TSTP Solution File: GRP039-7 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GRP039-7 : TPTP v8.1.2. Bugfixed v1.0.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n016.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 12:09:48 EDT 2023
% Result : Unsatisfiable 0.20s 0.42s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP039-7 : TPTP v8.1.2. Bugfixed v1.0.1.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 11:56:29 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.20/0.42 % Refutation found
% 0.20/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/0.42 % SZS output start CNFRefutation for theBenchmark
% 0.20/0.42 fof(f1,axiom,(
% 0.20/0.42 (![X]: (multiply(identity,X) = X ))),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.42 fof(f2,axiom,(
% 0.20/0.42 (![X]: (multiply(inverse(X),X) = identity ))),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.42 fof(f3,axiom,(
% 0.20/0.42 (![X,Y,Z]: (multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ))),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.42 fof(f4,axiom,(
% 0.20/0.42 (![X]: (( ~ subgroup_member(X)| subgroup_member(inverse(X)) ) ))),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.42 fof(f5,axiom,(
% 0.20/0.42 (![X,Y,Z]: (( ~ subgroup_member(X)| ~ subgroup_member(Y)| multiply(X,Y) != Z| subgroup_member(Z) ) ))),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.42 fof(f6,axiom,(
% 0.20/0.42 (![X]: (multiply(X,identity) = X ))),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.42 fof(f7,axiom,(
% 0.20/0.42 (![X]: (multiply(X,inverse(X)) = identity ))),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.42 fof(f8,axiom,(
% 0.20/0.42 (![X]: (inverse(inverse(X)) = X ))),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.42 fof(f9,axiom,(
% 0.20/0.42 inverse(identity) = identity ),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.42 fof(f10,axiom,(
% 0.20/0.42 subgroup_member(identity) ),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.42 fof(f11,axiom,(
% 0.20/0.42 (![X,Y]: (( subgroup_member(X)| subgroup_member(Y)| subgroup_member(element_in_O2(X,Y)) ) ))),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.42 fof(f12,axiom,(
% 0.20/0.42 (![X,Y]: (( subgroup_member(X)| subgroup_member(Y)| multiply(X,element_in_O2(X,Y)) = Y ) ))),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.42 fof(f13,negated_conjecture,(
% 0.20/0.42 subgroup_member(b) ),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.42 fof(f14,negated_conjecture,(
% 0.20/0.42 multiply(b,inverse(a)) = c ),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.42 fof(f15,negated_conjecture,(
% 0.20/0.42 multiply(a,c) = d ),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.42 fof(f16,negated_conjecture,(
% 0.20/0.42 ~ subgroup_member(d) ),
% 0.20/0.42 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.20/0.42 fof(f17,plain,(
% 0.20/0.42 ![X0]: (multiply(identity,X0)=X0)),
% 0.20/0.42 inference(cnf_transformation,[status(esa)],[f1])).
% 0.20/0.42 fof(f18,plain,(
% 0.20/0.42 ![X0]: (multiply(inverse(X0),X0)=identity)),
% 0.20/0.42 inference(cnf_transformation,[status(esa)],[f2])).
% 0.20/0.42 fof(f19,plain,(
% 0.20/0.42 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X0,multiply(X1,X2)))),
% 0.20/0.42 inference(cnf_transformation,[status(esa)],[f3])).
% 0.20/0.42 fof(f20,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(X0)|subgroup_member(inverse(X0)))),
% 0.20/0.42 inference(cnf_transformation,[status(esa)],[f4])).
% 0.20/0.42 fof(f21,plain,(
% 0.20/0.42 ![Z]: ((![X,Y]: ((~subgroup_member(X)|~subgroup_member(Y))|~multiply(X,Y)=Z))|subgroup_member(Z))),
% 0.20/0.42 inference(miniscoping,[status(esa)],[f5])).
% 0.20/0.42 fof(f22,plain,(
% 0.20/0.42 ![X0,X1,X2]: (~subgroup_member(X0)|~subgroup_member(X1)|~multiply(X0,X1)=X2|subgroup_member(X2))),
% 0.20/0.42 inference(cnf_transformation,[status(esa)],[f21])).
% 0.20/0.42 fof(f23,plain,(
% 0.20/0.42 ![X0]: (multiply(X0,identity)=X0)),
% 0.20/0.42 inference(cnf_transformation,[status(esa)],[f6])).
% 0.20/0.42 fof(f24,plain,(
% 0.20/0.42 ![X0]: (multiply(X0,inverse(X0))=identity)),
% 0.20/0.42 inference(cnf_transformation,[status(esa)],[f7])).
% 0.20/0.42 fof(f25,plain,(
% 0.20/0.42 ![X0]: (inverse(inverse(X0))=X0)),
% 0.20/0.42 inference(cnf_transformation,[status(esa)],[f8])).
% 0.20/0.42 fof(f26,plain,(
% 0.20/0.42 inverse(identity)=identity),
% 0.20/0.42 inference(cnf_transformation,[status(esa)],[f9])).
% 0.20/0.42 fof(f27,plain,(
% 0.20/0.42 subgroup_member(identity)),
% 0.20/0.42 inference(cnf_transformation,[status(esa)],[f10])).
% 0.20/0.42 fof(f28,plain,(
% 0.20/0.42 ![X0,X1]: (subgroup_member(X0)|subgroup_member(X1)|subgroup_member(element_in_O2(X0,X1)))),
% 0.20/0.42 inference(cnf_transformation,[status(esa)],[f11])).
% 0.20/0.42 fof(f29,plain,(
% 0.20/0.42 ![X0,X1]: (subgroup_member(X0)|subgroup_member(X1)|multiply(X0,element_in_O2(X0,X1))=X1)),
% 0.20/0.42 inference(cnf_transformation,[status(esa)],[f12])).
% 0.20/0.42 fof(f30,plain,(
% 0.20/0.42 subgroup_member(b)),
% 0.20/0.42 inference(cnf_transformation,[status(esa)],[f13])).
% 0.20/0.42 fof(f31,plain,(
% 0.20/0.42 multiply(b,inverse(a))=c),
% 0.20/0.42 inference(cnf_transformation,[status(esa)],[f14])).
% 0.20/0.42 fof(f32,plain,(
% 0.20/0.42 multiply(a,c)=d),
% 0.20/0.42 inference(cnf_transformation,[status(esa)],[f15])).
% 0.20/0.42 fof(f33,plain,(
% 0.20/0.42 ~subgroup_member(d)),
% 0.20/0.42 inference(cnf_transformation,[status(esa)],[f16])).
% 0.20/0.42 fof(f34,plain,(
% 0.20/0.42 ![X0,X1]: (~subgroup_member(X0)|~subgroup_member(X1)|subgroup_member(multiply(X0,X1)))),
% 0.20/0.42 inference(destructive_equality_resolution,[status(esa)],[f22])).
% 0.20/0.42 fof(f38,plain,(
% 0.20/0.42 spl0_0 <=> subgroup_member(identity)),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f40,plain,(
% 0.20/0.42 ~subgroup_member(identity)|spl0_0),
% 0.20/0.42 inference(component_clause,[status(thm)],[f38])).
% 0.20/0.42 fof(f56,plain,(
% 0.20/0.42 spl0_2 <=> subgroup_member(b)),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f58,plain,(
% 0.20/0.42 ~subgroup_member(b)|spl0_2),
% 0.20/0.42 inference(component_clause,[status(thm)],[f56])).
% 0.20/0.42 fof(f59,plain,(
% 0.20/0.42 spl0_3 <=> subgroup_member(inverse(a))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f61,plain,(
% 0.20/0.42 ~subgroup_member(inverse(a))|spl0_3),
% 0.20/0.42 inference(component_clause,[status(thm)],[f59])).
% 0.20/0.42 fof(f62,plain,(
% 0.20/0.42 spl0_4 <=> subgroup_member(c)),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f64,plain,(
% 0.20/0.42 ~subgroup_member(c)|spl0_4),
% 0.20/0.42 inference(component_clause,[status(thm)],[f62])).
% 0.20/0.42 fof(f65,plain,(
% 0.20/0.42 ~subgroup_member(b)|~subgroup_member(inverse(a))|subgroup_member(c)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f31,f34])).
% 0.20/0.42 fof(f66,plain,(
% 0.20/0.42 ~spl0_2|~spl0_3|spl0_4),
% 0.20/0.42 inference(split_clause,[status(thm)],[f65,f56,f59,f62])).
% 0.20/0.42 fof(f67,plain,(
% 0.20/0.42 spl0_5 <=> subgroup_member(a)),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f70,plain,(
% 0.20/0.42 spl0_6 <=> subgroup_member(d)),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f71,plain,(
% 0.20/0.42 subgroup_member(d)|~spl0_6),
% 0.20/0.42 inference(component_clause,[status(thm)],[f70])).
% 0.20/0.42 fof(f73,plain,(
% 0.20/0.42 ~subgroup_member(a)|~subgroup_member(c)|subgroup_member(d)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f32,f34])).
% 0.20/0.42 fof(f74,plain,(
% 0.20/0.42 ~spl0_5|~spl0_4|spl0_6),
% 0.20/0.42 inference(split_clause,[status(thm)],[f73,f67,f62,f70])).
% 0.20/0.42 fof(f78,plain,(
% 0.20/0.42 ![X0,X1]: (identity=multiply(X0,multiply(X1,inverse(multiply(X0,X1)))))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f24,f19])).
% 0.20/0.42 fof(f83,plain,(
% 0.20/0.42 ![X0,X1]: (multiply(identity,X0)=multiply(inverse(X1),multiply(X1,X0)))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f18,f19])).
% 0.20/0.42 fof(f84,plain,(
% 0.20/0.42 ![X0]: (multiply(c,X0)=multiply(b,multiply(inverse(a),X0)))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f31,f19])).
% 0.20/0.42 fof(f85,plain,(
% 0.20/0.42 ![X0]: (multiply(d,X0)=multiply(a,multiply(c,X0)))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f32,f19])).
% 0.20/0.42 fof(f88,plain,(
% 0.20/0.42 ![X0,X1,X2]: (~subgroup_member(multiply(X0,X1))|~subgroup_member(X2)|subgroup_member(multiply(X0,multiply(X1,X2))))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f19,f34])).
% 0.20/0.42 fof(f89,plain,(
% 0.20/0.42 ![X0,X1,X2]: (identity=multiply(X0,multiply(X1,multiply(X2,inverse(multiply(multiply(X0,X1),X2))))))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f19,f78])).
% 0.20/0.42 fof(f90,plain,(
% 0.20/0.42 ![X0,X1,X2]: (identity=multiply(X0,multiply(X1,multiply(X2,inverse(multiply(X0,multiply(X1,X2)))))))),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f19,f89])).
% 0.20/0.42 fof(f141,plain,(
% 0.20/0.42 multiply(c,a)=multiply(b,identity)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f18,f84])).
% 0.20/0.42 fof(f154,plain,(
% 0.20/0.42 spl0_8 <=> ~subgroup_member(multiply(inverse(a),X0))|subgroup_member(multiply(c,X0))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f155,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(multiply(inverse(a),X0))|subgroup_member(multiply(c,X0))|~spl0_8)),
% 0.20/0.42 inference(component_clause,[status(thm)],[f154])).
% 0.20/0.42 fof(f157,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(b)|~subgroup_member(multiply(inverse(a),X0))|subgroup_member(multiply(c,X0)))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f84,f34])).
% 0.20/0.42 fof(f158,plain,(
% 0.20/0.42 ~spl0_2|spl0_8),
% 0.20/0.42 inference(split_clause,[status(thm)],[f157,f56,f154])).
% 0.20/0.42 fof(f159,plain,(
% 0.20/0.42 $false|spl0_2),
% 0.20/0.42 inference(forward_subsumption_resolution,[status(thm)],[f58,f30])).
% 0.20/0.42 fof(f160,plain,(
% 0.20/0.42 spl0_2),
% 0.20/0.42 inference(contradiction_clause,[status(thm)],[f159])).
% 0.20/0.42 fof(f161,plain,(
% 0.20/0.42 ![X0,X1]: (X0=multiply(inverse(X1),multiply(X1,X0)))),
% 0.20/0.42 inference(backward_demodulation,[status(thm)],[f17,f83])).
% 0.20/0.42 fof(f172,plain,(
% 0.20/0.42 spl0_9 <=> ~subgroup_member(X0)|subgroup_member(X0)),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f177,plain,(
% 0.20/0.42 $false|spl0_0),
% 0.20/0.42 inference(forward_subsumption_resolution,[status(thm)],[f40,f27])).
% 0.20/0.42 fof(f178,plain,(
% 0.20/0.42 spl0_0),
% 0.20/0.42 inference(contradiction_clause,[status(thm)],[f177])).
% 0.20/0.42 fof(f195,plain,(
% 0.20/0.42 ![X0,X1]: (X0=multiply(X1,multiply(inverse(X1),X0)))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f25,f161])).
% 0.20/0.42 fof(f203,plain,(
% 0.20/0.42 inverse(a)=multiply(inverse(b),c)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f31,f161])).
% 0.20/0.42 fof(f204,plain,(
% 0.20/0.42 c=multiply(inverse(a),d)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f32,f161])).
% 0.20/0.42 fof(f206,plain,(
% 0.20/0.42 ![X0,X1]: (multiply(X0,inverse(multiply(X1,X0)))=multiply(inverse(X1),identity))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f78,f161])).
% 0.20/0.42 fof(f207,plain,(
% 0.20/0.42 ![X0,X1]: (multiply(X0,inverse(multiply(X1,X0)))=inverse(X1))),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f23,f206])).
% 0.20/0.42 fof(f209,plain,(
% 0.20/0.42 ![X0]: (multiply(c,multiply(a,X0))=multiply(b,X0))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f161,f84])).
% 0.20/0.42 fof(f217,plain,(
% 0.20/0.42 ![X0,X1]: (~subgroup_member(inverse(X0))|~subgroup_member(multiply(X0,X1))|subgroup_member(X1))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f161,f34])).
% 0.20/0.42 fof(f245,plain,(
% 0.20/0.42 ![X0,X1]: (~subgroup_member(X0)|~subgroup_member(multiply(inverse(X0),X1))|subgroup_member(X1))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f195,f34])).
% 0.20/0.42 fof(f246,plain,(
% 0.20/0.42 multiply(c,d)=multiply(b,c)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f204,f84])).
% 0.20/0.42 fof(f251,plain,(
% 0.20/0.42 ![X0]: (multiply(c,X0)=multiply(inverse(a),multiply(d,X0)))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f204,f19])).
% 0.20/0.42 fof(f254,plain,(
% 0.20/0.42 multiply(c,a)=b),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f23,f141])).
% 0.20/0.42 fof(f255,plain,(
% 0.20/0.42 a=multiply(inverse(c),b)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f254,f161])).
% 0.20/0.42 fof(f280,plain,(
% 0.20/0.42 spl0_11 <=> subgroup_member(inverse(b))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f281,plain,(
% 0.20/0.42 subgroup_member(inverse(b))|~spl0_11),
% 0.20/0.42 inference(component_clause,[status(thm)],[f280])).
% 0.20/0.42 fof(f282,plain,(
% 0.20/0.42 ~subgroup_member(inverse(b))|spl0_11),
% 0.20/0.42 inference(component_clause,[status(thm)],[f280])).
% 0.20/0.42 fof(f283,plain,(
% 0.20/0.42 ~subgroup_member(inverse(b))|~subgroup_member(c)|subgroup_member(inverse(a))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f203,f34])).
% 0.20/0.42 fof(f284,plain,(
% 0.20/0.42 ~spl0_11|~spl0_4|spl0_3),
% 0.20/0.42 inference(split_clause,[status(thm)],[f283,f280,f62,f59])).
% 0.20/0.42 fof(f285,plain,(
% 0.20/0.42 ![X0,X1,X2]: (subgroup_member(multiply(X0,X1))|subgroup_member(X2)|multiply(X0,multiply(X1,element_in_O2(multiply(X0,X1),X2)))=X2)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f19,f29])).
% 0.20/0.42 fof(f294,plain,(
% 0.20/0.42 spl0_14 <=> subgroup_member(X1)|X1=X1|subgroup_member(X1)),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f308,plain,(
% 0.20/0.42 ![X0,X1]: (element_in_O2(X0,X1)=multiply(inverse(X0),X1)|subgroup_member(X0)|subgroup_member(X1))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f29,f161])).
% 0.20/0.42 fof(f310,plain,(
% 0.20/0.42 ![X0,X1,X2]: (multiply(X0,X1)=multiply(X2,multiply(element_in_O2(X2,X0),X1))|subgroup_member(X2)|subgroup_member(X0))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f29,f19])).
% 0.20/0.42 fof(f314,plain,(
% 0.20/0.42 multiply(d,a)=multiply(a,b)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f254,f85])).
% 0.20/0.42 fof(f322,plain,(
% 0.20/0.42 ![X0]: (multiply(d,multiply(inverse(c),X0))=multiply(a,X0))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f195,f85])).
% 0.20/0.42 fof(f325,plain,(
% 0.20/0.42 multiply(d,inverse(c))=multiply(a,identity)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f24,f85])).
% 0.20/0.42 fof(f326,plain,(
% 0.20/0.42 multiply(d,inverse(c))=a),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f23,f325])).
% 0.20/0.42 fof(f343,plain,(
% 0.20/0.42 ~subgroup_member(b)|spl0_11),
% 0.20/0.42 inference(resolution,[status(thm)],[f282,f20])).
% 0.20/0.42 fof(f344,plain,(
% 0.20/0.42 ~spl0_2|spl0_11),
% 0.20/0.42 inference(split_clause,[status(thm)],[f343,f56,f280])).
% 0.20/0.42 fof(f355,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(X0)|subgroup_member(multiply(c,multiply(a,X0)))|~spl0_8)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f161,f155])).
% 0.20/0.42 fof(f356,plain,(
% 0.20/0.42 spl0_20 <=> subgroup_member(multiply(c,a))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f359,plain,(
% 0.20/0.42 ~subgroup_member(identity)|subgroup_member(multiply(c,a))|~spl0_8),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f18,f155])).
% 0.20/0.42 fof(f360,plain,(
% 0.20/0.42 ~spl0_0|spl0_20|~spl0_8),
% 0.20/0.42 inference(split_clause,[status(thm)],[f359,f38,f356,f154])).
% 0.20/0.42 fof(f366,plain,(
% 0.20/0.42 spl0_22 <=> subgroup_member(multiply(c,identity))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f367,plain,(
% 0.20/0.42 subgroup_member(multiply(c,identity))|~spl0_22),
% 0.20/0.42 inference(component_clause,[status(thm)],[f366])).
% 0.20/0.42 fof(f371,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(X0)|subgroup_member(multiply(c,multiply(inverse(inverse(a)),X0)))|~spl0_8)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f195,f155])).
% 0.20/0.42 fof(f372,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(X0)|subgroup_member(multiply(c,multiply(a,X0)))|~spl0_8)),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f25,f371])).
% 0.20/0.42 fof(f373,plain,(
% 0.20/0.42 spl0_23 <=> subgroup_member(multiply(c,multiply(X0,inverse(multiply(inverse(a),X0)))))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f376,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(identity)|subgroup_member(multiply(c,multiply(X0,inverse(multiply(inverse(a),X0)))))|~spl0_8)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f78,f155])).
% 0.20/0.42 fof(f377,plain,(
% 0.20/0.42 ~spl0_0|spl0_23|~spl0_8),
% 0.20/0.42 inference(split_clause,[status(thm)],[f376,f38,f373,f154])).
% 0.20/0.42 fof(f378,plain,(
% 0.20/0.42 spl0_24 <=> subgroup_member(multiply(c,inverse(inverse(a))))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f381,plain,(
% 0.20/0.42 ~subgroup_member(identity)|subgroup_member(multiply(c,inverse(inverse(a))))|~spl0_8),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f24,f155])).
% 0.20/0.42 fof(f382,plain,(
% 0.20/0.42 ~spl0_0|spl0_24|~spl0_8),
% 0.20/0.42 inference(split_clause,[status(thm)],[f381,f38,f378,f154])).
% 0.20/0.42 fof(f387,plain,(
% 0.20/0.42 spl0_25 <=> subgroup_member(inverse(multiply(c,a)))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f389,plain,(
% 0.20/0.42 ~subgroup_member(inverse(multiply(c,a)))|spl0_25),
% 0.20/0.42 inference(component_clause,[status(thm)],[f387])).
% 0.20/0.42 fof(f403,plain,(
% 0.20/0.42 spl0_27 <=> ~subgroup_member(multiply(X0,inverse(multiply(a,X0))))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f404,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(multiply(X0,inverse(multiply(a,X0))))|~spl0_27)),
% 0.20/0.42 inference(component_clause,[status(thm)],[f403])).
% 0.20/0.42 fof(f406,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(multiply(X0,inverse(multiply(a,X0))))|subgroup_member(multiply(c,identity))|~spl0_8)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f78,f355])).
% 0.20/0.42 fof(f407,plain,(
% 0.20/0.42 spl0_27|spl0_22|~spl0_8),
% 0.20/0.42 inference(split_clause,[status(thm)],[f406,f403,f366,f154])).
% 0.20/0.42 fof(f410,plain,(
% 0.20/0.42 subgroup_member(c)|~spl0_22),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f23,f367])).
% 0.20/0.42 fof(f411,plain,(
% 0.20/0.42 ~subgroup_member(a)|spl0_3),
% 0.20/0.42 inference(resolution,[status(thm)],[f61,f20])).
% 0.20/0.42 fof(f412,plain,(
% 0.20/0.42 ~spl0_5|spl0_3),
% 0.20/0.42 inference(split_clause,[status(thm)],[f411,f67,f59])).
% 0.20/0.42 fof(f413,plain,(
% 0.20/0.42 $false|spl0_4|~spl0_22),
% 0.20/0.42 inference(forward_subsumption_resolution,[status(thm)],[f410,f64])).
% 0.20/0.42 fof(f414,plain,(
% 0.20/0.42 spl0_4|~spl0_22),
% 0.20/0.42 inference(contradiction_clause,[status(thm)],[f413])).
% 0.20/0.42 fof(f415,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(X0)|~subgroup_member(inverse(multiply(a,X0)))|~spl0_27)),
% 0.20/0.42 inference(resolution,[status(thm)],[f404,f34])).
% 0.20/0.42 fof(f436,plain,(
% 0.20/0.42 spl0_29 <=> subgroup_member(inverse(d))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f438,plain,(
% 0.20/0.42 ~subgroup_member(inverse(d))|spl0_29),
% 0.20/0.42 inference(component_clause,[status(thm)],[f436])).
% 0.20/0.42 fof(f441,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(X0)|~subgroup_member(multiply(a,X0))|~spl0_27)),
% 0.20/0.42 inference(resolution,[status(thm)],[f415,f20])).
% 0.20/0.42 fof(f453,plain,(
% 0.20/0.42 spl0_31 <=> subgroup_member(inverse(identity))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f485,plain,(
% 0.20/0.42 ~subgroup_member(identity)|~subgroup_member(a)|~spl0_27),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f23,f441])).
% 0.20/0.42 fof(f486,plain,(
% 0.20/0.42 ~spl0_0|~spl0_5|~spl0_27),
% 0.20/0.42 inference(split_clause,[status(thm)],[f485,f38,f67,f403])).
% 0.20/0.42 fof(f493,plain,(
% 0.20/0.42 ~subgroup_member(inverse(b))|spl0_25),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f254,f389])).
% 0.20/0.42 fof(f494,plain,(
% 0.20/0.42 $false|~spl0_11|spl0_25),
% 0.20/0.42 inference(forward_subsumption_resolution,[status(thm)],[f493,f281])).
% 0.20/0.42 fof(f495,plain,(
% 0.20/0.42 ~spl0_11|spl0_25),
% 0.20/0.42 inference(contradiction_clause,[status(thm)],[f494])).
% 0.20/0.42 fof(f560,plain,(
% 0.20/0.42 $false|~spl0_6),
% 0.20/0.42 inference(forward_subsumption_resolution,[status(thm)],[f33,f71])).
% 0.20/0.42 fof(f561,plain,(
% 0.20/0.42 ~spl0_6),
% 0.20/0.42 inference(contradiction_clause,[status(thm)],[f560])).
% 0.20/0.42 fof(f571,plain,(
% 0.20/0.42 d=multiply(inverse(c),multiply(b,c))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f246,f161])).
% 0.20/0.42 fof(f586,plain,(
% 0.20/0.42 multiply(inverse(c),inverse(a))=inverse(d)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f326,f207])).
% 0.20/0.42 fof(f588,plain,(
% 0.20/0.42 multiply(a,inverse(b))=inverse(c)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f254,f207])).
% 0.20/0.42 fof(f610,plain,(
% 0.20/0.42 ![X0]: (multiply(multiply(c,X0),inverse(multiply(d,X0)))=inverse(a))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f85,f207])).
% 0.20/0.42 fof(f611,plain,(
% 0.20/0.42 ![X0]: (multiply(c,multiply(X0,inverse(multiply(d,X0))))=inverse(a))),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f19,f610])).
% 0.20/0.42 fof(f612,plain,(
% 0.20/0.42 multiply(c,inverse(d))=inverse(a)),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f207,f611])).
% 0.20/0.42 fof(f618,plain,(
% 0.20/0.42 ![X0,X1]: (multiply(inverse(multiply(X0,X1)),inverse(inverse(X0)))=inverse(X1))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f207,f207])).
% 0.20/0.42 fof(f619,plain,(
% 0.20/0.42 ![X0,X1]: (multiply(inverse(multiply(X0,X1)),X0)=inverse(X1))),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f25,f618])).
% 0.20/0.42 fof(f632,plain,(
% 0.20/0.42 multiply(a,inverse(multiply(a,b)))=inverse(d)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f314,f207])).
% 0.20/0.42 fof(f675,plain,(
% 0.20/0.42 ![X0,X1]: (~subgroup_member(X0)|~subgroup_member(inverse(multiply(X1,X0)))|subgroup_member(inverse(X1)))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f207,f34])).
% 0.20/0.42 fof(f687,plain,(
% 0.20/0.42 spl0_41 <=> subgroup_member(multiply(c,inverse(c)))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f690,plain,(
% 0.20/0.42 ~subgroup_member(inverse(b))|subgroup_member(multiply(c,inverse(c)))|~spl0_8),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f588,f372])).
% 0.20/0.42 fof(f691,plain,(
% 0.20/0.42 ~spl0_11|spl0_41|~spl0_8),
% 0.20/0.42 inference(split_clause,[status(thm)],[f690,f280,f687,f154])).
% 0.20/0.42 fof(f728,plain,(
% 0.20/0.42 spl0_45 <=> subgroup_member(multiply(a,c))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f729,plain,(
% 0.20/0.42 subgroup_member(multiply(a,c))|~spl0_45),
% 0.20/0.42 inference(component_clause,[status(thm)],[f728])).
% 0.20/0.42 fof(f751,plain,(
% 0.20/0.42 spl0_50 <=> ~subgroup_member(multiply(X0,c))|subgroup_member(multiply(X0,inverse(a)))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f754,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(multiply(X0,c))|~subgroup_member(inverse(d))|subgroup_member(multiply(X0,inverse(a))))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f612,f88])).
% 0.20/0.42 fof(f755,plain,(
% 0.20/0.42 spl0_50|~spl0_29),
% 0.20/0.42 inference(split_clause,[status(thm)],[f754,f751,f436])).
% 0.20/0.42 fof(f779,plain,(
% 0.20/0.42 spl0_55 <=> ~subgroup_member(multiply(X0,inverse(c)))|subgroup_member(multiply(X0,a))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f782,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(multiply(X0,inverse(c)))|~subgroup_member(b)|subgroup_member(multiply(X0,a)))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f255,f88])).
% 0.20/0.42 fof(f783,plain,(
% 0.20/0.42 spl0_55|~spl0_2),
% 0.20/0.42 inference(split_clause,[status(thm)],[f782,f779,f56])).
% 0.20/0.42 fof(f790,plain,(
% 0.20/0.42 ![X0,X1]: (~subgroup_member(multiply(X0,inverse(X1)))|~subgroup_member(X1)|subgroup_member(multiply(X0,identity)))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f18,f88])).
% 0.20/0.42 fof(f791,plain,(
% 0.20/0.42 ![X0,X1]: (~subgroup_member(multiply(X0,inverse(X1)))|~subgroup_member(X1)|subgroup_member(X0))),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f23,f790])).
% 0.20/0.42 fof(f798,plain,(
% 0.20/0.42 spl0_58 <=> ~subgroup_member(multiply(X0,a))|subgroup_member(multiply(X0,inverse(c)))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f801,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(multiply(X0,a))|~subgroup_member(inverse(b))|subgroup_member(multiply(X0,inverse(c))))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f588,f88])).
% 0.20/0.42 fof(f802,plain,(
% 0.20/0.42 spl0_58|~spl0_11),
% 0.20/0.42 inference(split_clause,[status(thm)],[f801,f798,f280])).
% 0.20/0.42 fof(f809,plain,(
% 0.20/0.42 spl0_60 <=> ~subgroup_member(multiply(X0,X1))|subgroup_member(multiply(X0,X1))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f812,plain,(
% 0.20/0.42 ![X0,X1]: (~subgroup_member(multiply(X0,X1))|~subgroup_member(identity)|subgroup_member(multiply(X0,X1)))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f23,f88])).
% 0.20/0.42 fof(f813,plain,(
% 0.20/0.42 spl0_60|~spl0_0),
% 0.20/0.42 inference(split_clause,[status(thm)],[f812,f809,f38])).
% 0.20/0.42 fof(f816,plain,(
% 0.20/0.42 ![X0,X1]: (~subgroup_member(multiply(X0,X1))|~subgroup_member(inverse(X1))|subgroup_member(multiply(X0,identity)))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f24,f88])).
% 0.20/0.42 fof(f817,plain,(
% 0.20/0.42 ![X0,X1]: (~subgroup_member(multiply(X0,X1))|~subgroup_member(inverse(X1))|subgroup_member(X0))),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f23,f816])).
% 0.20/0.42 fof(f827,plain,(
% 0.20/0.42 multiply(inverse(multiply(b,c)),c)=inverse(d)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f246,f619])).
% 0.20/0.42 fof(f852,plain,(
% 0.20/0.42 ![X0,X1]: (multiply(inverse(X0),X1)=inverse(multiply(inverse(X1),X0)))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f195,f619])).
% 0.20/0.42 fof(f862,plain,(
% 0.20/0.42 ![X0,X1,X2]: (~subgroup_member(multiply(inverse(multiply(multiply(X0,X1),X2)),X0))|~subgroup_member(X1)|subgroup_member(inverse(X2)))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f619,f88])).
% 0.20/0.42 fof(f863,plain,(
% 0.20/0.42 ![X0,X1,X2]: (~subgroup_member(multiply(inverse(multiply(X0,multiply(X1,X2))),X0))|~subgroup_member(X1)|subgroup_member(inverse(X2)))),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f19,f862])).
% 0.20/0.42 fof(f864,plain,(
% 0.20/0.42 ![X0,X1]: (~subgroup_member(inverse(multiply(X0,X1)))|~subgroup_member(X0)|subgroup_member(inverse(X1)))),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f619,f863])).
% 0.20/0.42 fof(f882,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(X0)|subgroup_member(multiply(b,X0))|~spl0_8)),
% 0.20/0.42 inference(backward_demodulation,[status(thm)],[f209,f372])).
% 0.20/0.42 fof(f894,plain,(
% 0.20/0.42 spl0_61 <=> ~subgroup_member(X0)|subgroup_member(multiply(b,X0))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f897,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(multiply(c,a))|~subgroup_member(X0)|subgroup_member(multiply(b,X0)))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f209,f88])).
% 0.20/0.42 fof(f898,plain,(
% 0.20/0.42 ~spl0_20|spl0_61),
% 0.20/0.42 inference(split_clause,[status(thm)],[f897,f356,f894])).
% 0.20/0.42 fof(f941,plain,(
% 0.20/0.42 spl0_65 <=> subgroup_member(inverse(inverse(b)))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f958,plain,(
% 0.20/0.42 spl0_68 <=> ~subgroup_member(inverse(inverse(X0)))|subgroup_member(X0)),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f963,plain,(
% 0.20/0.42 spl0_69 <=> ~subgroup_member(multiply(c,X0))|subgroup_member(multiply(inverse(a),X0))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f966,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(inverse(b))|~subgroup_member(multiply(c,X0))|subgroup_member(multiply(inverse(a),X0)))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f84,f217])).
% 0.20/0.42 fof(f967,plain,(
% 0.20/0.42 ~spl0_11|spl0_69),
% 0.20/0.42 inference(split_clause,[status(thm)],[f966,f280,f963])).
% 0.20/0.42 fof(f983,plain,(
% 0.20/0.42 spl0_71 <=> ~subgroup_member(inverse(X0))|subgroup_member(inverse(X0))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f1008,plain,(
% 0.20/0.42 spl0_72 <=> ~subgroup_member(X0)|subgroup_member(inverse(inverse(X0)))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f1013,plain,(
% 0.20/0.42 spl0_73 <=> ~subgroup_member(multiply(identity,X0))|subgroup_member(X0)),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f1016,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(identity)|~subgroup_member(multiply(identity,X0))|subgroup_member(X0))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f26,f245])).
% 0.20/0.42 fof(f1017,plain,(
% 0.20/0.42 ~spl0_0|spl0_73),
% 0.20/0.42 inference(split_clause,[status(thm)],[f1016,f38,f1013])).
% 0.20/0.42 fof(f1065,plain,(
% 0.20/0.42 spl0_77 <=> subgroup_member(X0)|multiply(d,element_in_O2(multiply(a,c),X0))=X0),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f1066,plain,(
% 0.20/0.42 ![X0]: (subgroup_member(X0)|multiply(d,element_in_O2(multiply(a,c),X0))=X0|~spl0_77)),
% 0.20/0.42 inference(component_clause,[status(thm)],[f1065])).
% 0.20/0.42 fof(f1068,plain,(
% 0.20/0.42 ![X0]: (subgroup_member(multiply(a,c))|subgroup_member(X0)|multiply(d,element_in_O2(multiply(a,c),X0))=X0)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f85,f285])).
% 0.20/0.42 fof(f1069,plain,(
% 0.20/0.42 spl0_45|spl0_77),
% 0.20/0.42 inference(split_clause,[status(thm)],[f1068,f728,f1065])).
% 0.20/0.42 fof(f1182,plain,(
% 0.20/0.42 spl0_96 <=> subgroup_member(X0)|multiply(a,multiply(c,element_in_O2(d,X0)))=X0),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f1185,plain,(
% 0.20/0.42 ![X0]: (subgroup_member(multiply(a,c))|subgroup_member(X0)|multiply(a,multiply(c,element_in_O2(d,X0)))=X0)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f32,f285])).
% 0.20/0.42 fof(f1186,plain,(
% 0.20/0.42 spl0_45|spl0_96),
% 0.20/0.42 inference(split_clause,[status(thm)],[f1185,f728,f1182])).
% 0.20/0.42 fof(f1244,plain,(
% 0.20/0.42 subgroup_member(d)|~spl0_45),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f32,f729])).
% 0.20/0.42 fof(f1245,plain,(
% 0.20/0.42 $false|~spl0_45),
% 0.20/0.42 inference(forward_subsumption_resolution,[status(thm)],[f1244,f33])).
% 0.20/0.42 fof(f1246,plain,(
% 0.20/0.42 ~spl0_45),
% 0.20/0.42 inference(contradiction_clause,[status(thm)],[f1245])).
% 0.20/0.42 fof(f1247,plain,(
% 0.20/0.42 ![X0]: (subgroup_member(X0)|multiply(d,element_in_O2(d,X0))=X0|~spl0_77)),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f32,f1066])).
% 0.20/0.42 fof(f1345,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(multiply(inverse(b),X0))|subgroup_member(X0)|~spl0_8)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f195,f882])).
% 0.20/0.42 fof(f1348,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(inverse(multiply(X0,b)))|subgroup_member(inverse(X0))|~spl0_8)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f207,f882])).
% 0.20/0.42 fof(f1387,plain,(
% 0.20/0.42 ![X0]: (subgroup_member(X0)|X0=X0|subgroup_member(d)|subgroup_member(X0)|~spl0_77)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f29,f1247])).
% 0.20/0.42 fof(f1388,plain,(
% 0.20/0.42 spl0_14|spl0_6|~spl0_77),
% 0.20/0.42 inference(split_clause,[status(thm)],[f1387,f294,f70,f1065])).
% 0.20/0.42 fof(f1392,plain,(
% 0.20/0.42 spl0_104 <=> ~subgroup_member(X0)|subgroup_member(element_in_O2(d,X0))|subgroup_member(X0)),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f1395,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(inverse(d))|~subgroup_member(X0)|subgroup_member(element_in_O2(d,X0))|subgroup_member(X0)|~spl0_77)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f1247,f217])).
% 0.20/0.42 fof(f1396,plain,(
% 0.20/0.42 ~spl0_29|spl0_104|~spl0_77),
% 0.20/0.42 inference(split_clause,[status(thm)],[f1395,f436,f1392,f1065])).
% 0.20/0.42 fof(f1399,plain,(
% 0.20/0.42 spl0_105 <=> ~subgroup_member(element_in_O2(d,X0))|subgroup_member(X0)|subgroup_member(X0)),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f1412,plain,(
% 0.20/0.42 spl0_106 <=> subgroup_member(multiply(inverse(c),multiply(b,c)))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f1413,plain,(
% 0.20/0.42 subgroup_member(multiply(inverse(c),multiply(b,c)))|~spl0_106),
% 0.20/0.42 inference(component_clause,[status(thm)],[f1412])).
% 0.20/0.42 fof(f1415,plain,(
% 0.20/0.42 spl0_107 <=> subgroup_member(X0)|multiply(inverse(c),multiply(multiply(b,c),element_in_O2(d,X0)))=X0),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f1418,plain,(
% 0.20/0.42 ![X0]: (subgroup_member(multiply(inverse(c),multiply(b,c)))|subgroup_member(X0)|multiply(inverse(c),multiply(multiply(b,c),element_in_O2(d,X0)))=X0)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f571,f285])).
% 0.20/0.42 fof(f1419,plain,(
% 0.20/0.42 spl0_106|spl0_107),
% 0.20/0.42 inference(split_clause,[status(thm)],[f1418,f1412,f1415])).
% 0.20/0.42 fof(f1438,plain,(
% 0.20/0.42 subgroup_member(d)|~spl0_106),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f571,f1413])).
% 0.20/0.42 fof(f1439,plain,(
% 0.20/0.42 $false|~spl0_106),
% 0.20/0.42 inference(forward_subsumption_resolution,[status(thm)],[f1438,f33])).
% 0.20/0.42 fof(f1440,plain,(
% 0.20/0.42 ~spl0_106),
% 0.20/0.42 inference(contradiction_clause,[status(thm)],[f1439])).
% 0.20/0.42 fof(f1446,plain,(
% 0.20/0.42 spl0_109 <=> subgroup_member(multiply(inverse(c),inverse(a)))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f1447,plain,(
% 0.20/0.42 subgroup_member(multiply(inverse(c),inverse(a)))|~spl0_109),
% 0.20/0.42 inference(component_clause,[status(thm)],[f1446])).
% 0.20/0.42 fof(f1449,plain,(
% 0.20/0.42 spl0_110 <=> subgroup_member(X0)|multiply(inverse(c),multiply(inverse(a),element_in_O2(inverse(d),X0)))=X0),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f1452,plain,(
% 0.20/0.42 ![X0]: (subgroup_member(multiply(inverse(c),inverse(a)))|subgroup_member(X0)|multiply(inverse(c),multiply(inverse(a),element_in_O2(inverse(d),X0)))=X0)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f586,f285])).
% 0.20/0.42 fof(f1453,plain,(
% 0.20/0.42 spl0_109|spl0_110),
% 0.20/0.42 inference(split_clause,[status(thm)],[f1452,f1446,f1449])).
% 0.20/0.42 fof(f1472,plain,(
% 0.20/0.42 subgroup_member(inverse(d))|~spl0_109),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f586,f1447])).
% 0.20/0.42 fof(f1473,plain,(
% 0.20/0.42 $false|spl0_29|~spl0_109),
% 0.20/0.42 inference(forward_subsumption_resolution,[status(thm)],[f1472,f438])).
% 0.20/0.42 fof(f1474,plain,(
% 0.20/0.42 spl0_29|~spl0_109),
% 0.20/0.42 inference(contradiction_clause,[status(thm)],[f1473])).
% 0.20/0.42 fof(f1681,plain,(
% 0.20/0.42 spl0_118 <=> ~subgroup_member(multiply(X0,identity))|subgroup_member(X0)),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f1684,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(multiply(X0,identity))|~subgroup_member(identity)|subgroup_member(X0))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f26,f791])).
% 0.20/0.42 fof(f1685,plain,(
% 0.20/0.42 spl0_118|~spl0_0),
% 0.20/0.42 inference(split_clause,[status(thm)],[f1684,f1681,f38])).
% 0.20/0.42 fof(f1692,plain,(
% 0.20/0.42 spl0_119 <=> ~subgroup_member(X0)|~subgroup_member(inverse(element_in_O2(d,X0)))|subgroup_member(X0)),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f1695,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(X0)|~subgroup_member(inverse(element_in_O2(d,X0)))|subgroup_member(d)|subgroup_member(X0)|~spl0_77)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f1247,f817])).
% 0.20/0.42 fof(f1696,plain,(
% 0.20/0.42 spl0_119|spl0_6|~spl0_77),
% 0.20/0.42 inference(split_clause,[status(thm)],[f1695,f1692,f70,f1065])).
% 0.20/0.42 fof(f2374,plain,(
% 0.20/0.42 spl0_138 <=> multiply(c,element_in_O2(d,X0))=multiply(inverse(a),X0)|subgroup_member(X0)),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f2377,plain,(
% 0.20/0.42 ![X0]: (multiply(c,element_in_O2(d,X0))=multiply(inverse(a),X0)|subgroup_member(d)|subgroup_member(X0))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f29,f251])).
% 0.20/0.42 fof(f2378,plain,(
% 0.20/0.42 spl0_138|spl0_6),
% 0.20/0.42 inference(split_clause,[status(thm)],[f2377,f2374,f70])).
% 0.20/0.42 fof(f2381,plain,(
% 0.20/0.42 spl0_139 <=> multiply(c,multiply(element_in_O2(d,X0),X1))=multiply(inverse(a),multiply(X0,X1))|subgroup_member(X0)),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f2384,plain,(
% 0.20/0.42 ![X0,X1]: (multiply(c,multiply(element_in_O2(d,X0),X1))=multiply(inverse(a),multiply(X0,X1))|subgroup_member(d)|subgroup_member(X0))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f310,f251])).
% 0.20/0.42 fof(f2385,plain,(
% 0.20/0.42 spl0_139|spl0_6),
% 0.20/0.42 inference(split_clause,[status(thm)],[f2384,f2381,f70])).
% 0.20/0.42 fof(f2592,plain,(
% 0.20/0.42 ~subgroup_member(identity)|subgroup_member(inverse(inverse(b)))|~spl0_8),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f24,f1345])).
% 0.20/0.42 fof(f2593,plain,(
% 0.20/0.42 ~spl0_0|spl0_65|~spl0_8),
% 0.20/0.42 inference(split_clause,[status(thm)],[f2592,f38,f941,f154])).
% 0.20/0.42 fof(f2897,plain,(
% 0.20/0.42 ![X0]: (subgroup_member(inverse(X0))|~subgroup_member(multiply(X0,b))|~spl0_8)),
% 0.20/0.42 inference(resolution,[status(thm)],[f1348,f20])).
% 0.20/0.42 fof(f2913,plain,(
% 0.20/0.42 spl0_167 <=> subgroup_member(inverse(X0))|~subgroup_member(X0)),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f2916,plain,(
% 0.20/0.42 ![X0]: (subgroup_member(inverse(X0))|~subgroup_member(X0)|~subgroup_member(b)|~spl0_8)),
% 0.20/0.42 inference(resolution,[status(thm)],[f2897,f34])).
% 0.20/0.42 fof(f2917,plain,(
% 0.20/0.42 spl0_167|~spl0_2|~spl0_8),
% 0.20/0.42 inference(split_clause,[status(thm)],[f2916,f2913,f56,f154])).
% 0.20/0.42 fof(f2919,plain,(
% 0.20/0.42 subgroup_member(inverse(identity))|~subgroup_member(b)|~spl0_8),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f17,f2897])).
% 0.20/0.42 fof(f2920,plain,(
% 0.20/0.42 spl0_31|~spl0_2|~spl0_8),
% 0.20/0.42 inference(split_clause,[status(thm)],[f2919,f453,f56,f154])).
% 0.20/0.42 fof(f2921,plain,(
% 0.20/0.42 ![X0]: (subgroup_member(inverse(inverse(multiply(b,X0))))|~subgroup_member(inverse(X0))|~spl0_8)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f619,f2897])).
% 0.20/0.42 fof(f2922,plain,(
% 0.20/0.42 ![X0]: (subgroup_member(multiply(b,X0))|~subgroup_member(inverse(X0))|~spl0_8)),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f25,f2921])).
% 0.20/0.42 fof(f2943,plain,(
% 0.20/0.42 spl0_170 <=> ~subgroup_member(inverse(X0))|subgroup_member(X0)),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f2964,plain,(
% 0.20/0.42 ![X0]: (subgroup_member(X0)|~subgroup_member(inverse(multiply(inverse(b),X0)))|~spl0_8)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f195,f2922])).
% 0.20/0.42 fof(f2965,plain,(
% 0.20/0.42 ![X0]: (subgroup_member(X0)|~subgroup_member(multiply(inverse(X0),b))|~spl0_8)),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f852,f2964])).
% 0.20/0.42 fof(f2973,plain,(
% 0.20/0.42 ![X0]: (subgroup_member(X0)|~subgroup_member(inverse(X0))|~subgroup_member(b)|~spl0_8)),
% 0.20/0.42 inference(resolution,[status(thm)],[f2965,f34])).
% 0.20/0.42 fof(f2974,plain,(
% 0.20/0.42 spl0_170|~spl0_2|~spl0_8),
% 0.20/0.42 inference(split_clause,[status(thm)],[f2973,f2943,f56,f154])).
% 0.20/0.42 fof(f3340,plain,(
% 0.20/0.42 spl0_200 <=> ~subgroup_member(multiply(a,X0))|~subgroup_member(inverse(multiply(inverse(c),X0)))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f3343,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(multiply(a,X0))|~subgroup_member(inverse(multiply(inverse(c),X0)))|subgroup_member(d))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f322,f817])).
% 0.20/0.42 fof(f3344,plain,(
% 0.20/0.42 spl0_200|spl0_6),
% 0.20/0.42 inference(split_clause,[status(thm)],[f3343,f3340,f70])).
% 0.20/0.42 fof(f3349,plain,(
% 0.20/0.42 spl0_201 <=> ~subgroup_member(multiply(a,X0))|subgroup_member(multiply(inverse(c),X0))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f3352,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(inverse(d))|~subgroup_member(multiply(a,X0))|subgroup_member(multiply(inverse(c),X0)))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f322,f217])).
% 0.20/0.42 fof(f3353,plain,(
% 0.20/0.42 ~spl0_29|spl0_201),
% 0.20/0.42 inference(split_clause,[status(thm)],[f3352,f436,f3349])).
% 0.20/0.42 fof(f3357,plain,(
% 0.20/0.42 spl0_202 <=> ~subgroup_member(multiply(inverse(c),X0))|subgroup_member(multiply(a,X0))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f3408,plain,(
% 0.20/0.42 spl0_209 <=> element_in_O2(a,d)=c),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f3409,plain,(
% 0.20/0.42 element_in_O2(a,d)=c|~spl0_209),
% 0.20/0.42 inference(component_clause,[status(thm)],[f3408])).
% 0.20/0.42 fof(f3411,plain,(
% 0.20/0.42 element_in_O2(a,d)=c|subgroup_member(a)|subgroup_member(d)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f204,f308])).
% 0.20/0.42 fof(f3412,plain,(
% 0.20/0.42 spl0_209|spl0_5|spl0_6),
% 0.20/0.42 inference(split_clause,[status(thm)],[f3411,f3408,f67,f70])).
% 0.20/0.42 fof(f3415,plain,(
% 0.20/0.42 ![X0]: (element_in_O2(X0,X0)=identity|subgroup_member(X0)|subgroup_member(X0))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f18,f308])).
% 0.20/0.42 fof(f3416,plain,(
% 0.20/0.42 ![X0]: (element_in_O2(X0,X0)=identity|subgroup_member(X0))),
% 0.20/0.42 inference(duplicate_literals_removal,[status(esa)],[f3415])).
% 0.20/0.42 fof(f3597,plain,(
% 0.20/0.42 spl0_223 <=> multiply(d,identity)=d),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f3600,plain,(
% 0.20/0.42 subgroup_member(d)|multiply(d,identity)=d|subgroup_member(d)|~spl0_77),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f3416,f1247])).
% 0.20/0.42 fof(f3601,plain,(
% 0.20/0.42 spl0_6|spl0_223|~spl0_77),
% 0.20/0.42 inference(split_clause,[status(thm)],[f3600,f70,f3597,f1065])).
% 0.20/0.42 fof(f3799,plain,(
% 0.20/0.42 spl0_246 <=> subgroup_member(multiply(a,inverse(multiply(a,b))))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f3800,plain,(
% 0.20/0.42 subgroup_member(multiply(a,inverse(multiply(a,b))))|~spl0_246),
% 0.20/0.42 inference(component_clause,[status(thm)],[f3799])).
% 0.20/0.42 fof(f3802,plain,(
% 0.20/0.42 spl0_247 <=> subgroup_member(X0)|multiply(a,multiply(inverse(multiply(a,b)),element_in_O2(inverse(d),X0)))=X0),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f3805,plain,(
% 0.20/0.42 ![X0]: (subgroup_member(multiply(a,inverse(multiply(a,b))))|subgroup_member(X0)|multiply(a,multiply(inverse(multiply(a,b)),element_in_O2(inverse(d),X0)))=X0)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f632,f285])).
% 0.20/0.42 fof(f3806,plain,(
% 0.20/0.42 spl0_246|spl0_247),
% 0.20/0.42 inference(split_clause,[status(thm)],[f3805,f3799,f3802])).
% 0.20/0.42 fof(f3827,plain,(
% 0.20/0.42 subgroup_member(inverse(d))|~spl0_246),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f632,f3800])).
% 0.20/0.42 fof(f3828,plain,(
% 0.20/0.42 $false|spl0_29|~spl0_246),
% 0.20/0.42 inference(forward_subsumption_resolution,[status(thm)],[f3827,f438])).
% 0.20/0.42 fof(f3829,plain,(
% 0.20/0.42 spl0_29|~spl0_246),
% 0.20/0.42 inference(contradiction_clause,[status(thm)],[f3828])).
% 0.20/0.42 fof(f3830,plain,(
% 0.20/0.42 ![X0,X1]: (~subgroup_member(X0)|subgroup_member(inverse(X1))|~subgroup_member(multiply(X1,X0)))),
% 0.20/0.42 inference(resolution,[status(thm)],[f675,f20])).
% 0.20/0.42 fof(f3834,plain,(
% 0.20/0.42 spl0_249 <=> ~subgroup_member(multiply(inverse(c),X0))|~subgroup_member(inverse(multiply(a,X0)))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f3837,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(multiply(inverse(c),X0))|~subgroup_member(inverse(multiply(a,X0)))|subgroup_member(inverse(d)))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f322,f675])).
% 0.20/0.42 fof(f3838,plain,(
% 0.20/0.42 spl0_249|spl0_29),
% 0.20/0.42 inference(split_clause,[status(thm)],[f3837,f3834,f436])).
% 0.20/0.42 fof(f3846,plain,(
% 0.20/0.42 spl0_251 <=> ~subgroup_member(element_in_O2(d,X0))|~subgroup_member(inverse(X0))|subgroup_member(X0)),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f3849,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(element_in_O2(d,X0))|~subgroup_member(inverse(X0))|subgroup_member(inverse(d))|subgroup_member(X0)|~spl0_77)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f1247,f675])).
% 0.20/0.42 fof(f3850,plain,(
% 0.20/0.42 spl0_251|spl0_29|~spl0_77),
% 0.20/0.42 inference(split_clause,[status(thm)],[f3849,f3846,f436,f1065])).
% 0.20/0.42 fof(f3911,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(X0)|~subgroup_member(inverse(identity))|subgroup_member(inverse(inverse(X0))))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f18,f675])).
% 0.20/0.42 fof(f3912,plain,(
% 0.20/0.42 spl0_72|~spl0_31),
% 0.20/0.42 inference(split_clause,[status(thm)],[f3911,f1008,f453])).
% 0.20/0.42 fof(f3942,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(inverse(X0))|~subgroup_member(inverse(identity))|subgroup_member(inverse(X0)))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f24,f675])).
% 0.20/0.42 fof(f3943,plain,(
% 0.20/0.42 spl0_71|~spl0_31),
% 0.20/0.42 inference(split_clause,[status(thm)],[f3942,f983,f453])).
% 0.20/0.42 fof(f3951,plain,(
% 0.20/0.42 spl0_256 <=> ~subgroup_member(multiply(inverse(c),X0))|~subgroup_member(multiply(a,X0))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f3963,plain,(
% 0.20/0.42 spl0_258 <=> ~subgroup_member(element_in_O2(d,X0))|~subgroup_member(X0)|subgroup_member(X0)),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f4010,plain,(
% 0.20/0.42 ![X0,X1]: (~subgroup_member(X0)|subgroup_member(inverse(inverse(multiply(X0,X1))))|~subgroup_member(inverse(X1)))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f619,f3830])).
% 0.20/0.42 fof(f4011,plain,(
% 0.20/0.42 ![X0,X1]: (~subgroup_member(X0)|subgroup_member(multiply(X0,X1))|~subgroup_member(inverse(X1)))),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f25,f4010])).
% 0.20/0.42 fof(f4033,plain,(
% 0.20/0.42 ![X0,X1]: (~subgroup_member(multiply(X0,X1))|subgroup_member(inverse(inverse(X0)))|~subgroup_member(X1))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f161,f3830])).
% 0.20/0.42 fof(f4034,plain,(
% 0.20/0.42 ![X0,X1]: (~subgroup_member(multiply(X0,X1))|subgroup_member(X0)|~subgroup_member(X1))),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f25,f4033])).
% 0.20/0.42 fof(f4398,plain,(
% 0.20/0.42 spl0_267 <=> subgroup_member(multiply(X0,multiply(X1,inverse(multiply(inverse(b),multiply(X0,X1))))))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f4401,plain,(
% 0.20/0.42 ![X0,X1]: (~subgroup_member(identity)|subgroup_member(multiply(X0,multiply(X1,inverse(multiply(inverse(b),multiply(X0,X1))))))|~spl0_8)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f90,f1345])).
% 0.20/0.42 fof(f4402,plain,(
% 0.20/0.42 ~spl0_0|spl0_267|~spl0_8),
% 0.20/0.42 inference(split_clause,[status(thm)],[f4401,f38,f4398,f154])).
% 0.20/0.42 fof(f4421,plain,(
% 0.20/0.42 spl0_270 <=> subgroup_member(multiply(c,multiply(X0,multiply(X1,inverse(multiply(inverse(a),multiply(X0,X1)))))))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f4424,plain,(
% 0.20/0.42 ![X0,X1]: (~subgroup_member(identity)|subgroup_member(multiply(c,multiply(X0,multiply(X1,inverse(multiply(inverse(a),multiply(X0,X1)))))))|~spl0_8)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f90,f155])).
% 0.20/0.42 fof(f4425,plain,(
% 0.20/0.42 ~spl0_0|spl0_270|~spl0_8),
% 0.20/0.42 inference(split_clause,[status(thm)],[f4424,f38,f4421,f154])).
% 0.20/0.42 fof(f4443,plain,(
% 0.20/0.42 spl0_271 <=> ~subgroup_member(X0)|subgroup_member(multiply(X1,multiply(X2,inverse(multiply(inverse(X0),multiply(X1,X2))))))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f4446,plain,(
% 0.20/0.42 ![X0,X1,X2]: (~subgroup_member(X0)|~subgroup_member(identity)|subgroup_member(multiply(X1,multiply(X2,inverse(multiply(inverse(X0),multiply(X1,X2)))))))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f90,f245])).
% 0.20/0.42 fof(f4447,plain,(
% 0.20/0.42 spl0_271|~spl0_0),
% 0.20/0.42 inference(split_clause,[status(thm)],[f4446,f4443,f38])).
% 0.20/0.42 fof(f4505,plain,(
% 0.20/0.42 spl0_277 <=> ~subgroup_member(multiply(X0,multiply(X1,inverse(multiply(X2,multiply(X0,X1))))))|subgroup_member(inverse(X2))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f4510,plain,(
% 0.20/0.42 ![X0,X1,X2]: (~subgroup_member(multiply(X0,multiply(X1,inverse(multiply(X2,multiply(X0,X1))))))|~subgroup_member(inverse(identity))|subgroup_member(inverse(X2)))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f90,f675])).
% 0.20/0.42 fof(f4511,plain,(
% 0.20/0.42 spl0_277|~spl0_31),
% 0.20/0.42 inference(split_clause,[status(thm)],[f4510,f4505,f453])).
% 0.20/0.42 fof(f4525,plain,(
% 0.20/0.42 spl0_278 <=> ~subgroup_member(inverse(multiply(X0,multiply(X1,inverse(multiply(X2,multiply(X0,X1)))))))|subgroup_member(X2)),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f4528,plain,(
% 0.20/0.42 ![X0,X1,X2]: (~subgroup_member(identity)|~subgroup_member(inverse(multiply(X0,multiply(X1,inverse(multiply(X2,multiply(X0,X1)))))))|subgroup_member(X2))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f90,f817])).
% 0.20/0.42 fof(f4529,plain,(
% 0.20/0.42 ~spl0_0|spl0_278),
% 0.20/0.42 inference(split_clause,[status(thm)],[f4528,f38,f4525])).
% 0.20/0.42 fof(f4534,plain,(
% 0.20/0.42 spl0_279 <=> ~subgroup_member(inverse(X0))|subgroup_member(multiply(X1,multiply(X2,inverse(multiply(X0,multiply(X1,X2))))))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f4537,plain,(
% 0.20/0.42 ![X0,X1,X2]: (~subgroup_member(inverse(X0))|~subgroup_member(identity)|subgroup_member(multiply(X1,multiply(X2,inverse(multiply(X0,multiply(X1,X2)))))))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f90,f217])).
% 0.20/0.42 fof(f4538,plain,(
% 0.20/0.42 spl0_279|~spl0_0),
% 0.20/0.42 inference(split_clause,[status(thm)],[f4537,f4534,f38])).
% 0.20/0.42 fof(f4575,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(multiply(a,X0))|subgroup_member(d)|~subgroup_member(multiply(inverse(c),X0)))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f322,f4034])).
% 0.20/0.42 fof(f4576,plain,(
% 0.20/0.42 spl0_256|spl0_6),
% 0.20/0.42 inference(split_clause,[status(thm)],[f4575,f3951,f70])).
% 0.20/0.42 fof(f4581,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(X0)|subgroup_member(d)|~subgroup_member(element_in_O2(d,X0))|subgroup_member(X0)|~spl0_77)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f1247,f4034])).
% 0.20/0.42 fof(f4582,plain,(
% 0.20/0.42 spl0_258|spl0_6|~spl0_77),
% 0.20/0.42 inference(split_clause,[status(thm)],[f4581,f3963,f70,f1065])).
% 0.20/0.42 fof(f4650,plain,(
% 0.20/0.42 ![X0,X1]: (~subgroup_member(X0)|subgroup_member(X1)|~subgroup_member(multiply(inverse(X1),X0)))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f195,f4034])).
% 0.20/0.42 fof(f4652,plain,(
% 0.20/0.42 spl0_281 <=> subgroup_member(X0)|~subgroup_member(multiply(X1,multiply(X2,inverse(multiply(X0,multiply(X1,X2))))))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f4655,plain,(
% 0.20/0.42 ![X0,X1,X2]: (~subgroup_member(identity)|subgroup_member(X0)|~subgroup_member(multiply(X1,multiply(X2,inverse(multiply(X0,multiply(X1,X2)))))))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f90,f4034])).
% 0.20/0.42 fof(f4656,plain,(
% 0.20/0.42 ~spl0_0|spl0_281),
% 0.20/0.42 inference(split_clause,[status(thm)],[f4655,f38,f4652])).
% 0.20/0.42 fof(f4800,plain,(
% 0.20/0.42 spl0_295 <=> subgroup_member(multiply(c,X0))|~subgroup_member(inverse(multiply(inverse(a),X0)))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f4803,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(b)|subgroup_member(multiply(c,X0))|~subgroup_member(inverse(multiply(inverse(a),X0))))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f84,f4011])).
% 0.20/0.42 fof(f4804,plain,(
% 0.20/0.42 ~spl0_2|spl0_295),
% 0.20/0.42 inference(split_clause,[status(thm)],[f4803,f56,f4800])).
% 0.20/0.42 fof(f4879,plain,(
% 0.20/0.42 spl0_299 <=> ~subgroup_member(multiply(X0,multiply(X1,inverse(multiply(inverse(X2),multiply(X0,X1))))))|subgroup_member(X2)),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f4882,plain,(
% 0.20/0.42 ![X0,X1,X2]: (~subgroup_member(multiply(X0,multiply(X1,inverse(multiply(inverse(X2),multiply(X0,X1))))))|subgroup_member(X2)|~subgroup_member(identity))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f90,f4650])).
% 0.20/0.42 fof(f4883,plain,(
% 0.20/0.42 spl0_299|~spl0_0),
% 0.20/0.42 inference(split_clause,[status(thm)],[f4882,f4879,f38])).
% 0.20/0.42 fof(f5012,plain,(
% 0.20/0.42 spl0_306 <=> subgroup_member(multiply(inverse(multiply(b,c)),c))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f5013,plain,(
% 0.20/0.42 subgroup_member(multiply(inverse(multiply(b,c)),c))|~spl0_306),
% 0.20/0.42 inference(component_clause,[status(thm)],[f5012])).
% 0.20/0.42 fof(f5015,plain,(
% 0.20/0.42 spl0_307 <=> subgroup_member(X0)|multiply(inverse(multiply(b,c)),multiply(c,element_in_O2(inverse(d),X0)))=X0),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f5018,plain,(
% 0.20/0.42 ![X0]: (subgroup_member(multiply(inverse(multiply(b,c)),c))|subgroup_member(X0)|multiply(inverse(multiply(b,c)),multiply(c,element_in_O2(inverse(d),X0)))=X0)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f827,f285])).
% 0.20/0.42 fof(f5019,plain,(
% 0.20/0.42 spl0_306|spl0_307),
% 0.20/0.42 inference(split_clause,[status(thm)],[f5018,f5012,f5015])).
% 0.20/0.42 fof(f5041,plain,(
% 0.20/0.42 subgroup_member(inverse(d))|~spl0_306),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f827,f5013])).
% 0.20/0.42 fof(f5042,plain,(
% 0.20/0.42 $false|spl0_29|~spl0_306),
% 0.20/0.42 inference(forward_subsumption_resolution,[status(thm)],[f5041,f438])).
% 0.20/0.42 fof(f5043,plain,(
% 0.20/0.42 spl0_29|~spl0_306),
% 0.20/0.42 inference(contradiction_clause,[status(thm)],[f5042])).
% 0.20/0.42 fof(f5044,plain,(
% 0.20/0.42 ![X0,X1]: (~subgroup_member(X0)|subgroup_member(inverse(X1))|~subgroup_member(multiply(X0,X1)))),
% 0.20/0.42 inference(resolution,[status(thm)],[f864,f20])).
% 0.20/0.42 fof(f5147,plain,(
% 0.20/0.42 spl0_321 <=> ~subgroup_member(inverse(multiply(c,X0)))|subgroup_member(inverse(multiply(inverse(a),X0)))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f5150,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(inverse(multiply(c,X0)))|~subgroup_member(b)|subgroup_member(inverse(multiply(inverse(a),X0))))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f84,f864])).
% 0.20/0.42 fof(f5151,plain,(
% 0.20/0.42 spl0_321|~spl0_2),
% 0.20/0.42 inference(split_clause,[status(thm)],[f5150,f5147,f56])).
% 0.20/0.42 fof(f5177,plain,(
% 0.20/0.42 spl0_324 <=> ~subgroup_member(X0)|subgroup_member(inverse(multiply(X1,multiply(X2,inverse(multiply(X0,multiply(X1,X2)))))))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f5180,plain,(
% 0.20/0.42 ![X0,X1,X2]: (~subgroup_member(inverse(identity))|~subgroup_member(X0)|subgroup_member(inverse(multiply(X1,multiply(X2,inverse(multiply(X0,multiply(X1,X2))))))))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f90,f864])).
% 0.20/0.42 fof(f5181,plain,(
% 0.20/0.42 ~spl0_31|spl0_324),
% 0.20/0.42 inference(split_clause,[status(thm)],[f5180,f453,f5177])).
% 0.20/0.42 fof(f5292,plain,(
% 0.20/0.42 spl0_336 <=> subgroup_member(inverse(multiply(inverse(a),X0)))|~subgroup_member(multiply(c,X0))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f5295,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(b)|subgroup_member(inverse(multiply(inverse(a),X0)))|~subgroup_member(multiply(c,X0)))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f84,f5044])).
% 0.20/0.42 fof(f5296,plain,(
% 0.20/0.42 ~spl0_2|spl0_336),
% 0.20/0.42 inference(split_clause,[status(thm)],[f5295,f56,f5292])).
% 0.20/0.42 fof(f5319,plain,(
% 0.20/0.42 ![X0,X1]: (~subgroup_member(X0)|subgroup_member(inverse(multiply(inverse(X0),X1)))|~subgroup_member(X1))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f195,f5044])).
% 0.20/0.42 fof(f5320,plain,(
% 0.20/0.42 ![X0,X1]: (~subgroup_member(X0)|subgroup_member(multiply(inverse(X1),X0))|~subgroup_member(X1))),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f852,f5319])).
% 0.20/0.42 fof(f5324,plain,(
% 0.20/0.42 ![X0,X1]: (~subgroup_member(X0)|subgroup_member(inverse(inverse(multiply(X1,X0))))|~subgroup_member(inverse(X1)))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f207,f5044])).
% 0.20/0.42 fof(f5325,plain,(
% 0.20/0.42 ![X0,X1]: (~subgroup_member(X0)|subgroup_member(multiply(X1,X0))|~subgroup_member(inverse(X1)))),
% 0.20/0.42 inference(forward_demodulation,[status(thm)],[f25,f5324])).
% 0.20/0.42 fof(f5383,plain,(
% 0.20/0.42 ~subgroup_member(b)|subgroup_member(a)|~subgroup_member(c)),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f255,f5320])).
% 0.20/0.42 fof(f5384,plain,(
% 0.20/0.42 ~spl0_2|spl0_5|~spl0_4),
% 0.20/0.42 inference(split_clause,[status(thm)],[f5383,f56,f67,f62])).
% 0.20/0.42 fof(f5390,plain,(
% 0.20/0.42 ![X0,X1]: (~subgroup_member(multiply(X0,X1))|subgroup_member(X1)|~subgroup_member(X0))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f161,f5320])).
% 0.20/0.42 fof(f5419,plain,(
% 0.20/0.42 spl0_340 <=> ~subgroup_member(X0)|subgroup_member(multiply(identity,X0))),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f5422,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(X0)|subgroup_member(multiply(identity,X0))|~subgroup_member(identity))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f26,f5320])).
% 0.20/0.42 fof(f5423,plain,(
% 0.20/0.42 spl0_340|~spl0_0),
% 0.20/0.42 inference(split_clause,[status(thm)],[f5422,f5419,f38])).
% 0.20/0.42 fof(f5489,plain,(
% 0.20/0.42 ~subgroup_member(c)|subgroup_member(d)|~subgroup_member(inverse(a))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f204,f5390])).
% 0.20/0.42 fof(f5490,plain,(
% 0.20/0.42 ~spl0_4|spl0_6|~spl0_3),
% 0.20/0.42 inference(split_clause,[status(thm)],[f5489,f62,f70,f59])).
% 0.20/0.42 fof(f5517,plain,(
% 0.20/0.42 spl0_341 <=> subgroup_member(multiply(X0,multiply(X1,inverse(multiply(X2,multiply(X0,X1))))))|~subgroup_member(X2)),
% 0.20/0.42 introduced(split_symbol_definition)).
% 0.20/0.42 fof(f5520,plain,(
% 0.20/0.42 ![X0,X1,X2]: (~subgroup_member(identity)|subgroup_member(multiply(X0,multiply(X1,inverse(multiply(X2,multiply(X0,X1))))))|~subgroup_member(X2))),
% 0.20/0.42 inference(paramodulation,[status(thm)],[f90,f5390])).
% 0.20/0.42 fof(f5521,plain,(
% 0.20/0.42 ~spl0_0|spl0_341),
% 0.20/0.42 inference(split_clause,[status(thm)],[f5520,f38,f5517])).
% 0.20/0.42 fof(f5535,plain,(
% 0.20/0.42 ![X0]: (~subgroup_member(X0)|~subgroup_member(inverse(inverse(b)))|subgroup_member(X0)|~spl0_8)),
% 0.20/0.42 inference(resolution,[status(thm)],[f5325,f1345])).
% 0.20/0.42 fof(f5536,plain,(
% 0.20/0.42 spl0_9|~spl0_65|~spl0_8),
% 0.20/0.42 inference(split_clause,[status(thm)],[f5535,f172,f941,f154])).
% 0.20/0.46 fof(f5543,plain,(
% 0.20/0.46 ![X0]: (~subgroup_member(b)|~subgroup_member(inverse(inverse(X0)))|subgroup_member(X0)|~spl0_8)),
% 0.20/0.46 inference(resolution,[status(thm)],[f5325,f2965])).
% 0.20/0.46 fof(f5544,plain,(
% 0.20/0.46 ~spl0_2|spl0_68|~spl0_8),
% 0.20/0.46 inference(split_clause,[status(thm)],[f5543,f56,f958,f154])).
% 0.20/0.46 fof(f5575,plain,(
% 0.20/0.46 ![X0]: (~subgroup_member(multiply(inverse(c),X0))|subgroup_member(multiply(a,X0))|~subgroup_member(inverse(d)))),
% 0.20/0.46 inference(paramodulation,[status(thm)],[f322,f5325])).
% 0.20/0.46 fof(f5576,plain,(
% 0.20/0.46 spl0_202|~spl0_29),
% 0.20/0.46 inference(split_clause,[status(thm)],[f5575,f3357,f436])).
% 0.20/0.46 fof(f5581,plain,(
% 0.20/0.46 ![X0]: (~subgroup_member(element_in_O2(d,X0))|subgroup_member(X0)|~subgroup_member(inverse(d))|subgroup_member(X0)|~spl0_77)),
% 0.20/0.46 inference(paramodulation,[status(thm)],[f1247,f5325])).
% 0.20/0.46 fof(f5582,plain,(
% 0.20/0.46 spl0_105|~spl0_29|~spl0_77),
% 0.20/0.46 inference(split_clause,[status(thm)],[f5581,f1399,f436,f1065])).
% 0.20/0.46 fof(f5707,plain,(
% 0.20/0.46 subgroup_member(a)|subgroup_member(d)|subgroup_member(c)|~spl0_209),
% 0.20/0.46 inference(paramodulation,[status(thm)],[f3409,f28])).
% 0.20/0.46 fof(f5708,plain,(
% 0.20/0.46 spl0_5|spl0_6|spl0_4|~spl0_209),
% 0.20/0.46 inference(split_clause,[status(thm)],[f5707,f67,f70,f62,f3408])).
% 0.20/0.46 fof(f5709,plain,(
% 0.20/0.46 $false),
% 0.20/0.46 inference(sat_refutation,[status(thm)],[f66,f74,f158,f160,f178,f284,f344,f360,f377,f382,f407,f412,f414,f486,f495,f561,f691,f755,f783,f802,f813,f898,f967,f1017,f1069,f1186,f1246,f1388,f1396,f1419,f1440,f1453,f1474,f1685,f1696,f2378,f2385,f2593,f2917,f2920,f2974,f3344,f3353,f3412,f3601,f3806,f3829,f3838,f3850,f3912,f3943,f4402,f4425,f4447,f4511,f4529,f4538,f4576,f4582,f4656,f4804,f4883,f5019,f5043,f5151,f5181,f5296,f5384,f5423,f5490,f5521,f5536,f5544,f5576,f5582,f5708])).
% 0.20/0.46 % SZS output end CNFRefutation for theBenchmark.p
% 0.20/0.46 % Elapsed time: 0.114149 seconds
% 0.20/0.46 % CPU time: 0.179249 seconds
% 0.20/0.46 % Memory used: 25.792 MB
%------------------------------------------------------------------------------