%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP135-2.002 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/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 12:36:04 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.37s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP135-2.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n012.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sun Sep 20 20:01:51 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Drodi V4.1.1
% 0.11/0.37 % Refutation found
% 0.11/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.37 % SZS output start CNFRefutation for theBenchmark
% 0.11/0.37 fof(f4,axiom,(
% 0.11/0.37 group_element(e_1) ),
% 0.11/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.37 fof(f5,axiom,(
% 0.11/0.37 group_element(e_2) ),
% 0.11/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.37 fof(f6,axiom,(
% 0.11/0.37 ~ equalish(e_1,e_2) ),
% 0.11/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.37 fof(f7,axiom,(
% 0.11/0.37 ~ equalish(e_2,e_1) ),
% 0.11/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.37 fof(f8,axiom,(
% 0.11/0.37 (![X,Y]: (( ~ group_element(X)| ~ group_element(Y)| product(X,Y,e_1)| product(X,Y,e_2) ) ))),
% 0.11/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.37 fof(f10,axiom,(
% 0.11/0.37 (![X,W,Y,Z]: (( ~ product(X,W,Y)| ~ product(X,Z,Y)| equalish(W,Z) ) ))),
% 0.11/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.37 fof(f11,axiom,(
% 0.11/0.37 (![W,Y,X,Z]: (( ~ product(W,Y,X)| ~ product(Z,Y,X)| equalish(W,Z) ) ))),
% 0.11/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.37 fof(f12,negated_conjecture,(
% 0.11/0.37 (![Y,X,Z1,Z2]: (( ~ product(Y,X,Z1)| ~ product(Z1,Y,Z2)| product(Z2,Y,X) ) ))),
% 0.11/0.37 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.11/0.37 fof(f17,plain,(
% 0.11/0.37 group_element(e_1)),
% 0.11/0.37 inference(cnf_transformation,[status(thm)],[f4])).
% 0.11/0.37 fof(f18,plain,(
% 0.11/0.37 group_element(e_2)),
% 0.11/0.37 inference(cnf_transformation,[status(thm)],[f5])).
% 0.11/0.37 fof(f19,plain,(
% 0.11/0.37 ~equalish(e_1,e_2)),
% 0.11/0.37 inference(cnf_transformation,[status(thm)],[f6])).
% 0.11/0.37 fof(f20,plain,(
% 0.11/0.37 ~equalish(e_2,e_1)),
% 0.11/0.37 inference(cnf_transformation,[status(thm)],[f7])).
% 0.11/0.37 fof(f21,plain,(
% 0.11/0.37 ![X0,X1]: (~group_element(X0)|~group_element(X1)|product(X0,X1,e_1)|product(X0,X1,e_2))),
% 0.11/0.37 inference(cnf_transformation,[status(thm)],[f8])).
% 0.11/0.37 fof(f24,plain,(
% 0.11/0.37 ![W,Z]: ((![X,Y]: (~product(X,W,Y)|~product(X,Z,Y)))|equalish(W,Z))),
% 0.11/0.37 inference(miniscoping,[status(thm)],[f10])).
% 0.11/0.37 fof(f25,plain,(
% 0.11/0.37 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X3,X2)|equalish(X1,X3))),
% 0.11/0.37 inference(cnf_transformation,[status(thm)],[f24])).
% 0.11/0.37 fof(f26,plain,(
% 0.11/0.37 ![W,Z]: ((![Y,X]: (~product(W,Y,X)|~product(Z,Y,X)))|equalish(W,Z))),
% 0.11/0.37 inference(miniscoping,[status(thm)],[f11])).
% 0.11/0.37 fof(f27,plain,(
% 0.11/0.37 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X3,X1,X2)|equalish(X0,X3))),
% 0.11/0.37 inference(cnf_transformation,[status(thm)],[f26])).
% 0.11/0.37 fof(f28,plain,(
% 0.11/0.37 ![Y,X,Z2]: ((![Z1]: (~product(Y,X,Z1)|~product(Z1,Y,Z2)))|product(Z2,Y,X))),
% 0.11/0.37 inference(miniscoping,[status(thm)],[f12])).
% 0.11/0.37 fof(f29,plain,(
% 0.11/0.37 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X2,X0,X3)|product(X3,X0,X1))),
% 0.11/0.37 inference(cnf_transformation,[status(thm)],[f28])).
% 0.11/0.37 fof(f30,plain,(
% 0.11/0.37 ![X0]: (~group_element(X0)|product(e_2,X0,e_1)|product(e_2,X0,e_2))),
% 0.11/0.37 inference(resolution,[status(thm)],[f21,f18])).
% 0.11/0.37 fof(f31,plain,(
% 0.11/0.37 ![X0]: (~group_element(X0)|product(e_1,X0,e_1)|product(e_1,X0,e_2))),
% 0.11/0.37 inference(resolution,[status(thm)],[f21,f17])).
% 0.11/0.37 fof(f32,plain,(
% 0.11/0.37 product(e_2,e_2,e_1)|product(e_2,e_2,e_2)),
% 0.11/0.37 inference(resolution,[status(thm)],[f30,f18])).
% 0.11/0.37 fof(f33,plain,(
% 0.11/0.37 product(e_2,e_1,e_1)|product(e_2,e_1,e_2)),
% 0.11/0.37 inference(resolution,[status(thm)],[f30,f17])).
% 0.11/0.37 fof(f34,definition,(
% 0.11/0.37 sQ0_spl <=> (product(e_2,e_2,e_1))),
% 0.11/0.37 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.11/0.37 fof(f35,plain,(
% 0.11/0.37 product(e_2,e_2,e_1)|~sQ0_spl),
% 0.11/0.37 inference(component_clause,[status(thm)],[f34])).
% 0.11/0.37 fof(f37,definition,(
% 0.11/0.37 sQ1_spl <=> (product(e_2,e_2,e_2))),
% 0.11/0.37 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.11/0.37 fof(f38,plain,(
% 0.11/0.37 product(e_2,e_2,e_2)|~sQ1_spl),
% 0.11/0.37 inference(component_clause,[status(thm)],[f37])).
% 0.11/0.37 fof(f40,plain,(
% 0.11/0.37 sQ0_spl|sQ1_spl),
% 0.11/0.37 inference(split_clause,[status(thm)],[f32,f34,f37])).
% 0.11/0.37 fof(f41,definition,(
% 0.11/0.37 sQ2_spl <=> (product(e_2,e_1,e_1))),
% 0.11/0.37 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.11/0.37 fof(f42,plain,(
% 0.11/0.37 product(e_2,e_1,e_1)|~sQ2_spl),
% 0.11/0.37 inference(component_clause,[status(thm)],[f41])).
% 0.11/0.37 fof(f44,definition,(
% 0.11/0.37 sQ3_spl <=> (product(e_2,e_1,e_2))),
% 0.11/0.37 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.11/0.37 fof(f45,plain,(
% 0.11/0.37 product(e_2,e_1,e_2)|~sQ3_spl),
% 0.11/0.37 inference(component_clause,[status(thm)],[f44])).
% 0.11/0.37 fof(f47,plain,(
% 0.11/0.37 sQ2_spl|sQ3_spl),
% 0.11/0.37 inference(split_clause,[status(thm)],[f33,f41,f44])).
% 0.11/0.37 fof(f50,plain,(
% 0.11/0.37 ![X0]: (~product(e_2,X0,e_1)|equalish(e_1,X0)|~sQ2_spl)),
% 0.11/0.37 inference(resolution,[status(thm)],[f42,f25])).
% 0.11/0.37 fof(f52,plain,(
% 0.11/0.37 ![X0]: (~product(e_1,e_2,X0)|product(X0,e_2,e_1)|~sQ2_spl)),
% 0.11/0.37 inference(resolution,[status(thm)],[f42,f29])).
% 0.11/0.37 fof(f56,plain,(
% 0.11/0.37 ![X0]: (~product(e_1,e_2,X0)|product(X0,e_2,e_2)|~sQ0_spl)),
% 0.11/0.37 inference(resolution,[status(thm)],[f35,f29])).
% 0.11/0.37 fof(f58,plain,(
% 0.11/0.37 equalish(e_1,e_2)|~sQ2_spl|~sQ0_spl),
% 0.11/0.37 inference(resolution,[status(thm)],[f50,f35])).
% 0.11/0.37 fof(f60,plain,(
% 0.11/0.37 $false|~sQ2_spl|~sQ0_spl),
% 0.11/0.37 inference(forward_subsumption_resolution,[status(thm)],[f58,f19])).
% 0.11/0.37 fof(f61,plain,(
% 0.11/0.37 ~sQ2_spl|~sQ0_spl),
% 0.11/0.37 inference(contradiction_clause,[status(thm)],[f60])).
% 0.11/0.37 fof(f62,plain,(
% 0.11/0.37 product(e_1,e_2,e_1)|product(e_1,e_2,e_2)),
% 0.11/0.37 inference(resolution,[status(thm)],[f31,f18])).
% 0.11/0.37 fof(f63,plain,(
% 0.11/0.37 product(e_1,e_1,e_1)|product(e_1,e_1,e_2)),
% 0.11/0.37 inference(resolution,[status(thm)],[f31,f17])).
% 0.11/0.37 fof(f64,definition,(
% 0.11/0.37 sQ4_spl <=> (product(e_1,e_2,e_1))),
% 0.11/0.37 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.11/0.37 fof(f65,plain,(
% 0.11/0.37 product(e_1,e_2,e_1)|~sQ4_spl),
% 0.11/0.37 inference(component_clause,[status(thm)],[f64])).
% 0.11/0.37 fof(f67,definition,(
% 0.11/0.37 sQ5_spl <=> (product(e_1,e_2,e_2))),
% 0.11/0.37 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.11/0.37 fof(f68,plain,(
% 0.11/0.37 product(e_1,e_2,e_2)|~sQ5_spl),
% 0.11/0.37 inference(component_clause,[status(thm)],[f67])).
% 0.11/0.37 fof(f70,plain,(
% 0.11/0.37 sQ4_spl|sQ5_spl),
% 0.11/0.37 inference(split_clause,[status(thm)],[f62,f64,f67])).
% 0.11/0.37 fof(f71,definition,(
% 0.11/0.37 sQ6_spl <=> (product(e_1,e_1,e_1))),
% 0.11/0.37 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.11/0.37 fof(f72,plain,(
% 0.11/0.37 product(e_1,e_1,e_1)|~sQ6_spl),
% 0.11/0.37 inference(component_clause,[status(thm)],[f71])).
% 0.11/0.37 fof(f74,definition,(
% 0.11/0.37 sQ7_spl <=> (product(e_1,e_1,e_2))),
% 0.11/0.37 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.11/0.37 fof(f75,plain,(
% 0.11/0.37 product(e_1,e_1,e_2)|~sQ7_spl),
% 0.11/0.37 inference(component_clause,[status(thm)],[f74])).
% 0.11/0.37 fof(f77,plain,(
% 0.11/0.37 sQ6_spl|sQ7_spl),
% 0.11/0.37 inference(split_clause,[status(thm)],[f63,f71,f74])).
% 0.11/0.37 fof(f82,plain,(
% 0.11/0.37 ![X0]: (~product(e_2,e_2,X0)|product(X0,e_2,e_1)|~sQ3_spl)),
% 0.11/0.37 inference(resolution,[status(thm)],[f45,f29])).
% 0.11/0.37 fof(f83,plain,(
% 0.11/0.37 product(e_2,e_2,e_1)|~sQ1_spl|~sQ3_spl),
% 0.11/0.37 inference(resolution,[status(thm)],[f38,f82])).
% 0.11/0.37 fof(f90,plain,(
% 0.11/0.37 product(e_1,e_2,e_1)|~sQ1_spl|~sQ3_spl),
% 0.11/0.37 inference(resolution,[status(thm)],[f83,f82])).
% 0.11/0.37 fof(f91,plain,(
% 0.11/0.37 ![X0]: (~product(X0,e_2,e_1)|equalish(e_2,X0)|~sQ1_spl|~sQ3_spl)),
% 0.11/0.37 inference(resolution,[status(thm)],[f83,f27])).
% 0.11/0.37 fof(f103,plain,(
% 0.11/0.37 equalish(e_2,e_1)|~sQ1_spl|~sQ3_spl),
% 0.11/0.37 inference(resolution,[status(thm)],[f91,f90])).
% 0.11/0.37 fof(f105,plain,(
% 0.11/0.37 $false|~sQ1_spl|~sQ3_spl),
% 0.11/0.37 inference(forward_subsumption_resolution,[status(thm)],[f103,f20])).
% 0.11/0.37 fof(f106,plain,(
% 0.11/0.37 ~sQ1_spl|~sQ3_spl),
% 0.11/0.37 inference(contradiction_clause,[status(thm)],[f105])).
% 0.11/0.37 fof(f113,plain,(
% 0.11/0.37 product(e_1,e_2,e_2)|~sQ4_spl|~sQ0_spl),
% 0.11/0.37 inference(resolution,[status(thm)],[f65,f56])).
% 0.11/0.37 fof(f117,plain,(
% 0.11/0.37 ![X0]: (~product(e_1,e_1,X0)|product(X0,e_1,e_2)|~sQ4_spl)),
% 0.11/0.37 inference(resolution,[status(thm)],[f65,f29])).
% 0.11/0.37 fof(f118,plain,(
% 0.11/0.37 product(e_2,e_2,e_2)|~sQ4_spl|~sQ0_spl),
% 0.11/0.37 inference(resolution,[status(thm)],[f113,f56])).
% 0.11/0.37 fof(f123,plain,(
% 0.11/0.37 sQ1_spl|~sQ4_spl|~sQ0_spl),
% 0.11/0.37 inference(split_clause,[status(thm)],[f118,f37,f64,f34])).
% 0.11/0.37 fof(f124,plain,(
% 0.11/0.37 product(e_1,e_2,e_1)|~sQ0_spl|~sQ3_spl),
% 0.11/0.37 inference(resolution,[status(thm)],[f35,f82])).
% 0.11/0.37 fof(f129,plain,(
% 0.11/0.37 sQ4_spl|~sQ0_spl|~sQ3_spl),
% 0.11/0.37 inference(split_clause,[status(thm)],[f124,f64,f34,f44])).
% 0.11/0.37 fof(f130,plain,(
% 0.11/0.37 product(e_1,e_1,e_2)|~sQ4_spl|~sQ6_spl),
% 0.11/0.37 inference(resolution,[status(thm)],[f117,f72])).
% 0.11/0.37 fof(f131,plain,(
% 0.11/0.37 product(e_2,e_1,e_2)|~sQ6_spl|~sQ4_spl),
% 0.11/0.37 inference(resolution,[status(thm)],[f130,f117])).
% 0.11/0.37 fof(f138,plain,(
% 0.11/0.37 sQ3_spl|~sQ6_spl|~sQ4_spl),
% 0.11/0.37 inference(split_clause,[status(thm)],[f131,f44,f71,f64])).
% 0.11/0.37 fof(f153,plain,(
% 0.11/0.37 ![X0]: (~product(e_2,e_1,X0)|product(X0,e_1,e_1)|~sQ7_spl)),
% 0.11/0.37 inference(resolution,[status(thm)],[f75,f29])).
% 0.11/0.37 fof(f154,plain,(
% 0.11/0.37 product(e_1,e_1,e_1)|~sQ7_spl|~sQ2_spl),
% 0.11/0.37 inference(resolution,[status(thm)],[f153,f42])).
% 0.11/0.37 fof(f155,plain,(
% 0.11/0.37 sQ6_spl|~sQ7_spl|~sQ2_spl),
% 0.11/0.37 inference(split_clause,[status(thm)],[f154,f71,f74,f41])).
% 0.11/0.37 fof(f156,plain,(
% 0.11/0.37 product(e_2,e_2,e_1)|~sQ5_spl|~sQ2_spl),
% 0.11/0.37 inference(resolution,[status(thm)],[f68,f52])).
% 0.11/0.37 fof(f161,plain,(
% 0.11/0.37 sQ0_spl|~sQ5_spl|~sQ2_spl),
% 0.11/0.37 inference(split_clause,[status(thm)],[f156,f34,f67,f41])).
% 0.11/0.37 fof(f162,plain,(
% 0.11/0.37 $false),
% 0.11/0.37 inference(sat_refutation,[status(thm)],[f40,f47,f61,f70,f77,f106,f123,f129,f138,f155,f161])).
% 0.11/0.37 % SZS output end CNFRefutation for theBenchmark.p
% 0.11/0.40 % Elapsed time: 0.036248 seconds
% 0.11/0.40 % CPU time: 0.088756 seconds
% 0.11/0.40 % Total memory used: 16.975 MB
% 0.11/0.40 % Net memory used: 16.556 MB
%------------------------------------------------------------------------------