%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP125-1.003 : 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 : n013.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 12:35:49 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP125-1.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 19:58:36 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.39 % Refutation found
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.10/0.39 fof(f2,axiom,(
% 0.10/0.39 group_element(e_2) ),
% 0.10/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f3,axiom,(
% 0.10/0.39 group_element(e_3) ),
% 0.10/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f5,axiom,(
% 0.10/0.39 ~ equalish(e_1,e_3) ),
% 0.10/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f7,axiom,(
% 0.10/0.39 ~ equalish(e_2,e_3) ),
% 0.10/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f9,axiom,(
% 0.10/0.39 ~ equalish(e_3,e_2) ),
% 0.10/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f10,axiom,(
% 0.10/0.39 (![X,Y]: (( ~ group_element(X)| ~ group_element(Y)| product(X,Y,e_1)| product(X,Y,e_2)| product(X,Y,e_3) ) ))),
% 0.10/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f11,axiom,(
% 0.10/0.39 (![X,Y,W,Z]: (( ~ product(X,Y,W)| ~ product(X,Y,Z)| equalish(W,Z) ) ))),
% 0.10/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f12,axiom,(
% 0.10/0.39 (![X,W,Y,Z]: (( ~ product(X,W,Y)| ~ product(X,Z,Y)| equalish(W,Z) ) ))),
% 0.10/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f13,axiom,(
% 0.10/0.39 (![W,Y,X,Z]: (( ~ product(W,Y,X)| ~ product(Z,Y,X)| equalish(W,Z) ) ))),
% 0.10/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f14,axiom,(
% 0.10/0.39 (![X]: (product(X,X,X) ))),
% 0.10/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f15,negated_conjecture,(
% 0.10/0.39 (![X,Y,Z1,Z2]: (( ~ product(X,Y,Z1)| ~ product(Y,X,Z2)| product(Z1,Z2,X) ) ))),
% 0.10/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.10/0.39 fof(f17,plain,(
% 0.10/0.39 group_element(e_2)),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f2])).
% 0.10/0.39 fof(f18,plain,(
% 0.10/0.39 group_element(e_3)),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f3])).
% 0.10/0.39 fof(f20,plain,(
% 0.10/0.39 ~equalish(e_1,e_3)),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f5])).
% 0.10/0.39 fof(f22,plain,(
% 0.10/0.39 ~equalish(e_2,e_3)),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f7])).
% 0.10/0.39 fof(f24,plain,(
% 0.10/0.39 ~equalish(e_3,e_2)),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f9])).
% 0.10/0.39 fof(f25,plain,(
% 0.10/0.39 ![X0,X1]: (~group_element(X0)|~group_element(X1)|product(X0,X1,e_1)|product(X0,X1,e_2)|product(X0,X1,e_3))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f10])).
% 0.10/0.39 fof(f26,plain,(
% 0.10/0.39 ![W,Z]: ((![X,Y]: (~product(X,Y,W)|~product(X,Y,Z)))|equalish(W,Z))),
% 0.10/0.39 inference(miniscoping,[status(thm)],[f11])).
% 0.10/0.39 fof(f27,plain,(
% 0.10/0.39 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X1,X3)|equalish(X2,X3))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f26])).
% 0.10/0.39 fof(f28,plain,(
% 0.10/0.39 ![W,Z]: ((![X,Y]: (~product(X,W,Y)|~product(X,Z,Y)))|equalish(W,Z))),
% 0.10/0.39 inference(miniscoping,[status(thm)],[f12])).
% 0.10/0.39 fof(f29,plain,(
% 0.10/0.39 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X3,X2)|equalish(X1,X3))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f28])).
% 0.10/0.39 fof(f30,plain,(
% 0.10/0.39 ![W,Z]: ((![Y,X]: (~product(W,Y,X)|~product(Z,Y,X)))|equalish(W,Z))),
% 0.10/0.39 inference(miniscoping,[status(thm)],[f13])).
% 0.10/0.39 fof(f31,plain,(
% 0.10/0.39 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X3,X1,X2)|equalish(X0,X3))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f30])).
% 0.10/0.39 fof(f32,plain,(
% 0.10/0.39 ![X0]: (product(X0,X0,X0))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f14])).
% 0.10/0.39 fof(f33,plain,(
% 0.10/0.39 ![X,Z1,Z2]: ((![Y]: (~product(X,Y,Z1)|~product(Y,X,Z2)))|product(Z1,Z2,X))),
% 0.10/0.39 inference(miniscoping,[status(thm)],[f15])).
% 0.10/0.39 fof(f34,plain,(
% 0.10/0.39 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X1,X0,X3)|product(X2,X3,X0))),
% 0.10/0.39 inference(cnf_transformation,[status(thm)],[f33])).
% 0.10/0.39 fof(f37,plain,(
% 0.10/0.39 ![X0,X1]: (~product(X0,X0,X1)|equalish(X0,X1))),
% 0.10/0.39 inference(resolution,[status(thm)],[f27,f32])).
% 0.10/0.39 fof(f38,plain,(
% 0.10/0.39 ![X0,X1]: (~product(X0,X1,X0)|equalish(X0,X1))),
% 0.10/0.39 inference(resolution,[status(thm)],[f29,f32])).
% 0.10/0.39 fof(f39,plain,(
% 0.10/0.39 ![X0,X1]: (~product(X0,X1,X1)|equalish(X1,X0))),
% 0.10/0.39 inference(resolution,[status(thm)],[f31,f32])).
% 0.10/0.39 fof(f43,plain,(
% 0.10/0.39 ![X0]: (~group_element(X0)|product(e_3,X0,e_1)|product(e_3,X0,e_2)|product(e_3,X0,e_3))),
% 0.10/0.39 inference(resolution,[status(thm)],[f25,f18])).
% 0.10/0.39 fof(f44,plain,(
% 0.10/0.39 ![X0]: (~group_element(X0)|product(e_2,X0,e_1)|product(e_2,X0,e_2)|product(e_2,X0,e_3))),
% 0.10/0.39 inference(resolution,[status(thm)],[f25,f17])).
% 0.14/0.40 fof(f47,plain,(
% 0.14/0.40 product(e_3,e_2,e_1)|product(e_3,e_2,e_2)|product(e_3,e_2,e_3)),
% 0.14/0.40 inference(resolution,[status(thm)],[f43,f17])).
% 0.14/0.40 fof(f59,definition,(
% 0.14/0.40 sQ3_spl <=> (product(e_3,e_2,e_1))),
% 0.14/0.40 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.14/0.40 fof(f60,plain,(
% 0.14/0.40 product(e_3,e_2,e_1)|~sQ3_spl),
% 0.14/0.40 inference(component_clause,[status(thm)],[f59])).
% 0.14/0.40 fof(f62,definition,(
% 0.14/0.40 sQ4_spl <=> (product(e_3,e_2,e_2))),
% 0.14/0.40 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.14/0.40 fof(f63,plain,(
% 0.14/0.40 product(e_3,e_2,e_2)|~sQ4_spl),
% 0.14/0.40 inference(component_clause,[status(thm)],[f62])).
% 0.14/0.40 fof(f65,definition,(
% 0.14/0.40 sQ5_spl <=> (product(e_3,e_2,e_3))),
% 0.14/0.40 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.14/0.40 fof(f66,plain,(
% 0.14/0.40 product(e_3,e_2,e_3)|~sQ5_spl),
% 0.14/0.40 inference(component_clause,[status(thm)],[f65])).
% 0.14/0.40 fof(f68,plain,(
% 0.14/0.40 sQ3_spl|sQ4_spl|sQ5_spl),
% 0.14/0.40 inference(split_clause,[status(thm)],[f47,f59,f62,f65])).
% 0.14/0.40 fof(f79,plain,(
% 0.14/0.40 product(e_2,e_3,e_1)|product(e_2,e_3,e_2)|product(e_2,e_3,e_3)),
% 0.14/0.40 inference(resolution,[status(thm)],[f44,f18])).
% 0.14/0.40 fof(f82,definition,(
% 0.14/0.40 sQ9_spl <=> (product(e_2,e_3,e_1))),
% 0.14/0.40 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.14/0.40 fof(f83,plain,(
% 0.14/0.40 product(e_2,e_3,e_1)|~sQ9_spl),
% 0.14/0.40 inference(component_clause,[status(thm)],[f82])).
% 0.14/0.40 fof(f85,definition,(
% 0.14/0.40 sQ10_spl <=> (product(e_2,e_3,e_2))),
% 0.14/0.40 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.14/0.40 fof(f86,plain,(
% 0.14/0.40 product(e_2,e_3,e_2)|~sQ10_spl),
% 0.14/0.40 inference(component_clause,[status(thm)],[f85])).
% 0.14/0.40 fof(f88,definition,(
% 0.14/0.40 sQ11_spl <=> (product(e_2,e_3,e_3))),
% 0.14/0.40 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.14/0.40 fof(f89,plain,(
% 0.14/0.40 product(e_2,e_3,e_3)|~sQ11_spl),
% 0.14/0.40 inference(component_clause,[status(thm)],[f88])).
% 0.14/0.40 fof(f91,plain,(
% 0.14/0.40 sQ9_spl|sQ10_spl|sQ11_spl),
% 0.14/0.40 inference(split_clause,[status(thm)],[f79,f82,f85,f88])).
% 0.14/0.40 fof(f163,plain,(
% 0.14/0.40 equalish(e_3,e_2)|~sQ5_spl),
% 0.14/0.40 inference(resolution,[status(thm)],[f66,f38])).
% 0.14/0.40 fof(f168,plain,(
% 0.14/0.40 $false|~sQ5_spl),
% 0.14/0.40 inference(forward_subsumption_resolution,[status(thm)],[f163,f24])).
% 0.14/0.40 fof(f169,plain,(
% 0.14/0.40 ~sQ5_spl),
% 0.14/0.40 inference(contradiction_clause,[status(thm)],[f168])).
% 0.14/0.40 fof(f170,plain,(
% 0.14/0.40 equalish(e_2,e_3)|~sQ4_spl),
% 0.14/0.40 inference(resolution,[status(thm)],[f63,f39])).
% 0.14/0.40 fof(f175,plain,(
% 0.14/0.40 $false|~sQ4_spl),
% 0.14/0.40 inference(forward_subsumption_resolution,[status(thm)],[f170,f22])).
% 0.14/0.40 fof(f176,plain,(
% 0.14/0.40 ~sQ4_spl),
% 0.14/0.40 inference(contradiction_clause,[status(thm)],[f175])).
% 0.14/0.40 fof(f180,plain,(
% 0.14/0.40 ![X0]: (~product(e_2,e_3,X0)|product(e_1,X0,e_3)|~sQ3_spl)),
% 0.14/0.40 inference(resolution,[status(thm)],[f60,f34])).
% 0.14/0.40 fof(f216,plain,(
% 0.14/0.40 equalish(e_3,e_2)|~sQ11_spl),
% 0.14/0.40 inference(resolution,[status(thm)],[f89,f39])).
% 0.14/0.40 fof(f221,plain,(
% 0.14/0.40 $false|~sQ11_spl),
% 0.14/0.40 inference(forward_subsumption_resolution,[status(thm)],[f216,f24])).
% 0.14/0.40 fof(f222,plain,(
% 0.14/0.40 ~sQ11_spl),
% 0.14/0.40 inference(contradiction_clause,[status(thm)],[f221])).
% 0.14/0.40 fof(f224,plain,(
% 0.14/0.40 equalish(e_2,e_3)|~sQ10_spl),
% 0.14/0.40 inference(resolution,[status(thm)],[f86,f38])).
% 0.14/0.40 fof(f229,plain,(
% 0.14/0.40 $false|~sQ10_spl),
% 0.14/0.40 inference(forward_subsumption_resolution,[status(thm)],[f224,f22])).
% 0.14/0.40 fof(f230,plain,(
% 0.14/0.40 ~sQ10_spl),
% 0.14/0.40 inference(contradiction_clause,[status(thm)],[f229])).
% 0.14/0.40 fof(f231,plain,(
% 0.14/0.40 product(e_1,e_1,e_3)|~sQ9_spl|~sQ3_spl),
% 0.14/0.40 inference(resolution,[status(thm)],[f83,f180])).
% 0.14/0.40 fof(f237,plain,(
% 0.14/0.40 equalish(e_1,e_3)|~sQ9_spl|~sQ3_spl),
% 0.14/0.40 inference(resolution,[status(thm)],[f231,f37])).
% 0.14/0.40 fof(f243,plain,(
% 0.14/0.40 $false|~sQ9_spl|~sQ3_spl),
% 0.14/0.40 inference(forward_subsumption_resolution,[status(thm)],[f237,f20])).
% 0.14/0.40 fof(f244,plain,(
% 0.14/0.40 ~sQ9_spl|~sQ3_spl),
% 0.14/0.40 inference(contradiction_clause,[status(thm)],[f243])).
% 0.14/0.40 fof(f245,plain,(
% 0.14/0.40 $false),
% 0.14/0.40 inference(sat_refutation,[status(thm)],[f68,f91,f169,f176,f222,f230,f244])).
% 0.14/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.40 % Elapsed time: 0.038853 seconds
% 0.14/0.40 % CPU time: 0.110215 seconds
% 0.14/0.40 % Total memory used: 9.893 MB
% 0.14/0.40 % Net memory used: 9.731 MB
%------------------------------------------------------------------------------