%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP069-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 12:35:35 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP069-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n010.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 19:56:55 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% 0.13/0.40 fof(f1,axiom,(
% 0.13/0.40 (![X,Y,Z]: (divide(X,divide(divide(divide(divide(X,X),Y),Z),divide(divide(identity,X),Z))) = Y ))),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f2,axiom,(
% 0.13/0.40 (![X,Y]: (multiply(X,Y) = divide(X,divide(identity,Y)) ))),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f3,axiom,(
% 0.13/0.40 (![X]: (inverse(X) = divide(identity,X) ))),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f4,axiom,(
% 0.13/0.40 (![X]: (identity = divide(X,X) ))),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f5,negated_conjecture,(
% 0.13/0.40 ( multiply(inverse(a1),a1) != identity| multiply(identity,a2) != a2| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ) ),
% 0.13/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.13/0.40 fof(f6,plain,(
% 0.13/0.40 ![X0,X1,X2]: (divide(X0,divide(divide(divide(divide(X0,X0),X1),X2),divide(divide(identity,X0),X2)))=X1)),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f1])).
% 0.13/0.40 fof(f7,plain,(
% 0.13/0.40 ![X0,X1]: (multiply(X0,X1)=divide(X0,divide(identity,X1)))),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f2])).
% 0.13/0.40 fof(f8,plain,(
% 0.13/0.40 ![X0]: (inverse(X0)=divide(identity,X0))),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f3])).
% 0.13/0.40 fof(f9,plain,(
% 0.13/0.40 ![X0]: (identity=divide(X0,X0))),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f4])).
% 0.13/0.40 fof(f10,plain,(
% 0.13/0.40 ~multiply(inverse(a1),a1)=identity|~multiply(identity,a2)=a2|~multiply(multiply(a3,b3),c3)=multiply(a3,multiply(b3,c3))),
% 0.13/0.40 inference(cnf_transformation,[status(thm)],[f5])).
% 0.13/0.40 fof(f11,definition,(
% 0.13/0.40 sQ0_spl <=> (multiply(inverse(a1),a1)=identity)),
% 0.13/0.40 introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition])).
% 0.13/0.40 fof(f13,plain,(
% 0.13/0.40 ~multiply(inverse(a1),a1)=identity|sQ0_spl),
% 0.13/0.40 inference(component_clause,[status(thm)],[f11])).
% 0.13/0.40 fof(f14,definition,(
% 0.13/0.40 sQ1_spl <=> (multiply(identity,a2)=a2)),
% 0.13/0.40 introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition])).
% 0.13/0.40 fof(f16,plain,(
% 0.13/0.40 ~multiply(identity,a2)=a2|sQ1_spl),
% 0.13/0.40 inference(component_clause,[status(thm)],[f14])).
% 0.13/0.40 fof(f17,definition,(
% 0.13/0.40 sQ2_spl <=> (multiply(multiply(a3,b3),c3)=multiply(a3,multiply(b3,c3)))),
% 0.13/0.40 introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition])).
% 0.13/0.40 fof(f19,plain,(
% 0.13/0.40 ~multiply(multiply(a3,b3),c3)=multiply(a3,multiply(b3,c3))|sQ2_spl),
% 0.13/0.40 inference(component_clause,[status(thm)],[f17])).
% 0.13/0.40 fof(f20,plain,(
% 0.13/0.40 ~sQ0_spl|~sQ1_spl|~sQ2_spl),
% 0.13/0.40 inference(split_clause,[status(thm)],[f10,f11,f14,f17])).
% 0.13/0.40 fof(f21,plain,(
% 0.13/0.40 inverse(identity)=identity),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f9,f8])).
% 0.13/0.40 fof(f23,plain,(
% 0.13/0.40 ![X0,X1]: (multiply(X0,X1)=divide(X0,inverse(X1)))),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f8,f7])).
% 0.13/0.40 fof(f24,plain,(
% 0.13/0.40 ![X0]: (multiply(identity,X0)=inverse(inverse(X0)))),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f8,f23])).
% 0.13/0.40 fof(f25,plain,(
% 0.13/0.40 ![X0]: (multiply(inverse(X0),X0)=identity)),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f9,f23])).
% 0.13/0.40 fof(f26,plain,(
% 0.13/0.40 ![X0]: (multiply(X0,identity)=divide(X0,identity))),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f21,f23])).
% 0.13/0.40 fof(f29,plain,(
% 0.13/0.40 ![X0,X1,X2]: (divide(X0,divide(divide(divide(identity,X1),X2),divide(divide(identity,X0),X2)))=X1)),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f9,f6])).
% 0.13/0.40 fof(f30,plain,(
% 0.13/0.40 ![X0,X1,X2]: (divide(X0,divide(divide(inverse(X1),X2),divide(divide(identity,X0),X2)))=X1)),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f8,f29])).
% 0.13/0.40 fof(f31,plain,(
% 0.13/0.40 ![X0,X1,X2]: (divide(X0,divide(divide(inverse(X1),X2),divide(inverse(X0),X2)))=X1)),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f8,f30])).
% 0.13/0.40 fof(f33,plain,(
% 0.13/0.40 ![X0]: (divide(X0,identity)=X0)),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f9,f31])).
% 0.13/0.40 fof(f36,plain,(
% 0.13/0.40 ![X0,X1]: (divide(X0,divide(identity,divide(inverse(X0),inverse(X1))))=X1)),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f9,f31])).
% 0.13/0.40 fof(f38,plain,(
% 0.13/0.40 ![X0,X1,X2,X3]: (divide(X0,divide(divide(inverse(X1),divide(divide(inverse(X2),X3),divide(inverse(inverse(X0)),X3))),X2))=X1)),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f31,f31])).
% 0.13/0.40 fof(f47,plain,(
% 0.13/0.40 ![X0,X1]: (divide(X0,inverse(divide(inverse(X0),inverse(X1))))=X1)),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f8,f36])).
% 0.13/0.40 fof(f48,plain,(
% 0.13/0.40 ![X0,X1]: (multiply(X0,divide(inverse(X0),inverse(X1)))=X1)),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f23,f47])).
% 0.13/0.40 fof(f49,plain,(
% 0.13/0.40 ![X0,X1]: (multiply(X0,multiply(inverse(X0),X1))=X1)),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f23,f48])).
% 0.13/0.40 fof(f61,plain,(
% 0.13/0.40 ![X0,X1]: (divide(X0,divide(divide(inverse(X1),identity),inverse(X0)))=X1)),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f33,f31])).
% 0.13/0.40 fof(f65,plain,(
% 0.13/0.40 ![X0,X1]: (divide(X0,multiply(divide(inverse(X1),identity),X0))=X1)),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f23,f61])).
% 0.13/0.40 fof(f66,plain,(
% 0.13/0.40 ![X0,X1]: (divide(X0,multiply(inverse(X1),X0))=X1)),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f33,f65])).
% 0.13/0.40 fof(f72,plain,(
% 0.13/0.40 ![X0]: (multiply(X0,identity)=X0)),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f33,f26])).
% 0.13/0.40 fof(f82,plain,(
% 0.13/0.40 ![X0]: (multiply(X0,inverse(X0))=identity)),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f72,f49])).
% 0.13/0.40 fof(f94,plain,(
% 0.13/0.40 ![X0]: (multiply(X0,identity)=inverse(inverse(X0)))),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f82,f49])).
% 0.13/0.40 fof(f101,plain,(
% 0.13/0.40 ![X0]: (X0=inverse(inverse(X0)))),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f72,f94])).
% 0.13/0.40 fof(f102,plain,(
% 0.13/0.40 ![X0]: (multiply(identity,X0)=X0)),
% 0.13/0.40 inference(backward_demodulation,[status(thm)],[f101,f24])).
% 0.13/0.40 fof(f110,plain,(
% 0.13/0.40 ![X0,X1]: (multiply(X0,inverse(X1))=divide(X0,X1))),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f101,f23])).
% 0.13/0.40 fof(f142,plain,(
% 0.13/0.40 ![X0,X1]: (divide(multiply(inverse(inverse(X0)),X1),X1)=X0)),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f49,f66])).
% 0.13/0.40 fof(f145,plain,(
% 0.13/0.40 ![X0,X1]: (divide(X0,multiply(X1,X0))=inverse(X1))),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f101,f66])).
% 0.13/0.40 fof(f153,plain,(
% 0.13/0.40 ![X0,X1]: (divide(multiply(X0,X1),X1)=X0)),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f101,f142])).
% 0.13/0.40 fof(f260,plain,(
% 0.13/0.40 ![X0,X1]: (divide(divide(X0,X1),inverse(X1))=X0)),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f110,f153])).
% 0.13/0.40 fof(f266,plain,(
% 0.13/0.40 ![X0,X1]: (multiply(divide(X0,X1),X1)=X0)),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f23,f260])).
% 0.13/0.40 fof(f335,plain,(
% 0.13/0.40 ![X0,X1]: (divide(X0,X1)=inverse(divide(X1,X0)))),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f266,f145])).
% 0.13/0.40 fof(f358,plain,(
% 0.13/0.40 ![X0,X1,X2,X3]: (divide(X0,divide(divide(inverse(X1),divide(divide(inverse(X2),X3),divide(X0,X3))),X2))=X1)),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f101,f38])).
% 0.13/0.40 fof(f466,plain,(
% 0.13/0.40 ![X0,X1]: (divide(inverse(X0),X1)=inverse(multiply(X1,X0)))),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f23,f335])).
% 0.13/0.40 fof(f723,plain,(
% 0.13/0.40 ![X0,X1,X2,X3]: (divide(X0,divide(inverse(multiply(divide(divide(inverse(X1),X2),divide(X0,X2)),X3)),X1))=X3)),
% 0.13/0.40 inference(backward_demodulation,[status(thm)],[f466,f358])).
% 0.13/0.40 fof(f744,plain,(
% 0.13/0.40 ![X0,X1,X2,X3]: (divide(X0,inverse(multiply(X1,multiply(divide(divide(inverse(X1),X2),divide(X0,X2)),X3))))=X3)),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f466,f723])).
% 0.13/0.40 fof(f745,plain,(
% 0.13/0.40 ![X0,X1,X2,X3]: (multiply(X0,multiply(X1,multiply(divide(divide(inverse(X1),X2),divide(X0,X2)),X3)))=X3)),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f23,f744])).
% 0.13/0.40 fof(f746,plain,(
% 0.13/0.40 ![X0,X1,X2,X3]: (multiply(X0,multiply(X1,multiply(divide(inverse(multiply(X2,X1)),divide(X0,X2)),X3)))=X3)),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f466,f745])).
% 0.13/0.40 fof(f747,plain,(
% 0.13/0.40 ![X0,X1,X2,X3]: (multiply(X0,multiply(X1,multiply(inverse(multiply(divide(X0,X2),multiply(X2,X1))),X3)))=X3)),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f466,f746])).
% 0.13/0.40 fof(f886,plain,(
% 0.13/0.40 ![X0,X1,X2]: (multiply(X0,multiply(X1,identity))=multiply(divide(X0,X2),multiply(X2,X1)))),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f25,f747])).
% 0.13/0.40 fof(f939,plain,(
% 0.13/0.40 ![X0,X1,X2]: (multiply(X0,X1)=multiply(divide(X0,X2),multiply(X2,X1)))),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f72,f886])).
% 0.13/0.40 fof(f1405,plain,(
% 0.13/0.40 ![X0,X1,X2]: (multiply(multiply(X0,X1),X2)=multiply(X0,multiply(X1,X2)))),
% 0.13/0.40 inference(paramodulation,[status(thm)],[f153,f939])).
% 0.13/0.40 fof(f1912,plain,(
% 0.13/0.40 ~multiply(a3,multiply(b3,c3))=multiply(a3,multiply(b3,c3))|sQ2_spl),
% 0.13/0.40 inference(backward_demodulation,[status(thm)],[f1405,f19])).
% 0.13/0.40 fof(f1956,plain,(
% 0.13/0.40 $false|sQ2_spl),
% 0.13/0.40 inference(trivial_equality_resolution,[status(thm)],[f1912])).
% 0.13/0.40 fof(f1957,plain,(
% 0.13/0.40 sQ2_spl),
% 0.13/0.40 inference(contradiction_clause,[status(thm)],[f1956])).
% 0.13/0.40 fof(f1978,plain,(
% 0.13/0.40 ~identity=identity|sQ0_spl),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f25,f13])).
% 0.13/0.40 fof(f1979,plain,(
% 0.13/0.40 $false|sQ0_spl),
% 0.13/0.40 inference(trivial_equality_resolution,[status(thm)],[f1978])).
% 0.13/0.40 fof(f1980,plain,(
% 0.13/0.40 sQ0_spl),
% 0.13/0.40 inference(contradiction_clause,[status(thm)],[f1979])).
% 0.13/0.40 fof(f1981,plain,(
% 0.13/0.40 ~a2=a2|sQ1_spl),
% 0.13/0.40 inference(forward_demodulation,[status(thm)],[f102,f16])).
% 0.13/0.40 fof(f1982,plain,(
% 0.13/0.40 $false|sQ1_spl),
% 0.13/0.40 inference(trivial_equality_resolution,[status(thm)],[f1981])).
% 0.13/0.40 fof(f1983,plain,(
% 0.13/0.40 sQ1_spl),
% 0.13/0.40 inference(contradiction_clause,[status(thm)],[f1982])).
% 0.13/0.40 fof(f1984,plain,(
% 0.13/0.40 $false),
% 0.13/0.40 inference(sat_refutation,[status(thm)],[f20,f1957,f1980,f1983])).
% 0.13/0.40 % SZS output end CNFRefutation for theBenchmark.p
% 0.13/0.44 % Elapsed time: 0.068320 seconds
% 0.13/0.44 % CPU time: 0.271060 seconds
% 0.13/0.44 % Total memory used: 54.348 MB
% 0.13/0.44 % Net memory used: 54.005 MB
%------------------------------------------------------------------------------