%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP135-1.002 : 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 : 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 12:36:04 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP135-1.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:04:31 UTC 2026
% 0.09/0.35 % 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 group_element(e_1) ),
% 0.12/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f2,axiom,(
% 0.12/0.38 group_element(e_2) ),
% 0.12/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f3,axiom,(
% 0.12/0.38 ~ equalish(e_1,e_2) ),
% 0.12/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f4,axiom,(
% 0.12/0.38 ~ equalish(e_2,e_1) ),
% 0.12/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f5,axiom,(
% 0.12/0.38 (![X,Y]: (( ~ group_element(X)| ~ group_element(Y)| product(X,Y,e_1)| product(X,Y,e_2) ) ))),
% 0.12/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f6,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/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f7,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/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f9,negated_conjecture,(
% 0.12/0.38 (![Y,X,Z1,Z2]: (( ~ product(Y,X,Z1)| ~ product(Z1,Y,Z2)| product(Z2,Y,X) ) ))),
% 0.12/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.12/0.38 fof(f10,plain,(
% 0.12/0.38 group_element(e_1)),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f1])).
% 0.12/0.38 fof(f11,plain,(
% 0.12/0.38 group_element(e_2)),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f2])).
% 0.12/0.38 fof(f12,plain,(
% 0.12/0.38 ~equalish(e_1,e_2)),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f3])).
% 0.12/0.38 fof(f13,plain,(
% 0.12/0.38 ~equalish(e_2,e_1)),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f4])).
% 0.12/0.38 fof(f14,plain,(
% 0.12/0.38 ![X0,X1]: (~group_element(X0)|~group_element(X1)|product(X0,X1,e_1)|product(X0,X1,e_2))),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f5])).
% 0.12/0.38 fof(f15,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)],[f6])).
% 0.12/0.38 fof(f16,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)],[f15])).
% 0.12/0.38 fof(f17,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)],[f7])).
% 0.12/0.38 fof(f18,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)],[f17])).
% 0.12/0.38 fof(f21,plain,(
% 0.12/0.38 ![Y,X,Z2]: ((![Z1]: (~product(Y,X,Z1)|~product(Z1,Y,Z2)))|product(Z2,Y,X))),
% 0.12/0.38 inference(miniscoping,[status(thm)],[f9])).
% 0.12/0.38 fof(f22,plain,(
% 0.12/0.38 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X2,X0,X3)|product(X3,X0,X1))),
% 0.12/0.38 inference(cnf_transformation,[status(thm)],[f21])).
% 0.12/0.38 fof(f23,plain,(
% 0.12/0.38 ![X0]: (~group_element(X0)|product(e_2,X0,e_1)|product(e_2,X0,e_2))),
% 0.12/0.38 inference(resolution,[status(thm)],[f14,f11])).
% 0.12/0.38 fof(f24,plain,(
% 0.12/0.38 ![X0]: (~group_element(X0)|product(e_1,X0,e_1)|product(e_1,X0,e_2))),
% 0.12/0.38 inference(resolution,[status(thm)],[f14,f10])).
% 0.12/0.38 fof(f25,plain,(
% 0.12/0.38 product(e_2,e_2,e_1)|product(e_2,e_2,e_2)),
% 0.12/0.38 inference(resolution,[status(thm)],[f23,f11])).
% 0.12/0.38 fof(f26,plain,(
% 0.12/0.38 product(e_2,e_1,e_1)|product(e_2,e_1,e_2)),
% 0.12/0.38 inference(resolution,[status(thm)],[f23,f10])).
% 0.12/0.38 fof(f27,definition,(
% 0.12/0.38 sQ0_spl <=> (product(e_2,e_2,e_1))),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.12/0.38 fof(f28,plain,(
% 0.12/0.38 product(e_2,e_2,e_1)|~sQ0_spl),
% 0.12/0.38 inference(component_clause,[status(thm)],[f27])).
% 0.12/0.38 fof(f30,definition,(
% 0.12/0.38 sQ1_spl <=> (product(e_2,e_2,e_2))),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.12/0.38 fof(f31,plain,(
% 0.12/0.38 product(e_2,e_2,e_2)|~sQ1_spl),
% 0.12/0.38 inference(component_clause,[status(thm)],[f30])).
% 0.12/0.38 fof(f33,plain,(
% 0.12/0.38 sQ0_spl|sQ1_spl),
% 0.12/0.38 inference(split_clause,[status(thm)],[f25,f27,f30])).
% 0.12/0.38 fof(f34,definition,(
% 0.12/0.38 sQ2_spl <=> (product(e_2,e_1,e_1))),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.12/0.38 fof(f35,plain,(
% 0.12/0.38 product(e_2,e_1,e_1)|~sQ2_spl),
% 0.12/0.38 inference(component_clause,[status(thm)],[f34])).
% 0.12/0.38 fof(f37,definition,(
% 0.12/0.38 sQ3_spl <=> (product(e_2,e_1,e_2))),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.12/0.38 fof(f38,plain,(
% 0.12/0.38 product(e_2,e_1,e_2)|~sQ3_spl),
% 0.12/0.38 inference(component_clause,[status(thm)],[f37])).
% 0.12/0.38 fof(f40,plain,(
% 0.12/0.38 sQ2_spl|sQ3_spl),
% 0.12/0.38 inference(split_clause,[status(thm)],[f26,f34,f37])).
% 0.12/0.38 fof(f42,plain,(
% 0.12/0.38 ![X0]: (~product(e_2,X0,e_1)|equalish(X0,e_1)|~sQ2_spl)),
% 0.12/0.38 inference(resolution,[status(thm)],[f35,f18])).
% 0.12/0.38 fof(f44,plain,(
% 0.12/0.38 ![X0]: (~product(e_1,X0,e_2)|product(e_1,e_1,X0)|~sQ2_spl)),
% 0.12/0.38 inference(resolution,[status(thm)],[f35,f22])).
% 0.12/0.38 fof(f48,plain,(
% 0.12/0.38 ![X0]: (~product(e_2,X0,e_2)|product(e_1,e_2,X0)|~sQ0_spl)),
% 0.12/0.38 inference(resolution,[status(thm)],[f28,f22])).
% 0.12/0.38 fof(f50,plain,(
% 0.12/0.38 equalish(e_2,e_1)|~sQ2_spl|~sQ0_spl),
% 0.12/0.38 inference(resolution,[status(thm)],[f42,f28])).
% 0.12/0.38 fof(f52,plain,(
% 0.12/0.38 $false|~sQ2_spl|~sQ0_spl),
% 0.12/0.38 inference(forward_subsumption_resolution,[status(thm)],[f50,f13])).
% 0.12/0.38 fof(f53,plain,(
% 0.12/0.38 ~sQ2_spl|~sQ0_spl),
% 0.12/0.38 inference(contradiction_clause,[status(thm)],[f52])).
% 0.12/0.38 fof(f57,plain,(
% 0.12/0.38 ![X0]: (~product(e_1,X0,e_2)|product(e_2,e_1,X0)|~sQ3_spl)),
% 0.12/0.38 inference(resolution,[status(thm)],[f38,f22])).
% 0.12/0.38 fof(f61,plain,(
% 0.12/0.38 ![X0]: (~product(e_2,X0,e_2)|product(e_2,e_2,X0)|~sQ1_spl)),
% 0.12/0.38 inference(resolution,[status(thm)],[f31,f22])).
% 0.12/0.38 fof(f62,plain,(
% 0.12/0.38 product(e_1,e_2,e_1)|product(e_1,e_2,e_2)),
% 0.12/0.38 inference(resolution,[status(thm)],[f24,f11])).
% 0.12/0.38 fof(f63,plain,(
% 0.12/0.38 product(e_1,e_1,e_1)|product(e_1,e_1,e_2)),
% 0.12/0.38 inference(resolution,[status(thm)],[f24,f10])).
% 0.12/0.38 fof(f64,definition,(
% 0.12/0.38 sQ4_spl <=> (product(e_1,e_2,e_1))),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.12/0.38 fof(f65,plain,(
% 0.12/0.38 product(e_1,e_2,e_1)|~sQ4_spl),
% 0.12/0.38 inference(component_clause,[status(thm)],[f64])).
% 0.12/0.38 fof(f67,definition,(
% 0.12/0.38 sQ5_spl <=> (product(e_1,e_2,e_2))),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.12/0.38 fof(f68,plain,(
% 0.12/0.38 product(e_1,e_2,e_2)|~sQ5_spl),
% 0.12/0.38 inference(component_clause,[status(thm)],[f67])).
% 0.12/0.38 fof(f70,plain,(
% 0.12/0.38 sQ4_spl|sQ5_spl),
% 0.12/0.38 inference(split_clause,[status(thm)],[f62,f64,f67])).
% 0.12/0.38 fof(f71,definition,(
% 0.12/0.38 sQ6_spl <=> (product(e_1,e_1,e_1))),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.12/0.38 fof(f72,plain,(
% 0.12/0.38 product(e_1,e_1,e_1)|~sQ6_spl),
% 0.12/0.38 inference(component_clause,[status(thm)],[f71])).
% 0.12/0.38 fof(f74,definition,(
% 0.12/0.38 sQ7_spl <=> (product(e_1,e_1,e_2))),
% 0.12/0.38 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.12/0.38 fof(f75,plain,(
% 0.12/0.38 product(e_1,e_1,e_2)|~sQ7_spl),
% 0.12/0.38 inference(component_clause,[status(thm)],[f74])).
% 0.12/0.38 fof(f77,plain,(
% 0.12/0.38 sQ6_spl|sQ7_spl),
% 0.12/0.38 inference(split_clause,[status(thm)],[f63,f71,f74])).
% 0.12/0.38 fof(f79,plain,(
% 0.12/0.38 product(e_2,e_2,e_1)|~sQ1_spl|~sQ3_spl),
% 0.12/0.38 inference(resolution,[status(thm)],[f61,f38])).
% 0.12/0.38 fof(f82,plain,(
% 0.12/0.38 ![X0]: (~product(e_2,e_2,X0)|equalish(X0,e_1)|~sQ1_spl|~sQ3_spl)),
% 0.12/0.38 inference(resolution,[status(thm)],[f79,f16])).
% 0.12/0.38 fof(f87,plain,(
% 0.12/0.38 equalish(e_2,e_1)|~sQ3_spl|~sQ1_spl),
% 0.12/0.38 inference(resolution,[status(thm)],[f82,f31])).
% 0.12/0.38 fof(f88,plain,(
% 0.12/0.38 $false|~sQ3_spl|~sQ1_spl),
% 0.12/0.38 inference(forward_subsumption_resolution,[status(thm)],[f87,f13])).
% 0.12/0.38 fof(f89,plain,(
% 0.12/0.38 ~sQ3_spl|~sQ1_spl),
% 0.12/0.38 inference(contradiction_clause,[status(thm)],[f88])).
% 0.12/0.38 fof(f93,plain,(
% 0.12/0.38 ![X0]: (~product(e_1,X0,e_1)|product(e_1,e_1,X0)|~sQ6_spl)),
% 0.12/0.38 inference(resolution,[status(thm)],[f72,f22])).
% 0.12/0.38 fof(f95,plain,(
% 0.12/0.38 product(e_1,e_1,e_2)|~sQ4_spl|~sQ6_spl),
% 0.12/0.38 inference(resolution,[status(thm)],[f65,f93])).
% 0.12/0.38 fof(f103,plain,(
% 0.12/0.38 ![X0]: (~product(e_1,e_1,X0)|equalish(X0,e_2)|~sQ4_spl|~sQ6_spl)),
% 0.12/0.38 inference(resolution,[status(thm)],[f95,f16])).
% 0.12/0.38 fof(f108,plain,(
% 0.12/0.38 equalish(e_1,e_2)|~sQ4_spl|~sQ6_spl),
% 0.12/0.38 inference(resolution,[status(thm)],[f103,f72])).
% 0.12/0.38 fof(f109,plain,(
% 0.12/0.38 $false|~sQ4_spl|~sQ6_spl),
% 0.12/0.38 inference(forward_subsumption_resolution,[status(thm)],[f108,f12])).
% 0.12/0.38 fof(f110,plain,(
% 0.12/0.38 ~sQ4_spl|~sQ6_spl),
% 0.12/0.38 inference(contradiction_clause,[status(thm)],[f109])).
% 0.12/0.38 fof(f115,plain,(
% 0.12/0.38 product(e_1,e_1,e_2)|~sQ5_spl|~sQ2_spl),
% 0.12/0.38 inference(resolution,[status(thm)],[f68,f44])).
% 0.12/0.38 fof(f122,plain,(
% 0.12/0.38 ![X0]: (~product(e_1,X0,e_2)|equalish(X0,e_1)|~sQ5_spl|~sQ2_spl)),
% 0.12/0.38 inference(resolution,[status(thm)],[f115,f18])).
% 0.12/0.38 fof(f131,plain,(
% 0.12/0.38 equalish(e_2,e_1)|~sQ2_spl|~sQ5_spl),
% 0.12/0.38 inference(resolution,[status(thm)],[f122,f68])).
% 0.12/0.38 fof(f132,plain,(
% 0.12/0.38 $false|~sQ2_spl|~sQ5_spl),
% 0.12/0.38 inference(forward_subsumption_resolution,[status(thm)],[f131,f13])).
% 0.12/0.38 fof(f133,plain,(
% 0.12/0.38 ~sQ2_spl|~sQ5_spl),
% 0.12/0.38 inference(contradiction_clause,[status(thm)],[f132])).
% 0.12/0.38 fof(f134,plain,(
% 0.12/0.38 product(e_2,e_1,e_1)|~sQ7_spl|~sQ3_spl),
% 0.12/0.38 inference(resolution,[status(thm)],[f75,f57])).
% 0.12/0.38 fof(f138,plain,(
% 0.12/0.38 ![X0]: (~product(e_1,X0,e_1)|product(e_2,e_1,X0)|~sQ7_spl)),
% 0.12/0.38 inference(resolution,[status(thm)],[f75,f22])).
% 0.12/0.38 fof(f139,plain,(
% 0.12/0.38 sQ2_spl|~sQ7_spl|~sQ3_spl),
% 0.12/0.38 inference(split_clause,[status(thm)],[f134,f34,f74,f37])).
% 0.12/0.38 fof(f140,plain,(
% 0.12/0.38 product(e_1,e_2,e_1)|~sQ3_spl|~sQ0_spl),
% 0.12/0.38 inference(resolution,[status(thm)],[f38,f48])).
% 0.12/0.38 fof(f145,plain,(
% 0.12/0.38 sQ4_spl|~sQ3_spl|~sQ0_spl),
% 0.12/0.38 inference(split_clause,[status(thm)],[f140,f64,f37,f27])).
% 0.12/0.38 fof(f146,plain,(
% 0.12/0.38 product(e_2,e_1,e_2)|~sQ4_spl|~sQ7_spl),
% 0.12/0.38 inference(resolution,[status(thm)],[f65,f138])).
% 0.12/0.38 fof(f151,plain,(
% 0.12/0.38 sQ3_spl|~sQ4_spl|~sQ7_spl),
% 0.12/0.38 inference(split_clause,[status(thm)],[f146,f37,f64,f74])).
% 0.12/0.38 fof(f152,plain,(
% 0.12/0.38 $false),
% 0.12/0.38 inference(sat_refutation,[status(thm)],[f33,f40,f53,f70,f77,f89,f110,f133,f139,f145,f151])).
% 0.12/0.38 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/0.42 % Elapsed time: 0.052909 seconds
% 0.12/0.42 % CPU time: 0.137072 seconds
% 0.12/0.42 % Total memory used: 16.788 MB
% 0.12/0.42 % Net memory used: 16.315 MB
%------------------------------------------------------------------------------