%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP125-4.003 : 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 : n017.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 12:35:50 PM UTC 2026
% Result : Unsatisfiable 0.14s 5.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP125-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n017.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Sun Sep 20 19:55:16 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.39 % Drodi V4.1.1
% 0.14/5.41 % Refutation found
% 0.14/5.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/5.41 % SZS output start CNFRefutation for theBenchmark
% 0.14/5.41 fof(f1,axiom,(
% 0.14/5.41 (![X,Y]: (( ~ group_element(X)| ~ group_element(Y)| product(e_1,X,Y)| product(e_2,X,Y)| product(e_3,X,Y) ) ))),
% 0.14/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.41 fof(f2,axiom,(
% 0.14/5.41 (![X,Y]: (( ~ group_element(X)| ~ group_element(Y)| product(X,e_1,Y)| product(X,e_2,Y)| product(X,e_3,Y) ) ))),
% 0.14/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.41 fof(f5,axiom,(
% 0.14/5.41 group_element(e_1) ),
% 0.14/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.41 fof(f6,axiom,(
% 0.14/5.41 group_element(e_2) ),
% 0.14/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.41 fof(f8,axiom,(
% 0.14/5.41 ~ equalish(e_1,e_2) ),
% 0.14/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.41 fof(f10,axiom,(
% 0.14/5.41 ~ equalish(e_2,e_1) ),
% 0.14/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.41 fof(f15,axiom,(
% 0.14/5.41 (![X,Y,W,Z]: (( ~ product(X,Y,W)| ~ product(X,Y,Z)| equalish(W,Z) ) ))),
% 0.14/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.41 fof(f16,axiom,(
% 0.14/5.41 (![X,W,Y,Z]: (( ~ product(X,W,Y)| ~ product(X,Z,Y)| equalish(W,Z) ) ))),
% 0.14/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.41 fof(f17,axiom,(
% 0.14/5.41 (![W,Y,X,Z]: (( ~ product(W,Y,X)| ~ product(Z,Y,X)| equalish(W,Z) ) ))),
% 0.14/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.41 fof(f18,axiom,(
% 0.14/5.41 (![X]: (product(X,X,X) ))),
% 0.14/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.41 fof(f19,negated_conjecture,(
% 0.14/5.41 (![X,Y,Z1,Z2]: (( ~ product(X,Y,Z1)| ~ product(Y,X,Z2)| product(Z1,Z2,X) ) ))),
% 0.14/5.41 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/5.41 fof(f20,plain,(
% 0.14/5.41 ![X0,X1]: (~group_element(X0)|~group_element(X1)|product(e_1,X0,X1)|product(e_2,X0,X1)|product(e_3,X0,X1))),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f1])).
% 0.14/5.41 fof(f21,plain,(
% 0.14/5.41 ![X0,X1]: (~group_element(X0)|~group_element(X1)|product(X0,e_1,X1)|product(X0,e_2,X1)|product(X0,e_3,X1))),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f2])).
% 0.14/5.41 fof(f26,plain,(
% 0.14/5.41 group_element(e_1)),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f5])).
% 0.14/5.41 fof(f27,plain,(
% 0.14/5.41 group_element(e_2)),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f6])).
% 0.14/5.41 fof(f29,plain,(
% 0.14/5.41 ~equalish(e_1,e_2)),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f8])).
% 0.14/5.41 fof(f31,plain,(
% 0.14/5.41 ~equalish(e_2,e_1)),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f10])).
% 0.14/5.41 fof(f36,plain,(
% 0.14/5.41 ![W,Z]: ((![X,Y]: (~product(X,Y,W)|~product(X,Y,Z)))|equalish(W,Z))),
% 0.14/5.41 inference(miniscoping,[status(thm)],[f15])).
% 0.14/5.41 fof(f37,plain,(
% 0.14/5.41 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|equalish(X2,X3))),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f36])).
% 0.14/5.41 fof(f38,plain,(
% 0.14/5.41 ![W,Z]: ((![X,Y]: (~product(X,W,Y)|~product(X,Z,Y)))|equalish(W,Z))),
% 0.14/5.41 inference(miniscoping,[status(thm)],[f16])).
% 0.14/5.41 fof(f39,plain,(
% 0.14/5.41 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X3,X2)|equalish(X1,X3))),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f38])).
% 0.14/5.41 fof(f40,plain,(
% 0.14/5.41 ![W,Z]: ((![Y,X]: (~product(W,Y,X)|~product(Z,Y,X)))|equalish(W,Z))),
% 0.14/5.41 inference(miniscoping,[status(thm)],[f17])).
% 0.14/5.41 fof(f41,plain,(
% 0.14/5.41 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X3,X1,X2)|equalish(X0,X3))),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f40])).
% 0.14/5.41 fof(f42,plain,(
% 0.14/5.41 ![X0]: (product(X0,X0,X0))),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f18])).
% 0.14/5.41 fof(f43,plain,(
% 0.14/5.41 ![X,Z1,Z2]: ((![Y]: (~product(X,Y,Z1)|~product(Y,X,Z2)))|product(Z1,Z2,X))),
% 0.14/5.41 inference(miniscoping,[status(thm)],[f19])).
% 0.14/5.41 fof(f44,plain,(
% 0.14/5.41 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X1,X0,X3)|product(X2,X3,X0))),
% 0.14/5.41 inference(cnf_transformation,[status(thm)],[f43])).
% 0.14/5.41 fof(f55,plain,(
% 0.14/5.41 ![X0]: (~group_element(X0)|product(e_1,X0,e_2)|product(e_2,X0,e_2)|product(e_3,X0,e_2))),
% 0.14/5.41 inference(resolution,[status(thm)],[f20,f27])).
% 0.14/5.41 fof(f57,plain,(
% 0.14/5.41 ![X0]: (~group_element(X0)|product(X0,e_1,e_2)|product(X0,e_2,e_2)|product(X0,e_3,e_2))),
% 0.14/5.41 inference(resolution,[status(thm)],[f21,f27])).
% 0.14/5.41 fof(f61,plain,(
% 0.14/5.41 ![X0,X1]: (~product(X0,X0,X1)|equalish(X1,X0))),
% 0.14/5.41 inference(resolution,[status(thm)],[f37,f42])).
% 0.14/5.41 fof(f66,plain,(
% 0.14/5.41 ![X0,X1]: (~product(X0,X1,X0)|equalish(X1,X0))),
% 0.14/5.41 inference(resolution,[status(thm)],[f39,f42])).
% 0.14/5.41 fof(f67,plain,(
% 0.14/5.41 ![X0,X1]: (~product(X0,X1,X1)|equalish(X0,X1))),
% 0.14/5.41 inference(resolution,[status(thm)],[f41,f42])).
% 0.14/5.41 fof(f72,plain,(
% 0.14/5.41 product(e_1,e_1,e_2)|product(e_2,e_1,e_2)|product(e_3,e_1,e_2)),
% 0.14/5.41 inference(resolution,[status(thm)],[f55,f26])).
% 0.14/5.41 fof(f73,definition,(
% 0.14/5.41 sQ0_spl <=> (product(e_1,e_3,e_2))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f74,plain,(
% 0.14/5.41 product(e_1,e_3,e_2)|~sQ0_spl),
% 0.14/5.41 inference(component_clause,[status(thm)],[f73])).
% 0.14/5.41 fof(f83,definition,(
% 0.14/5.41 sQ3_spl <=> (product(e_1,e_2,e_2))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f84,plain,(
% 0.14/5.41 product(e_1,e_2,e_2)|~sQ3_spl),
% 0.14/5.41 inference(component_clause,[status(thm)],[f83])).
% 0.14/5.41 fof(f93,definition,(
% 0.14/5.41 sQ6_spl <=> (product(e_1,e_1,e_2))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f94,plain,(
% 0.14/5.41 product(e_1,e_1,e_2)|~sQ6_spl),
% 0.14/5.41 inference(component_clause,[status(thm)],[f93])).
% 0.14/5.41 fof(f96,definition,(
% 0.14/5.41 sQ7_spl <=> (product(e_2,e_1,e_2))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f97,plain,(
% 0.14/5.41 product(e_2,e_1,e_2)|~sQ7_spl),
% 0.14/5.41 inference(component_clause,[status(thm)],[f96])).
% 0.14/5.41 fof(f99,definition,(
% 0.14/5.41 sQ8_spl <=> (product(e_3,e_1,e_2))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f100,plain,(
% 0.14/5.41 product(e_3,e_1,e_2)|~sQ8_spl),
% 0.14/5.41 inference(component_clause,[status(thm)],[f99])).
% 0.14/5.41 fof(f102,plain,(
% 0.14/5.41 sQ6_spl|sQ7_spl|sQ8_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f72,f93,f96,f99])).
% 0.14/5.41 fof(f106,plain,(
% 0.14/5.41 ![X0]: (~product(e_1,e_3,X0)|product(X0,e_2,e_1)|~sQ8_spl)),
% 0.14/5.41 inference(resolution,[status(thm)],[f100,f44])).
% 0.14/5.41 fof(f110,plain,(
% 0.14/5.41 equalish(e_1,e_2)|~sQ7_spl),
% 0.14/5.41 inference(resolution,[status(thm)],[f97,f66])).
% 0.14/5.41 fof(f119,plain,(
% 0.14/5.41 $false|~sQ7_spl),
% 0.14/5.41 inference(forward_subsumption_resolution,[status(thm)],[f110,f29])).
% 0.14/5.41 fof(f120,plain,(
% 0.14/5.41 ~sQ7_spl),
% 0.14/5.41 inference(contradiction_clause,[status(thm)],[f119])).
% 0.14/5.41 fof(f137,definition,(
% 0.14/5.41 sQ13_spl <=> (product(e_2,e_2,e_1))),
% 0.14/5.41 introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition])).
% 0.14/5.41 fof(f138,plain,(
% 0.14/5.41 product(e_2,e_2,e_1)|~sQ13_spl),
% 0.14/5.41 inference(component_clause,[status(thm)],[f137])).
% 0.14/5.41 fof(f156,plain,(
% 0.14/5.41 product(e_1,e_1,e_2)|product(e_1,e_2,e_2)|product(e_1,e_3,e_2)),
% 0.14/5.41 inference(resolution,[status(thm)],[f57,f26])).
% 0.14/5.41 fof(f159,plain,(
% 0.14/5.41 sQ6_spl|sQ3_spl|sQ0_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f156,f93,f83,f73])).
% 0.14/5.41 fof(f162,plain,(
% 0.14/5.41 equalish(e_2,e_1)|~sQ6_spl),
% 0.14/5.41 inference(resolution,[status(thm)],[f94,f61])).
% 0.14/5.41 fof(f169,plain,(
% 0.14/5.41 $false|~sQ6_spl),
% 0.14/5.41 inference(forward_subsumption_resolution,[status(thm)],[f162,f31])).
% 0.14/5.41 fof(f170,plain,(
% 0.14/5.41 ~sQ6_spl),
% 0.14/5.41 inference(contradiction_clause,[status(thm)],[f169])).
% 0.14/5.41 fof(f185,plain,(
% 0.14/5.41 equalish(e_1,e_2)|~sQ3_spl),
% 0.14/5.41 inference(resolution,[status(thm)],[f84,f67])).
% 0.14/5.41 fof(f197,plain,(
% 0.14/5.41 $false|~sQ3_spl),
% 0.14/5.41 inference(forward_subsumption_resolution,[status(thm)],[f185,f29])).
% 0.14/5.41 fof(f198,plain,(
% 0.14/5.41 ~sQ3_spl),
% 0.14/5.41 inference(contradiction_clause,[status(thm)],[f197])).
% 0.14/5.41 fof(f251,plain,(
% 0.14/5.41 equalish(e_1,e_2)|~sQ13_spl),
% 0.14/5.41 inference(resolution,[status(thm)],[f138,f61])).
% 0.14/5.41 fof(f258,plain,(
% 0.14/5.41 $false|~sQ13_spl),
% 0.14/5.41 inference(forward_subsumption_resolution,[status(thm)],[f251,f29])).
% 0.14/5.41 fof(f259,plain,(
% 0.14/5.41 ~sQ13_spl),
% 0.14/5.41 inference(contradiction_clause,[status(thm)],[f258])).
% 0.14/5.41 fof(f320,plain,(
% 0.14/5.41 product(e_2,e_2,e_1)|~sQ0_spl|~sQ8_spl),
% 0.14/5.41 inference(resolution,[status(thm)],[f74,f106])).
% 0.14/5.41 fof(f328,plain,(
% 0.14/5.41 sQ13_spl|~sQ0_spl|~sQ8_spl),
% 0.14/5.41 inference(split_clause,[status(thm)],[f320,f137,f73,f99])).
% 0.14/5.41 fof(f329,plain,(
% 0.14/5.41 $false),
% 0.14/5.41 inference(sat_refutation,[status(thm)],[f102,f120,f159,f170,f198,f259,f328])).
% 0.14/5.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/5.43 % Elapsed time: 0.039821 seconds
% 0.14/5.43 % CPU time: 0.130737 seconds
% 0.14/5.43 % Total memory used: 17.748 MB
% 0.14/5.43 % Net memory used: 17.394 MB
%------------------------------------------------------------------------------