%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP123-6.003 : 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 : 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 12:35:42 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-6.003 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 19:58:21 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.39 fof(f1,axiom,(
% 0.09/0.39 group_element(e_1) ),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f2,axiom,(
% 0.09/0.39 group_element(e_2) ),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f3,axiom,(
% 0.09/0.39 group_element(e_3) ),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f4,axiom,(
% 0.09/0.39 ~ equalish(e_1,e_2) ),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f5,axiom,(
% 0.09/0.39 ~ equalish(e_1,e_3) ),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f6,axiom,(
% 0.09/0.39 ~ equalish(e_2,e_1) ),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f7,axiom,(
% 0.09/0.39 ~ equalish(e_2,e_3) ),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f8,axiom,(
% 0.09/0.39 ~ equalish(e_3,e_1) ),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f10,axiom,(
% 0.09/0.39 (![X,Y]: (( ~ group_element(X)| ~ group_element(Y)| product1(X,Y,e_1)| product1(X,Y,e_2)| product1(X,Y,e_3) ) ))),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f12,axiom,(
% 0.09/0.39 (![X,W,Y,Z]: (( ~ product1(X,W,Y)| ~ product1(X,Z,Y)| equalish(W,Z) ) ))),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f13,axiom,(
% 0.09/0.39 (![W,Y,X,Z]: (( ~ product1(W,Y,X)| ~ product1(Z,Y,X)| equalish(W,Z) ) ))),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f14,axiom,(
% 0.09/0.39 (![X]: (product1(X,X,X) ))),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f16,axiom,(
% 0.09/0.39 (![X,Y,W,Z]: (( ~ product2(X,Y,W)| ~ product2(X,Y,Z)| equalish(W,Z) ) ))),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f19,axiom,(
% 0.09/0.39 (![X]: (product2(X,X,X) ))),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f20,negated_conjecture,(
% 0.09/0.39 (![X,Y,Z1,Z2]: (( ~ product1(X,Y,Z1)| ~ product1(Z1,Y,Z2)| product2(Z2,X,Y) ) ))),
% 0.09/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.09/0.39 fof(f21,plain,(
% 0.09/0.39 group_element(e_1)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f1])).
% 0.09/0.39 fof(f22,plain,(
% 0.09/0.39 group_element(e_2)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f2])).
% 0.09/0.39 fof(f23,plain,(
% 0.09/0.39 group_element(e_3)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f3])).
% 0.09/0.39 fof(f24,plain,(
% 0.09/0.39 ~equalish(e_1,e_2)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f4])).
% 0.09/0.39 fof(f25,plain,(
% 0.09/0.39 ~equalish(e_1,e_3)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f5])).
% 0.09/0.39 fof(f26,plain,(
% 0.09/0.39 ~equalish(e_2,e_1)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f6])).
% 0.09/0.39 fof(f27,plain,(
% 0.09/0.39 ~equalish(e_2,e_3)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f7])).
% 0.09/0.39 fof(f28,plain,(
% 0.09/0.39 ~equalish(e_3,e_1)),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f8])).
% 0.09/0.39 fof(f30,plain,(
% 0.09/0.39 ![X0,X1]: (~group_element(X0)|~group_element(X1)|product1(X0,X1,e_1)|product1(X0,X1,e_2)|product1(X0,X1,e_3))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f10])).
% 0.09/0.39 fof(f33,plain,(
% 0.09/0.39 ![W,Z]: ((![X,Y]: (~product1(X,W,Y)|~product1(X,Z,Y)))|equalish(W,Z))),
% 0.09/0.39 inference(miniscoping,[status(thm)],[f12])).
% 0.09/0.39 fof(f34,plain,(
% 0.09/0.39 ![X0,X1,X2,X3]: (~product1(X0,X1,X2)|~product1(X0,X3,X2)|equalish(X1,X3))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f33])).
% 0.09/0.39 fof(f35,plain,(
% 0.09/0.39 ![W,Z]: ((![Y,X]: (~product1(W,Y,X)|~product1(Z,Y,X)))|equalish(W,Z))),
% 0.09/0.39 inference(miniscoping,[status(thm)],[f13])).
% 0.09/0.39 fof(f36,plain,(
% 0.09/0.39 ![X0,X1,X2,X3]: (~product1(X0,X1,X2)|~product1(X3,X1,X2)|equalish(X0,X3))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f35])).
% 0.09/0.39 fof(f37,plain,(
% 0.09/0.39 ![X0]: (product1(X0,X0,X0))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f14])).
% 0.09/0.39 fof(f39,plain,(
% 0.09/0.39 ![W,Z]: ((![X,Y]: (~product2(X,Y,W)|~product2(X,Y,Z)))|equalish(W,Z))),
% 0.09/0.39 inference(miniscoping,[status(thm)],[f16])).
% 0.09/0.39 fof(f40,plain,(
% 0.09/0.39 ![X0,X1,X2,X3]: (~product2(X0,X1,X2)|~product2(X0,X1,X3)|equalish(X2,X3))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f39])).
% 0.09/0.39 fof(f45,plain,(
% 0.09/0.39 ![X0]: (product2(X0,X0,X0))),
% 0.09/0.39 inference(cnf_transformation,[status(thm)],[f19])).
% 0.09/0.39 fof(f46,plain,(
% 0.09/0.39 ![X,Y,Z2]: ((![Z1]: (~product1(X,Y,Z1)|~product1(Z1,Y,Z2)))|product2(Z2,X,Y))),
% 0.09/0.40 inference(miniscoping,[status(thm)],[f20])).
% 0.09/0.40 fof(f47,plain,(
% 0.09/0.40 ![X0,X1,X2,X3]: (~product1(X0,X1,X2)|~product1(X2,X1,X3)|product2(X3,X0,X1))),
% 0.09/0.40 inference(cnf_transformation,[status(thm)],[f46])).
% 0.09/0.40 fof(f52,plain,(
% 0.09/0.40 ![X0,X1]: (~product1(X0,X1,X0)|equalish(X1,X0))),
% 0.09/0.40 inference(resolution,[status(thm)],[f34,f37])).
% 0.09/0.40 fof(f53,plain,(
% 0.09/0.40 ![X0,X1]: (~product1(X0,X1,X1)|equalish(X0,X1))),
% 0.09/0.40 inference(resolution,[status(thm)],[f36,f37])).
% 0.09/0.40 fof(f54,plain,(
% 0.09/0.40 ![X0]: (~group_element(X0)|product1(e_3,X0,e_1)|product1(e_3,X0,e_2)|product1(e_3,X0,e_3))),
% 0.09/0.40 inference(resolution,[status(thm)],[f30,f23])).
% 0.09/0.40 fof(f55,plain,(
% 0.09/0.40 ![X0]: (~group_element(X0)|product1(e_2,X0,e_1)|product1(e_2,X0,e_2)|product1(e_2,X0,e_3))),
% 0.09/0.40 inference(resolution,[status(thm)],[f30,f22])).
% 0.09/0.40 fof(f62,plain,(
% 0.09/0.40 product1(e_3,e_1,e_1)|product1(e_3,e_1,e_2)|product1(e_3,e_1,e_3)),
% 0.09/0.40 inference(resolution,[status(thm)],[f54,f21])).
% 0.09/0.40 fof(f83,definition,(
% 0.09/0.40 sQ6_spl <=> (product1(e_3,e_1,e_1))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f84,plain,(
% 0.09/0.40 product1(e_3,e_1,e_1)|~sQ6_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f83])).
% 0.09/0.40 fof(f86,definition,(
% 0.09/0.40 sQ7_spl <=> (product1(e_3,e_1,e_2))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f87,plain,(
% 0.09/0.40 product1(e_3,e_1,e_2)|~sQ7_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f86])).
% 0.09/0.40 fof(f89,definition,(
% 0.09/0.40 sQ8_spl <=> (product1(e_3,e_1,e_3))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f90,plain,(
% 0.09/0.40 product1(e_3,e_1,e_3)|~sQ8_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f89])).
% 0.09/0.40 fof(f92,plain,(
% 0.09/0.40 sQ6_spl|sQ7_spl|sQ8_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f62,f83,f86,f89])).
% 0.09/0.40 fof(f95,plain,(
% 0.09/0.40 product1(e_2,e_1,e_1)|product1(e_2,e_1,e_2)|product1(e_2,e_1,e_3)),
% 0.09/0.40 inference(resolution,[status(thm)],[f55,f21])).
% 0.09/0.40 fof(f116,definition,(
% 0.09/0.40 sQ15_spl <=> (product1(e_2,e_1,e_1))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f117,plain,(
% 0.09/0.40 product1(e_2,e_1,e_1)|~sQ15_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f116])).
% 0.09/0.40 fof(f119,definition,(
% 0.09/0.40 sQ16_spl <=> (product1(e_2,e_1,e_2))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f120,plain,(
% 0.09/0.40 product1(e_2,e_1,e_2)|~sQ16_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f119])).
% 0.09/0.40 fof(f122,definition,(
% 0.09/0.40 sQ17_spl <=> (product1(e_2,e_1,e_3))),
% 0.09/0.40 introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 0.09/0.40 fof(f123,plain,(
% 0.09/0.40 product1(e_2,e_1,e_3)|~sQ17_spl),
% 0.09/0.40 inference(component_clause,[status(thm)],[f122])).
% 0.09/0.40 fof(f125,plain,(
% 0.09/0.40 sQ15_spl|sQ16_spl|sQ17_spl),
% 0.09/0.40 inference(split_clause,[status(thm)],[f95,f116,f119,f122])).
% 0.09/0.40 fof(f258,plain,(
% 0.09/0.40 ![X0,X1]: (~product2(X0,X0,X1)|equalish(X1,X0))),
% 0.09/0.40 inference(resolution,[status(thm)],[f40,f45])).
% 0.09/0.40 fof(f266,plain,(
% 0.09/0.40 equalish(e_1,e_3)|~sQ8_spl),
% 0.09/0.40 inference(resolution,[status(thm)],[f90,f52])).
% 0.09/0.40 fof(f271,plain,(
% 0.09/0.40 $false|~sQ8_spl),
% 0.09/0.40 inference(forward_subsumption_resolution,[status(thm)],[f266,f25])).
% 0.09/0.40 fof(f272,plain,(
% 0.09/0.40 ~sQ8_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f271])).
% 0.09/0.40 fof(f273,plain,(
% 0.09/0.40 ![X0]: (~product1(X0,e_1,e_2)|equalish(X0,e_3)|~sQ7_spl)),
% 0.09/0.40 inference(resolution,[status(thm)],[f87,f36])).
% 0.09/0.40 fof(f276,plain,(
% 0.09/0.40 ![X0]: (~product1(X0,e_1,e_3)|product2(e_2,X0,e_1)|~sQ7_spl)),
% 0.09/0.40 inference(resolution,[status(thm)],[f87,f47])).
% 0.09/0.40 fof(f281,plain,(
% 0.09/0.40 equalish(e_3,e_1)|~sQ6_spl),
% 0.09/0.40 inference(resolution,[status(thm)],[f84,f53])).
% 0.09/0.40 fof(f289,plain,(
% 0.09/0.40 $false|~sQ6_spl),
% 0.09/0.40 inference(forward_subsumption_resolution,[status(thm)],[f281,f28])).
% 0.09/0.40 fof(f290,plain,(
% 0.09/0.40 ~sQ6_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f289])).
% 0.09/0.40 fof(f314,plain,(
% 0.09/0.40 product2(e_2,e_2,e_1)|~sQ17_spl|~sQ7_spl),
% 0.09/0.40 inference(resolution,[status(thm)],[f123,f276])).
% 0.09/0.40 fof(f319,plain,(
% 0.09/0.40 equalish(e_1,e_2)|~sQ17_spl|~sQ7_spl),
% 0.09/0.40 inference(resolution,[status(thm)],[f314,f258])).
% 0.09/0.40 fof(f323,plain,(
% 0.09/0.40 $false|~sQ17_spl|~sQ7_spl),
% 0.09/0.40 inference(forward_subsumption_resolution,[status(thm)],[f319,f24])).
% 0.09/0.40 fof(f324,plain,(
% 0.09/0.40 ~sQ17_spl|~sQ7_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f323])).
% 0.09/0.40 fof(f325,plain,(
% 0.09/0.40 equalish(e_2,e_3)|~sQ16_spl|~sQ7_spl),
% 0.09/0.40 inference(resolution,[status(thm)],[f120,f273])).
% 0.09/0.40 fof(f331,plain,(
% 0.09/0.40 $false|~sQ16_spl|~sQ7_spl),
% 0.09/0.40 inference(forward_subsumption_resolution,[status(thm)],[f325,f27])).
% 0.09/0.40 fof(f332,plain,(
% 0.09/0.40 ~sQ16_spl|~sQ7_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f331])).
% 0.09/0.40 fof(f333,plain,(
% 0.09/0.40 equalish(e_2,e_1)|~sQ15_spl),
% 0.09/0.40 inference(resolution,[status(thm)],[f117,f53])).
% 0.09/0.40 fof(f339,plain,(
% 0.09/0.40 $false|~sQ15_spl),
% 0.09/0.40 inference(forward_subsumption_resolution,[status(thm)],[f333,f26])).
% 0.09/0.40 fof(f340,plain,(
% 0.09/0.40 ~sQ15_spl),
% 0.09/0.40 inference(contradiction_clause,[status(thm)],[f339])).
% 0.09/0.40 fof(f341,plain,(
% 0.09/0.40 $false),
% 0.09/0.40 inference(sat_refutation,[status(thm)],[f92,f125,f272,f290,f324,f332,f340])).
% 0.09/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.43 % Elapsed time: 0.044652 seconds
% 0.09/0.43 % CPU time: 0.123998 seconds
% 0.09/0.43 % Total memory used: 17.642 MB
% 0.09/0.43 % Net memory used: 17.293 MB
%------------------------------------------------------------------------------