%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP123-4.003 : 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 : n002.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 12:35:42 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP123-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n002.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 20:01:17 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.38 fof(f1,axiom,(
% 0.12/0.38 (![X,Y]: (( ~ group_element(X)| ~ group_element(Y)| product(e_1,X,Y)| product(e_2,X,Y)| product(e_3,X,Y) ) ))),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f3,axiom,(
% 0.12/0.38 group_element(e_1) ),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f4,axiom,(
% 0.12/0.38 group_element(e_2) ),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f6,axiom,(
% 0.12/0.38 ~ equalish(e_1,e_2) ),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f12,axiom,(
% 0.12/0.38 (![X,Y]: (( ~ group_element(X)| ~ group_element(Y)| product(X,Y,e_1)| product(X,Y,e_2)| product(X,Y,e_3) ) ))),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f13,axiom,(
% 0.12/0.38 (![X,Y,W,Z]: (( ~ product(X,Y,W)| ~ product(X,Y,Z)| equalish(W,Z) ) ))),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f14,axiom,(
% 0.12/0.38 (![X,W,Y,Z]: (( ~ product(X,W,Y)| ~ product(X,Z,Y)| equalish(W,Z) ) ))),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f15,axiom,(
% 0.12/0.38 (![W,Y,X,Z]: (( ~ product(W,Y,X)| ~ product(Z,Y,X)| equalish(W,Z) ) ))),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f16,axiom,(
% 0.12/0.38 (![X]: (product(X,X,X) ))),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f18,negated_conjecture,(
% 0.12/0.38 (![X1,Y1,Z1,X2,Y2,Z2]: (( ~ product(X1,Y1,Z1)| ~ product(X2,Y2,Z1)| ~ product(Z2,Y1,X1)| ~ product(Z2,Y2,X2)| equalish(Y1,Y2) ) ))),
% 0.12/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f19,plain,(
% 0.12/0.38 ![X0,X1]: (~group_element(X0)|~group_element(X1)|product(e_1,X0,X1)|product(e_2,X0,X1)|product(e_3,X0,X1))),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f1])).
% 0.12/0.38 fof(f21,plain,(
% 0.12/0.38 group_element(e_1)),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f3])).
% 0.12/0.38 fof(f22,plain,(
% 0.12/0.38 group_element(e_2)),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f4])).
% 0.12/0.38 fof(f24,plain,(
% 0.12/0.38 ~equalish(e_1,e_2)),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f6])).
% 0.12/0.38 fof(f30,plain,(
% 0.12/0.38 ![X0,X1]: (~group_element(X0)|~group_element(X1)|product(X0,X1,e_1)|product(X0,X1,e_2)|product(X0,X1,e_3))),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f12])).
% 0.12/0.38 fof(f31,plain,(
% 0.12/0.38 ![W,Z]: ((![X,Y]: (~product(X,Y,W)|~product(X,Y,Z)))|equalish(W,Z))),
% 0.12/0.38 inference(miniscoping,[status(thm)],[f13])).
% 0.12/0.38 fof(f32,plain,(
% 0.12/0.38 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|equalish(X2,X3))),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f31])).
% 0.12/0.38 fof(f33,plain,(
% 0.12/0.38 ![W,Z]: ((![X,Y]: (~product(X,W,Y)|~product(X,Z,Y)))|equalish(W,Z))),
% 0.12/0.38 inference(miniscoping,[status(thm)],[f14])).
% 0.12/0.38 fof(f34,plain,(
% 0.12/0.38 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X3,X2)|equalish(X1,X3))),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f33])).
% 0.12/0.38 fof(f35,plain,(
% 0.12/0.38 ![W,Z]: ((![Y,X]: (~product(W,Y,X)|~product(Z,Y,X)))|equalish(W,Z))),
% 0.12/0.38 inference(miniscoping,[status(thm)],[f15])).
% 0.12/0.38 fof(f36,plain,(
% 0.12/0.38 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X3,X1,X2)|equalish(X0,X3))),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f35])).
% 0.12/0.38 fof(f37,plain,(
% 0.12/0.38 ![X0]: (product(X0,X0,X0))),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f16])).
% 0.12/0.38 fof(f40,plain,(
% 0.12/0.38 ![Y1,Y2]: ((![X2,Z2]: ((![X1]: ((![Z1]: (~product(X1,Y1,Z1)|~product(X2,Y2,Z1)))|~product(Z2,Y1,X1)))|~product(Z2,Y2,X2)))|equalish(Y1,Y2))),
% 0.12/0.38 inference(miniscoping,[status(thm)],[f18])).
% 0.12/0.38 fof(f41,plain,(
% 0.12/0.38 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~product(X3,X4,X2)|~product(X5,X1,X0)|~product(X5,X4,X3)|equalish(X1,X4))),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f40])).
% 0.12/0.38 fof(f42,plain,(
% 0.12/0.38 ![X0,X1]: (~product(e_1,X0,X1)|~product(e_2,X0,X1))),
% 0.12/0.38 inference(resolution,[status(thm)],[f24,f36])).
% 0.12/0.38 fof(f43,plain,(
% 0.12/0.38 ![X0,X1]: (~product(X0,e_1,X1)|~product(X0,e_2,X1))),
% 0.12/0.38 inference(resolution,[status(thm)],[f24,f34])).
% 0.12/0.38 fof(f44,plain,(
% 0.12/0.38 ![X0,X1]: (~product(X0,X1,e_1)|~product(X0,X1,e_2))),
% 0.12/0.38 inference(resolution,[status(thm)],[f24,f32])).
% 0.12/0.38 fof(f45,plain,(
% 0.12/0.38 ![X0,X1,X2,X3]: (~product(X0,e_1,X1)|~product(X2,e_2,X1)|~product(X3,e_1,X0)|~product(X3,e_2,X2))),
% 0.12/0.38 inference(resolution,[status(thm)],[f24,f41])).
% 0.12/0.39 fof(f48,plain,(
% 0.12/0.39 ~product(e_2,e_1,e_2)),
% 0.12/0.39 inference(resolution,[status(thm)],[f43,f37])).
% 0.12/0.39 fof(f77,definition,(
% 0.12/0.39 sQ0_spl <=> (group_element(e_2))),
% 0.12/0.39 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.12/0.39 fof(f79,plain,(
% 0.12/0.39 ~group_element(e_2)|sQ0_spl),
% 0.12/0.39 inference(component_clause,[status(thm)],[f77])).
% 0.12/0.39 fof(f88,plain,(
% 0.12/0.39 $false|sQ0_spl),
% 0.12/0.39 inference(forward_subsumption_resolution,[status(thm)],[f79,f22])).
% 0.12/0.39 fof(f89,plain,(
% 0.12/0.39 sQ0_spl),
% 0.12/0.39 inference(contradiction_clause,[status(thm)],[f88])).
% 0.12/0.39 fof(f114,plain,(
% 0.12/0.39 ![X0]: (~product(X0,e_1,e_2)|~product(e_2,e_1,X0))),
% 0.12/0.39 inference(resolution,[status(thm)],[f45,f37])).
% 0.12/0.39 fof(f153,definition,(
% 0.12/0.39 sQ16_spl <=> (group_element(e_1))),
% 0.12/0.39 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.12/0.39 fof(f155,plain,(
% 0.12/0.39 ~group_element(e_1)|sQ16_spl),
% 0.12/0.39 inference(component_clause,[status(thm)],[f153])).
% 0.12/0.39 fof(f169,plain,(
% 0.12/0.39 $false|sQ16_spl),
% 0.12/0.39 inference(forward_subsumption_resolution,[status(thm)],[f155,f21])).
% 0.12/0.39 fof(f170,plain,(
% 0.12/0.39 sQ16_spl),
% 0.12/0.39 inference(contradiction_clause,[status(thm)],[f169])).
% 0.12/0.39 fof(f173,plain,(
% 0.12/0.39 ~product(e_3,e_1,e_2)|~group_element(e_2)|~group_element(e_1)|product(e_2,e_1,e_1)|product(e_2,e_1,e_2)),
% 0.12/0.39 inference(resolution,[status(thm)],[f114,f30])).
% 0.12/0.39 fof(f174,definition,(
% 0.12/0.39 sQ20_spl <=> (product(e_3,e_1,e_2))),
% 0.12/0.39 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.12/0.39 fof(f176,plain,(
% 0.12/0.39 ~product(e_3,e_1,e_2)|sQ20_spl),
% 0.12/0.39 inference(component_clause,[status(thm)],[f174])).
% 0.12/0.39 fof(f177,definition,(
% 0.12/0.39 sQ21_spl <=> (product(e_2,e_1,e_1))),
% 0.12/0.39 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.12/0.39 fof(f178,plain,(
% 0.12/0.39 product(e_2,e_1,e_1)|~sQ21_spl),
% 0.12/0.39 inference(component_clause,[status(thm)],[f177])).
% 0.12/0.39 fof(f180,definition,(
% 0.12/0.39 sQ22_spl <=> (product(e_2,e_1,e_2))),
% 0.12/0.39 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.12/0.39 fof(f181,plain,(
% 0.12/0.39 product(e_2,e_1,e_2)|~sQ22_spl),
% 0.12/0.39 inference(component_clause,[status(thm)],[f180])).
% 0.12/0.39 fof(f183,plain,(
% 0.12/0.39 ~sQ20_spl|~sQ0_spl|~sQ16_spl|sQ21_spl|sQ22_spl),
% 0.12/0.39 inference(split_clause,[status(thm)],[f173,f174,f77,f153,f177,f180])).
% 0.12/0.39 fof(f184,plain,(
% 0.12/0.39 $false|~sQ22_spl),
% 0.12/0.39 inference(forward_subsumption_resolution,[status(thm)],[f181,f48])).
% 0.12/0.39 fof(f185,plain,(
% 0.12/0.39 ~sQ22_spl),
% 0.12/0.39 inference(contradiction_clause,[status(thm)],[f184])).
% 0.12/0.39 fof(f186,plain,(
% 0.12/0.39 ~group_element(e_1)|~group_element(e_2)|product(e_1,e_1,e_2)|product(e_2,e_1,e_2)|sQ20_spl),
% 0.12/0.39 inference(resolution,[status(thm)],[f176,f19])).
% 0.12/0.39 fof(f187,definition,(
% 0.12/0.39 sQ23_spl <=> (product(e_1,e_1,e_2))),
% 0.12/0.39 introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition])).
% 0.12/0.39 fof(f188,plain,(
% 0.12/0.39 product(e_1,e_1,e_2)|~sQ23_spl),
% 0.12/0.39 inference(component_clause,[status(thm)],[f187])).
% 0.12/0.39 fof(f190,plain,(
% 0.12/0.39 ~sQ16_spl|~sQ0_spl|sQ23_spl|sQ22_spl|sQ20_spl),
% 0.12/0.39 inference(split_clause,[status(thm)],[f186,f153,f77,f187,f180,f174])).
% 0.12/0.39 fof(f204,plain,(
% 0.12/0.39 ~product(e_1,e_1,e_1)|~sQ21_spl),
% 0.12/0.39 inference(resolution,[status(thm)],[f178,f42])).
% 0.12/0.39 fof(f206,plain,(
% 0.12/0.39 $false|~sQ21_spl),
% 0.12/0.39 inference(forward_subsumption_resolution,[status(thm)],[f204,f37])).
% 0.12/0.39 fof(f207,plain,(
% 0.12/0.39 ~sQ21_spl),
% 0.12/0.39 inference(contradiction_clause,[status(thm)],[f206])).
% 0.12/0.39 fof(f209,plain,(
% 0.12/0.39 ~product(e_1,e_1,e_1)|~sQ23_spl),
% 0.12/0.39 inference(resolution,[status(thm)],[f188,f44])).
% 0.12/0.39 fof(f210,plain,(
% 0.12/0.39 $false|~sQ23_spl),
% 0.12/0.39 inference(forward_subsumption_resolution,[status(thm)],[f209,f37])).
% 0.12/0.39 fof(f211,plain,(
% 0.12/0.39 ~sQ23_spl),
% 0.12/0.39 inference(contradiction_clause,[status(thm)],[f210])).
% 0.12/0.39 fof(f212,plain,(
% 0.12/0.39 $false),
% 0.12/0.39 inference(sat_refutation,[status(thm)],[f89,f170,f183,f185,f190,f207,f211])).
% 0.12/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.40 % Elapsed time: 0.038246 seconds
% 0.12/0.40 % CPU time: 0.117324 seconds
% 0.12/0.40 % Total memory used: 15.896 MB
% 0.12/0.40 % Net memory used: 15.542 MB
%------------------------------------------------------------------------------