%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP123-1.003 : 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 : n012.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 12:35:40 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 : GRP123-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n012.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 20 19:57:37 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 % 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 group_element(e_1) ),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f2,axiom,(
% 0.10/0.40 group_element(e_2) ),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f3,axiom,(
% 0.10/0.40 group_element(e_3) ),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f5,axiom,(
% 0.10/0.40 ~ equalish(e_1,e_3) ),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f7,axiom,(
% 0.10/0.40 ~ equalish(e_2,e_3) ),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f10,axiom,(
% 0.10/0.40 (![X,Y]: (( ~ group_element(X)| ~ group_element(Y)| product(X,Y,e_1)| product(X,Y,e_2)| product(X,Y,e_3) ) ))),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f12,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/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f13,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/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f14,axiom,(
% 0.10/0.40 (![X]: (product(X,X,X) ))),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f16,negated_conjecture,(
% 0.10/0.40 (![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) ) ))),
% 0.10/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.40 fof(f17,plain,(
% 0.10/0.40 group_element(e_1)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f1])).
% 0.10/0.40 fof(f18,plain,(
% 0.10/0.40 group_element(e_2)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f2])).
% 0.10/0.40 fof(f19,plain,(
% 0.10/0.40 group_element(e_3)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f3])).
% 0.10/0.40 fof(f21,plain,(
% 0.10/0.40 ~equalish(e_1,e_3)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f5])).
% 0.10/0.40 fof(f23,plain,(
% 0.10/0.40 ~equalish(e_2,e_3)),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f7])).
% 0.10/0.40 fof(f26,plain,(
% 0.10/0.40 ![X0,X1]: (~group_element(X0)|~group_element(X1)|product(X0,X1,e_1)|product(X0,X1,e_2)|product(X0,X1,e_3))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f10])).
% 0.10/0.40 fof(f29,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)],[f12])).
% 0.10/0.40 fof(f30,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)],[f29])).
% 0.10/0.40 fof(f31,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)],[f13])).
% 0.10/0.40 fof(f32,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)],[f31])).
% 0.10/0.40 fof(f33,plain,(
% 0.10/0.40 ![X0]: (product(X0,X0,X0))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f14])).
% 0.10/0.40 fof(f36,plain,(
% 0.10/0.40 ![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))),
% 0.10/0.40 inference(miniscoping,[status(thm)],[f16])).
% 0.10/0.40 fof(f37,plain,(
% 0.10/0.40 ![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))),
% 0.10/0.40 inference(cnf_transformation,[status(thm)],[f36])).
% 0.10/0.40 fof(f45,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)],[f21,f32])).
% 0.10/0.40 fof(f46,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)],[f21,f30])).
% 0.10/0.40 fof(f48,plain,(
% 0.10/0.40 ![X0,X1,X2,X3]: (~product(X0,e_1,X1)|~product(X2,e_3,X1)|~product(X3,e_1,X0)|~product(X3,e_3,X2))),
% 0.10/0.40 inference(resolution,[status(thm)],[f21,f37])).
% 0.10/0.40 fof(f55,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)],[f23,f32])).
% 0.10/0.40 fof(f56,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)],[f23,f30])).
% 0.10/0.40 fof(f71,plain,(
% 0.10/0.40 ![X0]: (~group_element(X0)|product(X0,e_3,e_1)|product(X0,e_3,e_2)|product(X0,e_3,e_3))),
% 0.10/0.40 inference(resolution,[status(thm)],[f26,f19])).
% 0.10/0.40 fof(f76,plain,(
% 0.10/0.40 ![X0,X1]: (~product(e_1,e_1,X0)|~product(X1,e_3,X0)|~product(e_1,e_3,X1))),
% 0.10/0.40 inference(resolution,[status(thm)],[f48,f33])).
% 0.10/0.40 fof(f79,plain,(
% 0.10/0.40 ~product(e_1,e_3,e_1)),
% 0.10/0.40 inference(resolution,[status(thm)],[f46,f33])).
% 0.10/0.40 fof(f82,plain,(
% 0.10/0.40 ~product(e_2,e_3,e_2)),
% 0.10/0.40 inference(resolution,[status(thm)],[f56,f33])).
% 0.10/0.40 fof(f87,plain,(
% 0.10/0.40 product(e_2,e_3,e_1)|product(e_2,e_3,e_2)|product(e_2,e_3,e_3)),
% 0.10/0.40 inference(resolution,[status(thm)],[f71,f18])).
% 0.10/0.40 fof(f88,plain,(
% 0.10/0.40 product(e_1,e_3,e_1)|product(e_1,e_3,e_2)|product(e_1,e_3,e_3)),
% 0.10/0.40 inference(resolution,[status(thm)],[f71,f17])).
% 0.10/0.40 fof(f99,definition,(
% 0.10/0.40 sQ3_spl <=> (product(e_2,e_3,e_1))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f100,plain,(
% 0.10/0.40 product(e_2,e_3,e_1)|~sQ3_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f99])).
% 0.10/0.40 fof(f102,definition,(
% 0.10/0.40 sQ4_spl <=> (product(e_2,e_3,e_2))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f103,plain,(
% 0.10/0.40 product(e_2,e_3,e_2)|~sQ4_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f102])).
% 0.10/0.40 fof(f105,definition,(
% 0.10/0.40 sQ5_spl <=> (product(e_2,e_3,e_3))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f106,plain,(
% 0.10/0.40 product(e_2,e_3,e_3)|~sQ5_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f105])).
% 0.10/0.40 fof(f108,plain,(
% 0.10/0.40 sQ3_spl|sQ4_spl|sQ5_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f87,f99,f102,f105])).
% 0.10/0.40 fof(f109,definition,(
% 0.10/0.40 sQ6_spl <=> (product(e_1,e_3,e_1))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f110,plain,(
% 0.10/0.40 product(e_1,e_3,e_1)|~sQ6_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f109])).
% 0.10/0.40 fof(f112,definition,(
% 0.10/0.40 sQ7_spl <=> (product(e_1,e_3,e_2))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f113,plain,(
% 0.10/0.40 product(e_1,e_3,e_2)|~sQ7_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f112])).
% 0.10/0.40 fof(f115,definition,(
% 0.10/0.40 sQ8_spl <=> (product(e_1,e_3,e_3))),
% 0.10/0.40 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.10/0.40 fof(f116,plain,(
% 0.10/0.40 product(e_1,e_3,e_3)|~sQ8_spl),
% 0.10/0.40 inference(component_clause,[status(thm)],[f115])).
% 0.10/0.40 fof(f118,plain,(
% 0.10/0.40 sQ6_spl|sQ7_spl|sQ8_spl),
% 0.10/0.40 inference(split_clause,[status(thm)],[f88,f109,f112,f115])).
% 0.10/0.40 fof(f119,plain,(
% 0.10/0.40 $false|~sQ6_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f110,f79])).
% 0.10/0.40 fof(f120,plain,(
% 0.10/0.40 ~sQ6_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f119])).
% 0.10/0.40 fof(f121,plain,(
% 0.10/0.40 $false|~sQ4_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f103,f82])).
% 0.10/0.40 fof(f122,plain,(
% 0.10/0.40 ~sQ4_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f121])).
% 0.10/0.40 fof(f204,plain,(
% 0.10/0.40 ~product(e_3,e_3,e_3)|~sQ8_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f116,f45])).
% 0.10/0.40 fof(f208,plain,(
% 0.10/0.40 $false|~sQ8_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f204,f33])).
% 0.10/0.40 fof(f209,plain,(
% 0.10/0.40 ~sQ8_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f208])).
% 0.10/0.40 fof(f210,plain,(
% 0.10/0.40 ![X0]: (~product(e_1,e_1,X0)|~product(e_2,e_3,X0)|~sQ7_spl)),
% 0.10/0.40 inference(resolution,[status(thm)],[f113,f76])).
% 0.10/0.40 fof(f219,plain,(
% 0.10/0.40 ~product(e_3,e_3,e_3)|~sQ5_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f106,f55])).
% 0.10/0.40 fof(f220,plain,(
% 0.10/0.40 $false|~sQ5_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f219,f33])).
% 0.10/0.40 fof(f221,plain,(
% 0.10/0.40 ~sQ5_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f220])).
% 0.10/0.40 fof(f222,plain,(
% 0.10/0.40 ~product(e_1,e_1,e_1)|~sQ3_spl|~sQ7_spl),
% 0.10/0.40 inference(resolution,[status(thm)],[f100,f210])).
% 0.10/0.40 fof(f230,plain,(
% 0.10/0.40 $false|~sQ3_spl|~sQ7_spl),
% 0.10/0.40 inference(forward_subsumption_resolution,[status(thm)],[f222,f33])).
% 0.10/0.40 fof(f231,plain,(
% 0.10/0.40 ~sQ3_spl|~sQ7_spl),
% 0.10/0.40 inference(contradiction_clause,[status(thm)],[f230])).
% 0.10/0.40 fof(f232,plain,(
% 0.10/0.40 $false),
% 0.10/0.40 inference(sat_refutation,[status(thm)],[f108,f118,f120,f122,f209,f221,f231])).
% 0.10/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.10/0.44 % Elapsed time: 0.043598 seconds
% 0.10/0.44 % CPU time: 0.049647 seconds
% 0.10/0.44 % Total memory used: 3.976 MB
% 0.10/0.44 % Net memory used: 3.927 MB
%------------------------------------------------------------------------------