%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP123-9.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 12:35:44 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.38s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP123-9.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n017.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
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 19:54:11 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.38 fof(f3,axiom,(
% 0.13/0.38 group_element(e_1) ),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.38 fof(f4,axiom,(
% 0.13/0.38 group_element(e_2) ),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.38 fof(f5,axiom,(
% 0.13/0.38 group_element(e_3) ),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.38 fof(f6,axiom,(
% 0.13/0.38 ~ equalish(e_1,e_2) ),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.38 fof(f7,axiom,(
% 0.13/0.38 ~ equalish(e_1,e_3) ),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.38 fof(f8,axiom,(
% 0.13/0.38 ~ equalish(e_2,e_1) ),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.38 fof(f9,axiom,(
% 0.13/0.38 ~ equalish(e_2,e_3) ),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.38 fof(f10,axiom,(
% 0.13/0.38 ~ equalish(e_3,e_1) ),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.38 fof(f12,axiom,(
% 0.13/0.38 (![X,Y]: (( ~ group_element(X)| ~ group_element(Y)| product1(X,Y,e_1)| product1(X,Y,e_2)| product1(X,Y,e_3) ) ))),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.38 fof(f14,axiom,(
% 0.13/0.38 (![X,W,Y,Z]: (( ~ product1(X,W,Y)| ~ product1(X,Z,Y)| equalish(W,Z) ) ))),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.38 fof(f15,axiom,(
% 0.13/0.38 (![W,Y,X,Z]: (( ~ product1(W,Y,X)| ~ product1(Z,Y,X)| equalish(W,Z) ) ))),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.38 fof(f16,axiom,(
% 0.13/0.38 (![X]: (product1(X,X,X) ))),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.38 fof(f18,axiom,(
% 0.13/0.38 (![X,Y,W,Z]: (( ~ product2(X,Y,W)| ~ product2(X,Y,Z)| equalish(W,Z) ) ))),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.38 fof(f21,axiom,(
% 0.13/0.38 (![X]: (product2(X,X,X) ))),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.38 fof(f22,negated_conjecture,(
% 0.13/0.38 (![X,Y,Z1,Z2]: (( ~ product1(X,Y,Z1)| ~ product1(Z1,Y,Z2)| product2(Z2,X,Y) ) ))),
% 0.13/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.38 fof(f25,plain,(
% 0.13/0.38 group_element(e_1)),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f3])).
% 0.13/0.38 fof(f26,plain,(
% 0.13/0.38 group_element(e_2)),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f4])).
% 0.13/0.38 fof(f27,plain,(
% 0.13/0.38 group_element(e_3)),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f5])).
% 0.13/0.38 fof(f28,plain,(
% 0.13/0.38 ~equalish(e_1,e_2)),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f6])).
% 0.13/0.38 fof(f29,plain,(
% 0.13/0.38 ~equalish(e_1,e_3)),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f7])).
% 0.13/0.38 fof(f30,plain,(
% 0.13/0.38 ~equalish(e_2,e_1)),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f8])).
% 0.13/0.38 fof(f31,plain,(
% 0.13/0.38 ~equalish(e_2,e_3)),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f9])).
% 0.13/0.38 fof(f32,plain,(
% 0.13/0.38 ~equalish(e_3,e_1)),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f10])).
% 0.13/0.38 fof(f34,plain,(
% 0.13/0.38 ![X0,X1]: (~group_element(X0)|~group_element(X1)|product1(X0,X1,e_1)|product1(X0,X1,e_2)|product1(X0,X1,e_3))),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f12])).
% 0.13/0.38 fof(f37,plain,(
% 0.13/0.38 ![W,Z]: ((![X,Y]: (~product1(X,W,Y)|~product1(X,Z,Y)))|equalish(W,Z))),
% 0.13/0.38 inference(miniscoping,[status(thm)],[f14])).
% 0.13/0.38 fof(f38,plain,(
% 0.13/0.38 ![X0,X1,X2,X3]: (~product1(X0,X1,X2)|~product1(X0,X3,X2)|equalish(X1,X3))),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f37])).
% 0.13/0.38 fof(f39,plain,(
% 0.13/0.38 ![W,Z]: ((![Y,X]: (~product1(W,Y,X)|~product1(Z,Y,X)))|equalish(W,Z))),
% 0.13/0.38 inference(miniscoping,[status(thm)],[f15])).
% 0.13/0.38 fof(f40,plain,(
% 0.13/0.38 ![X0,X1,X2,X3]: (~product1(X0,X1,X2)|~product1(X3,X1,X2)|equalish(X0,X3))),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f39])).
% 0.13/0.38 fof(f41,plain,(
% 0.13/0.38 ![X0]: (product1(X0,X0,X0))),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f16])).
% 0.13/0.38 fof(f43,plain,(
% 0.13/0.38 ![W,Z]: ((![X,Y]: (~product2(X,Y,W)|~product2(X,Y,Z)))|equalish(W,Z))),
% 0.13/0.38 inference(miniscoping,[status(thm)],[f18])).
% 0.13/0.38 fof(f44,plain,(
% 0.13/0.38 ![X0,X1,X2,X3]: (~product2(X0,X1,X2)|~product2(X0,X1,X3)|equalish(X2,X3))),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f43])).
% 0.13/0.38 fof(f49,plain,(
% 0.13/0.38 ![X0]: (product2(X0,X0,X0))),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f21])).
% 0.13/0.38 fof(f50,plain,(
% 0.13/0.38 ![X,Y,Z2]: ((![Z1]: (~product1(X,Y,Z1)|~product1(Z1,Y,Z2)))|product2(Z2,X,Y))),
% 0.13/0.38 inference(miniscoping,[status(thm)],[f22])).
% 0.13/0.38 fof(f51,plain,(
% 0.13/0.38 ![X0,X1,X2,X3]: (~product1(X0,X1,X2)|~product1(X2,X1,X3)|product2(X3,X0,X1))),
% 0.13/0.38 inference(cnf_transformation,[status(thm)],[f50])).
% 0.13/0.38 fof(f56,plain,(
% 0.13/0.38 ![X0,X1]: (~product1(X0,X1,X0)|equalish(X1,X0))),
% 0.13/0.38 inference(resolution,[status(thm)],[f38,f41])).
% 0.13/0.38 fof(f57,plain,(
% 0.13/0.38 ![X0,X1]: (~product1(X0,X1,X1)|equalish(X0,X1))),
% 0.13/0.38 inference(resolution,[status(thm)],[f40,f41])).
% 0.13/0.38 fof(f64,plain,(
% 0.13/0.38 ![X0]: (~group_element(X0)|product1(e_3,X0,e_1)|product1(e_3,X0,e_2)|product1(e_3,X0,e_3))),
% 0.13/0.38 inference(resolution,[status(thm)],[f34,f27])).
% 0.13/0.38 fof(f65,plain,(
% 0.13/0.38 ![X0]: (~group_element(X0)|product1(e_2,X0,e_1)|product1(e_2,X0,e_2)|product1(e_2,X0,e_3))),
% 0.13/0.38 inference(resolution,[status(thm)],[f34,f26])).
% 0.13/0.38 fof(f189,plain,(
% 0.13/0.38 product1(e_3,e_1,e_1)|product1(e_3,e_1,e_2)|product1(e_3,e_1,e_3)),
% 0.13/0.38 inference(resolution,[status(thm)],[f64,f25])).
% 0.13/0.38 fof(f210,definition,(
% 0.13/0.38 sQ33_spl <=> (product1(e_3,e_1,e_1))),
% 0.13/0.38 introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition])).
% 0.13/0.38 fof(f211,plain,(
% 0.13/0.38 product1(e_3,e_1,e_1)|~sQ33_spl),
% 0.13/0.38 inference(component_clause,[status(thm)],[f210])).
% 0.13/0.38 fof(f213,definition,(
% 0.13/0.38 sQ34_spl <=> (product1(e_3,e_1,e_2))),
% 0.13/0.38 introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition])).
% 0.13/0.38 fof(f214,plain,(
% 0.13/0.38 product1(e_3,e_1,e_2)|~sQ34_spl),
% 0.13/0.38 inference(component_clause,[status(thm)],[f213])).
% 0.13/0.38 fof(f216,definition,(
% 0.13/0.38 sQ35_spl <=> (product1(e_3,e_1,e_3))),
% 0.13/0.38 introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition])).
% 0.13/0.38 fof(f217,plain,(
% 0.13/0.38 product1(e_3,e_1,e_3)|~sQ35_spl),
% 0.13/0.38 inference(component_clause,[status(thm)],[f216])).
% 0.13/0.38 fof(f219,plain,(
% 0.13/0.38 sQ33_spl|sQ34_spl|sQ35_spl),
% 0.13/0.38 inference(split_clause,[status(thm)],[f189,f210,f213,f216])).
% 0.13/0.38 fof(f222,plain,(
% 0.13/0.38 product1(e_2,e_1,e_1)|product1(e_2,e_1,e_2)|product1(e_2,e_1,e_3)),
% 0.13/0.38 inference(resolution,[status(thm)],[f65,f25])).
% 0.13/0.38 fof(f243,definition,(
% 0.13/0.38 sQ42_spl <=> (product1(e_2,e_1,e_1))),
% 0.13/0.38 introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition])).
% 0.13/0.38 fof(f244,plain,(
% 0.13/0.38 product1(e_2,e_1,e_1)|~sQ42_spl),
% 0.13/0.38 inference(component_clause,[status(thm)],[f243])).
% 0.13/0.38 fof(f246,definition,(
% 0.13/0.38 sQ43_spl <=> (product1(e_2,e_1,e_2))),
% 0.13/0.38 introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition])).
% 0.13/0.38 fof(f247,plain,(
% 0.13/0.38 product1(e_2,e_1,e_2)|~sQ43_spl),
% 0.13/0.38 inference(component_clause,[status(thm)],[f246])).
% 0.13/0.38 fof(f249,definition,(
% 0.13/0.38 sQ44_spl <=> (product1(e_2,e_1,e_3))),
% 0.13/0.38 introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition])).
% 0.13/0.38 fof(f250,plain,(
% 0.13/0.38 product1(e_2,e_1,e_3)|~sQ44_spl),
% 0.13/0.38 inference(component_clause,[status(thm)],[f249])).
% 0.13/0.38 fof(f252,plain,(
% 0.13/0.38 sQ42_spl|sQ43_spl|sQ44_spl),
% 0.13/0.38 inference(split_clause,[status(thm)],[f222,f243,f246,f249])).
% 0.13/0.38 fof(f387,plain,(
% 0.13/0.38 ![X0,X1]: (~product2(X0,X0,X1)|equalish(X1,X0))),
% 0.13/0.38 inference(resolution,[status(thm)],[f44,f49])).
% 0.13/0.38 fof(f393,plain,(
% 0.13/0.38 equalish(e_1,e_3)|~sQ35_spl),
% 0.13/0.38 inference(resolution,[status(thm)],[f217,f56])).
% 0.13/0.38 fof(f398,plain,(
% 0.13/0.38 $false|~sQ35_spl),
% 0.13/0.38 inference(forward_subsumption_resolution,[status(thm)],[f393,f29])).
% 0.13/0.38 fof(f399,plain,(
% 0.13/0.38 ~sQ35_spl),
% 0.13/0.38 inference(contradiction_clause,[status(thm)],[f398])).
% 0.13/0.38 fof(f400,plain,(
% 0.13/0.38 ![X0]: (~product1(X0,e_1,e_2)|equalish(X0,e_3)|~sQ34_spl)),
% 0.13/0.38 inference(resolution,[status(thm)],[f214,f40])).
% 0.13/0.38 fof(f403,plain,(
% 0.13/0.38 ![X0]: (~product1(X0,e_1,e_3)|product2(e_2,X0,e_1)|~sQ34_spl)),
% 0.13/0.38 inference(resolution,[status(thm)],[f214,f51])).
% 0.13/0.38 fof(f408,plain,(
% 0.13/0.38 equalish(e_3,e_1)|~sQ33_spl),
% 0.13/0.38 inference(resolution,[status(thm)],[f211,f57])).
% 0.13/0.38 fof(f416,plain,(
% 0.13/0.38 $false|~sQ33_spl),
% 0.13/0.38 inference(forward_subsumption_resolution,[status(thm)],[f408,f32])).
% 0.13/0.38 fof(f417,plain,(
% 0.13/0.38 ~sQ33_spl),
% 0.13/0.38 inference(contradiction_clause,[status(thm)],[f416])).
% 0.13/0.38 fof(f441,plain,(
% 0.13/0.38 product2(e_2,e_2,e_1)|~sQ44_spl|~sQ34_spl),
% 0.13/0.38 inference(resolution,[status(thm)],[f250,f403])).
% 0.13/0.38 fof(f448,plain,(
% 0.13/0.38 equalish(e_1,e_2)|~sQ44_spl|~sQ34_spl),
% 0.13/0.38 inference(resolution,[status(thm)],[f441,f387])).
% 0.13/0.38 fof(f450,plain,(
% 0.13/0.38 $false|~sQ44_spl|~sQ34_spl),
% 0.13/0.38 inference(forward_subsumption_resolution,[status(thm)],[f448,f28])).
% 0.13/0.38 fof(f451,plain,(
% 0.13/0.38 ~sQ44_spl|~sQ34_spl),
% 0.13/0.38 inference(contradiction_clause,[status(thm)],[f450])).
% 0.13/0.38 fof(f452,plain,(
% 0.13/0.38 equalish(e_2,e_3)|~sQ43_spl|~sQ34_spl),
% 0.13/0.38 inference(resolution,[status(thm)],[f247,f400])).
% 0.13/0.38 fof(f458,plain,(
% 0.13/0.38 $false|~sQ43_spl|~sQ34_spl),
% 0.13/0.38 inference(forward_subsumption_resolution,[status(thm)],[f452,f31])).
% 0.13/0.38 fof(f459,plain,(
% 0.13/0.38 ~sQ43_spl|~sQ34_spl),
% 0.13/0.38 inference(contradiction_clause,[status(thm)],[f458])).
% 0.13/0.38 fof(f460,plain,(
% 0.13/0.38 equalish(e_2,e_1)|~sQ42_spl),
% 0.13/0.38 inference(resolution,[status(thm)],[f244,f57])).
% 0.13/0.38 fof(f466,plain,(
% 0.13/0.38 $false|~sQ42_spl),
% 0.13/0.38 inference(forward_subsumption_resolution,[status(thm)],[f460,f30])).
% 0.13/0.38 fof(f467,plain,(
% 0.13/0.38 ~sQ42_spl),
% 0.13/0.38 inference(contradiction_clause,[status(thm)],[f466])).
% 0.13/0.38 fof(f468,plain,(
% 0.13/0.38 $false),
% 0.13/0.38 inference(sat_refutation,[status(thm)],[f219,f252,f399,f417,f451,f459,f467])).
% 0.13/0.38 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.40 % Elapsed time: 0.042675 seconds
% 0.13/0.40 % CPU time: 0.128214 seconds
% 0.13/0.40 % Total memory used: 16.157 MB
% 0.13/0.40 % Net memory used: 15.882 MB
%------------------------------------------------------------------------------