TSTP Solution File: GRP039-2 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GRP039-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n012.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 0.17s 0.38s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP039-2 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.32 % Computer : n012.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue May 30 11:28:55 EDT 2023
% 0.17/0.32 % CPUTime :
% 0.17/0.32 % Drodi V3.5.1
% 0.17/0.38 % Refutation found
% 0.17/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.38 % SZS output start CNFRefutation for theBenchmark
% 0.17/0.38 fof(f1,axiom,(
% 0.17/0.38 (![X]: (multiply(identity,X) = X ))),
% 0.17/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.38 fof(f2,axiom,(
% 0.17/0.38 (![X]: (multiply(inverse(X),X) = identity ))),
% 0.17/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.38 fof(f3,axiom,(
% 0.17/0.38 (![X,Y,Z]: (multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ))),
% 0.17/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.38 fof(f4,axiom,(
% 0.17/0.38 (![X]: (( ~ subgroup_member(X)| subgroup_member(inverse(X)) ) ))),
% 0.17/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.38 fof(f5,axiom,(
% 0.17/0.38 (![X,Y,Z]: (( ~ subgroup_member(X)| ~ subgroup_member(Y)| multiply(X,Y) != Z| subgroup_member(Z) ) ))),
% 0.17/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.38 fof(f6,axiom,(
% 0.17/0.38 (![X]: (multiply(X,identity) = X ))),
% 0.17/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.38 fof(f7,axiom,(
% 0.17/0.38 (![X]: (multiply(X,inverse(X)) = identity ))),
% 0.17/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.38 fof(f8,axiom,(
% 0.17/0.38 (![X,Y]: (( subgroup_member(X)| subgroup_member(Y)| subgroup_member(element_in_O2(X,Y)) ) ))),
% 0.17/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.38 fof(f9,axiom,(
% 0.17/0.38 (![X,Y]: (( subgroup_member(X)| subgroup_member(Y)| multiply(X,element_in_O2(X,Y)) = Y ) ))),
% 0.17/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.38 fof(f10,negated_conjecture,(
% 0.17/0.38 subgroup_member(b) ),
% 0.17/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.38 fof(f11,negated_conjecture,(
% 0.17/0.38 multiply(b,inverse(a)) = c ),
% 0.17/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.38 fof(f12,negated_conjecture,(
% 0.17/0.38 multiply(a,c) = d ),
% 0.17/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.38 fof(f13,negated_conjecture,(
% 0.17/0.38 ~ subgroup_member(d) ),
% 0.17/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.17/0.38 fof(f14,plain,(
% 0.17/0.38 ![X0]: (multiply(identity,X0)=X0)),
% 0.17/0.38 inference(cnf_transformation,[status(esa)],[f1])).
% 0.17/0.38 fof(f15,plain,(
% 0.17/0.38 ![X0]: (multiply(inverse(X0),X0)=identity)),
% 0.17/0.38 inference(cnf_transformation,[status(esa)],[f2])).
% 0.17/0.38 fof(f16,plain,(
% 0.17/0.38 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X0,multiply(X1,X2)))),
% 0.17/0.38 inference(cnf_transformation,[status(esa)],[f3])).
% 0.17/0.38 fof(f17,plain,(
% 0.17/0.38 ![X0]: (~subgroup_member(X0)|subgroup_member(inverse(X0)))),
% 0.17/0.38 inference(cnf_transformation,[status(esa)],[f4])).
% 0.17/0.38 fof(f18,plain,(
% 0.17/0.38 ![Z]: ((![X,Y]: ((~subgroup_member(X)|~subgroup_member(Y))|~multiply(X,Y)=Z))|subgroup_member(Z))),
% 0.17/0.38 inference(miniscoping,[status(esa)],[f5])).
% 0.17/0.38 fof(f19,plain,(
% 0.17/0.38 ![X0,X1,X2]: (~subgroup_member(X0)|~subgroup_member(X1)|~multiply(X0,X1)=X2|subgroup_member(X2))),
% 0.17/0.38 inference(cnf_transformation,[status(esa)],[f18])).
% 0.17/0.38 fof(f20,plain,(
% 0.17/0.38 ![X0]: (multiply(X0,identity)=X0)),
% 0.17/0.38 inference(cnf_transformation,[status(esa)],[f6])).
% 0.17/0.38 fof(f21,plain,(
% 0.17/0.38 ![X0]: (multiply(X0,inverse(X0))=identity)),
% 0.17/0.38 inference(cnf_transformation,[status(esa)],[f7])).
% 0.17/0.38 fof(f22,plain,(
% 0.17/0.38 ![X0,X1]: (subgroup_member(X0)|subgroup_member(X1)|subgroup_member(element_in_O2(X0,X1)))),
% 0.17/0.38 inference(cnf_transformation,[status(esa)],[f8])).
% 0.17/0.38 fof(f23,plain,(
% 0.17/0.38 ![X0,X1]: (subgroup_member(X0)|subgroup_member(X1)|multiply(X0,element_in_O2(X0,X1))=X1)),
% 0.17/0.38 inference(cnf_transformation,[status(esa)],[f9])).
% 0.17/0.38 fof(f24,plain,(
% 0.17/0.38 subgroup_member(b)),
% 0.17/0.38 inference(cnf_transformation,[status(esa)],[f10])).
% 0.17/0.38 fof(f25,plain,(
% 0.17/0.38 multiply(b,inverse(a))=c),
% 0.17/0.38 inference(cnf_transformation,[status(esa)],[f11])).
% 0.17/0.38 fof(f26,plain,(
% 0.17/0.38 multiply(a,c)=d),
% 0.17/0.38 inference(cnf_transformation,[status(esa)],[f12])).
% 0.17/0.38 fof(f27,plain,(
% 0.17/0.38 ~subgroup_member(d)),
% 0.17/0.38 inference(cnf_transformation,[status(esa)],[f13])).
% 0.17/0.38 fof(f28,plain,(
% 0.17/0.38 ![X0,X1]: (~subgroup_member(X0)|~subgroup_member(X1)|subgroup_member(multiply(X0,X1)))),
% 0.17/0.38 inference(destructive_equality_resolution,[status(esa)],[f19])).
% 0.17/0.38 fof(f32,plain,(
% 0.17/0.38 ![X0,X1]: (multiply(identity,X0)=multiply(inverse(X1),multiply(X1,X0)))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f15,f16])).
% 0.17/0.38 fof(f33,plain,(
% 0.17/0.38 ![X0]: (multiply(c,X0)=multiply(b,multiply(inverse(a),X0)))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f25,f16])).
% 0.17/0.38 fof(f34,plain,(
% 0.17/0.38 ![X0]: (multiply(d,X0)=multiply(a,multiply(c,X0)))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f26,f16])).
% 0.17/0.38 fof(f35,plain,(
% 0.17/0.38 ![X0,X1]: (multiply(X0,multiply(X1,inverse(multiply(X0,X1))))=identity)),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f16,f21])).
% 0.17/0.38 fof(f37,plain,(
% 0.17/0.38 ![X0,X1]: (multiply(identity,X0)=multiply(X1,multiply(inverse(X1),X0)))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f21,f16])).
% 0.17/0.38 fof(f38,plain,(
% 0.17/0.38 ![X0,X1,X2]: (~subgroup_member(multiply(X0,X1))|~subgroup_member(X2)|subgroup_member(multiply(X0,multiply(X1,X2))))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f16,f28])).
% 0.17/0.38 fof(f39,plain,(
% 0.17/0.38 spl0_0 <=> ~subgroup_member(inverse(X0))|~subgroup_member(X0)),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f40,plain,(
% 0.17/0.38 ![X0]: (~subgroup_member(inverse(X0))|~subgroup_member(X0)|~spl0_0)),
% 0.17/0.38 inference(component_clause,[status(thm)],[f39])).
% 0.17/0.38 fof(f42,plain,(
% 0.17/0.38 spl0_1 <=> subgroup_member(identity)),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f43,plain,(
% 0.17/0.38 subgroup_member(identity)|~spl0_1),
% 0.17/0.38 inference(component_clause,[status(thm)],[f42])).
% 0.17/0.38 fof(f47,plain,(
% 0.17/0.38 spl0_2 <=> subgroup_member(b)),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f49,plain,(
% 0.17/0.38 ~subgroup_member(b)|spl0_2),
% 0.17/0.38 inference(component_clause,[status(thm)],[f47])).
% 0.17/0.38 fof(f50,plain,(
% 0.17/0.38 spl0_3 <=> subgroup_member(inverse(a))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f52,plain,(
% 0.17/0.38 ~subgroup_member(inverse(a))|spl0_3),
% 0.17/0.38 inference(component_clause,[status(thm)],[f50])).
% 0.17/0.38 fof(f53,plain,(
% 0.17/0.38 spl0_4 <=> subgroup_member(c)),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f54,plain,(
% 0.17/0.38 subgroup_member(c)|~spl0_4),
% 0.17/0.38 inference(component_clause,[status(thm)],[f53])).
% 0.17/0.38 fof(f55,plain,(
% 0.17/0.38 ~subgroup_member(c)|spl0_4),
% 0.17/0.38 inference(component_clause,[status(thm)],[f53])).
% 0.17/0.38 fof(f56,plain,(
% 0.17/0.38 ~subgroup_member(b)|~subgroup_member(inverse(a))|subgroup_member(c)),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f25,f28])).
% 0.17/0.38 fof(f57,plain,(
% 0.17/0.38 ~spl0_2|~spl0_3|spl0_4),
% 0.17/0.38 inference(split_clause,[status(thm)],[f56,f47,f50,f53])).
% 0.17/0.38 fof(f58,plain,(
% 0.17/0.38 spl0_5 <=> subgroup_member(a)),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f61,plain,(
% 0.17/0.38 spl0_6 <=> subgroup_member(d)),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f62,plain,(
% 0.17/0.38 subgroup_member(d)|~spl0_6),
% 0.17/0.38 inference(component_clause,[status(thm)],[f61])).
% 0.17/0.38 fof(f64,plain,(
% 0.17/0.38 ~subgroup_member(a)|~subgroup_member(c)|subgroup_member(d)),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f26,f28])).
% 0.17/0.38 fof(f65,plain,(
% 0.17/0.38 ~spl0_5|~spl0_4|spl0_6),
% 0.17/0.38 inference(split_clause,[status(thm)],[f64,f58,f53,f61])).
% 0.17/0.38 fof(f68,plain,(
% 0.17/0.38 ![X0]: (~subgroup_member(X0)|~spl0_0)),
% 0.17/0.38 inference(forward_subsumption_resolution,[status(thm)],[f40,f17])).
% 0.17/0.38 fof(f71,plain,(
% 0.17/0.38 ![X0]: (multiply(identity,X0)=multiply(inverse(inverse(X0)),identity))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f15,f32])).
% 0.17/0.38 fof(f80,plain,(
% 0.17/0.38 ![X0]: (multiply(identity,multiply(c,X0))=multiply(inverse(a),multiply(d,X0)))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f34,f32])).
% 0.17/0.38 fof(f131,plain,(
% 0.17/0.38 ![X0]: (multiply(identity,X0)=multiply(X0,identity))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f15,f37])).
% 0.17/0.38 fof(f151,plain,(
% 0.17/0.38 spl0_9 <=> ~subgroup_member(X0)|subgroup_member(multiply(X0,identity))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f154,plain,(
% 0.17/0.38 ![X0]: (~subgroup_member(identity)|~subgroup_member(X0)|subgroup_member(multiply(X0,identity)))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f131,f28])).
% 0.17/0.38 fof(f155,plain,(
% 0.17/0.38 ~spl0_1|spl0_9),
% 0.17/0.38 inference(split_clause,[status(thm)],[f154,f42,f151])).
% 0.17/0.38 fof(f165,plain,(
% 0.17/0.38 spl0_10 <=> ~subgroup_member(X0)|subgroup_member(multiply(identity,X0))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f168,plain,(
% 0.17/0.38 ![X0]: (~subgroup_member(X0)|~subgroup_member(identity)|subgroup_member(multiply(identity,X0)))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f131,f28])).
% 0.17/0.38 fof(f169,plain,(
% 0.17/0.38 spl0_10|~spl0_1),
% 0.17/0.38 inference(split_clause,[status(thm)],[f168,f165,f42])).
% 0.17/0.38 fof(f172,plain,(
% 0.17/0.38 ![X0]: (multiply(identity,X0)=multiply(identity,inverse(inverse(X0))))),
% 0.17/0.38 inference(forward_demodulation,[status(thm)],[f131,f71])).
% 0.17/0.38 fof(f176,plain,(
% 0.17/0.38 spl0_11 <=> ~subgroup_member(inverse(inverse(X0)))|subgroup_member(multiply(identity,X0))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f179,plain,(
% 0.17/0.38 ![X0]: (~subgroup_member(identity)|~subgroup_member(inverse(inverse(X0)))|subgroup_member(multiply(identity,X0)))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f172,f28])).
% 0.17/0.38 fof(f180,plain,(
% 0.17/0.38 ~spl0_1|spl0_11),
% 0.17/0.38 inference(split_clause,[status(thm)],[f179,f42,f176])).
% 0.17/0.38 fof(f186,plain,(
% 0.17/0.38 multiply(c,a)=multiply(b,identity)),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f15,f33])).
% 0.17/0.38 fof(f187,plain,(
% 0.17/0.38 multiply(c,a)=multiply(identity,b)),
% 0.17/0.38 inference(forward_demodulation,[status(thm)],[f131,f186])).
% 0.17/0.38 fof(f201,plain,(
% 0.17/0.38 spl0_12 <=> ~subgroup_member(multiply(inverse(a),X0))|subgroup_member(multiply(c,X0))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f202,plain,(
% 0.17/0.38 ![X0]: (~subgroup_member(multiply(inverse(a),X0))|subgroup_member(multiply(c,X0))|~spl0_12)),
% 0.17/0.38 inference(component_clause,[status(thm)],[f201])).
% 0.17/0.38 fof(f204,plain,(
% 0.17/0.38 ![X0]: (~subgroup_member(b)|~subgroup_member(multiply(inverse(a),X0))|subgroup_member(multiply(c,X0)))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f33,f28])).
% 0.17/0.38 fof(f205,plain,(
% 0.17/0.38 ~spl0_2|spl0_12),
% 0.17/0.38 inference(split_clause,[status(thm)],[f204,f47,f201])).
% 0.17/0.38 fof(f209,plain,(
% 0.17/0.38 $false|spl0_2),
% 0.17/0.38 inference(forward_subsumption_resolution,[status(thm)],[f49,f24])).
% 0.17/0.38 fof(f210,plain,(
% 0.17/0.38 spl0_2),
% 0.17/0.38 inference(contradiction_clause,[status(thm)],[f209])).
% 0.17/0.38 fof(f223,plain,(
% 0.17/0.38 spl0_15 <=> subgroup_member(multiply(b,inverse(a)))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f224,plain,(
% 0.17/0.38 subgroup_member(multiply(b,inverse(a)))|~spl0_15),
% 0.17/0.38 inference(component_clause,[status(thm)],[f223])).
% 0.17/0.38 fof(f225,plain,(
% 0.17/0.38 ~subgroup_member(multiply(b,inverse(a)))|spl0_15),
% 0.17/0.38 inference(component_clause,[status(thm)],[f223])).
% 0.17/0.38 fof(f231,plain,(
% 0.17/0.38 spl0_17 <=> subgroup_member(multiply(a,c))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f232,plain,(
% 0.17/0.38 subgroup_member(multiply(a,c))|~spl0_17),
% 0.17/0.38 inference(component_clause,[status(thm)],[f231])).
% 0.17/0.38 fof(f261,plain,(
% 0.17/0.38 spl0_22 <=> ~subgroup_member(multiply(X0,a))|subgroup_member(multiply(X0,d))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f262,plain,(
% 0.17/0.38 ![X0]: (~subgroup_member(multiply(X0,a))|subgroup_member(multiply(X0,d))|~spl0_22)),
% 0.17/0.38 inference(component_clause,[status(thm)],[f261])).
% 0.17/0.38 fof(f264,plain,(
% 0.17/0.38 ![X0]: (~subgroup_member(multiply(X0,a))|~subgroup_member(c)|subgroup_member(multiply(X0,d)))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f26,f38])).
% 0.17/0.38 fof(f265,plain,(
% 0.17/0.38 spl0_22|~spl0_4),
% 0.17/0.38 inference(split_clause,[status(thm)],[f264,f261,f53])).
% 0.17/0.38 fof(f266,plain,(
% 0.17/0.38 spl0_23 <=> ~subgroup_member(multiply(X0,X1))|subgroup_member(multiply(X0,multiply(identity,X1)))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f269,plain,(
% 0.17/0.38 ![X0,X1]: (~subgroup_member(multiply(X0,X1))|~subgroup_member(identity)|subgroup_member(multiply(X0,multiply(identity,X1))))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f131,f38])).
% 0.17/0.38 fof(f270,plain,(
% 0.17/0.38 spl0_23|~spl0_1),
% 0.17/0.38 inference(split_clause,[status(thm)],[f269,f266,f42])).
% 0.17/0.38 fof(f275,plain,(
% 0.17/0.38 ~subgroup_member(c)|spl0_15),
% 0.17/0.38 inference(forward_demodulation,[status(thm)],[f25,f225])).
% 0.17/0.38 fof(f277,plain,(
% 0.17/0.38 ![X0]: (multiply(identity,X0)=inverse(inverse(X0)))),
% 0.17/0.38 inference(backward_demodulation,[status(thm)],[f14,f172])).
% 0.17/0.38 fof(f278,plain,(
% 0.17/0.38 ![X0]: (X0=inverse(inverse(X0)))),
% 0.17/0.38 inference(forward_demodulation,[status(thm)],[f14,f277])).
% 0.17/0.38 fof(f280,plain,(
% 0.17/0.38 ![X0,X1]: (X0=multiply(X1,multiply(inverse(X1),X0)))),
% 0.17/0.38 inference(backward_demodulation,[status(thm)],[f14,f37])).
% 0.17/0.38 fof(f281,plain,(
% 0.17/0.38 ![X0,X1]: (X0=multiply(inverse(X1),multiply(X1,X0)))),
% 0.17/0.38 inference(backward_demodulation,[status(thm)],[f14,f32])).
% 0.17/0.38 fof(f284,plain,(
% 0.17/0.38 identity=inverse(identity)),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f21,f14])).
% 0.17/0.38 fof(f294,plain,(
% 0.17/0.38 spl0_24 <=> ~subgroup_member(X0)|subgroup_member(X0)),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f297,plain,(
% 0.17/0.38 ![X0]: (~subgroup_member(identity)|~subgroup_member(X0)|subgroup_member(X0))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f14,f28])).
% 0.17/0.38 fof(f298,plain,(
% 0.17/0.38 ~spl0_1|spl0_24),
% 0.17/0.38 inference(split_clause,[status(thm)],[f297,f42,f294])).
% 0.17/0.38 fof(f308,plain,(
% 0.17/0.38 spl0_25 <=> ~subgroup_member(multiply(X0,X1))|subgroup_member(multiply(X0,X1))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f311,plain,(
% 0.17/0.38 ![X0,X1]: (~subgroup_member(multiply(X0,X1))|~subgroup_member(identity)|subgroup_member(multiply(X0,X1)))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f20,f38])).
% 0.17/0.38 fof(f312,plain,(
% 0.17/0.38 spl0_25|~spl0_1),
% 0.17/0.38 inference(split_clause,[status(thm)],[f311,f308,f42])).
% 0.17/0.38 fof(f338,plain,(
% 0.17/0.38 ![X0,X1]: (multiply(X0,inverse(multiply(inverse(X1),X0)))=multiply(X1,identity))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f35,f280])).
% 0.17/0.38 fof(f339,plain,(
% 0.17/0.38 ![X0,X1]: (multiply(X0,inverse(multiply(inverse(X1),X0)))=X1)),
% 0.17/0.38 inference(forward_demodulation,[status(thm)],[f20,f338])).
% 0.17/0.38 fof(f349,plain,(
% 0.17/0.38 ![X0]: (multiply(c,multiply(inverse(inverse(a)),X0))=multiply(b,X0))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f280,f33])).
% 0.17/0.38 fof(f350,plain,(
% 0.17/0.38 ![X0]: (multiply(c,multiply(a,X0))=multiply(b,X0))),
% 0.17/0.38 inference(forward_demodulation,[status(thm)],[f278,f349])).
% 0.17/0.38 fof(f359,plain,(
% 0.17/0.38 ![X0,X1]: (~subgroup_member(X0)|~subgroup_member(multiply(inverse(X0),X1))|subgroup_member(X1))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f280,f28])).
% 0.17/0.38 fof(f377,plain,(
% 0.17/0.38 c=multiply(inverse(a),d)),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f26,f281])).
% 0.17/0.38 fof(f379,plain,(
% 0.17/0.38 ![X0,X1]: (multiply(X0,inverse(multiply(X1,X0)))=multiply(inverse(X1),identity))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f35,f281])).
% 0.17/0.38 fof(f380,plain,(
% 0.17/0.38 ![X0,X1]: (multiply(X0,inverse(multiply(X1,X0)))=inverse(X1))),
% 0.17/0.38 inference(forward_demodulation,[status(thm)],[f20,f379])).
% 0.17/0.38 fof(f391,plain,(
% 0.17/0.38 ![X0,X1]: (~subgroup_member(inverse(X0))|~subgroup_member(multiply(X0,X1))|subgroup_member(X1))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f281,f28])).
% 0.17/0.38 fof(f394,plain,(
% 0.17/0.38 multiply(c,d)=multiply(b,c)),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f377,f33])).
% 0.17/0.38 fof(f407,plain,(
% 0.17/0.38 multiply(c,a)=b),
% 0.17/0.38 inference(forward_demodulation,[status(thm)],[f14,f187])).
% 0.17/0.38 fof(f409,plain,(
% 0.17/0.38 a=multiply(inverse(c),b)),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f407,f281])).
% 0.17/0.38 fof(f419,plain,(
% 0.17/0.38 $false|~spl0_6),
% 0.17/0.38 inference(forward_subsumption_resolution,[status(thm)],[f62,f27])).
% 0.17/0.38 fof(f420,plain,(
% 0.17/0.38 ~spl0_6),
% 0.17/0.38 inference(contradiction_clause,[status(thm)],[f419])).
% 0.17/0.38 fof(f426,plain,(
% 0.17/0.38 ![X0,X1,X2]: (subgroup_member(multiply(X0,X1))|subgroup_member(X2)|multiply(X0,multiply(X1,element_in_O2(multiply(X0,X1),X2)))=X2)),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f16,f23])).
% 0.17/0.38 fof(f430,plain,(
% 0.17/0.38 spl0_30 <=> subgroup_member(X1)|X1=X1|subgroup_member(X1)),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f453,plain,(
% 0.17/0.38 ![X0,X1,X2]: (multiply(X0,X1)=multiply(X2,multiply(element_in_O2(X2,X0),X1))|subgroup_member(X2)|subgroup_member(X0))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f23,f16])).
% 0.17/0.38 fof(f469,plain,(
% 0.17/0.38 spl0_34 <=> subgroup_member(X0)|multiply(d,element_in_O2(multiply(a,c),X0))=X0),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f470,plain,(
% 0.17/0.38 ![X0]: (subgroup_member(X0)|multiply(d,element_in_O2(multiply(a,c),X0))=X0|~spl0_34)),
% 0.17/0.38 inference(component_clause,[status(thm)],[f469])).
% 0.17/0.38 fof(f472,plain,(
% 0.17/0.38 ![X0]: (subgroup_member(multiply(a,c))|subgroup_member(X0)|multiply(d,element_in_O2(multiply(a,c),X0))=X0)),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f34,f426])).
% 0.17/0.38 fof(f473,plain,(
% 0.17/0.38 spl0_17|spl0_34),
% 0.17/0.38 inference(split_clause,[status(thm)],[f472,f231,f469])).
% 0.17/0.38 fof(f486,plain,(
% 0.17/0.38 spl0_36 <=> subgroup_member(multiply(c,a))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f500,plain,(
% 0.17/0.38 spl0_38 <=> subgroup_member(multiply(inverse(a),d))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f501,plain,(
% 0.17/0.38 subgroup_member(multiply(inverse(a),d))|~spl0_38),
% 0.17/0.38 inference(component_clause,[status(thm)],[f500])).
% 0.17/0.38 fof(f528,plain,(
% 0.17/0.38 spl0_41 <=> subgroup_member(X0)|multiply(a,multiply(c,element_in_O2(d,X0)))=X0),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f531,plain,(
% 0.17/0.38 ![X0]: (subgroup_member(multiply(a,c))|subgroup_member(X0)|multiply(a,multiply(c,element_in_O2(d,X0)))=X0)),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f26,f426])).
% 0.17/0.38 fof(f532,plain,(
% 0.17/0.38 spl0_17|spl0_41),
% 0.17/0.38 inference(split_clause,[status(thm)],[f531,f231,f528])).
% 0.17/0.38 fof(f576,plain,(
% 0.17/0.38 subgroup_member(c)|~spl0_38),
% 0.17/0.38 inference(forward_demodulation,[status(thm)],[f377,f501])).
% 0.17/0.38 fof(f578,plain,(
% 0.17/0.38 subgroup_member(d)|~spl0_17),
% 0.17/0.38 inference(forward_demodulation,[status(thm)],[f26,f232])).
% 0.17/0.38 fof(f579,plain,(
% 0.17/0.38 $false|~spl0_17),
% 0.17/0.38 inference(forward_subsumption_resolution,[status(thm)],[f578,f27])).
% 0.17/0.38 fof(f580,plain,(
% 0.17/0.38 ~spl0_17),
% 0.17/0.38 inference(contradiction_clause,[status(thm)],[f579])).
% 0.17/0.38 fof(f581,plain,(
% 0.17/0.38 ![X0]: (subgroup_member(X0)|multiply(d,element_in_O2(d,X0))=X0|~spl0_34)),
% 0.17/0.38 inference(forward_demodulation,[status(thm)],[f26,f470])).
% 0.17/0.38 fof(f585,plain,(
% 0.17/0.38 $false|~spl0_38|spl0_15),
% 0.17/0.38 inference(forward_subsumption_resolution,[status(thm)],[f275,f576])).
% 0.17/0.38 fof(f586,plain,(
% 0.17/0.38 ~spl0_38|spl0_15),
% 0.17/0.38 inference(contradiction_clause,[status(thm)],[f585])).
% 0.17/0.38 fof(f587,plain,(
% 0.17/0.38 subgroup_member(c)|~spl0_15),
% 0.17/0.38 inference(forward_demodulation,[status(thm)],[f25,f224])).
% 0.17/0.38 fof(f588,plain,(
% 0.17/0.38 ![X0,X1]: (subgroup_member(multiply(c,multiply(X0,X1)))|~subgroup_member(multiply(inverse(a),X0))|~subgroup_member(X1)|~spl0_12)),
% 0.17/0.38 inference(resolution,[status(thm)],[f202,f38])).
% 0.17/0.38 fof(f596,plain,(
% 0.17/0.38 ![X0]: (~subgroup_member(X0)|subgroup_member(multiply(c,multiply(a,X0)))|~spl0_12)),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f281,f202])).
% 0.17/0.38 fof(f597,plain,(
% 0.17/0.38 ~subgroup_member(identity)|subgroup_member(multiply(c,a))|~spl0_12),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f15,f202])).
% 0.17/0.38 fof(f598,plain,(
% 0.17/0.38 ~spl0_1|spl0_36|~spl0_12),
% 0.17/0.38 inference(split_clause,[status(thm)],[f597,f42,f486,f201])).
% 0.17/0.38 fof(f611,plain,(
% 0.17/0.38 spl0_45 <=> subgroup_member(multiply(c,multiply(X0,inverse(multiply(inverse(a),X0)))))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f614,plain,(
% 0.17/0.38 ![X0]: (~subgroup_member(identity)|subgroup_member(multiply(c,multiply(X0,inverse(multiply(inverse(a),X0)))))|~spl0_12)),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f35,f202])).
% 0.17/0.38 fof(f615,plain,(
% 0.17/0.38 ~spl0_1|spl0_45|~spl0_12),
% 0.17/0.38 inference(split_clause,[status(thm)],[f614,f42,f611,f201])).
% 0.17/0.38 fof(f616,plain,(
% 0.17/0.38 spl0_46 <=> subgroup_member(multiply(c,inverse(inverse(a))))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f617,plain,(
% 0.17/0.38 subgroup_member(multiply(c,inverse(inverse(a))))|~spl0_46),
% 0.17/0.38 inference(component_clause,[status(thm)],[f616])).
% 0.17/0.38 fof(f619,plain,(
% 0.17/0.38 ~subgroup_member(identity)|subgroup_member(multiply(c,inverse(inverse(a))))|~spl0_12),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f21,f202])).
% 0.17/0.38 fof(f620,plain,(
% 0.17/0.38 ~spl0_1|spl0_46|~spl0_12),
% 0.17/0.38 inference(split_clause,[status(thm)],[f619,f42,f616,f201])).
% 0.17/0.38 fof(f628,plain,(
% 0.17/0.38 $false|~spl0_0),
% 0.17/0.38 inference(backward_subsumption_resolution,[status(thm)],[f24,f68])).
% 0.17/0.38 fof(f629,plain,(
% 0.17/0.38 ~spl0_0),
% 0.17/0.38 inference(contradiction_clause,[status(thm)],[f628])).
% 0.17/0.38 fof(f630,plain,(
% 0.17/0.38 subgroup_member(multiply(c,a))|~spl0_46),
% 0.17/0.38 inference(forward_demodulation,[status(thm)],[f278,f617])).
% 0.17/0.38 fof(f631,plain,(
% 0.17/0.38 subgroup_member(b)|~spl0_46),
% 0.17/0.38 inference(forward_demodulation,[status(thm)],[f407,f630])).
% 0.17/0.38 fof(f632,plain,(
% 0.17/0.38 ![X0]: (element_in_O2(d,X0)=multiply(inverse(d),X0)|subgroup_member(X0)|~spl0_34)),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f581,f281])).
% 0.17/0.38 fof(f647,plain,(
% 0.17/0.38 spl0_47 <=> subgroup_member(inverse(multiply(c,a)))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f649,plain,(
% 0.17/0.38 ~subgroup_member(inverse(multiply(c,a)))|spl0_47),
% 0.17/0.38 inference(component_clause,[status(thm)],[f647])).
% 0.17/0.38 fof(f650,plain,(
% 0.17/0.38 ~subgroup_member(inverse(multiply(c,a)))|subgroup_member(identity)|~spl0_12),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f35,f596])).
% 0.17/0.38 fof(f651,plain,(
% 0.17/0.38 ~spl0_47|spl0_1|~spl0_12),
% 0.17/0.38 inference(split_clause,[status(thm)],[f650,f647,f42,f201])).
% 0.17/0.38 fof(f693,plain,(
% 0.17/0.38 ~subgroup_member(identity)|subgroup_member(multiply(inverse(a),d))|~spl0_22),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f15,f262])).
% 0.17/0.38 fof(f694,plain,(
% 0.17/0.38 ~spl0_1|spl0_38|~spl0_22),
% 0.17/0.38 inference(split_clause,[status(thm)],[f693,f42,f500,f261])).
% 0.17/0.38 fof(f696,plain,(
% 0.17/0.38 spl0_50 <=> element_in_O2(d,d)=identity),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f697,plain,(
% 0.17/0.38 element_in_O2(d,d)=identity|~spl0_50),
% 0.17/0.38 inference(component_clause,[status(thm)],[f696])).
% 0.17/0.38 fof(f699,plain,(
% 0.17/0.38 element_in_O2(d,d)=identity|subgroup_member(d)|~spl0_34),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f15,f632])).
% 0.17/0.38 fof(f700,plain,(
% 0.17/0.38 spl0_50|spl0_6|~spl0_34),
% 0.17/0.38 inference(split_clause,[status(thm)],[f699,f696,f61,f469])).
% 0.17/0.38 fof(f710,plain,(
% 0.17/0.38 spl0_52 <=> element_in_O2(d,inverse(inverse(d)))=identity),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f713,plain,(
% 0.17/0.38 spl0_53 <=> subgroup_member(inverse(inverse(d)))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f714,plain,(
% 0.17/0.38 subgroup_member(inverse(inverse(d)))|~spl0_53),
% 0.17/0.38 inference(component_clause,[status(thm)],[f713])).
% 0.17/0.38 fof(f716,plain,(
% 0.17/0.38 element_in_O2(d,inverse(inverse(d)))=identity|subgroup_member(inverse(inverse(d)))|~spl0_34),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f21,f632])).
% 0.17/0.38 fof(f717,plain,(
% 0.17/0.38 spl0_52|spl0_53|~spl0_34),
% 0.17/0.38 inference(split_clause,[status(thm)],[f716,f710,f713,f469])).
% 0.17/0.38 fof(f744,plain,(
% 0.17/0.38 spl0_56 <=> multiply(d,identity)=d),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f850,plain,(
% 0.17/0.38 spl0_74 <=> subgroup_member(multiply(c,multiply(d,X0)))|~subgroup_member(multiply(c,X0))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f853,plain,(
% 0.17/0.38 spl0_75 <=> subgroup_member(multiply(inverse(a),a))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f855,plain,(
% 0.17/0.38 ~subgroup_member(multiply(inverse(a),a))|spl0_75),
% 0.17/0.38 inference(component_clause,[status(thm)],[f853])).
% 0.17/0.38 fof(f856,plain,(
% 0.17/0.38 ![X0]: (subgroup_member(multiply(c,multiply(d,X0)))|~subgroup_member(multiply(inverse(a),a))|~subgroup_member(multiply(c,X0))|~spl0_12)),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f34,f588])).
% 0.17/0.38 fof(f857,plain,(
% 0.17/0.38 spl0_74|~spl0_75|~spl0_12),
% 0.17/0.38 inference(split_clause,[status(thm)],[f856,f850,f853,f201])).
% 0.17/0.38 fof(f873,plain,(
% 0.17/0.38 ~subgroup_member(identity)|spl0_75),
% 0.17/0.38 inference(forward_demodulation,[status(thm)],[f15,f855])).
% 0.17/0.38 fof(f874,plain,(
% 0.17/0.38 $false|~spl0_1|spl0_75),
% 0.17/0.38 inference(forward_subsumption_resolution,[status(thm)],[f873,f43])).
% 0.17/0.38 fof(f875,plain,(
% 0.17/0.38 ~spl0_1|spl0_75),
% 0.17/0.38 inference(contradiction_clause,[status(thm)],[f874])).
% 0.17/0.38 fof(f877,plain,(
% 0.17/0.38 ~subgroup_member(inverse(b))|spl0_47),
% 0.17/0.38 inference(forward_demodulation,[status(thm)],[f407,f649])).
% 0.17/0.38 fof(f912,plain,(
% 0.17/0.38 d=multiply(inverse(c),multiply(b,c))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f394,f281])).
% 0.17/0.38 fof(f932,plain,(
% 0.17/0.38 multiply(d,inverse(c))=a),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f377,f339])).
% 0.17/0.38 fof(f969,plain,(
% 0.17/0.38 spl0_81 <=> subgroup_member(inverse(c))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f971,plain,(
% 0.17/0.38 ~subgroup_member(inverse(c))|spl0_81),
% 0.17/0.38 inference(component_clause,[status(thm)],[f969])).
% 0.17/0.38 fof(f974,plain,(
% 0.17/0.38 inverse(c)=multiply(inverse(d),a)),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f932,f281])).
% 0.17/0.38 fof(f985,plain,(
% 0.17/0.38 multiply(a,inverse(b))=inverse(c)),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f407,f380])).
% 0.17/0.38 fof(f1067,plain,(
% 0.17/0.38 spl0_86 <=> subgroup_member(inverse(b))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f1069,plain,(
% 0.17/0.38 ~subgroup_member(inverse(b))|spl0_86),
% 0.17/0.38 inference(component_clause,[status(thm)],[f1067])).
% 0.17/0.38 fof(f1072,plain,(
% 0.17/0.38 ~subgroup_member(inverse(c))|~subgroup_member(b)|subgroup_member(a)),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f409,f28])).
% 0.17/0.38 fof(f1073,plain,(
% 0.17/0.38 ~spl0_81|~spl0_2|spl0_5),
% 0.17/0.38 inference(split_clause,[status(thm)],[f1072,f969,f47,f58])).
% 0.17/0.38 fof(f1117,plain,(
% 0.17/0.38 ![X0,X1]: (multiply(X0,identity)=multiply(X1,element_in_O2(X1,X0))|subgroup_member(X1)|subgroup_member(X0))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f20,f453])).
% 0.17/0.38 fof(f1118,plain,(
% 0.17/0.38 ![X0,X1]: (X0=multiply(X1,element_in_O2(X1,X0))|subgroup_member(X1)|subgroup_member(X0))),
% 0.17/0.38 inference(forward_demodulation,[status(thm)],[f20,f1117])).
% 0.17/0.38 fof(f1124,plain,(
% 0.17/0.38 spl0_92 <=> multiply(d,X0)=multiply(d,multiply(identity,X0))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f1127,plain,(
% 0.17/0.38 ![X0]: (multiply(d,X0)=multiply(d,multiply(identity,X0))|subgroup_member(d)|subgroup_member(d)|~spl0_50)),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f697,f453])).
% 0.17/0.38 fof(f1128,plain,(
% 0.17/0.38 spl0_92|spl0_6|~spl0_50),
% 0.17/0.38 inference(split_clause,[status(thm)],[f1127,f1124,f61,f696])).
% 0.17/0.38 fof(f1169,plain,(
% 0.17/0.38 ~subgroup_member(a)|spl0_3),
% 0.17/0.38 inference(resolution,[status(thm)],[f52,f17])).
% 0.17/0.38 fof(f1170,plain,(
% 0.17/0.38 ~spl0_5|spl0_3),
% 0.17/0.38 inference(split_clause,[status(thm)],[f1169,f58,f50])).
% 0.17/0.38 fof(f1215,plain,(
% 0.17/0.38 spl0_102 <=> ~subgroup_member(multiply(X0,inverse(c)))|subgroup_member(multiply(X0,a))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f1218,plain,(
% 0.17/0.38 ![X0]: (~subgroup_member(multiply(X0,inverse(c)))|~subgroup_member(b)|subgroup_member(multiply(X0,a)))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f409,f38])).
% 0.17/0.38 fof(f1219,plain,(
% 0.17/0.38 spl0_102|~spl0_2),
% 0.17/0.38 inference(split_clause,[status(thm)],[f1218,f1215,f47])).
% 0.17/0.38 fof(f1223,plain,(
% 0.17/0.38 ![X0,X1]: (~subgroup_member(multiply(X0,inverse(X1)))|~subgroup_member(X1)|subgroup_member(multiply(X0,identity)))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f15,f38])).
% 0.17/0.38 fof(f1224,plain,(
% 0.17/0.38 ![X0,X1]: (~subgroup_member(multiply(X0,inverse(X1)))|~subgroup_member(X1)|subgroup_member(X0))),
% 0.17/0.38 inference(forward_demodulation,[status(thm)],[f20,f1223])).
% 0.17/0.38 fof(f1236,plain,(
% 0.17/0.38 ![X0,X1]: (~subgroup_member(multiply(X0,X1))|~subgroup_member(inverse(X1))|subgroup_member(multiply(X0,identity)))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f21,f38])).
% 0.17/0.38 fof(f1237,plain,(
% 0.17/0.38 ![X0,X1]: (~subgroup_member(multiply(X0,X1))|~subgroup_member(inverse(X1))|subgroup_member(X0))),
% 0.17/0.38 inference(forward_demodulation,[status(thm)],[f20,f1236])).
% 0.17/0.38 fof(f1240,plain,(
% 0.17/0.38 spl0_103 <=> inverse(c)=element_in_O2(d,a)),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f1241,plain,(
% 0.17/0.38 inverse(c)=element_in_O2(d,a)|~spl0_103),
% 0.17/0.38 inference(component_clause,[status(thm)],[f1240])).
% 0.17/0.38 fof(f1243,plain,(
% 0.17/0.38 inverse(c)=element_in_O2(d,a)|subgroup_member(a)|~spl0_34),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f632,f974])).
% 0.17/0.38 fof(f1244,plain,(
% 0.17/0.38 spl0_103|spl0_5|~spl0_34),
% 0.17/0.38 inference(split_clause,[status(thm)],[f1243,f1240,f58,f469])).
% 0.17/0.38 fof(f1258,plain,(
% 0.17/0.38 spl0_105 <=> subgroup_member(multiply(c,inverse(c)))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f1266,plain,(
% 0.17/0.38 ~subgroup_member(inverse(b))|subgroup_member(multiply(c,inverse(c)))|~spl0_12),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f985,f596])).
% 0.17/0.38 fof(f1267,plain,(
% 0.17/0.38 ~spl0_86|spl0_105|~spl0_12),
% 0.17/0.38 inference(split_clause,[status(thm)],[f1266,f1067,f1258,f201])).
% 0.17/0.38 fof(f1268,plain,(
% 0.17/0.38 spl0_106 <=> ~subgroup_member(multiply(X0,a))|subgroup_member(multiply(X0,inverse(c)))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f1271,plain,(
% 0.17/0.38 ![X0]: (~subgroup_member(multiply(X0,a))|~subgroup_member(inverse(b))|subgroup_member(multiply(X0,inverse(c))))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f985,f38])).
% 0.17/0.38 fof(f1272,plain,(
% 0.17/0.38 spl0_106|~spl0_86),
% 0.17/0.38 inference(split_clause,[status(thm)],[f1271,f1268,f1067])).
% 0.17/0.38 fof(f1357,plain,(
% 0.17/0.38 ![X0]: (subgroup_member(d)|subgroup_member(X0)|X0=X0|subgroup_member(X0)|~spl0_34)),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f581,f23])).
% 0.17/0.38 fof(f1358,plain,(
% 0.17/0.38 spl0_6|spl0_30|~spl0_34),
% 0.17/0.38 inference(split_clause,[status(thm)],[f1357,f61,f430,f469])).
% 0.17/0.38 fof(f1361,plain,(
% 0.17/0.38 ![X0,X1,X2]: (subgroup_member(multiply(X0,X1))|subgroup_member(X2)|multiply(X0,multiply(X1,element_in_O2(multiply(X0,X1),X2)))=X2)),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f16,f23])).
% 0.17/0.38 fof(f1369,plain,(
% 0.17/0.38 subgroup_member(d)|subgroup_member(d)|multiply(d,identity)=d|~spl0_50),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f697,f23])).
% 0.17/0.38 fof(f1370,plain,(
% 0.17/0.38 spl0_6|spl0_56|~spl0_50),
% 0.17/0.38 inference(split_clause,[status(thm)],[f1369,f61,f744,f696])).
% 0.17/0.38 fof(f1577,plain,(
% 0.17/0.38 $false|~spl0_15|spl0_4),
% 0.17/0.38 inference(forward_subsumption_resolution,[status(thm)],[f55,f587])).
% 0.17/0.38 fof(f1578,plain,(
% 0.17/0.38 ~spl0_15|spl0_4),
% 0.17/0.38 inference(contradiction_clause,[status(thm)],[f1577])).
% 0.17/0.38 fof(f1674,plain,(
% 0.17/0.38 ![X0]: (multiply(c,X0)=multiply(inverse(a),multiply(d,X0)))),
% 0.17/0.38 inference(forward_demodulation,[status(thm)],[f14,f80])).
% 0.17/0.38 fof(f1702,plain,(
% 0.17/0.38 ~subgroup_member(b)|spl0_86),
% 0.17/0.38 inference(resolution,[status(thm)],[f17,f1069])).
% 0.17/0.38 fof(f1703,plain,(
% 0.17/0.38 ~spl0_2|spl0_86),
% 0.17/0.38 inference(split_clause,[status(thm)],[f1702,f47,f1067])).
% 0.17/0.38 fof(f1793,plain,(
% 0.17/0.38 spl0_132 <=> ~subgroup_member(X0)|subgroup_member(inverse(inverse(X0)))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f1796,plain,(
% 0.17/0.38 ![X0]: (~subgroup_member(X0)|~subgroup_member(identity)|subgroup_member(inverse(inverse(X0))))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f21,f359])).
% 0.17/0.38 fof(f1797,plain,(
% 0.17/0.38 spl0_132|~spl0_1),
% 0.17/0.38 inference(split_clause,[status(thm)],[f1796,f1793,f42])).
% 0.17/0.38 fof(f1798,plain,(
% 0.17/0.38 spl0_133 <=> ~subgroup_member(multiply(identity,X0))|subgroup_member(X0)),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f1801,plain,(
% 0.17/0.38 ![X0]: (~subgroup_member(identity)|~subgroup_member(multiply(identity,X0))|subgroup_member(X0))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f284,f359])).
% 0.17/0.38 fof(f1802,plain,(
% 0.17/0.38 ~spl0_1|spl0_133),
% 0.17/0.38 inference(split_clause,[status(thm)],[f1801,f42,f1798])).
% 0.17/0.38 fof(f1831,plain,(
% 0.17/0.38 spl0_137 <=> subgroup_member(inverse(identity))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f1833,plain,(
% 0.17/0.38 ~subgroup_member(inverse(identity))|spl0_137),
% 0.17/0.38 inference(component_clause,[status(thm)],[f1831])).
% 0.17/0.38 fof(f1839,plain,(
% 0.17/0.38 spl0_138 <=> subgroup_member(inverse(inverse(b)))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f1841,plain,(
% 0.17/0.38 ~subgroup_member(inverse(inverse(b)))|spl0_138),
% 0.17/0.38 inference(component_clause,[status(thm)],[f1839])).
% 0.17/0.38 fof(f1860,plain,(
% 0.17/0.38 spl0_141 <=> ~subgroup_member(inverse(inverse(X0)))|subgroup_member(X0)),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f1863,plain,(
% 0.17/0.38 ![X0]: (~subgroup_member(inverse(inverse(X0)))|~subgroup_member(identity)|subgroup_member(X0))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f15,f391])).
% 0.17/0.38 fof(f1864,plain,(
% 0.17/0.38 spl0_141|~spl0_1),
% 0.17/0.38 inference(split_clause,[status(thm)],[f1863,f1860,f42])).
% 0.17/0.38 fof(f1865,plain,(
% 0.17/0.38 spl0_142 <=> ~subgroup_member(multiply(c,X0))|subgroup_member(multiply(inverse(a),X0))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f1868,plain,(
% 0.17/0.38 ![X0]: (~subgroup_member(inverse(b))|~subgroup_member(multiply(c,X0))|subgroup_member(multiply(inverse(a),X0)))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f33,f391])).
% 0.17/0.38 fof(f1869,plain,(
% 0.17/0.38 ~spl0_86|spl0_142),
% 0.17/0.38 inference(split_clause,[status(thm)],[f1868,f1067,f1865])).
% 0.17/0.38 fof(f1882,plain,(
% 0.17/0.38 spl0_143 <=> ~subgroup_member(inverse(X0))|subgroup_member(inverse(X0))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f1885,plain,(
% 0.17/0.38 ![X0]: (~subgroup_member(inverse(X0))|~subgroup_member(identity)|subgroup_member(inverse(X0)))),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f21,f391])).
% 0.17/0.38 fof(f1886,plain,(
% 0.17/0.38 spl0_143|~spl0_1),
% 0.17/0.38 inference(split_clause,[status(thm)],[f1885,f1882,f42])).
% 0.17/0.38 fof(f2010,plain,(
% 0.17/0.38 spl0_146 <=> subgroup_member(multiply(inverse(c),multiply(b,c)))),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f2011,plain,(
% 0.17/0.38 subgroup_member(multiply(inverse(c),multiply(b,c)))|~spl0_146),
% 0.17/0.38 inference(component_clause,[status(thm)],[f2010])).
% 0.17/0.38 fof(f2013,plain,(
% 0.17/0.38 spl0_147 <=> subgroup_member(X0)|multiply(inverse(c),multiply(multiply(b,c),element_in_O2(d,X0)))=X0),
% 0.17/0.38 introduced(split_symbol_definition)).
% 0.17/0.38 fof(f2016,plain,(
% 0.17/0.38 ![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)),
% 0.17/0.38 inference(paramodulation,[status(thm)],[f912,f1361])).
% 0.17/0.38 fof(f2017,plain,(
% 0.17/0.38 spl0_146|spl0_147),
% 0.17/0.38 inference(split_clause,[status(thm)],[f2016,f2010,f2013])).
% 0.17/0.38 fof(f2096,plain,(
% 0.17/0.38 ~subgroup_member(b)|spl0_138),
% 0.17/0.38 inference(forward_demodulation,[status(thm)],[f278,f1841])).
% 0.17/0.38 fof(f2097,plain,(
% 0.17/0.38 $false|~spl0_46|spl0_138),
% 0.17/0.38 inference(forward_subsumption_resolution,[status(thm)],[f2096,f631])).
% 0.17/0.38 fof(f2098,plain,(
% 0.17/0.38 ~spl0_46|spl0_138),
% 0.17/0.38 inference(contradiction_clause,[status(thm)],[f2097])).
% 0.17/0.38 fof(f2099,plain,(
% 0.17/0.38 subgroup_member(d)|~spl0_146),
% 0.17/0.38 inference(forward_demodulation,[status(thm)],[f912,f2011])).
% 0.17/0.38 fof(f2100,plain,(
% 0.17/0.38 $false|~spl0_146),
% 0.17/0.38 inference(forward_subsumption_resolution,[status(thm)],[f2099,f27])).
% 0.17/0.38 fof(f2101,plain,(
% 0.17/0.38 ~spl0_146),
% 0.17/0.38 inference(contradiction_clause,[status(thm)],[f2100])).
% 0.17/0.38 fof(f2102,plain,(
% 0.17/0.38 ~subgroup_member(c)|spl0_81),
% 0.17/0.38 inference(resolution,[status(thm)],[f17,f971])).
% 0.17/0.38 fof(f2388,plain,(
% 0.17/0.38 subgroup_member(d)|~spl0_53),
% 0.17/0.38 inference(forward_demodulation,[status(thm)],[f278,f714])).
% 0.17/0.38 fof(f2389,plain,(
% 0.17/0.38 $false|~spl0_53),
% 0.17/0.38 inference(forward_subsumption_resolution,[status(thm)],[f2388,f27])).
% 0.17/0.38 fof(f2390,plain,(
% 0.17/0.38 ~spl0_53),
% 0.17/0.38 inference(contradiction_clause,[status(thm)],[f2389])).
% 0.17/0.38 fof(f2400,plain,(
% 0.17/0.38 spl0_153 <=> multiply(c,element_in_O2(d,X0))=multiply(inverse(a),X0)|subgroup_member(X0)),
% 0.17/0.41 introduced(split_symbol_definition)).
% 0.17/0.41 fof(f2403,plain,(
% 0.17/0.41 ![X0]: (multiply(c,element_in_O2(d,X0))=multiply(inverse(a),X0)|subgroup_member(d)|subgroup_member(X0))),
% 0.17/0.41 inference(paramodulation,[status(thm)],[f1118,f1674])).
% 0.17/0.41 fof(f2404,plain,(
% 0.17/0.41 spl0_153|spl0_6),
% 0.17/0.41 inference(split_clause,[status(thm)],[f2403,f2400,f61])).
% 0.17/0.41 fof(f2447,plain,(
% 0.17/0.41 spl0_155 <=> ~subgroup_member(multiply(X0,identity))|subgroup_member(X0)),
% 0.17/0.41 introduced(split_symbol_definition)).
% 0.17/0.41 fof(f2450,plain,(
% 0.17/0.41 ![X0]: (~subgroup_member(multiply(X0,identity))|~subgroup_member(identity)|subgroup_member(X0))),
% 0.17/0.41 inference(paramodulation,[status(thm)],[f284,f1224])).
% 0.17/0.41 fof(f2451,plain,(
% 0.17/0.41 spl0_155|~spl0_1),
% 0.17/0.41 inference(split_clause,[status(thm)],[f2450,f2447,f42])).
% 0.17/0.41 fof(f2545,plain,(
% 0.17/0.41 spl0_162 <=> multiply(c,multiply(element_in_O2(d,X0),X1))=multiply(inverse(a),multiply(X0,X1))|subgroup_member(X0)),
% 0.17/0.41 introduced(split_symbol_definition)).
% 0.17/0.41 fof(f2548,plain,(
% 0.17/0.41 ![X0,X1]: (multiply(c,multiply(element_in_O2(d,X0),X1))=multiply(inverse(a),multiply(X0,X1))|subgroup_member(d)|subgroup_member(X0))),
% 0.17/0.41 inference(paramodulation,[status(thm)],[f453,f1674])).
% 0.17/0.41 fof(f2549,plain,(
% 0.17/0.41 spl0_162|spl0_6),
% 0.17/0.41 inference(split_clause,[status(thm)],[f2548,f2545,f61])).
% 0.17/0.41 fof(f2610,plain,(
% 0.17/0.41 spl0_164 <=> ~subgroup_member(X0)|~subgroup_member(inverse(element_in_O2(d,X0)))|subgroup_member(X0)),
% 0.17/0.41 introduced(split_symbol_definition)).
% 0.17/0.41 fof(f2613,plain,(
% 0.17/0.41 ![X0]: (~subgroup_member(X0)|~subgroup_member(inverse(element_in_O2(d,X0)))|subgroup_member(d)|subgroup_member(X0)|~spl0_34)),
% 0.17/0.41 inference(paramodulation,[status(thm)],[f581,f1237])).
% 0.17/0.41 fof(f2614,plain,(
% 0.17/0.41 spl0_164|spl0_6|~spl0_34),
% 0.17/0.41 inference(split_clause,[status(thm)],[f2613,f2610,f61,f469])).
% 0.17/0.41 fof(f2629,plain,(
% 0.17/0.41 ~subgroup_member(identity)|spl0_137),
% 0.17/0.41 inference(forward_demodulation,[status(thm)],[f284,f1833])).
% 0.17/0.41 fof(f2630,plain,(
% 0.17/0.41 $false|~spl0_1|spl0_137),
% 0.17/0.41 inference(forward_subsumption_resolution,[status(thm)],[f2629,f43])).
% 0.17/0.41 fof(f2631,plain,(
% 0.17/0.41 ~spl0_1|spl0_137),
% 0.17/0.41 inference(contradiction_clause,[status(thm)],[f2630])).
% 0.17/0.41 fof(f2632,plain,(
% 0.17/0.41 ~spl0_86|spl0_47),
% 0.17/0.41 inference(split_clause,[status(thm)],[f877,f1067,f647])).
% 0.17/0.41 fof(f2634,plain,(
% 0.17/0.41 $false|spl0_81|~spl0_4),
% 0.17/0.41 inference(forward_subsumption_resolution,[status(thm)],[f54,f2102])).
% 0.17/0.41 fof(f2635,plain,(
% 0.17/0.41 spl0_81|~spl0_4),
% 0.17/0.41 inference(contradiction_clause,[status(thm)],[f2634])).
% 0.17/0.41 fof(f2726,plain,(
% 0.17/0.41 spl0_171 <=> ~subgroup_member(X0)|subgroup_member(multiply(b,X0))),
% 0.17/0.41 introduced(split_symbol_definition)).
% 0.17/0.41 fof(f2729,plain,(
% 0.17/0.41 ![X0]: (~subgroup_member(multiply(c,a))|~subgroup_member(X0)|subgroup_member(multiply(b,X0)))),
% 0.17/0.41 inference(paramodulation,[status(thm)],[f350,f38])).
% 0.17/0.41 fof(f2730,plain,(
% 0.17/0.41 ~spl0_36|spl0_171),
% 0.17/0.41 inference(split_clause,[status(thm)],[f2729,f486,f2726])).
% 0.17/0.41 fof(f3108,plain,(
% 0.17/0.41 subgroup_member(d)|subgroup_member(a)|subgroup_member(inverse(c))|~spl0_103),
% 0.17/0.41 inference(paramodulation,[status(thm)],[f1241,f22])).
% 0.17/0.41 fof(f3109,plain,(
% 0.17/0.41 spl0_6|spl0_5|spl0_81|~spl0_103),
% 0.17/0.41 inference(split_clause,[status(thm)],[f3108,f61,f58,f969,f1240])).
% 0.17/0.41 fof(f3110,plain,(
% 0.17/0.41 $false),
% 0.17/0.41 inference(sat_refutation,[status(thm)],[f57,f65,f155,f169,f180,f205,f210,f265,f270,f298,f312,f420,f473,f532,f580,f586,f598,f615,f620,f629,f651,f694,f700,f717,f857,f875,f1073,f1128,f1170,f1219,f1244,f1267,f1272,f1358,f1370,f1578,f1703,f1797,f1802,f1864,f1869,f1886,f2017,f2098,f2101,f2390,f2404,f2451,f2549,f2614,f2631,f2632,f2635,f2730,f3109])).
% 0.17/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.17/0.41 % Elapsed time: 0.088850 seconds
% 0.17/0.41 % CPU time: 0.136260 seconds
% 0.17/0.41 % Memory used: 27.164 MB
%------------------------------------------------------------------------------