%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : HAL002+1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:45:13 PM UTC 2026
% Result : Theorem 0.13s 0.47s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HAL002+1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.38 % Computer : n004.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 20 20:44:20 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.40 % Drodi V4.1.1
% 0.13/0.47 % Refutation found
% 0.13/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.47 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.47 fof(f1,axiom,(
% 0.13/0.47 (! [Morphism,Dom,Cod] :( morphism(Morphism,Dom,Cod)=> ( (! [El] :( element(El,Dom)=> element(apply(Morphism,El),Cod) ))& apply(Morphism,zero(Dom)) = zero(Cod) ) ) )),
% 0.13/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.47 fof(f2,axiom,(
% 0.13/0.47 (! [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 ) )) )),
% 0.13/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.47 fof(f3,axiom,(
% 0.13/0.47 (! [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) ) )),
% 0.13/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.47 fof(f10,axiom,(
% 0.13/0.47 (! [Dom,El1,El2] :( ( element(El1,Dom)& element(El2,Dom) )=> element(subtract(Dom,El1,El2),Dom) ) )),
% 0.13/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.47 fof(f11,axiom,(
% 0.13/0.47 (! [Dom,El] :( element(El,Dom)=> subtract(Dom,El,El) = zero(Dom) ) )),
% 0.13/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.47 fof(f12,axiom,(
% 0.13/0.47 (! [Dom,El1,El2] :( ( element(El1,Dom)& element(El2,Dom) )=> subtract(Dom,El1,subtract(Dom,El1,El2)) = El2 ) )),
% 0.13/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.47 fof(f13,axiom,(
% 0.13/0.47 (! [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)) ) )) )),
% 0.13/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.47 fof(f14,axiom,(
% 0.13/0.47 (! [Morphism,Dom,Cod] :( ( injection_2(Morphism)& morphism(Morphism,Dom,Cod) )=> (! [El] :( ( element(El,Dom)& apply(Morphism,El) = zero(Cod) )=> El = zero(Dom) ) )) )),
% 0.13/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.47 fof(f15,axiom,(
% 0.13/0.47 (! [Morphism,Dom,Cod] :( ( morphism(Morphism,Dom,Cod)& (! [El] :( ( element(El,Dom)& apply(Morphism,El) = zero(Cod) )=> El = zero(Dom) ) ))=> injection_2(Morphism) ) )),
% 0.13/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.47 fof(f16,hypothesis,(
% 0.13/0.47 morphism(x,any1,any2) ),
% 0.13/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.47 fof(f17,conjecture,(
% 0.13/0.47 ( injection(x)<=> injection_2(x) ) ),
% 0.13/0.47 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.47 fof(f18,negated_conjecture,(
% 0.13/0.47 ~(( injection(x)<=> injection_2(x) ) )),
% 0.13/0.47 inference(negated_conjecture,[status(cth)],[f17])).
% 0.13/0.47 fof(f19,plain,(
% 0.13/0.47 ![Morphism,Dom,Cod]: (~morphism(Morphism,Dom,Cod)|((![El]: (~element(El,Dom)|element(apply(Morphism,El),Cod)))&apply(Morphism,zero(Dom))=zero(Cod)))),
% 0.13/0.47 inference(pre_NNF_transformation,[status(thm)],[f1])).
% 0.13/0.47 fof(f20,plain,(
% 0.13/0.47 ![X0,X1,X2,X3]: (~morphism(X0,X1,X2)|~element(X3,X1)|element(apply(X0,X3),X2))),
% 0.13/0.47 inference(cnf_transformation,[status(thm)],[f19])).
% 0.13/0.47 fof(f21,plain,(
% 0.13/0.47 ![X0,X1,X2]: (~morphism(X0,X1,X2)|apply(X0,zero(X1))=zero(X2))),
% 0.13/0.47 inference(cnf_transformation,[status(thm)],[f19])).
% 0.13/0.47 fof(f22,plain,(
% 0.13/0.47 ![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)))),
% 0.13/0.47 inference(pre_NNF_transformation,[status(thm)],[f2])).
% 0.13/0.47 fof(f23,plain,(
% 0.13/0.47 ![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)))),
% 0.13/0.47 inference(miniscoping,[status(thm)],[f22])).
% 0.13/0.47 fof(f24,plain,(
% 0.13/0.47 ![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)),
% 0.13/0.47 inference(cnf_transformation,[status(thm)],[f23])).
% 0.13/0.47 fof(f25,plain,(
% 0.13/0.47 ![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))),
% 0.13/0.47 inference(pre_NNF_transformation,[status(thm)],[f3])).
% 0.13/0.47 fof(f26,plain,(
% 0.13/0.47 ![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))),
% 0.13/0.47 inference(miniscoping,[status(thm)],[f25])).
% 0.13/0.47 fof(f27,plain,(
% 0.13/0.47 ![Morphism]: ((![Dom]: ((![Cod]: ~morphism(Morphism,Dom,Cod))|(((element(sK0_skl(Dom,Morphism),Dom)&element(sK1_skl(Dom,Morphism),Dom))&apply(Morphism,sK0_skl(Dom,Morphism))=apply(Morphism,sK1_skl(Dom,Morphism)))&~sK0_skl(Dom,Morphism)=sK1_skl(Dom,Morphism))))|injection(Morphism))),
% 0.13/0.47 inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(El1,sK0_skl(Dom,Morphism)),skolemize(El2,sK1_skl(Dom,Morphism))],[f26])).
% 0.13/0.47 fof(f28,plain,(
% 0.13/0.47 ![X0,X1,X2]: (~morphism(X0,X1,X2)|element(sK0_skl(X1,X0),X1)|injection(X0))),
% 0.13/0.47 inference(cnf_transformation,[status(thm)],[f27])).
% 0.13/0.47 fof(f29,plain,(
% 0.13/0.47 ![X0,X1,X2]: (~morphism(X0,X1,X2)|element(sK1_skl(X1,X0),X1)|injection(X0))),
% 0.13/0.47 inference(cnf_transformation,[status(thm)],[f27])).
% 0.13/0.47 fof(f30,plain,(
% 0.13/0.47 ![X0,X1,X2]: (~morphism(X0,X1,X2)|apply(X0,sK0_skl(X1,X0))=apply(X0,sK1_skl(X1,X0))|injection(X0))),
% 0.13/0.47 inference(cnf_transformation,[status(thm)],[f27])).
% 0.13/0.47 fof(f31,plain,(
% 0.13/0.47 ![X0,X1,X2]: (~morphism(X0,X1,X2)|~sK0_skl(X1,X0)=sK1_skl(X1,X0)|injection(X0))),
% 0.13/0.47 inference(cnf_transformation,[status(thm)],[f27])).
% 0.13/0.47 fof(f66,plain,(
% 0.13/0.47 ![Dom,El1,El2]: ((~element(El1,Dom)|~element(El2,Dom))|element(subtract(Dom,El1,El2),Dom))),
% 0.13/0.47 inference(pre_NNF_transformation,[status(thm)],[f10])).
% 0.13/0.47 fof(f67,plain,(
% 0.13/0.47 ![X0,X1,X2]: (~element(X0,X1)|~element(X2,X1)|element(subtract(X1,X0,X2),X1))),
% 0.13/0.47 inference(cnf_transformation,[status(thm)],[f66])).
% 0.13/0.47 fof(f68,plain,(
% 0.13/0.47 ![Dom,El]: (~element(El,Dom)|subtract(Dom,El,El)=zero(Dom))),
% 0.13/0.47 inference(pre_NNF_transformation,[status(thm)],[f11])).
% 0.13/0.47 fof(f69,plain,(
% 0.13/0.47 ![X0,X1]: (~element(X0,X1)|subtract(X1,X0,X0)=zero(X1))),
% 0.13/0.47 inference(cnf_transformation,[status(thm)],[f68])).
% 0.13/0.47 fof(f70,plain,(
% 0.13/0.47 ![Dom,El1,El2]: ((~element(El1,Dom)|~element(El2,Dom))|subtract(Dom,El1,subtract(Dom,El1,El2))=El2)),
% 0.13/0.47 inference(pre_NNF_transformation,[status(thm)],[f12])).
% 0.13/0.47 fof(f71,plain,(
% 0.13/0.47 ![X0,X1,X2]: (~element(X0,X1)|~element(X2,X1)|subtract(X1,X0,subtract(X1,X0,X2))=X2)),
% 0.13/0.47 inference(cnf_transformation,[status(thm)],[f70])).
% 0.13/0.47 fof(f72,plain,(
% 0.13/0.47 ![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)))))),
% 0.13/0.47 inference(pre_NNF_transformation,[status(thm)],[f13])).
% 0.13/0.47 fof(f73,plain,(
% 0.13/0.47 ![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)))),
% 0.13/0.47 inference(cnf_transformation,[status(thm)],[f72])).
% 0.13/0.47 fof(f74,plain,(
% 0.13/0.47 ![Morphism,Dom,Cod]: ((~injection_2(Morphism)|~morphism(Morphism,Dom,Cod))|(![El]: ((~element(El,Dom)|~apply(Morphism,El)=zero(Cod))|El=zero(Dom))))),
% 0.13/0.47 inference(pre_NNF_transformation,[status(thm)],[f14])).
% 0.13/0.47 fof(f75,plain,(
% 0.13/0.47 ![X0,X1,X2,X3]: (~injection_2(X0)|~morphism(X0,X1,X2)|~element(X3,X1)|~apply(X0,X3)=zero(X2)|X3=zero(X1))),
% 0.13/0.47 inference(cnf_transformation,[status(thm)],[f74])).
% 0.13/0.47 fof(f76,plain,(
% 0.13/0.47 ![Morphism,Dom,Cod]: ((~morphism(Morphism,Dom,Cod)|(?[El]: ((element(El,Dom)&apply(Morphism,El)=zero(Cod))&~El=zero(Dom))))|injection_2(Morphism))),
% 0.13/0.47 inference(pre_NNF_transformation,[status(thm)],[f15])).
% 0.13/0.47 fof(f77,plain,(
% 0.13/0.47 ![Morphism]: ((![Dom,Cod]: (~morphism(Morphism,Dom,Cod)|(?[El]: ((element(El,Dom)&apply(Morphism,El)=zero(Cod))&~El=zero(Dom)))))|injection_2(Morphism))),
% 0.13/0.47 inference(miniscoping,[status(thm)],[f76])).
% 0.13/0.47 fof(f78,plain,(
% 0.13/0.47 ![Morphism]: ((![Dom,Cod]: (~morphism(Morphism,Dom,Cod)|((element(sK8_skl(Cod,Dom,Morphism),Dom)&apply(Morphism,sK8_skl(Cod,Dom,Morphism))=zero(Cod))&~sK8_skl(Cod,Dom,Morphism)=zero(Dom))))|injection_2(Morphism))),
% 0.13/0.47 inference(skolemize,[status(esa),new_symbols(skolem,[sK8_skl]),skolemize(El,sK8_skl(Cod,Dom,Morphism))],[f77])).
% 0.13/0.47 fof(f79,plain,(
% 0.13/0.47 ![X0,X1,X2]: (~morphism(X0,X1,X2)|element(sK8_skl(X2,X1,X0),X1)|injection_2(X0))),
% 0.13/0.47 inference(cnf_transformation,[status(thm)],[f78])).
% 0.13/0.47 fof(f80,plain,(
% 0.13/0.47 ![X0,X1,X2]: (~morphism(X0,X1,X2)|apply(X0,sK8_skl(X2,X1,X0))=zero(X2)|injection_2(X0))),
% 0.13/0.47 inference(cnf_transformation,[status(thm)],[f78])).
% 0.13/0.47 fof(f81,plain,(
% 0.13/0.47 ![X0,X1,X2]: (~morphism(X0,X1,X2)|~sK8_skl(X2,X1,X0)=zero(X1)|injection_2(X0))),
% 0.13/0.47 inference(cnf_transformation,[status(thm)],[f78])).
% 0.13/0.47 fof(f82,plain,(
% 0.13/0.47 morphism(x,any1,any2)),
% 0.13/0.47 inference(cnf_transformation,[status(thm)],[f16])).
% 0.13/0.47 fof(f83,plain,(
% 0.13/0.47 (injection(x)<~>injection_2(x))),
% 0.13/0.47 inference(pre_NNF_transformation,[status(thm)],[f18])).
% 0.13/0.47 fof(f84,plain,(
% 0.13/0.47 (injection(x)|injection_2(x))&(~injection(x)|~injection_2(x))),
% 0.13/0.47 inference(NNF_transformation,[status(thm)],[f83])).
% 0.13/0.47 fof(f85,plain,(
% 0.13/0.47 injection(x)|injection_2(x)),
% 0.13/0.47 inference(cnf_transformation,[status(thm)],[f84])).
% 0.13/0.47 fof(f86,plain,(
% 0.13/0.47 ~injection(x)|~injection_2(x)),
% 0.13/0.47 inference(cnf_transformation,[status(thm)],[f84])).
% 0.13/0.47 fof(f92,definition,(
% 0.13/0.47 sQ0_spl <=> (injection(x))),
% 0.13/0.47 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.13/0.47 fof(f95,definition,(
% 0.13/0.47 sQ1_spl <=> (injection_2(x))),
% 0.13/0.47 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.13/0.47 fof(f98,plain,(
% 0.13/0.47 sQ0_spl|sQ1_spl),
% 0.13/0.47 inference(split_clause,[status(thm)],[f85,f92,f95])).
% 0.13/0.47 fof(f99,plain,(
% 0.13/0.47 ~sQ0_spl|~sQ1_spl),
% 0.13/0.47 inference(split_clause,[status(thm)],[f86,f92,f95])).
% 0.13/0.47 fof(f103,plain,(
% 0.13/0.47 ![X0]: (~element(X0,any1)|element(apply(x,X0),any2))),
% 0.13/0.47 inference(resolution,[status(thm)],[f20,f82])).
% 0.13/0.47 fof(f104,plain,(
% 0.13/0.47 apply(x,zero(any1))=zero(any2)),
% 0.13/0.47 inference(resolution,[status(thm)],[f21,f82])).
% 0.13/0.47 fof(f105,plain,(
% 0.13/0.47 element(sK0_skl(any1,x),any1)|injection(x)),
% 0.13/0.47 inference(resolution,[status(thm)],[f28,f82])).
% 0.13/0.47 fof(f106,definition,(
% 0.13/0.47 sQ2_spl <=> (element(sK0_skl(any1,x),any1))),
% 0.13/0.47 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.13/0.47 fof(f107,plain,(
% 0.13/0.47 element(sK0_skl(any1,x),any1)|~sQ2_spl),
% 0.13/0.47 inference(component_clause,[status(thm)],[f106])).
% 0.13/0.47 fof(f109,plain,(
% 0.13/0.47 sQ2_spl|sQ0_spl),
% 0.13/0.47 inference(split_clause,[status(thm)],[f105,f106,f92])).
% 0.13/0.47 fof(f110,plain,(
% 0.13/0.47 element(sK1_skl(any1,x),any1)|injection(x)),
% 0.13/0.47 inference(resolution,[status(thm)],[f29,f82])).
% 0.13/0.47 fof(f111,definition,(
% 0.13/0.47 sQ3_spl <=> (element(sK1_skl(any1,x),any1))),
% 0.13/0.47 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.13/0.47 fof(f112,plain,(
% 0.13/0.47 element(sK1_skl(any1,x),any1)|~sQ3_spl),
% 0.13/0.47 inference(component_clause,[status(thm)],[f111])).
% 0.13/0.47 fof(f114,plain,(
% 0.13/0.47 sQ3_spl|sQ0_spl),
% 0.13/0.47 inference(split_clause,[status(thm)],[f110,f111,f92])).
% 0.13/0.47 fof(f115,plain,(
% 0.13/0.47 apply(x,sK0_skl(any1,x))=apply(x,sK1_skl(any1,x))|injection(x)),
% 0.13/0.47 inference(resolution,[status(thm)],[f30,f82])).
% 0.13/0.47 fof(f116,definition,(
% 0.13/0.47 sQ4_spl <=> (apply(x,sK0_skl(any1,x))=apply(x,sK1_skl(any1,x)))),
% 0.13/0.47 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.13/0.47 fof(f117,plain,(
% 0.13/0.47 apply(x,sK0_skl(any1,x))=apply(x,sK1_skl(any1,x))|~sQ4_spl),
% 0.13/0.47 inference(component_clause,[status(thm)],[f116])).
% 0.13/0.47 fof(f119,plain,(
% 0.13/0.47 sQ4_spl|sQ0_spl),
% 0.13/0.47 inference(split_clause,[status(thm)],[f115,f116,f92])).
% 0.13/0.47 fof(f161,plain,(
% 0.13/0.47 subtract(any1,sK1_skl(any1,x),sK1_skl(any1,x))=zero(any1)|~sQ3_spl),
% 0.13/0.47 inference(resolution,[status(thm)],[f112,f69])).
% 0.13/0.47 fof(f173,plain,(
% 0.13/0.47 element(apply(x,sK1_skl(any1,x)),any2)|~sQ3_spl),
% 0.13/0.47 inference(resolution,[status(thm)],[f103,f112])).
% 0.13/0.47 fof(f175,plain,(
% 0.13/0.47 element(apply(x,sK0_skl(any1,x)),any2)|~sQ4_spl|~sQ3_spl),
% 0.13/0.47 inference(forward_demodulation,[status(thm)],[f117,f173])).
% 0.13/0.47 fof(f176,plain,(
% 0.13/0.47 subtract(any2,apply(x,sK0_skl(any1,x)),apply(x,sK0_skl(any1,x)))=zero(any2)|~sQ4_spl|~sQ3_spl),
% 0.13/0.47 inference(resolution,[status(thm)],[f175,f69])).
% 0.13/0.47 fof(f179,plain,(
% 0.13/0.47 ![X0]: (~element(X0,any1)|element(subtract(any1,sK1_skl(any1,x),X0),any1)|~sQ3_spl)),
% 0.13/0.47 inference(resolution,[status(thm)],[f67,f112])).
% 0.13/0.47 fof(f183,plain,(
% 0.13/0.47 ![X0]: (~element(X0,any1)|subtract(any1,X0,subtract(any1,X0,sK1_skl(any1,x)))=sK1_skl(any1,x)|~sQ3_spl)),
% 0.13/0.47 inference(resolution,[status(thm)],[f71,f112])).
% 0.13/0.47 fof(f184,plain,(
% 0.13/0.47 ![X0]: (~element(X0,any1)|subtract(any1,X0,subtract(any1,X0,sK0_skl(any1,x)))=sK0_skl(any1,x)|~sQ2_spl)),
% 0.13/0.47 inference(resolution,[status(thm)],[f71,f107])).
% 0.13/0.47 fof(f185,plain,(
% 0.13/0.47 ![X0,X1]: (~element(X0,any1)|~element(X1,any1)|apply(x,subtract(any1,X0,X1))=subtract(any2,apply(x,X0),apply(x,X1)))),
% 0.13/0.47 inference(resolution,[status(thm)],[f73,f82])).
% 0.13/0.47 fof(f186,plain,(
% 0.13/0.47 element(sK8_skl(any2,any1,x),any1)|injection_2(x)),
% 0.13/0.47 inference(resolution,[status(thm)],[f79,f82])).
% 0.13/0.47 fof(f187,definition,(
% 0.13/0.47 sQ13_spl <=> (element(sK8_skl(any2,any1,x),any1))),
% 0.13/0.47 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.13/0.47 fof(f188,plain,(
% 0.13/0.47 element(sK8_skl(any2,any1,x),any1)|~sQ13_spl),
% 0.13/0.47 inference(component_clause,[status(thm)],[f187])).
% 0.13/0.47 fof(f190,plain,(
% 0.13/0.47 sQ13_spl|sQ1_spl),
% 0.13/0.47 inference(split_clause,[status(thm)],[f186,f187,f95])).
% 0.13/0.47 fof(f193,plain,(
% 0.13/0.47 ![X0]: (~element(X0,any1)|element(subtract(any1,sK8_skl(any2,any1,x),X0),any1)|~sQ13_spl)),
% 0.13/0.47 inference(resolution,[status(thm)],[f188,f67])).
% 0.13/0.47 fof(f194,plain,(
% 0.13/0.47 subtract(any1,sK8_skl(any2,any1,x),sK8_skl(any2,any1,x))=zero(any1)|~sQ13_spl),
% 0.13/0.47 inference(resolution,[status(thm)],[f188,f69])).
% 0.13/0.47 fof(f195,plain,(
% 0.13/0.47 apply(x,sK8_skl(any2,any1,x))=zero(any2)|injection_2(x)),
% 0.13/0.47 inference(resolution,[status(thm)],[f80,f82])).
% 0.13/0.47 fof(f196,definition,(
% 0.13/0.47 sQ14_spl <=> (apply(x,sK8_skl(any2,any1,x))=zero(any2))),
% 0.13/0.47 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 0.13/0.47 fof(f197,plain,(
% 0.13/0.47 apply(x,sK8_skl(any2,any1,x))=zero(any2)|~sQ14_spl),
% 0.13/0.47 inference(component_clause,[status(thm)],[f196])).
% 0.13/0.47 fof(f199,plain,(
% 0.13/0.47 sQ14_spl|sQ1_spl),
% 0.13/0.47 inference(split_clause,[status(thm)],[f195,f196,f95])).
% 0.13/0.47 fof(f228,plain,(
% 0.13/0.47 ![X0,X1,X2]: (~injection(x)|~morphism(x,X0,X1)|~element(X2,X0)|~element(sK8_skl(any2,any1,x),X0)|~apply(x,X2)=zero(any2)|X2=sK8_skl(any2,any1,x)|~sQ14_spl)),
% 0.13/0.47 inference(paramodulation,[status(thm)],[f197,f24])).
% 0.13/0.47 fof(f242,definition,(
% 0.13/0.47 ![X0,X1,X2]: (sQ21_spl <=> (~morphism(x,X0,X1)|~element(X2,X0)|~element(sK8_skl(any2,any1,x),X0)|~apply(x,X2)=zero(any2)|X2=sK8_skl(any2,any1,x)))),
% 0.13/0.47 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.13/0.47 fof(f243,plain,(
% 0.13/0.47 ![X0,X1,X2]: (~morphism(x,X0,X1)|~element(X2,X0)|~element(sK8_skl(any2,any1,x),X0)|~apply(x,X2)=zero(any2)|X2=sK8_skl(any2,any1,x)|~sQ21_spl)),
% 0.13/0.47 inference(component_clause,[status(thm)],[f242])).
% 0.13/0.47 fof(f245,plain,(
% 0.13/0.47 ~sQ0_spl|sQ21_spl|~sQ14_spl),
% 0.13/0.47 inference(split_clause,[status(thm)],[f228,f92,f242,f196])).
% 0.13/0.47 fof(f247,plain,(
% 0.13/0.47 ![X0,X1]: (~morphism(x,any1,X0)|~element(X1,any1)|~apply(x,X1)=zero(any2)|X1=sK8_skl(any2,any1,x)|~sQ21_spl|~sQ13_spl)),
% 0.13/0.47 inference(resolution,[status(thm)],[f243,f188])).
% 0.13/0.47 fof(f248,definition,(
% 0.13/0.47 ![X0]: (sQ22_spl <=> (~morphism(x,any1,X0)))),
% 0.13/0.47 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.13/0.47 fof(f249,plain,(
% 0.13/0.47 ![X0]: (~morphism(x,any1,X0)|~sQ22_spl)),
% 0.13/0.47 inference(component_clause,[status(thm)],[f248])).
% 0.13/0.47 fof(f251,definition,(
% 0.13/0.47 ![X1]: (sQ23_spl <=> (~element(X1,any1)|~apply(x,X1)=zero(any2)|X1=sK8_skl(any2,any1,x)))),
% 0.13/0.47 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 0.13/0.47 fof(f252,plain,(
% 0.13/0.47 ![X0]: (~element(X0,any1)|~apply(x,X0)=zero(any2)|X0=sK8_skl(any2,any1,x)|~sQ23_spl)),
% 0.13/0.47 inference(component_clause,[status(thm)],[f251])).
% 0.13/0.47 fof(f254,plain,(
% 0.13/0.47 sQ22_spl|sQ23_spl|~sQ21_spl|~sQ13_spl),
% 0.13/0.47 inference(split_clause,[status(thm)],[f247,f248,f251,f242,f187])).
% 0.13/0.47 fof(f255,plain,(
% 0.13/0.47 $false|~sQ22_spl),
% 0.13/0.47 inference(backward_subsumption_resolution,[status(thm)],[f82,f249])).
% 0.13/0.47 fof(f256,plain,(
% 0.13/0.47 ~sQ22_spl),
% 0.13/0.47 inference(contradiction_clause,[status(thm)],[f255])).
% 0.13/0.47 fof(f258,plain,(
% 0.13/0.47 ~element(zero(any1),any1)|zero(any1)=sK8_skl(any2,any1,x)|~sQ23_spl),
% 0.13/0.47 inference(resolution,[status(thm)],[f252,f104])).
% 0.13/0.47 fof(f265,definition,(
% 0.13/0.47 sQ25_spl <=> (element(zero(any1),any1))),
% 0.13/0.47 introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition])).
% 0.13/0.47 fof(f267,plain,(
% 0.13/0.47 ~element(zero(any1),any1)|sQ25_spl),
% 0.13/0.47 inference(component_clause,[status(thm)],[f265])).
% 0.13/0.47 fof(f268,definition,(
% 0.13/0.47 sQ26_spl <=> (zero(any1)=sK8_skl(any2,any1,x))),
% 0.13/0.47 introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 0.13/0.47 fof(f269,plain,(
% 0.13/0.47 zero(any1)=sK8_skl(any2,any1,x)|~sQ26_spl),
% 0.13/0.47 inference(component_clause,[status(thm)],[f268])).
% 0.13/0.47 fof(f271,plain,(
% 0.13/0.47 ~sQ25_spl|sQ26_spl|~sQ23_spl),
% 0.13/0.47 inference(split_clause,[status(thm)],[f258,f265,f268,f251])).
% 0.13/0.47 fof(f342,plain,(
% 0.13/0.47 element(subtract(any1,sK8_skl(any2,any1,x),sK8_skl(any2,any1,x)),any1)|~sQ13_spl),
% 0.13/0.47 inference(resolution,[status(thm)],[f193,f188])).
% 0.13/0.47 fof(f343,plain,(
% 0.13/0.47 element(zero(any1),any1)|~sQ13_spl),
% 0.13/0.47 inference(forward_demodulation,[status(thm)],[f194,f342])).
% 0.13/0.47 fof(f344,plain,(
% 0.13/0.47 $false|sQ25_spl|~sQ13_spl),
% 0.13/0.47 inference(forward_subsumption_resolution,[status(thm)],[f343,f267])).
% 0.13/0.47 fof(f345,plain,(
% 0.13/0.47 sQ25_spl|~sQ13_spl),
% 0.13/0.47 inference(contradiction_clause,[status(thm)],[f344])).
% 0.13/0.47 fof(f370,plain,(
% 0.13/0.47 ![X0]: (~element(X0,any1)|apply(x,subtract(any1,X0,sK0_skl(any1,x)))=subtract(any2,apply(x,X0),apply(x,sK0_skl(any1,x)))|~sQ2_spl)),
% 0.13/0.47 inference(resolution,[status(thm)],[f107,f185])).
% 0.13/0.47 fof(f393,definition,(
% 0.13/0.47 sQ31_spl <=> (sK0_skl(any1,x)=sK1_skl(any1,x))),
% 0.13/0.47 introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition])).
% 0.13/0.47 fof(f394,plain,(
% 0.13/0.47 sK0_skl(any1,x)=sK1_skl(any1,x)|~sQ31_spl),
% 0.13/0.47 inference(component_clause,[status(thm)],[f393])).
% 0.13/0.47 fof(f441,plain,(
% 0.13/0.47 ~morphism(x,any1,any2)|injection_2(x)|~sQ26_spl),
% 0.13/0.47 inference(resolution,[status(thm)],[f269,f81])).
% 0.13/0.47 fof(f443,definition,(
% 0.13/0.47 sQ35_spl <=> (morphism(x,any1,any2))),
% 0.13/0.47 introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition])).
% 0.13/0.47 fof(f445,plain,(
% 0.13/0.47 ~morphism(x,any1,any2)|sQ35_spl),
% 0.13/0.47 inference(component_clause,[status(thm)],[f443])).
% 0.13/0.47 fof(f446,plain,(
% 0.13/0.47 ~sQ35_spl|sQ1_spl|~sQ26_spl),
% 0.13/0.47 inference(split_clause,[status(thm)],[f441,f443,f95,f268])).
% 0.13/0.47 fof(f448,plain,(
% 0.13/0.47 $false|sQ35_spl),
% 0.13/0.47 inference(forward_subsumption_resolution,[status(thm)],[f445,f82])).
% 0.13/0.47 fof(f449,plain,(
% 0.13/0.47 sQ35_spl),
% 0.13/0.47 inference(contradiction_clause,[status(thm)],[f448])).
% 0.13/0.47 fof(f492,plain,(
% 0.13/0.47 ![X0]: (~morphism(x,any1,X0)|injection(x)|~sQ31_spl)),
% 0.13/0.47 inference(resolution,[status(thm)],[f394,f31])).
% 0.13/0.47 fof(f494,plain,(
% 0.13/0.47 sQ22_spl|sQ0_spl|~sQ31_spl),
% 0.13/0.47 inference(split_clause,[status(thm)],[f492,f248,f92,f393])).
% 0.13/0.47 fof(f534,plain,(
% 0.13/0.47 subtract(any1,sK1_skl(any1,x),subtract(any1,sK1_skl(any1,x),sK0_skl(any1,x)))=sK0_skl(any1,x)|~sQ2_spl|~sQ3_spl),
% 0.13/0.47 inference(resolution,[status(thm)],[f184,f112])).
% 0.13/0.47 fof(f537,plain,(
% 0.13/0.47 apply(x,subtract(any1,sK1_skl(any1,x),sK0_skl(any1,x)))=subtract(any2,apply(x,sK1_skl(any1,x)),apply(x,sK0_skl(any1,x)))|~sQ2_spl|~sQ3_spl),
% 0.13/0.47 inference(resolution,[status(thm)],[f370,f112])).
% 0.13/0.47 fof(f539,plain,(
% 0.13/0.47 apply(x,subtract(any1,sK1_skl(any1,x),sK0_skl(any1,x)))=subtract(any2,apply(x,sK0_skl(any1,x)),apply(x,sK0_skl(any1,x)))|~sQ4_spl|~sQ2_spl|~sQ3_spl),
% 0.13/0.47 inference(forward_demodulation,[status(thm)],[f117,f537])).
% 0.13/0.47 fof(f540,plain,(
% 0.13/0.47 apply(x,subtract(any1,sK1_skl(any1,x),sK0_skl(any1,x)))=zero(any2)|~sQ4_spl|~sQ2_spl|~sQ3_spl),
% 0.13/0.47 inference(forward_demodulation,[status(thm)],[f176,f539])).
% 0.13/0.47 fof(f588,definition,(
% 0.13/0.47 ![X0]: (sQ41_spl <=> (~morphism(x,any1,X0)|~zero(any2)=zero(X0)))),
% 0.13/0.47 introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition])).
% 0.13/0.47 fof(f589,plain,(
% 0.13/0.47 ![X0]: (~morphism(x,any1,X0)|~zero(any2)=zero(X0)|~sQ41_spl)),
% 0.13/0.47 inference(component_clause,[status(thm)],[f588])).
% 0.13/0.47 fof(f597,plain,(
% 0.13/0.47 ~zero(any2)=zero(any2)|~sQ41_spl),
% 0.13/0.47 inference(resolution,[status(thm)],[f589,f82])).
% 0.13/0.47 fof(f598,plain,(
% 0.13/0.47 $false|~sQ41_spl),
% 0.13/0.47 inference(trivial_equality_resolution,[status(thm)],[f597])).
% 0.13/0.47 fof(f599,plain,(
% 0.13/0.47 ~sQ41_spl),
% 0.13/0.47 inference(contradiction_clause,[status(thm)],[f598])).
% 0.13/0.47 fof(f602,plain,(
% 0.13/0.47 element(subtract(any1,sK1_skl(any1,x),sK0_skl(any1,x)),any1)|~sQ3_spl|~sQ2_spl),
% 0.13/0.47 inference(resolution,[status(thm)],[f179,f107])).
% 0.13/0.47 fof(f626,plain,(
% 0.13/0.47 subtract(any1,sK1_skl(any1,x),subtract(any1,sK1_skl(any1,x),sK1_skl(any1,x)))=sK1_skl(any1,x)|~sQ3_spl),
% 0.13/0.47 inference(resolution,[status(thm)],[f183,f112])).
% 0.13/0.47 fof(f629,plain,(
% 0.13/0.47 subtract(any1,sK1_skl(any1,x),zero(any1))=sK1_skl(any1,x)|~sQ3_spl),
% 0.13/0.47 inference(forward_demodulation,[status(thm)],[f161,f626])).
% 0.13/0.47 fof(f737,plain,(
% 0.13/0.47 ![X0]: (~injection_2(x)|~morphism(x,X0,any2)|~element(subtract(any1,sK1_skl(any1,x),sK0_skl(any1,x)),X0)|subtract(any1,sK1_skl(any1,x),sK0_skl(any1,x))=zero(X0)|~sQ4_spl|~sQ2_spl|~sQ3_spl)),
% 0.13/0.48 inference(resolution,[status(thm)],[f540,f75])).
% 0.13/0.48 fof(f742,definition,(
% 0.13/0.48 ![X0]: (sQ47_spl <=> (~morphism(x,X0,any2)|~element(subtract(any1,sK1_skl(any1,x),sK0_skl(any1,x)),X0)|subtract(any1,sK1_skl(any1,x),sK0_skl(any1,x))=zero(X0)))),
% 0.13/0.48 introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition])).
% 0.13/0.48 fof(f743,plain,(
% 0.13/0.48 ![X0]: (~morphism(x,X0,any2)|~element(subtract(any1,sK1_skl(any1,x),sK0_skl(any1,x)),X0)|subtract(any1,sK1_skl(any1,x),sK0_skl(any1,x))=zero(X0)|~sQ47_spl)),
% 0.13/0.48 inference(component_clause,[status(thm)],[f742])).
% 0.13/0.48 fof(f745,plain,(
% 0.13/0.48 ~sQ1_spl|sQ47_spl|~sQ4_spl|~sQ2_spl|~sQ3_spl),
% 0.13/0.48 inference(split_clause,[status(thm)],[f737,f95,f742,f116,f106,f111])).
% 0.13/0.48 fof(f779,plain,(
% 0.13/0.48 ~morphism(x,any1,any2)|subtract(any1,sK1_skl(any1,x),sK0_skl(any1,x))=zero(any1)|~sQ47_spl|~sQ3_spl|~sQ2_spl),
% 0.13/0.48 inference(resolution,[status(thm)],[f743,f602])).
% 0.13/0.48 fof(f780,definition,(
% 0.13/0.48 sQ51_spl <=> (subtract(any1,sK1_skl(any1,x),sK0_skl(any1,x))=zero(any1))),
% 0.13/0.48 introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition])).
% 0.13/0.48 fof(f781,plain,(
% 0.13/0.48 subtract(any1,sK1_skl(any1,x),sK0_skl(any1,x))=zero(any1)|~sQ51_spl),
% 0.13/0.48 inference(component_clause,[status(thm)],[f780])).
% 0.13/0.48 fof(f783,plain,(
% 0.13/0.48 ~sQ35_spl|sQ51_spl|~sQ47_spl|~sQ3_spl|~sQ2_spl),
% 0.13/0.48 inference(split_clause,[status(thm)],[f779,f443,f780,f742,f111,f106])).
% 0.13/0.48 fof(f787,plain,(
% 0.13/0.48 subtract(any1,sK1_skl(any1,x),zero(any1))=sK0_skl(any1,x)|~sQ51_spl|~sQ2_spl|~sQ3_spl),
% 0.13/0.48 inference(backward_demodulation,[status(thm)],[f781,f534])).
% 0.13/0.48 fof(f803,plain,(
% 0.13/0.48 sK0_skl(any1,x)=sK1_skl(any1,x)|~sQ51_spl|~sQ2_spl|~sQ3_spl),
% 0.13/0.48 inference(backward_demodulation,[status(thm)],[f787,f629])).
% 0.13/0.48 fof(f813,plain,(
% 0.13/0.48 sQ31_spl|~sQ51_spl|~sQ2_spl|~sQ3_spl),
% 0.13/0.48 inference(split_clause,[status(thm)],[f803,f393,f780,f106,f111])).
% 0.13/0.48 fof(f814,plain,(
% 0.13/0.48 $false),
% 0.13/0.48 inference(sat_refutation,[status(thm)],[f98,f99,f109,f114,f119,f190,f199,f245,f254,f256,f271,f345,f446,f449,f494,f599,f745,f783,f813])).
% 0.13/0.48 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.50 % Elapsed time: 0.107422 seconds
% 0.13/0.50 % CPU time: 0.531602 seconds
% 0.13/0.50 % Total memory used: 89.564 MB
% 0.13/0.50 % Net memory used: 89.088 MB
%------------------------------------------------------------------------------