%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP130-2.003 : 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 : n003.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 12:35:58 PM UTC 2026
% Result : Unsatisfiable 0.19s 0.52s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP130-2.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n003.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sun Sep 20 20:03:00 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.46 % Drodi V4.1.1
% 0.19/0.52 % Refutation found
% 0.19/0.52 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/0.52 % SZS output start CNFRefutation for theBenchmark
% 0.19/0.52 fof(f1,axiom,(
% 0.19/0.52 next(e_1,e_2) ),
% 0.19/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.52 fof(f5,axiom,(
% 0.19/0.52 greater(e_3,e_2) ),
% 0.19/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.52 fof(f6,axiom,(
% 0.19/0.52 (![X,Y,X1]: (( ~ product(X,e_1,Y)| ~ next(X,X1)| ~ greater(Y,X1) ) ))),
% 0.19/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.52 fof(f7,axiom,(
% 0.19/0.52 group_element(e_1) ),
% 0.19/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.52 fof(f8,axiom,(
% 0.19/0.52 group_element(e_2) ),
% 0.19/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.52 fof(f9,axiom,(
% 0.19/0.52 group_element(e_3) ),
% 0.19/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.52 fof(f10,axiom,(
% 0.19/0.52 ~ equalish(e_1,e_2) ),
% 0.19/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.52 fof(f11,axiom,(
% 0.19/0.52 ~ equalish(e_1,e_3) ),
% 0.19/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.52 fof(f12,axiom,(
% 0.19/0.52 ~ equalish(e_2,e_1) ),
% 0.19/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.52 fof(f13,axiom,(
% 0.19/0.52 ~ equalish(e_2,e_3) ),
% 0.19/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.52 fof(f16,axiom,(
% 0.19/0.52 (![X,Y]: (( ~ group_element(X)| ~ group_element(Y)| product(X,Y,e_1)| product(X,Y,e_2)| product(X,Y,e_3) ) ))),
% 0.19/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.52 fof(f17,axiom,(
% 0.19/0.52 (![X,Y,W,Z]: (( ~ product(X,Y,W)| ~ product(X,Y,Z)| equalish(W,Z) ) ))),
% 0.19/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.52 fof(f18,axiom,(
% 0.19/0.52 (![X,W,Y,Z]: (( ~ product(X,W,Y)| ~ product(X,Z,Y)| equalish(W,Z) ) ))),
% 0.19/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.52 fof(f20,negated_conjecture,(
% 0.19/0.52 (![X,Y,Z1,Z2]: (( ~ product(X,Y,Z1)| ~ product(X,Z1,Z2)| product(Z2,Y,X) ) ))),
% 0.19/0.52 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.19/0.52 fof(f21,plain,(
% 0.19/0.52 next(e_1,e_2)),
% 0.19/0.52 inference(cnf_transformation,[status(thm)],[f1])).
% 0.19/0.52 fof(f25,plain,(
% 0.19/0.52 greater(e_3,e_2)),
% 0.19/0.52 inference(cnf_transformation,[status(thm)],[f5])).
% 0.19/0.52 fof(f26,plain,(
% 0.19/0.52 ![Y,X1]: ((![X]: (~product(X,e_1,Y)|~next(X,X1)))|~greater(Y,X1))),
% 0.19/0.52 inference(miniscoping,[status(thm)],[f6])).
% 0.19/0.52 fof(f27,plain,(
% 0.19/0.52 ![X0,X1,X2]: (~product(X0,e_1,X1)|~next(X0,X2)|~greater(X1,X2))),
% 0.19/0.52 inference(cnf_transformation,[status(thm)],[f26])).
% 0.19/0.52 fof(f28,plain,(
% 0.19/0.52 group_element(e_1)),
% 0.19/0.52 inference(cnf_transformation,[status(thm)],[f7])).
% 0.19/0.52 fof(f29,plain,(
% 0.19/0.52 group_element(e_2)),
% 0.19/0.52 inference(cnf_transformation,[status(thm)],[f8])).
% 0.19/0.52 fof(f30,plain,(
% 0.19/0.52 group_element(e_3)),
% 0.19/0.52 inference(cnf_transformation,[status(thm)],[f9])).
% 0.19/0.52 fof(f31,plain,(
% 0.19/0.52 ~equalish(e_1,e_2)),
% 0.19/0.52 inference(cnf_transformation,[status(thm)],[f10])).
% 0.19/0.52 fof(f32,plain,(
% 0.19/0.52 ~equalish(e_1,e_3)),
% 0.19/0.52 inference(cnf_transformation,[status(thm)],[f11])).
% 0.19/0.52 fof(f33,plain,(
% 0.19/0.52 ~equalish(e_2,e_1)),
% 0.19/0.52 inference(cnf_transformation,[status(thm)],[f12])).
% 0.19/0.52 fof(f34,plain,(
% 0.19/0.52 ~equalish(e_2,e_3)),
% 0.19/0.52 inference(cnf_transformation,[status(thm)],[f13])).
% 0.19/0.52 fof(f37,plain,(
% 0.19/0.52 ![X0,X1]: (~group_element(X0)|~group_element(X1)|product(X0,X1,e_1)|product(X0,X1,e_2)|product(X0,X1,e_3))),
% 0.19/0.52 inference(cnf_transformation,[status(thm)],[f16])).
% 0.19/0.52 fof(f38,plain,(
% 0.19/0.52 ![W,Z]: ((![X,Y]: (~product(X,Y,W)|~product(X,Y,Z)))|equalish(W,Z))),
% 0.19/0.52 inference(miniscoping,[status(thm)],[f17])).
% 0.19/0.52 fof(f39,plain,(
% 0.19/0.52 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|equalish(X2,X3))),
% 0.19/0.52 inference(cnf_transformation,[status(thm)],[f38])).
% 0.19/0.52 fof(f40,plain,(
% 0.19/0.52 ![W,Z]: ((![X,Y]: (~product(X,W,Y)|~product(X,Z,Y)))|equalish(W,Z))),
% 0.19/0.52 inference(miniscoping,[status(thm)],[f18])).
% 0.19/0.52 fof(f41,plain,(
% 0.19/0.52 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X3,X2)|equalish(X1,X3))),
% 0.19/0.52 inference(cnf_transformation,[status(thm)],[f40])).
% 0.19/0.52 fof(f44,plain,(
% 0.19/0.52 ![X,Y,Z2]: ((![Z1]: (~product(X,Y,Z1)|~product(X,Z1,Z2)))|product(Z2,Y,X))),
% 0.19/0.52 inference(miniscoping,[status(thm)],[f20])).
% 0.19/0.52 fof(f45,plain,(
% 0.19/0.52 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X2,X3)|product(X3,X1,X0))),
% 0.19/0.52 inference(cnf_transformation,[status(thm)],[f44])).
% 0.19/0.52 fof(f46,plain,(
% 0.19/0.52 ![X0]: (~group_element(X0)|product(e_3,X0,e_1)|product(e_3,X0,e_2)|product(e_3,X0,e_3))),
% 0.19/0.52 inference(resolution,[status(thm)],[f37,f30])).
% 0.19/0.52 fof(f47,plain,(
% 0.19/0.52 ![X0]: (~group_element(X0)|product(e_2,X0,e_1)|product(e_2,X0,e_2)|product(e_2,X0,e_3))),
% 0.19/0.52 inference(resolution,[status(thm)],[f37,f29])).
% 0.19/0.52 fof(f48,plain,(
% 0.19/0.52 ![X0]: (~group_element(X0)|product(e_1,X0,e_1)|product(e_1,X0,e_2)|product(e_1,X0,e_3))),
% 0.19/0.52 inference(resolution,[status(thm)],[f37,f28])).
% 0.19/0.52 fof(f49,plain,(
% 0.19/0.52 product(e_3,e_3,e_1)|product(e_3,e_3,e_2)|product(e_3,e_3,e_3)),
% 0.19/0.52 inference(resolution,[status(thm)],[f46,f30])).
% 0.19/0.52 fof(f50,plain,(
% 0.19/0.52 product(e_3,e_2,e_1)|product(e_3,e_2,e_2)|product(e_3,e_2,e_3)),
% 0.19/0.52 inference(resolution,[status(thm)],[f46,f29])).
% 0.19/0.52 fof(f51,plain,(
% 0.19/0.52 product(e_3,e_1,e_1)|product(e_3,e_1,e_2)|product(e_3,e_1,e_3)),
% 0.19/0.52 inference(resolution,[status(thm)],[f46,f28])).
% 0.19/0.52 fof(f52,definition,(
% 0.19/0.52 sQ0_spl <=> (product(e_3,e_3,e_1))),
% 0.19/0.52 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.19/0.52 fof(f53,plain,(
% 0.19/0.52 product(e_3,e_3,e_1)|~sQ0_spl),
% 0.19/0.52 inference(component_clause,[status(thm)],[f52])).
% 0.19/0.52 fof(f55,definition,(
% 0.19/0.52 sQ1_spl <=> (product(e_3,e_3,e_2))),
% 0.19/0.52 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.19/0.52 fof(f56,plain,(
% 0.19/0.52 product(e_3,e_3,e_2)|~sQ1_spl),
% 0.19/0.52 inference(component_clause,[status(thm)],[f55])).
% 0.19/0.52 fof(f58,definition,(
% 0.19/0.52 sQ2_spl <=> (product(e_3,e_3,e_3))),
% 0.19/0.52 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.19/0.52 fof(f59,plain,(
% 0.19/0.52 product(e_3,e_3,e_3)|~sQ2_spl),
% 0.19/0.52 inference(component_clause,[status(thm)],[f58])).
% 0.19/0.52 fof(f61,plain,(
% 0.19/0.52 sQ0_spl|sQ1_spl|sQ2_spl),
% 0.19/0.52 inference(split_clause,[status(thm)],[f49,f52,f55,f58])).
% 0.19/0.52 fof(f62,definition,(
% 0.19/0.52 sQ3_spl <=> (product(e_3,e_2,e_1))),
% 0.19/0.52 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.19/0.52 fof(f63,plain,(
% 0.19/0.52 product(e_3,e_2,e_1)|~sQ3_spl),
% 0.19/0.52 inference(component_clause,[status(thm)],[f62])).
% 0.19/0.52 fof(f65,definition,(
% 0.19/0.52 sQ4_spl <=> (product(e_3,e_2,e_2))),
% 0.19/0.52 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.19/0.52 fof(f66,plain,(
% 0.19/0.52 product(e_3,e_2,e_2)|~sQ4_spl),
% 0.19/0.52 inference(component_clause,[status(thm)],[f65])).
% 0.19/0.52 fof(f68,definition,(
% 0.19/0.52 sQ5_spl <=> (product(e_3,e_2,e_3))),
% 0.19/0.52 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.19/0.52 fof(f69,plain,(
% 0.19/0.52 product(e_3,e_2,e_3)|~sQ5_spl),
% 0.19/0.52 inference(component_clause,[status(thm)],[f68])).
% 0.19/0.52 fof(f71,plain,(
% 0.19/0.52 sQ3_spl|sQ4_spl|sQ5_spl),
% 0.19/0.52 inference(split_clause,[status(thm)],[f50,f62,f65,f68])).
% 0.19/0.52 fof(f72,definition,(
% 0.19/0.52 sQ6_spl <=> (product(e_3,e_1,e_1))),
% 0.19/0.52 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.19/0.52 fof(f73,plain,(
% 0.19/0.52 product(e_3,e_1,e_1)|~sQ6_spl),
% 0.19/0.52 inference(component_clause,[status(thm)],[f72])).
% 0.19/0.52 fof(f75,definition,(
% 0.19/0.52 sQ7_spl <=> (product(e_3,e_1,e_2))),
% 0.19/0.52 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.19/0.52 fof(f76,plain,(
% 0.19/0.52 product(e_3,e_1,e_2)|~sQ7_spl),
% 0.19/0.52 inference(component_clause,[status(thm)],[f75])).
% 0.19/0.52 fof(f78,definition,(
% 0.19/0.52 sQ8_spl <=> (product(e_3,e_1,e_3))),
% 0.19/0.52 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.19/0.52 fof(f79,plain,(
% 0.19/0.52 product(e_3,e_1,e_3)|~sQ8_spl),
% 0.19/0.52 inference(component_clause,[status(thm)],[f78])).
% 0.19/0.52 fof(f81,plain,(
% 0.19/0.52 sQ6_spl|sQ7_spl|sQ8_spl),
% 0.19/0.52 inference(split_clause,[status(thm)],[f51,f72,f75,f78])).
% 0.19/0.52 fof(f84,plain,(
% 0.19/0.52 product(e_2,e_1,e_1)|product(e_2,e_1,e_2)|product(e_2,e_1,e_3)),
% 0.19/0.52 inference(resolution,[status(thm)],[f47,f28])).
% 0.19/0.52 fof(f105,definition,(
% 0.19/0.52 sQ15_spl <=> (product(e_2,e_1,e_1))),
% 0.19/0.52 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.19/0.52 fof(f106,plain,(
% 0.19/0.52 product(e_2,e_1,e_1)|~sQ15_spl),
% 0.19/0.52 inference(component_clause,[status(thm)],[f105])).
% 0.19/0.52 fof(f108,definition,(
% 0.19/0.52 sQ16_spl <=> (product(e_2,e_1,e_2))),
% 0.19/0.52 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.19/0.52 fof(f109,plain,(
% 0.19/0.52 product(e_2,e_1,e_2)|~sQ16_spl),
% 0.19/0.52 inference(component_clause,[status(thm)],[f108])).
% 0.19/0.52 fof(f111,definition,(
% 0.19/0.52 sQ17_spl <=> (product(e_2,e_1,e_3))),
% 0.19/0.52 introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 0.19/0.52 fof(f112,plain,(
% 0.19/0.52 product(e_2,e_1,e_3)|~sQ17_spl),
% 0.19/0.52 inference(component_clause,[status(thm)],[f111])).
% 0.19/0.52 fof(f114,plain,(
% 0.19/0.52 sQ15_spl|sQ16_spl|sQ17_spl),
% 0.19/0.52 inference(split_clause,[status(thm)],[f84,f105,f108,f111])).
% 0.19/0.52 fof(f115,plain,(
% 0.19/0.52 product(e_1,e_3,e_1)|product(e_1,e_3,e_2)|product(e_1,e_3,e_3)),
% 0.19/0.52 inference(resolution,[status(thm)],[f48,f30])).
% 0.19/0.52 fof(f116,plain,(
% 0.19/0.52 product(e_1,e_2,e_1)|product(e_1,e_2,e_2)|product(e_1,e_2,e_3)),
% 0.19/0.52 inference(resolution,[status(thm)],[f48,f29])).
% 0.19/0.52 fof(f117,plain,(
% 0.19/0.52 product(e_1,e_1,e_1)|product(e_1,e_1,e_2)|product(e_1,e_1,e_3)),
% 0.19/0.52 inference(resolution,[status(thm)],[f48,f28])).
% 0.19/0.52 fof(f118,definition,(
% 0.19/0.52 sQ18_spl <=> (product(e_1,e_3,e_1))),
% 0.19/0.52 introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 0.19/0.52 fof(f119,plain,(
% 0.19/0.52 product(e_1,e_3,e_1)|~sQ18_spl),
% 0.19/0.52 inference(component_clause,[status(thm)],[f118])).
% 0.19/0.52 fof(f121,definition,(
% 0.19/0.52 sQ19_spl <=> (product(e_1,e_3,e_2))),
% 0.19/0.52 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.19/0.52 fof(f122,plain,(
% 0.19/0.52 product(e_1,e_3,e_2)|~sQ19_spl),
% 0.19/0.52 inference(component_clause,[status(thm)],[f121])).
% 0.19/0.52 fof(f124,definition,(
% 0.19/0.52 sQ20_spl <=> (product(e_1,e_3,e_3))),
% 0.19/0.52 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.19/0.52 fof(f125,plain,(
% 0.19/0.52 product(e_1,e_3,e_3)|~sQ20_spl),
% 0.19/0.52 inference(component_clause,[status(thm)],[f124])).
% 0.19/0.52 fof(f127,plain,(
% 0.19/0.52 sQ18_spl|sQ19_spl|sQ20_spl),
% 0.19/0.52 inference(split_clause,[status(thm)],[f115,f118,f121,f124])).
% 0.19/0.52 fof(f128,definition,(
% 0.19/0.52 sQ21_spl <=> (product(e_1,e_2,e_1))),
% 0.19/0.52 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.19/0.52 fof(f129,plain,(
% 0.19/0.52 product(e_1,e_2,e_1)|~sQ21_spl),
% 0.19/0.52 inference(component_clause,[status(thm)],[f128])).
% 0.19/0.52 fof(f131,definition,(
% 0.19/0.52 sQ22_spl <=> (product(e_1,e_2,e_2))),
% 0.19/0.52 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.19/0.52 fof(f132,plain,(
% 0.19/0.52 product(e_1,e_2,e_2)|~sQ22_spl),
% 0.19/0.52 inference(component_clause,[status(thm)],[f131])).
% 0.19/0.52 fof(f134,definition,(
% 0.19/0.52 sQ23_spl <=> (product(e_1,e_2,e_3))),
% 0.19/0.52 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 0.19/0.52 fof(f135,plain,(
% 0.19/0.52 product(e_1,e_2,e_3)|~sQ23_spl),
% 0.19/0.52 inference(component_clause,[status(thm)],[f134])).
% 0.19/0.52 fof(f137,plain,(
% 0.19/0.52 sQ21_spl|sQ22_spl|sQ23_spl),
% 0.19/0.52 inference(split_clause,[status(thm)],[f116,f128,f131,f134])).
% 0.19/0.52 fof(f138,definition,(
% 0.19/0.52 sQ24_spl <=> (product(e_1,e_1,e_1))),
% 0.19/0.52 introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition])).
% 0.19/0.52 fof(f139,plain,(
% 0.19/0.52 product(e_1,e_1,e_1)|~sQ24_spl),
% 0.19/0.52 inference(component_clause,[status(thm)],[f138])).
% 0.19/0.52 fof(f141,definition,(
% 0.19/0.52 sQ25_spl <=> (product(e_1,e_1,e_2))),
% 0.19/0.52 introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition])).
% 0.19/0.52 fof(f142,plain,(
% 0.19/0.52 product(e_1,e_1,e_2)|~sQ25_spl),
% 0.19/0.52 inference(component_clause,[status(thm)],[f141])).
% 0.19/0.52 fof(f144,definition,(
% 0.19/0.52 sQ26_spl <=> (product(e_1,e_1,e_3))),
% 0.19/0.52 introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition])).
% 0.19/0.52 fof(f145,plain,(
% 0.19/0.52 product(e_1,e_1,e_3)|~sQ26_spl),
% 0.19/0.52 inference(component_clause,[status(thm)],[f144])).
% 0.19/0.52 fof(f147,plain,(
% 0.19/0.52 sQ24_spl|sQ25_spl|sQ26_spl),
% 0.19/0.52 inference(split_clause,[status(thm)],[f117,f138,f141,f144])).
% 0.19/0.52 fof(f152,plain,(
% 0.19/0.52 ![X0]: (~product(e_3,e_3,X0)|product(X0,e_1,e_3)|~sQ8_spl)),
% 0.19/0.52 inference(resolution,[status(thm)],[f79,f45])).
% 0.19/0.52 fof(f157,plain,(
% 0.19/0.52 ![X0]: (~product(e_3,e_2,X0)|product(X0,e_1,e_3)|~sQ7_spl)),
% 0.19/0.52 inference(resolution,[status(thm)],[f76,f45])).
% 0.19/0.52 fof(f162,plain,(
% 0.19/0.52 ![X0]: (~product(e_3,e_1,X0)|product(X0,e_1,e_3)|~sQ6_spl)),
% 0.19/0.52 inference(resolution,[status(thm)],[f73,f45])).
% 0.19/0.52 fof(f163,plain,(
% 0.19/0.52 product(e_1,e_1,e_3)|~sQ6_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f162,f73])).
% 0.19/0.52 fof(f166,plain,(
% 0.19/0.52 ![X0]: (~next(e_1,X0)|~greater(e_3,X0)|~sQ6_spl)),
% 0.19/0.52 inference(resolution,[status(thm)],[f163,f27])).
% 0.19/0.52 fof(f176,plain,(
% 0.19/0.52 ~next(e_1,e_2)|~sQ6_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f166,f25])).
% 0.19/0.52 fof(f178,plain,(
% 0.19/0.52 $false|~sQ6_spl),
% 0.19/0.52 inference(forward_subsumption_resolution,[status(thm)],[f176,f21])).
% 0.19/0.52 fof(f179,plain,(
% 0.19/0.52 ~sQ6_spl),
% 0.19/0.52 inference(contradiction_clause,[status(thm)],[f178])).
% 0.19/0.52 fof(f180,plain,(
% 0.19/0.52 product(e_3,e_1,e_3)|~sQ5_spl|~sQ7_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f69,f157])).
% 0.19/0.52 fof(f184,plain,(
% 0.19/0.52 ![X0]: (~product(e_3,e_3,X0)|product(X0,e_2,e_3)|~sQ5_spl)),
% 0.19/0.52 inference(resolution,[status(thm)],[f69,f45])).
% 0.19/0.52 fof(f185,plain,(
% 0.19/0.52 product(e_2,e_1,e_3)|~sQ4_spl|~sQ7_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f66,f157])).
% 0.19/0.52 fof(f189,plain,(
% 0.19/0.52 ![X0]: (~product(e_3,e_2,X0)|product(X0,e_2,e_3)|~sQ4_spl)),
% 0.19/0.52 inference(resolution,[status(thm)],[f66,f45])).
% 0.19/0.52 fof(f192,plain,(
% 0.19/0.52 ![X0]: (~product(e_2,X0,e_3)|equalish(e_1,X0)|~sQ4_spl|~sQ7_spl)),
% 0.19/0.52 inference(resolution,[status(thm)],[f185,f41])).
% 0.19/0.52 fof(f197,plain,(
% 0.19/0.52 product(e_2,e_2,e_3)|~sQ4_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f189,f66])).
% 0.19/0.52 fof(f200,plain,(
% 0.19/0.52 ![X0]: (~product(e_2,X0,e_3)|equalish(e_2,X0)|~sQ4_spl)),
% 0.19/0.52 inference(resolution,[status(thm)],[f197,f41])).
% 0.19/0.52 fof(f209,plain,(
% 0.19/0.52 ![X0]: (~product(e_3,X0,e_3)|equalish(e_1,X0)|~sQ5_spl|~sQ7_spl)),
% 0.19/0.52 inference(resolution,[status(thm)],[f180,f41])).
% 0.19/0.52 fof(f215,plain,(
% 0.19/0.52 equalish(e_1,e_2)|~sQ7_spl|~sQ5_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f209,f69])).
% 0.19/0.52 fof(f217,plain,(
% 0.19/0.52 $false|~sQ7_spl|~sQ5_spl),
% 0.19/0.52 inference(forward_subsumption_resolution,[status(thm)],[f215,f31])).
% 0.19/0.52 fof(f218,plain,(
% 0.19/0.52 ~sQ7_spl|~sQ5_spl),
% 0.19/0.52 inference(contradiction_clause,[status(thm)],[f217])).
% 0.19/0.52 fof(f219,plain,(
% 0.19/0.52 product(e_1,e_1,e_3)|~sQ3_spl|~sQ7_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f63,f157])).
% 0.19/0.52 fof(f223,plain,(
% 0.19/0.52 ![X0]: (~product(e_3,e_1,X0)|product(X0,e_2,e_3)|~sQ3_spl)),
% 0.19/0.52 inference(resolution,[status(thm)],[f63,f45])).
% 0.19/0.52 fof(f225,plain,(
% 0.19/0.52 ![X0]: (~next(e_1,X0)|~greater(e_3,X0)|~sQ3_spl|~sQ7_spl)),
% 0.19/0.52 inference(resolution,[status(thm)],[f219,f27])).
% 0.19/0.52 fof(f234,plain,(
% 0.19/0.52 ~next(e_1,e_2)|~sQ3_spl|~sQ7_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f225,f25])).
% 0.19/0.52 fof(f236,plain,(
% 0.19/0.52 $false|~sQ3_spl|~sQ7_spl),
% 0.19/0.52 inference(forward_subsumption_resolution,[status(thm)],[f234,f21])).
% 0.19/0.52 fof(f237,plain,(
% 0.19/0.52 ~sQ3_spl|~sQ7_spl),
% 0.19/0.52 inference(contradiction_clause,[status(thm)],[f236])).
% 0.19/0.52 fof(f247,plain,(
% 0.19/0.52 equalish(e_1,e_2)|~sQ7_spl|~sQ4_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f192,f197])).
% 0.19/0.52 fof(f249,plain,(
% 0.19/0.52 $false|~sQ7_spl|~sQ4_spl),
% 0.19/0.52 inference(forward_subsumption_resolution,[status(thm)],[f247,f31])).
% 0.19/0.52 fof(f250,plain,(
% 0.19/0.52 ~sQ7_spl|~sQ4_spl),
% 0.19/0.52 inference(contradiction_clause,[status(thm)],[f249])).
% 0.19/0.52 fof(f251,plain,(
% 0.19/0.52 product(e_3,e_1,e_3)|~sQ2_spl|~sQ8_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f59,f152])).
% 0.19/0.52 fof(f259,plain,(
% 0.19/0.52 ![X0]: (~product(e_3,X0,e_3)|equalish(e_1,X0)|~sQ2_spl|~sQ8_spl)),
% 0.19/0.52 inference(resolution,[status(thm)],[f251,f41])).
% 0.19/0.52 fof(f271,plain,(
% 0.19/0.52 equalish(e_1,e_3)|~sQ8_spl|~sQ2_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f259,f59])).
% 0.19/0.52 fof(f281,plain,(
% 0.19/0.52 equalish(e_2,e_1)|~sQ17_spl|~sQ4_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f112,f200])).
% 0.19/0.52 fof(f287,plain,(
% 0.19/0.52 $false|~sQ17_spl|~sQ4_spl),
% 0.19/0.52 inference(forward_subsumption_resolution,[status(thm)],[f281,f33])).
% 0.19/0.52 fof(f288,plain,(
% 0.19/0.52 ~sQ17_spl|~sQ4_spl),
% 0.19/0.52 inference(contradiction_clause,[status(thm)],[f287])).
% 0.19/0.52 fof(f293,plain,(
% 0.19/0.52 ![X0]: (~product(e_2,e_2,X0)|product(X0,e_1,e_2)|~sQ16_spl)),
% 0.19/0.52 inference(resolution,[status(thm)],[f109,f45])).
% 0.19/0.52 fof(f294,plain,(
% 0.19/0.52 product(e_3,e_1,e_2)|~sQ16_spl|~sQ4_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f293,f197])).
% 0.19/0.52 fof(f295,plain,(
% 0.19/0.52 sQ7_spl|~sQ16_spl|~sQ4_spl),
% 0.19/0.52 inference(split_clause,[status(thm)],[f294,f75,f108,f65])).
% 0.19/0.52 fof(f300,plain,(
% 0.19/0.52 ![X0]: (~product(e_2,e_1,X0)|product(X0,e_1,e_2)|~sQ15_spl)),
% 0.19/0.52 inference(resolution,[status(thm)],[f106,f45])).
% 0.19/0.52 fof(f301,plain,(
% 0.19/0.52 product(e_1,e_1,e_2)|~sQ15_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f300,f106])).
% 0.19/0.52 fof(f304,plain,(
% 0.19/0.52 ![X0]: (~product(e_1,X0,e_2)|equalish(e_1,X0)|~sQ15_spl)),
% 0.19/0.52 inference(resolution,[status(thm)],[f301,f41])).
% 0.19/0.52 fof(f305,plain,(
% 0.19/0.52 ![X0]: (~product(e_1,e_1,X0)|equalish(e_2,X0)|~sQ15_spl)),
% 0.19/0.52 inference(resolution,[status(thm)],[f301,f39])).
% 0.19/0.52 fof(f306,plain,(
% 0.19/0.52 ![X0]: (~product(e_1,e_2,X0)|product(X0,e_1,e_1)|~sQ15_spl)),
% 0.19/0.52 inference(resolution,[status(thm)],[f301,f45])).
% 0.19/0.52 fof(f344,plain,(
% 0.19/0.52 equalish(e_2,e_3)|~sQ26_spl|~sQ15_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f145,f305])).
% 0.19/0.52 fof(f349,plain,(
% 0.19/0.52 ![X0]: (~product(e_1,e_3,X0)|product(X0,e_1,e_1)|~sQ26_spl)),
% 0.19/0.52 inference(resolution,[status(thm)],[f145,f45])).
% 0.19/0.52 fof(f350,plain,(
% 0.19/0.52 $false|~sQ26_spl|~sQ15_spl),
% 0.19/0.52 inference(forward_subsumption_resolution,[status(thm)],[f344,f34])).
% 0.19/0.52 fof(f351,plain,(
% 0.19/0.52 ~sQ26_spl|~sQ15_spl),
% 0.19/0.52 inference(contradiction_clause,[status(thm)],[f350])).
% 0.19/0.52 fof(f352,plain,(
% 0.19/0.52 equalish(e_2,e_1)|~sQ24_spl|~sQ15_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f139,f305])).
% 0.19/0.52 fof(f358,plain,(
% 0.19/0.52 $false|~sQ24_spl|~sQ15_spl),
% 0.19/0.52 inference(forward_subsumption_resolution,[status(thm)],[f352,f33])).
% 0.19/0.52 fof(f359,plain,(
% 0.19/0.52 ~sQ24_spl|~sQ15_spl),
% 0.19/0.52 inference(contradiction_clause,[status(thm)],[f358])).
% 0.19/0.52 fof(f365,plain,(
% 0.19/0.52 ![X0]: (~product(e_1,e_3,X0)|product(X0,e_2,e_1)|~sQ23_spl)),
% 0.19/0.52 inference(resolution,[status(thm)],[f135,f45])).
% 0.19/0.52 fof(f370,plain,(
% 0.19/0.52 equalish(e_1,e_2)|~sQ22_spl|~sQ15_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f132,f304])).
% 0.19/0.52 fof(f375,plain,(
% 0.19/0.52 $false|~sQ22_spl|~sQ15_spl),
% 0.19/0.52 inference(forward_subsumption_resolution,[status(thm)],[f370,f31])).
% 0.19/0.52 fof(f376,plain,(
% 0.19/0.52 ~sQ22_spl|~sQ15_spl),
% 0.19/0.52 inference(contradiction_clause,[status(thm)],[f375])).
% 0.19/0.52 fof(f377,plain,(
% 0.19/0.52 product(e_1,e_1,e_1)|~sQ21_spl|~sQ15_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f129,f306])).
% 0.19/0.52 fof(f382,plain,(
% 0.19/0.52 sQ24_spl|~sQ21_spl|~sQ15_spl),
% 0.19/0.52 inference(split_clause,[status(thm)],[f377,f138,f128,f105])).
% 0.19/0.52 fof(f386,plain,(
% 0.19/0.52 ![X0]: (~product(e_1,e_3,X0)|product(X0,e_3,e_1)|~sQ20_spl)),
% 0.19/0.52 inference(resolution,[status(thm)],[f125,f45])).
% 0.19/0.52 fof(f387,plain,(
% 0.19/0.52 product(e_3,e_3,e_1)|~sQ20_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f386,f125])).
% 0.19/0.52 fof(f389,plain,(
% 0.19/0.52 product(e_1,e_1,e_3)|~sQ20_spl|~sQ8_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f387,f152])).
% 0.19/0.52 fof(f425,plain,(
% 0.19/0.52 product(e_1,e_2,e_1)|~sQ18_spl|~sQ23_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f119,f365])).
% 0.19/0.52 fof(f431,plain,(
% 0.19/0.52 ![X0]: (~product(e_1,X0,e_1)|equalish(e_2,X0)|~sQ18_spl|~sQ23_spl)),
% 0.19/0.52 inference(resolution,[status(thm)],[f425,f41])).
% 0.19/0.52 fof(f436,plain,(
% 0.19/0.52 equalish(e_2,e_3)|~sQ23_spl|~sQ18_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f431,f119])).
% 0.19/0.52 fof(f437,plain,(
% 0.19/0.52 $false|~sQ23_spl|~sQ18_spl),
% 0.19/0.52 inference(forward_subsumption_resolution,[status(thm)],[f436,f34])).
% 0.19/0.52 fof(f438,plain,(
% 0.19/0.52 ~sQ23_spl|~sQ18_spl),
% 0.19/0.52 inference(contradiction_clause,[status(thm)],[f437])).
% 0.19/0.52 fof(f455,plain,(
% 0.19/0.52 product(e_2,e_2,e_3)|~sQ1_spl|~sQ5_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f56,f184])).
% 0.19/0.52 fof(f456,plain,(
% 0.19/0.52 product(e_2,e_1,e_3)|~sQ1_spl|~sQ8_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f56,f152])).
% 0.19/0.52 fof(f492,plain,(
% 0.19/0.52 ![X0]: (~product(e_1,e_2,X0)|product(X0,e_1,e_1)|~sQ25_spl)),
% 0.19/0.52 inference(resolution,[status(thm)],[f142,f45])).
% 0.19/0.52 fof(f517,plain,(
% 0.19/0.52 product(e_3,e_1,e_1)|~sQ25_spl|~sQ23_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f492,f135])).
% 0.19/0.52 fof(f518,plain,(
% 0.19/0.52 sQ6_spl|~sQ25_spl|~sQ23_spl),
% 0.19/0.52 inference(split_clause,[status(thm)],[f517,f72,f141,f134])).
% 0.19/0.52 fof(f526,plain,(
% 0.19/0.52 ![X0]: (~next(e_1,X0)|~greater(e_3,X0)|~sQ20_spl|~sQ8_spl)),
% 0.19/0.52 inference(resolution,[status(thm)],[f389,f27])).
% 0.19/0.52 fof(f544,plain,(
% 0.19/0.52 product(e_2,e_1,e_1)|~sQ19_spl|~sQ26_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f122,f349])).
% 0.19/0.52 fof(f550,plain,(
% 0.19/0.52 sQ15_spl|~sQ19_spl|~sQ26_spl),
% 0.19/0.52 inference(split_clause,[status(thm)],[f544,f105,f121,f144])).
% 0.19/0.52 fof(f563,plain,(
% 0.19/0.52 ~next(e_1,e_2)|~sQ20_spl|~sQ8_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f526,f25])).
% 0.19/0.52 fof(f565,plain,(
% 0.19/0.52 $false|~sQ20_spl|~sQ8_spl),
% 0.19/0.52 inference(forward_subsumption_resolution,[status(thm)],[f563,f21])).
% 0.19/0.52 fof(f566,plain,(
% 0.19/0.52 ~sQ20_spl|~sQ8_spl),
% 0.19/0.52 inference(contradiction_clause,[status(thm)],[f565])).
% 0.19/0.52 fof(f567,plain,(
% 0.19/0.52 product(e_3,e_2,e_3)|~sQ3_spl|~sQ8_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f223,f79])).
% 0.19/0.52 fof(f568,plain,(
% 0.19/0.52 sQ5_spl|~sQ3_spl|~sQ8_spl),
% 0.19/0.52 inference(split_clause,[status(thm)],[f567,f68,f62,f78])).
% 0.19/0.52 fof(f581,plain,(
% 0.19/0.52 product(e_1,e_2,e_3)|~sQ0_spl|~sQ5_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f53,f184])).
% 0.19/0.52 fof(f582,plain,(
% 0.19/0.52 product(e_1,e_1,e_3)|~sQ0_spl|~sQ8_spl),
% 0.19/0.52 inference(resolution,[status(thm)],[f53,f152])).
% 0.19/0.53 fof(f587,plain,(
% 0.19/0.53 sQ23_spl|~sQ0_spl|~sQ5_spl),
% 0.19/0.53 inference(split_clause,[status(thm)],[f581,f134,f52,f68])).
% 0.19/0.53 fof(f588,plain,(
% 0.19/0.53 sQ26_spl|~sQ0_spl|~sQ8_spl),
% 0.19/0.53 inference(split_clause,[status(thm)],[f582,f144,f52,f78])).
% 0.19/0.53 fof(f591,plain,(
% 0.19/0.53 ![X0]: (~product(e_2,X0,e_3)|equalish(e_2,X0)|~sQ1_spl|~sQ5_spl)),
% 0.19/0.53 inference(resolution,[status(thm)],[f455,f41])).
% 0.19/0.53 fof(f610,plain,(
% 0.19/0.53 equalish(e_2,e_1)|~sQ5_spl|~sQ1_spl|~sQ8_spl),
% 0.19/0.53 inference(resolution,[status(thm)],[f591,f456])).
% 0.19/0.53 fof(f612,plain,(
% 0.19/0.53 $false|~sQ5_spl|~sQ1_spl|~sQ8_spl),
% 0.19/0.53 inference(forward_subsumption_resolution,[status(thm)],[f610,f33])).
% 0.19/0.53 fof(f613,plain,(
% 0.19/0.53 ~sQ5_spl|~sQ1_spl|~sQ8_spl),
% 0.19/0.53 inference(contradiction_clause,[status(thm)],[f612])).
% 0.19/0.53 fof(f614,plain,(
% 0.19/0.53 $false|~sQ8_spl|~sQ2_spl),
% 0.19/0.53 inference(forward_subsumption_resolution,[status(thm)],[f271,f32])).
% 0.19/0.53 fof(f615,plain,(
% 0.19/0.53 ~sQ8_spl|~sQ2_spl),
% 0.19/0.53 inference(contradiction_clause,[status(thm)],[f614])).
% 0.19/0.53 fof(f616,plain,(
% 0.19/0.53 $false),
% 0.19/0.53 inference(sat_refutation,[status(thm)],[f61,f71,f81,f114,f127,f137,f147,f179,f218,f237,f250,f288,f295,f351,f359,f376,f382,f438,f518,f550,f566,f568,f587,f588,f613,f615])).
% 0.19/0.53 % SZS output end CNFRefutation for theBenchmark.p
% 0.19/0.56 % Elapsed time: 0.100781 seconds
% 0.19/0.56 % CPU time: 0.367075 seconds
% 0.19/0.56 % Total memory used: 14.738 MB
% 0.19/0.56 % Net memory used: 14.616 MB
%------------------------------------------------------------------------------