%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP123-8.003 : 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 : n011.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 12:35:43 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-8.003 : 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 : n011.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 19:58:55 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % 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(f17,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(f18,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(f19,axiom,(
% 0.13/0.39 group_element(e_3) ),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f20,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(f21,axiom,(
% 0.13/0.39 ~ equalish(e_1,e_3) ),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f23,axiom,(
% 0.13/0.39 ~ equalish(e_2,e_3) ),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f26,axiom,(
% 0.13/0.39 (![X,Y]: (( ~ group_element(X)| ~ group_element(Y)| product1(X,Y,e_1)| product1(X,Y,e_2)| product1(X,Y,e_3) ) ))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f28,axiom,(
% 0.13/0.39 (![X,W,Y,Z]: (( ~ product1(X,W,Y)| ~ product1(X,Z,Y)| equalish(W,Z) ) ))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f29,axiom,(
% 0.13/0.39 (![W,Y,X,Z]: (( ~ product1(W,Y,X)| ~ product1(Z,Y,X)| equalish(W,Z) ) ))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f30,axiom,(
% 0.13/0.39 (![X]: (product1(X,X,X) ))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f32,axiom,(
% 0.13/0.39 (![X,Y,W,Z]: (( ~ product2(X,Y,W)| ~ product2(X,Y,Z)| equalish(W,Z) ) ))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f33,axiom,(
% 0.13/0.39 (![X,W,Y,Z]: (( ~ product2(X,W,Y)| ~ product2(X,Z,Y)| equalish(W,Z) ) ))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f35,axiom,(
% 0.13/0.39 (![X]: (product2(X,X,X) ))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f36,negated_conjecture,(
% 0.13/0.39 (![X,Y,Z1,Z2]: (( ~ product1(X,Y,Z1)| ~ product1(Z1,Y,Z2)| product2(Z2,X,Y) ) ))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p')).
% 0.13/0.39 fof(f57,plain,(
% 0.13/0.39 group_element(e_1)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f17])).
% 0.13/0.39 fof(f58,plain,(
% 0.13/0.39 group_element(e_2)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f18])).
% 0.13/0.39 fof(f59,plain,(
% 0.13/0.39 group_element(e_3)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f19])).
% 0.13/0.39 fof(f60,plain,(
% 0.13/0.39 ~equalish(e_1,e_2)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f20])).
% 0.13/0.39 fof(f61,plain,(
% 0.13/0.39 ~equalish(e_1,e_3)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f21])).
% 0.13/0.39 fof(f63,plain,(
% 0.13/0.39 ~equalish(e_2,e_3)),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f23])).
% 0.13/0.39 fof(f66,plain,(
% 0.13/0.39 ![X0,X1]: (~group_element(X0)|~group_element(X1)|product1(X0,X1,e_1)|product1(X0,X1,e_2)|product1(X0,X1,e_3))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f26])).
% 0.13/0.39 fof(f69,plain,(
% 0.13/0.39 ![W,Z]: ((![X,Y]: (~product1(X,W,Y)|~product1(X,Z,Y)))|equalish(W,Z))),
% 0.13/0.39 inference(miniscoping,[status(thm)],[f28])).
% 0.13/0.39 fof(f70,plain,(
% 0.13/0.39 ![X0,X1,X2,X3]: (~product1(X0,X1,X2)|~product1(X0,X3,X2)|equalish(X1,X3))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f69])).
% 0.13/0.39 fof(f71,plain,(
% 0.13/0.39 ![W,Z]: ((![Y,X]: (~product1(W,Y,X)|~product1(Z,Y,X)))|equalish(W,Z))),
% 0.13/0.39 inference(miniscoping,[status(thm)],[f29])).
% 0.13/0.39 fof(f72,plain,(
% 0.13/0.39 ![X0,X1,X2,X3]: (~product1(X0,X1,X2)|~product1(X3,X1,X2)|equalish(X0,X3))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f71])).
% 0.13/0.39 fof(f73,plain,(
% 0.13/0.39 ![X0]: (product1(X0,X0,X0))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f30])).
% 0.13/0.39 fof(f75,plain,(
% 0.13/0.39 ![W,Z]: ((![X,Y]: (~product2(X,Y,W)|~product2(X,Y,Z)))|equalish(W,Z))),
% 0.13/0.39 inference(miniscoping,[status(thm)],[f32])).
% 0.13/0.39 fof(f76,plain,(
% 0.13/0.39 ![X0,X1,X2,X3]: (~product2(X0,X1,X2)|~product2(X0,X1,X3)|equalish(X2,X3))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f75])).
% 0.13/0.39 fof(f77,plain,(
% 0.13/0.39 ![W,Z]: ((![X,Y]: (~product2(X,W,Y)|~product2(X,Z,Y)))|equalish(W,Z))),
% 0.13/0.39 inference(miniscoping,[status(thm)],[f33])).
% 0.13/0.39 fof(f78,plain,(
% 0.13/0.39 ![X0,X1,X2,X3]: (~product2(X0,X1,X2)|~product2(X0,X3,X2)|equalish(X1,X3))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f77])).
% 0.13/0.39 fof(f81,plain,(
% 0.13/0.39 ![X0]: (product2(X0,X0,X0))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f35])).
% 0.13/0.39 fof(f82,plain,(
% 0.13/0.39 ![X,Y,Z2]: ((![Z1]: (~product1(X,Y,Z1)|~product1(Z1,Y,Z2)))|product2(Z2,X,Y))),
% 0.13/0.39 inference(miniscoping,[status(thm)],[f36])).
% 0.13/0.39 fof(f83,plain,(
% 0.13/0.39 ![X0,X1,X2,X3]: (~product1(X0,X1,X2)|~product1(X2,X1,X3)|product2(X3,X0,X1))),
% 0.13/0.39 inference(cnf_transformation,[status(thm)],[f82])).
% 0.13/0.39 fof(f84,plain,(
% 0.13/0.39 ![X0,X1]: (~product1(X0,X1,X1)|product2(X1,X0,X1))),
% 0.13/0.39 inference(resolution,[status(thm)],[f73,f83])).
% 0.13/0.39 fof(f91,plain,(
% 0.13/0.39 ![X0,X1]: (~product1(e_1,X0,X1)|~product1(e_2,X0,X1))),
% 0.13/0.39 inference(resolution,[status(thm)],[f60,f72])).
% 0.13/0.39 fof(f112,plain,(
% 0.13/0.39 ![X0,X1]: (~product2(X0,e_1,X1)|~product2(X0,e_3,X1))),
% 0.13/0.39 inference(resolution,[status(thm)],[f61,f78])).
% 0.13/0.39 fof(f115,plain,(
% 0.13/0.39 ![X0,X1]: (~product1(X0,e_1,X1)|~product1(X0,e_3,X1))),
% 0.13/0.39 inference(resolution,[status(thm)],[f61,f70])).
% 0.13/0.39 fof(f127,plain,(
% 0.13/0.39 ![X0,X1]: (~product2(X0,X1,e_2)|~product2(X0,X1,e_3))),
% 0.13/0.39 inference(resolution,[status(thm)],[f63,f76])).
% 0.13/0.39 fof(f128,plain,(
% 0.13/0.39 ![X0,X1]: (~product1(e_2,X0,X1)|~product1(e_3,X0,X1))),
% 0.13/0.39 inference(resolution,[status(thm)],[f63,f72])).
% 0.13/0.39 fof(f155,plain,(
% 0.13/0.39 ~product2(e_3,e_1,e_3)),
% 0.13/0.39 inference(resolution,[status(thm)],[f112,f81])).
% 0.13/0.39 fof(f158,plain,(
% 0.13/0.39 ~product1(e_1,e_3,e_3)),
% 0.13/0.39 inference(resolution,[status(thm)],[f155,f84])).
% 0.13/0.39 fof(f166,plain,(
% 0.13/0.39 ![X0]: (~group_element(X0)|product1(X0,e_3,e_1)|product1(X0,e_3,e_2)|product1(X0,e_3,e_3))),
% 0.13/0.39 inference(resolution,[status(thm)],[f66,f59])).
% 0.13/0.39 fof(f185,plain,(
% 0.13/0.39 ![X0,X1,X2]: (~product2(X0,X1,e_2)|~product1(X1,e_3,X2)|~product1(X2,e_3,X0))),
% 0.13/0.39 inference(resolution,[status(thm)],[f127,f83])).
% 0.13/0.39 fof(f186,plain,(
% 0.13/0.39 ~product1(e_2,e_3,e_3)),
% 0.13/0.39 inference(resolution,[status(thm)],[f128,f73])).
% 0.13/0.39 fof(f279,plain,(
% 0.13/0.39 product1(e_2,e_3,e_1)|product1(e_2,e_3,e_2)|product1(e_2,e_3,e_3)),
% 0.13/0.39 inference(resolution,[status(thm)],[f166,f58])).
% 0.13/0.39 fof(f280,plain,(
% 0.13/0.39 product1(e_1,e_3,e_1)|product1(e_1,e_3,e_2)|product1(e_1,e_3,e_3)),
% 0.13/0.39 inference(resolution,[status(thm)],[f166,f57])).
% 0.13/0.39 fof(f291,definition,(
% 0.13/0.39 sQ17_spl <=> (product1(e_2,e_3,e_1))),
% 0.13/0.39 introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition])).
% 0.13/0.39 fof(f292,plain,(
% 0.13/0.39 product1(e_2,e_3,e_1)|~sQ17_spl),
% 0.13/0.39 inference(component_clause,[status(thm)],[f291])).
% 0.13/0.39 fof(f294,definition,(
% 0.13/0.39 sQ18_spl <=> (product1(e_2,e_3,e_2))),
% 0.13/0.39 introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition])).
% 0.13/0.39 fof(f295,plain,(
% 0.13/0.39 product1(e_2,e_3,e_2)|~sQ18_spl),
% 0.13/0.39 inference(component_clause,[status(thm)],[f294])).
% 0.13/0.39 fof(f297,definition,(
% 0.13/0.39 sQ19_spl <=> (product1(e_2,e_3,e_3))),
% 0.13/0.39 introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition])).
% 0.13/0.39 fof(f298,plain,(
% 0.13/0.39 product1(e_2,e_3,e_3)|~sQ19_spl),
% 0.13/0.39 inference(component_clause,[status(thm)],[f297])).
% 0.13/0.39 fof(f300,plain,(
% 0.13/0.39 sQ17_spl|sQ18_spl|sQ19_spl),
% 0.13/0.39 inference(split_clause,[status(thm)],[f279,f291,f294,f297])).
% 0.13/0.39 fof(f301,definition,(
% 0.13/0.39 sQ20_spl <=> (product1(e_1,e_3,e_1))),
% 0.13/0.39 introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition])).
% 0.13/0.39 fof(f302,plain,(
% 0.13/0.39 product1(e_1,e_3,e_1)|~sQ20_spl),
% 0.13/0.39 inference(component_clause,[status(thm)],[f301])).
% 0.13/0.39 fof(f304,definition,(
% 0.13/0.39 sQ21_spl <=> (product1(e_1,e_3,e_2))),
% 0.13/0.39 introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition])).
% 0.13/0.39 fof(f305,plain,(
% 0.13/0.39 product1(e_1,e_3,e_2)|~sQ21_spl),
% 0.13/0.39 inference(component_clause,[status(thm)],[f304])).
% 0.13/0.39 fof(f307,definition,(
% 0.13/0.39 sQ22_spl <=> (product1(e_1,e_3,e_3))),
% 0.13/0.39 introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition])).
% 0.13/0.39 fof(f308,plain,(
% 0.13/0.39 product1(e_1,e_3,e_3)|~sQ22_spl),
% 0.13/0.39 inference(component_clause,[status(thm)],[f307])).
% 0.13/0.39 fof(f310,plain,(
% 0.13/0.39 sQ20_spl|sQ21_spl|sQ22_spl),
% 0.13/0.39 inference(split_clause,[status(thm)],[f280,f301,f304,f307])).
% 0.13/0.39 fof(f311,plain,(
% 0.13/0.39 $false|~sQ22_spl),
% 0.13/0.39 inference(forward_subsumption_resolution,[status(thm)],[f308,f158])).
% 0.13/0.39 fof(f312,plain,(
% 0.13/0.39 ~sQ22_spl),
% 0.13/0.39 inference(contradiction_clause,[status(thm)],[f311])).
% 0.13/0.39 fof(f313,plain,(
% 0.13/0.39 $false|~sQ19_spl),
% 0.13/0.39 inference(forward_subsumption_resolution,[status(thm)],[f298,f186])).
% 0.13/0.39 fof(f314,plain,(
% 0.13/0.39 ~sQ19_spl),
% 0.13/0.39 inference(contradiction_clause,[status(thm)],[f313])).
% 0.13/0.39 fof(f403,plain,(
% 0.13/0.39 ![X0]: (~product2(e_2,X0,e_2)|~product1(X0,e_3,e_1)|~sQ21_spl)),
% 0.13/0.39 inference(resolution,[status(thm)],[f305,f185])).
% 0.13/0.39 fof(f418,plain,(
% 0.13/0.39 ~product1(e_1,e_1,e_1)|~sQ20_spl),
% 0.13/0.39 inference(resolution,[status(thm)],[f302,f115])).
% 0.13/0.39 fof(f420,plain,(
% 0.13/0.39 $false|~sQ20_spl),
% 0.13/0.39 inference(forward_subsumption_resolution,[status(thm)],[f418,f73])).
% 0.13/0.39 fof(f421,plain,(
% 0.13/0.39 ~sQ20_spl),
% 0.13/0.39 inference(contradiction_clause,[status(thm)],[f420])).
% 0.13/0.39 fof(f424,plain,(
% 0.13/0.39 ~product1(e_1,e_3,e_2)|~sQ18_spl),
% 0.13/0.39 inference(resolution,[status(thm)],[f295,f91])).
% 0.13/0.39 fof(f434,plain,(
% 0.13/0.39 $false|~sQ21_spl|~sQ18_spl),
% 0.13/0.39 inference(forward_subsumption_resolution,[status(thm)],[f424,f305])).
% 0.13/0.39 fof(f435,plain,(
% 0.13/0.39 ~sQ21_spl|~sQ18_spl),
% 0.13/0.39 inference(contradiction_clause,[status(thm)],[f434])).
% 0.13/0.39 fof(f440,plain,(
% 0.13/0.39 ~product2(e_2,e_2,e_2)|~sQ17_spl|~sQ21_spl),
% 0.13/0.39 inference(resolution,[status(thm)],[f292,f403])).
% 0.13/0.39 fof(f448,plain,(
% 0.13/0.39 $false|~sQ17_spl|~sQ21_spl),
% 0.13/0.39 inference(forward_subsumption_resolution,[status(thm)],[f440,f81])).
% 0.13/0.39 fof(f449,plain,(
% 0.13/0.39 ~sQ17_spl|~sQ21_spl),
% 0.13/0.39 inference(contradiction_clause,[status(thm)],[f448])).
% 0.13/0.39 fof(f450,plain,(
% 0.13/0.39 $false),
% 0.13/0.39 inference(sat_refutation,[status(thm)],[f300,f310,f312,f314,f421,f435,f449])).
% 0.13/0.39 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.43 % Elapsed time: 0.056255 seconds
% 0.13/0.43 % CPU time: 0.171092 seconds
% 0.13/0.43 % Total memory used: 17.984 MB
% 0.13/0.43 % Net memory used: 17.827 MB
%------------------------------------------------------------------------------