TSTP Solution File: HAL002+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% 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 : n026.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 12:12:44 EDT 2023
% Result : Theorem 0.13s 0.44s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : HAL002+1 : TPTP v8.1.2. Released v2.6.0.
% 0.04/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n026.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 11:20:13 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.09/0.31 % Drodi V3.5.1
% 0.13/0.44 % Refutation found
% 0.13/0.44 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.44 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.44 fof(f1,axiom,(
% 0.13/0.44 (! [Morphism,Dom,Cod] :( morphism(Morphism,Dom,Cod)=> ( (! [El] :( element(El,Dom)=> element(apply(Morphism,El),Cod) ))& apply(Morphism,zero(Dom)) = zero(Cod) ) ) )),
% 0.13/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.44 fof(f2,axiom,(
% 0.13/0.44 (! [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 ) )) )),
% 0.13/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.44 fof(f3,axiom,(
% 0.13/0.44 (! [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) ) )),
% 0.13/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.44 fof(f10,axiom,(
% 0.13/0.44 (! [Dom,El1,El2] :( ( element(El1,Dom)& element(El2,Dom) )=> element(subtract(Dom,El1,El2),Dom) ) )),
% 0.13/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.44 fof(f11,axiom,(
% 0.13/0.44 (! [Dom,El] :( element(El,Dom)=> subtract(Dom,El,El) = zero(Dom) ) )),
% 0.13/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.44 fof(f12,axiom,(
% 0.13/0.44 (! [Dom,El1,El2] :( ( element(El1,Dom)& element(El2,Dom) )=> subtract(Dom,El1,subtract(Dom,El1,El2)) = El2 ) )),
% 0.13/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.44 fof(f13,axiom,(
% 0.13/0.44 (! [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)) ) )) )),
% 0.13/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.44 fof(f14,axiom,(
% 0.13/0.44 (! [Morphism,Dom,Cod] :( ( injection_2(Morphism)& morphism(Morphism,Dom,Cod) )=> (! [El] :( ( element(El,Dom)& apply(Morphism,El) = zero(Cod) )=> El = zero(Dom) ) )) )),
% 0.13/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.44 fof(f15,axiom,(
% 0.13/0.44 (! [Morphism,Dom,Cod] :( ( morphism(Morphism,Dom,Cod)& (! [El] :( ( element(El,Dom)& apply(Morphism,El) = zero(Cod) )=> El = zero(Dom) ) ))=> injection_2(Morphism) ) )),
% 0.13/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.44 fof(f16,hypothesis,(
% 0.13/0.44 morphism(x,any1,any2) ),
% 0.13/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.44 fof(f17,conjecture,(
% 0.13/0.44 ( injection(x)<=> injection_2(x) ) ),
% 0.13/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.44 fof(f18,negated_conjecture,(
% 0.13/0.44 ~(( injection(x)<=> injection_2(x) ) )),
% 0.13/0.44 inference(negated_conjecture,[status(cth)],[f17])).
% 0.13/0.44 fof(f19,plain,(
% 0.13/0.44 ![Morphism,Dom,Cod]: (~morphism(Morphism,Dom,Cod)|((![El]: (~element(El,Dom)|element(apply(Morphism,El),Cod)))&apply(Morphism,zero(Dom))=zero(Cod)))),
% 0.13/0.44 inference(pre_NNF_transformation,[status(esa)],[f1])).
% 0.13/0.44 fof(f20,plain,(
% 0.13/0.44 ![X0,X1,X2,X3]: (~morphism(X0,X1,X2)|~element(X3,X1)|element(apply(X0,X3),X2))),
% 0.13/0.44 inference(cnf_transformation,[status(esa)],[f19])).
% 0.13/0.44 fof(f21,plain,(
% 0.13/0.44 ![X0,X1,X2]: (~morphism(X0,X1,X2)|apply(X0,zero(X1))=zero(X2))),
% 0.13/0.44 inference(cnf_transformation,[status(esa)],[f19])).
% 0.13/0.45 fof(f22,plain,(
% 0.13/0.45 ![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)))),
% 0.13/0.45 inference(pre_NNF_transformation,[status(esa)],[f2])).
% 0.13/0.45 fof(f23,plain,(
% 0.13/0.45 ![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)))),
% 0.13/0.45 inference(miniscoping,[status(esa)],[f22])).
% 0.13/0.45 fof(f24,plain,(
% 0.13/0.45 ![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)),
% 0.13/0.45 inference(cnf_transformation,[status(esa)],[f23])).
% 0.13/0.45 fof(f25,plain,(
% 0.13/0.45 ![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))),
% 0.13/0.45 inference(pre_NNF_transformation,[status(esa)],[f3])).
% 0.13/0.45 fof(f26,plain,(
% 0.13/0.45 ![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))),
% 0.13/0.45 inference(miniscoping,[status(esa)],[f25])).
% 0.13/0.45 fof(f27,plain,(
% 0.13/0.45 ![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))),
% 0.13/0.45 inference(skolemization,[status(esa)],[f26])).
% 0.13/0.45 fof(f28,plain,(
% 0.13/0.45 ![X0,X1,X2]: (~morphism(X0,X1,X2)|element(sk0_0(X1,X0),X1)|injection(X0))),
% 0.13/0.45 inference(cnf_transformation,[status(esa)],[f27])).
% 0.13/0.45 fof(f29,plain,(
% 0.13/0.45 ![X0,X1,X2]: (~morphism(X0,X1,X2)|element(sk0_1(X1,X0),X1)|injection(X0))),
% 0.13/0.45 inference(cnf_transformation,[status(esa)],[f27])).
% 0.13/0.45 fof(f30,plain,(
% 0.13/0.45 ![X0,X1,X2]: (~morphism(X0,X1,X2)|apply(X0,sk0_0(X1,X0))=apply(X0,sk0_1(X1,X0))|injection(X0))),
% 0.13/0.45 inference(cnf_transformation,[status(esa)],[f27])).
% 0.13/0.45 fof(f31,plain,(
% 0.13/0.45 ![X0,X1,X2]: (~morphism(X0,X1,X2)|~sk0_0(X1,X0)=sk0_1(X1,X0)|injection(X0))),
% 0.13/0.45 inference(cnf_transformation,[status(esa)],[f27])).
% 0.13/0.45 fof(f66,plain,(
% 0.13/0.45 ![Dom,El1,El2]: ((~element(El1,Dom)|~element(El2,Dom))|element(subtract(Dom,El1,El2),Dom))),
% 0.13/0.45 inference(pre_NNF_transformation,[status(esa)],[f10])).
% 0.13/0.45 fof(f67,plain,(
% 0.13/0.45 ![X0,X1,X2]: (~element(X0,X1)|~element(X2,X1)|element(subtract(X1,X0,X2),X1))),
% 0.13/0.45 inference(cnf_transformation,[status(esa)],[f66])).
% 0.13/0.45 fof(f68,plain,(
% 0.13/0.45 ![Dom,El]: (~element(El,Dom)|subtract(Dom,El,El)=zero(Dom))),
% 0.13/0.45 inference(pre_NNF_transformation,[status(esa)],[f11])).
% 0.13/0.45 fof(f69,plain,(
% 0.13/0.45 ![X0,X1]: (~element(X0,X1)|subtract(X1,X0,X0)=zero(X1))),
% 0.13/0.45 inference(cnf_transformation,[status(esa)],[f68])).
% 0.13/0.45 fof(f70,plain,(
% 0.13/0.45 ![Dom,El1,El2]: ((~element(El1,Dom)|~element(El2,Dom))|subtract(Dom,El1,subtract(Dom,El1,El2))=El2)),
% 0.13/0.45 inference(pre_NNF_transformation,[status(esa)],[f12])).
% 0.13/0.45 fof(f71,plain,(
% 0.13/0.45 ![X0,X1,X2]: (~element(X0,X1)|~element(X2,X1)|subtract(X1,X0,subtract(X1,X0,X2))=X2)),
% 0.13/0.45 inference(cnf_transformation,[status(esa)],[f70])).
% 0.13/0.45 fof(f72,plain,(
% 0.13/0.45 ![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)))))),
% 0.13/0.45 inference(pre_NNF_transformation,[status(esa)],[f13])).
% 0.13/0.45 fof(f73,plain,(
% 0.13/0.45 ![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)))),
% 0.13/0.45 inference(cnf_transformation,[status(esa)],[f72])).
% 0.13/0.45 fof(f74,plain,(
% 0.13/0.45 ![Morphism,Dom,Cod]: ((~injection_2(Morphism)|~morphism(Morphism,Dom,Cod))|(![El]: ((~element(El,Dom)|~apply(Morphism,El)=zero(Cod))|El=zero(Dom))))),
% 0.13/0.45 inference(pre_NNF_transformation,[status(esa)],[f14])).
% 0.13/0.45 fof(f75,plain,(
% 0.13/0.45 ![X0,X1,X2,X3]: (~injection_2(X0)|~morphism(X0,X1,X2)|~element(X3,X1)|~apply(X0,X3)=zero(X2)|X3=zero(X1))),
% 0.13/0.45 inference(cnf_transformation,[status(esa)],[f74])).
% 0.13/0.45 fof(f76,plain,(
% 0.13/0.45 ![Morphism,Dom,Cod]: ((~morphism(Morphism,Dom,Cod)|(?[El]: ((element(El,Dom)&apply(Morphism,El)=zero(Cod))&~El=zero(Dom))))|injection_2(Morphism))),
% 0.13/0.45 inference(pre_NNF_transformation,[status(esa)],[f15])).
% 0.13/0.45 fof(f77,plain,(
% 0.13/0.45 ![Morphism]: ((![Dom,Cod]: (~morphism(Morphism,Dom,Cod)|(?[El]: ((element(El,Dom)&apply(Morphism,El)=zero(Cod))&~El=zero(Dom)))))|injection_2(Morphism))),
% 0.13/0.45 inference(miniscoping,[status(esa)],[f76])).
% 0.13/0.45 fof(f78,plain,(
% 0.13/0.45 ![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))),
% 0.13/0.45 inference(skolemization,[status(esa)],[f77])).
% 0.13/0.45 fof(f79,plain,(
% 0.13/0.45 ![X0,X1,X2]: (~morphism(X0,X1,X2)|element(sk0_8(X2,X1,X0),X1)|injection_2(X0))),
% 0.13/0.45 inference(cnf_transformation,[status(esa)],[f78])).
% 0.13/0.45 fof(f80,plain,(
% 0.13/0.45 ![X0,X1,X2]: (~morphism(X0,X1,X2)|apply(X0,sk0_8(X2,X1,X0))=zero(X2)|injection_2(X0))),
% 0.13/0.45 inference(cnf_transformation,[status(esa)],[f78])).
% 0.13/0.45 fof(f81,plain,(
% 0.13/0.45 ![X0,X1,X2]: (~morphism(X0,X1,X2)|~sk0_8(X2,X1,X0)=zero(X1)|injection_2(X0))),
% 0.13/0.45 inference(cnf_transformation,[status(esa)],[f78])).
% 0.13/0.45 fof(f82,plain,(
% 0.13/0.45 morphism(x,any1,any2)),
% 0.13/0.45 inference(cnf_transformation,[status(esa)],[f16])).
% 0.13/0.45 fof(f83,plain,(
% 0.13/0.45 (injection(x)<~>injection_2(x))),
% 0.13/0.45 inference(pre_NNF_transformation,[status(esa)],[f18])).
% 0.13/0.45 fof(f84,plain,(
% 0.13/0.45 (injection(x)|injection_2(x))&(~injection(x)|~injection_2(x))),
% 0.13/0.45 inference(NNF_transformation,[status(esa)],[f83])).
% 0.13/0.45 fof(f85,plain,(
% 0.13/0.45 injection(x)|injection_2(x)),
% 0.13/0.45 inference(cnf_transformation,[status(esa)],[f84])).
% 0.13/0.45 fof(f86,plain,(
% 0.13/0.45 ~injection(x)|~injection_2(x)),
% 0.13/0.45 inference(cnf_transformation,[status(esa)],[f84])).
% 0.13/0.45 fof(f92,plain,(
% 0.13/0.45 spl0_0 <=> injection(x)),
% 0.13/0.45 introduced(split_symbol_definition)).
% 0.13/0.45 fof(f95,plain,(
% 0.13/0.45 spl0_1 <=> injection_2(x)),
% 0.13/0.45 introduced(split_symbol_definition)).
% 0.13/0.45 fof(f98,plain,(
% 0.13/0.45 spl0_0|spl0_1),
% 0.13/0.45 inference(split_clause,[status(thm)],[f85,f92,f95])).
% 0.13/0.45 fof(f99,plain,(
% 0.13/0.45 ~spl0_0|~spl0_1),
% 0.13/0.45 inference(split_clause,[status(thm)],[f86,f92,f95])).
% 0.13/0.45 fof(f102,plain,(
% 0.13/0.45 ![X0]: (~element(X0,any1)|element(apply(x,X0),any2))),
% 0.13/0.45 inference(resolution,[status(thm)],[f20,f82])).
% 0.13/0.45 fof(f103,plain,(
% 0.13/0.45 apply(x,zero(any1))=zero(any2)),
% 0.13/0.45 inference(resolution,[status(thm)],[f21,f82])).
% 0.13/0.45 fof(f109,plain,(
% 0.13/0.45 spl0_3 <=> ~morphism(x,X0,X1)|~element(X2,X0)|~element(zero(any1),X0)|~apply(x,X2)=zero(any2)|X2=zero(any1)),
% 0.13/0.45 introduced(split_symbol_definition)).
% 0.13/0.45 fof(f110,plain,(
% 0.13/0.45 ![X0,X1,X2]: (~morphism(x,X0,X1)|~element(X2,X0)|~element(zero(any1),X0)|~apply(x,X2)=zero(any2)|X2=zero(any1)|~spl0_3)),
% 0.13/0.45 inference(component_clause,[status(thm)],[f109])).
% 0.13/0.45 fof(f112,plain,(
% 0.13/0.45 ![X0,X1,X2]: (~injection(x)|~morphism(x,X0,X1)|~element(X2,X0)|~element(zero(any1),X0)|~apply(x,X2)=zero(any2)|X2=zero(any1))),
% 0.13/0.45 inference(paramodulation,[status(thm)],[f103,f24])).
% 0.13/0.45 fof(f113,plain,(
% 0.13/0.45 ~spl0_0|spl0_3),
% 0.13/0.45 inference(split_clause,[status(thm)],[f112,f92,f109])).
% 0.13/0.45 fof(f152,plain,(
% 0.13/0.45 ![X0,X1]: (~element(X0,any1)|~element(X1,any1)|apply(x,subtract(any1,X0,X1))=subtract(any2,apply(x,X0),apply(x,X1)))),
% 0.13/0.45 inference(resolution,[status(thm)],[f73,f82])).
% 0.13/0.45 fof(f154,plain,(
% 0.13/0.45 spl0_11 <=> element(sk0_0(any1,x),any1)),
% 0.13/0.45 introduced(split_symbol_definition)).
% 0.13/0.45 fof(f155,plain,(
% 0.13/0.45 element(sk0_0(any1,x),any1)|~spl0_11),
% 0.13/0.45 inference(component_clause,[status(thm)],[f154])).
% 0.13/0.45 fof(f157,plain,(
% 0.13/0.45 element(sk0_0(any1,x),any1)|injection(x)),
% 0.13/0.45 inference(resolution,[status(thm)],[f28,f82])).
% 0.13/0.45 fof(f158,plain,(
% 0.13/0.45 spl0_11|spl0_0),
% 0.13/0.45 inference(split_clause,[status(thm)],[f157,f154,f92])).
% 0.13/0.45 fof(f159,plain,(
% 0.13/0.45 spl0_12 <=> element(sk0_1(any1,x),any1)),
% 0.13/0.45 introduced(split_symbol_definition)).
% 0.13/0.45 fof(f160,plain,(
% 0.13/0.45 element(sk0_1(any1,x),any1)|~spl0_12),
% 0.13/0.45 inference(component_clause,[status(thm)],[f159])).
% 0.13/0.45 fof(f162,plain,(
% 0.13/0.45 element(sk0_1(any1,x),any1)|injection(x)),
% 0.13/0.45 inference(resolution,[status(thm)],[f29,f82])).
% 0.13/0.45 fof(f163,plain,(
% 0.13/0.45 spl0_12|spl0_0),
% 0.13/0.45 inference(split_clause,[status(thm)],[f162,f159,f92])).
% 0.13/0.45 fof(f169,plain,(
% 0.13/0.45 spl0_14 <=> element(sk0_8(any2,any1,x),any1)),
% 0.13/0.45 introduced(split_symbol_definition)).
% 0.13/0.45 fof(f170,plain,(
% 0.13/0.45 element(sk0_8(any2,any1,x),any1)|~spl0_14),
% 0.13/0.45 inference(component_clause,[status(thm)],[f169])).
% 0.13/0.45 fof(f172,plain,(
% 0.13/0.45 element(sk0_8(any2,any1,x),any1)|injection_2(x)),
% 0.13/0.45 inference(resolution,[status(thm)],[f79,f82])).
% 0.13/0.45 fof(f173,plain,(
% 0.13/0.45 spl0_14|spl0_1),
% 0.13/0.45 inference(split_clause,[status(thm)],[f172,f169,f95])).
% 0.13/0.45 fof(f174,plain,(
% 0.13/0.45 spl0_15 <=> apply(x,sk0_8(any2,any1,x))=zero(any2)),
% 0.13/0.45 introduced(split_symbol_definition)).
% 0.13/0.45 fof(f175,plain,(
% 0.13/0.45 apply(x,sk0_8(any2,any1,x))=zero(any2)|~spl0_15),
% 0.13/0.45 inference(component_clause,[status(thm)],[f174])).
% 0.13/0.45 fof(f177,plain,(
% 0.13/0.45 apply(x,sk0_8(any2,any1,x))=zero(any2)|injection_2(x)),
% 0.13/0.45 inference(resolution,[status(thm)],[f80,f82])).
% 0.13/0.45 fof(f178,plain,(
% 0.13/0.45 spl0_15|spl0_1),
% 0.13/0.45 inference(split_clause,[status(thm)],[f177,f174,f95])).
% 0.13/0.45 fof(f179,plain,(
% 0.13/0.45 spl0_16 <=> apply(x,sk0_0(any1,x))=apply(x,sk0_1(any1,x))),
% 0.13/0.45 introduced(split_symbol_definition)).
% 0.13/0.45 fof(f180,plain,(
% 0.13/0.45 apply(x,sk0_0(any1,x))=apply(x,sk0_1(any1,x))|~spl0_16),
% 0.13/0.45 inference(component_clause,[status(thm)],[f179])).
% 0.13/0.45 fof(f182,plain,(
% 0.13/0.45 apply(x,sk0_0(any1,x))=apply(x,sk0_1(any1,x))|injection(x)),
% 0.13/0.45 inference(resolution,[status(thm)],[f30,f82])).
% 0.13/0.45 fof(f183,plain,(
% 0.13/0.45 spl0_16|spl0_0),
% 0.13/0.45 inference(split_clause,[status(thm)],[f182,f179,f92])).
% 0.13/0.45 fof(f200,plain,(
% 0.13/0.45 ![X0]: (~element(X0,any1)|element(subtract(any1,sk0_8(any2,any1,x),X0),any1)|~spl0_14)),
% 0.13/0.45 inference(resolution,[status(thm)],[f170,f67])).
% 0.13/0.45 fof(f201,plain,(
% 0.13/0.45 subtract(any1,sk0_8(any2,any1,x),sk0_8(any2,any1,x))=zero(any1)|~spl0_14),
% 0.13/0.45 inference(resolution,[status(thm)],[f170,f69])).
% 0.13/0.45 fof(f228,plain,(
% 0.13/0.45 spl0_21 <=> morphism(x,any1,any2)),
% 0.13/0.45 introduced(split_symbol_definition)).
% 0.13/0.45 fof(f230,plain,(
% 0.13/0.45 ~morphism(x,any1,any2)|spl0_21),
% 0.13/0.45 inference(component_clause,[status(thm)],[f228])).
% 0.13/0.45 fof(f231,plain,(
% 0.13/0.45 spl0_22 <=> sk0_8(any2,any1,x)=zero(any1)),
% 0.13/0.45 introduced(split_symbol_definition)).
% 0.13/0.45 fof(f232,plain,(
% 0.13/0.45 sk0_8(any2,any1,x)=zero(any1)|~spl0_22),
% 0.13/0.45 inference(component_clause,[status(thm)],[f231])).
% 0.13/0.45 fof(f236,plain,(
% 0.13/0.45 $false|spl0_21),
% 0.13/0.45 inference(forward_subsumption_resolution,[status(thm)],[f230,f82])).
% 0.13/0.45 fof(f237,plain,(
% 0.13/0.45 spl0_21),
% 0.13/0.45 inference(contradiction_clause,[status(thm)],[f236])).
% 0.13/0.45 fof(f238,plain,(
% 0.13/0.45 ~morphism(x,any1,any2)|injection_2(x)|~spl0_22),
% 0.13/0.45 inference(resolution,[status(thm)],[f232,f81])).
% 0.13/0.45 fof(f239,plain,(
% 0.13/0.45 ~spl0_21|spl0_1|~spl0_22),
% 0.13/0.45 inference(split_clause,[status(thm)],[f238,f228,f95,f231])).
% 0.13/0.45 fof(f244,plain,(
% 0.13/0.45 ![X0]: (~element(X0,any1)|apply(x,subtract(any1,X0,sk0_0(any1,x)))=subtract(any2,apply(x,X0),apply(x,sk0_0(any1,x)))|~spl0_11)),
% 0.13/0.45 inference(resolution,[status(thm)],[f155,f152])).
% 0.13/0.45 fof(f245,plain,(
% 0.13/0.45 element(apply(x,sk0_0(any1,x)),any2)|~spl0_11),
% 0.13/0.45 inference(resolution,[status(thm)],[f155,f102])).
% 0.13/0.45 fof(f246,plain,(
% 0.13/0.45 ![X0]: (~element(X0,any1)|subtract(any1,X0,subtract(any1,X0,sk0_0(any1,x)))=sk0_0(any1,x)|~spl0_11)),
% 0.13/0.45 inference(resolution,[status(thm)],[f155,f71])).
% 0.13/0.45 fof(f251,plain,(
% 0.13/0.45 ![X0]: (~element(X0,any1)|subtract(any1,X0,subtract(any1,X0,sk0_1(any1,x)))=sk0_1(any1,x)|~spl0_12)),
% 0.13/0.45 inference(resolution,[status(thm)],[f160,f71])).
% 0.13/0.45 fof(f252,plain,(
% 0.13/0.45 ![X0]: (~element(X0,any1)|element(subtract(any1,sk0_1(any1,x),X0),any1)|~spl0_12)),
% 0.13/0.45 inference(resolution,[status(thm)],[f160,f67])).
% 0.13/0.45 fof(f253,plain,(
% 0.13/0.45 subtract(any1,sk0_1(any1,x),sk0_1(any1,x))=zero(any1)|~spl0_12),
% 0.13/0.45 inference(resolution,[status(thm)],[f160,f69])).
% 0.13/0.45 fof(f256,plain,(
% 0.13/0.45 subtract(any2,apply(x,sk0_0(any1,x)),apply(x,sk0_0(any1,x)))=zero(any2)|~spl0_11),
% 0.13/0.45 inference(resolution,[status(thm)],[f245,f69])).
% 0.13/0.45 fof(f299,plain,(
% 0.13/0.45 spl0_28 <=> ~morphism(x,any1,X0)),
% 0.13/0.45 introduced(split_symbol_definition)).
% 0.13/0.45 fof(f300,plain,(
% 0.13/0.45 ![X0]: (~morphism(x,any1,X0)|~spl0_28)),
% 0.13/0.45 inference(component_clause,[status(thm)],[f299])).
% 0.13/0.45 fof(f313,plain,(
% 0.13/0.45 $false|~spl0_28),
% 0.13/0.45 inference(backward_subsumption_resolution,[status(thm)],[f82,f300])).
% 0.13/0.45 fof(f314,plain,(
% 0.13/0.45 ~spl0_28),
% 0.13/0.45 inference(contradiction_clause,[status(thm)],[f313])).
% 0.13/0.45 fof(f410,plain,(
% 0.13/0.45 apply(x,subtract(any1,sk0_1(any1,x),sk0_0(any1,x)))=subtract(any2,apply(x,sk0_1(any1,x)),apply(x,sk0_0(any1,x)))|~spl0_11|~spl0_12),
% 0.13/0.45 inference(resolution,[status(thm)],[f244,f160])).
% 0.13/0.45 fof(f411,plain,(
% 0.13/0.45 apply(x,subtract(any1,sk0_1(any1,x),sk0_0(any1,x)))=subtract(any2,apply(x,sk0_0(any1,x)),apply(x,sk0_0(any1,x)))|~spl0_16|~spl0_11|~spl0_12),
% 0.13/0.45 inference(forward_demodulation,[status(thm)],[f180,f410])).
% 0.13/0.45 fof(f416,plain,(
% 0.13/0.45 element(subtract(any1,sk0_1(any1,x),sk0_0(any1,x)),any1)|~spl0_12|~spl0_11),
% 0.13/0.45 inference(resolution,[status(thm)],[f252,f155])).
% 0.13/0.45 fof(f673,plain,(
% 0.13/0.45 subtract(any1,sk0_1(any1,x),subtract(any1,sk0_1(any1,x),sk0_0(any1,x)))=sk0_0(any1,x)|~spl0_11|~spl0_12),
% 0.13/0.45 inference(resolution,[status(thm)],[f246,f160])).
% 0.13/0.45 fof(f688,plain,(
% 0.13/0.45 subtract(any1,sk0_1(any1,x),subtract(any1,sk0_1(any1,x),sk0_1(any1,x)))=sk0_1(any1,x)|~spl0_12),
% 0.13/0.45 inference(resolution,[status(thm)],[f251,f160])).
% 0.13/0.45 fof(f689,plain,(
% 0.13/0.45 subtract(any1,sk0_1(any1,x),zero(any1))=sk0_1(any1,x)|~spl0_12),
% 0.13/0.45 inference(forward_demodulation,[status(thm)],[f253,f688])).
% 0.13/0.45 fof(f1153,plain,(
% 0.13/0.45 apply(x,subtract(any1,sk0_1(any1,x),sk0_0(any1,x)))=zero(any2)|~spl0_16|~spl0_11|~spl0_12),
% 0.13/0.45 inference(forward_demodulation,[status(thm)],[f256,f411])).
% 0.13/0.45 fof(f1157,plain,(
% 0.13/0.45 spl0_39 <=> ~morphism(x,X0,any2)|~element(subtract(any1,sk0_1(any1,x),sk0_0(any1,x)),X0)|subtract(any1,sk0_1(any1,x),sk0_0(any1,x))=zero(X0)),
% 0.13/0.46 introduced(split_symbol_definition)).
% 0.13/0.46 fof(f1158,plain,(
% 0.13/0.46 ![X0]: (~morphism(x,X0,any2)|~element(subtract(any1,sk0_1(any1,x),sk0_0(any1,x)),X0)|subtract(any1,sk0_1(any1,x),sk0_0(any1,x))=zero(X0)|~spl0_39)),
% 0.13/0.46 inference(component_clause,[status(thm)],[f1157])).
% 0.13/0.46 fof(f1160,plain,(
% 0.13/0.46 ![X0]: (~injection_2(x)|~morphism(x,X0,any2)|~element(subtract(any1,sk0_1(any1,x),sk0_0(any1,x)),X0)|subtract(any1,sk0_1(any1,x),sk0_0(any1,x))=zero(X0)|~spl0_16|~spl0_11|~spl0_12)),
% 0.13/0.46 inference(resolution,[status(thm)],[f1153,f75])).
% 0.13/0.46 fof(f1161,plain,(
% 0.13/0.46 ~spl0_1|spl0_39|~spl0_16|~spl0_11|~spl0_12),
% 0.13/0.46 inference(split_clause,[status(thm)],[f1160,f95,f1157,f179,f154,f159])).
% 0.13/0.46 fof(f1185,plain,(
% 0.13/0.46 spl0_43 <=> subtract(any1,sk0_1(any1,x),sk0_0(any1,x))=zero(any1)),
% 0.13/0.46 introduced(split_symbol_definition)).
% 0.13/0.46 fof(f1186,plain,(
% 0.13/0.46 subtract(any1,sk0_1(any1,x),sk0_0(any1,x))=zero(any1)|~spl0_43),
% 0.13/0.46 inference(component_clause,[status(thm)],[f1185])).
% 0.13/0.46 fof(f1188,plain,(
% 0.13/0.46 ~morphism(x,any1,any2)|subtract(any1,sk0_1(any1,x),sk0_0(any1,x))=zero(any1)|~spl0_39|~spl0_12|~spl0_11),
% 0.13/0.46 inference(resolution,[status(thm)],[f1158,f416])).
% 0.13/0.46 fof(f1189,plain,(
% 0.13/0.46 ~spl0_21|spl0_43|~spl0_39|~spl0_12|~spl0_11),
% 0.13/0.46 inference(split_clause,[status(thm)],[f1188,f228,f1185,f1157,f159,f154])).
% 0.13/0.46 fof(f1503,plain,(
% 0.13/0.46 subtract(any1,sk0_1(any1,x),zero(any1))=sk0_0(any1,x)|~spl0_43|~spl0_11|~spl0_12),
% 0.13/0.46 inference(forward_demodulation,[status(thm)],[f1186,f673])).
% 0.13/0.46 fof(f1504,plain,(
% 0.13/0.46 sk0_1(any1,x)=sk0_0(any1,x)|~spl0_43|~spl0_11|~spl0_12),
% 0.13/0.46 inference(forward_demodulation,[status(thm)],[f689,f1503])).
% 0.13/0.46 fof(f1563,plain,(
% 0.13/0.46 ![X0]: (~morphism(x,any1,X0)|injection(x)|~spl0_43|~spl0_11|~spl0_12)),
% 0.13/0.46 inference(resolution,[status(thm)],[f1504,f31])).
% 0.13/0.46 fof(f1564,plain,(
% 0.13/0.46 spl0_28|spl0_0|~spl0_43|~spl0_11|~spl0_12),
% 0.13/0.46 inference(split_clause,[status(thm)],[f1563,f299,f92,f1185,f154,f159])).
% 0.13/0.46 fof(f1592,plain,(
% 0.13/0.46 spl0_52 <=> ~morphism(x,X0,X1)|~element(sk0_8(any2,any1,x),X0)|~element(zero(any1),X0)),
% 0.13/0.46 introduced(split_symbol_definition)).
% 0.13/0.46 fof(f1593,plain,(
% 0.13/0.46 ![X0,X1]: (~morphism(x,X0,X1)|~element(sk0_8(any2,any1,x),X0)|~element(zero(any1),X0)|~spl0_52)),
% 0.13/0.46 inference(component_clause,[status(thm)],[f1592])).
% 0.13/0.46 fof(f1595,plain,(
% 0.13/0.46 ![X0,X1]: (~morphism(x,X0,X1)|~element(sk0_8(any2,any1,x),X0)|~element(zero(any1),X0)|sk0_8(any2,any1,x)=zero(any1)|~spl0_15|~spl0_3)),
% 0.13/0.46 inference(resolution,[status(thm)],[f175,f110])).
% 0.13/0.46 fof(f1596,plain,(
% 0.13/0.46 spl0_52|spl0_22|~spl0_15|~spl0_3),
% 0.13/0.46 inference(split_clause,[status(thm)],[f1595,f1592,f231,f174,f109])).
% 0.13/0.46 fof(f1613,plain,(
% 0.13/0.46 spl0_53 <=> element(zero(any1),any1)),
% 0.13/0.46 introduced(split_symbol_definition)).
% 0.13/0.46 fof(f1615,plain,(
% 0.13/0.46 ~element(zero(any1),any1)|spl0_53),
% 0.13/0.46 inference(component_clause,[status(thm)],[f1613])).
% 0.13/0.46 fof(f1616,plain,(
% 0.13/0.46 ![X0]: (~morphism(x,any1,X0)|~element(zero(any1),any1)|~spl0_52|~spl0_14)),
% 0.13/0.46 inference(resolution,[status(thm)],[f1593,f170])).
% 0.13/0.46 fof(f1617,plain,(
% 0.13/0.46 spl0_28|~spl0_53|~spl0_52|~spl0_14),
% 0.13/0.46 inference(split_clause,[status(thm)],[f1616,f299,f1613,f1592,f169])).
% 0.13/0.46 fof(f1646,plain,(
% 0.13/0.46 element(subtract(any1,sk0_8(any2,any1,x),sk0_8(any2,any1,x)),any1)|~spl0_14),
% 0.13/0.46 inference(resolution,[status(thm)],[f200,f170])).
% 0.13/0.46 fof(f1651,plain,(
% 0.13/0.46 element(zero(any1),any1)|~spl0_14),
% 0.13/0.46 inference(forward_demodulation,[status(thm)],[f201,f1646])).
% 0.13/0.46 fof(f1652,plain,(
% 0.13/0.46 $false|spl0_53|~spl0_14),
% 0.13/0.46 inference(forward_subsumption_resolution,[status(thm)],[f1651,f1615])).
% 0.13/0.46 fof(f1653,plain,(
% 0.13/0.46 spl0_53|~spl0_14),
% 0.13/0.46 inference(contradiction_clause,[status(thm)],[f1652])).
% 0.13/0.46 fof(f1654,plain,(
% 0.13/0.46 $false),
% 0.13/0.46 inference(sat_refutation,[status(thm)],[f98,f99,f113,f158,f163,f173,f178,f183,f237,f239,f314,f1161,f1189,f1564,f1596,f1617,f1653])).
% 0.13/0.46 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.47 % Elapsed time: 0.161770 seconds
% 0.13/0.47 % CPU time: 0.605046 seconds
% 0.13/0.47 % Memory used: 54.345 MB
%------------------------------------------------------------------------------