%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP123-2.003 : 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 : n004.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 12:35:41 PM UTC 2026
% Result : Unsatisfiable 0.09s 5.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-2.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n004.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sun Sep 20 19:57:41 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.37 % Drodi V4.1.1
% 0.09/5.39 % Refutation found
% 0.09/5.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/5.39 % SZS output start CNFRefutation for theBenchmark
% 0.09/5.39 fof(f7,axiom,(
% 0.09/5.39 group_element(e_1) ),
% 0.09/5.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f8,axiom,(
% 0.09/5.39 group_element(e_2) ),
% 0.09/5.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f9,axiom,(
% 0.09/5.39 group_element(e_3) ),
% 0.09/5.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f10,axiom,(
% 0.09/5.39 ~ equalish(e_1,e_2) ),
% 0.09/5.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f11,axiom,(
% 0.09/5.39 ~ equalish(e_1,e_3) ),
% 0.09/5.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f16,axiom,(
% 0.09/5.39 (![X,Y]: (( ~ group_element(X)| ~ group_element(Y)| product(X,Y,e_1)| product(X,Y,e_2)| product(X,Y,e_3) ) ))),
% 0.09/5.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f18,axiom,(
% 0.09/5.39 (![X,W,Y,Z]: (( ~ product(X,W,Y)| ~ product(X,Z,Y)| equalish(W,Z) ) ))),
% 0.09/5.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f19,axiom,(
% 0.09/5.39 (![W,Y,X,Z]: (( ~ product(W,Y,X)| ~ product(Z,Y,X)| equalish(W,Z) ) ))),
% 0.09/5.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f20,axiom,(
% 0.09/5.39 (![X]: (product(X,X,X) ))),
% 0.09/5.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f22,negated_conjecture,(
% 0.09/5.39 (![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) ) ))),
% 0.09/5.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/5.39 fof(f30,plain,(
% 0.09/5.39 group_element(e_1)),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f7])).
% 0.09/5.39 fof(f31,plain,(
% 0.09/5.39 group_element(e_2)),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f8])).
% 0.09/5.39 fof(f32,plain,(
% 0.09/5.39 group_element(e_3)),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f9])).
% 0.09/5.39 fof(f33,plain,(
% 0.09/5.39 ~equalish(e_1,e_2)),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f10])).
% 0.09/5.39 fof(f34,plain,(
% 0.09/5.39 ~equalish(e_1,e_3)),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f11])).
% 0.09/5.39 fof(f39,plain,(
% 0.09/5.39 ![X0,X1]: (~group_element(X0)|~group_element(X1)|product(X0,X1,e_1)|product(X0,X1,e_2)|product(X0,X1,e_3))),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f16])).
% 0.09/5.39 fof(f42,plain,(
% 0.09/5.39 ![W,Z]: ((![X,Y]: (~product(X,W,Y)|~product(X,Z,Y)))|equalish(W,Z))),
% 0.09/5.39 inference(miniscoping,[status(thm)],[f18])).
% 0.09/5.39 fof(f43,plain,(
% 0.09/5.39 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X3,X2)|equalish(X1,X3))),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f42])).
% 0.09/5.39 fof(f44,plain,(
% 0.09/5.39 ![W,Z]: ((![Y,X]: (~product(W,Y,X)|~product(Z,Y,X)))|equalish(W,Z))),
% 0.09/5.39 inference(miniscoping,[status(thm)],[f19])).
% 0.09/5.39 fof(f45,plain,(
% 0.09/5.39 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X3,X1,X2)|equalish(X0,X3))),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f44])).
% 0.09/5.39 fof(f46,plain,(
% 0.09/5.39 ![X0]: (product(X0,X0,X0))),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f20])).
% 0.09/5.39 fof(f49,plain,(
% 0.09/5.39 ![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))),
% 0.09/5.39 inference(miniscoping,[status(thm)],[f22])).
% 0.09/5.39 fof(f50,plain,(
% 0.09/5.39 ![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))),
% 0.09/5.39 inference(cnf_transformation,[status(thm)],[f49])).
% 0.09/5.39 fof(f51,plain,(
% 0.09/5.39 ![X0,X1]: (~product(e_1,X0,X1)|~product(e_2,X0,X1))),
% 0.09/5.39 inference(resolution,[status(thm)],[f33,f45])).
% 0.09/5.39 fof(f52,plain,(
% 0.09/5.39 ![X0,X1]: (~product(X0,e_1,X1)|~product(X0,e_2,X1))),
% 0.09/5.39 inference(resolution,[status(thm)],[f33,f43])).
% 0.09/5.39 fof(f54,plain,(
% 0.09/5.39 ![X0,X1,X2,X3]: (~product(X0,e_1,X1)|~product(X2,e_2,X1)|~product(X3,e_1,X0)|~product(X3,e_2,X2))),
% 0.09/5.39 inference(resolution,[status(thm)],[f33,f50])).
% 0.09/5.39 fof(f56,plain,(
% 0.09/5.39 ![X0,X1]: (~product(e_1,X0,X1)|~product(e_3,X0,X1))),
% 0.09/5.39 inference(resolution,[status(thm)],[f34,f45])).
% 0.09/5.39 fof(f57,plain,(
% 0.09/5.39 ![X0,X1]: (~product(X0,e_1,X1)|~product(X0,e_3,X1))),
% 0.09/5.39 inference(resolution,[status(thm)],[f34,f43])).
% 0.09/5.39 fof(f85,definition,(
% 0.09/5.39 sQ0_spl <=> (group_element(e_2))),
% 0.09/5.39 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.09/5.39 fof(f87,plain,(
% 0.09/5.39 ~group_element(e_2)|sQ0_spl),
% 0.09/5.39 inference(component_clause,[status(thm)],[f85])).
% 0.09/5.39 fof(f95,definition,(
% 0.09/5.39 sQ3_spl <=> (group_element(e_1))),
% 0.09/5.39 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.09/5.39 fof(f97,plain,(
% 0.09/5.39 ~group_element(e_1)|sQ3_spl),
% 0.09/5.39 inference(component_clause,[status(thm)],[f95])).
% 0.09/5.39 fof(f99,plain,(
% 0.09/5.39 $false|sQ0_spl),
% 0.09/5.39 inference(forward_subsumption_resolution,[status(thm)],[f87,f31])).
% 0.09/5.39 fof(f100,plain,(
% 0.09/5.39 sQ0_spl),
% 0.09/5.39 inference(contradiction_clause,[status(thm)],[f99])).
% 0.09/5.39 fof(f102,plain,(
% 0.09/5.39 ~product(e_2,e_1,e_2)),
% 0.09/5.39 inference(resolution,[status(thm)],[f52,f46])).
% 0.09/5.39 fof(f109,plain,(
% 0.09/5.39 ![X0]: (~product(X0,e_1,e_2)|~product(e_2,e_1,X0))),
% 0.09/5.39 inference(resolution,[status(thm)],[f54,f46])).
% 0.09/5.39 fof(f118,definition,(
% 0.09/5.39 sQ6_spl <=> (group_element(e_3))),
% 0.09/5.39 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.09/5.39 fof(f120,plain,(
% 0.09/5.39 ~group_element(e_3)|sQ6_spl),
% 0.09/5.39 inference(component_clause,[status(thm)],[f118])).
% 0.09/5.39 fof(f140,plain,(
% 0.09/5.39 $false|sQ3_spl),
% 0.09/5.39 inference(forward_subsumption_resolution,[status(thm)],[f97,f30])).
% 0.09/5.39 fof(f141,plain,(
% 0.09/5.39 sQ3_spl),
% 0.09/5.39 inference(contradiction_clause,[status(thm)],[f140])).
% 0.09/5.39 fof(f148,plain,(
% 0.09/5.39 ~product(e_3,e_1,e_1)),
% 0.09/5.39 inference(resolution,[status(thm)],[f56,f46])).
% 0.09/5.39 fof(f154,plain,(
% 0.09/5.39 ~product(e_3,e_1,e_3)),
% 0.09/5.39 inference(resolution,[status(thm)],[f57,f46])).
% 0.09/5.39 fof(f159,plain,(
% 0.09/5.39 $false|sQ6_spl),
% 0.09/5.39 inference(forward_subsumption_resolution,[status(thm)],[f120,f32])).
% 0.09/5.39 fof(f160,plain,(
% 0.09/5.39 sQ6_spl),
% 0.09/5.39 inference(contradiction_clause,[status(thm)],[f159])).
% 0.09/5.39 fof(f162,plain,(
% 0.09/5.39 ~group_element(e_3)|~group_element(e_1)|product(e_3,e_1,e_1)|product(e_3,e_1,e_2)),
% 0.09/5.39 inference(resolution,[status(thm)],[f154,f39])).
% 0.09/5.39 fof(f163,definition,(
% 0.09/5.39 sQ14_spl <=> (product(e_3,e_1,e_1))),
% 0.09/5.39 introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition])).
% 0.09/5.39 fof(f164,plain,(
% 0.09/5.39 product(e_3,e_1,e_1)|~sQ14_spl),
% 0.09/5.39 inference(component_clause,[status(thm)],[f163])).
% 0.09/5.39 fof(f166,definition,(
% 0.09/5.39 sQ15_spl <=> (product(e_3,e_1,e_2))),
% 0.09/5.39 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.09/5.39 fof(f169,plain,(
% 0.09/5.39 ~sQ6_spl|~sQ3_spl|sQ14_spl|sQ15_spl),
% 0.09/5.39 inference(split_clause,[status(thm)],[f162,f118,f95,f163,f166])).
% 0.09/5.39 fof(f170,plain,(
% 0.09/5.39 $false|~sQ14_spl),
% 0.09/5.39 inference(forward_subsumption_resolution,[status(thm)],[f164,f148])).
% 0.09/5.39 fof(f171,plain,(
% 0.09/5.39 ~sQ14_spl),
% 0.09/5.39 inference(contradiction_clause,[status(thm)],[f170])).
% 0.09/5.39 fof(f196,plain,(
% 0.09/5.39 ~product(e_3,e_1,e_2)|~group_element(e_2)|~group_element(e_1)|product(e_2,e_1,e_1)|product(e_2,e_1,e_2)),
% 0.09/5.39 inference(resolution,[status(thm)],[f109,f39])).
% 0.09/5.39 fof(f197,definition,(
% 0.09/5.39 sQ19_spl <=> (product(e_2,e_1,e_1))),
% 0.09/5.39 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.09/5.39 fof(f198,plain,(
% 0.09/5.39 product(e_2,e_1,e_1)|~sQ19_spl),
% 0.09/5.39 inference(component_clause,[status(thm)],[f197])).
% 0.09/5.39 fof(f200,definition,(
% 0.09/5.39 sQ20_spl <=> (product(e_2,e_1,e_2))),
% 0.09/5.39 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.09/5.39 fof(f201,plain,(
% 0.09/5.39 product(e_2,e_1,e_2)|~sQ20_spl),
% 0.09/5.39 inference(component_clause,[status(thm)],[f200])).
% 0.09/5.39 fof(f203,plain,(
% 0.09/5.39 ~sQ15_spl|~sQ0_spl|~sQ3_spl|sQ19_spl|sQ20_spl),
% 0.09/5.39 inference(split_clause,[status(thm)],[f196,f166,f85,f95,f197,f200])).
% 0.09/5.39 fof(f205,plain,(
% 0.09/5.39 ~product(e_1,e_1,e_1)|~sQ19_spl),
% 0.09/5.39 inference(resolution,[status(thm)],[f198,f51])).
% 0.09/5.39 fof(f212,plain,(
% 0.09/5.39 $false|~sQ19_spl),
% 0.09/5.39 inference(forward_subsumption_resolution,[status(thm)],[f205,f46])).
% 0.09/5.39 fof(f213,plain,(
% 0.09/5.39 ~sQ19_spl),
% 0.09/5.39 inference(contradiction_clause,[status(thm)],[f212])).
% 0.09/5.39 fof(f214,plain,(
% 0.09/5.39 $false|~sQ20_spl),
% 0.09/5.39 inference(forward_subsumption_resolution,[status(thm)],[f201,f102])).
% 0.09/5.39 fof(f215,plain,(
% 0.09/5.39 ~sQ20_spl),
% 0.09/5.39 inference(contradiction_clause,[status(thm)],[f214])).
% 0.09/5.39 fof(f216,plain,(
% 0.09/5.39 $false),
% 0.09/5.39 inference(sat_refutation,[status(thm)],[f100,f141,f160,f169,f171,f203,f213,f215])).
% 0.09/5.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.12/5.41 % Elapsed time: 0.046536 seconds
% 0.12/5.41 % CPU time: 0.131988 seconds
% 0.12/5.41 % Total memory used: 17.584 MB
% 0.12/5.41 % Net memory used: 17.215 MB
%------------------------------------------------------------------------------