%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP131-2.002 : 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 : n018.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 12:36:01 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP131-2.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n018.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 20 20:03:13 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.12/0.40 fof(f4,axiom,(
% 0.12/0.40 group_element(e_1) ),
% 0.12/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f5,axiom,(
% 0.12/0.40 group_element(e_2) ),
% 0.12/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f6,axiom,(
% 0.12/0.40 ~ equalish(e_1,e_2) ),
% 0.12/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f8,axiom,(
% 0.12/0.40 (![X,Y]: (( ~ group_element(X)| ~ group_element(Y)| product(X,Y,e_1)| product(X,Y,e_2) ) ))),
% 0.12/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f10,axiom,(
% 0.12/0.40 (![X,W,Y,Z]: (( ~ product(X,W,Y)| ~ product(X,Z,Y)| equalish(W,Z) ) ))),
% 0.12/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f11,axiom,(
% 0.12/0.40 (![W,Y,X,Z]: (( ~ product(W,Y,X)| ~ product(Z,Y,X)| equalish(W,Z) ) ))),
% 0.12/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.40 fof(f12,negated_conjecture,(
% 0.12/0.40 (![X1,Y1,Z1,X2,Y2,Z2]: (( ~ product(X1,Y1,Z1)| ~ product(X2,Y2,Z1)| ~ product(Z2,Y1,X1)| ~ product(Z2,Y2,X2)| equalish(X1,X2) ) ))),
% 0.12/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f13,negated_conjecture,(
% 0.12/0.41 (![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) ) ))),
% 0.12/0.41 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.41 fof(f18,plain,(
% 0.12/0.41 group_element(e_1)),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f4])).
% 0.12/0.41 fof(f19,plain,(
% 0.12/0.41 group_element(e_2)),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f5])).
% 0.12/0.41 fof(f20,plain,(
% 0.12/0.41 ~equalish(e_1,e_2)),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f6])).
% 0.12/0.41 fof(f22,plain,(
% 0.12/0.41 ![X0,X1]: (~group_element(X0)|~group_element(X1)|product(X0,X1,e_1)|product(X0,X1,e_2))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f8])).
% 0.12/0.41 fof(f25,plain,(
% 0.12/0.41 ![W,Z]: ((![X,Y]: (~product(X,W,Y)|~product(X,Z,Y)))|equalish(W,Z))),
% 0.12/0.41 inference(miniscoping,[status(thm)],[f10])).
% 0.12/0.41 fof(f26,plain,(
% 0.12/0.41 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X3,X2)|equalish(X1,X3))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f25])).
% 0.12/0.41 fof(f27,plain,(
% 0.12/0.41 ![W,Z]: ((![Y,X]: (~product(W,Y,X)|~product(Z,Y,X)))|equalish(W,Z))),
% 0.12/0.41 inference(miniscoping,[status(thm)],[f11])).
% 0.12/0.41 fof(f28,plain,(
% 0.12/0.41 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X3,X1,X2)|equalish(X0,X3))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f27])).
% 0.12/0.41 fof(f29,plain,(
% 0.12/0.41 ![X1,X2]: ((![Y2,Z2]: ((![Y1]: ((![Z1]: (~product(X1,Y1,Z1)|~product(X2,Y2,Z1)))|~product(Z2,Y1,X1)))|~product(Z2,Y2,X2)))|equalish(X1,X2))),
% 0.12/0.41 inference(miniscoping,[status(thm)],[f12])).
% 0.12/0.41 fof(f30,plain,(
% 0.12/0.41 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~product(X3,X4,X2)|~product(X5,X1,X0)|~product(X5,X4,X3)|equalish(X0,X3))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f29])).
% 0.12/0.41 fof(f31,plain,(
% 0.12/0.41 ![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))),
% 0.12/0.41 inference(miniscoping,[status(thm)],[f13])).
% 0.12/0.41 fof(f32,plain,(
% 0.12/0.41 ![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))),
% 0.12/0.41 inference(cnf_transformation,[status(thm)],[f31])).
% 0.12/0.41 fof(f33,plain,(
% 0.12/0.41 ![X0,X1]: (~product(e_1,X0,X1)|~product(e_2,X0,X1))),
% 0.12/0.41 inference(resolution,[status(thm)],[f20,f28])).
% 0.12/0.41 fof(f34,plain,(
% 0.12/0.41 ![X0,X1]: (~product(X0,e_1,X1)|~product(X0,e_2,X1))),
% 0.12/0.41 inference(resolution,[status(thm)],[f20,f26])).
% 0.12/0.41 fof(f36,plain,(
% 0.12/0.41 ![X0,X1,X2,X3]: (~product(X0,e_1,X1)|~product(X2,e_2,X1)|~product(X3,e_1,X0)|~product(X3,e_2,X2))),
% 0.12/0.41 inference(resolution,[status(thm)],[f20,f32])).
% 0.12/0.41 fof(f37,plain,(
% 0.12/0.41 ![X0,X1,X2,X3]: (~product(e_1,X0,X1)|~product(e_2,X2,X1)|~product(X3,X0,e_1)|~product(X3,X2,e_2))),
% 0.12/0.41 inference(resolution,[status(thm)],[f20,f30])).
% 0.12/0.41 fof(f43,plain,(
% 0.12/0.41 ![X0]: (~group_element(X0)|product(X0,e_2,e_1)|product(X0,e_2,e_2))),
% 0.12/0.41 inference(resolution,[status(thm)],[f22,f19])).
% 0.12/0.41 fof(f44,plain,(
% 0.12/0.41 ![X0]: (~group_element(X0)|product(X0,e_1,e_1)|product(X0,e_1,e_2))),
% 0.12/0.41 inference(resolution,[status(thm)],[f22,f18])).
% 0.12/0.41 fof(f45,plain,(
% 0.12/0.41 ~group_element(e_1)|product(e_1,e_2,e_2)|~product(e_2,e_2,e_1)),
% 0.12/0.41 inference(resolution,[status(thm)],[f43,f33])).
% 0.12/0.41 fof(f47,definition,(
% 0.12/0.41 sQ0_spl <=> (group_element(e_1))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f49,plain,(
% 0.12/0.41 ~group_element(e_1)|sQ0_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f47])).
% 0.12/0.41 fof(f50,definition,(
% 0.12/0.41 sQ1_spl <=> (product(e_1,e_2,e_2))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f51,plain,(
% 0.12/0.41 product(e_1,e_2,e_2)|~sQ1_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f50])).
% 0.12/0.41 fof(f53,definition,(
% 0.12/0.41 sQ2_spl <=> (product(e_2,e_2,e_1))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f55,plain,(
% 0.12/0.41 ~product(e_2,e_2,e_1)|sQ2_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f53])).
% 0.12/0.41 fof(f56,plain,(
% 0.12/0.41 ~sQ0_spl|sQ1_spl|~sQ2_spl),
% 0.12/0.41 inference(split_clause,[status(thm)],[f45,f47,f50,f53])).
% 0.12/0.41 fof(f57,plain,(
% 0.12/0.41 ~group_element(e_2)|product(e_2,e_2,e_2)|sQ2_spl),
% 0.12/0.41 inference(resolution,[status(thm)],[f55,f43])).
% 0.12/0.41 fof(f58,definition,(
% 0.12/0.41 sQ3_spl <=> (group_element(e_2))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f60,plain,(
% 0.12/0.41 ~group_element(e_2)|sQ3_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f58])).
% 0.12/0.41 fof(f61,definition,(
% 0.12/0.41 sQ4_spl <=> (product(e_2,e_2,e_2))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f62,plain,(
% 0.12/0.41 product(e_2,e_2,e_2)|~sQ4_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f61])).
% 0.12/0.41 fof(f64,plain,(
% 0.12/0.41 ~sQ3_spl|sQ4_spl|sQ2_spl),
% 0.12/0.41 inference(split_clause,[status(thm)],[f57,f58,f61,f53])).
% 0.12/0.41 fof(f65,plain,(
% 0.12/0.41 $false|sQ3_spl),
% 0.12/0.41 inference(forward_subsumption_resolution,[status(thm)],[f60,f19])).
% 0.12/0.41 fof(f66,plain,(
% 0.12/0.41 sQ3_spl),
% 0.12/0.41 inference(contradiction_clause,[status(thm)],[f65])).
% 0.12/0.41 fof(f67,plain,(
% 0.12/0.41 ~product(e_2,e_2,e_2)|~sQ1_spl),
% 0.12/0.41 inference(resolution,[status(thm)],[f51,f33])).
% 0.12/0.41 fof(f68,plain,(
% 0.12/0.41 $false|~sQ4_spl|~sQ1_spl),
% 0.12/0.41 inference(forward_subsumption_resolution,[status(thm)],[f67,f62])).
% 0.12/0.41 fof(f69,plain,(
% 0.12/0.41 ~sQ4_spl|~sQ1_spl),
% 0.12/0.41 inference(contradiction_clause,[status(thm)],[f68])).
% 0.12/0.41 fof(f70,plain,(
% 0.12/0.41 $false|sQ0_spl),
% 0.12/0.41 inference(forward_subsumption_resolution,[status(thm)],[f49,f18])).
% 0.12/0.41 fof(f71,plain,(
% 0.12/0.41 sQ0_spl),
% 0.12/0.41 inference(contradiction_clause,[status(thm)],[f70])).
% 0.12/0.41 fof(f77,plain,(
% 0.12/0.41 product(e_2,e_1,e_1)|product(e_2,e_1,e_2)),
% 0.12/0.41 inference(resolution,[status(thm)],[f44,f19])).
% 0.12/0.41 fof(f78,plain,(
% 0.12/0.41 product(e_1,e_1,e_1)|product(e_1,e_1,e_2)),
% 0.12/0.41 inference(resolution,[status(thm)],[f44,f18])).
% 0.12/0.41 fof(f79,definition,(
% 0.12/0.41 sQ6_spl <=> (product(e_2,e_1,e_1))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f80,plain,(
% 0.12/0.41 product(e_2,e_1,e_1)|~sQ6_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f79])).
% 0.12/0.41 fof(f82,definition,(
% 0.12/0.41 sQ7_spl <=> (product(e_2,e_1,e_2))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f83,plain,(
% 0.12/0.41 product(e_2,e_1,e_2)|~sQ7_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f82])).
% 0.12/0.41 fof(f85,plain,(
% 0.12/0.41 sQ6_spl|sQ7_spl),
% 0.12/0.41 inference(split_clause,[status(thm)],[f77,f79,f82])).
% 0.12/0.41 fof(f86,definition,(
% 0.12/0.41 sQ8_spl <=> (product(e_1,e_1,e_1))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f87,plain,(
% 0.12/0.41 product(e_1,e_1,e_1)|~sQ8_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f86])).
% 0.12/0.41 fof(f89,definition,(
% 0.12/0.41 sQ9_spl <=> (product(e_1,e_1,e_2))),
% 0.12/0.41 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.12/0.41 fof(f90,plain,(
% 0.12/0.41 product(e_1,e_1,e_2)|~sQ9_spl),
% 0.12/0.41 inference(component_clause,[status(thm)],[f89])).
% 0.12/0.41 fof(f92,plain,(
% 0.12/0.41 sQ8_spl|sQ9_spl),
% 0.12/0.41 inference(split_clause,[status(thm)],[f78,f86,f89])).
% 0.12/0.41 fof(f102,plain,(
% 0.12/0.41 ![X0,X1]: (~product(e_1,e_1,X0)|~product(X1,e_2,X0)|~product(e_1,e_2,X1)|~sQ8_spl)),
% 0.12/0.41 inference(resolution,[status(thm)],[f87,f36])).
% 0.12/0.41 fof(f104,plain,(
% 0.12/0.41 ~product(e_1,e_2,e_1)|~sQ8_spl),
% 0.12/0.41 inference(resolution,[status(thm)],[f87,f34])).
% 0.12/0.41 fof(f110,plain,(
% 0.12/0.41 ~product(e_2,e_2,e_2)|~sQ7_spl),
% 0.12/0.41 inference(resolution,[status(thm)],[f83,f34])).
% 0.12/0.41 fof(f111,plain,(
% 0.12/0.41 $false|~sQ4_spl|~sQ7_spl),
% 0.12/0.41 inference(forward_subsumption_resolution,[status(thm)],[f110,f62])).
% 0.12/0.41 fof(f112,plain,(
% 0.12/0.41 ~sQ4_spl|~sQ7_spl),
% 0.12/0.41 inference(contradiction_clause,[status(thm)],[f111])).
% 0.12/0.41 fof(f113,plain,(
% 0.12/0.41 ![X0,X1]: (~product(e_2,X0,e_2)|~product(X1,e_1,e_1)|~product(X1,X0,e_2)|~sQ9_spl)),
% 0.12/0.41 inference(resolution,[status(thm)],[f90,f37])).
% 0.12/0.41 fof(f117,plain,(
% 0.12/0.41 ~product(e_1,e_2,e_2)|~sQ9_spl),
% 0.12/0.41 inference(resolution,[status(thm)],[f90,f34])).
% 0.12/0.41 fof(f120,plain,(
% 0.12/0.41 ![X0]: (~product(e_2,X0,e_2)|~product(e_2,X0,e_2)|~sQ6_spl|~sQ9_spl)),
% 0.12/0.41 inference(resolution,[status(thm)],[f80,f113])).
% 0.12/0.41 fof(f125,plain,(
% 0.12/0.41 $false|~sQ6_spl|~sQ9_spl|~sQ4_spl),
% 0.12/0.41 inference(backward_subsumption_resolution,[status(thm)],[f62,f126])).
% 0.12/0.41 fof(f126,plain,(
% 0.12/0.41 ![X0]: (~product(e_2,X0,e_2)|~sQ6_spl|~sQ9_spl)),
% 0.12/0.41 inference(duplicate_literals_removal,[status(thm)],[f120])).
% 0.12/0.41 fof(f127,plain,(
% 0.12/0.41 ~sQ6_spl|~sQ9_spl|~sQ4_spl),
% 0.12/0.41 inference(contradiction_clause,[status(thm)],[f125])).
% 0.12/0.41 fof(f128,plain,(
% 0.12/0.41 ~sQ1_spl|~sQ9_spl),
% 0.12/0.41 inference(split_clause,[status(thm)],[f117,f50,f89])).
% 0.12/0.41 fof(f139,plain,(
% 0.12/0.41 ~group_element(e_1)|product(e_1,e_2,e_2)|~sQ8_spl),
% 0.12/0.41 inference(resolution,[status(thm)],[f104,f43])).
% 0.12/0.41 fof(f140,plain,(
% 0.12/0.41 ~sQ0_spl|sQ1_spl|~sQ8_spl),
% 0.12/0.41 inference(split_clause,[status(thm)],[f139,f47,f50,f86])).
% 0.12/0.41 fof(f144,plain,(
% 0.12/0.41 ![X0]: (~product(X0,e_2,e_1)|~product(e_1,e_2,X0)|~sQ8_spl)),
% 0.12/0.41 inference(resolution,[status(thm)],[f102,f87])).
% 0.12/0.41 fof(f145,plain,(
% 0.12/0.41 ~product(e_2,e_2,e_1)|~sQ8_spl|~sQ1_spl),
% 0.12/0.41 inference(resolution,[status(thm)],[f144,f51])).
% 0.12/0.41 fof(f147,plain,(
% 0.12/0.41 ~sQ2_spl|~sQ8_spl|~sQ1_spl),
% 0.12/0.41 inference(split_clause,[status(thm)],[f145,f53,f86,f50])).
% 0.12/0.41 fof(f152,plain,(
% 0.12/0.41 $false),
% 0.12/0.41 inference(sat_refutation,[status(thm)],[f56,f64,f66,f69,f71,f85,f92,f112,f127,f128,f140,f147])).
% 0.12/0.41 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.43 % Elapsed time: 0.042928 seconds
% 0.12/0.43 % CPU time: 0.124959 seconds
% 0.12/0.43 % Total memory used: 17.241 MB
% 0.12/0.43 % Net memory used: 16.753 MB
%------------------------------------------------------------------------------