%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP124-1.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 12:35:44 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.45s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP124-1.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n010.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sun Sep 20 19:59:09 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Drodi V4.1.1
% 0.12/0.45 % Refutation found
% 0.12/0.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.45 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.45 fof(f1,axiom,(
% 0.12/0.45 group_element(e_1) ),
% 0.12/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f2,axiom,(
% 0.12/0.45 group_element(e_2) ),
% 0.12/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f3,axiom,(
% 0.12/0.45 group_element(e_3) ),
% 0.12/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f4,axiom,(
% 0.12/0.45 group_element(e_4) ),
% 0.12/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f5,axiom,(
% 0.12/0.45 ~ equalish(e_1,e_2) ),
% 0.12/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f6,axiom,(
% 0.12/0.45 ~ equalish(e_1,e_3) ),
% 0.12/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f7,axiom,(
% 0.12/0.45 ~ equalish(e_1,e_4) ),
% 0.12/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f9,axiom,(
% 0.12/0.45 ~ equalish(e_2,e_3) ),
% 0.12/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f10,axiom,(
% 0.12/0.45 ~ equalish(e_2,e_4) ),
% 0.12/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f13,axiom,(
% 0.12/0.45 ~ equalish(e_3,e_4) ),
% 0.12/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f17,axiom,(
% 0.12/0.45 (![X,Y]: (( ~ group_element(X)| ~ group_element(Y)| product(X,Y,e_1)| product(X,Y,e_2)| product(X,Y,e_3)| product(X,Y,e_4) ) ))),
% 0.12/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f18,axiom,(
% 0.12/0.45 (![X,Y,W,Z]: (( ~ product(X,Y,W)| ~ product(X,Y,Z)| equalish(W,Z) ) ))),
% 0.12/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f19,axiom,(
% 0.12/0.45 (![X,W,Y,Z]: (( ~ product(X,W,Y)| ~ product(X,Z,Y)| equalish(W,Z) ) ))),
% 0.12/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f20,axiom,(
% 0.12/0.45 (![W,Y,X,Z]: (( ~ product(W,Y,X)| ~ product(Z,Y,X)| equalish(W,Z) ) ))),
% 0.12/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f21,axiom,(
% 0.12/0.45 (![X]: (product(X,X,X) ))),
% 0.12/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f22,negated_conjecture,(
% 0.12/0.45 (![X1,Y1,Z1,X2,Y2,Z2]: (( ~ product(X1,Y1,Z1)| ~ product(X2,Y2,Z1)| ~ product(Z2,X1,Y1)| ~ product(Z2,X2,Y2)| equalish(X1,X2) ) ))),
% 0.12/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f23,negated_conjecture,(
% 0.12/0.45 (![X1,Y1,Z1,X2,Y2,Z2]: (( ~ product(X1,Y1,Z1)| ~ product(X2,Y2,Z1)| ~ product(Z2,X1,Y1)| ~ product(Z2,X2,Y2)| equalish(Y1,Y2) ) ))),
% 0.12/0.45 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.45 fof(f24,plain,(
% 0.12/0.45 group_element(e_1)),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f1])).
% 0.12/0.45 fof(f25,plain,(
% 0.12/0.45 group_element(e_2)),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f2])).
% 0.12/0.45 fof(f26,plain,(
% 0.12/0.45 group_element(e_3)),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f3])).
% 0.12/0.45 fof(f27,plain,(
% 0.12/0.45 group_element(e_4)),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f4])).
% 0.12/0.45 fof(f28,plain,(
% 0.12/0.45 ~equalish(e_1,e_2)),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f5])).
% 0.12/0.45 fof(f29,plain,(
% 0.12/0.45 ~equalish(e_1,e_3)),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f6])).
% 0.12/0.45 fof(f30,plain,(
% 0.12/0.45 ~equalish(e_1,e_4)),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f7])).
% 0.12/0.45 fof(f32,plain,(
% 0.12/0.45 ~equalish(e_2,e_3)),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f9])).
% 0.12/0.45 fof(f33,plain,(
% 0.12/0.45 ~equalish(e_2,e_4)),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f10])).
% 0.12/0.45 fof(f36,plain,(
% 0.12/0.45 ~equalish(e_3,e_4)),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f13])).
% 0.12/0.45 fof(f40,plain,(
% 0.12/0.45 ![X0,X1]: (~group_element(X0)|~group_element(X1)|product(X0,X1,e_1)|product(X0,X1,e_2)|product(X0,X1,e_3)|product(X0,X1,e_4))),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f17])).
% 0.12/0.45 fof(f41,plain,(
% 0.12/0.45 ![W,Z]: ((![X,Y]: (~product(X,Y,W)|~product(X,Y,Z)))|equalish(W,Z))),
% 0.12/0.45 inference(miniscoping,[status(thm)],[f18])).
% 0.12/0.45 fof(f42,plain,(
% 0.12/0.45 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|equalish(X2,X3))),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f41])).
% 0.12/0.45 fof(f43,plain,(
% 0.12/0.45 ![W,Z]: ((![X,Y]: (~product(X,W,Y)|~product(X,Z,Y)))|equalish(W,Z))),
% 0.12/0.45 inference(miniscoping,[status(thm)],[f19])).
% 0.12/0.45 fof(f44,plain,(
% 0.12/0.45 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X3,X2)|equalish(X1,X3))),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f43])).
% 0.12/0.45 fof(f45,plain,(
% 0.12/0.45 ![W,Z]: ((![Y,X]: (~product(W,Y,X)|~product(Z,Y,X)))|equalish(W,Z))),
% 0.12/0.45 inference(miniscoping,[status(thm)],[f20])).
% 0.12/0.45 fof(f46,plain,(
% 0.12/0.45 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X3,X1,X2)|equalish(X0,X3))),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f45])).
% 0.12/0.45 fof(f47,plain,(
% 0.12/0.45 ![X0]: (product(X0,X0,X0))),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f21])).
% 0.12/0.45 fof(f48,plain,(
% 0.12/0.45 ![X1,X2]: ((![Y2,Z2]: ((![Y1]: ((![Z1]: (~product(X1,Y1,Z1)|~product(X2,Y2,Z1)))|~product(Z2,X1,Y1)))|~product(Z2,X2,Y2)))|equalish(X1,X2))),
% 0.12/0.45 inference(miniscoping,[status(thm)],[f22])).
% 0.12/0.45 fof(f49,plain,(
% 0.12/0.45 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~product(X3,X4,X2)|~product(X5,X0,X1)|~product(X5,X3,X4)|equalish(X0,X3))),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f48])).
% 0.12/0.45 fof(f50,plain,(
% 0.12/0.45 ![Y1,Y2]: ((![X2,Z2]: ((![X1]: ((![Z1]: (~product(X1,Y1,Z1)|~product(X2,Y2,Z1)))|~product(Z2,X1,Y1)))|~product(Z2,X2,Y2)))|equalish(Y1,Y2))),
% 0.12/0.45 inference(miniscoping,[status(thm)],[f23])).
% 0.12/0.45 fof(f51,plain,(
% 0.12/0.45 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~product(X3,X4,X2)|~product(X5,X0,X1)|~product(X5,X3,X4)|equalish(X1,X4))),
% 0.12/0.45 inference(cnf_transformation,[status(thm)],[f50])).
% 0.12/0.45 fof(f52,plain,(
% 0.12/0.45 ![X0,X1]: (~product(e_1,X0,X1)|~product(e_2,X0,X1))),
% 0.12/0.45 inference(resolution,[status(thm)],[f28,f46])).
% 0.12/0.45 fof(f53,plain,(
% 0.12/0.45 ![X0,X1]: (~product(X0,e_1,X1)|~product(X0,e_2,X1))),
% 0.12/0.45 inference(resolution,[status(thm)],[f28,f44])).
% 0.12/0.45 fof(f54,plain,(
% 0.12/0.45 ![X0,X1]: (~product(X0,X1,e_1)|~product(X0,X1,e_2))),
% 0.12/0.45 inference(resolution,[status(thm)],[f28,f42])).
% 0.12/0.45 fof(f56,plain,(
% 0.12/0.45 ![X0,X1,X2,X3]: (~product(e_1,X0,X1)|~product(e_2,X2,X1)|~product(X3,e_1,X0)|~product(X3,e_2,X2))),
% 0.12/0.45 inference(resolution,[status(thm)],[f28,f49])).
% 0.12/0.45 fof(f58,plain,(
% 0.12/0.45 ![X0,X1]: (~product(e_1,X0,X1)|~product(e_3,X0,X1))),
% 0.12/0.45 inference(resolution,[status(thm)],[f29,f46])).
% 0.12/0.45 fof(f59,plain,(
% 0.12/0.45 ![X0,X1]: (~product(X0,e_1,X1)|~product(X0,e_3,X1))),
% 0.12/0.45 inference(resolution,[status(thm)],[f29,f44])).
% 0.12/0.45 fof(f60,plain,(
% 0.12/0.45 ![X0,X1]: (~product(X0,X1,e_1)|~product(X0,X1,e_3))),
% 0.12/0.45 inference(resolution,[status(thm)],[f29,f42])).
% 0.12/0.45 fof(f62,plain,(
% 0.12/0.45 ![X0,X1,X2,X3]: (~product(e_1,X0,X1)|~product(e_3,X2,X1)|~product(X3,e_1,X0)|~product(X3,e_3,X2))),
% 0.12/0.45 inference(resolution,[status(thm)],[f29,f49])).
% 0.12/0.45 fof(f63,plain,(
% 0.12/0.45 ![X0,X1]: (~product(e_1,X0,X1)|~product(e_4,X0,X1))),
% 0.12/0.45 inference(resolution,[status(thm)],[f30,f46])).
% 0.12/0.45 fof(f64,plain,(
% 0.12/0.45 ![X0,X1]: (~product(X0,e_1,X1)|~product(X0,e_4,X1))),
% 0.12/0.45 inference(resolution,[status(thm)],[f30,f44])).
% 0.12/0.45 fof(f67,plain,(
% 0.12/0.45 ![X0,X1,X2,X3]: (~product(e_1,X0,X1)|~product(e_4,X2,X1)|~product(X3,e_1,X0)|~product(X3,e_4,X2))),
% 0.12/0.45 inference(resolution,[status(thm)],[f30,f49])).
% 0.12/0.45 fof(f73,plain,(
% 0.12/0.45 ![X0,X1]: (~product(e_2,X0,X1)|~product(e_3,X0,X1))),
% 0.12/0.45 inference(resolution,[status(thm)],[f32,f46])).
% 0.12/0.45 fof(f74,plain,(
% 0.12/0.45 ![X0,X1]: (~product(X0,e_2,X1)|~product(X0,e_3,X1))),
% 0.12/0.45 inference(resolution,[status(thm)],[f32,f44])).
% 0.12/0.45 fof(f75,plain,(
% 0.12/0.45 ![X0,X1]: (~product(X0,X1,e_2)|~product(X0,X1,e_3))),
% 0.12/0.45 inference(resolution,[status(thm)],[f32,f42])).
% 0.12/0.45 fof(f76,plain,(
% 0.12/0.45 ![X0,X1,X2,X3]: (~product(X0,e_2,X1)|~product(X2,e_3,X1)|~product(X3,X0,e_2)|~product(X3,X2,e_3))),
% 0.12/0.45 inference(resolution,[status(thm)],[f32,f51])).
% 0.12/0.45 fof(f77,plain,(
% 0.12/0.45 ![X0,X1,X2,X3]: (~product(e_2,X0,X1)|~product(e_3,X2,X1)|~product(X3,e_2,X0)|~product(X3,e_3,X2))),
% 0.12/0.45 inference(resolution,[status(thm)],[f32,f49])).
% 0.12/0.45 fof(f78,plain,(
% 0.12/0.45 ![X0,X1]: (~product(e_2,X0,X1)|~product(e_4,X0,X1))),
% 0.12/0.45 inference(resolution,[status(thm)],[f33,f46])).
% 0.12/0.45 fof(f79,plain,(
% 0.12/0.45 ![X0,X1]: (~product(X0,e_2,X1)|~product(X0,e_4,X1))),
% 0.12/0.45 inference(resolution,[status(thm)],[f33,f44])).
% 0.12/0.45 fof(f80,plain,(
% 0.12/0.45 ![X0,X1]: (~product(X0,X1,e_2)|~product(X0,X1,e_4))),
% 0.12/0.45 inference(resolution,[status(thm)],[f33,f42])).
% 0.12/0.45 fof(f82,plain,(
% 0.12/0.45 ![X0,X1,X2,X3]: (~product(e_2,X0,X1)|~product(e_4,X2,X1)|~product(X3,e_2,X0)|~product(X3,e_4,X2))),
% 0.12/0.45 inference(resolution,[status(thm)],[f33,f49])).
% 0.12/0.45 fof(f93,plain,(
% 0.12/0.45 ![X0,X1]: (~product(e_3,X0,X1)|~product(e_4,X0,X1))),
% 0.12/0.45 inference(resolution,[status(thm)],[f36,f46])).
% 0.12/0.45 fof(f94,plain,(
% 0.12/0.45 ![X0,X1]: (~product(X0,e_3,X1)|~product(X0,e_4,X1))),
% 0.12/0.45 inference(resolution,[status(thm)],[f36,f44])).
% 0.12/0.45 fof(f96,plain,(
% 0.12/0.45 ![X0,X1,X2,X3]: (~product(X0,e_3,X1)|~product(X2,e_4,X1)|~product(X3,X0,e_3)|~product(X3,X2,e_4))),
% 0.12/0.45 inference(resolution,[status(thm)],[f36,f51])).
% 0.12/0.45 fof(f97,plain,(
% 0.12/0.45 ![X0,X1,X2,X3]: (~product(e_3,X0,X1)|~product(e_4,X2,X1)|~product(X3,e_3,X0)|~product(X3,e_4,X2))),
% 0.12/0.45 inference(resolution,[status(thm)],[f36,f49])).
% 0.12/0.45 fof(f113,plain,(
% 0.12/0.45 ![X0]: (~group_element(e_2)|~group_element(X0)|product(e_2,X0,e_1)|product(e_2,X0,e_2)|product(e_2,X0,e_3)|~product(e_1,X0,e_4))),
% 0.12/0.45 inference(resolution,[status(thm)],[f40,f52])).
% 0.12/0.45 fof(f114,definition,(
% 0.12/0.45 sQ0_spl <=> (group_element(e_2))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f116,plain,(
% 0.12/0.45 ~group_element(e_2)|sQ0_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f114])).
% 0.12/0.45 fof(f117,definition,(
% 0.12/0.45 ![X0]: (sQ1_spl <=> (~group_element(X0)|product(e_2,X0,e_1)|product(e_2,X0,e_2)|product(e_2,X0,e_3)|~product(e_1,X0,e_4)))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f120,plain,(
% 0.12/0.45 ~sQ0_spl|sQ1_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f113,f114,f117])).
% 0.12/0.45 fof(f121,plain,(
% 0.12/0.45 $false|sQ0_spl),
% 0.12/0.45 inference(forward_subsumption_resolution,[status(thm)],[f116,f25])).
% 0.12/0.45 fof(f122,plain,(
% 0.12/0.45 sQ0_spl),
% 0.12/0.45 inference(contradiction_clause,[status(thm)],[f121])).
% 0.12/0.45 fof(f124,plain,(
% 0.12/0.45 ![X0,X1,X2]: (~product(e_1,X0,e_4)|~product(X1,e_1,X0)|~product(X1,e_2,X2)|~group_element(e_2)|~group_element(X2)|product(e_2,X2,e_1)|product(e_2,X2,e_2)|product(e_2,X2,e_3))),
% 0.12/0.45 inference(resolution,[status(thm)],[f56,f40])).
% 0.12/0.45 fof(f125,plain,(
% 0.12/0.45 ![X0,X1]: (~product(e_1,X0,e_2)|~product(X1,e_1,X0)|~product(X1,e_2,e_2))),
% 0.12/0.45 inference(resolution,[status(thm)],[f56,f47])).
% 0.12/0.45 fof(f126,definition,(
% 0.12/0.45 ![X0,X1,X2]: (sQ2_spl <=> (~product(e_1,X0,e_4)|~product(X1,e_1,X0)|~product(X1,e_2,X2)|~group_element(X2)|product(e_2,X2,e_1)|product(e_2,X2,e_2)|product(e_2,X2,e_3)))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f129,plain,(
% 0.12/0.45 sQ2_spl|~sQ0_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f124,f126,f114])).
% 0.12/0.45 fof(f131,plain,(
% 0.12/0.45 ![X0]: (~product(X0,e_1,e_4)|~group_element(X0)|~group_element(e_2)|product(X0,e_2,e_1)|product(X0,e_2,e_2)|product(X0,e_2,e_3))),
% 0.12/0.45 inference(resolution,[status(thm)],[f53,f40])).
% 0.12/0.45 fof(f132,plain,(
% 0.12/0.45 ~product(e_2,e_1,e_2)),
% 0.12/0.45 inference(resolution,[status(thm)],[f53,f47])).
% 0.12/0.45 fof(f133,definition,(
% 0.12/0.45 ![X0]: (sQ3_spl <=> (~product(X0,e_1,e_4)|~group_element(X0)|product(X0,e_2,e_1)|product(X0,e_2,e_2)|product(X0,e_2,e_3)))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f136,plain,(
% 0.12/0.45 sQ3_spl|~sQ0_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f131,f133,f114])).
% 0.12/0.45 fof(f137,plain,(
% 0.12/0.45 ~product(e_2,e_2,e_1)),
% 0.12/0.45 inference(resolution,[status(thm)],[f54,f47])).
% 0.12/0.45 fof(f138,plain,(
% 0.12/0.45 ![X0]: (~product(e_1,X0,e_4)|~group_element(e_3)|~group_element(X0)|product(e_3,X0,e_1)|product(e_3,X0,e_2)|product(e_3,X0,e_3))),
% 0.12/0.45 inference(resolution,[status(thm)],[f58,f40])).
% 0.12/0.45 fof(f140,definition,(
% 0.12/0.45 ![X0]: (sQ4_spl <=> (~product(e_1,X0,e_4)|~group_element(X0)|product(e_3,X0,e_1)|product(e_3,X0,e_2)|product(e_3,X0,e_3)))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f143,definition,(
% 0.12/0.45 sQ5_spl <=> (group_element(e_3))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f145,plain,(
% 0.12/0.45 ~group_element(e_3)|sQ5_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f143])).
% 0.12/0.45 fof(f146,plain,(
% 0.12/0.45 sQ4_spl|~sQ5_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f138,f140,f143])).
% 0.12/0.45 fof(f147,plain,(
% 0.12/0.45 ![X0]: (~product(X0,e_1,e_4)|~group_element(X0)|~group_element(e_3)|product(X0,e_3,e_1)|product(X0,e_3,e_2)|product(X0,e_3,e_3))),
% 0.12/0.45 inference(resolution,[status(thm)],[f59,f40])).
% 0.12/0.45 fof(f148,plain,(
% 0.12/0.45 ~product(e_3,e_1,e_3)),
% 0.12/0.45 inference(resolution,[status(thm)],[f59,f47])).
% 0.12/0.45 fof(f149,definition,(
% 0.12/0.45 ![X0]: (sQ6_spl <=> (~product(X0,e_1,e_4)|~group_element(X0)|product(X0,e_3,e_1)|product(X0,e_3,e_2)|product(X0,e_3,e_3)))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f152,plain,(
% 0.12/0.45 sQ6_spl|~sQ5_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f147,f149,f143])).
% 0.12/0.45 fof(f153,plain,(
% 0.12/0.45 $false|sQ5_spl),
% 0.12/0.45 inference(forward_subsumption_resolution,[status(thm)],[f145,f26])).
% 0.12/0.45 fof(f154,plain,(
% 0.12/0.45 sQ5_spl),
% 0.12/0.45 inference(contradiction_clause,[status(thm)],[f153])).
% 0.12/0.45 fof(f155,plain,(
% 0.12/0.45 ~product(e_3,e_3,e_1)),
% 0.12/0.45 inference(resolution,[status(thm)],[f60,f47])).
% 0.12/0.45 fof(f156,plain,(
% 0.12/0.45 ![X0]: (~product(e_1,X0,e_4)|~group_element(e_4)|~group_element(X0)|product(e_4,X0,e_1)|product(e_4,X0,e_2)|product(e_4,X0,e_3))),
% 0.12/0.45 inference(resolution,[status(thm)],[f63,f40])).
% 0.12/0.45 fof(f157,plain,(
% 0.12/0.45 ~product(e_1,e_4,e_4)),
% 0.12/0.45 inference(resolution,[status(thm)],[f63,f47])).
% 0.12/0.45 fof(f158,definition,(
% 0.12/0.45 ![X0]: (sQ7_spl <=> (~product(e_1,X0,e_4)|~group_element(X0)|product(e_4,X0,e_1)|product(e_4,X0,e_2)|product(e_4,X0,e_3)))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f161,definition,(
% 0.12/0.45 sQ8_spl <=> (group_element(e_4))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f163,plain,(
% 0.12/0.45 ~group_element(e_4)|sQ8_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f161])).
% 0.12/0.45 fof(f164,plain,(
% 0.12/0.45 sQ7_spl|~sQ8_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f156,f158,f161])).
% 0.12/0.45 fof(f165,plain,(
% 0.12/0.45 ~group_element(e_1)|~group_element(e_4)|product(e_1,e_4,e_1)|product(e_1,e_4,e_2)|product(e_1,e_4,e_3)),
% 0.12/0.45 inference(resolution,[status(thm)],[f157,f40])).
% 0.12/0.45 fof(f166,definition,(
% 0.12/0.45 sQ9_spl <=> (group_element(e_1))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f168,plain,(
% 0.12/0.45 ~group_element(e_1)|sQ9_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f166])).
% 0.12/0.45 fof(f169,definition,(
% 0.12/0.45 sQ10_spl <=> (product(e_1,e_4,e_1))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f170,plain,(
% 0.12/0.45 product(e_1,e_4,e_1)|~sQ10_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f169])).
% 0.12/0.45 fof(f172,definition,(
% 0.12/0.45 sQ11_spl <=> (product(e_1,e_4,e_2))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f173,plain,(
% 0.12/0.45 product(e_1,e_4,e_2)|~sQ11_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f172])).
% 0.12/0.45 fof(f175,definition,(
% 0.12/0.45 sQ12_spl <=> (product(e_1,e_4,e_3))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f176,plain,(
% 0.12/0.45 product(e_1,e_4,e_3)|~sQ12_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f175])).
% 0.12/0.45 fof(f178,plain,(
% 0.12/0.45 ~sQ9_spl|~sQ8_spl|sQ10_spl|sQ11_spl|sQ12_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f165,f166,f161,f169,f172,f175])).
% 0.12/0.45 fof(f179,plain,(
% 0.12/0.45 $false|sQ8_spl),
% 0.12/0.45 inference(forward_subsumption_resolution,[status(thm)],[f163,f27])).
% 0.12/0.45 fof(f180,plain,(
% 0.12/0.45 sQ8_spl),
% 0.12/0.45 inference(contradiction_clause,[status(thm)],[f179])).
% 0.12/0.45 fof(f183,plain,(
% 0.12/0.45 ![X0]: (~product(X0,e_4,e_4)|~group_element(X0)|~group_element(e_1)|product(X0,e_1,e_1)|product(X0,e_1,e_2)|product(X0,e_1,e_3))),
% 0.12/0.45 inference(resolution,[status(thm)],[f64,f40])).
% 0.12/0.45 fof(f184,plain,(
% 0.12/0.45 ~product(e_1,e_4,e_1)),
% 0.12/0.45 inference(resolution,[status(thm)],[f64,f47])).
% 0.12/0.45 fof(f185,definition,(
% 0.12/0.45 ![X0]: (sQ13_spl <=> (~product(X0,e_4,e_4)|~group_element(X0)|product(X0,e_1,e_1)|product(X0,e_1,e_2)|product(X0,e_1,e_3)))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f188,plain,(
% 0.12/0.45 sQ13_spl|~sQ9_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f183,f185,f166])).
% 0.12/0.45 fof(f189,plain,(
% 0.12/0.45 $false|sQ9_spl),
% 0.12/0.45 inference(forward_subsumption_resolution,[status(thm)],[f168,f24])).
% 0.12/0.45 fof(f190,plain,(
% 0.12/0.45 sQ9_spl),
% 0.12/0.45 inference(contradiction_clause,[status(thm)],[f189])).
% 0.12/0.45 fof(f191,plain,(
% 0.12/0.45 ![X0,X1,X2]: (~product(e_1,X0,e_4)|~product(X1,e_1,X0)|~product(X1,e_3,X2)|~group_element(e_3)|~group_element(X2)|product(e_3,X2,e_1)|product(e_3,X2,e_2)|product(e_3,X2,e_3))),
% 0.12/0.45 inference(resolution,[status(thm)],[f62,f40])).
% 0.12/0.45 fof(f192,plain,(
% 0.12/0.45 ![X0,X1]: (~product(e_1,X0,e_3)|~product(X1,e_1,X0)|~product(X1,e_3,e_3))),
% 0.12/0.45 inference(resolution,[status(thm)],[f62,f47])).
% 0.12/0.45 fof(f193,definition,(
% 0.12/0.45 ![X0,X1,X2]: (sQ14_spl <=> (~product(e_1,X0,e_4)|~product(X1,e_1,X0)|~product(X1,e_3,X2)|~group_element(X2)|product(e_3,X2,e_1)|product(e_3,X2,e_2)|product(e_3,X2,e_3)))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f196,plain,(
% 0.12/0.45 sQ14_spl|~sQ5_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f191,f193,f143])).
% 0.12/0.45 fof(f213,plain,(
% 0.12/0.45 ![X0,X1,X2]: (~product(e_1,X0,e_4)|~product(X1,e_1,X0)|~product(X1,e_4,X2)|~group_element(e_4)|~group_element(X2)|product(e_4,X2,e_1)|product(e_4,X2,e_2)|product(e_4,X2,e_3))),
% 0.12/0.45 inference(resolution,[status(thm)],[f67,f40])).
% 0.12/0.45 fof(f215,definition,(
% 0.12/0.45 ![X0,X1,X2]: (sQ19_spl <=> (~product(e_1,X0,e_4)|~product(X1,e_1,X0)|~product(X1,e_4,X2)|~group_element(X2)|product(e_4,X2,e_1)|product(e_4,X2,e_2)|product(e_4,X2,e_3)))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f218,plain,(
% 0.12/0.45 sQ19_spl|~sQ8_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f213,f215,f161])).
% 0.12/0.45 fof(f226,definition,(
% 0.12/0.45 sQ22_spl <=> (product(e_1,e_1,e_3))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f227,plain,(
% 0.12/0.45 product(e_1,e_1,e_3)|~sQ22_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f226])).
% 0.12/0.45 fof(f245,plain,(
% 0.12/0.45 ![X0]: (~product(X0,e_1,e_4)|~product(X0,e_2,e_2)|~sQ11_spl)),
% 0.12/0.45 inference(resolution,[status(thm)],[f173,f125])).
% 0.12/0.45 fof(f249,plain,(
% 0.12/0.45 ~product(e_1,e_1,e_1)|~sQ22_spl),
% 0.12/0.45 inference(resolution,[status(thm)],[f227,f60])).
% 0.12/0.45 fof(f251,plain,(
% 0.12/0.45 $false|~sQ22_spl),
% 0.12/0.45 inference(forward_subsumption_resolution,[status(thm)],[f249,f47])).
% 0.12/0.45 fof(f252,plain,(
% 0.12/0.45 ~sQ22_spl),
% 0.12/0.45 inference(contradiction_clause,[status(thm)],[f251])).
% 0.12/0.45 fof(f259,plain,(
% 0.12/0.45 $false|~sQ10_spl),
% 0.12/0.45 inference(forward_subsumption_resolution,[status(thm)],[f170,f184])).
% 0.12/0.45 fof(f260,plain,(
% 0.12/0.45 ~sQ10_spl),
% 0.12/0.45 inference(contradiction_clause,[status(thm)],[f259])).
% 0.12/0.45 fof(f264,plain,(
% 0.12/0.45 ![X0]: (~product(e_2,X0,e_4)|~group_element(e_3)|~group_element(X0)|product(e_3,X0,e_1)|product(e_3,X0,e_2)|product(e_3,X0,e_3))),
% 0.12/0.45 inference(resolution,[status(thm)],[f73,f40])).
% 0.12/0.45 fof(f266,definition,(
% 0.12/0.45 ![X0]: (sQ23_spl <=> (~product(e_2,X0,e_4)|~group_element(X0)|product(e_3,X0,e_1)|product(e_3,X0,e_2)|product(e_3,X0,e_3)))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f269,plain,(
% 0.12/0.45 sQ23_spl|~sQ5_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f264,f266,f143])).
% 0.12/0.45 fof(f270,plain,(
% 0.12/0.45 ![X0]: (~product(X0,e_3,e_4)|~group_element(X0)|~group_element(e_2)|product(X0,e_2,e_1)|product(X0,e_2,e_2)|product(X0,e_2,e_3))),
% 0.12/0.45 inference(resolution,[status(thm)],[f74,f40])).
% 0.12/0.45 fof(f272,definition,(
% 0.12/0.45 ![X0]: (sQ24_spl <=> (~product(X0,e_3,e_4)|~group_element(X0)|product(X0,e_2,e_1)|product(X0,e_2,e_2)|product(X0,e_2,e_3)))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f275,plain,(
% 0.12/0.45 sQ24_spl|~sQ0_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f270,f272,f114])).
% 0.12/0.45 fof(f277,plain,(
% 0.12/0.45 ~product(e_3,e_3,e_2)),
% 0.12/0.45 inference(resolution,[status(thm)],[f75,f47])).
% 0.12/0.45 fof(f278,plain,(
% 0.12/0.45 ~product(e_2,e_1,e_4)|~sQ11_spl),
% 0.12/0.45 inference(resolution,[status(thm)],[f245,f47])).
% 0.12/0.45 fof(f279,plain,(
% 0.12/0.45 ~group_element(e_2)|~group_element(e_1)|product(e_2,e_1,e_1)|product(e_2,e_1,e_2)|product(e_2,e_1,e_3)|~sQ11_spl),
% 0.12/0.45 inference(resolution,[status(thm)],[f278,f40])).
% 0.12/0.45 fof(f280,definition,(
% 0.12/0.45 sQ25_spl <=> (product(e_2,e_1,e_1))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f281,plain,(
% 0.12/0.45 product(e_2,e_1,e_1)|~sQ25_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f280])).
% 0.12/0.45 fof(f283,definition,(
% 0.12/0.45 sQ26_spl <=> (product(e_2,e_1,e_2))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f284,plain,(
% 0.12/0.45 product(e_2,e_1,e_2)|~sQ26_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f283])).
% 0.12/0.45 fof(f286,definition,(
% 0.12/0.45 sQ27_spl <=> (product(e_2,e_1,e_3))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f287,plain,(
% 0.12/0.45 product(e_2,e_1,e_3)|~sQ27_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f286])).
% 0.12/0.45 fof(f289,plain,(
% 0.12/0.45 ~sQ0_spl|~sQ9_spl|sQ25_spl|sQ26_spl|sQ27_spl|~sQ11_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f279,f114,f166,f280,f283,f286,f172])).
% 0.12/0.45 fof(f290,plain,(
% 0.12/0.45 $false|~sQ26_spl),
% 0.12/0.45 inference(forward_subsumption_resolution,[status(thm)],[f284,f132])).
% 0.12/0.45 fof(f291,plain,(
% 0.12/0.45 ~sQ26_spl),
% 0.12/0.45 inference(contradiction_clause,[status(thm)],[f290])).
% 0.12/0.45 fof(f292,plain,(
% 0.12/0.45 ![X0,X1,X2]: (~product(X0,e_3,e_4)|~product(X1,X2,e_2)|~product(X1,X0,e_3)|~group_element(X2)|~group_element(e_2)|product(X2,e_2,e_1)|product(X2,e_2,e_2)|product(X2,e_2,e_3))),
% 0.12/0.45 inference(resolution,[status(thm)],[f76,f40])).
% 0.12/0.45 fof(f294,definition,(
% 0.12/0.45 ![X0,X1,X2]: (sQ28_spl <=> (~product(X0,e_3,e_4)|~product(X1,X2,e_2)|~product(X1,X0,e_3)|~group_element(X2)|product(X2,e_2,e_1)|product(X2,e_2,e_2)|product(X2,e_2,e_3)))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f297,plain,(
% 0.12/0.45 sQ28_spl|~sQ0_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f292,f294,f114])).
% 0.12/0.45 fof(f300,plain,(
% 0.12/0.45 ~product(e_2,e_4,e_3)|~sQ27_spl),
% 0.12/0.45 inference(resolution,[status(thm)],[f287,f64])).
% 0.12/0.45 fof(f306,plain,(
% 0.12/0.45 ~product(e_1,e_1,e_1)|~sQ25_spl),
% 0.12/0.45 inference(resolution,[status(thm)],[f281,f52])).
% 0.12/0.45 fof(f310,plain,(
% 0.12/0.45 $false|~sQ25_spl),
% 0.12/0.45 inference(forward_subsumption_resolution,[status(thm)],[f306,f47])).
% 0.12/0.45 fof(f311,plain,(
% 0.12/0.45 ~sQ25_spl),
% 0.12/0.45 inference(contradiction_clause,[status(thm)],[f310])).
% 0.12/0.45 fof(f312,plain,(
% 0.12/0.45 ![X0,X1,X2]: (~product(e_2,X0,e_4)|~product(X1,e_2,X0)|~product(X1,e_3,X2)|~group_element(e_3)|~group_element(X2)|product(e_3,X2,e_1)|product(e_3,X2,e_2)|product(e_3,X2,e_3))),
% 0.12/0.45 inference(resolution,[status(thm)],[f77,f40])).
% 0.12/0.45 fof(f314,definition,(
% 0.12/0.45 ![X0,X1,X2]: (sQ29_spl <=> (~product(e_2,X0,e_4)|~product(X1,e_2,X0)|~product(X1,e_3,X2)|~group_element(X2)|product(e_3,X2,e_1)|product(e_3,X2,e_2)|product(e_3,X2,e_3)))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f317,plain,(
% 0.12/0.45 sQ29_spl|~sQ5_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f312,f314,f143])).
% 0.12/0.45 fof(f319,plain,(
% 0.12/0.45 ![X0]: (~product(e_2,X0,e_4)|~group_element(e_4)|~group_element(X0)|product(e_4,X0,e_1)|product(e_4,X0,e_2)|product(e_4,X0,e_3))),
% 0.12/0.45 inference(resolution,[status(thm)],[f78,f40])).
% 0.12/0.45 fof(f320,plain,(
% 0.12/0.45 ~product(e_2,e_4,e_4)),
% 0.12/0.45 inference(resolution,[status(thm)],[f78,f47])).
% 0.12/0.45 fof(f321,definition,(
% 0.12/0.45 ![X0]: (sQ30_spl <=> (~product(e_2,X0,e_4)|~group_element(X0)|product(e_4,X0,e_1)|product(e_4,X0,e_2)|product(e_4,X0,e_3)))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f324,plain,(
% 0.12/0.45 sQ30_spl|~sQ8_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f319,f321,f161])).
% 0.12/0.45 fof(f325,plain,(
% 0.12/0.45 ~group_element(e_2)|~group_element(e_4)|product(e_2,e_4,e_1)|product(e_2,e_4,e_2)|product(e_2,e_4,e_3)),
% 0.12/0.45 inference(resolution,[status(thm)],[f320,f40])).
% 0.12/0.45 fof(f326,definition,(
% 0.12/0.45 sQ31_spl <=> (product(e_2,e_4,e_1))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f327,plain,(
% 0.12/0.45 product(e_2,e_4,e_1)|~sQ31_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f326])).
% 0.12/0.45 fof(f329,definition,(
% 0.12/0.45 sQ32_spl <=> (product(e_2,e_4,e_2))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f330,plain,(
% 0.12/0.45 product(e_2,e_4,e_2)|~sQ32_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f329])).
% 0.12/0.45 fof(f332,definition,(
% 0.12/0.45 sQ33_spl <=> (product(e_2,e_4,e_3))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f333,plain,(
% 0.12/0.45 product(e_2,e_4,e_3)|~sQ33_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f332])).
% 0.12/0.45 fof(f335,plain,(
% 0.12/0.45 ~sQ0_spl|~sQ8_spl|sQ31_spl|sQ32_spl|sQ33_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f325,f114,f161,f326,f329,f332])).
% 0.12/0.45 fof(f336,plain,(
% 0.12/0.45 $false|~sQ27_spl|~sQ33_spl),
% 0.12/0.45 inference(forward_subsumption_resolution,[status(thm)],[f333,f300])).
% 0.12/0.45 fof(f337,plain,(
% 0.12/0.45 ~sQ27_spl|~sQ33_spl),
% 0.12/0.45 inference(contradiction_clause,[status(thm)],[f336])).
% 0.12/0.45 fof(f350,plain,(
% 0.12/0.45 ![X0]: (~product(X0,e_4,e_4)|~group_element(X0)|~group_element(e_2)|product(X0,e_2,e_1)|product(X0,e_2,e_2)|product(X0,e_2,e_3))),
% 0.12/0.45 inference(resolution,[status(thm)],[f79,f40])).
% 0.12/0.45 fof(f351,plain,(
% 0.12/0.45 ~product(e_2,e_4,e_2)),
% 0.12/0.45 inference(resolution,[status(thm)],[f79,f47])).
% 0.12/0.45 fof(f352,definition,(
% 0.12/0.45 ![X0]: (sQ34_spl <=> (~product(X0,e_4,e_4)|~group_element(X0)|product(X0,e_2,e_1)|product(X0,e_2,e_2)|product(X0,e_2,e_3)))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f355,plain,(
% 0.12/0.45 sQ34_spl|~sQ0_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f350,f352,f114])).
% 0.12/0.45 fof(f356,plain,(
% 0.12/0.45 $false|~sQ32_spl),
% 0.12/0.45 inference(forward_subsumption_resolution,[status(thm)],[f351,f330])).
% 0.12/0.45 fof(f357,plain,(
% 0.12/0.45 ~sQ32_spl),
% 0.12/0.45 inference(contradiction_clause,[status(thm)],[f356])).
% 0.12/0.45 fof(f358,plain,(
% 0.12/0.45 ~product(e_2,e_2,e_4)),
% 0.12/0.45 inference(resolution,[status(thm)],[f80,f47])).
% 0.12/0.45 fof(f364,definition,(
% 0.12/0.45 sQ36_spl <=> (product(e_4,e_1,e_1))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f365,plain,(
% 0.12/0.45 product(e_4,e_1,e_1)|~sQ36_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f364])).
% 0.12/0.45 fof(f390,plain,(
% 0.12/0.45 ~product(e_1,e_1,e_1)|~sQ36_spl),
% 0.12/0.45 inference(resolution,[status(thm)],[f365,f63])).
% 0.12/0.45 fof(f394,plain,(
% 0.12/0.45 $false|~sQ36_spl),
% 0.12/0.45 inference(forward_subsumption_resolution,[status(thm)],[f390,f47])).
% 0.12/0.45 fof(f395,plain,(
% 0.12/0.45 ~sQ36_spl),
% 0.12/0.45 inference(contradiction_clause,[status(thm)],[f394])).
% 0.12/0.45 fof(f396,plain,(
% 0.12/0.45 ![X0,X1,X2]: (~product(e_2,X0,e_4)|~product(X1,e_2,X0)|~product(X1,e_4,X2)|~group_element(e_4)|~group_element(X2)|product(e_4,X2,e_1)|product(e_4,X2,e_2)|product(e_4,X2,e_3))),
% 0.12/0.45 inference(resolution,[status(thm)],[f82,f40])).
% 0.12/0.45 fof(f398,definition,(
% 0.12/0.45 ![X0,X1,X2]: (sQ39_spl <=> (~product(e_2,X0,e_4)|~product(X1,e_2,X0)|~product(X1,e_4,X2)|~group_element(X2)|product(e_4,X2,e_1)|product(e_4,X2,e_2)|product(e_4,X2,e_3)))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f401,plain,(
% 0.12/0.45 sQ39_spl|~sQ8_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f396,f398,f161])).
% 0.12/0.45 fof(f402,plain,(
% 0.12/0.45 ~group_element(e_2)|~group_element(e_2)|product(e_2,e_2,e_1)|product(e_2,e_2,e_2)|product(e_2,e_2,e_3)),
% 0.12/0.45 inference(resolution,[status(thm)],[f358,f40])).
% 0.12/0.45 fof(f403,definition,(
% 0.12/0.45 sQ40_spl <=> (product(e_2,e_2,e_1))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f404,plain,(
% 0.12/0.45 product(e_2,e_2,e_1)|~sQ40_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f403])).
% 0.12/0.45 fof(f406,definition,(
% 0.12/0.45 sQ41_spl <=> (product(e_2,e_2,e_2))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f409,definition,(
% 0.12/0.45 sQ42_spl <=> (product(e_2,e_2,e_3))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f410,plain,(
% 0.12/0.45 product(e_2,e_2,e_3)|~sQ42_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f409])).
% 0.12/0.45 fof(f412,plain,(
% 0.12/0.45 ~sQ0_spl|sQ40_spl|sQ41_spl|sQ42_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f402,f114,f403,f406,f409])).
% 0.12/0.45 fof(f413,plain,(
% 0.12/0.45 $false|~sQ40_spl),
% 0.12/0.45 inference(forward_subsumption_resolution,[status(thm)],[f404,f137])).
% 0.12/0.45 fof(f414,plain,(
% 0.12/0.45 ~sQ40_spl),
% 0.12/0.45 inference(contradiction_clause,[status(thm)],[f413])).
% 0.12/0.45 fof(f430,plain,(
% 0.12/0.45 ~product(e_2,e_2,e_2)|~sQ42_spl),
% 0.12/0.45 inference(resolution,[status(thm)],[f410,f75])).
% 0.12/0.45 fof(f433,plain,(
% 0.12/0.45 $false|~sQ42_spl),
% 0.12/0.45 inference(forward_subsumption_resolution,[status(thm)],[f430,f47])).
% 0.12/0.45 fof(f434,plain,(
% 0.12/0.45 ~sQ42_spl),
% 0.12/0.45 inference(contradiction_clause,[status(thm)],[f433])).
% 0.12/0.45 fof(f437,plain,(
% 0.12/0.45 ![X0]: (~product(X0,e_1,e_4)|~product(X0,e_3,e_3)|~sQ12_spl)),
% 0.12/0.45 inference(resolution,[status(thm)],[f192,f176])).
% 0.12/0.45 fof(f438,plain,(
% 0.12/0.45 ~product(e_3,e_1,e_4)|~sQ12_spl),
% 0.12/0.45 inference(resolution,[status(thm)],[f437,f47])).
% 0.12/0.45 fof(f439,plain,(
% 0.12/0.45 ~group_element(e_3)|~group_element(e_1)|product(e_3,e_1,e_1)|product(e_3,e_1,e_2)|product(e_3,e_1,e_3)|~sQ12_spl),
% 0.12/0.45 inference(resolution,[status(thm)],[f438,f40])).
% 0.12/0.45 fof(f440,definition,(
% 0.12/0.45 sQ43_spl <=> (product(e_3,e_1,e_1))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f441,plain,(
% 0.12/0.45 product(e_3,e_1,e_1)|~sQ43_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f440])).
% 0.12/0.45 fof(f443,definition,(
% 0.12/0.45 sQ44_spl <=> (product(e_3,e_1,e_2))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f444,plain,(
% 0.12/0.45 product(e_3,e_1,e_2)|~sQ44_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f443])).
% 0.12/0.45 fof(f446,definition,(
% 0.12/0.45 sQ45_spl <=> (product(e_3,e_1,e_3))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f447,plain,(
% 0.12/0.45 product(e_3,e_1,e_3)|~sQ45_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f446])).
% 0.12/0.45 fof(f449,plain,(
% 0.12/0.45 ~sQ5_spl|~sQ9_spl|sQ43_spl|sQ44_spl|sQ45_spl|~sQ12_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f439,f143,f166,f440,f443,f446,f175])).
% 0.12/0.45 fof(f450,plain,(
% 0.12/0.45 $false|~sQ45_spl),
% 0.12/0.45 inference(forward_subsumption_resolution,[status(thm)],[f447,f148])).
% 0.12/0.45 fof(f451,plain,(
% 0.12/0.45 ~sQ45_spl),
% 0.12/0.45 inference(contradiction_clause,[status(thm)],[f450])).
% 0.12/0.45 fof(f456,plain,(
% 0.12/0.45 ~product(e_3,e_4,e_2)|~sQ44_spl),
% 0.12/0.45 inference(resolution,[status(thm)],[f444,f64])).
% 0.12/0.45 fof(f465,plain,(
% 0.12/0.45 ~product(e_1,e_1,e_1)|~sQ43_spl),
% 0.12/0.45 inference(resolution,[status(thm)],[f441,f58])).
% 0.12/0.45 fof(f469,plain,(
% 0.12/0.45 $false|~sQ43_spl),
% 0.12/0.45 inference(forward_subsumption_resolution,[status(thm)],[f465,f47])).
% 0.12/0.45 fof(f470,plain,(
% 0.12/0.45 ~sQ43_spl),
% 0.12/0.45 inference(contradiction_clause,[status(thm)],[f469])).
% 0.12/0.45 fof(f472,plain,(
% 0.12/0.45 ![X0]: (~product(e_3,X0,e_4)|~group_element(e_4)|~group_element(X0)|product(e_4,X0,e_1)|product(e_4,X0,e_2)|product(e_4,X0,e_3))),
% 0.12/0.45 inference(resolution,[status(thm)],[f93,f40])).
% 0.12/0.45 fof(f473,plain,(
% 0.12/0.45 ~product(e_3,e_4,e_4)),
% 0.12/0.45 inference(resolution,[status(thm)],[f93,f47])).
% 0.12/0.45 fof(f474,definition,(
% 0.12/0.45 ![X0]: (sQ46_spl <=> (~product(e_3,X0,e_4)|~group_element(X0)|product(e_4,X0,e_1)|product(e_4,X0,e_2)|product(e_4,X0,e_3)))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f477,plain,(
% 0.12/0.45 sQ46_spl|~sQ8_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f472,f474,f161])).
% 0.12/0.45 fof(f478,plain,(
% 0.12/0.45 ~group_element(e_3)|~group_element(e_4)|product(e_3,e_4,e_1)|product(e_3,e_4,e_2)|product(e_3,e_4,e_3)),
% 0.12/0.45 inference(resolution,[status(thm)],[f473,f40])).
% 0.12/0.45 fof(f479,definition,(
% 0.12/0.45 sQ47_spl <=> (product(e_3,e_4,e_1))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f480,plain,(
% 0.12/0.45 product(e_3,e_4,e_1)|~sQ47_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f479])).
% 0.12/0.45 fof(f482,definition,(
% 0.12/0.45 sQ48_spl <=> (product(e_3,e_4,e_2))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f483,plain,(
% 0.12/0.45 product(e_3,e_4,e_2)|~sQ48_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f482])).
% 0.12/0.45 fof(f485,definition,(
% 0.12/0.45 sQ49_spl <=> (product(e_3,e_4,e_3))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f486,plain,(
% 0.12/0.45 product(e_3,e_4,e_3)|~sQ49_spl),
% 0.12/0.45 inference(component_clause,[status(thm)],[f485])).
% 0.12/0.45 fof(f488,plain,(
% 0.12/0.45 ~sQ5_spl|~sQ8_spl|sQ47_spl|sQ48_spl|sQ49_spl),
% 0.12/0.45 inference(split_clause,[status(thm)],[f478,f143,f161,f479,f482,f485])).
% 0.12/0.45 fof(f489,plain,(
% 0.12/0.45 $false|~sQ44_spl|~sQ48_spl),
% 0.12/0.45 inference(forward_subsumption_resolution,[status(thm)],[f483,f456])).
% 0.12/0.45 fof(f490,plain,(
% 0.12/0.45 ~sQ44_spl|~sQ48_spl),
% 0.12/0.45 inference(contradiction_clause,[status(thm)],[f489])).
% 0.12/0.45 fof(f502,plain,(
% 0.12/0.45 ~product(e_2,e_4,e_1)|~sQ47_spl),
% 0.12/0.45 inference(resolution,[status(thm)],[f480,f73])).
% 0.12/0.45 fof(f507,plain,(
% 0.12/0.45 $false|~sQ31_spl|~sQ47_spl),
% 0.12/0.45 inference(forward_subsumption_resolution,[status(thm)],[f502,f327])).
% 0.12/0.45 fof(f508,plain,(
% 0.12/0.45 ~sQ31_spl|~sQ47_spl),
% 0.12/0.45 inference(contradiction_clause,[status(thm)],[f507])).
% 0.12/0.45 fof(f510,plain,(
% 0.12/0.45 ![X0]: (~product(X0,e_4,e_4)|~group_element(X0)|~group_element(e_3)|product(X0,e_3,e_1)|product(X0,e_3,e_2)|product(X0,e_3,e_3))),
% 0.12/0.45 inference(resolution,[status(thm)],[f94,f40])).
% 0.12/0.45 fof(f511,plain,(
% 0.12/0.45 ~product(e_3,e_4,e_3)),
% 0.12/0.45 inference(resolution,[status(thm)],[f94,f47])).
% 0.12/0.45 fof(f512,definition,(
% 0.12/0.45 ![X0]: (sQ50_spl <=> (~product(X0,e_4,e_4)|~group_element(X0)|product(X0,e_3,e_1)|product(X0,e_3,e_2)|product(X0,e_3,e_3)))),
% 0.12/0.45 introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition])).
% 0.12/0.45 fof(f515,plain,(
% 0.12/0.46 sQ50_spl|~sQ5_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f510,f512,f143])).
% 0.12/0.46 fof(f524,definition,(
% 0.12/0.46 sQ52_spl <=> (product(e_3,e_3,e_1))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f525,plain,(
% 0.12/0.46 product(e_3,e_3,e_1)|~sQ52_spl),
% 0.12/0.46 inference(component_clause,[status(thm)],[f524])).
% 0.12/0.46 fof(f527,definition,(
% 0.12/0.46 sQ53_spl <=> (product(e_3,e_3,e_2))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f528,plain,(
% 0.12/0.46 product(e_3,e_3,e_2)|~sQ53_spl),
% 0.12/0.46 inference(component_clause,[status(thm)],[f527])).
% 0.12/0.46 fof(f534,plain,(
% 0.12/0.46 $false|~sQ53_spl),
% 0.12/0.46 inference(forward_subsumption_resolution,[status(thm)],[f528,f277])).
% 0.12/0.46 fof(f535,plain,(
% 0.12/0.46 ~sQ53_spl),
% 0.12/0.46 inference(contradiction_clause,[status(thm)],[f534])).
% 0.12/0.46 fof(f536,plain,(
% 0.12/0.46 $false|~sQ52_spl),
% 0.12/0.46 inference(forward_subsumption_resolution,[status(thm)],[f525,f155])).
% 0.12/0.46 fof(f537,plain,(
% 0.12/0.46 ~sQ52_spl),
% 0.12/0.46 inference(contradiction_clause,[status(thm)],[f536])).
% 0.12/0.46 fof(f540,plain,(
% 0.12/0.46 ![X0,X1,X2]: (~product(X0,e_4,e_4)|~product(X1,X2,e_3)|~product(X1,X0,e_4)|~group_element(X2)|~group_element(e_3)|product(X2,e_3,e_1)|product(X2,e_3,e_2)|product(X2,e_3,e_3))),
% 0.12/0.46 inference(resolution,[status(thm)],[f96,f40])).
% 0.12/0.46 fof(f542,definition,(
% 0.12/0.46 ![X0,X1,X2]: (sQ55_spl <=> (~product(X0,e_4,e_4)|~product(X1,X2,e_3)|~product(X1,X0,e_4)|~group_element(X2)|product(X2,e_3,e_1)|product(X2,e_3,e_2)|product(X2,e_3,e_3)))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f545,plain,(
% 0.12/0.46 sQ55_spl|~sQ5_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f540,f542,f143])).
% 0.12/0.46 fof(f547,plain,(
% 0.12/0.46 ~product(e_1,e_4,e_3)|~sQ33_spl),
% 0.12/0.46 inference(resolution,[status(thm)],[f333,f52])).
% 0.12/0.46 fof(f551,plain,(
% 0.12/0.46 $false|~sQ12_spl|~sQ33_spl),
% 0.12/0.46 inference(forward_subsumption_resolution,[status(thm)],[f547,f176])).
% 0.12/0.46 fof(f552,plain,(
% 0.12/0.46 ~sQ12_spl|~sQ33_spl),
% 0.12/0.46 inference(contradiction_clause,[status(thm)],[f551])).
% 0.12/0.46 fof(f558,plain,(
% 0.12/0.46 ![X0,X1,X2]: (~product(e_3,X0,e_4)|~product(X1,e_3,X0)|~product(X1,e_4,X2)|~group_element(e_4)|~group_element(X2)|product(e_4,X2,e_1)|product(e_4,X2,e_2)|product(e_4,X2,e_3))),
% 0.12/0.46 inference(resolution,[status(thm)],[f97,f40])).
% 0.12/0.46 fof(f560,definition,(
% 0.12/0.46 ![X0,X1,X2]: (sQ56_spl <=> (~product(e_3,X0,e_4)|~product(X1,e_3,X0)|~product(X1,e_4,X2)|~group_element(X2)|product(e_4,X2,e_1)|product(e_4,X2,e_2)|product(e_4,X2,e_3)))),
% 0.12/0.46 introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition])).
% 0.12/0.46 fof(f563,plain,(
% 0.12/0.46 sQ56_spl|~sQ8_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f558,f560,f161])).
% 0.12/0.46 fof(f580,plain,(
% 0.12/0.46 ~product(e_1,e_4,e_2)|~sQ48_spl),
% 0.12/0.46 inference(resolution,[status(thm)],[f483,f58])).
% 0.12/0.46 fof(f585,plain,(
% 0.12/0.46 ~sQ11_spl|~sQ48_spl),
% 0.12/0.46 inference(split_clause,[status(thm)],[f580,f172,f482])).
% 0.12/0.46 fof(f589,plain,(
% 0.12/0.46 $false|~sQ49_spl),
% 0.12/0.46 inference(forward_subsumption_resolution,[status(thm)],[f486,f511])).
% 0.12/0.46 fof(f590,plain,(
% 0.12/0.46 ~sQ49_spl),
% 0.12/0.46 inference(contradiction_clause,[status(thm)],[f589])).
% 0.12/0.46 fof(f591,plain,(
% 0.12/0.46 $false),
% 0.12/0.46 inference(sat_refutation,[status(thm)],[f120,f122,f129,f136,f146,f152,f154,f164,f178,f180,f188,f190,f196,f218,f252,f260,f269,f275,f289,f291,f297,f311,f317,f324,f335,f337,f355,f357,f395,f401,f412,f414,f434,f449,f451,f470,f477,f488,f490,f508,f515,f535,f537,f545,f552,f563,f585,f590])).
% 0.12/0.46 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.47 % Elapsed time: 0.104769 seconds
% 0.12/0.47 % CPU time: 0.563442 seconds
% 0.12/0.47 % Total memory used: 23.144 MB
% 0.12/0.47 % Net memory used: 22.695 MB
%------------------------------------------------------------------------------