TSTP Solution File: HAL002+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : HAL002+1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n011.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 : Tue Apr 30 20:21:39 EDT 2024
% Result : Theorem 0.20s 0.44s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : HAL002+1 : TPTP v8.1.2. Released v2.6.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Apr 29 23:31:31 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % Drodi V3.6.0
% 0.20/0.44 % Refutation found
% 0.20/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.44 % SZS output start CNFRefutation for theBenchmark
% 0.20/0.44 fof(f1,axiom,(
% 0.20/0.44 (! [Morphism,Dom,Cod] :( morphism(Morphism,Dom,Cod)=> ( (! [El] :( element(El,Dom)=> element(apply(Morphism,El),Cod) ))& apply(Morphism,zero(Dom)) = zero(Cod) ) ) )),
% 0.20/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.44 fof(f2,axiom,(
% 0.20/0.44 (! [Morphism,Dom,Cod] :( ( injection(Morphism)& morphism(Morphism,Dom,Cod) )=> (! [El1,El2] :( ( element(El1,Dom)& element(El2,Dom)& apply(Morphism,El1) = apply(Morphism,El2) )=> El1 = El2 ) )) )),
% 0.20/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.44 fof(f3,axiom,(
% 0.20/0.44 (! [Morphism,Dom,Cod] :( ( morphism(Morphism,Dom,Cod)& (! [El1,El2] :( ( element(El1,Dom)& element(El2,Dom)& apply(Morphism,El1) = apply(Morphism,El2) )=> El1 = El2 ) ))=> injection(Morphism) ) )),
% 0.20/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.44 fof(f10,axiom,(
% 0.20/0.44 (! [Dom,El1,El2] :( ( element(El1,Dom)& element(El2,Dom) )=> element(subtract(Dom,El1,El2),Dom) ) )),
% 0.20/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.44 fof(f11,axiom,(
% 0.20/0.44 (! [Dom,El] :( element(El,Dom)=> subtract(Dom,El,El) = zero(Dom) ) )),
% 0.20/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.44 fof(f12,axiom,(
% 0.20/0.44 (! [Dom,El1,El2] :( ( element(El1,Dom)& element(El2,Dom) )=> subtract(Dom,El1,subtract(Dom,El1,El2)) = El2 ) )),
% 0.20/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.44 fof(f13,axiom,(
% 0.20/0.44 (! [Morphism,Dom,Cod] :( morphism(Morphism,Dom,Cod)=> (! [El1,El2] :( ( element(El1,Dom)& element(El2,Dom) )=> apply(Morphism,subtract(Dom,El1,El2)) = subtract(Cod,apply(Morphism,El1),apply(Morphism,El2)) ) )) )),
% 0.20/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.44 fof(f14,axiom,(
% 0.20/0.44 (! [Morphism,Dom,Cod] :( ( injection_2(Morphism)& morphism(Morphism,Dom,Cod) )=> (! [El] :( ( element(El,Dom)& apply(Morphism,El) = zero(Cod) )=> El = zero(Dom) ) )) )),
% 0.20/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.44 fof(f15,axiom,(
% 0.20/0.44 (! [Morphism,Dom,Cod] :( ( morphism(Morphism,Dom,Cod)& (! [El] :( ( element(El,Dom)& apply(Morphism,El) = zero(Cod) )=> El = zero(Dom) ) ))=> injection_2(Morphism) ) )),
% 0.20/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.44 fof(f16,hypothesis,(
% 0.20/0.44 morphism(x,any1,any2) ),
% 0.20/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.44 fof(f17,conjecture,(
% 0.20/0.44 ( injection(x)<=> injection_2(x) ) ),
% 0.20/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.20/0.44 fof(f18,negated_conjecture,(
% 0.20/0.44 ~(( injection(x)<=> injection_2(x) ) )),
% 0.20/0.44 inference(negated_conjecture,[status(cth)],[f17])).
% 0.20/0.44 fof(f19,plain,(
% 0.20/0.44 ![Morphism,Dom,Cod]: (~morphism(Morphism,Dom,Cod)|((![El]: (~element(El,Dom)|element(apply(Morphism,El),Cod)))&apply(Morphism,zero(Dom))=zero(Cod)))),
% 0.20/0.44 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 0.20/0.44 fof(f20,plain,(
% 0.20/0.44 ![X0,X1,X2,X3]: (~morphism(X0,X1,X2)|~element(X3,X1)|element(apply(X0,X3),X2))),
% 0.20/0.44 inference(cnf_transformation,[status(esa)],[f19])).
% 0.20/0.44 fof(f21,plain,(
% 0.20/0.44 ![X0,X1,X2]: (~morphism(X0,X1,X2)|apply(X0,zero(X1))=zero(X2))),
% 0.20/0.44 inference(cnf_transformation,[status(esa)],[f19])).
% 0.20/0.44 fof(f22,plain,(
% 0.20/0.44 ![Morphism,Dom,Cod]: ((~injection(Morphism)|~morphism(Morphism,Dom,Cod))|(![El1,El2]: (((~element(El1,Dom)|~element(El2,Dom))|~apply(Morphism,El1)=apply(Morphism,El2))|El1=El2)))),
% 0.20/0.44 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 0.20/0.44 fof(f23,plain,(
% 0.20/0.44 ![Morphism,Dom]: ((~injection(Morphism)|(![Cod]: ~morphism(Morphism,Dom,Cod)))|(![El1,El2]: (((~element(El1,Dom)|~element(El2,Dom))|~apply(Morphism,El1)=apply(Morphism,El2))|El1=El2)))),
% 0.20/0.44 inference(miniscoping,[status(esa)],[f22])).
% 0.20/0.44 fof(f24,plain,(
% 0.20/0.44 ![X0,X1,X2,X3,X4]: (~injection(X0)|~morphism(X0,X1,X2)|~element(X3,X1)|~element(X4,X1)|~apply(X0,X3)=apply(X0,X4)|X3=X4)),
% 0.20/0.44 inference(cnf_transformation,[status(esa)],[f23])).
% 0.20/0.44 fof(f25,plain,(
% 0.20/0.44 ![Morphism,Dom,Cod]: ((~morphism(Morphism,Dom,Cod)|(?[El1,El2]: (((element(El1,Dom)&element(El2,Dom))&apply(Morphism,El1)=apply(Morphism,El2))&~El1=El2)))|injection(Morphism))),
% 0.20/0.44 inference(pre_NNF_transformation,[status(esa)],[f3])).
% 0.20/0.44 fof(f26,plain,(
% 0.20/0.44 ![Morphism]: ((![Dom]: ((![Cod]: ~morphism(Morphism,Dom,Cod))|(?[El1,El2]: (((element(El1,Dom)&element(El2,Dom))&apply(Morphism,El1)=apply(Morphism,El2))&~El1=El2))))|injection(Morphism))),
% 0.20/0.44 inference(miniscoping,[status(esa)],[f25])).
% 0.20/0.44 fof(f27,plain,(
% 0.20/0.44 ![Morphism]: ((![Dom]: ((![Cod]: ~morphism(Morphism,Dom,Cod))|(((element(sk0_0(Dom,Morphism),Dom)&element(sk0_1(Dom,Morphism),Dom))&apply(Morphism,sk0_0(Dom,Morphism))=apply(Morphism,sk0_1(Dom,Morphism)))&~sk0_0(Dom,Morphism)=sk0_1(Dom,Morphism))))|injection(Morphism))),
% 0.20/0.44 inference(skolemization,[status(esa)],[f26])).
% 0.20/0.44 fof(f28,plain,(
% 0.20/0.44 ![X0,X1,X2]: (~morphism(X0,X1,X2)|element(sk0_0(X1,X0),X1)|injection(X0))),
% 0.20/0.44 inference(cnf_transformation,[status(esa)],[f27])).
% 0.20/0.44 fof(f29,plain,(
% 0.20/0.44 ![X0,X1,X2]: (~morphism(X0,X1,X2)|element(sk0_1(X1,X0),X1)|injection(X0))),
% 0.20/0.44 inference(cnf_transformation,[status(esa)],[f27])).
% 0.20/0.44 fof(f30,plain,(
% 0.20/0.44 ![X0,X1,X2]: (~morphism(X0,X1,X2)|apply(X0,sk0_0(X1,X0))=apply(X0,sk0_1(X1,X0))|injection(X0))),
% 0.20/0.44 inference(cnf_transformation,[status(esa)],[f27])).
% 0.20/0.44 fof(f31,plain,(
% 0.20/0.44 ![X0,X1,X2]: (~morphism(X0,X1,X2)|~sk0_0(X1,X0)=sk0_1(X1,X0)|injection(X0))),
% 0.20/0.44 inference(cnf_transformation,[status(esa)],[f27])).
% 0.20/0.44 fof(f66,plain,(
% 0.20/0.44 ![Dom,El1,El2]: ((~element(El1,Dom)|~element(El2,Dom))|element(subtract(Dom,El1,El2),Dom))),
% 0.20/0.44 inference(pre_NNF_transformation,[status(esa)],[f10])).
% 0.20/0.44 fof(f67,plain,(
% 0.20/0.44 ![X0,X1,X2]: (~element(X0,X1)|~element(X2,X1)|element(subtract(X1,X0,X2),X1))),
% 0.20/0.44 inference(cnf_transformation,[status(esa)],[f66])).
% 0.20/0.44 fof(f68,plain,(
% 0.20/0.44 ![Dom,El]: (~element(El,Dom)|subtract(Dom,El,El)=zero(Dom))),
% 0.20/0.44 inference(pre_NNF_transformation,[status(esa)],[f11])).
% 0.20/0.44 fof(f69,plain,(
% 0.20/0.44 ![X0,X1]: (~element(X0,X1)|subtract(X1,X0,X0)=zero(X1))),
% 0.20/0.44 inference(cnf_transformation,[status(esa)],[f68])).
% 0.20/0.44 fof(f70,plain,(
% 0.20/0.44 ![Dom,El1,El2]: ((~element(El1,Dom)|~element(El2,Dom))|subtract(Dom,El1,subtract(Dom,El1,El2))=El2)),
% 0.20/0.44 inference(pre_NNF_transformation,[status(esa)],[f12])).
% 0.20/0.44 fof(f71,plain,(
% 0.20/0.44 ![X0,X1,X2]: (~element(X0,X1)|~element(X2,X1)|subtract(X1,X0,subtract(X1,X0,X2))=X2)),
% 0.20/0.44 inference(cnf_transformation,[status(esa)],[f70])).
% 0.20/0.44 fof(f72,plain,(
% 0.20/0.44 ![Morphism,Dom,Cod]: (~morphism(Morphism,Dom,Cod)|(![El1,El2]: ((~element(El1,Dom)|~element(El2,Dom))|apply(Morphism,subtract(Dom,El1,El2))=subtract(Cod,apply(Morphism,El1),apply(Morphism,El2)))))),
% 0.20/0.44 inference(pre_NNF_transformation,[status(esa)],[f13])).
% 0.20/0.44 fof(f73,plain,(
% 0.20/0.44 ![X0,X1,X2,X3,X4]: (~morphism(X0,X1,X2)|~element(X3,X1)|~element(X4,X1)|apply(X0,subtract(X1,X3,X4))=subtract(X2,apply(X0,X3),apply(X0,X4)))),
% 0.20/0.44 inference(cnf_transformation,[status(esa)],[f72])).
% 0.20/0.44 fof(f74,plain,(
% 0.20/0.44 ![Morphism,Dom,Cod]: ((~injection_2(Morphism)|~morphism(Morphism,Dom,Cod))|(![El]: ((~element(El,Dom)|~apply(Morphism,El)=zero(Cod))|El=zero(Dom))))),
% 0.20/0.44 inference(pre_NNF_transformation,[status(esa)],[f14])).
% 0.20/0.44 fof(f75,plain,(
% 0.20/0.44 ![X0,X1,X2,X3]: (~injection_2(X0)|~morphism(X0,X1,X2)|~element(X3,X1)|~apply(X0,X3)=zero(X2)|X3=zero(X1))),
% 0.20/0.44 inference(cnf_transformation,[status(esa)],[f74])).
% 0.20/0.44 fof(f76,plain,(
% 0.20/0.44 ![Morphism,Dom,Cod]: ((~morphism(Morphism,Dom,Cod)|(?[El]: ((element(El,Dom)&apply(Morphism,El)=zero(Cod))&~El=zero(Dom))))|injection_2(Morphism))),
% 0.20/0.44 inference(pre_NNF_transformation,[status(esa)],[f15])).
% 0.20/0.44 fof(f77,plain,(
% 0.20/0.44 ![Morphism]: ((![Dom,Cod]: (~morphism(Morphism,Dom,Cod)|(?[El]: ((element(El,Dom)&apply(Morphism,El)=zero(Cod))&~El=zero(Dom)))))|injection_2(Morphism))),
% 0.20/0.44 inference(miniscoping,[status(esa)],[f76])).
% 0.20/0.44 fof(f78,plain,(
% 0.20/0.44 ![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_2(Morphism))),
% 0.20/0.44 inference(skolemization,[status(esa)],[f77])).
% 0.20/0.44 fof(f79,plain,(
% 0.20/0.44 ![X0,X1,X2]: (~morphism(X0,X1,X2)|element(sk0_8(X2,X1,X0),X1)|injection_2(X0))),
% 0.20/0.44 inference(cnf_transformation,[status(esa)],[f78])).
% 0.20/0.44 fof(f80,plain,(
% 0.20/0.44 ![X0,X1,X2]: (~morphism(X0,X1,X2)|apply(X0,sk0_8(X2,X1,X0))=zero(X2)|injection_2(X0))),
% 0.20/0.44 inference(cnf_transformation,[status(esa)],[f78])).
% 0.20/0.44 fof(f81,plain,(
% 0.20/0.44 ![X0,X1,X2]: (~morphism(X0,X1,X2)|~sk0_8(X2,X1,X0)=zero(X1)|injection_2(X0))),
% 0.20/0.44 inference(cnf_transformation,[status(esa)],[f78])).
% 0.20/0.44 fof(f82,plain,(
% 0.20/0.44 morphism(x,any1,any2)),
% 0.20/0.44 inference(cnf_transformation,[status(esa)],[f16])).
% 0.20/0.44 fof(f83,plain,(
% 0.20/0.44 (injection(x)<~>injection_2(x))),
% 0.20/0.44 inference(pre_NNF_transformation,[status(esa)],[f18])).
% 0.20/0.44 fof(f84,plain,(
% 0.20/0.44 (injection(x)|injection_2(x))&(~injection(x)|~injection_2(x))),
% 0.20/0.44 inference(NNF_transformation,[status(esa)],[f83])).
% 0.20/0.44 fof(f85,plain,(
% 0.20/0.44 injection(x)|injection_2(x)),
% 0.20/0.44 inference(cnf_transformation,[status(esa)],[f84])).
% 0.20/0.44 fof(f86,plain,(
% 0.20/0.44 ~injection(x)|~injection_2(x)),
% 0.20/0.44 inference(cnf_transformation,[status(esa)],[f84])).
% 0.20/0.44 fof(f92,plain,(
% 0.20/0.44 spl0_0 <=> injection(x)),
% 0.20/0.44 introduced(split_symbol_definition)).
% 0.20/0.44 fof(f95,plain,(
% 0.20/0.44 spl0_1 <=> injection_2(x)),
% 0.20/0.44 introduced(split_symbol_definition)).
% 0.20/0.44 fof(f98,plain,(
% 0.20/0.44 spl0_0|spl0_1),
% 0.20/0.44 inference(split_clause,[status(thm)],[f85,f92,f95])).
% 0.20/0.44 fof(f99,plain,(
% 0.20/0.44 ~spl0_0|~spl0_1),
% 0.20/0.44 inference(split_clause,[status(thm)],[f86,f92,f95])).
% 0.20/0.44 fof(f102,plain,(
% 0.20/0.44 ![X0]: (~element(X0,any1)|element(apply(x,X0),any2))),
% 0.20/0.44 inference(resolution,[status(thm)],[f20,f82])).
% 0.20/0.44 fof(f103,plain,(
% 0.20/0.44 apply(x,zero(any1))=zero(any2)),
% 0.20/0.44 inference(resolution,[status(thm)],[f21,f82])).
% 0.20/0.44 fof(f104,plain,(
% 0.20/0.44 spl0_2 <=> ~morphism(x,X0,any2)|~element(zero(any1),X0)|zero(any1)=zero(X0)),
% 0.20/0.44 introduced(split_symbol_definition)).
% 0.20/0.44 fof(f105,plain,(
% 0.20/0.44 ![X0]: (~morphism(x,X0,any2)|~element(zero(any1),X0)|zero(any1)=zero(X0)|~spl0_2)),
% 0.20/0.44 inference(component_clause,[status(thm)],[f104])).
% 0.20/0.44 fof(f107,plain,(
% 0.20/0.44 ![X0]: (~injection_2(x)|~morphism(x,X0,any2)|~element(zero(any1),X0)|zero(any1)=zero(X0))),
% 0.20/0.44 inference(resolution,[status(thm)],[f103,f75])).
% 0.20/0.44 fof(f108,plain,(
% 0.20/0.44 ~spl0_1|spl0_2),
% 0.20/0.44 inference(split_clause,[status(thm)],[f107,f95,f104])).
% 0.20/0.44 fof(f109,plain,(
% 0.20/0.44 spl0_3 <=> ~morphism(x,X0,X1)|~element(X2,X0)|~element(zero(any1),X0)|~apply(x,X2)=zero(any2)|X2=zero(any1)),
% 0.20/0.44 introduced(split_symbol_definition)).
% 0.20/0.44 fof(f110,plain,(
% 0.20/0.44 ![X0,X1,X2]: (~morphism(x,X0,X1)|~element(X2,X0)|~element(zero(any1),X0)|~apply(x,X2)=zero(any2)|X2=zero(any1)|~spl0_3)),
% 0.20/0.44 inference(component_clause,[status(thm)],[f109])).
% 0.20/0.44 fof(f112,plain,(
% 0.20/0.44 ![X0,X1,X2]: (~injection(x)|~morphism(x,X0,X1)|~element(X2,X0)|~element(zero(any1),X0)|~apply(x,X2)=zero(any2)|X2=zero(any1))),
% 0.20/0.44 inference(paramodulation,[status(thm)],[f103,f24])).
% 0.20/0.44 fof(f113,plain,(
% 0.20/0.44 ~spl0_0|spl0_3),
% 0.20/0.44 inference(split_clause,[status(thm)],[f112,f92,f109])).
% 0.20/0.44 fof(f121,plain,(
% 0.20/0.44 spl0_5 <=> ~morphism(x,X0,X1)|~element(zero(any1),X0)|~element(zero(any1),X0)),
% 0.20/0.44 introduced(split_symbol_definition)).
% 0.20/0.44 fof(f122,plain,(
% 0.20/0.44 ![X0,X1]: (~morphism(x,X0,X1)|~element(zero(any1),X0)|~element(zero(any1),X0)|~spl0_5)),
% 0.20/0.44 inference(component_clause,[status(thm)],[f121])).
% 0.20/0.44 fof(f124,plain,(
% 0.20/0.44 spl0_6 <=> zero(any1)=zero(any1)),
% 0.20/0.44 introduced(split_symbol_definition)).
% 0.20/0.44 fof(f127,plain,(
% 0.20/0.44 ![X0,X1]: (~morphism(x,X0,X1)|~element(zero(any1),X0)|~element(zero(any1),X0)|zero(any1)=zero(any1)|~spl0_3)),
% 0.20/0.44 inference(resolution,[status(thm)],[f110,f103])).
% 0.20/0.44 fof(f128,plain,(
% 0.20/0.44 spl0_5|spl0_6|~spl0_3),
% 0.20/0.44 inference(split_clause,[status(thm)],[f127,f121,f124,f109])).
% 0.20/0.44 fof(f134,plain,(
% 0.20/0.44 ![X0,X1]: (~morphism(x,X0,X1)|~element(zero(any1),X0)|~spl0_5)),
% 0.20/0.44 inference(duplicate_literals_removal,[status(esa)],[f122])).
% 0.20/0.44 fof(f135,plain,(
% 0.20/0.44 spl0_8 <=> element(sk0_0(any1,x),any1)),
% 0.20/0.44 introduced(split_symbol_definition)).
% 0.20/0.44 fof(f136,plain,(
% 0.20/0.44 element(sk0_0(any1,x),any1)|~spl0_8),
% 0.20/0.44 inference(component_clause,[status(thm)],[f135])).
% 0.20/0.44 fof(f138,plain,(
% 0.20/0.44 element(sk0_0(any1,x),any1)|injection(x)),
% 0.20/0.44 inference(resolution,[status(thm)],[f28,f82])).
% 0.20/0.44 fof(f139,plain,(
% 0.20/0.44 spl0_8|spl0_0),
% 0.20/0.44 inference(split_clause,[status(thm)],[f138,f135,f92])).
% 0.20/0.44 fof(f140,plain,(
% 0.20/0.44 element(apply(x,sk0_0(any1,x)),any2)|~spl0_8),
% 0.20/0.44 inference(resolution,[status(thm)],[f136,f102])).
% 0.20/0.44 fof(f142,plain,(
% 0.20/0.44 subtract(any2,apply(x,sk0_0(any1,x)),apply(x,sk0_0(any1,x)))=zero(any2)|~spl0_8),
% 0.20/0.44 inference(resolution,[status(thm)],[f140,f69])).
% 0.20/0.44 fof(f143,plain,(
% 0.20/0.44 spl0_9 <=> element(sk0_1(any1,x),any1)),
% 0.20/0.44 introduced(split_symbol_definition)).
% 0.20/0.44 fof(f144,plain,(
% 0.20/0.44 element(sk0_1(any1,x),any1)|~spl0_9),
% 0.20/0.44 inference(component_clause,[status(thm)],[f143])).
% 0.20/0.44 fof(f146,plain,(
% 0.20/0.44 element(sk0_1(any1,x),any1)|injection(x)),
% 0.20/0.44 inference(resolution,[status(thm)],[f29,f82])).
% 0.20/0.44 fof(f147,plain,(
% 0.20/0.44 spl0_9|spl0_0),
% 0.20/0.44 inference(split_clause,[status(thm)],[f146,f143,f92])).
% 0.20/0.44 fof(f164,plain,(
% 0.20/0.44 ![X0]: (~element(X0,any1)|element(subtract(any1,sk0_0(any1,x),X0),any1)|~spl0_8)),
% 0.20/0.44 inference(resolution,[status(thm)],[f67,f136])).
% 0.20/0.44 fof(f165,plain,(
% 0.20/0.44 spl0_12 <=> element(sk0_8(any2,any1,x),any1)),
% 0.20/0.44 introduced(split_symbol_definition)).
% 0.20/0.44 fof(f166,plain,(
% 0.20/0.44 element(sk0_8(any2,any1,x),any1)|~spl0_12),
% 0.20/0.44 inference(component_clause,[status(thm)],[f165])).
% 0.20/0.44 fof(f168,plain,(
% 0.20/0.44 element(sk0_8(any2,any1,x),any1)|injection_2(x)),
% 0.20/0.44 inference(resolution,[status(thm)],[f79,f82])).
% 0.20/0.44 fof(f169,plain,(
% 0.20/0.44 spl0_12|spl0_1),
% 0.20/0.44 inference(split_clause,[status(thm)],[f168,f165,f95])).
% 0.20/0.44 fof(f171,plain,(
% 0.20/0.44 ![X0]: (~element(X0,any1)|element(subtract(any1,sk0_8(any2,any1,x),X0),any1)|~spl0_12)),
% 0.20/0.44 inference(resolution,[status(thm)],[f166,f67])).
% 0.20/0.44 fof(f172,plain,(
% 0.20/0.44 subtract(any1,sk0_8(any2,any1,x),sk0_8(any2,any1,x))=zero(any1)|~spl0_12),
% 0.20/0.44 inference(resolution,[status(thm)],[f166,f69])).
% 0.20/0.44 fof(f175,plain,(
% 0.20/0.44 spl0_13 <=> apply(x,sk0_0(any1,x))=apply(x,sk0_1(any1,x))),
% 0.20/0.44 introduced(split_symbol_definition)).
% 0.20/0.44 fof(f176,plain,(
% 0.20/0.44 apply(x,sk0_0(any1,x))=apply(x,sk0_1(any1,x))|~spl0_13),
% 0.20/0.44 inference(component_clause,[status(thm)],[f175])).
% 0.20/0.44 fof(f178,plain,(
% 0.20/0.44 apply(x,sk0_0(any1,x))=apply(x,sk0_1(any1,x))|injection(x)),
% 0.20/0.44 inference(resolution,[status(thm)],[f30,f82])).
% 0.20/0.44 fof(f179,plain,(
% 0.20/0.44 spl0_13|spl0_0),
% 0.20/0.44 inference(split_clause,[status(thm)],[f178,f175,f92])).
% 0.20/0.44 fof(f182,plain,(
% 0.20/0.44 spl0_14 <=> apply(x,sk0_8(any2,any1,x))=zero(any2)),
% 0.20/0.44 introduced(split_symbol_definition)).
% 0.20/0.44 fof(f183,plain,(
% 0.20/0.44 apply(x,sk0_8(any2,any1,x))=zero(any2)|~spl0_14),
% 0.20/0.44 inference(component_clause,[status(thm)],[f182])).
% 0.20/0.44 fof(f185,plain,(
% 0.20/0.44 apply(x,sk0_8(any2,any1,x))=zero(any2)|injection_2(x)),
% 0.20/0.44 inference(resolution,[status(thm)],[f80,f82])).
% 0.20/0.44 fof(f186,plain,(
% 0.20/0.44 spl0_14|spl0_1),
% 0.20/0.44 inference(split_clause,[status(thm)],[f185,f182,f95])).
% 0.20/0.44 fof(f194,plain,(
% 0.20/0.44 spl0_16 <=> ~morphism(x,X0,X1)|~element(X2,X0)|~element(sk0_8(any2,any1,x),X0)|~apply(x,X2)=zero(any2)|X2=sk0_8(any2,any1,x)),
% 0.20/0.44 introduced(split_symbol_definition)).
% 0.20/0.44 fof(f195,plain,(
% 0.20/0.44 ![X0,X1,X2]: (~morphism(x,X0,X1)|~element(X2,X0)|~element(sk0_8(any2,any1,x),X0)|~apply(x,X2)=zero(any2)|X2=sk0_8(any2,any1,x)|~spl0_16)),
% 0.20/0.44 inference(component_clause,[status(thm)],[f194])).
% 0.20/0.44 fof(f197,plain,(
% 0.20/0.44 ![X0,X1,X2]: (~injection(x)|~morphism(x,X0,X1)|~element(X2,X0)|~element(sk0_8(any2,any1,x),X0)|~apply(x,X2)=zero(any2)|X2=sk0_8(any2,any1,x)|~spl0_14)),
% 0.20/0.44 inference(paramodulation,[status(thm)],[f183,f24])).
% 0.20/0.44 fof(f198,plain,(
% 0.20/0.44 ~spl0_0|spl0_16|~spl0_14),
% 0.20/0.44 inference(split_clause,[status(thm)],[f197,f92,f194,f182])).
% 0.20/0.44 fof(f206,plain,(
% 0.20/0.44 spl0_18 <=> ~morphism(x,any1,X0)),
% 0.20/0.44 introduced(split_symbol_definition)).
% 0.20/0.44 fof(f207,plain,(
% 0.20/0.44 ![X0]: (~morphism(x,any1,X0)|~spl0_18)),
% 0.20/0.44 inference(component_clause,[status(thm)],[f206])).
% 0.20/0.44 fof(f209,plain,(
% 0.20/0.44 spl0_19 <=> ~element(X1,any1)|~apply(x,X1)=zero(any2)|X1=sk0_8(any2,any1,x)),
% 0.20/0.44 introduced(split_symbol_definition)).
% 0.20/0.44 fof(f210,plain,(
% 0.20/0.44 ![X0]: (~element(X0,any1)|~apply(x,X0)=zero(any2)|X0=sk0_8(any2,any1,x)|~spl0_19)),
% 0.20/0.44 inference(component_clause,[status(thm)],[f209])).
% 0.20/0.44 fof(f212,plain,(
% 0.20/0.44 ![X0,X1]: (~morphism(x,any1,X0)|~element(X1,any1)|~apply(x,X1)=zero(any2)|X1=sk0_8(any2,any1,x)|~spl0_16|~spl0_12)),
% 0.20/0.44 inference(resolution,[status(thm)],[f195,f166])).
% 0.20/0.44 fof(f213,plain,(
% 0.20/0.44 spl0_18|spl0_19|~spl0_16|~spl0_12),
% 0.20/0.44 inference(split_clause,[status(thm)],[f212,f206,f209,f194,f165])).
% 0.20/0.44 fof(f214,plain,(
% 0.20/0.44 $false|~spl0_18),
% 0.20/0.44 inference(backward_subsumption_resolution,[status(thm)],[f82,f207])).
% 0.20/0.44 fof(f215,plain,(
% 0.20/0.44 ~spl0_18),
% 0.20/0.44 inference(contradiction_clause,[status(thm)],[f214])).
% 0.20/0.44 fof(f236,plain,(
% 0.20/0.44 ![X0]: (~element(X0,any1)|subtract(any1,X0,subtract(any1,X0,sk0_0(any1,x)))=sk0_0(any1,x)|~spl0_8)),
% 0.20/0.44 inference(resolution,[status(thm)],[f136,f71])).
% 0.20/0.44 fof(f237,plain,(
% 0.20/0.44 ![X0]: (~element(X0,any1)|element(subtract(any1,sk0_0(any1,x),X0),any1)|~spl0_8)),
% 0.20/0.44 inference(resolution,[status(thm)],[f136,f67])).
% 0.20/0.44 fof(f238,plain,(
% 0.20/0.44 subtract(any1,sk0_0(any1,x),sk0_0(any1,x))=zero(any1)|~spl0_8),
% 0.20/0.44 inference(resolution,[status(thm)],[f136,f69])).
% 0.20/0.44 fof(f240,plain,(
% 0.20/0.44 ![X0]: (~element(X0,any1)|subtract(any1,X0,subtract(any1,X0,sk0_1(any1,x)))=sk0_1(any1,x)|~spl0_9)),
% 0.20/0.44 inference(resolution,[status(thm)],[f144,f71])).
% 0.20/0.44 fof(f249,plain,(
% 0.20/0.44 element(subtract(any1,sk0_0(any1,x),sk0_1(any1,x)),any1)|~spl0_8|~spl0_9),
% 0.20/0.44 inference(resolution,[status(thm)],[f164,f144])).
% 0.20/0.44 fof(f268,plain,(
% 0.20/0.44 spl0_24 <=> sk0_0(any1,x)=sk0_1(any1,x)),
% 0.20/0.44 introduced(split_symbol_definition)).
% 0.20/0.44 fof(f269,plain,(
% 0.20/0.44 sk0_0(any1,x)=sk0_1(any1,x)|~spl0_24),
% 0.20/0.44 inference(component_clause,[status(thm)],[f268])).
% 0.20/0.44 fof(f270,plain,(
% 0.20/0.44 ~sk0_0(any1,x)=sk0_1(any1,x)|spl0_24),
% 0.20/0.44 inference(component_clause,[status(thm)],[f268])).
% 0.20/0.44 fof(f320,plain,(
% 0.20/0.44 element(subtract(any1,sk0_8(any2,any1,x),sk0_8(any2,any1,x)),any1)|~spl0_12),
% 0.20/0.44 inference(resolution,[status(thm)],[f171,f166])).
% 0.20/0.44 fof(f326,plain,(
% 0.20/0.44 element(zero(any1),any1)|~spl0_12),
% 0.20/0.44 inference(forward_demodulation,[status(thm)],[f172,f320])).
% 0.20/0.44 fof(f327,plain,(
% 0.20/0.44 ![X0]: (~morphism(x,any1,X0)|~spl0_12|~spl0_5)),
% 0.20/0.44 inference(resolution,[status(thm)],[f326,f134])).
% 0.20/0.44 fof(f328,plain,(
% 0.20/0.44 spl0_18|~spl0_12|~spl0_5),
% 0.20/0.44 inference(split_clause,[status(thm)],[f327,f206,f165,f121])).
% 0.20/0.44 fof(f330,plain,(
% 0.20/0.44 spl0_29 <=> apply(x,zero(any1))=zero(any2)),
% 0.20/0.44 introduced(split_symbol_definition)).
% 0.20/0.44 fof(f332,plain,(
% 0.20/0.44 ~apply(x,zero(any1))=zero(any2)|spl0_29),
% 0.20/0.44 inference(component_clause,[status(thm)],[f330])).
% 0.20/0.44 fof(f333,plain,(
% 0.20/0.44 spl0_30 <=> zero(any1)=sk0_8(any2,any1,x)),
% 0.20/0.44 introduced(split_symbol_definition)).
% 0.20/0.44 fof(f334,plain,(
% 0.20/0.44 zero(any1)=sk0_8(any2,any1,x)|~spl0_30),
% 0.20/0.44 inference(component_clause,[status(thm)],[f333])).
% 0.20/0.44 fof(f336,plain,(
% 0.20/0.44 ~apply(x,zero(any1))=zero(any2)|zero(any1)=sk0_8(any2,any1,x)|~spl0_12|~spl0_19),
% 0.20/0.44 inference(resolution,[status(thm)],[f326,f210])).
% 0.20/0.44 fof(f337,plain,(
% 0.20/0.44 ~spl0_29|spl0_30|~spl0_12|~spl0_19),
% 0.20/0.44 inference(split_clause,[status(thm)],[f336,f330,f333,f165,f209])).
% 0.20/0.44 fof(f342,plain,(
% 0.20/0.44 ~zero(any2)=zero(any2)|spl0_29),
% 0.20/0.44 inference(forward_demodulation,[status(thm)],[f103,f332])).
% 0.20/0.44 fof(f343,plain,(
% 0.20/0.44 $false|spl0_29),
% 0.20/0.44 inference(trivial_equality_resolution,[status(esa)],[f342])).
% 0.20/0.44 fof(f344,plain,(
% 0.20/0.44 spl0_29),
% 0.20/0.44 inference(contradiction_clause,[status(thm)],[f343])).
% 0.20/0.44 fof(f348,plain,(
% 0.20/0.44 spl0_31 <=> morphism(x,any1,any2)),
% 0.20/0.44 introduced(split_symbol_definition)).
% 0.20/0.44 fof(f350,plain,(
% 0.20/0.44 ~morphism(x,any1,any2)|spl0_31),
% 0.20/0.44 inference(component_clause,[status(thm)],[f348])).
% 0.20/0.44 fof(f351,plain,(
% 0.20/0.44 ~morphism(x,any1,any2)|injection_2(x)|~spl0_30),
% 0.20/0.44 inference(resolution,[status(thm)],[f334,f81])).
% 0.20/0.44 fof(f352,plain,(
% 0.20/0.44 ~spl0_31|spl0_1|~spl0_30),
% 0.20/0.44 inference(split_clause,[status(thm)],[f351,f348,f95,f333])).
% 0.20/0.44 fof(f355,plain,(
% 0.20/0.44 $false|spl0_31),
% 0.20/0.44 inference(forward_subsumption_resolution,[status(thm)],[f350,f82])).
% 0.20/0.44 fof(f356,plain,(
% 0.20/0.44 spl0_31),
% 0.20/0.44 inference(contradiction_clause,[status(thm)],[f355])).
% 0.20/0.44 fof(f357,plain,(
% 0.20/0.44 ![X0]: (~morphism(x,any1,X0)|injection(x)|~spl0_24)),
% 0.20/0.44 inference(resolution,[status(thm)],[f269,f31])).
% 0.20/0.44 fof(f358,plain,(
% 0.20/0.44 spl0_18|spl0_0|~spl0_24),
% 0.20/0.44 inference(split_clause,[status(thm)],[f357,f206,f92,f268])).
% 0.20/0.44 fof(f385,plain,(
% 0.20/0.44 element(subtract(any1,sk0_0(any1,x),sk0_0(any1,x)),any1)|~spl0_8),
% 0.20/0.44 inference(resolution,[status(thm)],[f237,f136])).
% 0.20/0.44 fof(f422,plain,(
% 0.20/0.44 element(zero(any1),any1)|~spl0_8),
% 0.20/0.44 inference(forward_demodulation,[status(thm)],[f238,f385])).
% 0.20/0.44 fof(f423,plain,(
% 0.20/0.44 ~morphism(x,any1,any2)|zero(any1)=zero(any1)|~spl0_8|~spl0_2),
% 0.20/0.44 inference(resolution,[status(thm)],[f422,f105])).
% 0.20/0.44 fof(f424,plain,(
% 0.20/0.44 ~spl0_31|spl0_6|~spl0_8|~spl0_2),
% 0.20/0.44 inference(split_clause,[status(thm)],[f423,f348,f124,f135,f104])).
% 0.20/0.44 fof(f434,plain,(
% 0.20/0.44 subtract(any1,sk0_0(any1,x),subtract(any1,sk0_0(any1,x),sk0_0(any1,x)))=sk0_0(any1,x)|~spl0_8),
% 0.20/0.44 inference(resolution,[status(thm)],[f236,f136])).
% 0.20/0.44 fof(f435,plain,(
% 0.20/0.44 subtract(any1,sk0_0(any1,x),zero(any1))=sk0_0(any1,x)|~spl0_8),
% 0.20/0.44 inference(forward_demodulation,[status(thm)],[f238,f434])).
% 0.20/0.44 fof(f441,plain,(
% 0.20/0.44 subtract(any1,sk0_0(any1,x),subtract(any1,sk0_0(any1,x),sk0_1(any1,x)))=sk0_1(any1,x)|~spl0_9|~spl0_8),
% 0.20/0.45 inference(resolution,[status(thm)],[f240,f136])).
% 0.20/0.45 fof(f449,plain,(
% 0.20/0.45 ![X0,X1]: (~element(X0,any1)|~element(X1,any1)|apply(x,subtract(any1,X0,X1))=subtract(any2,apply(x,X0),apply(x,X1)))),
% 0.20/0.45 inference(resolution,[status(thm)],[f73,f82])).
% 0.20/0.45 fof(f452,plain,(
% 0.20/0.45 ![X0]: (~element(X0,any1)|apply(x,subtract(any1,X0,sk0_1(any1,x)))=subtract(any2,apply(x,X0),apply(x,sk0_1(any1,x)))|~spl0_9)),
% 0.20/0.45 inference(resolution,[status(thm)],[f449,f144])).
% 0.20/0.45 fof(f453,plain,(
% 0.20/0.45 ![X0]: (~element(X0,any1)|apply(x,subtract(any1,X0,sk0_1(any1,x)))=subtract(any2,apply(x,X0),apply(x,sk0_0(any1,x)))|~spl0_13|~spl0_9)),
% 0.20/0.45 inference(forward_demodulation,[status(thm)],[f176,f452])).
% 0.20/0.45 fof(f463,plain,(
% 0.20/0.45 apply(x,subtract(any1,sk0_0(any1,x),sk0_1(any1,x)))=subtract(any2,apply(x,sk0_0(any1,x)),apply(x,sk0_0(any1,x)))|~spl0_13|~spl0_9|~spl0_8),
% 0.20/0.45 inference(resolution,[status(thm)],[f453,f136])).
% 0.20/0.45 fof(f464,plain,(
% 0.20/0.45 apply(x,subtract(any1,sk0_0(any1,x),sk0_1(any1,x)))=zero(any2)|~spl0_13|~spl0_9|~spl0_8),
% 0.20/0.45 inference(forward_demodulation,[status(thm)],[f142,f463])).
% 0.20/0.45 fof(f469,plain,(
% 0.20/0.45 spl0_33 <=> ~morphism(x,X0,any2)|~element(subtract(any1,sk0_0(any1,x),sk0_1(any1,x)),X0)|subtract(any1,sk0_0(any1,x),sk0_1(any1,x))=zero(X0)),
% 0.20/0.45 introduced(split_symbol_definition)).
% 0.20/0.45 fof(f470,plain,(
% 0.20/0.45 ![X0]: (~morphism(x,X0,any2)|~element(subtract(any1,sk0_0(any1,x),sk0_1(any1,x)),X0)|subtract(any1,sk0_0(any1,x),sk0_1(any1,x))=zero(X0)|~spl0_33)),
% 0.20/0.45 inference(component_clause,[status(thm)],[f469])).
% 0.20/0.45 fof(f472,plain,(
% 0.20/0.45 ![X0]: (~injection_2(x)|~morphism(x,X0,any2)|~element(subtract(any1,sk0_0(any1,x),sk0_1(any1,x)),X0)|subtract(any1,sk0_0(any1,x),sk0_1(any1,x))=zero(X0)|~spl0_13|~spl0_9|~spl0_8)),
% 0.20/0.45 inference(resolution,[status(thm)],[f464,f75])).
% 0.20/0.45 fof(f473,plain,(
% 0.20/0.45 ~spl0_1|spl0_33|~spl0_13|~spl0_9|~spl0_8),
% 0.20/0.45 inference(split_clause,[status(thm)],[f472,f95,f469,f175,f143,f135])).
% 0.20/0.45 fof(f533,plain,(
% 0.20/0.45 spl0_41 <=> subtract(any1,sk0_0(any1,x),sk0_1(any1,x))=zero(any1)),
% 0.20/0.45 introduced(split_symbol_definition)).
% 0.20/0.45 fof(f534,plain,(
% 0.20/0.45 subtract(any1,sk0_0(any1,x),sk0_1(any1,x))=zero(any1)|~spl0_41),
% 0.20/0.45 inference(component_clause,[status(thm)],[f533])).
% 0.20/0.45 fof(f536,plain,(
% 0.20/0.45 ~morphism(x,any1,any2)|subtract(any1,sk0_0(any1,x),sk0_1(any1,x))=zero(any1)|~spl0_33|~spl0_8|~spl0_9),
% 0.20/0.45 inference(resolution,[status(thm)],[f470,f249])).
% 0.20/0.45 fof(f537,plain,(
% 0.20/0.45 ~spl0_31|spl0_41|~spl0_33|~spl0_8|~spl0_9),
% 0.20/0.45 inference(split_clause,[status(thm)],[f536,f348,f533,f469,f135,f143])).
% 0.20/0.45 fof(f540,plain,(
% 0.20/0.45 subtract(any1,sk0_0(any1,x),zero(any1))=sk0_1(any1,x)|~spl0_41|~spl0_9|~spl0_8),
% 0.20/0.45 inference(backward_demodulation,[status(thm)],[f534,f441])).
% 0.20/0.45 fof(f541,plain,(
% 0.20/0.45 sk0_0(any1,x)=sk0_1(any1,x)|~spl0_41|~spl0_9|~spl0_8),
% 0.20/0.45 inference(forward_demodulation,[status(thm)],[f435,f540])).
% 0.20/0.45 fof(f542,plain,(
% 0.20/0.45 $false|spl0_24|~spl0_41|~spl0_9|~spl0_8),
% 0.20/0.45 inference(forward_subsumption_resolution,[status(thm)],[f541,f270])).
% 0.20/0.45 fof(f543,plain,(
% 0.20/0.45 spl0_24|~spl0_41|~spl0_9|~spl0_8),
% 0.20/0.45 inference(contradiction_clause,[status(thm)],[f542])).
% 0.20/0.45 fof(f544,plain,(
% 0.20/0.45 $false),
% 0.20/0.45 inference(sat_refutation,[status(thm)],[f98,f99,f108,f113,f128,f139,f147,f169,f179,f186,f198,f213,f215,f328,f337,f344,f352,f356,f358,f424,f473,f537,f543])).
% 0.20/0.45 % SZS output end CNFRefutation for theBenchmark.p
% 0.20/0.45 % Elapsed time: 0.094679 seconds
% 0.20/0.45 % CPU time: 0.619669 seconds
% 0.20/0.45 % Total memory used: 59.918 MB
% 0.20/0.45 % Net memory used: 59.421 MB
%------------------------------------------------------------------------------