
% 124.55/15.95 injection(f)),
% 124.55/15.95 inference(cnf_transformation,[status(esa)],[f31])).
% 124.55/15.95 fof(f114,plain,(
% 124.55/15.95 injection(h)),
% 124.55/15.95 inference(cnf_transformation,[status(esa)],[f32])).
% 124.55/15.95 fof(f115,plain,(
% 124.55/15.95 ~injection(g)),
% 124.55/15.95 inference(cnf_transformation,[status(esa)],[f34])).
% 124.55/15.95 fof(f124,plain,(
% 124.55/15.95 apply(alpha,zero(a))=zero(b)),
% 124.55/15.95 inference(resolution,[status(thm)],[f37,f98])).
% 124.55/15.95 fof(f126,plain,(
% 124.55/15.95 apply(delta,zero(e))=zero(r)),
% 124.55/15.95 inference(resolution,[status(thm)],[f101,f37])).
% 124.55/15.95 fof(f129,plain,(
% 124.55/15.95 apply(h,zero(c))=zero(r)),
% 124.55/15.95 inference(resolution,[status(thm)],[f104,f37])).
% 124.55/15.95 fof(f155,plain,(
% 124.55/15.95 spl0_4 <=> injection(gamma)),
% 124.55/15.95 introduced(split_symbol_definition)).
% 124.55/15.95 fof(f157,plain,(
% 124.55/15.95 ~injection(gamma)|spl0_4),
% 124.55/15.95 inference(component_clause,[status(thm)],[f155])).
% 124.55/15.95 fof(f165,plain,(
% 124.55/15.95 $false|spl0_4),
% 124.55/15.95 inference(forward_subsumption_resolution,[status(thm)],[f157,f106])).
% 124.55/15.95 fof(f166,plain,(
% 124.55/15.95 spl0_4),
% 124.55/15.95 inference(contradiction_clause,[status(thm)],[f165])).
% 124.55/15.95 fof(f179,plain,(
% 124.55/15.95 spl0_8 <=> injection(f)),
% 124.55/15.95 introduced(split_symbol_definition)).
% 124.55/15.95 fof(f181,plain,(
% 124.55/15.95 ~injection(f)|spl0_8),
% 124.55/15.95 inference(component_clause,[status(thm)],[f179])).
% 124.55/15.95 fof(f189,plain,(
% 124.55/15.95 $false|spl0_8),
% 124.55/15.95 inference(forward_subsumption_resolution,[status(thm)],[f181,f113])).
% 124.55/15.95 fof(f190,plain,(
% 124.55/15.95 spl0_8),
% 124.55/15.95 inference(contradiction_clause,[status(thm)],[f189])).
% 124.55/15.95 fof(f192,plain,(
% 124.55/15.95 spl0_10 <=> injection(g)),
% 124.55/15.95 introduced(split_symbol_definition)).
% 124.55/15.95 fof(f193,plain,(
% 124.55/15.95 injection(g)|~spl0_10),
% 124.55/15.95 inference(component_clause,[status(thm)],[f192])).
% 124.55/15.95 fof(f203,plain,(
% 124.55/15.95 spl0_12 <=> injection(h)),
% 124.55/15.95 introduced(split_symbol_definition)).
% 124.55/15.95 fof(f205,plain,(
% 124.55/15.95 ~injection(h)|spl0_12),
% 124.55/15.95 inference(component_clause,[status(thm)],[f203])).
% 124.55/15.95 fof(f213,plain,(
% 124.55/15.95 $false|spl0_12),
% 124.55/15.95 inference(forward_subsumption_resolution,[status(thm)],[f205,f114])).
% 124.55/15.95 fof(f214,plain,(
% 124.55/15.95 spl0_12),
% 124.55/15.95 inference(contradiction_clause,[status(thm)],[f213])).
% 124.55/15.95 fof(f287,plain,(
% 124.55/15.95 ![X0,X1]: (~morphism(g,X0,X1)|~sk0_8(X1,X0,g)=zero(X0))),
% 124.55/15.95 inference(resolution,[status(thm)],[f97,f115])).
% 124.55/15.95 fof(f290,plain,(
% 124.55/15.95 ~sk0_8(e,b,g)=zero(b)),
% 124.55/15.95 inference(resolution,[status(thm)],[f287,f103])).
% 124.55/15.95 fof(f294,plain,(
% 124.55/15.95 spl0_23 <=> ~apply(X1,zero(c))=zero(X2)),
% 124.55/15.95 introduced(split_symbol_definition)).
% 124.55/15.95 fof(f295,plain,(
% 124.55/15.95 ![X0,X1]: (~apply(X0,zero(c))=zero(X1)|~spl0_23)),
% 124.55/15.95 inference(component_clause,[status(thm)],[f294])).
% 124.55/15.95 fof(f331,plain,(
% 124.55/15.95 ![X0,X1]: (~morphism(g,X0,X1)|apply(g,sk0_8(X1,X0,g))=zero(X1))),
% 124.55/15.95 inference(resolution,[status(thm)],[f96,f115])).
% 124.55/15.95 fof(f332,plain,(
% 124.55/15.95 apply(g,sk0_8(e,b,g))=zero(e)),
% 124.55/15.95 inference(resolution,[status(thm)],[f331,f103])).
% 124.55/15.95 fof(f342,plain,(
% 124.55/15.95 spl0_29 <=> element(sk0_8(e,b,g),b)),
% 124.55/15.95 introduced(split_symbol_definition)).
% 124.55/15.95 fof(f343,plain,(
% 124.55/15.95 element(sk0_8(e,b,g),b)|~spl0_29),
% 124.55/15.95 inference(component_clause,[status(thm)],[f342])).
% 124.55/15.95 fof(f344,plain,(
% 124.55/15.95 ~element(sk0_8(e,b,g),b)|spl0_29),
% 124.55/15.95 inference(component_clause,[status(thm)],[f342])).
% 124.55/15.95 fof(f495,plain,(
% 124.55/15.95 spl0_58 <=> ~element(X0,c)|~apply(h,X0)=zero(r)|X0=zero(c)),
% 124.55/15.95 introduced(split_symbol_definition)).
% 124.55/15.95 fof(f496,plain,(
% 124.55/15.95 ![X0]: (~element(X0,c)|~apply(h,X0)=zero(r)|X0=zero(c)|~spl0_58)),
% 124.55/15.95 inference(component_clause,[status(thm)],[f495])).
% 124.55/15.95 fof(f498,plain,(
% 124.55/15.95 ![X0]: (~injection(h)|~element(X0,c)|~apply(h,X0)=zero(r)|X0=zero(c))),
% 124.55/15.95 inference(resolution,[status(thm)],[f91,f104])).
% 124.55/15.95 fof(f499,plain,(
% 124.55/15.95 ~spl0_12|spl0_58),
% 124.55/15.95 inference(split_clause,[status(thm)],[f498,f203,f495])).
% 124.55/15.95 fof(f505,plain,(
% 124.55/15.95 spl0_60 <=> ~element(X0,a)|~apply(f,X0)=zero(d)|X0=zero(a)),
% 124.55/15.95 introduced(split_symbol_definition)).
% 124.55/15.95 fof(f506,plain,(
% 124.55/15.95 ![X0]: (~element(X0,a)|~apply(f,X0)=zero(d)|X0=zero(a)|~spl0_60)),
% 124.55/15.95 inference(component_clause,[status(thm)],[f505])).
% 124.55/15.95 fof(f508,plain,(
% 124.55/15.95 ![X0]: (~injection(f)|~element(X0,a)|~apply(f,X0)=zero(d)|X0=zero(a))),
% 124.55/15.95 inference(resolution,[status(thm)],[f91,f102])).
% 124.55/15.95 fof(f509,plain,(
% 124.55/15.95 ~spl0_8|spl0_60),
% 124.55/15.95 inference(split_clause,[status(thm)],[f508,f179,f505])).
% 124.55/15.95 fof(f515,plain,(
% 124.55/15.95 spl0_62 <=> ~element(X0,d)|~apply(gamma,X0)=zero(e)|X0=zero(d)),
% 124.55/15.95 introduced(split_symbol_definition)).
% 124.55/15.95 fof(f516,plain,(
% 124.55/15.95 ![X0]: (~element(X0,d)|~apply(gamma,X0)=zero(e)|X0=zero(d)|~spl0_62)),
% 124.55/15.95 inference(component_clause,[status(thm)],[f515])).
% 124.55/15.95 fof(f518,plain,(
% 124.55/15.95 ![X0]: (~injection(gamma)|~element(X0,d)|~apply(gamma,X0)=zero(e)|X0=zero(d))),
% 124.55/15.95 inference(resolution,[status(thm)],[f91,f100])).
% 124.55/15.95 fof(f519,plain,(
% 124.55/15.95 ~spl0_4|spl0_62),
% 124.55/15.95 inference(split_clause,[status(thm)],[f518,f155,f515])).
% 124.55/15.95 fof(f536,plain,(
% 124.55/15.95 ![X0,X1,X2,X3]: (~morphism(alpha,X0,X1)|~morphism(beta,X1,X2)|~element(X3,X1)|~apply(beta,X3)=zero(X2)|apply(alpha,sk0_4(X3,X2,X1,X0,beta,alpha))=X3)),
% 124.55/15.95 inference(resolution,[status(thm)],[f62,f109])).
% 124.55/15.95 fof(f549,plain,(
% 124.55/15.95 $false|~spl0_10),
% 124.55/15.95 inference(forward_subsumption_resolution,[status(thm)],[f193,f115])).
% 124.55/15.95 fof(f550,plain,(
% 124.55/15.95 ~spl0_10),
% 124.55/15.95 inference(contradiction_clause,[status(thm)],[f549])).
% 124.55/15.95 fof(f552,plain,(
% 124.55/15.95 spl0_66 <=> morphism(g,b,e)),
% 124.55/15.95 introduced(split_symbol_definition)).
% 124.55/15.95 fof(f554,plain,(
% 124.55/15.95 ~morphism(g,b,e)|spl0_66),
% 124.55/15.95 inference(component_clause,[status(thm)],[f552])).
% 124.55/15.95 fof(f555,plain,(
% 124.55/15.95 ~morphism(g,b,e)|injection(g)|spl0_29),
% 124.55/15.95 inference(resolution,[status(thm)],[f344,f95])).
% 124.55/15.95 fof(f556,plain,(
% 124.55/15.95 ~spl0_66|spl0_10|spl0_29),
% 124.55/15.95 inference(split_clause,[status(thm)],[f555,f552,f192,f342])).
% 124.55/15.95 fof(f558,plain,(
% 124.55/15.95 $false|spl0_66),
% 124.55/15.95 inference(forward_subsumption_resolution,[status(thm)],[f554,f103])).
% 124.55/15.95 fof(f559,plain,(
% 124.55/15.95 spl0_66),
% 124.55/15.95 inference(contradiction_clause,[status(thm)],[f558])).
% 124.55/15.95 fof(f999,plain,(
% 124.55/15.95 ![X0,X1,X2,X3,X4]: (~morphism(beta,X0,X1)|~morphism(h,X1,X2)|~morphism(g,X0,X3)|~morphism(delta,X3,X2)|~element(X4,X0)|apply(h,apply(beta,X4))=apply(delta,apply(g,X4)))),
% 124.55/15.95 inference(resolution,[status(thm)],[f76,f112])).
% 124.55/15.95 fof(f1000,plain,(
% 124.55/15.95 ![X0,X1,X2,X3,X4]: (~morphism(alpha,X0,X1)|~morphism(g,X1,X2)|~morphism(f,X0,X3)|~morphism(gamma,X3,X2)|~element(X4,X0)|apply(g,apply(alpha,X4))=apply(gamma,apply(f,X4)))),
% 124.55/15.95 inference(resolution,[status(thm)],[f76,f111])).
% 124.55/15.95 fof(f1091,plain,(
% 124.55/15.95 spl0_125 <=> morphism(beta,b,c)),
% 124.55/15.95 introduced(split_symbol_definition)).
% 124.55/15.95 fof(f1093,plain,(
% 124.55/15.95 ~morphism(beta,b,c)|spl0_125),
% 124.55/15.95 inference(component_clause,[status(thm)],[f1091])).
% 124.55/15.95 fof(f1097,plain,(
% 124.55/15.95 $false|spl0_125),
% 124.55/15.95 inference(forward_subsumption_resolution,[status(thm)],[f1093,f99])).
% 124.55/15.95 fof(f1098,plain,(
% 124.55/15.95 spl0_125),
% 124.55/15.95 inference(contradiction_clause,[status(thm)],[f1097])).
% 124.55/15.95 fof(f1640,plain,(
% 124.55/15.95 ![X0,X1]: (~morphism(alpha,X0,b)|~element(X1,b)|~apply(beta,X1)=zero(c)|apply(alpha,sk0_4(X1,c,b,X0,beta,alpha))=X1)),
% 124.55/15.95 inference(resolution,[status(thm)],[f536,f99])).
% 124.55/15.95 fof(f2050,plain,(
% 124.55/15.95 ![X0]: (~element(X0,b)|~apply(beta,X0)=zero(c)|apply(alpha,sk0_4(X0,c,b,a,beta,alpha))=X0)),
% 124.55/15.95 inference(resolution,[status(thm)],[f1640,f98])).
% 124.55/15.95 fof(f2082,plain,(
% 124.55/15.95 spl0_258 <=> apply(beta,sk0_8(e,b,g))=zero(c)),
% 124.55/15.95 introduced(split_symbol_definition)).
% 124.55/15.95 fof(f2085,plain,(
% 124.55/15.95 spl0_259 <=> apply(alpha,sk0_4(sk0_8(e,b,g),c,b,a,beta,alpha))=sk0_8(e,b,g)),
% 124.55/15.96 introduced(split_symbol_definition)).
% 124.55/15.96 fof(f2086,plain,(
% 124.55/15.96 apply(alpha,sk0_4(sk0_8(e,b,g),c,b,a,beta,alpha))=sk0_8(e,b,g)|~spl0_259),
% 124.55/15.96 inference(component_clause,[status(thm)],[f2085])).
% 124.55/15.96 fof(f2088,plain,(
% 124.55/15.96 ~apply(beta,sk0_8(e,b,g))=zero(c)|apply(alpha,sk0_4(sk0_8(e,b,g),c,b,a,beta,alpha))=sk0_8(e,b,g)|~spl0_29),
% 124.55/15.96 inference(resolution,[status(thm)],[f2050,f343])).
% 124.55/15.96 fof(f2089,plain,(
% 124.55/15.96 ~spl0_258|spl0_259|~spl0_29),
% 124.55/15.96 inference(split_clause,[status(thm)],[f2088,f2082,f2085,f342])).
% 124.55/15.96 fof(f2211,plain,(
% 124.55/15.96 spl0_274 <=> ~morphism(beta,b,X0)|~morphism(h,X0,X1)|~morphism(delta,e,X1)),
% 124.55/15.96 introduced(split_symbol_definition)).
% 124.55/15.96 fof(f2212,plain,(
% 124.55/15.96 ![X0,X1]: (~morphism(beta,b,X0)|~morphism(h,X0,X1)|~morphism(delta,e,X1)|~spl0_274)),
% 124.55/15.96 inference(component_clause,[status(thm)],[f2211])).
% 124.55/15.96 fof(f2214,plain,(
% 124.55/15.96 spl0_275 <=> ~element(X2,b)|apply(h,apply(beta,X2))=apply(delta,apply(g,X2))),
% 124.55/15.96 introduced(split_symbol_definition)).
% 124.55/15.96 fof(f2215,plain,(
% 124.55/15.96 ![X0]: (~element(X0,b)|apply(h,apply(beta,X0))=apply(delta,apply(g,X0))|~spl0_275)),
% 124.55/15.96 inference(component_clause,[status(thm)],[f2214])).
% 124.55/15.96 fof(f2217,plain,(
% 124.55/15.96 ![X0,X1,X2]: (~morphism(beta,b,X0)|~morphism(h,X0,X1)|~morphism(delta,e,X1)|~element(X2,b)|apply(h,apply(beta,X2))=apply(delta,apply(g,X2)))),
% 124.55/15.96 inference(resolution,[status(thm)],[f999,f103])).
% 124.55/15.96 fof(f2218,plain,(
% 124.55/15.96 spl0_274|spl0_275),
% 124.55/15.96 inference(split_clause,[status(thm)],[f2217,f2211,f2214])).
% 124.55/15.96 fof(f2459,plain,(
% 124.55/15.96 ![X0,X1,X2]: (~morphism(alpha,X0,b)|~morphism(f,X0,X1)|~morphism(gamma,X1,e)|~element(X2,X0)|apply(g,apply(alpha,X2))=apply(gamma,apply(f,X2)))),
% 124.55/15.96 inference(resolution,[status(thm)],[f1000,f103])).
% 124.55/15.96 fof(f2463,plain,(
% 124.55/15.96 spl0_291 <=> ~element(X2,a)|apply(g,apply(alpha,X2))=apply(gamma,apply(f,X2))),
% 124.55/15.96 introduced(split_symbol_definition)).
% 124.55/15.96 fof(f2464,plain,(
% 124.55/15.96 ![X0]: (~element(X0,a)|apply(g,apply(alpha,X0))=apply(gamma,apply(f,X0))|~spl0_291)),
% 124.55/15.96 inference(component_clause,[status(thm)],[f2463])).
% 124.55/15.96 fof(f3743,plain,(
% 124.55/15.96 ![X0]: (~morphism(beta,b,X0)|~morphism(h,X0,r)|~spl0_274)),
% 124.55/15.96 inference(resolution,[status(thm)],[f2212,f101])).
% 124.55/15.96 fof(f3744,plain,(
% 124.55/15.96 ~morphism(beta,b,c)|~spl0_274),
% 124.55/15.96 inference(resolution,[status(thm)],[f3743,f104])).
% 124.55/15.96 fof(f3745,plain,(
% 124.55/15.96 ~spl0_125|~spl0_274),
% 124.55/15.96 inference(split_clause,[status(thm)],[f3744,f1091,f2211])).
% 124.55/15.96 fof(f4185,plain,(
% 124.55/15.96 spl0_389 <=> exact(alpha,beta)),
% 124.55/15.96 introduced(split_symbol_definition)).
% 124.55/15.96 fof(f4187,plain,(
% 124.55/15.96 ~exact(alpha,beta)|spl0_389),
% 124.55/15.96 inference(component_clause,[status(thm)],[f4185])).
% 124.55/15.96 fof(f4188,plain,(
% 124.55/15.96 spl0_390 <=> morphism(alpha,a,b)),
% 124.55/15.96 introduced(split_symbol_definition)).
% 124.55/15.96 fof(f4190,plain,(
% 124.55/15.96 ~morphism(alpha,a,b)|spl0_390),
% 124.55/15.96 inference(component_clause,[status(thm)],[f4188])).
% 124.55/15.96 fof(f4194,plain,(
% 124.55/15.96 $false|spl0_390),
% 124.55/15.96 inference(forward_subsumption_resolution,[status(thm)],[f4190,f98])).
% 124.55/15.96 fof(f4195,plain,(
% 124.55/15.96 spl0_390),
% 124.55/15.96 inference(contradiction_clause,[status(thm)],[f4194])).
% 124.55/15.96 fof(f4196,plain,(
% 124.55/15.96 $false|spl0_389),
% 124.55/15.96 inference(forward_subsumption_resolution,[status(thm)],[f4187,f109])).
% 124.55/15.96 fof(f4197,plain,(
% 124.55/15.96 spl0_389),
% 124.55/15.96 inference(contradiction_clause,[status(thm)],[f4196])).
% 124.55/15.96 fof(f4432,plain,(
% 124.55/15.96 ![X0,X1]: (~morphism(alpha,X0,b)|~morphism(f,X0,d)|~element(X1,X0)|apply(g,apply(alpha,X1))=apply(gamma,apply(f,X1)))),
% 124.55/15.96 inference(resolution,[status(thm)],[f2459,f100])).
% 124.55/15.96 fof(f4433,plain,(
% 124.55/15.96 ![X0]: (~morphism(alpha,a,b)|~element(X0,a)|apply(g,apply(alpha,X0))=apply(gamma,apply(f,X0)))),
% 124.55/15.96 inference(resolution,[status(thm)],[f4432,f102])).
% 124.55/15.96 fof(f4434,plain,(
% 124.55/15.96 ~spl0_390|spl0_291),
% 124.55/15.96 inference(split_clause,[status(thm)],[f4433,f4188,f2463])).
% 124.55/15.96 fof(f4568,plain,(
% 124.55/15.96 spl0_425 <=> morphism(h,c,r)),
% 124.55/15.96 introduced(split_symbol_definition)).
% 124.55/15.96 fof(f4570,plain,(
% 124.55/15.96 ~morphism(h,c,r)|spl0_425),
% 124.55/15.96 inference(component_clause,[status(thm)],[f4568])).
% 124.55/15.96 fof(f4574,plain,(
% 124.55/15.96 $false|spl0_425),
% 124.55/15.96 inference(forward_subsumption_resolution,[status(thm)],[f4570,f104])).
% 124.55/15.96 fof(f4575,plain,(
% 124.55/15.96 spl0_425),
% 124.55/15.96 inference(contradiction_clause,[status(thm)],[f4574])).
% 124.55/15.96 fof(f4579,plain,(
% 124.55/15.96 spl0_427 <=> morphism(gamma,d,e)),
% 124.55/15.96 introduced(split_symbol_definition)).
% 124.55/15.96 fof(f4581,plain,(
% 124.55/15.96 ~morphism(gamma,d,e)|spl0_427),
% 124.55/15.96 inference(component_clause,[status(thm)],[f4579])).
% 124.55/15.96 fof(f4585,plain,(
% 124.55/15.96 $false|spl0_427),
% 124.55/15.96 inference(forward_subsumption_resolution,[status(thm)],[f4581,f100])).
% 124.55/15.96 fof(f4586,plain,(
% 124.55/15.96 spl0_427),
% 124.55/15.96 inference(contradiction_clause,[status(thm)],[f4585])).
% 124.55/15.96 fof(f4612,plain,(
% 124.55/15.96 $false|~spl0_23),
% 124.55/15.96 inference(backward_subsumption_resolution,[status(thm)],[f129,f295])).
% 124.55/15.96 fof(f4613,plain,(
% 124.55/15.96 ~spl0_23),
% 124.55/15.96 inference(contradiction_clause,[status(thm)],[f4612])).
% 124.55/15.96 fof(f5137,plain,(
% 124.55/15.96 spl0_460 <=> ~morphism(delta,e,X0)),
% 124.55/15.96 introduced(split_symbol_definition)).
% 124.55/15.96 fof(f5138,plain,(
% 124.55/15.96 ![X0]: (~morphism(delta,e,X0)|~spl0_460)),
% 124.55/15.96 inference(component_clause,[status(thm)],[f5137])).
% 124.55/15.96 fof(f5143,plain,(
% 124.55/15.96 $false|~spl0_460),
% 124.55/15.96 inference(backward_subsumption_resolution,[status(thm)],[f101,f5138])).
% 124.55/15.96 fof(f5144,plain,(
% 124.55/15.96 ~spl0_460),
% 124.55/15.96 inference(contradiction_clause,[status(thm)],[f5143])).
% 124.55/15.96 fof(f5716,plain,(
% 124.55/15.96 spl0_482 <=> apply(delta,apply(delta,sk0_7(e,delta,delta,delta,delta)))=apply(delta,apply(delta,sk0_7(e,delta,delta,delta,delta)))),
% 124.55/15.96 introduced(split_symbol_definition)).
% 124.55/15.96 fof(f5718,plain,(
% 124.55/15.96 ~apply(delta,apply(delta,sk0_7(e,delta,delta,delta,delta)))=apply(delta,apply(delta,sk0_7(e,delta,delta,delta,delta)))|spl0_482),
% 124.55/15.96 inference(component_clause,[status(thm)],[f5716])).
% 124.55/15.96 fof(f5817,plain,(
% 124.55/15.96 $false|spl0_482),
% 124.55/15.96 inference(trivial_equality_resolution,[status(esa)],[f5718])).
% 124.55/15.96 fof(f5818,plain,(
% 124.55/15.96 spl0_482),
% 124.55/15.96 inference(contradiction_clause,[status(thm)],[f5817])).
% 124.55/15.96 fof(f6022,plain,(
% 124.55/15.96 apply(h,apply(beta,sk0_8(e,b,g)))=apply(delta,apply(g,sk0_8(e,b,g)))|~spl0_275|~spl0_29),
% 124.55/15.96 inference(resolution,[status(thm)],[f2215,f343])).
% 124.55/15.96 fof(f6023,plain,(
% 124.55/15.96 apply(h,apply(beta,sk0_8(e,b,g)))=apply(delta,zero(e))|~spl0_275|~spl0_29),
% 124.55/15.96 inference(forward_demodulation,[status(thm)],[f332,f6022])).
% 124.55/15.96 fof(f6024,plain,(
% 124.55/15.96 apply(h,apply(beta,sk0_8(e,b,g)))=zero(r)|~spl0_275|~spl0_29),
% 124.55/15.96 inference(forward_demodulation,[status(thm)],[f126,f6023])).
% 124.55/15.96 fof(f6050,plain,(
% 124.55/15.96 spl0_494 <=> element(apply(beta,sk0_8(e,b,g)),c)),
% 124.55/15.96 introduced(split_symbol_definition)).
% 124.55/15.96 fof(f6052,plain,(
% 124.55/15.96 ~element(apply(beta,sk0_8(e,b,g)),c)|spl0_494),
% 124.55/15.96 inference(component_clause,[status(thm)],[f6050])).
% 124.55/15.96 fof(f6053,plain,(
% 124.55/15.96 ~element(apply(beta,sk0_8(e,b,g)),c)|apply(beta,sk0_8(e,b,g))=zero(c)|~spl0_275|~spl0_29|~spl0_58),
% 124.55/15.96 inference(resolution,[status(thm)],[f6024,f496])).
% 124.55/15.96 fof(f6054,plain,(
% 124.55/15.96 ~spl0_494|spl0_258|~spl0_275|~spl0_29|~spl0_58),
% 124.55/15.96 inference(split_clause,[status(thm)],[f6053,f6050,f2082,f2214,f342,f495])).
% 124.55/15.96 fof(f6124,plain,(
% 124.55/15.96 spl0_504 <=> ~apply(X1,sk0_8(e,b,g))=zero(X2)),
% 124.55/15.96 introduced(split_symbol_definition)).
% 124.55/15.96 fof(f6125,plain,(
% 124.55/15.96 ![X0,X1]: (~apply(X0,sk0_8(e,b,g))=zero(X1)|~spl0_504)),
% 124.55/15.96 inference(component_clause,[status(thm)],[f6124])).
% 124.55/15.96 fof(f6198,plain,(
% 124.55/15.96 $false|~spl0_504),
% 124.55/15.96 inference(backward_subsumption_resolution,[status(thm)],[f332,f6125])).
% 124.55/15.96 fof(f6199,plain,(
% 124.55/15.96 ~spl0_504),
% 124.55/15.96 inference(contradiction_clause,[status(thm)],[f6198])).
% 124.55/15.96 fof(f6474,plain,(
% 124.55/15.96 ![X0]: (~morphism(beta,X0,c)|~element(sk0_8(e,b,g),X0)|spl0_494)),
% 124.55/15.96 inference(resolution,[status(thm)],[f6052,f36])).
% 124.55/15.96 fof(f6476,plain,(
% 124.55/15.96 ~element(sk0_8(e,b,g),b)|spl0_494),
% 124.55/15.96 inference(resolution,[status(thm)],[f6474,f99])).
% 124.55/15.96 fof(f6477,plain,(
% 124.55/15.96 ~spl0_29|spl0_494),
% 124.55/15.96 inference(split_clause,[status(thm)],[f6476,f342,f6050])).
% 124.55/15.96 fof(f9316,plain,(
% 124.55/15.96 spl0_809 <=> element(sk0_4(sk0_8(e,b,g),c,b,a,beta,alpha),a)),
% 124.55/15.96 introduced(split_symbol_definition)).
% 124.55/15.96 fof(f9317,plain,(
% 124.55/15.96 element(sk0_4(sk0_8(e,b,g),c,b,a,beta,alpha),a)|~spl0_809),
% 124.55/15.96 inference(component_clause,[status(thm)],[f9316])).
% 124.55/15.96 fof(f9318,plain,(
% 124.55/15.96 ~element(sk0_4(sk0_8(e,b,g),c,b,a,beta,alpha),a)|spl0_809),
% 124.55/15.96 inference(component_clause,[status(thm)],[f9316])).
% 124.55/15.96 fof(f9328,plain,(
% 124.55/15.96 spl0_811 <=> sk0_4(sk0_8(e,b,g),c,b,a,beta,alpha)=zero(a)),
% 124.55/15.96 introduced(split_symbol_definition)).
% 124.55/15.96 fof(f9329,plain,(
% 124.55/15.96 sk0_4(sk0_8(e,b,g),c,b,a,beta,alpha)=zero(a)|~spl0_811),
% 124.55/15.96 inference(component_clause,[status(thm)],[f9328])).
% 124.55/15.96 fof(f9433,plain,(
% 124.55/15.96 ~exact(alpha,beta)|~morphism(alpha,a,b)|~morphism(beta,b,c)|~element(sk0_8(e,b,g),b)|~apply(beta,sk0_8(e,b,g))=zero(c)|spl0_809),
% 124.55/15.96 inference(resolution,[status(thm)],[f9318,f61])).
% 124.55/16.00 fof(f9434,plain,(
% 124.55/16.00 ~spl0_389|~spl0_390|~spl0_125|~spl0_29|~spl0_258|spl0_809),
% 124.55/16.00 inference(split_clause,[status(thm)],[f9433,f4185,f4188,f1091,f342,f2082,f9316])).
% 124.55/16.00 fof(f9480,plain,(
% 124.55/16.00 apply(g,apply(alpha,sk0_4(sk0_8(e,b,g),c,b,a,beta,alpha)))=apply(gamma,apply(f,sk0_4(sk0_8(e,b,g),c,b,a,beta,alpha)))|~spl0_809|~spl0_291),
% 124.55/16.00 inference(resolution,[status(thm)],[f9317,f2464])).
% 124.55/16.00 fof(f9481,plain,(
% 124.55/16.00 apply(g,sk0_8(e,b,g))=apply(gamma,apply(f,sk0_4(sk0_8(e,b,g),c,b,a,beta,alpha)))|~spl0_259|~spl0_809|~spl0_291),
% 124.55/16.00 inference(forward_demodulation,[status(thm)],[f2086,f9480])).
% 124.55/16.00 fof(f9482,plain,(
% 124.55/16.00 zero(e)=apply(gamma,apply(f,sk0_4(sk0_8(e,b,g),c,b,a,beta,alpha)))|~spl0_259|~spl0_809|~spl0_291),
% 124.55/16.00 inference(forward_demodulation,[status(thm)],[f332,f9481])).
% 124.55/16.00 fof(f9860,plain,(
% 124.55/16.00 spl0_838 <=> element(apply(f,sk0_4(sk0_8(e,b,g),c,b,a,beta,alpha)),d)),
% 124.55/16.00 introduced(split_symbol_definition)).
% 124.55/16.00 fof(f9862,plain,(
% 124.55/16.00 ~element(apply(f,sk0_4(sk0_8(e,b,g),c,b,a,beta,alpha)),d)|spl0_838),
% 124.55/16.00 inference(component_clause,[status(thm)],[f9860])).
% 124.55/16.00 fof(f9863,plain,(
% 124.55/16.00 spl0_839 <=> apply(f,sk0_4(sk0_8(e,b,g),c,b,a,beta,alpha))=zero(d)),
% 124.55/16.00 introduced(split_symbol_definition)).
% 124.55/16.00 fof(f9864,plain,(
% 124.55/16.00 apply(f,sk0_4(sk0_8(e,b,g),c,b,a,beta,alpha))=zero(d)|~spl0_839),
% 124.55/16.00 inference(component_clause,[status(thm)],[f9863])).
% 124.55/16.00 fof(f9866,plain,(
% 124.55/16.00 ~element(apply(f,sk0_4(sk0_8(e,b,g),c,b,a,beta,alpha)),d)|apply(f,sk0_4(sk0_8(e,b,g),c,b,a,beta,alpha))=zero(d)|~spl0_259|~spl0_809|~spl0_291|~spl0_62),
% 124.55/16.00 inference(resolution,[status(thm)],[f9482,f516])).
% 124.55/16.00 fof(f9867,plain,(
% 124.55/16.00 ~spl0_838|spl0_839|~spl0_259|~spl0_809|~spl0_291|~spl0_62),
% 124.55/16.00 inference(split_clause,[status(thm)],[f9866,f9860,f9863,f2085,f9316,f2463,f515])).
% 124.55/16.00 fof(f9959,plain,(
% 124.55/16.00 ![X0]: (~morphism(f,X0,d)|~element(sk0_4(sk0_8(e,b,g),c,b,a,beta,alpha),X0)|spl0_838)),
% 124.55/16.00 inference(resolution,[status(thm)],[f9862,f36])).
% 124.55/16.00 fof(f9961,plain,(
% 124.55/16.00 ~element(sk0_4(sk0_8(e,b,g),c,b,a,beta,alpha),a)|spl0_838),
% 124.55/16.00 inference(resolution,[status(thm)],[f9959,f102])).
% 124.55/16.00 fof(f9962,plain,(
% 124.55/16.00 ~spl0_809|spl0_838),
% 124.55/16.00 inference(split_clause,[status(thm)],[f9961,f9316,f9860])).
% 124.55/16.00 fof(f9982,plain,(
% 124.55/16.00 ~element(sk0_4(sk0_8(e,b,g),c,b,a,beta,alpha),a)|sk0_4(sk0_8(e,b,g),c,b,a,beta,alpha)=zero(a)|~spl0_839|~spl0_60),
% 124.55/16.00 inference(resolution,[status(thm)],[f9864,f506])).
% 124.55/16.00 fof(f9983,plain,(
% 124.55/16.00 ~spl0_809|spl0_811|~spl0_839|~spl0_60),
% 124.55/16.00 inference(split_clause,[status(thm)],[f9982,f9316,f9328,f9863,f505])).
% 124.55/16.00 fof(f10009,plain,(
% 124.55/16.00 apply(alpha,zero(a))=sk0_8(e,b,g)|~spl0_811|~spl0_259),
% 124.55/16.00 inference(backward_demodulation,[status(thm)],[f9329,f2086])).
% 124.55/16.00 fof(f10010,plain,(
% 124.55/16.00 zero(b)=sk0_8(e,b,g)|~spl0_811|~spl0_259),
% 124.55/16.00 inference(forward_demodulation,[status(thm)],[f124,f10009])).
% 124.55/16.00 fof(f10011,plain,(
% 124.55/16.00 $false|~spl0_811|~spl0_259),
% 124.55/16.00 inference(forward_subsumption_resolution,[status(thm)],[f10010,f290])).
% 124.55/16.00 fof(f10012,plain,(
% 124.55/16.00 ~spl0_811|~spl0_259),
% 124.55/16.00 inference(contradiction_clause,[status(thm)],[f10011])).
% 124.55/16.00 fof(f10013,plain,(
% 124.55/16.00 $false),
% 124.55/16.00 inference(sat_refutation,[status(thm)],[f166,f190,f214,f499,f509,f519,f550,f556,f559,f1098,f2089,f2218,f3745,f4195,f4197,f4434,f4575,f4586,f4613,f5144,f5818,f6054,f6199,f6477,f9434,f9867,f9962,f9983,f10012])).
% 124.55/16.00 % SZS output end CNFRefutation for theBenchmark.p
% 125.66/16.16 % Elapsed time: 15.860457 seconds
% 125.66/16.16 % CPU time: 125.446093 seconds
% 125.66/16.16 % Memory used: 929.535 MB
%------------------------------------------------------------------------------