%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP039-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:35:32 PM UTC 2026
% Result : Unsatisfiable 3.04s 0.88s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP039-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 19:55:34 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 3.04/0.88 % Refutation found
% 3.04/0.88 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.04/0.88 % SZS output start CNFRefutation for theBenchmark
% 3.04/0.88 fof(f1,axiom,(
% 3.04/0.88 (![X]: (product(identity,X,X) ))),
% 3.04/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.04/0.88 fof(f2,axiom,(
% 3.04/0.88 (![X]: (product(X,identity,X) ))),
% 3.04/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.04/0.88 fof(f3,axiom,(
% 3.04/0.88 (![X]: (product(inverse(X),X,identity) ))),
% 3.04/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.04/0.88 fof(f4,axiom,(
% 3.04/0.88 (![X]: (product(X,inverse(X),identity) ))),
% 3.04/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.04/0.88 fof(f5,axiom,(
% 3.04/0.88 (![X,Y]: (product(X,Y,multiply(X,Y)) ))),
% 3.04/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.04/0.88 fof(f6,axiom,(
% 3.04/0.88 (![X,Y,Z,W]: (( ~ product(X,Y,Z)| ~ product(X,Y,W)| Z = W ) ))),
% 3.04/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.04/0.88 fof(f7,axiom,(
% 3.04/0.88 (![X,Y,U,Z,V,W]: (( ~ product(X,Y,U)| ~ product(Y,Z,V)| ~ product(U,Z,W)| product(X,V,W) ) ))),
% 3.04/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.04/0.88 fof(f8,axiom,(
% 3.04/0.88 (![X,Y,U,Z,V,W]: (( ~ product(X,Y,U)| ~ product(Y,Z,V)| ~ product(X,V,W)| product(U,Z,W) ) ))),
% 3.04/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.04/0.88 fof(f9,axiom,(
% 3.04/0.88 (![X]: (( ~ subgroup_member(X)| subgroup_member(inverse(X)) ) ))),
% 3.04/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.04/0.88 fof(f10,axiom,(
% 3.04/0.88 (![A,B,C]: (( ~ subgroup_member(A)| ~ subgroup_member(B)| ~ product(A,B,C)| subgroup_member(C) ) ))),
% 3.04/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.04/0.88 fof(f11,axiom,(
% 3.04/0.88 subgroup_member(identity) ),
% 3.04/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.04/0.88 fof(f12,axiom,(
% 3.04/0.88 (![A,B]: (( subgroup_member(element_in_O2(A,B))| subgroup_member(B)| subgroup_member(A) ) ))),
% 3.04/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.04/0.88 fof(f13,axiom,(
% 3.04/0.88 (![A,B]: (( product(A,element_in_O2(A,B),B)| subgroup_member(B)| subgroup_member(A) ) ))),
% 3.04/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.04/0.88 fof(f14,negated_conjecture,(
% 3.04/0.88 subgroup_member(b) ),
% 3.04/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.04/0.88 fof(f15,negated_conjecture,(
% 3.04/0.88 product(b,inverse(a),c) ),
% 3.04/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.04/0.88 fof(f16,negated_conjecture,(
% 3.04/0.88 product(a,c,d) ),
% 3.04/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.04/0.88 fof(f17,negated_conjecture,(
% 3.04/0.88 ~ subgroup_member(d) ),
% 3.04/0.88 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 3.04/0.88 fof(f18,plain,(
% 3.04/0.88 ![X0]: (product(identity,X0,X0))),
% 3.04/0.88 inference(cnf_transformation,[status(thm)],[f1])).
% 3.04/0.88 fof(f19,plain,(
% 3.04/0.88 ![X0]: (product(X0,identity,X0))),
% 3.04/0.88 inference(cnf_transformation,[status(thm)],[f2])).
% 3.04/0.88 fof(f20,plain,(
% 3.04/0.88 ![X0]: (product(inverse(X0),X0,identity))),
% 3.04/0.88 inference(cnf_transformation,[status(thm)],[f3])).
% 3.04/0.88 fof(f21,plain,(
% 3.04/0.88 ![X0]: (product(X0,inverse(X0),identity))),
% 3.04/0.88 inference(cnf_transformation,[status(thm)],[f4])).
% 3.04/0.88 fof(f22,plain,(
% 3.04/0.88 ![X0,X1]: (product(X0,X1,multiply(X0,X1)))),
% 3.04/0.88 inference(cnf_transformation,[status(thm)],[f5])).
% 3.04/0.88 fof(f23,plain,(
% 3.04/0.88 ![Z,W]: ((![X,Y]: (~product(X,Y,Z)|~product(X,Y,W)))|Z=W)),
% 3.04/0.88 inference(miniscoping,[status(thm)],[f6])).
% 3.04/0.88 fof(f24,plain,(
% 3.04/0.88 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|X2=X3)),
% 3.04/0.88 inference(cnf_transformation,[status(thm)],[f23])).
% 3.04/0.88 fof(f25,plain,(
% 3.04/0.88 ![X,V,W]: ((![U,Z]: ((![Y]: (~product(X,Y,U)|~product(Y,Z,V)))|~product(U,Z,W)))|product(X,V,W))),
% 3.04/0.88 inference(miniscoping,[status(thm)],[f7])).
% 3.04/0.88 fof(f26,plain,(
% 3.04/0.88 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~product(X1,X3,X4)|~product(X2,X3,X5)|product(X0,X4,X5))),
% 3.04/0.88 inference(cnf_transformation,[status(thm)],[f25])).
% 3.04/0.88 fof(f27,plain,(
% 3.04/0.88 ![U,Z,W]: ((![X,V]: ((![Y]: (~product(X,Y,U)|~product(Y,Z,V)))|~product(X,V,W)))|product(U,Z,W))),
% 3.04/0.88 inference(miniscoping,[status(thm)],[f8])).
% 3.04/0.88 fof(f28,plain,(
% 3.04/0.88 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~product(X1,X3,X4)|~product(X0,X4,X5)|product(X2,X3,X5))),
% 3.04/0.88 inference(cnf_transformation,[status(thm)],[f27])).
% 3.04/0.88 fof(f29,plain,(
% 3.04/0.88 ![X0]: (~subgroup_member(X0)|subgroup_member(inverse(X0)))),
% 3.04/0.88 inference(cnf_transformation,[status(thm)],[f9])).
% 3.04/0.88 fof(f30,plain,(
% 3.04/0.88 ![C]: ((![A,B]: ((~subgroup_member(A)|~subgroup_member(B))|~product(A,B,C)))|subgroup_member(C))),
% 3.04/0.88 inference(miniscoping,[status(thm)],[f10])).
% 3.04/0.88 fof(f31,plain,(
% 3.04/0.88 ![X0,X1,X2]: (~subgroup_member(X0)|~subgroup_member(X1)|~product(X0,X1,X2)|subgroup_member(X2))),
% 3.04/0.88 inference(cnf_transformation,[status(thm)],[f30])).
% 3.04/0.88 fof(f32,plain,(
% 3.04/0.88 subgroup_member(identity)),
% 3.04/0.88 inference(cnf_transformation,[status(thm)],[f11])).
% 3.04/0.88 fof(f33,plain,(
% 3.04/0.88 ![A]: ((![B]: (subgroup_member(element_in_O2(A,B))|subgroup_member(B)))|subgroup_member(A))),
% 3.04/0.88 inference(miniscoping,[status(thm)],[f12])).
% 3.04/0.88 fof(f34,plain,(
% 3.04/0.88 ![X0,X1]: (subgroup_member(element_in_O2(X0,X1))|subgroup_member(X1)|subgroup_member(X0))),
% 3.04/0.88 inference(cnf_transformation,[status(thm)],[f33])).
% 3.04/0.88 fof(f35,plain,(
% 3.04/0.88 ![A]: ((![B]: (product(A,element_in_O2(A,B),B)|subgroup_member(B)))|subgroup_member(A))),
% 3.04/0.88 inference(miniscoping,[status(thm)],[f13])).
% 3.04/0.88 fof(f36,plain,(
% 3.04/0.88 ![X0,X1]: (product(X0,element_in_O2(X0,X1),X1)|subgroup_member(X1)|subgroup_member(X0))),
% 3.04/0.88 inference(cnf_transformation,[status(thm)],[f35])).
% 3.04/0.88 fof(f37,plain,(
% 3.04/0.88 subgroup_member(b)),
% 3.04/0.88 inference(cnf_transformation,[status(thm)],[f14])).
% 3.04/0.88 fof(f38,plain,(
% 3.04/0.88 product(b,inverse(a),c)),
% 3.04/0.88 inference(cnf_transformation,[status(thm)],[f15])).
% 3.04/0.88 fof(f39,plain,(
% 3.04/0.88 product(a,c,d)),
% 3.04/0.88 inference(cnf_transformation,[status(thm)],[f16])).
% 3.04/0.88 fof(f40,plain,(
% 3.04/0.88 ~subgroup_member(d)),
% 3.04/0.88 inference(cnf_transformation,[status(thm)],[f17])).
% 3.04/0.88 fof(f41,plain,(
% 3.04/0.88 ![X0,X1]: (~product(inverse(X0),X0,X1)|identity=X1)),
% 3.04/0.88 inference(resolution,[status(thm)],[f24,f20])).
% 3.04/0.88 fof(f42,plain,(
% 3.04/0.88 ![X0]: (~product(a,c,X0)|d=X0)),
% 3.04/0.88 inference(resolution,[status(thm)],[f24,f39])).
% 3.04/0.88 fof(f45,plain,(
% 3.04/0.88 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(identity,X1,X3)|product(inverse(X0),X2,X3))),
% 3.04/0.88 inference(resolution,[status(thm)],[f26,f20])).
% 3.04/0.88 fof(f46,plain,(
% 3.04/0.88 ![X0,X1,X2]: (~product(c,X0,X1)|~product(d,X0,X2)|product(a,X1,X2))),
% 3.04/0.88 inference(resolution,[status(thm)],[f26,f39])).
% 3.04/0.88 fof(f47,plain,(
% 3.04/0.88 ![X0,X1,X2]: (~product(inverse(a),X0,X1)|~product(c,X0,X2)|product(b,X1,X2))),
% 3.04/0.88 inference(resolution,[status(thm)],[f26,f38])).
% 3.04/0.88 fof(f48,plain,(
% 3.04/0.88 ![X0,X1,X2,X3]: (~product(inverse(X0),X1,X2)|~product(identity,X1,X3)|product(X0,X2,X3))),
% 3.04/0.88 inference(resolution,[status(thm)],[f26,f21])).
% 3.04/0.88 fof(f49,plain,(
% 3.04/0.88 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(inverse(X0),X2,X3)|product(identity,X1,X3))),
% 3.04/0.88 inference(resolution,[status(thm)],[f28,f20])).
% 3.04/0.88 fof(f50,plain,(
% 3.04/0.88 ![X0,X1,X2]: (~product(c,X0,X1)|~product(a,X1,X2)|product(d,X0,X2))),
% 3.04/0.88 inference(resolution,[status(thm)],[f28,f39])).
% 3.04/0.88 fof(f51,plain,(
% 3.04/0.88 ![X0,X1,X2]: (~product(inverse(a),X0,X1)|~product(b,X1,X2)|product(c,X0,X2))),
% 3.04/0.88 inference(resolution,[status(thm)],[f28,f38])).
% 3.04/0.88 fof(f52,plain,(
% 3.04/0.88 ![X0,X1,X2,X3]: (~product(inverse(X0),X1,X2)|~product(X0,X2,X3)|product(identity,X1,X3))),
% 3.04/0.88 inference(resolution,[status(thm)],[f28,f21])).
% 3.04/0.88 fof(f54,plain,(
% 3.04/0.88 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|product(identity,X2,X3))),
% 3.04/0.88 inference(resolution,[status(thm)],[f18,f26])).
% 3.04/0.88 fof(f58,plain,(
% 3.04/0.88 ![X0,X1]: (~product(X0,identity,X1)|X0=X1)),
% 3.04/0.88 inference(resolution,[status(thm)],[f19,f24])).
% 3.04/0.88 fof(f59,plain,(
% 3.04/0.88 ![X0,X1,X2,X3,X4]: (~product(X0,X1,X2)|~product(X3,X2,X4)|product(multiply(X3,X0),X1,X4))),
% 3.04/0.88 inference(resolution,[status(thm)],[f22,f28])).
% 3.04/0.88 fof(f60,plain,(
% 3.04/0.88 ![X0,X1,X2,X3,X4]: (~product(X0,X1,X2)|~product(multiply(X3,X0),X1,X4)|product(X3,X2,X4))),
% 3.04/0.88 inference(resolution,[status(thm)],[f22,f26])).
% 3.04/0.88 fof(f61,plain,(
% 3.04/0.88 ![X0,X1,X2]: (~product(X0,X1,X2)|multiply(X0,X1)=X2)),
% 3.04/0.88 inference(resolution,[status(thm)],[f22,f24])).
% 3.04/0.88 fof(f64,plain,(
% 3.04/0.88 ![X0]: (~subgroup_member(identity)|~subgroup_member(X0)|subgroup_member(X0))),
% 3.04/0.88 inference(resolution,[status(thm)],[f31,f18])).
% 3.04/0.88 fof(f66,plain,(
% 3.04/0.88 ~subgroup_member(a)|~subgroup_member(c)|subgroup_member(d)),
% 3.04/0.88 inference(resolution,[status(thm)],[f31,f39])).
% 3.04/0.88 fof(f67,plain,(
% 3.04/0.88 ~subgroup_member(b)|~subgroup_member(inverse(a))|subgroup_member(c)),
% 3.04/0.88 inference(resolution,[status(thm)],[f31,f38])).
% 3.04/0.88 fof(f70,plain,(
% 3.04/0.88 ![X0,X1]: (~subgroup_member(X0)|~subgroup_member(X1)|subgroup_member(multiply(X0,X1)))),
% 3.04/0.88 inference(resolution,[status(thm)],[f31,f22])).
% 3.04/0.88 fof(f71,definition,(
% 3.04/0.88 sQ0_spl <=> (subgroup_member(identity))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f74,definition,(
% 3.04/0.88 ![X0]: (sQ1_spl <=> (~subgroup_member(X0)|subgroup_member(X0)))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f77,plain,(
% 3.04/0.88 ~sQ0_spl|sQ1_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f64,f71,f74])).
% 3.04/0.88 fof(f78,definition,(
% 3.04/0.88 ![X0]: (sQ2_spl <=> (~subgroup_member(inverse(X0))|~subgroup_member(X0)))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f79,plain,(
% 3.04/0.88 ![X0]: (~subgroup_member(inverse(X0))|~subgroup_member(X0)|~sQ2_spl)),
% 3.04/0.88 inference(component_clause,[status(thm)],[f78])).
% 3.04/0.88 fof(f82,definition,(
% 3.04/0.88 sQ3_spl <=> (subgroup_member(a))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f83,plain,(
% 3.04/0.88 subgroup_member(a)|~sQ3_spl),
% 3.04/0.88 inference(component_clause,[status(thm)],[f82])).
% 3.04/0.88 fof(f84,plain,(
% 3.04/0.88 ~subgroup_member(a)|sQ3_spl),
% 3.04/0.88 inference(component_clause,[status(thm)],[f82])).
% 3.04/0.88 fof(f85,definition,(
% 3.04/0.88 sQ4_spl <=> (subgroup_member(c))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f86,plain,(
% 3.04/0.88 subgroup_member(c)|~sQ4_spl),
% 3.04/0.88 inference(component_clause,[status(thm)],[f85])).
% 3.04/0.88 fof(f88,definition,(
% 3.04/0.88 sQ5_spl <=> (subgroup_member(d))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f89,plain,(
% 3.04/0.88 subgroup_member(d)|~sQ5_spl),
% 3.04/0.88 inference(component_clause,[status(thm)],[f88])).
% 3.04/0.88 fof(f91,plain,(
% 3.04/0.88 ~sQ3_spl|~sQ4_spl|sQ5_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f66,f82,f85,f88])).
% 3.04/0.88 fof(f92,definition,(
% 3.04/0.88 sQ6_spl <=> (subgroup_member(b))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f94,plain,(
% 3.04/0.88 ~subgroup_member(b)|sQ6_spl),
% 3.04/0.88 inference(component_clause,[status(thm)],[f92])).
% 3.04/0.88 fof(f95,definition,(
% 3.04/0.88 sQ7_spl <=> (subgroup_member(inverse(a)))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f96,plain,(
% 3.04/0.88 subgroup_member(inverse(a))|~sQ7_spl),
% 3.04/0.88 inference(component_clause,[status(thm)],[f95])).
% 3.04/0.88 fof(f98,plain,(
% 3.04/0.88 ~sQ6_spl|~sQ7_spl|sQ4_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f67,f92,f95,f85])).
% 3.04/0.88 fof(f101,plain,(
% 3.04/0.88 ![X0]: (~subgroup_member(X0)|~sQ2_spl)),
% 3.04/0.88 inference(forward_subsumption_resolution,[status(thm)],[f79,f29])).
% 3.04/0.88 fof(f102,plain,(
% 3.04/0.88 $false|sQ6_spl),
% 3.04/0.88 inference(forward_subsumption_resolution,[status(thm)],[f94,f37])).
% 3.04/0.88 fof(f103,plain,(
% 3.04/0.88 sQ6_spl),
% 3.04/0.88 inference(contradiction_clause,[status(thm)],[f102])).
% 3.04/0.88 fof(f104,plain,(
% 3.04/0.88 $false|~sQ5_spl),
% 3.04/0.88 inference(forward_subsumption_resolution,[status(thm)],[f89,f40])).
% 3.04/0.88 fof(f105,plain,(
% 3.04/0.88 ~sQ5_spl),
% 3.04/0.88 inference(contradiction_clause,[status(thm)],[f104])).
% 3.04/0.88 fof(f106,plain,(
% 3.04/0.88 ![X0,X1]: (subgroup_member(X0)|subgroup_member(X1)|subgroup_member(inverse(element_in_O2(X1,X0))))),
% 3.04/0.88 inference(resolution,[status(thm)],[f34,f29])).
% 3.04/0.88 fof(f108,plain,(
% 3.04/0.88 ![X0,X1,X2,X3,X4]: (subgroup_member(X0)|subgroup_member(X1)|~product(element_in_O2(X1,X0),X2,X3)|~product(X1,X3,X4)|product(X0,X2,X4))),
% 3.04/0.88 inference(resolution,[status(thm)],[f36,f28])).
% 3.04/0.88 fof(f109,plain,(
% 3.04/0.88 ![X0,X1,X2,X3,X4]: (subgroup_member(X0)|subgroup_member(X1)|~product(element_in_O2(X1,X0),X2,X3)|~product(X0,X2,X4)|product(X1,X3,X4))),
% 3.04/0.88 inference(resolution,[status(thm)],[f36,f26])).
% 3.04/0.88 fof(f110,plain,(
% 3.04/0.88 ![X0,X1,X2]: (subgroup_member(X0)|subgroup_member(X1)|~product(X1,element_in_O2(X1,X0),X2)|X0=X2)),
% 3.04/0.88 inference(resolution,[status(thm)],[f36,f24])).
% 3.04/0.88 fof(f120,plain,(
% 3.04/0.88 $false|~sQ2_spl),
% 3.04/0.88 inference(backward_subsumption_resolution,[status(thm)],[f32,f101])).
% 3.04/0.88 fof(f124,plain,(
% 3.04/0.88 ~sQ2_spl),
% 3.04/0.88 inference(contradiction_clause,[status(thm)],[f120])).
% 3.04/0.88 fof(f150,plain,(
% 3.04/0.88 ![X0,X1]: (~product(identity,X0,X1)|product(inverse(inverse(X0)),identity,X1))),
% 3.04/0.88 inference(resolution,[status(thm)],[f45,f20])).
% 3.04/0.88 fof(f151,plain,(
% 3.04/0.88 ![X0]: (~product(identity,c,X0)|product(inverse(a),d,X0))),
% 3.04/0.88 inference(resolution,[status(thm)],[f45,f39])).
% 3.04/0.88 fof(f153,plain,(
% 3.04/0.88 ![X0,X1,X2]: (~product(identity,element_in_O2(X0,X1),X2)|product(inverse(X0),X1,X2)|subgroup_member(X1)|subgroup_member(X0))),
% 3.04/0.88 inference(resolution,[status(thm)],[f45,f36])).
% 3.04/0.88 fof(f156,plain,(
% 3.04/0.88 ![X0,X1,X2]: (~product(identity,X0,X1)|product(inverse(X2),multiply(X2,X0),X1))),
% 3.04/0.88 inference(resolution,[status(thm)],[f45,f22])).
% 3.04/0.88 fof(f160,plain,(
% 3.04/0.88 ![X0,X1]: (~product(d,X0,X1)|product(a,multiply(c,X0),X1))),
% 3.04/0.88 inference(resolution,[status(thm)],[f46,f22])).
% 3.04/0.88 fof(f169,plain,(
% 3.04/0.88 ![X0,X1]: (~product(c,X0,X1)|product(b,multiply(inverse(a),X0),X1))),
% 3.04/0.88 inference(resolution,[status(thm)],[f47,f22])).
% 3.04/0.88 fof(f174,plain,(
% 3.04/0.88 subgroup_member(inverse(c))|~sQ4_spl),
% 3.04/0.88 inference(resolution,[status(thm)],[f86,f29])).
% 3.04/0.88 fof(f177,plain,(
% 3.04/0.88 ![X0]: (~product(a,identity,X0)|product(d,inverse(c),X0))),
% 3.04/0.88 inference(resolution,[status(thm)],[f50,f21])).
% 3.04/0.88 fof(f178,plain,(
% 3.04/0.88 ![X0,X1]: (~product(a,multiply(c,X0),X1)|product(d,X0,X1))),
% 3.04/0.88 inference(resolution,[status(thm)],[f50,f22])).
% 3.04/0.88 fof(f183,plain,(
% 3.04/0.88 ![X0]: (~product(b,identity,X0)|product(c,a,X0))),
% 3.04/0.88 inference(resolution,[status(thm)],[f51,f20])).
% 3.04/0.88 fof(f199,plain,(
% 3.04/0.88 ![X0,X1,X2]: (~product(identity,element_in_O2(inverse(X0),X1),X2)|product(X0,X1,X2)|subgroup_member(X1)|subgroup_member(inverse(X0)))),
% 3.04/0.88 inference(resolution,[status(thm)],[f48,f36])).
% 3.04/0.88 fof(f208,plain,(
% 3.04/0.88 ![X0,X1,X2]: (~product(inverse(X0),X1,X2)|product(identity,element_in_O2(X0,X1),X2)|subgroup_member(X1)|subgroup_member(X0))),
% 3.04/0.88 inference(resolution,[status(thm)],[f49,f36])).
% 3.04/0.88 fof(f213,plain,(
% 3.04/0.88 ![X0,X1,X2]: (~product(X0,X1,X2)|product(identity,element_in_O2(inverse(X0),X1),X2)|subgroup_member(X1)|subgroup_member(inverse(X0)))),
% 3.04/0.88 inference(resolution,[status(thm)],[f52,f36])).
% 3.04/0.88 fof(f231,plain,(
% 3.04/0.88 ![X0,X1,X2]: (~product(X0,element_in_O2(X0,X1),X2)|product(identity,X1,X2)|subgroup_member(X1)|subgroup_member(X0))),
% 3.04/0.88 inference(resolution,[status(thm)],[f54,f36])).
% 3.04/0.88 fof(f268,plain,(
% 3.04/0.88 ![X0,X1]: (~product(X0,d,X1)|product(multiply(X0,a),c,X1))),
% 3.04/0.88 inference(resolution,[status(thm)],[f59,f39])).
% 3.04/0.88 fof(f270,plain,(
% 3.04/0.88 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|product(multiply(X0,X3),element_in_O2(X3,X1),X2)|subgroup_member(X1)|subgroup_member(X3))),
% 3.04/0.88 inference(resolution,[status(thm)],[f59,f36])).
% 3.04/0.88 fof(f285,plain,(
% 3.04/0.88 ![X0,X1,X2,X3]: (~product(multiply(X0,X1),element_in_O2(X1,X2),X3)|product(X0,X2,X3)|subgroup_member(X2)|subgroup_member(X1))),
% 3.04/0.88 inference(resolution,[status(thm)],[f60,f36])).
% 3.04/0.88 fof(f302,plain,(
% 3.04/0.88 ![X0]: (~subgroup_member(X0)|subgroup_member(multiply(b,X0)))),
% 3.04/0.88 inference(resolution,[status(thm)],[f70,f37])).
% 3.04/0.88 fof(f316,plain,(
% 3.04/0.88 ![X0,X1,X2]: (subgroup_member(X0)|subgroup_member(X1)|~product(X1,element_in_O2(X1,X0),X2)|product(X0,identity,X2))),
% 3.04/0.88 inference(resolution,[status(thm)],[f108,f19])).
% 3.04/0.88 fof(f317,plain,(
% 3.04/0.88 ![X0,X1,X2]: (subgroup_member(X0)|subgroup_member(X1)|~product(X1,identity,X2)|product(X0,inverse(element_in_O2(X1,X0)),X2))),
% 3.04/0.88 inference(resolution,[status(thm)],[f108,f21])).
% 3.04/0.88 fof(f318,plain,(
% 3.04/0.88 ![X0,X1,X2,X3]: (subgroup_member(X0)|subgroup_member(X1)|~product(X1,multiply(element_in_O2(X1,X0),X2),X3)|product(X0,X2,X3))),
% 3.04/0.88 inference(resolution,[status(thm)],[f108,f22])).
% 3.04/0.88 fof(f320,plain,(
% 3.04/0.88 ![X0,X1,X2]: (subgroup_member(X0)|subgroup_member(X1)|~product(X0,identity,X2)|product(X1,element_in_O2(X1,X0),X2))),
% 3.04/0.88 inference(resolution,[status(thm)],[f109,f19])).
% 3.04/0.88 fof(f321,plain,(
% 3.04/0.88 ![X0,X1,X2]: (subgroup_member(X0)|subgroup_member(X1)|~product(X0,inverse(element_in_O2(X1,X0)),X2)|product(X1,identity,X2))),
% 3.04/0.88 inference(resolution,[status(thm)],[f109,f21])).
% 3.04/0.88 fof(f322,plain,(
% 3.04/0.88 ![X0,X1,X2,X3]: (subgroup_member(X0)|subgroup_member(X1)|~product(X0,X2,X3)|product(X1,multiply(element_in_O2(X1,X0),X2),X3))),
% 3.04/0.88 inference(resolution,[status(thm)],[f109,f22])).
% 3.04/0.88 fof(f336,plain,(
% 3.04/0.88 product(inverse(a),d,c)),
% 3.04/0.88 inference(resolution,[status(thm)],[f151,f18])).
% 3.04/0.88 fof(f344,plain,(
% 3.04/0.88 ![X0]: (product(inverse(inverse(X0)),identity,X0))),
% 3.04/0.88 inference(resolution,[status(thm)],[f150,f18])).
% 3.04/0.88 fof(f359,plain,(
% 3.04/0.88 ![X0,X1]: (product(inverse(X0),X1,element_in_O2(X0,X1))|subgroup_member(X1)|subgroup_member(X0))),
% 3.04/0.88 inference(resolution,[status(thm)],[f153,f18])).
% 3.04/0.88 fof(f377,plain,(
% 3.04/0.88 ![X0,X1]: (product(inverse(X0),multiply(X0,X1),X1))),
% 3.04/0.88 inference(resolution,[status(thm)],[f156,f18])).
% 3.04/0.88 fof(f405,plain,(
% 3.04/0.88 ![X0]: (product(a,multiply(c,element_in_O2(d,X0)),X0)|subgroup_member(X0)|subgroup_member(d))),
% 3.04/0.88 inference(resolution,[status(thm)],[f160,f36])).
% 3.04/0.88 fof(f409,definition,(
% 3.04/0.88 ![X0]: (sQ20_spl <=> (product(a,multiply(c,element_in_O2(d,X0)),X0)|subgroup_member(X0)))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f410,plain,(
% 3.04/0.88 ![X0]: (product(a,multiply(c,element_in_O2(d,X0)),X0)|subgroup_member(X0)|~sQ20_spl)),
% 3.04/0.88 inference(component_clause,[status(thm)],[f409])).
% 3.04/0.88 fof(f412,plain,(
% 3.04/0.88 sQ20_spl|sQ5_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f405,f409,f88])).
% 3.04/0.88 fof(f428,plain,(
% 3.04/0.88 ![X0]: (product(b,multiply(inverse(a),X0),multiply(c,X0)))),
% 3.04/0.88 inference(resolution,[status(thm)],[f169,f22])).
% 3.04/0.88 fof(f438,plain,(
% 3.04/0.88 ![X0,X1]: (subgroup_member(multiply(b,element_in_O2(X0,X1)))|subgroup_member(X1)|subgroup_member(X0))),
% 3.04/0.88 inference(resolution,[status(thm)],[f302,f34])).
% 3.04/0.88 fof(f441,plain,(
% 3.04/0.88 ![X0,X1]: (subgroup_member(multiply(b,inverse(element_in_O2(X0,X1))))|subgroup_member(X1)|subgroup_member(X0))),
% 3.04/0.88 inference(resolution,[status(thm)],[f302,f106])).
% 3.04/0.88 fof(f459,plain,(
% 3.04/0.88 product(d,inverse(c),a)),
% 3.04/0.88 inference(resolution,[status(thm)],[f177,f19])).
% 3.04/0.88 fof(f462,plain,(
% 3.04/0.88 ![X0]: (product(d,X0,multiply(a,multiply(c,X0))))),
% 3.04/0.88 inference(resolution,[status(thm)],[f178,f22])).
% 3.04/0.88 fof(f465,plain,(
% 3.04/0.88 product(c,a,b)),
% 3.04/0.88 inference(resolution,[status(thm)],[f183,f19])).
% 3.04/0.88 fof(f478,plain,(
% 3.04/0.88 multiply(c,a)=b),
% 3.04/0.88 inference(resolution,[status(thm)],[f465,f61])).
% 3.04/0.88 fof(f530,plain,(
% 3.04/0.88 ![X0,X1]: (product(X0,X1,element_in_O2(inverse(X0),X1))|subgroup_member(X1)|subgroup_member(inverse(X0)))),
% 3.04/0.88 inference(resolution,[status(thm)],[f199,f18])).
% 3.04/0.88 fof(f537,definition,(
% 3.04/0.88 sQ29_spl <=> (subgroup_member(inverse(identity)))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f559,plain,(
% 3.04/0.88 multiply(inverse(a),d)=c),
% 3.04/0.88 inference(resolution,[status(thm)],[f336,f61])).
% 3.04/0.88 fof(f592,plain,(
% 3.04/0.88 ![X0]: (product(identity,element_in_O2(X0,X0),identity)|subgroup_member(X0)|subgroup_member(X0))),
% 3.04/0.88 inference(resolution,[status(thm)],[f208,f20])).
% 3.04/0.88 fof(f596,plain,(
% 3.04/0.88 ![X0,X1]: (product(identity,element_in_O2(X0,X1),multiply(inverse(X0),X1))|subgroup_member(X1)|subgroup_member(X0))),
% 3.04/0.88 inference(resolution,[status(thm)],[f208,f22])).
% 3.04/0.88 fof(f602,plain,(
% 3.04/0.88 ![X0]: (product(identity,element_in_O2(X0,X0),identity)|subgroup_member(X0))),
% 3.04/0.88 inference(duplicate_literals_removal,[status(thm)],[f592])).
% 3.04/0.88 fof(f631,plain,(
% 3.04/0.88 ![X0]: (inverse(inverse(X0))=X0)),
% 3.04/0.88 inference(resolution,[status(thm)],[f344,f58])).
% 3.04/0.88 fof(f639,plain,(
% 3.04/0.88 ![X0]: (~subgroup_member(inverse(inverse(X0)))|~subgroup_member(identity)|subgroup_member(X0))),
% 3.04/0.88 inference(resolution,[status(thm)],[f344,f31])).
% 3.04/0.88 fof(f649,definition,(
% 3.04/0.88 ![X0]: (sQ35_spl <=> (~subgroup_member(inverse(inverse(X0)))|subgroup_member(X0)))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f652,plain,(
% 3.04/0.88 sQ35_spl|~sQ0_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f639,f649,f71])).
% 3.04/0.88 fof(f691,definition,(
% 3.04/0.88 sQ37_spl <=> (subgroup_member(inverse(c)))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f693,plain,(
% 3.04/0.88 ~subgroup_member(inverse(c))|sQ37_spl),
% 3.04/0.88 inference(component_clause,[status(thm)],[f691])).
% 3.04/0.88 fof(f749,plain,(
% 3.04/0.88 subgroup_member(inverse(inverse(a)))|~sQ7_spl),
% 3.04/0.88 inference(resolution,[status(thm)],[f96,f29])).
% 3.04/0.88 fof(f751,plain,(
% 3.04/0.88 subgroup_member(a)|~sQ7_spl),
% 3.04/0.88 inference(forward_demodulation,[status(thm)],[f631,f749])).
% 3.04/0.88 fof(f752,plain,(
% 3.04/0.88 $false|sQ3_spl|~sQ7_spl),
% 3.04/0.88 inference(forward_subsumption_resolution,[status(thm)],[f751,f84])).
% 3.04/0.88 fof(f753,plain,(
% 3.04/0.88 sQ3_spl|~sQ7_spl),
% 3.04/0.88 inference(contradiction_clause,[status(thm)],[f752])).
% 3.04/0.88 fof(f821,plain,(
% 3.04/0.88 product(inverse(c),b,a)),
% 3.04/0.88 inference(paramodulation,[status(thm)],[f478,f377])).
% 3.04/0.88 fof(f1010,plain,(
% 3.04/0.88 ![X0]: (product(multiply(inverse(a),X0),element_in_O2(X0,d),c)|subgroup_member(d)|subgroup_member(X0))),
% 3.04/0.88 inference(resolution,[status(thm)],[f270,f336])).
% 3.04/0.88 fof(f1024,definition,(
% 3.04/0.88 ![X0]: (sQ50_spl <=> (product(multiply(inverse(a),X0),element_in_O2(X0,d),c)|subgroup_member(X0)))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f1027,plain,(
% 3.04/0.88 sQ50_spl|sQ5_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f1010,f1024,f88])).
% 3.04/0.88 fof(f1235,plain,(
% 3.04/0.88 ![X0,X1]: (~product(c,element_in_O2(d,X0),X1)|product(inverse(a),X0,X1)|subgroup_member(X0)|subgroup_member(d))),
% 3.04/0.88 inference(paramodulation,[status(thm)],[f559,f285])).
% 3.04/0.88 fof(f1241,definition,(
% 3.04/0.88 ![X0,X1]: (sQ56_spl <=> (~product(c,element_in_O2(d,X0),X1)|product(inverse(a),X0,X1)|subgroup_member(X0)))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f1244,plain,(
% 3.04/0.88 sQ56_spl|sQ5_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f1235,f1241,f88])).
% 3.04/0.88 fof(f1383,plain,(
% 3.04/0.88 ![X0]: (subgroup_member(d)|subgroup_member(X0)|product(X0,multiply(element_in_O2(X0,d),inverse(c)),a))),
% 3.04/0.88 inference(resolution,[status(thm)],[f322,f459])).
% 3.04/0.88 fof(f1396,definition,(
% 3.04/0.88 ![X0]: (sQ63_spl <=> (subgroup_member(X0)|product(X0,multiply(element_in_O2(X0,d),inverse(c)),a)))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f1399,plain,(
% 3.04/0.88 sQ5_spl|sQ63_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f1383,f88,f1396])).
% 3.04/0.88 fof(f1446,plain,(
% 3.04/0.88 ~subgroup_member(inverse(c))|~subgroup_member(b)|subgroup_member(a)),
% 3.04/0.88 inference(resolution,[status(thm)],[f821,f31])).
% 3.04/0.88 fof(f1466,plain,(
% 3.04/0.88 ~sQ37_spl|~sQ6_spl|sQ3_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f1446,f691,f92,f82])).
% 3.04/0.88 fof(f1469,plain,(
% 3.04/0.88 $false|~sQ4_spl|sQ37_spl),
% 3.04/0.88 inference(forward_subsumption_resolution,[status(thm)],[f693,f174])).
% 3.04/0.88 fof(f1470,plain,(
% 3.04/0.88 ~sQ4_spl|sQ37_spl),
% 3.04/0.88 inference(contradiction_clause,[status(thm)],[f1469])).
% 3.04/0.88 fof(f1480,plain,(
% 3.04/0.88 subgroup_member(inverse(a))|~sQ3_spl),
% 3.04/0.88 inference(resolution,[status(thm)],[f83,f29])).
% 3.04/0.88 fof(f1481,plain,(
% 3.04/0.88 sQ7_spl|~sQ3_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f1480,f95,f82])).
% 3.04/0.88 fof(f1507,definition,(
% 3.04/0.88 sQ72_spl <=> (subgroup_member(inverse(d)))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f1508,plain,(
% 3.04/0.88 subgroup_member(inverse(d))|~sQ72_spl),
% 3.04/0.88 inference(component_clause,[status(thm)],[f1507])).
% 3.04/0.88 fof(f1855,plain,(
% 3.04/0.88 ![X0]: (subgroup_member(X0)|subgroup_member(X0)|identity=element_in_O2(X0,X0))),
% 3.04/0.88 inference(resolution,[status(thm)],[f359,f41])).
% 3.04/0.88 fof(f1860,plain,(
% 3.04/0.88 ![X0]: (subgroup_member(d)|subgroup_member(X0)|product(multiply(inverse(X0),a),c,element_in_O2(X0,d)))),
% 3.04/0.88 inference(resolution,[status(thm)],[f359,f268])).
% 3.04/0.88 fof(f1906,plain,(
% 3.04/0.88 ![X0]: (subgroup_member(X0)|identity=element_in_O2(X0,X0))),
% 3.04/0.88 inference(duplicate_literals_removal,[status(thm)],[f1855])).
% 3.04/0.88 fof(f1911,definition,(
% 3.04/0.88 ![X0]: (sQ91_spl <=> (subgroup_member(X0)|product(multiply(inverse(X0),a),c,element_in_O2(X0,d))))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f1914,plain,(
% 3.04/0.88 sQ5_spl|sQ91_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f1860,f88,f1911])).
% 3.04/0.88 fof(f2001,plain,(
% 3.04/0.88 identity=element_in_O2(d,d)),
% 3.04/0.88 inference(resolution,[status(thm)],[f1906,f40])).
% 3.04/0.88 fof(f2210,plain,(
% 3.04/0.88 product(a,multiply(c,identity),d)|subgroup_member(d)|~sQ20_spl),
% 3.04/0.88 inference(paramodulation,[status(thm)],[f2001,f410])).
% 3.04/0.88 fof(f2211,plain,(
% 3.04/0.88 product(inverse(d),d,identity)|subgroup_member(d)|subgroup_member(d)),
% 3.04/0.88 inference(paramodulation,[status(thm)],[f2001,f359])).
% 3.04/0.88 fof(f2212,plain,(
% 3.04/0.88 ![X0]: (~product(identity,identity,X0)|product(inverse(d),d,X0)|subgroup_member(d)|subgroup_member(d))),
% 3.04/0.88 inference(paramodulation,[status(thm)],[f2001,f153])).
% 3.04/0.88 fof(f2213,plain,(
% 3.04/0.88 ![X0]: (~product(d,identity,X0)|product(identity,d,X0)|subgroup_member(d)|subgroup_member(d))),
% 3.04/0.88 inference(paramodulation,[status(thm)],[f2001,f231])).
% 3.04/0.88 fof(f2214,plain,(
% 3.04/0.88 ![X0]: (subgroup_member(d)|subgroup_member(d)|~product(d,inverse(identity),X0)|product(d,identity,X0))),
% 3.04/0.88 inference(paramodulation,[status(thm)],[f2001,f321])).
% 3.04/0.88 fof(f2215,plain,(
% 3.04/0.88 ![X0,X1]: (subgroup_member(d)|subgroup_member(d)|~product(d,multiply(identity,X0),X1)|product(d,X0,X1))),
% 3.04/0.88 inference(paramodulation,[status(thm)],[f2001,f318])).
% 3.04/0.88 fof(f2216,plain,(
% 3.04/0.88 ![X0]: (subgroup_member(d)|subgroup_member(d)|~product(d,identity,X0)|product(d,identity,X0))),
% 3.04/0.88 inference(paramodulation,[status(thm)],[f2001,f316])).
% 3.04/0.88 fof(f2217,plain,(
% 3.04/0.88 ![X0,X1]: (~product(multiply(X0,d),identity,X1)|product(X0,d,X1)|subgroup_member(d)|subgroup_member(d))),
% 3.04/0.88 inference(paramodulation,[status(thm)],[f2001,f285])).
% 3.04/0.88 fof(f2218,plain,(
% 3.04/0.88 subgroup_member(d)|subgroup_member(d)|subgroup_member(inverse(identity))),
% 3.04/0.88 inference(paramodulation,[status(thm)],[f2001,f106])).
% 3.04/0.88 fof(f2219,plain,(
% 3.04/0.88 ![X0,X1,X2]: (subgroup_member(d)|subgroup_member(d)|~product(identity,X0,X1)|~product(d,X1,X2)|product(d,X0,X2))),
% 3.04/0.88 inference(paramodulation,[status(thm)],[f2001,f108])).
% 3.04/0.88 fof(f2220,plain,(
% 3.04/0.88 ![X0,X1,X2]: (subgroup_member(d)|subgroup_member(d)|~product(identity,X0,X1)|~product(d,X0,X2)|product(d,X1,X2))),
% 3.04/0.88 inference(paramodulation,[status(thm)],[f2001,f109])).
% 3.04/0.88 fof(f2221,plain,(
% 3.04/0.88 ![X0]: (subgroup_member(d)|subgroup_member(d)|~product(d,identity,X0)|d=X0)),
% 3.04/0.88 inference(paramodulation,[status(thm)],[f2001,f110])).
% 3.04/0.88 fof(f2222,plain,(
% 3.04/0.88 product(d,identity,d)|subgroup_member(d)|subgroup_member(d)),
% 3.04/0.88 inference(paramodulation,[status(thm)],[f2001,f36])).
% 3.04/0.88 fof(f2223,plain,(
% 3.04/0.88 subgroup_member(identity)|subgroup_member(d)|subgroup_member(d)),
% 3.04/0.88 inference(paramodulation,[status(thm)],[f2001,f34])).
% 3.04/0.88 fof(f2224,definition,(
% 3.04/0.88 sQ132_spl <=> (product(a,multiply(c,identity),d))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f2227,plain,(
% 3.04/0.88 sQ132_spl|sQ5_spl|~sQ20_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f2210,f2224,f88,f409])).
% 3.04/0.88 fof(f2228,definition,(
% 3.04/0.88 sQ133_spl <=> (product(inverse(d),d,identity))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f2231,plain,(
% 3.04/0.88 sQ133_spl|sQ5_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f2211,f2228,f88])).
% 3.04/0.88 fof(f2232,definition,(
% 3.04/0.88 ![X0]: (sQ134_spl <=> (~product(identity,identity,X0)|product(inverse(d),d,X0)))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f2235,plain,(
% 3.04/0.88 sQ134_spl|sQ5_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f2212,f2232,f88])).
% 3.04/0.88 fof(f2236,definition,(
% 3.04/0.88 ![X0]: (sQ135_spl <=> (~product(d,identity,X0)|product(identity,d,X0)))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f2239,plain,(
% 3.04/0.88 sQ135_spl|sQ5_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f2213,f2236,f88])).
% 3.04/0.88 fof(f2240,definition,(
% 3.04/0.88 ![X0]: (sQ136_spl <=> (~product(d,inverse(identity),X0)|product(d,identity,X0)))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f2243,plain,(
% 3.04/0.88 sQ5_spl|sQ136_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f2214,f88,f2240])).
% 3.04/0.88 fof(f2244,definition,(
% 3.04/0.88 ![X0,X1]: (sQ137_spl <=> (~product(d,multiply(identity,X0),X1)|product(d,X0,X1)))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f2247,plain,(
% 3.04/0.88 sQ5_spl|sQ137_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f2215,f88,f2244])).
% 3.04/0.88 fof(f2248,definition,(
% 3.04/0.88 ![X0]: (sQ138_spl <=> (~product(d,identity,X0)|product(d,identity,X0)))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f2251,plain,(
% 3.04/0.88 sQ5_spl|sQ138_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f2216,f88,f2248])).
% 3.04/0.88 fof(f2252,definition,(
% 3.04/0.88 ![X0,X1]: (sQ139_spl <=> (~product(multiply(X0,d),identity,X1)|product(X0,d,X1)))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f2255,plain,(
% 3.04/0.88 sQ139_spl|sQ5_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f2217,f2252,f88])).
% 3.04/0.88 fof(f2256,plain,(
% 3.04/0.88 sQ5_spl|sQ29_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f2218,f88,f537])).
% 3.04/0.88 fof(f2257,definition,(
% 3.04/0.88 ![X0,X1,X2]: (sQ140_spl <=> (~product(identity,X0,X1)|~product(d,X1,X2)|product(d,X0,X2)))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f2260,plain,(
% 3.04/0.88 sQ5_spl|sQ140_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f2219,f88,f2257])).
% 3.04/0.88 fof(f2261,definition,(
% 3.04/0.88 ![X0,X1,X2]: (sQ141_spl <=> (~product(identity,X0,X1)|~product(d,X0,X2)|product(d,X1,X2)))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f2264,plain,(
% 3.04/0.88 sQ5_spl|sQ141_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f2220,f88,f2261])).
% 3.04/0.88 fof(f2265,definition,(
% 3.04/0.88 ![X0]: (sQ142_spl <=> (~product(d,identity,X0)|d=X0))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f2268,plain,(
% 3.04/0.88 sQ5_spl|sQ142_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f2221,f88,f2265])).
% 3.04/0.88 fof(f2269,definition,(
% 3.04/0.88 sQ143_spl <=> (product(d,identity,d))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f2272,plain,(
% 3.04/0.88 sQ143_spl|sQ5_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f2222,f2269,f88])).
% 3.04/0.88 fof(f2273,plain,(
% 3.04/0.88 sQ0_spl|sQ5_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f2223,f71,f88])).
% 3.04/0.88 fof(f2322,plain,(
% 3.04/0.88 ![X0]: (~subgroup_member(b)|~subgroup_member(multiply(inverse(a),X0))|subgroup_member(multiply(c,X0)))),
% 3.04/0.88 inference(resolution,[status(thm)],[f428,f31])).
% 3.04/0.88 fof(f2353,definition,(
% 3.04/0.88 ![X0]: (sQ151_spl <=> (~subgroup_member(multiply(inverse(a),X0))|subgroup_member(multiply(c,X0))))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f2356,plain,(
% 3.04/0.88 ~sQ6_spl|sQ151_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f2322,f92,f2353])).
% 3.04/0.88 fof(f2370,plain,(
% 3.04/0.88 subgroup_member(multiply(b,identity))|subgroup_member(d)|subgroup_member(d)),
% 3.04/0.88 inference(paramodulation,[status(thm)],[f2001,f438])).
% 3.04/0.88 fof(f2374,definition,(
% 3.04/0.88 sQ152_spl <=> (subgroup_member(multiply(b,identity)))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f2377,plain,(
% 3.04/0.88 sQ152_spl|sQ5_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f2370,f2374,f88])).
% 3.04/0.88 fof(f2388,plain,(
% 3.04/0.88 subgroup_member(multiply(b,inverse(identity)))|subgroup_member(d)|subgroup_member(d)),
% 3.04/0.88 inference(paramodulation,[status(thm)],[f2001,f441])).
% 3.04/0.88 fof(f2392,definition,(
% 3.04/0.88 sQ153_spl <=> (subgroup_member(multiply(b,inverse(identity))))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f2395,plain,(
% 3.04/0.88 sQ153_spl|sQ5_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f2388,f2392,f88])).
% 3.04/0.88 fof(f2404,plain,(
% 3.04/0.88 ![X0]: (product(identity,X0,multiply(a,multiply(c,element_in_O2(d,X0))))|subgroup_member(X0)|subgroup_member(d))),
% 3.04/0.88 inference(resolution,[status(thm)],[f462,f231])).
% 3.04/0.88 fof(f2405,plain,(
% 3.04/0.88 ![X0]: (subgroup_member(X0)|subgroup_member(d)|product(X0,identity,multiply(a,multiply(c,element_in_O2(d,X0)))))),
% 3.04/0.88 inference(resolution,[status(thm)],[f462,f316])).
% 3.04/0.88 fof(f2406,plain,(
% 3.04/0.88 ![X0]: (subgroup_member(X0)|subgroup_member(d)|X0=multiply(a,multiply(c,element_in_O2(d,X0))))),
% 3.04/0.88 inference(resolution,[status(thm)],[f462,f110])).
% 3.04/0.88 fof(f2409,plain,(
% 3.04/0.88 ![X0,X1]: (subgroup_member(X0)|subgroup_member(d)|product(X0,X1,multiply(a,multiply(c,multiply(element_in_O2(d,X0),X1)))))),
% 3.04/0.88 inference(resolution,[status(thm)],[f462,f318])).
% 3.04/0.88 fof(f2412,plain,(
% 3.04/0.88 ![X0]: (subgroup_member(d)|subgroup_member(X0)|product(X0,element_in_O2(X0,d),multiply(a,multiply(c,identity))))),
% 3.04/0.88 inference(resolution,[status(thm)],[f462,f320])).
% 3.04/0.88 fof(f2413,plain,(
% 3.04/0.88 ![X0]: (subgroup_member(X0)|subgroup_member(d)|product(X0,inverse(element_in_O2(d,X0)),multiply(a,multiply(c,identity))))),
% 3.04/0.88 inference(resolution,[status(thm)],[f462,f317])).
% 3.04/0.88 fof(f2418,plain,(
% 3.04/0.88 ![X0]: (subgroup_member(d)|subgroup_member(X0)|product(X0,identity,multiply(a,multiply(c,inverse(element_in_O2(X0,d))))))),
% 3.04/0.88 inference(resolution,[status(thm)],[f462,f321])).
% 3.04/0.88 fof(f2421,plain,(
% 3.04/0.88 ![X0]: (product(identity,element_in_O2(inverse(d),X0),multiply(a,multiply(c,X0)))|subgroup_member(X0)|subgroup_member(inverse(d)))),
% 3.04/0.88 inference(resolution,[status(thm)],[f462,f213])).
% 3.04/0.88 fof(f2422,plain,(
% 3.04/0.88 ![X0,X1]: (subgroup_member(d)|subgroup_member(X0)|product(X0,multiply(element_in_O2(X0,d),X1),multiply(a,multiply(c,X1))))),
% 3.04/0.88 inference(resolution,[status(thm)],[f462,f322])).
% 3.04/0.88 fof(f2445,definition,(
% 3.04/0.88 ![X0]: (sQ154_spl <=> (product(identity,X0,multiply(a,multiply(c,element_in_O2(d,X0))))|subgroup_member(X0)))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f2448,plain,(
% 3.04/0.88 sQ154_spl|sQ5_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f2404,f2445,f88])).
% 3.04/0.88 fof(f2449,definition,(
% 3.04/0.88 ![X0]: (sQ155_spl <=> (subgroup_member(X0)|product(X0,identity,multiply(a,multiply(c,element_in_O2(d,X0))))))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f2452,plain,(
% 3.04/0.88 sQ155_spl|sQ5_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f2405,f2449,f88])).
% 3.04/0.88 fof(f2453,definition,(
% 3.04/0.88 ![X0]: (sQ156_spl <=> (subgroup_member(X0)|X0=multiply(a,multiply(c,element_in_O2(d,X0)))))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f2456,plain,(
% 3.04/0.88 sQ156_spl|sQ5_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f2406,f2453,f88])).
% 3.04/0.88 fof(f2457,definition,(
% 3.04/0.88 ![X0,X1]: (sQ157_spl <=> (subgroup_member(X0)|product(X0,X1,multiply(a,multiply(c,multiply(element_in_O2(d,X0),X1))))))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f2460,plain,(
% 3.04/0.88 sQ157_spl|sQ5_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f2409,f2457,f88])).
% 3.04/0.88 fof(f2461,definition,(
% 3.04/0.88 ![X0]: (sQ158_spl <=> (subgroup_member(X0)|product(X0,element_in_O2(X0,d),multiply(a,multiply(c,identity)))))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f2464,plain,(
% 3.04/0.88 sQ5_spl|sQ158_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f2412,f88,f2461])).
% 3.04/0.88 fof(f2465,definition,(
% 3.04/0.88 ![X0]: (sQ159_spl <=> (subgroup_member(X0)|product(X0,inverse(element_in_O2(d,X0)),multiply(a,multiply(c,identity)))))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f2468,plain,(
% 3.04/0.88 sQ159_spl|sQ5_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f2413,f2465,f88])).
% 3.04/0.88 fof(f2476,definition,(
% 3.04/0.88 ![X0]: (sQ160_spl <=> (subgroup_member(X0)|product(X0,identity,multiply(a,multiply(c,inverse(element_in_O2(X0,d)))))))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f2479,plain,(
% 3.04/0.88 sQ5_spl|sQ160_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f2418,f88,f2476])).
% 3.04/0.88 fof(f2480,definition,(
% 3.04/0.88 ![X0]: (sQ161_spl <=> (product(identity,element_in_O2(inverse(d),X0),multiply(a,multiply(c,X0)))|subgroup_member(X0)))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f2483,plain,(
% 3.04/0.88 sQ161_spl|sQ72_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f2421,f2480,f1507])).
% 3.04/0.88 fof(f2484,definition,(
% 3.04/0.88 ![X0,X1]: (sQ162_spl <=> (subgroup_member(X0)|product(X0,multiply(element_in_O2(X0,d),X1),multiply(a,multiply(c,X1)))))),
% 3.04/0.88 introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition])).
% 3.04/0.88 fof(f2487,plain,(
% 3.04/0.88 sQ5_spl|sQ162_spl),
% 3.04/0.88 inference(split_clause,[status(thm)],[f2422,f88,f2484])).
% 3.04/0.88 fof(f2503,plain,(
% 3.04/0.88 subgroup_member(inverse(inverse(d)))|~sQ72_spl),
% 3.04/0.88 inference(resolution,[status(thm)],[f1508,f29])).
% 3.04/0.88 fof(f2504,plain,(
% 3.04/0.88 subgroup_member(d)|~sQ72_spl),
% 3.04/0.88 inference(forward_demodulation,[status(thm)],[f631,f2503])).
% 3.04/0.88 fof(f2505,plain,(
% 3.04/0.88 $false|~sQ72_spl),
% 3.04/0.88 inference(forward_subsumption_resolution,[status(thm)],[f2504,f40])).
% 3.04/0.88 fof(f2506,plain,(
% 3.04/0.88 ~sQ72_spl),
% 3.04/0.88 inference(contradiction_clause,[status(thm)],[f2505])).
% 3.04/0.88 fof(f2635,plain,(
% 3.04/0.88 ![X0]: (subgroup_member(X0)|subgroup_member(inverse(d))|product(a,multiply(c,X0),element_in_O2(inverse(d),X0)))),
% 3.04/0.88 inference(resolution,[status(thm)],[f530,f160])).
% 3.04/0.88 fof(f2669,plain,(
% 3.04/0.88 subgroup_member(c)|subgroup_member(inverse(a))|d=element_in_O2(inverse(a),c)),
% 3.04/0.88 inference(resolution,[status(thm)],[f530,f42])).
% 3.04/0.88 fof(f2685,plain,(
% 3.04/0.88 ![X0]: (subgroup_member(d)|subgroup_member(inverse(X0))|product(multiply(X0,a),c,element_in_O2(inverse(X0),d)))),
% 3.04/0.88 inference(resolution,[status(thm)],[f530,f268])).
% 3.04/0.88 fof(f2740,definition,(
% 3.04/0.88 ![X0]: (sQ180_spl <=> (subgroup_member(X0)|product(a,multiply(c,X0),element_in_O2(inverse(d),X0))))),
% 3.04/0.89 introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition])).
% 3.04/0.89 fof(f2743,plain,(
% 3.04/0.89 sQ180_spl|sQ72_spl),
% 3.04/0.89 inference(split_clause,[status(thm)],[f2635,f2740,f1507])).
% 3.04/0.89 fof(f2873,definition,(
% 3.04/0.89 sQ213_spl <=> (d=element_in_O2(inverse(a),c))),
% 3.04/0.89 introduced(definition,[new_symbols(definition,[sQ213_spl])],[split_symbol_definition])).
% 3.04/0.89 fof(f2874,plain,(
% 3.04/0.89 d=element_in_O2(inverse(a),c)|~sQ213_spl),
% 3.04/0.89 inference(component_clause,[status(thm)],[f2873])).
% 3.04/0.89 fof(f2876,plain,(
% 3.04/0.89 sQ4_spl|sQ7_spl|sQ213_spl),
% 3.04/0.89 inference(split_clause,[status(thm)],[f2669,f85,f95,f2873])).
% 3.04/0.89 fof(f2916,definition,(
% 3.04/0.89 ![X0]: (sQ220_spl <=> (subgroup_member(inverse(X0))|product(multiply(X0,a),c,element_in_O2(inverse(X0),d))))),
% 3.04/0.89 introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition])).
% 3.04/0.89 fof(f2919,plain,(
% 3.04/0.89 sQ5_spl|sQ220_spl),
% 3.04/0.89 inference(split_clause,[status(thm)],[f2685,f88,f2916])).
% 3.04/0.89 fof(f3111,plain,(
% 3.04/0.89 product(identity,identity,identity)|subgroup_member(d)),
% 3.04/0.89 inference(paramodulation,[status(thm)],[f2001,f602])).
% 3.04/0.89 fof(f3116,definition,(
% 3.04/0.89 sQ232_spl <=> (product(identity,identity,identity))),
% 3.04/0.89 introduced(definition,[new_symbols(definition,[sQ232_spl])],[split_symbol_definition])).
% 3.04/0.89 fof(f3145,plain,(
% 3.04/0.89 sQ232_spl|sQ5_spl),
% 3.04/0.89 inference(split_clause,[status(thm)],[f3111,f3116,f88])).
% 3.04/0.89 fof(f3167,plain,(
% 3.04/0.89 ![X0,X1]: (subgroup_member(X0)|subgroup_member(X1)|~subgroup_member(identity)|~subgroup_member(element_in_O2(X1,X0))|subgroup_member(multiply(inverse(X1),X0)))),
% 3.04/0.89 inference(resolution,[status(thm)],[f596,f31])).
% 3.04/0.89 fof(f3179,plain,(
% 3.04/0.89 product(identity,identity,multiply(inverse(d),d))|subgroup_member(d)|subgroup_member(d)),
% 3.04/0.89 inference(paramodulation,[status(thm)],[f2001,f596])).
% 3.04/0.89 fof(f3216,definition,(
% 3.04/0.89 ![X0,X1]: (sQ242_spl <=> (subgroup_member(X0)|subgroup_member(X1)|~subgroup_member(element_in_O2(X1,X0))|subgroup_member(multiply(inverse(X1),X0))))),
% 3.04/0.89 introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition])).
% 3.04/0.89 fof(f3219,plain,(
% 3.04/0.89 sQ242_spl|~sQ0_spl),
% 3.04/0.89 inference(split_clause,[status(thm)],[f3167,f3216,f71])).
% 3.04/0.89 fof(f3226,definition,(
% 3.04/0.89 sQ243_spl <=> (product(identity,identity,multiply(inverse(d),d)))),
% 3.04/0.89 introduced(definition,[new_symbols(definition,[sQ243_spl])],[split_symbol_definition])).
% 3.04/0.89 fof(f3229,plain,(
% 3.04/0.89 sQ243_spl|sQ5_spl),
% 3.04/0.89 inference(split_clause,[status(thm)],[f3179,f3226,f88])).
% 3.04/0.89 fof(f3453,plain,(
% 3.04/0.89 subgroup_member(d)|subgroup_member(c)|subgroup_member(inverse(a))|~sQ213_spl),
% 3.04/0.89 inference(paramodulation,[status(thm)],[f2874,f34])).
% 3.04/0.89 fof(f3527,plain,(
% 3.04/0.89 sQ5_spl|sQ4_spl|sQ7_spl|~sQ213_spl),
% 3.04/0.89 inference(split_clause,[status(thm)],[f3453,f88,f85,f95,f2873])).
% 3.04/0.89 fof(f3528,plain,(
% 3.04/0.89 $false),
% 3.04/0.89 inference(sat_refutation,[status(thm)],[f77,f91,f98,f103,f105,f124,f412,f652,f753,f1027,f1244,f1399,f1466,f1470,f1481,f1914,f2227,f2231,f2235,f2239,f2243,f2247,f2251,f2255,f2256,f2260,f2264,f2268,f2272,f2273,f2356,f2377,f2395,f2448,f2452,f2456,f2460,f2464,f2468,f2479,f2483,f2487,f2506,f2743,f2876,f2919,f3145,f3219,f3229,f3527])).
% 3.04/0.89 % SZS output end CNFRefutation for theBenchmark.p
% 3.04/0.89 % Elapsed time: 0.513307 seconds
% 3.04/0.89 % CPU time: 3.746017 seconds
% 3.04/0.89 % Total memory used: 105.419 MB
% 3.04/0.89 % Net memory used: 98.494 MB
%------------------------------------------------------------------------------