%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP039-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 12:35:32 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.44s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP039-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.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 19:55:13 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.14/0.44 % Refutation found
% 0.14/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.44 % SZS output start CNFRefutation for theBenchmark
% 0.14/0.44 fof(f1,axiom,(
% 0.14/0.44 (![X]: (multiply(identity,X) = X ))),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f2,axiom,(
% 0.14/0.44 (![X]: (multiply(inverse(X),X) = identity ))),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f3,axiom,(
% 0.14/0.44 (![X,Y,Z]: (multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ))),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f4,axiom,(
% 0.14/0.44 (![X]: (( ~ subgroup_member(X)| subgroup_member(inverse(X)) ) ))),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f5,axiom,(
% 0.14/0.44 (![X,Y,Z]: (( ~ subgroup_member(X)| ~ subgroup_member(Y)| multiply(X,Y) != Z| subgroup_member(Z) ) ))),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f6,axiom,(
% 0.14/0.44 (![X]: (multiply(X,identity) = X ))),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f7,axiom,(
% 0.14/0.44 (![X]: (multiply(X,inverse(X)) = identity ))),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f8,axiom,(
% 0.14/0.44 (![X,Y]: (( subgroup_member(X)| subgroup_member(Y)| subgroup_member(element_in_O2(X,Y)) ) ))),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f9,axiom,(
% 0.14/0.44 (![X,Y]: (( subgroup_member(X)| subgroup_member(Y)| multiply(X,element_in_O2(X,Y)) = Y ) ))),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f10,negated_conjecture,(
% 0.14/0.44 subgroup_member(b) ),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f11,negated_conjecture,(
% 0.14/0.44 multiply(b,inverse(a)) = c ),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f12,negated_conjecture,(
% 0.14/0.44 multiply(a,c) = d ),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f13,negated_conjecture,(
% 0.14/0.44 ~ subgroup_member(d) ),
% 0.14/0.44 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.14/0.44 fof(f14,plain,(
% 0.14/0.44 ![X0]: (multiply(identity,X0)=X0)),
% 0.14/0.44 inference(cnf_transformation,[status(thm)],[f1])).
% 0.14/0.44 fof(f15,plain,(
% 0.14/0.44 ![X0]: (multiply(inverse(X0),X0)=identity)),
% 0.14/0.44 inference(cnf_transformation,[status(thm)],[f2])).
% 0.14/0.44 fof(f16,plain,(
% 0.14/0.44 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X0,multiply(X1,X2)))),
% 0.14/0.44 inference(cnf_transformation,[status(thm)],[f3])).
% 0.14/0.44 fof(f17,plain,(
% 0.14/0.44 ![X0]: (~subgroup_member(X0)|subgroup_member(inverse(X0)))),
% 0.14/0.44 inference(cnf_transformation,[status(thm)],[f4])).
% 0.14/0.44 fof(f18,plain,(
% 0.14/0.44 ![Z]: ((![X,Y]: ((~subgroup_member(X)|~subgroup_member(Y))|~multiply(X,Y)=Z))|subgroup_member(Z))),
% 0.14/0.44 inference(miniscoping,[status(thm)],[f5])).
% 0.14/0.44 fof(f19,plain,(
% 0.14/0.44 ![X0,X1,X2]: (~subgroup_member(X0)|~subgroup_member(X1)|~multiply(X0,X1)=X2|subgroup_member(X2))),
% 0.14/0.44 inference(cnf_transformation,[status(thm)],[f18])).
% 0.14/0.44 fof(f20,plain,(
% 0.14/0.44 ![X0]: (multiply(X0,identity)=X0)),
% 0.14/0.44 inference(cnf_transformation,[status(thm)],[f6])).
% 0.14/0.44 fof(f21,plain,(
% 0.14/0.44 ![X0]: (multiply(X0,inverse(X0))=identity)),
% 0.14/0.44 inference(cnf_transformation,[status(thm)],[f7])).
% 0.14/0.44 fof(f22,plain,(
% 0.14/0.44 ![X0,X1]: (subgroup_member(X0)|subgroup_member(X1)|subgroup_member(element_in_O2(X0,X1)))),
% 0.14/0.44 inference(cnf_transformation,[status(thm)],[f8])).
% 0.14/0.44 fof(f23,plain,(
% 0.14/0.44 ![X0,X1]: (subgroup_member(X0)|subgroup_member(X1)|multiply(X0,element_in_O2(X0,X1))=X1)),
% 0.14/0.44 inference(cnf_transformation,[status(thm)],[f9])).
% 0.14/0.44 fof(f24,plain,(
% 0.14/0.44 subgroup_member(b)),
% 0.14/0.44 inference(cnf_transformation,[status(thm)],[f10])).
% 0.14/0.44 fof(f25,plain,(
% 0.14/0.44 multiply(b,inverse(a))=c),
% 0.14/0.44 inference(cnf_transformation,[status(thm)],[f11])).
% 0.14/0.44 fof(f26,plain,(
% 0.14/0.44 multiply(a,c)=d),
% 0.14/0.44 inference(cnf_transformation,[status(thm)],[f12])).
% 0.14/0.44 fof(f27,plain,(
% 0.14/0.44 ~subgroup_member(d)),
% 0.14/0.44 inference(cnf_transformation,[status(thm)],[f13])).
% 0.14/0.44 fof(f28,plain,(
% 0.14/0.44 ![X0,X1]: (~subgroup_member(X0)|~subgroup_member(X1)|subgroup_member(multiply(X0,X1)))),
% 0.14/0.44 inference(destructive_equality_resolution,[status(thm)],[f19])).
% 0.14/0.44 fof(f29,plain,(
% 0.14/0.44 ![X0,X1]: (~subgroup_member(X0)|subgroup_member(multiply(X0,inverse(X1)))|~subgroup_member(X1))),
% 0.14/0.44 inference(resolution,[status(thm)],[f28,f17])).
% 0.14/0.44 fof(f30,plain,(
% 0.14/0.44 ![X0]: (~subgroup_member(X0)|subgroup_member(multiply(X0,b)))),
% 0.14/0.44 inference(resolution,[status(thm)],[f28,f24])).
% 0.14/0.44 fof(f32,plain,(
% 0.14/0.44 ~subgroup_member(inverse(b))|subgroup_member(identity)),
% 0.14/0.44 inference(paramodulation,[status(thm)],[f15,f30])).
% 0.14/0.44 fof(f33,definition,(
% 0.14/0.44 sQ0_spl <=> (subgroup_member(inverse(b)))),
% 0.14/0.44 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.14/0.44 fof(f35,plain,(
% 0.14/0.44 ~subgroup_member(inverse(b))|sQ0_spl),
% 0.14/0.44 inference(component_clause,[status(thm)],[f33])).
% 0.14/0.44 fof(f36,definition,(
% 0.14/0.44 sQ1_spl <=> (subgroup_member(identity))),
% 0.14/0.44 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.14/0.44 fof(f39,plain,(
% 0.14/0.44 ~sQ0_spl|sQ1_spl),
% 0.14/0.44 inference(split_clause,[status(thm)],[f32,f33,f36])).
% 0.14/0.44 fof(f40,plain,(
% 0.14/0.44 ~subgroup_member(b)|sQ0_spl),
% 0.14/0.44 inference(resolution,[status(thm)],[f35,f17])).
% 0.14/0.44 fof(f41,plain,(
% 0.14/0.44 $false|sQ0_spl),
% 0.14/0.44 inference(forward_subsumption_resolution,[status(thm)],[f40,f24])).
% 0.14/0.44 fof(f42,plain,(
% 0.14/0.44 sQ0_spl),
% 0.14/0.44 inference(contradiction_clause,[status(thm)],[f41])).
% 0.14/0.44 fof(f52,definition,(
% 0.14/0.44 sQ3_spl <=> (subgroup_member(b))),
% 0.14/0.44 introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition])).
% 0.14/0.44 fof(f54,plain,(
% 0.14/0.44 ~subgroup_member(b)|sQ3_spl),
% 0.14/0.44 inference(component_clause,[status(thm)],[f52])).
% 0.14/0.44 fof(f58,plain,(
% 0.14/0.44 ![X0,X1]: (multiply(identity,X0)=multiply(inverse(X1),multiply(X1,X0)))),
% 0.14/0.44 inference(paramodulation,[status(thm)],[f15,f16])).
% 0.14/0.44 fof(f59,plain,(
% 0.14/0.44 ![X0]: (multiply(c,X0)=multiply(b,multiply(inverse(a),X0)))),
% 0.14/0.44 inference(paramodulation,[status(thm)],[f25,f16])).
% 0.14/0.44 fof(f60,plain,(
% 0.14/0.44 ![X0]: (multiply(d,X0)=multiply(a,multiply(c,X0)))),
% 0.14/0.44 inference(paramodulation,[status(thm)],[f26,f16])).
% 0.14/0.44 fof(f67,plain,(
% 0.14/0.44 ![X0,X1]: (X0=multiply(inverse(X1),multiply(X1,X0)))),
% 0.14/0.44 inference(forward_demodulation,[status(thm)],[f14,f58])).
% 0.14/0.44 fof(f72,plain,(
% 0.14/0.44 ~subgroup_member(b)|subgroup_member(c)|~subgroup_member(a)),
% 0.14/0.44 inference(paramodulation,[status(thm)],[f25,f29])).
% 0.14/0.44 fof(f78,definition,(
% 0.14/0.44 sQ5_spl <=> (subgroup_member(c))),
% 0.14/0.44 introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition])).
% 0.14/0.44 fof(f79,plain,(
% 0.14/0.44 subgroup_member(c)|~sQ5_spl),
% 0.14/0.44 inference(component_clause,[status(thm)],[f78])).
% 0.14/0.44 fof(f81,definition,(
% 0.14/0.44 sQ6_spl <=> (subgroup_member(a))),
% 0.14/0.44 introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition])).
% 0.14/0.44 fof(f83,plain,(
% 0.14/0.44 ~subgroup_member(a)|sQ6_spl),
% 0.14/0.44 inference(component_clause,[status(thm)],[f81])).
% 0.14/0.44 fof(f84,plain,(
% 0.14/0.44 ~sQ3_spl|sQ5_spl|~sQ6_spl),
% 0.14/0.44 inference(split_clause,[status(thm)],[f72,f52,f78,f81])).
% 0.14/0.44 fof(f89,plain,(
% 0.14/0.44 $false|sQ3_spl),
% 0.14/0.44 inference(forward_subsumption_resolution,[status(thm)],[f54,f24])).
% 0.14/0.44 fof(f90,plain,(
% 0.14/0.44 sQ3_spl),
% 0.14/0.44 inference(contradiction_clause,[status(thm)],[f89])).
% 0.14/0.44 fof(f91,plain,(
% 0.14/0.44 ![X0]: (~subgroup_member(X0)|subgroup_member(multiply(X0,c))|~sQ5_spl)),
% 0.14/0.44 inference(resolution,[status(thm)],[f79,f28])).
% 0.14/0.44 fof(f92,plain,(
% 0.14/0.44 identity=inverse(identity)),
% 0.14/0.44 inference(paramodulation,[status(thm)],[f21,f14])).
% 0.14/0.44 fof(f95,plain,(
% 0.14/0.44 ![X0]: (~subgroup_member(identity)|subgroup_member(inverse(X0))|~subgroup_member(X0))),
% 0.14/0.44 inference(paramodulation,[status(thm)],[f14,f29])).
% 0.14/0.44 fof(f100,definition,(
% 0.14/0.44 ![X0]: (sQ8_spl <=> (subgroup_member(inverse(X0))|~subgroup_member(X0)))),
% 0.14/0.44 introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition])).
% 0.14/0.44 fof(f103,plain,(
% 0.14/0.44 ~sQ1_spl|sQ8_spl),
% 0.14/0.44 inference(split_clause,[status(thm)],[f95,f36,f100])).
% 0.14/0.44 fof(f111,plain,(
% 0.14/0.44 ![X0]: (~subgroup_member(X0)|subgroup_member(multiply(X0,identity))|~subgroup_member(identity))),
% 0.14/0.44 inference(paramodulation,[status(thm)],[f92,f29])).
% 0.14/0.44 fof(f115,definition,(
% 0.14/0.44 ![X0]: (sQ9_spl <=> (~subgroup_member(X0)|subgroup_member(multiply(X0,identity))))),
% 0.14/0.44 introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition])).
% 0.14/0.44 fof(f118,plain,(
% 0.14/0.44 sQ9_spl|~sQ1_spl),
% 0.14/0.44 inference(split_clause,[status(thm)],[f111,f115,f36])).
% 0.14/0.44 fof(f169,plain,(
% 0.14/0.44 ~subgroup_member(a)|subgroup_member(d)|~sQ5_spl),
% 0.14/0.44 inference(paramodulation,[status(thm)],[f26,f91])).
% 0.14/0.44 fof(f171,definition,(
% 0.14/0.44 sQ10_spl <=> (subgroup_member(inverse(c)))),
% 0.14/0.44 introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition])).
% 0.14/0.45 fof(f173,plain,(
% 0.14/0.45 ~subgroup_member(inverse(c))|sQ10_spl),
% 0.14/0.45 inference(component_clause,[status(thm)],[f171])).
% 0.14/0.45 fof(f175,definition,(
% 0.14/0.45 sQ11_spl <=> (subgroup_member(d))),
% 0.14/0.45 introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition])).
% 0.14/0.45 fof(f176,plain,(
% 0.14/0.45 subgroup_member(d)|~sQ11_spl),
% 0.14/0.45 inference(component_clause,[status(thm)],[f175])).
% 0.14/0.45 fof(f178,plain,(
% 0.14/0.45 ~sQ6_spl|sQ11_spl|~sQ5_spl),
% 0.14/0.45 inference(split_clause,[status(thm)],[f169,f81,f175,f78])).
% 0.14/0.45 fof(f183,plain,(
% 0.14/0.45 ![X0,X1,X2]: (subgroup_member(X0)|subgroup_member(X1)|~subgroup_member(X2)|subgroup_member(multiply(X2,element_in_O2(X0,X1))))),
% 0.14/0.45 inference(resolution,[status(thm)],[f22,f28])).
% 0.14/0.45 fof(f189,plain,(
% 0.14/0.45 ![X0]: (subgroup_member(X0)|multiply(d,element_in_O2(d,X0))=X0)),
% 0.14/0.45 inference(resolution,[status(thm)],[f23,f27])).
% 0.14/0.45 fof(f252,plain,(
% 0.14/0.45 multiply(c,a)=multiply(b,identity)),
% 0.14/0.45 inference(paramodulation,[status(thm)],[f15,f59])).
% 0.14/0.45 fof(f258,plain,(
% 0.14/0.45 multiply(c,a)=b),
% 0.14/0.45 inference(forward_demodulation,[status(thm)],[f20,f252])).
% 0.14/0.45 fof(f265,plain,(
% 0.14/0.45 a=multiply(inverse(c),b)),
% 0.14/0.45 inference(paramodulation,[status(thm)],[f258,f67])).
% 0.14/0.45 fof(f268,plain,(
% 0.14/0.45 ~subgroup_member(inverse(c))|subgroup_member(a)),
% 0.14/0.45 inference(paramodulation,[status(thm)],[f265,f30])).
% 0.14/0.45 fof(f271,plain,(
% 0.14/0.45 ~sQ10_spl|sQ6_spl),
% 0.14/0.45 inference(split_clause,[status(thm)],[f268,f171,f81])).
% 0.14/0.45 fof(f274,plain,(
% 0.14/0.45 ~subgroup_member(c)|sQ10_spl),
% 0.14/0.45 inference(resolution,[status(thm)],[f173,f17])).
% 0.14/0.45 fof(f279,plain,(
% 0.14/0.45 $false|~sQ5_spl|sQ10_spl),
% 0.14/0.45 inference(forward_subsumption_resolution,[status(thm)],[f274,f79])).
% 0.14/0.45 fof(f280,plain,(
% 0.14/0.45 ~sQ5_spl|sQ10_spl),
% 0.14/0.45 inference(contradiction_clause,[status(thm)],[f279])).
% 0.14/0.45 fof(f281,plain,(
% 0.14/0.45 $false|~sQ11_spl),
% 0.14/0.45 inference(forward_subsumption_resolution,[status(thm)],[f176,f27])).
% 0.14/0.45 fof(f282,plain,(
% 0.14/0.45 ~sQ11_spl),
% 0.14/0.45 inference(contradiction_clause,[status(thm)],[f281])).
% 0.14/0.45 fof(f286,plain,(
% 0.14/0.45 multiply(d,inverse(c))=multiply(a,identity)),
% 0.14/0.45 inference(paramodulation,[status(thm)],[f21,f60])).
% 0.14/0.45 fof(f290,plain,(
% 0.14/0.45 multiply(d,inverse(c))=a),
% 0.14/0.45 inference(forward_demodulation,[status(thm)],[f20,f286])).
% 0.14/0.45 fof(f307,plain,(
% 0.14/0.45 inverse(c)=multiply(inverse(d),a)),
% 0.14/0.45 inference(paramodulation,[status(thm)],[f290,f67])).
% 0.14/0.45 fof(f374,plain,(
% 0.14/0.45 ![X0,X1]: (subgroup_member(X0)|subgroup_member(X1)|~subgroup_member(identity)|subgroup_member(element_in_O2(X0,X1)))),
% 0.14/0.45 inference(paramodulation,[status(thm)],[f14,f183])).
% 0.14/0.45 fof(f378,definition,(
% 0.14/0.45 ![X0,X1]: (sQ12_spl <=> (subgroup_member(X0)|subgroup_member(X1)|subgroup_member(element_in_O2(X0,X1))))),
% 0.14/0.45 introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition])).
% 0.14/0.45 fof(f381,plain,(
% 0.14/0.45 sQ12_spl|~sQ1_spl),
% 0.14/0.45 inference(split_clause,[status(thm)],[f374,f378,f36])).
% 0.14/0.45 fof(f387,plain,(
% 0.14/0.45 multiply(d,element_in_O2(d,a))=a|sQ6_spl),
% 0.14/0.45 inference(resolution,[status(thm)],[f189,f83])).
% 0.14/0.45 fof(f538,plain,(
% 0.14/0.45 element_in_O2(d,a)=multiply(inverse(d),a)|sQ6_spl),
% 0.14/0.45 inference(paramodulation,[status(thm)],[f387,f67])).
% 0.14/0.45 fof(f545,plain,(
% 0.14/0.45 element_in_O2(d,a)=inverse(c)|sQ6_spl),
% 0.14/0.45 inference(forward_demodulation,[status(thm)],[f307,f538])).
% 0.14/0.45 fof(f598,plain,(
% 0.14/0.45 subgroup_member(d)|subgroup_member(a)|subgroup_member(inverse(c))|sQ6_spl),
% 0.14/0.45 inference(paramodulation,[status(thm)],[f545,f22])).
% 0.14/0.45 fof(f603,plain,(
% 0.14/0.45 sQ11_spl|sQ6_spl|sQ10_spl),
% 0.14/0.45 inference(split_clause,[status(thm)],[f598,f175,f81,f171])).
% 0.14/0.45 fof(f604,plain,(
% 0.14/0.45 $false),
% 0.14/0.45 inference(sat_refutation,[status(thm)],[f39,f42,f84,f90,f103,f118,f178,f271,f280,f282,f381,f603])).
% 0.14/0.45 % SZS output end CNFRefutation for theBenchmark.p
% 0.14/0.46 % Elapsed time: 0.097147 seconds
% 0.14/0.46 % CPU time: 0.528325 seconds
% 0.14/0.46 % Total memory used: 108.665 MB
% 0.14/0.46 % Net memory used: 107.283 MB
%------------------------------------------------------------------------------