%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP124-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 12:35:46 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP124-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n026.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sun Sep 20 20:02:06 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.40 fof(f1,axiom,(
% 0.10/0.40 (![X,Y]: (( ~ group_element(X)| ~ group_element(Y)| product(e_1,X,Y)| product(e_2,X,Y)| product(e_3,X,Y)| product(e_4,X,Y) ) ))),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f2,axiom,(
% 0.10/0.40 (![X,Y]: (( ~ group_element(X)| ~ group_element(Y)| product(X,e_1,Y)| product(X,e_2,Y)| product(X,e_3,Y)| product(X,e_4,Y) ) ))),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f3,axiom,(
% 0.10/0.40 group_element(e_1) ),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f4,axiom,(
% 0.10/0.40 group_element(e_2) ),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f5,axiom,(
% 0.10/0.40 group_element(e_3) ),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f6,axiom,(
% 0.10/0.40 group_element(e_4) ),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f7,axiom,(
% 0.10/0.40 ~ equalish(e_1,e_2) ),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f8,axiom,(
% 0.10/0.40 ~ equalish(e_1,e_3) ),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f9,axiom,(
% 0.10/0.40 ~ equalish(e_1,e_4) ),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f11,axiom,(
% 0.10/0.40 ~ equalish(e_2,e_3) ),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f12,axiom,(
% 0.10/0.40 ~ equalish(e_2,e_4) ),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f15,axiom,(
% 0.10/0.40 ~ equalish(e_3,e_4) ),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f20,axiom,(
% 0.10/0.40 (![X,Y,W,Z]: (( ~ product(X,Y,W)| ~ product(X,Y,Z)| equalish(W,Z) ) ))),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f21,axiom,(
% 0.10/0.40 (![X,W,Y,Z]: (( ~ product(X,W,Y)| ~ product(X,Z,Y)| equalish(W,Z) ) ))),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f22,axiom,(
% 0.10/0.40 (![W,Y,X,Z]: (( ~ product(W,Y,X)| ~ product(Z,Y,X)| equalish(W,Z) ) ))),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f23,axiom,(
% 0.10/0.40 (![X]: (product(X,X,X) ))),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f24,negated_conjecture,(
% 0.10/0.40 (![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) ) ))),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f25,negated_conjecture,(
% 0.10/0.40 (![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) ) ))),
% 0.10/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f26,plain,(
% 0.10/0.40 ![X0,X1]: (~group_element(X0)|~group_element(X1)|product(e_1,X0,X1)|product(e_2,X0,X1)|product(e_3,X0,X1)|product(e_4,X0,X1))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f1])).
% 0.10/0.40 fof(f27,plain,(
% 0.10/0.40 ![X0,X1]: (~group_element(X0)|~group_element(X1)|product(X0,e_1,X1)|product(X0,e_2,X1)|product(X0,e_3,X1)|product(X0,e_4,X1))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f2])).
% 0.10/0.40 fof(f28,plain,(
% 0.10/0.40 group_element(e_1)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f3])).
% 0.10/0.40 fof(f29,plain,(
% 0.10/0.40 group_element(e_2)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f4])).
% 0.10/0.40 fof(f30,plain,(
% 0.10/0.40 group_element(e_3)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f5])).
% 0.10/0.40 fof(f31,plain,(
% 0.10/0.40 group_element(e_4)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f6])).
% 0.10/0.40 fof(f32,plain,(
% 0.10/0.40 ~equalish(e_1,e_2)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f7])).
% 0.10/0.40 fof(f33,plain,(
% 0.10/0.40 ~equalish(e_1,e_3)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f8])).
% 0.10/0.40 fof(f34,plain,(
% 0.10/0.40 ~equalish(e_1,e_4)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f9])).
% 0.10/0.40 fof(f36,plain,(
% 0.10/0.40 ~equalish(e_2,e_3)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f11])).
% 0.10/0.40 fof(f37,plain,(
% 0.10/0.40 ~equalish(e_2,e_4)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f12])).
% 0.10/0.40 fof(f40,plain,(
% 0.10/0.40 ~equalish(e_3,e_4)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f15])).
% 0.10/0.40 fof(f45,plain,(
% 0.10/0.40 ![W,Z]: ((![X,Y]: (~product(X,Y,W)|~product(X,Y,Z)))|equalish(W,Z))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f20])).
% 0.10/0.40 fof(f46,plain,(
% 0.10/0.40 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|equalish(X2,X3))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f45])).
% 0.10/0.40 fof(f47,plain,(
% 0.10/0.40 ![W,Z]: ((![X,Y]: (~product(X,W,Y)|~product(X,Z,Y)))|equalish(W,Z))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f21])).
% 0.10/0.40 fof(f48,plain,(
% 0.10/0.40 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X3,X2)|equalish(X1,X3))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f47])).
% 0.10/0.40 fof(f49,plain,(
% 0.10/0.40 ![W,Z]: ((![Y,X]: (~product(W,Y,X)|~product(Z,Y,X)))|equalish(W,Z))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f22])).
% 0.10/0.40 fof(f50,plain,(
% 0.10/0.40 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X3,X1,X2)|equalish(X0,X3))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f49])).
% 0.10/0.40 fof(f51,plain,(
% 0.10/0.40 ![X0]: (product(X0,X0,X0))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f23])).
% 0.10/0.40 fof(f52,plain,(
% 0.10/0.40 ![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))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f24])).
% 0.10/0.40 fof(f53,plain,(
% 0.10/0.40 ![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))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f52])).
% 0.10/0.40 fof(f54,plain,(
% 0.10/0.40 ![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))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f25])).
% 0.10/0.40 fof(f55,plain,(
% 0.10/0.40 ![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))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f54])).
% 0.10/0.40 fof(f56,plain,(
% 0.10/0.40 ![X0,X1]: (~product(e_1,X0,X1)|~product(e_2,X0,X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f32,f50])).
% 0.10/0.40 fof(f57,plain,(
% 0.10/0.40 ![X0,X1]: (~product(X0,e_1,X1)|~product(X0,e_2,X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f32,f48])).
% 0.10/0.40 fof(f58,plain,(
% 0.10/0.40 ![X0,X1]: (~product(X0,X1,e_1)|~product(X0,X1,e_2))),
% 0.10/0.40 inference(resolution,[status(thm)],[f32,f46])).
% 0.10/0.40 fof(f59,plain,(
% 0.10/0.40 ![X0,X1,X2,X3]: (~product(X0,e_1,X1)|~product(X2,e_2,X1)|~product(X3,X0,e_1)|~product(X3,X2,e_2))),
% 0.10/0.40 inference(resolution,[status(thm)],[f32,f55])).
% 0.10/0.40 fof(f60,plain,(
% 0.10/0.40 ![X0,X1,X2,X3]: (~product(e_1,X0,X1)|~product(e_2,X2,X1)|~product(X3,e_1,X0)|~product(X3,e_2,X2))),
% 0.10/0.40 inference(resolution,[status(thm)],[f32,f53])).
% 0.10/0.40 fof(f61,plain,(
% 0.10/0.40 ![X0,X1]: (~product(e_1,X0,X1)|~product(e_3,X0,X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f33,f50])).
% 0.10/0.40 fof(f62,plain,(
% 0.10/0.40 ![X0,X1]: (~product(X0,e_1,X1)|~product(X0,e_3,X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f33,f48])).
% 0.10/0.40 fof(f63,plain,(
% 0.10/0.40 ![X0,X1]: (~product(X0,X1,e_1)|~product(X0,X1,e_3))),
% 0.10/0.40 inference(resolution,[status(thm)],[f33,f46])).
% 0.10/0.40 fof(f64,plain,(
% 0.10/0.40 ![X0,X1,X2,X3]: (~product(X0,e_1,X1)|~product(X2,e_3,X1)|~product(X3,X0,e_1)|~product(X3,X2,e_3))),
% 0.10/0.40 inference(resolution,[status(thm)],[f33,f55])).
% 0.10/0.40 fof(f65,plain,(
% 0.10/0.40 ![X0,X1,X2,X3]: (~product(e_1,X0,X1)|~product(e_3,X2,X1)|~product(X3,e_1,X0)|~product(X3,e_3,X2))),
% 0.10/0.40 inference(resolution,[status(thm)],[f33,f53])).
% 0.10/0.40 fof(f66,plain,(
% 0.10/0.40 ![X0,X1]: (~product(e_1,X0,X1)|~product(e_4,X0,X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f34,f50])).
% 0.10/0.40 fof(f67,plain,(
% 0.10/0.40 ![X0,X1]: (~product(X0,e_1,X1)|~product(X0,e_4,X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f34,f48])).
% 0.10/0.40 fof(f68,plain,(
% 0.10/0.40 ![X0,X1]: (~product(X0,X1,e_1)|~product(X0,X1,e_4))),
% 0.10/0.40 inference(resolution,[status(thm)],[f34,f46])).
% 0.10/0.40 fof(f69,plain,(
% 0.10/0.40 ![X0,X1,X2,X3]: (~product(X0,e_1,X1)|~product(X2,e_4,X1)|~product(X3,X0,e_1)|~product(X3,X2,e_4))),
% 0.10/0.40 inference(resolution,[status(thm)],[f34,f55])).
% 0.10/0.40 fof(f70,plain,(
% 0.10/0.40 ![X0,X1,X2,X3]: (~product(e_1,X0,X1)|~product(e_4,X2,X1)|~product(X3,e_1,X0)|~product(X3,e_4,X2))),
% 0.10/0.40 inference(resolution,[status(thm)],[f34,f53])).
% 0.10/0.40 fof(f76,plain,(
% 0.10/0.40 ![X0,X1]: (~product(e_2,X0,X1)|~product(e_3,X0,X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f36,f50])).
% 0.10/0.40 fof(f77,plain,(
% 0.10/0.40 ![X0,X1]: (~product(X0,e_2,X1)|~product(X0,e_3,X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f36,f48])).
% 0.10/0.40 fof(f78,plain,(
% 0.10/0.40 ![X0,X1]: (~product(X0,X1,e_2)|~product(X0,X1,e_3))),
% 0.10/0.40 inference(resolution,[status(thm)],[f36,f46])).
% 0.10/0.40 fof(f79,plain,(
% 0.10/0.40 ![X0,X1,X2,X3]: (~product(X0,e_2,X1)|~product(X2,e_3,X1)|~product(X3,X0,e_2)|~product(X3,X2,e_3))),
% 0.10/0.40 inference(resolution,[status(thm)],[f36,f55])).
% 0.10/0.40 fof(f80,plain,(
% 0.10/0.40 ![X0,X1,X2,X3]: (~product(e_2,X0,X1)|~product(e_3,X2,X1)|~product(X3,e_2,X0)|~product(X3,e_3,X2))),
% 0.10/0.40 inference(resolution,[status(thm)],[f36,f53])).
% 0.10/0.40 fof(f81,plain,(
% 0.10/0.40 ![X0,X1]: (~product(e_2,X0,X1)|~product(e_4,X0,X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f37,f50])).
% 0.10/0.40 fof(f82,plain,(
% 0.10/0.40 ![X0,X1]: (~product(X0,e_2,X1)|~product(X0,e_4,X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f37,f48])).
% 0.10/0.40 fof(f83,plain,(
% 0.10/0.40 ![X0,X1]: (~product(X0,X1,e_2)|~product(X0,X1,e_4))),
% 0.10/0.40 inference(resolution,[status(thm)],[f37,f46])).
% 0.10/0.40 fof(f84,plain,(
% 0.10/0.40 ![X0,X1,X2,X3]: (~product(X0,e_2,X1)|~product(X2,e_4,X1)|~product(X3,X0,e_2)|~product(X3,X2,e_4))),
% 0.10/0.40 inference(resolution,[status(thm)],[f37,f55])).
% 0.10/0.40 fof(f85,plain,(
% 0.10/0.40 ![X0,X1,X2,X3]: (~product(e_2,X0,X1)|~product(e_4,X2,X1)|~product(X3,e_2,X0)|~product(X3,e_4,X2))),
% 0.10/0.40 inference(resolution,[status(thm)],[f37,f53])).
% 0.10/0.40 fof(f96,plain,(
% 0.10/0.40 ![X0,X1]: (~product(e_3,X0,X1)|~product(e_4,X0,X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f40,f50])).
% 0.10/0.40 fof(f97,plain,(
% 0.10/0.40 ![X0,X1]: (~product(X0,e_3,X1)|~product(X0,e_4,X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f40,f48])).
% 0.10/0.40 fof(f98,plain,(
% 0.10/0.40 ![X0,X1]: (~product(X0,X1,e_3)|~product(X0,X1,e_4))),
% 0.10/0.40 inference(resolution,[status(thm)],[f40,f46])).
% 0.10/0.40 fof(f99,plain,(
% 0.10/0.40 ![X0,X1,X2,X3]: (~product(X0,e_3,X1)|~product(X2,e_4,X1)|~product(X3,X0,e_3)|~product(X3,X2,e_4))),
% 0.10/0.40 inference(resolution,[status(thm)],[f40,f55])).
% 0.10/0.40 fof(f100,plain,(
% 0.10/0.40 ![X0,X1,X2,X3]: (~product(e_3,X0,X1)|~product(e_4,X2,X1)|~product(X3,e_3,X0)|~product(X3,e_4,X2))),
% 0.10/0.40 inference(resolution,[status(thm)],[f40,f53])).
% 0.10/0.40 fof(f116,plain,(
% 0.10/0.40 ![X0,X1,X2]: (~product(X0,e_1,X1)|~product(X2,X0,e_1)|~product(X2,e_4,e_2)|~group_element(e_2)|~group_element(X1)|product(e_1,e_2,X1)|product(e_2,e_2,X1)|product(e_3,e_2,X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f59,f26])).
% 0.10/0.40 fof(f117,plain,(
% 0.10/0.40 ![X0,X1]: (~product(X0,e_1,e_2)|~product(X1,X0,e_1)|~product(X1,e_2,e_2))),
% 0.10/0.40 inference(resolution,[status(thm)],[f59,f51])).
% 0.10/0.40 fof(f118,definition,(
% 0.10/0.40 ![X0,X1,X2]: (sQ0_spl <=> (~product(X0,e_1,X1)|~product(X2,X0,e_1)|~product(X2,e_4,e_2)|~group_element(X1)|product(e_1,e_2,X1)|product(e_2,e_2,X1)|product(e_3,e_2,X1)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f121,definition,(
% 0.10/0.40 sQ1_spl <=> (group_element(e_2))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f123,plain,(
% 0.10/0.40 ~group_element(e_2)|sQ1_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f121])).
% 0.10/0.40 fof(f124,plain,(
% 0.10/0.40 sQ0_spl|~sQ1_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f116,f118,f121])).
% 0.10/0.40 fof(f125,plain,(
% 0.10/0.40 ![X0]: (~product(X0,e_4,e_1)|~product(X0,e_2,e_2)|~group_element(e_1)|~group_element(e_2)|product(e_1,e_1,e_2)|product(e_2,e_1,e_2)|product(e_3,e_1,e_2))),
% 0.10/0.40 inference(resolution,[status(thm)],[f117,f26])).
% 0.10/0.40 fof(f126,definition,(
% 0.10/0.40 ![X0]: (sQ2_spl <=> (~product(X0,e_4,e_1)|~product(X0,e_2,e_2)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f127,plain,(
% 0.10/0.40 ![X0]: (~product(X0,e_4,e_1)|~product(X0,e_2,e_2)|~sQ2_spl)),
% 0.10/0.40 inference(component_clause,[status(thm)],[f126])).
% 0.10/0.40 fof(f129,definition,(
% 0.10/0.40 sQ3_spl <=> (group_element(e_1))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f131,plain,(
% 0.10/0.40 ~group_element(e_1)|sQ3_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f129])).
% 0.10/0.40 fof(f132,definition,(
% 0.10/0.40 sQ4_spl <=> (product(e_1,e_1,e_2))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f133,plain,(
% 0.10/0.40 product(e_1,e_1,e_2)|~sQ4_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f132])).
% 0.10/0.40 fof(f135,definition,(
% 0.10/0.40 sQ5_spl <=> (product(e_2,e_1,e_2))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f136,plain,(
% 0.10/0.40 product(e_2,e_1,e_2)|~sQ5_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f135])).
% 0.10/0.40 fof(f138,definition,(
% 0.10/0.40 sQ6_spl <=> (product(e_3,e_1,e_2))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f139,plain,(
% 0.10/0.40 product(e_3,e_1,e_2)|~sQ6_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f138])).
% 0.10/0.40 fof(f141,plain,(
% 0.10/0.40 sQ2_spl|~sQ3_spl|~sQ1_spl|sQ4_spl|sQ5_spl|sQ6_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f125,f126,f129,f121,f132,f135,f138])).
% 0.10/0.40 fof(f142,plain,(
% 0.10/0.40 $false|sQ1_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f123,f29])).
% 0.10/0.40 fof(f143,plain,(
% 0.10/0.40 sQ1_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f142])).
% 0.10/0.40 fof(f145,plain,(
% 0.10/0.40 ![X0,X1,X2]: (~product(e_1,X0,X1)|~product(X2,e_1,X0)|~product(X2,e_2,e_4)|~group_element(e_2)|~group_element(X1)|product(e_2,e_1,X1)|product(e_2,e_2,X1)|product(e_2,e_3,X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f60,f27])).
% 0.10/0.40 fof(f147,definition,(
% 0.10/0.40 ![X0,X1,X2]: (sQ7_spl <=> (~product(e_1,X0,X1)|~product(X2,e_1,X0)|~product(X2,e_2,e_4)|~group_element(X1)|product(e_2,e_1,X1)|product(e_2,e_2,X1)|product(e_2,e_3,X1)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f150,plain,(
% 0.10/0.40 sQ7_spl|~sQ1_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f145,f147,f121])).
% 0.10/0.40 fof(f151,plain,(
% 0.10/0.40 ![X0]: (~product(e_1,e_4,X0)|~group_element(e_2)|~group_element(X0)|product(e_2,e_1,X0)|product(e_2,e_2,X0)|product(e_2,e_3,X0))),
% 0.10/0.40 inference(resolution,[status(thm)],[f56,f27])).
% 0.10/0.40 fof(f152,plain,(
% 0.10/0.40 ~product(e_1,e_2,e_2)),
% 0.10/0.40 inference(resolution,[status(thm)],[f56,f51])).
% 0.10/0.40 fof(f153,definition,(
% 0.10/0.40 ![X0]: (sQ8_spl <=> (~product(e_1,e_4,X0)|~group_element(X0)|product(e_2,e_1,X0)|product(e_2,e_2,X0)|product(e_2,e_3,X0)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f156,plain,(
% 0.10/0.40 sQ8_spl|~sQ1_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f151,f153,f121])).
% 0.10/0.40 fof(f157,plain,(
% 0.10/0.40 ![X0]: (~product(e_4,e_1,X0)|~group_element(e_2)|~group_element(X0)|product(e_1,e_2,X0)|product(e_2,e_2,X0)|product(e_3,e_2,X0))),
% 0.10/0.40 inference(resolution,[status(thm)],[f57,f26])).
% 0.10/0.40 fof(f158,plain,(
% 0.10/0.40 ~product(e_2,e_1,e_2)),
% 0.10/0.40 inference(resolution,[status(thm)],[f57,f51])).
% 0.10/0.40 fof(f159,definition,(
% 0.10/0.40 ![X0]: (sQ9_spl <=> (~product(e_4,e_1,X0)|~group_element(X0)|product(e_1,e_2,X0)|product(e_2,e_2,X0)|product(e_3,e_2,X0)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f162,plain,(
% 0.10/0.40 sQ9_spl|~sQ1_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f157,f159,f121])).
% 0.10/0.40 fof(f163,plain,(
% 0.10/0.40 ![X0]: (~product(e_4,X0,e_2)|~group_element(X0)|~group_element(e_1)|product(e_1,X0,e_1)|product(e_2,X0,e_1)|product(e_3,X0,e_1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f58,f26])).
% 0.10/0.40 fof(f164,plain,(
% 0.10/0.40 ![X0]: (~product(X0,e_4,e_2)|~group_element(X0)|~group_element(e_1)|product(X0,e_1,e_1)|product(X0,e_2,e_1)|product(X0,e_3,e_1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f58,f27])).
% 0.10/0.40 fof(f165,plain,(
% 0.10/0.40 ~product(e_1,e_1,e_2)),
% 0.10/0.40 inference(resolution,[status(thm)],[f58,f51])).
% 0.10/0.40 fof(f166,definition,(
% 0.10/0.40 ![X0]: (sQ10_spl <=> (~product(e_4,X0,e_2)|~group_element(X0)|product(e_1,X0,e_1)|product(e_2,X0,e_1)|product(e_3,X0,e_1)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f169,plain,(
% 0.10/0.40 sQ10_spl|~sQ3_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f163,f166,f129])).
% 0.10/0.40 fof(f170,definition,(
% 0.10/0.40 ![X0]: (sQ11_spl <=> (~product(X0,e_4,e_2)|~group_element(X0)|product(X0,e_1,e_1)|product(X0,e_2,e_1)|product(X0,e_3,e_1)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f173,plain,(
% 0.10/0.40 sQ11_spl|~sQ3_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f164,f170,f129])).
% 0.10/0.40 fof(f174,plain,(
% 0.10/0.40 $false|sQ3_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f131,f28])).
% 0.10/0.40 fof(f175,plain,(
% 0.10/0.40 sQ3_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f174])).
% 0.10/0.40 fof(f176,plain,(
% 0.10/0.40 ![X0]: (~product(e_1,e_4,X0)|~group_element(e_3)|~group_element(X0)|product(e_3,e_1,X0)|product(e_3,e_2,X0)|product(e_3,e_3,X0))),
% 0.10/0.40 inference(resolution,[status(thm)],[f61,f27])).
% 0.10/0.40 fof(f177,plain,(
% 0.10/0.40 ~product(e_1,e_3,e_3)),
% 0.10/0.40 inference(resolution,[status(thm)],[f61,f51])).
% 0.10/0.40 fof(f178,definition,(
% 0.10/0.40 ![X0]: (sQ12_spl <=> (~product(e_1,e_4,X0)|~group_element(X0)|product(e_3,e_1,X0)|product(e_3,e_2,X0)|product(e_3,e_3,X0)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f181,definition,(
% 0.10/0.40 sQ13_spl <=> (group_element(e_3))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f183,plain,(
% 0.10/0.40 ~group_element(e_3)|sQ13_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f181])).
% 0.10/0.40 fof(f184,plain,(
% 0.10/0.40 sQ12_spl|~sQ13_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f176,f178,f181])).
% 0.10/0.40 fof(f185,plain,(
% 0.10/0.40 $false|sQ13_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f183,f30])).
% 0.10/0.40 fof(f186,plain,(
% 0.10/0.40 sQ13_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f185])).
% 0.10/0.40 fof(f187,plain,(
% 0.10/0.40 ![X0]: (~product(e_4,e_1,X0)|~group_element(e_3)|~group_element(X0)|product(e_1,e_3,X0)|product(e_2,e_3,X0)|product(e_3,e_3,X0))),
% 0.10/0.40 inference(resolution,[status(thm)],[f62,f26])).
% 0.10/0.40 fof(f188,plain,(
% 0.10/0.40 ~product(e_3,e_1,e_3)),
% 0.10/0.40 inference(resolution,[status(thm)],[f62,f51])).
% 0.10/0.40 fof(f189,definition,(
% 0.10/0.40 ![X0]: (sQ14_spl <=> (~product(e_4,e_1,X0)|~group_element(X0)|product(e_1,e_3,X0)|product(e_2,e_3,X0)|product(e_3,e_3,X0)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f192,plain,(
% 0.10/0.40 sQ14_spl|~sQ13_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f187,f189,f181])).
% 0.10/0.40 fof(f194,plain,(
% 0.10/0.40 ![X0]: (~product(X0,e_3,e_1)|~product(X0,e_2,e_2)|~sQ6_spl)),
% 0.10/0.40 inference(resolution,[status(thm)],[f139,f117])).
% 0.10/0.40 fof(f195,plain,(
% 0.10/0.40 ![X0]: (~product(e_4,X0,e_1)|~group_element(X0)|~group_element(e_3)|product(e_1,X0,e_3)|product(e_2,X0,e_3)|product(e_3,X0,e_3))),
% 0.10/0.40 inference(resolution,[status(thm)],[f63,f26])).
% 0.10/0.40 fof(f196,plain,(
% 0.10/0.40 ![X0]: (~product(X0,e_4,e_1)|~group_element(X0)|~group_element(e_3)|product(X0,e_1,e_3)|product(X0,e_2,e_3)|product(X0,e_3,e_3))),
% 0.10/0.40 inference(resolution,[status(thm)],[f63,f27])).
% 0.10/0.40 fof(f197,plain,(
% 0.10/0.40 ~product(e_3,e_3,e_1)),
% 0.10/0.40 inference(resolution,[status(thm)],[f63,f51])).
% 0.10/0.40 fof(f198,definition,(
% 0.10/0.40 ![X0]: (sQ15_spl <=> (~product(e_4,X0,e_1)|~group_element(X0)|product(e_1,X0,e_3)|product(e_2,X0,e_3)|product(e_3,X0,e_3)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f201,plain,(
% 0.10/0.40 sQ15_spl|~sQ13_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f195,f198,f181])).
% 0.10/0.40 fof(f202,definition,(
% 0.10/0.40 ![X0]: (sQ16_spl <=> (~product(X0,e_4,e_1)|~group_element(X0)|product(X0,e_1,e_3)|product(X0,e_2,e_3)|product(X0,e_3,e_3)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f205,plain,(
% 0.10/0.40 sQ16_spl|~sQ13_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f196,f202,f181])).
% 0.10/0.40 fof(f206,plain,(
% 0.10/0.40 ![X0]: (~product(e_4,e_4,X0)|~group_element(e_1)|~group_element(X0)|product(e_1,e_1,X0)|product(e_1,e_2,X0)|product(e_1,e_3,X0))),
% 0.10/0.40 inference(resolution,[status(thm)],[f66,f27])).
% 0.10/0.40 fof(f207,plain,(
% 0.10/0.40 ~product(e_4,e_1,e_1)),
% 0.10/0.40 inference(resolution,[status(thm)],[f66,f51])).
% 0.10/0.40 fof(f208,definition,(
% 0.10/0.40 ![X0]: (sQ17_spl <=> (~product(e_4,e_4,X0)|~group_element(X0)|product(e_1,e_1,X0)|product(e_1,e_2,X0)|product(e_1,e_3,X0)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f211,plain,(
% 0.10/0.40 sQ17_spl|~sQ3_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f206,f208,f129])).
% 0.10/0.40 fof(f212,plain,(
% 0.10/0.40 ~group_element(e_1)|~group_element(e_1)|product(e_1,e_1,e_1)|product(e_2,e_1,e_1)|product(e_3,e_1,e_1)),
% 0.10/0.40 inference(resolution,[status(thm)],[f207,f26])).
% 0.10/0.40 fof(f213,definition,(
% 0.10/0.40 sQ18_spl <=> (product(e_1,e_1,e_1))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f216,definition,(
% 0.10/0.40 sQ19_spl <=> (product(e_2,e_1,e_1))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f217,plain,(
% 0.10/0.40 product(e_2,e_1,e_1)|~sQ19_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f216])).
% 0.10/0.40 fof(f219,definition,(
% 0.10/0.40 sQ20_spl <=> (product(e_3,e_1,e_1))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f220,plain,(
% 0.10/0.40 product(e_3,e_1,e_1)|~sQ20_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f219])).
% 0.10/0.40 fof(f222,plain,(
% 0.10/0.40 ~sQ3_spl|sQ18_spl|sQ19_spl|sQ20_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f212,f129,f213,f216,f219])).
% 0.10/0.40 fof(f223,plain,(
% 0.10/0.40 ~product(e_1,e_1,e_1)|~sQ20_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f220,f61])).
% 0.10/0.40 fof(f225,plain,(
% 0.10/0.40 $false|~sQ20_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f223,f51])).
% 0.10/0.40 fof(f226,plain,(
% 0.10/0.40 ~sQ20_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f225])).
% 0.10/0.40 fof(f227,plain,(
% 0.10/0.40 ~product(e_1,e_1,e_1)|~sQ19_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f217,f56])).
% 0.10/0.40 fof(f230,plain,(
% 0.10/0.40 $false|~sQ19_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f227,f51])).
% 0.10/0.40 fof(f231,plain,(
% 0.10/0.40 ~sQ19_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f230])).
% 0.10/0.40 fof(f236,plain,(
% 0.10/0.40 ![X0,X1,X2]: (~product(X0,e_1,X1)|~product(X2,X0,e_1)|~product(X2,e_4,e_3)|~group_element(e_3)|~group_element(X1)|product(e_1,e_3,X1)|product(e_2,e_3,X1)|product(e_3,e_3,X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f64,f26])).
% 0.10/0.40 fof(f238,definition,(
% 0.10/0.40 ![X0,X1,X2]: (sQ21_spl <=> (~product(X0,e_1,X1)|~product(X2,X0,e_1)|~product(X2,e_4,e_3)|~group_element(X1)|product(e_1,e_3,X1)|product(e_2,e_3,X1)|product(e_3,e_3,X1)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f241,plain,(
% 0.10/0.40 sQ21_spl|~sQ13_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f236,f238,f181])).
% 0.10/0.40 fof(f242,plain,(
% 0.10/0.40 ![X0,X1,X2]: (~product(e_3,X0,X1)|~product(X2,e_1,e_4)|~product(X2,e_3,X0)|~group_element(e_1)|~group_element(X1)|product(e_1,e_1,X1)|product(e_1,e_2,X1)|product(e_1,e_3,X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f65,f27])).
% 0.10/0.40 fof(f244,definition,(
% 0.10/0.40 ![X0,X1,X2]: (sQ22_spl <=> (~product(e_3,X0,X1)|~product(X2,e_1,e_4)|~product(X2,e_3,X0)|~group_element(X1)|product(e_1,e_1,X1)|product(e_1,e_2,X1)|product(e_1,e_3,X1)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f247,plain,(
% 0.10/0.40 sQ22_spl|~sQ3_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f242,f244,f129])).
% 0.10/0.40 fof(f249,definition,(
% 0.10/0.40 sQ23_spl <=> (product(e_4,e_2,e_2))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f250,plain,(
% 0.10/0.40 product(e_4,e_2,e_2)|~sQ23_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f249])).
% 0.10/0.40 fof(f252,definition,(
% 0.10/0.40 sQ24_spl <=> (product(e_1,e_3,e_1))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f253,plain,(
% 0.10/0.40 product(e_1,e_3,e_1)|~sQ24_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f252])).
% 0.10/0.40 fof(f255,definition,(
% 0.10/0.40 sQ25_spl <=> (product(e_2,e_3,e_1))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f256,plain,(
% 0.10/0.40 product(e_2,e_3,e_1)|~sQ25_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f255])).
% 0.10/0.40 fof(f258,definition,(
% 0.10/0.40 sQ26_spl <=> (product(e_3,e_3,e_1))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f259,plain,(
% 0.10/0.40 product(e_3,e_3,e_1)|~sQ26_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f258])).
% 0.10/0.40 fof(f262,plain,(
% 0.10/0.40 $false|~sQ26_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f259,f197])).
% 0.10/0.40 fof(f263,plain,(
% 0.10/0.40 ~sQ26_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f262])).
% 0.10/0.40 fof(f264,plain,(
% 0.10/0.40 $false|~sQ5_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f136,f158])).
% 0.10/0.40 fof(f265,plain,(
% 0.10/0.40 ~sQ5_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f264])).
% 0.10/0.40 fof(f266,plain,(
% 0.10/0.40 $false|~sQ4_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f133,f165])).
% 0.10/0.40 fof(f267,plain,(
% 0.10/0.40 ~sQ4_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f266])).
% 0.10/0.40 fof(f273,plain,(
% 0.10/0.40 ![X0,X1,X2]: (~product(X0,e_4,X1)|~product(X2,e_4,e_1)|~product(X2,X0,e_4)|~group_element(e_1)|~group_element(X1)|product(e_1,e_1,X1)|product(e_2,e_1,X1)|product(e_3,e_1,X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f69,f26])).
% 0.10/0.40 fof(f275,definition,(
% 0.10/0.40 ![X0,X1,X2]: (sQ27_spl <=> (~product(X0,e_4,X1)|~product(X2,e_4,e_1)|~product(X2,X0,e_4)|~group_element(X1)|product(e_1,e_1,X1)|product(e_2,e_1,X1)|product(e_3,e_1,X1)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f278,plain,(
% 0.10/0.40 sQ27_spl|~sQ3_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f273,f275,f129])).
% 0.10/0.40 fof(f279,plain,(
% 0.10/0.40 ![X0]: (~product(e_4,e_4,X0)|~group_element(e_1)|~group_element(X0)|product(e_1,e_1,X0)|product(e_2,e_1,X0)|product(e_3,e_1,X0))),
% 0.10/0.40 inference(resolution,[status(thm)],[f67,f26])).
% 0.10/0.40 fof(f280,plain,(
% 0.10/0.40 ~product(e_1,e_4,e_1)),
% 0.10/0.40 inference(resolution,[status(thm)],[f67,f51])).
% 0.10/0.40 fof(f281,definition,(
% 0.10/0.40 ![X0]: (sQ28_spl <=> (~product(e_4,e_4,X0)|~group_element(X0)|product(e_1,e_1,X0)|product(e_2,e_1,X0)|product(e_3,e_1,X0)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f284,plain,(
% 0.10/0.40 sQ28_spl|~sQ3_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f279,f281,f129])).
% 0.10/0.40 fof(f286,definition,(
% 0.10/0.40 sQ29_spl <=> (product(e_1,e_2,e_1))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f287,plain,(
% 0.10/0.40 product(e_1,e_2,e_1)|~sQ29_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f286])).
% 0.10/0.40 fof(f290,plain,(
% 0.10/0.40 ![X0]: (~product(e_4,X0,e_1)|~group_element(X0)|~group_element(e_4)|product(e_1,X0,e_4)|product(e_2,X0,e_4)|product(e_3,X0,e_4))),
% 0.10/0.40 inference(resolution,[status(thm)],[f68,f26])).
% 0.10/0.40 fof(f291,plain,(
% 0.10/0.40 ![X0]: (~product(X0,e_4,e_1)|~group_element(X0)|~group_element(e_4)|product(X0,e_1,e_4)|product(X0,e_2,e_4)|product(X0,e_3,e_4))),
% 0.10/0.40 inference(resolution,[status(thm)],[f68,f27])).
% 0.10/0.40 fof(f292,plain,(
% 0.10/0.40 ~product(e_4,e_4,e_1)),
% 0.10/0.40 inference(resolution,[status(thm)],[f68,f51])).
% 0.10/0.40 fof(f293,definition,(
% 0.10/0.40 ![X0]: (sQ30_spl <=> (~product(e_4,X0,e_1)|~group_element(X0)|product(e_1,X0,e_4)|product(e_2,X0,e_4)|product(e_3,X0,e_4)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f296,definition,(
% 0.10/0.40 sQ31_spl <=> (group_element(e_4))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f298,plain,(
% 0.10/0.40 ~group_element(e_4)|sQ31_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f296])).
% 0.10/0.40 fof(f299,plain,(
% 0.10/0.40 sQ30_spl|~sQ31_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f290,f293,f296])).
% 0.10/0.40 fof(f300,definition,(
% 0.10/0.40 ![X0]: (sQ32_spl <=> (~product(X0,e_4,e_1)|~group_element(X0)|product(X0,e_1,e_4)|product(X0,e_2,e_4)|product(X0,e_3,e_4)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f303,plain,(
% 0.10/0.40 sQ32_spl|~sQ31_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f291,f300,f296])).
% 0.10/0.40 fof(f304,plain,(
% 0.10/0.40 $false|sQ31_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f298,f31])).
% 0.10/0.40 fof(f305,plain,(
% 0.10/0.40 sQ31_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f304])).
% 0.10/0.40 fof(f306,plain,(
% 0.10/0.40 ![X0,X1,X2]: (~product(e_4,X0,X1)|~product(X2,e_1,e_4)|~product(X2,e_4,X0)|~group_element(e_1)|~group_element(X1)|product(e_1,e_1,X1)|product(e_1,e_2,X1)|product(e_1,e_3,X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f70,f27])).
% 0.10/0.40 fof(f308,definition,(
% 0.10/0.40 ![X0,X1,X2]: (sQ33_spl <=> (~product(e_4,X0,X1)|~product(X2,e_1,e_4)|~product(X2,e_4,X0)|~group_element(X1)|product(e_1,e_1,X1)|product(e_1,e_2,X1)|product(e_1,e_3,X1)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f311,plain,(
% 0.10/0.40 sQ33_spl|~sQ3_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f306,f308,f129])).
% 0.10/0.40 fof(f316,plain,(
% 0.10/0.40 ~product(e_1,e_1,e_1)|~sQ24_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f253,f62])).
% 0.10/0.40 fof(f318,plain,(
% 0.10/0.40 $false|~sQ24_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f316,f51])).
% 0.10/0.40 fof(f319,plain,(
% 0.10/0.40 ~sQ24_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f318])).
% 0.10/0.40 fof(f320,plain,(
% 0.10/0.40 ~group_element(e_4)|~group_element(e_1)|product(e_1,e_4,e_1)|product(e_2,e_4,e_1)|product(e_3,e_4,e_1)),
% 0.10/0.40 inference(resolution,[status(thm)],[f292,f26])).
% 0.10/0.40 fof(f321,plain,(
% 0.10/0.40 ~group_element(e_4)|~group_element(e_1)|product(e_4,e_1,e_1)|product(e_4,e_2,e_1)|product(e_4,e_3,e_1)),
% 0.10/0.40 inference(resolution,[status(thm)],[f292,f27])).
% 0.10/0.40 fof(f322,definition,(
% 0.10/0.40 sQ34_spl <=> (product(e_1,e_4,e_1))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f323,plain,(
% 0.10/0.40 product(e_1,e_4,e_1)|~sQ34_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f322])).
% 0.10/0.40 fof(f325,definition,(
% 0.10/0.40 sQ35_spl <=> (product(e_2,e_4,e_1))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f326,plain,(
% 0.10/0.40 product(e_2,e_4,e_1)|~sQ35_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f325])).
% 0.10/0.40 fof(f328,definition,(
% 0.10/0.40 sQ36_spl <=> (product(e_3,e_4,e_1))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f329,plain,(
% 0.10/0.40 product(e_3,e_4,e_1)|~sQ36_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f328])).
% 0.10/0.40 fof(f331,plain,(
% 0.10/0.40 ~sQ31_spl|~sQ3_spl|sQ34_spl|sQ35_spl|sQ36_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f320,f296,f129,f322,f325,f328])).
% 0.10/0.40 fof(f332,definition,(
% 0.10/0.40 sQ37_spl <=> (product(e_4,e_1,e_1))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f333,plain,(
% 0.10/0.40 product(e_4,e_1,e_1)|~sQ37_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f332])).
% 0.10/0.40 fof(f335,definition,(
% 0.10/0.40 sQ38_spl <=> (product(e_4,e_2,e_1))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f336,plain,(
% 0.10/0.40 product(e_4,e_2,e_1)|~sQ38_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f335])).
% 0.10/0.40 fof(f338,definition,(
% 0.10/0.40 sQ39_spl <=> (product(e_4,e_3,e_1))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f339,plain,(
% 0.10/0.40 product(e_4,e_3,e_1)|~sQ39_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f338])).
% 0.10/0.40 fof(f341,plain,(
% 0.10/0.40 ~sQ31_spl|~sQ3_spl|sQ37_spl|sQ38_spl|sQ39_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f321,f296,f129,f332,f335,f338])).
% 0.10/0.40 fof(f342,plain,(
% 0.10/0.40 $false|~sQ37_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f333,f207])).
% 0.10/0.40 fof(f343,plain,(
% 0.10/0.40 ~sQ37_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f342])).
% 0.10/0.40 fof(f344,plain,(
% 0.10/0.40 $false|~sQ34_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f323,f280])).
% 0.10/0.40 fof(f345,plain,(
% 0.10/0.40 ~sQ34_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f344])).
% 0.10/0.40 fof(f349,plain,(
% 0.10/0.40 ~product(e_1,e_1,e_1)|~sQ29_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f287,f57])).
% 0.10/0.40 fof(f352,plain,(
% 0.10/0.40 $false|~sQ29_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f349,f51])).
% 0.10/0.40 fof(f353,plain,(
% 0.10/0.40 ~sQ29_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f352])).
% 0.10/0.40 fof(f361,plain,(
% 0.10/0.40 ~product(e_4,e_3,e_2)|~sQ39_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f339,f58])).
% 0.10/0.40 fof(f374,plain,(
% 0.10/0.40 ~product(e_3,e_2,e_2)|~sQ36_spl|~sQ2_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f329,f127])).
% 0.10/0.40 fof(f375,plain,(
% 0.10/0.40 ~product(e_3,e_4,e_2)|~sQ36_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f329,f58])).
% 0.10/0.40 fof(f378,plain,(
% 0.10/0.40 ~product(e_2,e_2,e_2)|~sQ35_spl|~sQ2_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f326,f127])).
% 0.10/0.40 fof(f380,plain,(
% 0.10/0.40 $false|~sQ35_spl|~sQ2_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f378,f51])).
% 0.10/0.40 fof(f381,plain,(
% 0.10/0.40 ~sQ35_spl|~sQ2_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f380])).
% 0.10/0.40 fof(f383,definition,(
% 0.10/0.40 sQ41_spl <=> (product(e_1,e_2,e_2))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f384,plain,(
% 0.10/0.40 product(e_1,e_2,e_2)|~sQ41_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f383])).
% 0.10/0.40 fof(f389,definition,(
% 0.10/0.40 sQ43_spl <=> (product(e_3,e_2,e_2))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f390,plain,(
% 0.10/0.40 product(e_3,e_2,e_2)|~sQ43_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f389])).
% 0.10/0.40 fof(f395,plain,(
% 0.10/0.40 $false|~sQ41_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f384,f152])).
% 0.10/0.40 fof(f396,plain,(
% 0.10/0.40 ~sQ41_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f395])).
% 0.10/0.40 fof(f397,plain,(
% 0.10/0.40 ![X0]: (~product(e_3,e_4,X0)|~group_element(e_2)|~group_element(X0)|product(e_2,e_1,X0)|product(e_2,e_2,X0)|product(e_2,e_3,X0))),
% 0.10/0.40 inference(resolution,[status(thm)],[f76,f27])).
% 0.10/0.40 fof(f399,definition,(
% 0.10/0.40 ![X0]: (sQ44_spl <=> (~product(e_3,e_4,X0)|~group_element(X0)|product(e_2,e_1,X0)|product(e_2,e_2,X0)|product(e_2,e_3,X0)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f402,plain,(
% 0.10/0.40 sQ44_spl|~sQ1_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f397,f399,f121])).
% 0.10/0.40 fof(f403,plain,(
% 0.10/0.40 ~group_element(e_3)|~group_element(e_2)|product(e_3,e_1,e_2)|product(e_3,e_2,e_2)|product(e_3,e_3,e_2)|~sQ36_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f375,f27])).
% 0.10/0.40 fof(f404,definition,(
% 0.10/0.40 sQ45_spl <=> (product(e_3,e_3,e_2))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f405,plain,(
% 0.10/0.40 product(e_3,e_3,e_2)|~sQ45_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f404])).
% 0.10/0.40 fof(f407,plain,(
% 0.10/0.40 ~sQ13_spl|~sQ1_spl|sQ6_spl|sQ43_spl|sQ45_spl|~sQ36_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f403,f181,f121,f138,f389,f404,f328])).
% 0.10/0.40 fof(f409,definition,(
% 0.10/0.40 sQ46_spl <=> (product(e_2,e_2,e_1))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f410,plain,(
% 0.10/0.40 product(e_2,e_2,e_1)|~sQ46_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f409])).
% 0.10/0.40 fof(f424,plain,(
% 0.10/0.40 $false|~sQ36_spl|~sQ2_spl|~sQ43_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f390,f374])).
% 0.10/0.40 fof(f425,plain,(
% 0.10/0.40 ~sQ36_spl|~sQ2_spl|~sQ43_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f424])).
% 0.10/0.40 fof(f432,plain,(
% 0.10/0.40 ![X0]: (~product(e_4,e_3,X0)|~group_element(e_2)|~group_element(X0)|product(e_1,e_2,X0)|product(e_2,e_2,X0)|product(e_3,e_2,X0))),
% 0.10/0.40 inference(resolution,[status(thm)],[f77,f26])).
% 0.10/0.40 fof(f434,definition,(
% 0.10/0.40 ![X0]: (sQ49_spl <=> (~product(e_4,e_3,X0)|~group_element(X0)|product(e_1,e_2,X0)|product(e_2,e_2,X0)|product(e_3,e_2,X0)))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f437,plain,(
% 0.10/0.40 sQ49_spl|~sQ1_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f432,f434,f121])).
% 0.10/0.40 fof(f438,plain,(
% 0.10/0.40 ![X0]: (~product(e_4,X0,e_2)|~group_element(X0)|~group_element(e_3)|product(e_1,X0,e_3)|product(e_2,X0,e_3)|product(e_3,X0,e_3))),
% 0.10/0.40 inference(resolution,[status(thm)],[f78,f26])).
% 0.10/0.40 fof(f439,plain,(
% 0.10/0.40 ![X0]: (~product(X0,e_4,e_2)|~group_element(X0)|~group_element(e_3)|product(X0,e_1,e_3)|product(X0,e_2,e_3)|product(X0,e_3,e_3))),
% 0.10/0.41 inference(resolution,[status(thm)],[f78,f27])).
% 0.10/0.41 fof(f440,plain,(
% 0.10/0.41 ~product(e_3,e_3,e_2)),
% 0.10/0.41 inference(resolution,[status(thm)],[f78,f51])).
% 0.10/0.41 fof(f441,definition,(
% 0.10/0.41 ![X0]: (sQ50_spl <=> (~product(e_4,X0,e_2)|~group_element(X0)|product(e_1,X0,e_3)|product(e_2,X0,e_3)|product(e_3,X0,e_3)))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f444,plain,(
% 0.10/0.41 sQ50_spl|~sQ13_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f438,f441,f181])).
% 0.10/0.41 fof(f445,definition,(
% 0.10/0.41 ![X0]: (sQ51_spl <=> (~product(X0,e_4,e_2)|~group_element(X0)|product(X0,e_1,e_3)|product(X0,e_2,e_3)|product(X0,e_3,e_3)))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f448,plain,(
% 0.10/0.41 sQ51_spl|~sQ13_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f439,f445,f181])).
% 0.10/0.41 fof(f449,plain,(
% 0.10/0.41 ![X0,X1,X2]: (~product(X0,e_3,X1)|~product(X2,e_4,e_2)|~product(X2,X0,e_3)|~group_element(e_2)|~group_element(X1)|product(e_1,e_2,X1)|product(e_2,e_2,X1)|product(e_3,e_2,X1))),
% 0.10/0.41 inference(resolution,[status(thm)],[f79,f26])).
% 0.10/0.41 fof(f451,definition,(
% 0.10/0.41 ![X0,X1,X2]: (sQ52_spl <=> (~product(X0,e_3,X1)|~product(X2,e_4,e_2)|~product(X2,X0,e_3)|~group_element(X1)|product(e_1,e_2,X1)|product(e_2,e_2,X1)|product(e_3,e_2,X1)))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f454,plain,(
% 0.10/0.41 sQ52_spl|~sQ1_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f449,f451,f121])).
% 0.10/0.41 fof(f470,definition,(
% 0.10/0.41 sQ57_spl <=> (product(e_3,e_1,e_3))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f471,plain,(
% 0.10/0.41 product(e_3,e_1,e_3)|~sQ57_spl),
% 0.10/0.41 inference(component_clause,[status(thm)],[f470])).
% 0.10/0.41 fof(f474,plain,(
% 0.10/0.41 $false|~sQ57_spl),
% 0.10/0.41 inference(forward_subsumption_resolution,[status(thm)],[f471,f188])).
% 0.10/0.41 fof(f475,plain,(
% 0.10/0.41 ~sQ57_spl),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f474])).
% 0.10/0.41 fof(f476,plain,(
% 0.10/0.41 ![X0,X1,X2]: (~product(e_2,X0,X1)|~product(e_3,X2,X1)|~product(e_4,e_3,X2)|~group_element(e_2)|~group_element(X0)|product(e_1,e_2,X0)|product(e_2,e_2,X0)|product(e_3,e_2,X0))),
% 0.10/0.41 inference(resolution,[status(thm)],[f80,f26])).
% 0.10/0.41 fof(f478,definition,(
% 0.10/0.41 ![X0,X1,X2]: (sQ58_spl <=> (~product(e_2,X0,X1)|~product(e_3,X2,X1)|~product(e_4,e_3,X2)|~group_element(X0)|product(e_1,e_2,X0)|product(e_2,e_2,X0)|product(e_3,e_2,X0)))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f481,plain,(
% 0.10/0.41 sQ58_spl|~sQ1_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f476,f478,f121])).
% 0.10/0.41 fof(f487,plain,(
% 0.10/0.41 ~product(e_4,e_3,e_1)|~sQ38_spl),
% 0.10/0.41 inference(resolution,[status(thm)],[f336,f77])).
% 0.10/0.41 fof(f493,plain,(
% 0.10/0.41 $false|~sQ45_spl),
% 0.10/0.41 inference(forward_subsumption_resolution,[status(thm)],[f440,f405])).
% 0.10/0.41 fof(f494,plain,(
% 0.10/0.41 ~sQ45_spl),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f493])).
% 0.10/0.41 fof(f502,plain,(
% 0.10/0.41 ![X0]: (~product(e_4,e_4,X0)|~group_element(e_2)|~group_element(X0)|product(e_2,e_1,X0)|product(e_2,e_2,X0)|product(e_2,e_3,X0))),
% 0.10/0.41 inference(resolution,[status(thm)],[f81,f27])).
% 0.10/0.41 fof(f503,plain,(
% 0.10/0.41 ~product(e_4,e_2,e_2)),
% 0.10/0.41 inference(resolution,[status(thm)],[f81,f51])).
% 0.10/0.41 fof(f504,definition,(
% 0.10/0.41 ![X0]: (sQ59_spl <=> (~product(e_4,e_4,X0)|~group_element(X0)|product(e_2,e_1,X0)|product(e_2,e_2,X0)|product(e_2,e_3,X0)))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f507,plain,(
% 0.10/0.41 sQ59_spl|~sQ1_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f502,f504,f121])).
% 0.10/0.41 fof(f509,plain,(
% 0.10/0.41 ![X0]: (~product(e_4,e_4,X0)|~group_element(e_2)|~group_element(X0)|product(e_1,e_2,X0)|product(e_2,e_2,X0)|product(e_3,e_2,X0))),
% 0.10/0.41 inference(resolution,[status(thm)],[f82,f26])).
% 0.10/0.41 fof(f510,plain,(
% 0.10/0.41 ~product(e_2,e_4,e_2)),
% 0.10/0.41 inference(resolution,[status(thm)],[f82,f51])).
% 0.10/0.41 fof(f511,definition,(
% 0.10/0.41 ![X0]: (sQ60_spl <=> (~product(e_4,e_4,X0)|~group_element(X0)|product(e_1,e_2,X0)|product(e_2,e_2,X0)|product(e_3,e_2,X0)))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f514,plain,(
% 0.10/0.41 sQ60_spl|~sQ1_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f509,f511,f121])).
% 0.10/0.41 fof(f524,plain,(
% 0.10/0.41 ~group_element(e_3)|~group_element(e_1)|product(e_1,e_3,e_1)|product(e_2,e_3,e_1)|product(e_3,e_3,e_1)|~sQ38_spl),
% 0.10/0.41 inference(resolution,[status(thm)],[f487,f26])).
% 0.10/0.41 fof(f525,plain,(
% 0.10/0.41 ~sQ13_spl|~sQ3_spl|sQ24_spl|sQ25_spl|sQ26_spl|~sQ38_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f524,f181,f129,f252,f255,f258,f335])).
% 0.10/0.41 fof(f536,plain,(
% 0.10/0.41 ![X0]: (~product(e_4,X0,e_2)|~group_element(X0)|~group_element(e_4)|product(e_1,X0,e_4)|product(e_2,X0,e_4)|product(e_3,X0,e_4))),
% 0.10/0.41 inference(resolution,[status(thm)],[f83,f26])).
% 0.10/0.41 fof(f537,plain,(
% 0.10/0.41 ![X0]: (~product(X0,e_4,e_2)|~group_element(X0)|~group_element(e_4)|product(X0,e_1,e_4)|product(X0,e_2,e_4)|product(X0,e_3,e_4))),
% 0.10/0.41 inference(resolution,[status(thm)],[f83,f27])).
% 0.10/0.41 fof(f538,plain,(
% 0.10/0.41 ~product(e_4,e_4,e_2)),
% 0.10/0.41 inference(resolution,[status(thm)],[f83,f51])).
% 0.10/0.41 fof(f539,definition,(
% 0.10/0.41 ![X0]: (sQ61_spl <=> (~product(e_4,X0,e_2)|~group_element(X0)|product(e_1,X0,e_4)|product(e_2,X0,e_4)|product(e_3,X0,e_4)))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f542,plain,(
% 0.10/0.41 sQ61_spl|~sQ31_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f536,f539,f296])).
% 0.10/0.41 fof(f543,definition,(
% 0.10/0.41 ![X0]: (sQ62_spl <=> (~product(X0,e_4,e_2)|~group_element(X0)|product(X0,e_1,e_4)|product(X0,e_2,e_4)|product(X0,e_3,e_4)))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f546,plain,(
% 0.10/0.41 sQ62_spl|~sQ31_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f537,f543,f296])).
% 0.10/0.41 fof(f548,plain,(
% 0.10/0.41 ![X0,X1,X2]: (~product(X0,e_4,X1)|~product(X2,e_4,e_2)|~product(X2,X0,e_4)|~group_element(e_2)|~group_element(X1)|product(e_1,e_2,X1)|product(e_2,e_2,X1)|product(e_3,e_2,X1))),
% 0.10/0.41 inference(resolution,[status(thm)],[f84,f26])).
% 0.10/0.41 fof(f550,definition,(
% 0.10/0.41 ![X0,X1,X2]: (sQ63_spl <=> (~product(X0,e_4,X1)|~product(X2,e_4,e_2)|~product(X2,X0,e_4)|~group_element(X1)|product(e_1,e_2,X1)|product(e_2,e_2,X1)|product(e_3,e_2,X1)))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f553,plain,(
% 0.10/0.41 sQ63_spl|~sQ1_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f548,f550,f121])).
% 0.10/0.41 fof(f555,plain,(
% 0.10/0.41 ![X0,X1,X2]: (~product(e_2,X0,X1)|~product(e_4,X2,X1)|~product(e_4,e_4,X2)|~group_element(e_2)|~group_element(X0)|product(e_1,e_2,X0)|product(e_2,e_2,X0)|product(e_3,e_2,X0))),
% 0.10/0.41 inference(resolution,[status(thm)],[f85,f26])).
% 0.10/0.41 fof(f557,definition,(
% 0.10/0.41 ![X0,X1,X2]: (sQ64_spl <=> (~product(e_2,X0,X1)|~product(e_4,X2,X1)|~product(e_4,e_4,X2)|~group_element(X0)|product(e_1,e_2,X0)|product(e_2,e_2,X0)|product(e_3,e_2,X0)))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f560,plain,(
% 0.10/0.41 sQ64_spl|~sQ1_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f555,f557,f121])).
% 0.10/0.41 fof(f567,definition,(
% 0.10/0.41 sQ66_spl <=> (product(e_2,e_3,e_3))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f568,plain,(
% 0.10/0.41 product(e_2,e_3,e_3)|~sQ66_spl),
% 0.10/0.41 inference(component_clause,[status(thm)],[f567])).
% 0.10/0.41 fof(f572,plain,(
% 0.10/0.41 ~group_element(e_4)|~group_element(e_2)|product(e_4,e_1,e_2)|product(e_4,e_2,e_2)|product(e_4,e_3,e_2)),
% 0.10/0.41 inference(resolution,[status(thm)],[f538,f27])).
% 0.10/0.41 fof(f576,definition,(
% 0.10/0.41 sQ68_spl <=> (product(e_2,e_4,e_2))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f577,plain,(
% 0.10/0.41 product(e_2,e_4,e_2)|~sQ68_spl),
% 0.10/0.41 inference(component_clause,[status(thm)],[f576])).
% 0.10/0.41 fof(f583,definition,(
% 0.10/0.41 sQ70_spl <=> (product(e_4,e_1,e_2))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f584,plain,(
% 0.10/0.41 product(e_4,e_1,e_2)|~sQ70_spl),
% 0.10/0.41 inference(component_clause,[status(thm)],[f583])).
% 0.10/0.41 fof(f586,definition,(
% 0.10/0.41 sQ71_spl <=> (product(e_4,e_3,e_2))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f589,plain,(
% 0.10/0.41 ~sQ31_spl|~sQ1_spl|sQ70_spl|sQ23_spl|sQ71_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f572,f296,f121,f583,f249,f586])).
% 0.10/0.41 fof(f594,plain,(
% 0.10/0.41 $false|~sQ68_spl),
% 0.10/0.41 inference(forward_subsumption_resolution,[status(thm)],[f577,f510])).
% 0.10/0.41 fof(f595,plain,(
% 0.10/0.41 ~sQ68_spl),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f594])).
% 0.10/0.41 fof(f603,plain,(
% 0.10/0.41 ~product(e_4,e_1,e_2)|~sQ6_spl),
% 0.10/0.41 inference(resolution,[status(thm)],[f96,f139])).
% 0.10/0.41 fof(f605,plain,(
% 0.10/0.41 ![X0]: (~product(e_4,e_4,X0)|~group_element(e_3)|~group_element(X0)|product(e_3,e_1,X0)|product(e_3,e_2,X0)|product(e_3,e_3,X0))),
% 0.10/0.41 inference(resolution,[status(thm)],[f96,f27])).
% 0.10/0.41 fof(f606,plain,(
% 0.10/0.41 ~product(e_4,e_3,e_3)),
% 0.10/0.41 inference(resolution,[status(thm)],[f96,f51])).
% 0.10/0.41 fof(f607,plain,(
% 0.10/0.41 $false|~sQ70_spl|~sQ6_spl),
% 0.10/0.41 inference(forward_subsumption_resolution,[status(thm)],[f603,f584])).
% 0.10/0.41 fof(f608,plain,(
% 0.10/0.41 ~sQ70_spl|~sQ6_spl),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f607])).
% 0.10/0.41 fof(f609,definition,(
% 0.10/0.41 ![X0]: (sQ72_spl <=> (~product(e_4,e_4,X0)|~group_element(X0)|product(e_3,e_1,X0)|product(e_3,e_2,X0)|product(e_3,e_3,X0)))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f612,plain,(
% 0.10/0.41 sQ72_spl|~sQ13_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f605,f609,f181])).
% 0.10/0.41 fof(f615,plain,(
% 0.10/0.41 ~group_element(e_3)|~group_element(e_3)|product(e_1,e_3,e_3)|product(e_2,e_3,e_3)|product(e_3,e_3,e_3)),
% 0.10/0.41 inference(resolution,[status(thm)],[f606,f26])).
% 0.10/0.41 fof(f616,definition,(
% 0.10/0.41 sQ73_spl <=> (product(e_1,e_3,e_3))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f617,plain,(
% 0.10/0.41 product(e_1,e_3,e_3)|~sQ73_spl),
% 0.10/0.41 inference(component_clause,[status(thm)],[f616])).
% 0.10/0.41 fof(f619,definition,(
% 0.10/0.41 sQ74_spl <=> (product(e_3,e_3,e_3))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f622,plain,(
% 0.10/0.41 ~sQ13_spl|sQ73_spl|sQ66_spl|sQ74_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f615,f181,f616,f567,f619])).
% 0.10/0.41 fof(f623,plain,(
% 0.10/0.41 $false|~sQ73_spl),
% 0.10/0.41 inference(forward_subsumption_resolution,[status(thm)],[f617,f177])).
% 0.10/0.41 fof(f624,plain,(
% 0.10/0.41 ~sQ73_spl),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f623])).
% 0.10/0.41 fof(f637,plain,(
% 0.10/0.41 $false|~sQ23_spl),
% 0.10/0.41 inference(forward_subsumption_resolution,[status(thm)],[f503,f250])).
% 0.10/0.41 fof(f638,plain,(
% 0.10/0.41 ~sQ23_spl),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f637])).
% 0.10/0.41 fof(f639,plain,(
% 0.10/0.41 ~sQ71_spl|~sQ39_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f361,f586,f338])).
% 0.10/0.41 fof(f641,plain,(
% 0.10/0.41 ![X0]: (~product(e_4,e_4,X0)|~group_element(e_3)|~group_element(X0)|product(e_1,e_3,X0)|product(e_2,e_3,X0)|product(e_3,e_3,X0))),
% 0.10/0.41 inference(resolution,[status(thm)],[f97,f26])).
% 0.10/0.41 fof(f643,definition,(
% 0.10/0.41 ![X0]: (sQ75_spl <=> (~product(e_4,e_4,X0)|~group_element(X0)|product(e_1,e_3,X0)|product(e_2,e_3,X0)|product(e_3,e_3,X0)))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f646,plain,(
% 0.10/0.41 sQ75_spl|~sQ13_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f641,f643,f181])).
% 0.10/0.41 fof(f648,plain,(
% 0.10/0.41 ~product(e_3,e_3,e_3)|~sQ66_spl),
% 0.10/0.41 inference(resolution,[status(thm)],[f568,f76])).
% 0.10/0.41 fof(f656,plain,(
% 0.10/0.41 $false|~sQ66_spl),
% 0.10/0.41 inference(forward_subsumption_resolution,[status(thm)],[f648,f51])).
% 0.10/0.41 fof(f657,plain,(
% 0.10/0.41 ~sQ66_spl),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f656])).
% 0.10/0.41 fof(f669,plain,(
% 0.10/0.41 ![X0,X1,X2]: (~product(X0,e_4,X1)|~product(X2,e_4,e_3)|~product(X2,X0,e_4)|~group_element(e_3)|~group_element(X1)|product(e_1,e_3,X1)|product(e_2,e_3,X1)|product(e_3,e_3,X1))),
% 0.10/0.41 inference(resolution,[status(thm)],[f99,f26])).
% 0.10/0.41 fof(f671,definition,(
% 0.10/0.41 ![X0,X1,X2]: (sQ76_spl <=> (~product(X0,e_4,X1)|~product(X2,e_4,e_3)|~product(X2,X0,e_4)|~group_element(X1)|product(e_1,e_3,X1)|product(e_2,e_3,X1)|product(e_3,e_3,X1)))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f674,plain,(
% 0.10/0.41 sQ76_spl|~sQ13_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f669,f671,f181])).
% 0.10/0.41 fof(f687,plain,(
% 0.10/0.41 ~product(e_2,e_2,e_2)|~sQ46_spl),
% 0.10/0.41 inference(resolution,[status(thm)],[f410,f58])).
% 0.10/0.41 fof(f690,plain,(
% 0.10/0.41 $false|~sQ46_spl),
% 0.10/0.41 inference(forward_subsumption_resolution,[status(thm)],[f687,f51])).
% 0.10/0.41 fof(f691,plain,(
% 0.10/0.41 ~sQ46_spl),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f690])).
% 0.10/0.41 fof(f705,plain,(
% 0.10/0.41 ![X0]: (~product(e_4,X0,e_3)|~group_element(X0)|~group_element(e_4)|product(e_1,X0,e_4)|product(e_2,X0,e_4)|product(e_3,X0,e_4))),
% 0.10/0.41 inference(resolution,[status(thm)],[f98,f26])).
% 0.10/0.41 fof(f706,plain,(
% 0.10/0.41 ![X0]: (~product(X0,e_4,e_3)|~group_element(X0)|~group_element(e_4)|product(X0,e_1,e_4)|product(X0,e_2,e_4)|product(X0,e_3,e_4))),
% 0.10/0.41 inference(resolution,[status(thm)],[f98,f27])).
% 0.10/0.41 fof(f708,definition,(
% 0.10/0.41 ![X0]: (sQ77_spl <=> (~product(e_4,X0,e_3)|~group_element(X0)|product(e_1,X0,e_4)|product(e_2,X0,e_4)|product(e_3,X0,e_4)))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f711,plain,(
% 0.10/0.41 sQ77_spl|~sQ31_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f705,f708,f296])).
% 0.10/0.41 fof(f712,definition,(
% 0.10/0.41 ![X0]: (sQ78_spl <=> (~product(X0,e_4,e_3)|~group_element(X0)|product(X0,e_1,e_4)|product(X0,e_2,e_4)|product(X0,e_3,e_4)))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f715,plain,(
% 0.10/0.41 sQ78_spl|~sQ31_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f706,f712,f296])).
% 0.10/0.41 fof(f718,plain,(
% 0.10/0.41 ![X0,X1,X2]: (~product(e_4,X0,X1)|~product(X2,e_3,e_4)|~product(X2,e_4,X0)|~group_element(e_3)|~group_element(X1)|product(e_3,e_1,X1)|product(e_3,e_2,X1)|product(e_3,e_3,X1))),
% 0.10/0.41 inference(resolution,[status(thm)],[f100,f27])).
% 0.10/0.41 fof(f720,definition,(
% 0.10/0.41 ![X0,X1,X2]: (sQ79_spl <=> (~product(e_4,X0,X1)|~product(X2,e_3,e_4)|~product(X2,e_4,X0)|~group_element(X1)|product(e_3,e_1,X1)|product(e_3,e_2,X1)|product(e_3,e_3,X1)))),
% 0.10/0.41 introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition])).
% 0.10/0.41 fof(f723,plain,(
% 0.10/0.41 sQ79_spl|~sQ13_spl),
% 0.10/0.41 inference(split_clause,[status(thm)],[f718,f720,f181])).
% 0.10/0.41 fof(f731,plain,(
% 0.10/0.41 ~product(e_2,e_2,e_2)|~sQ6_spl|~sQ25_spl),
% 0.10/0.41 inference(resolution,[status(thm)],[f194,f256])).
% 0.10/0.41 fof(f733,plain,(
% 0.10/0.41 $false|~sQ6_spl|~sQ25_spl),
% 0.10/0.41 inference(forward_subsumption_resolution,[status(thm)],[f731,f51])).
% 0.10/0.41 fof(f734,plain,(
% 0.10/0.41 ~sQ6_spl|~sQ25_spl),
% 0.10/0.41 inference(contradiction_clause,[status(thm)],[f733])).
% 0.10/0.41 fof(f735,plain,(
% 0.10/0.41 $false),
% 0.10/0.41 inference(sat_refutation,[status(thm)],[f124,f141,f143,f150,f156,f162,f169,f173,f175,f184,f186,f192,f201,f205,f211,f222,f226,f231,f241,f247,f263,f265,f267,f278,f284,f299,f303,f305,f311,f319,f331,f341,f343,f345,f353,f381,f396,f402,f407,f425,f437,f444,f448,f454,f475,f481,f494,f507,f514,f525,f542,f546,f553,f560,f589,f595,f608,f612,f622,f624,f638,f639,f646,f657,f674,f691,f711,f715,f723,f734])).
% 0.10/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.43 % Elapsed time: 0.053769 seconds
% 0.10/0.43 % CPU time: 0.206723 seconds
% 0.10/0.43 % Total memory used: 19.365 MB
% 0.10/0.43 % Net memory used: 18.992 MB
%------------------------------------------------------------------------------