%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP132-2.002 : 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 : n026.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 12:36:01 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP132-2.002 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 20:04:21 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.39 fof(f4,axiom,(
% 0.13/0.39 group_element(e_1) ),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f5,axiom,(
% 0.13/0.39 group_element(e_2) ),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f6,axiom,(
% 0.13/0.39 ~ equalish(e_1,e_2) ),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f8,axiom,(
% 0.13/0.39 (![X,Y]: (( ~ group_element(X)| ~ group_element(Y)| product(X,Y,e_1)| product(X,Y,e_2) ) ))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f10,axiom,(
% 0.13/0.39 (![X,W,Y,Z]: (( ~ product(X,W,Y)| ~ product(X,Z,Y)| equalish(W,Z) ) ))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f11,axiom,(
% 0.13/0.39 (![W,Y,X,Z]: (( ~ product(W,Y,X)| ~ product(Z,Y,X)| equalish(W,Z) ) ))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f12,negated_conjecture,(
% 0.13/0.39 (![X1,Y1,Z1,X2,Y2,Z2]: (( ~ product(X1,Y1,Z1)| ~ product(X2,Y2,Z1)| ~ product(Z2,X1,Y1)| ~ product(Z2,X2,Y2)| equalish(X1,X2) ) ))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f18,plain,(
% 0.13/0.39 group_element(e_1)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f4])).
% 0.13/0.39 fof(f19,plain,(
% 0.13/0.39 group_element(e_2)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f5])).
% 0.13/0.39 fof(f20,plain,(
% 0.13/0.39 ~equalish(e_1,e_2)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f6])).
% 0.13/0.39 fof(f22,plain,(
% 0.13/0.39 ![X0,X1]: (~group_element(X0)|~group_element(X1)|product(X0,X1,e_1)|product(X0,X1,e_2))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f8])).
% 0.13/0.39 fof(f25,plain,(
% 0.13/0.39 ![W,Z]: ((![X,Y]: (~product(X,W,Y)|~product(X,Z,Y)))|equalish(W,Z))),
% 0.13/0.39 inference(miniscoping,[status(thm)],[f10])).
% 0.13/0.39 fof(f26,plain,(
% 0.13/0.39 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X0,X3,X2)|equalish(X1,X3))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f25])).
% 0.13/0.39 fof(f27,plain,(
% 0.13/0.39 ![W,Z]: ((![Y,X]: (~product(W,Y,X)|~product(Z,Y,X)))|equalish(W,Z))),
% 0.13/0.39 inference(miniscoping,[status(thm)],[f11])).
% 0.13/0.39 fof(f28,plain,(
% 0.13/0.39 ![X0,X1,X2,X3]: (~product(X0,X1,X2)|~product(X3,X1,X2)|equalish(X0,X3))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f27])).
% 0.13/0.39 fof(f29,plain,(
% 0.13/0.39 ![X1,X2]: ((![Y2,Z2]: ((![Y1]: ((![Z1]: (~product(X1,Y1,Z1)|~product(X2,Y2,Z1)))|~product(Z2,X1,Y1)))|~product(Z2,X2,Y2)))|equalish(X1,X2))),
% 0.13/0.39 inference(miniscoping,[status(thm)],[f12])).
% 0.13/0.39 fof(f30,plain,(
% 0.13/0.39 ![X0,X1,X2,X3,X4,X5]: (~product(X0,X1,X2)|~product(X3,X4,X2)|~product(X5,X0,X1)|~product(X5,X3,X4)|equalish(X0,X3))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f29])).
% 0.13/0.39 fof(f33,plain,(
% 0.13/0.39 ![X0,X1]: (~product(e_1,X0,X1)|~product(e_2,X0,X1))),
% 0.13/0.39 inference(resolution,[status(thm)],[f20,f28])).
% 0.13/0.39 fof(f34,plain,(
% 0.13/0.39 ![X0,X1]: (~product(X0,e_1,X1)|~product(X0,e_2,X1))),
% 0.13/0.39 inference(resolution,[status(thm)],[f20,f26])).
% 0.13/0.39 fof(f37,plain,(
% 0.13/0.39 ![X0,X1,X2,X3]: (~product(e_1,X0,X1)|~product(e_2,X2,X1)|~product(X3,e_1,X0)|~product(X3,e_2,X2))),
% 0.13/0.39 inference(resolution,[status(thm)],[f20,f30])).
% 0.13/0.39 fof(f43,plain,(
% 0.13/0.39 ![X0]: (~group_element(X0)|product(X0,e_2,e_1)|product(X0,e_2,e_2))),
% 0.13/0.39 inference(resolution,[status(thm)],[f22,f19])).
% 0.13/0.39 fof(f44,plain,(
% 0.13/0.39 ![X0]: (~group_element(X0)|product(X0,e_1,e_1)|product(X0,e_1,e_2))),
% 0.13/0.39 inference(resolution,[status(thm)],[f22,f18])).
% 0.13/0.39 fof(f45,plain,(
% 0.13/0.39 product(e_2,e_2,e_1)|product(e_2,e_2,e_2)),
% 0.13/0.39 inference(resolution,[status(thm)],[f43,f19])).
% 0.13/0.39 fof(f46,plain,(
% 0.13/0.39 product(e_1,e_2,e_1)|product(e_1,e_2,e_2)),
% 0.13/0.39 inference(resolution,[status(thm)],[f43,f18])).
% 0.13/0.39 fof(f47,definition,(
% 0.13/0.39 sQ0_spl <=> (product(e_2,e_2,e_1))),
% 0.13/0.39 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.13/0.39 fof(f48,plain,(
% 0.13/0.39 product(e_2,e_2,e_1)|~sQ0_spl),
% 0.13/0.39 inference(component_clause,[status(thm)],[f47])).
% 0.13/0.39 fof(f50,definition,(
% 0.13/0.39 sQ1_spl <=> (product(e_2,e_2,e_2))),
% 0.13/0.39 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.13/0.39 fof(f51,plain,(
% 0.13/0.39 product(e_2,e_2,e_2)|~sQ1_spl),
% 0.13/0.39 inference(component_clause,[status(thm)],[f50])).
% 0.13/0.39 fof(f53,plain,(
% 0.13/0.39 sQ0_spl|sQ1_spl),
% 0.13/0.39 inference(split_clause,[status(thm)],[f45,f47,f50])).
% 0.13/0.39 fof(f54,definition,(
% 0.13/0.39 sQ2_spl <=> (product(e_1,e_2,e_1))),
% 0.13/0.39 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.13/0.39 fof(f55,plain,(
% 0.13/0.39 product(e_1,e_2,e_1)|~sQ2_spl),
% 0.13/0.39 inference(component_clause,[status(thm)],[f54])).
% 0.13/0.39 fof(f57,definition,(
% 0.13/0.39 sQ3_spl <=> (product(e_1,e_2,e_2))),
% 0.13/0.39 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.13/0.39 fof(f58,plain,(
% 0.13/0.39 product(e_1,e_2,e_2)|~sQ3_spl),
% 0.13/0.39 inference(component_clause,[status(thm)],[f57])).
% 0.13/0.39 fof(f60,plain,(
% 0.13/0.39 sQ2_spl|sQ3_spl),
% 0.13/0.39 inference(split_clause,[status(thm)],[f46,f54,f57])).
% 0.13/0.39 fof(f61,plain,(
% 0.13/0.39 ~product(e_1,e_1,e_1)|~sQ2_spl),
% 0.13/0.39 inference(resolution,[status(thm)],[f55,f34])).
% 0.13/0.39 fof(f62,plain,(
% 0.13/0.39 ~product(e_1,e_2,e_1)|~sQ0_spl),
% 0.13/0.39 inference(resolution,[status(thm)],[f48,f33])).
% 0.13/0.39 fof(f63,plain,(
% 0.13/0.39 ~product(e_2,e_1,e_1)|~sQ0_spl),
% 0.13/0.39 inference(resolution,[status(thm)],[f48,f34])).
% 0.13/0.39 fof(f64,plain,(
% 0.13/0.39 $false|~sQ2_spl|~sQ0_spl),
% 0.13/0.39 inference(forward_subsumption_resolution,[status(thm)],[f62,f55])).
% 0.13/0.39 fof(f65,plain,(
% 0.13/0.39 ~sQ2_spl|~sQ0_spl),
% 0.13/0.39 inference(contradiction_clause,[status(thm)],[f64])).
% 0.13/0.39 fof(f66,plain,(
% 0.13/0.39 ~product(e_1,e_1,e_2)|~sQ3_spl),
% 0.13/0.39 inference(resolution,[status(thm)],[f58,f34])).
% 0.13/0.39 fof(f68,plain,(
% 0.13/0.39 product(e_2,e_1,e_1)|product(e_2,e_1,e_2)),
% 0.13/0.39 inference(resolution,[status(thm)],[f44,f19])).
% 0.13/0.39 fof(f69,plain,(
% 0.13/0.39 product(e_1,e_1,e_1)|product(e_1,e_1,e_2)),
% 0.13/0.39 inference(resolution,[status(thm)],[f44,f18])).
% 0.13/0.39 fof(f70,definition,(
% 0.13/0.39 sQ4_spl <=> (product(e_2,e_1,e_1))),
% 0.13/0.39 introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition])).
% 0.13/0.39 fof(f71,plain,(
% 0.13/0.39 product(e_2,e_1,e_1)|~sQ4_spl),
% 0.13/0.39 inference(component_clause,[status(thm)],[f70])).
% 0.13/0.39 fof(f73,definition,(
% 0.13/0.39 sQ5_spl <=> (product(e_2,e_1,e_2))),
% 0.13/0.39 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.13/0.39 fof(f74,plain,(
% 0.13/0.39 product(e_2,e_1,e_2)|~sQ5_spl),
% 0.13/0.39 inference(component_clause,[status(thm)],[f73])).
% 0.13/0.39 fof(f76,plain,(
% 0.13/0.39 sQ4_spl|sQ5_spl),
% 0.13/0.39 inference(split_clause,[status(thm)],[f68,f70,f73])).
% 0.13/0.39 fof(f77,definition,(
% 0.13/0.39 sQ6_spl <=> (product(e_1,e_1,e_1))),
% 0.13/0.39 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.13/0.39 fof(f78,plain,(
% 0.13/0.39 product(e_1,e_1,e_1)|~sQ6_spl),
% 0.13/0.39 inference(component_clause,[status(thm)],[f77])).
% 0.13/0.39 fof(f80,definition,(
% 0.13/0.39 sQ7_spl <=> (product(e_1,e_1,e_2))),
% 0.13/0.39 introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition])).
% 0.13/0.39 fof(f81,plain,(
% 0.13/0.39 product(e_1,e_1,e_2)|~sQ7_spl),
% 0.13/0.39 inference(component_clause,[status(thm)],[f80])).
% 0.13/0.39 fof(f83,plain,(
% 0.13/0.39 sQ6_spl|sQ7_spl),
% 0.13/0.39 inference(split_clause,[status(thm)],[f69,f77,f80])).
% 0.13/0.39 fof(f85,plain,(
% 0.13/0.39 ~product(e_1,e_2,e_2)|~sQ1_spl),
% 0.13/0.39 inference(resolution,[status(thm)],[f51,f33])).
% 0.13/0.39 fof(f86,plain,(
% 0.13/0.39 ~product(e_2,e_1,e_2)|~sQ1_spl),
% 0.13/0.39 inference(resolution,[status(thm)],[f51,f34])).
% 0.13/0.39 fof(f88,plain,(
% 0.13/0.39 $false|~sQ3_spl|~sQ1_spl),
% 0.13/0.39 inference(forward_subsumption_resolution,[status(thm)],[f85,f58])).
% 0.13/0.39 fof(f89,plain,(
% 0.13/0.39 ~sQ3_spl|~sQ1_spl),
% 0.13/0.39 inference(contradiction_clause,[status(thm)],[f88])).
% 0.13/0.39 fof(f90,plain,(
% 0.13/0.39 $false|~sQ2_spl|~sQ6_spl),
% 0.13/0.39 inference(forward_subsumption_resolution,[status(thm)],[f78,f61])).
% 0.13/0.39 fof(f91,plain,(
% 0.13/0.39 ~sQ2_spl|~sQ6_spl),
% 0.13/0.39 inference(contradiction_clause,[status(thm)],[f90])).
% 0.13/0.39 fof(f92,plain,(
% 0.13/0.39 ![X0,X1]: (~product(e_1,X0,e_1)|~product(X1,e_1,X0)|~product(X1,e_2,e_1)|~sQ4_spl)),
% 0.13/0.39 inference(resolution,[status(thm)],[f71,f37])).
% 0.13/0.39 fof(f96,plain,(
% 0.13/0.39 $false|~sQ3_spl|~sQ7_spl),
% 0.13/0.39 inference(forward_subsumption_resolution,[status(thm)],[f81,f66])).
% 0.13/0.39 fof(f97,plain,(
% 0.13/0.39 ~sQ3_spl|~sQ7_spl),
% 0.13/0.39 inference(contradiction_clause,[status(thm)],[f96])).
% 0.13/0.39 fof(f106,plain,(
% 0.13/0.39 ![X0]: (~product(X0,e_1,e_2)|~product(X0,e_2,e_1)|~sQ4_spl|~sQ2_spl)),
% 0.13/0.39 inference(resolution,[status(thm)],[f92,f55])).
% 0.13/0.39 fof(f108,plain,(
% 0.13/0.39 ~product(e_1,e_1,e_2)|~sQ4_spl|~sQ2_spl),
% 0.13/0.39 inference(resolution,[status(thm)],[f106,f55])).
% 0.13/0.39 fof(f109,plain,(
% 0.13/0.39 $false|~sQ7_spl|~sQ4_spl|~sQ2_spl),
% 0.13/0.39 inference(forward_subsumption_resolution,[status(thm)],[f108,f81])).
% 0.13/0.39 fof(f110,plain,(
% 0.13/0.39 ~sQ7_spl|~sQ4_spl|~sQ2_spl),
% 0.13/0.39 inference(contradiction_clause,[status(thm)],[f109])).
% 0.13/0.39 fof(f112,plain,(
% 0.13/0.39 $false|~sQ1_spl|~sQ5_spl),
% 0.13/0.39 inference(forward_subsumption_resolution,[status(thm)],[f74,f86])).
% 0.13/0.39 fof(f113,plain,(
% 0.13/0.39 ~sQ1_spl|~sQ5_spl),
% 0.13/0.39 inference(contradiction_clause,[status(thm)],[f112])).
% 0.13/0.39 fof(f114,plain,(
% 0.13/0.39 ~sQ4_spl|~sQ0_spl),
% 0.13/0.39 inference(split_clause,[status(thm)],[f63,f70,f47])).
% 0.13/0.39 fof(f118,plain,(
% 0.13/0.39 ![X0,X1]: (~product(e_1,X0,e_1)|~product(X1,e_1,X0)|~product(X1,e_2,e_2)|~sQ0_spl)),
% 0.13/0.39 inference(resolution,[status(thm)],[f48,f37])).
% 0.13/0.39 fof(f128,plain,(
% 0.13/0.39 ![X0]: (~product(X0,e_1,e_1)|~product(X0,e_2,e_2)|~sQ0_spl|~sQ6_spl)),
% 0.13/0.39 inference(resolution,[status(thm)],[f118,f78])).
% 0.13/0.39 fof(f129,plain,(
% 0.13/0.39 ~product(e_1,e_1,e_1)|~sQ0_spl|~sQ6_spl|~sQ3_spl),
% 0.13/0.39 inference(resolution,[status(thm)],[f128,f58])).
% 0.13/0.39 fof(f130,plain,(
% 0.13/0.39 ~sQ6_spl|~sQ0_spl|~sQ3_spl),
% 0.13/0.39 inference(split_clause,[status(thm)],[f129,f77,f47,f57])).
% 0.13/0.39 fof(f131,plain,(
% 0.13/0.39 $false),
% 0.13/0.39 inference(sat_refutation,[status(thm)],[f53,f60,f65,f76,f83,f89,f91,f97,f110,f113,f114,f130])).
% 0.13/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.42 % Elapsed time: 0.051242 seconds
% 0.13/0.42 % CPU time: 0.129097 seconds
% 0.13/0.42 % Total memory used: 10.631 MB
% 0.13/0.42 % Net memory used: 10.344 MB
%------------------------------------------------------------------------------