%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP495-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 12:34:31 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 9
% Syntax : Number of formulae : 60 ( 60 unt; 4 def)
% Number of atoms : 60 ( 59 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 70 ( 70 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,C),double_divide(identity,identity)),double_divide(A,C))) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = double_divide(double_divide(B,A),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : inverse(A) = double_divide(A,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : identity = double_divide(A,inverse(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,X0),double_divide(double_divide(double_divide(X1,X2),double_divide(identity,identity)),double_divide(X0,X2))) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1] : multiply(X0,X1) = double_divide(double_divide(X1,X0),identity),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0] : inverse(X0) = double_divide(X0,identity),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f9,plain,
! [X0] : identity = double_divide(X0,inverse(X0)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f10,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,definition,
sF1_fnc = multiply(a3,b3),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f12,definition,
sF0_fnc = multiply(sF1_fnc,c3),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f13,definition,
sF3_fnc = multiply(b3,c3),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f14,definition,
sF2_fnc = multiply(a3,sF3_fnc),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f15,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f10,f14,f13,f12,f11]) ).
fof(f40,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f51,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,X0),double_divide(double_divide(double_divide(X1,X2),inverse(identity)),double_divide(X0,X2))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f6]) ).
fof(f54,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(double_divide(inverse(X1),inverse(identity)),double_divide(X0,identity))) = X1,
inference(paramodulation,[status(thm)],[f8,f51]) ).
fof(f58,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(double_divide(inverse(X1),inverse(identity)),inverse(X0))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f54]) ).
fof(f73,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),double_divide(double_divide(double_divide(X1,inverse(X0)),inverse(identity)),identity)) = X1,
inference(paramodulation,[status(thm)],[f9,f51]) ).
fof(f75,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f40]) ).
fof(f79,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),inverse(double_divide(double_divide(X1,inverse(X0)),inverse(identity)))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f73]) ).
fof(f80,plain,
! [X0,X1] : double_divide(double_divide(identity,X0),multiply(inverse(identity),double_divide(X1,inverse(X0)))) = X1,
inference(forward_demodulation,[status(thm)],[f40,f79]) ).
fof(f301,plain,
! [X0] : double_divide(double_divide(identity,double_divide(inverse(X0),inverse(identity))),identity) = X0,
inference(paramodulation,[status(thm)],[f9,f58]) ).
fof(f314,plain,
! [X0] : inverse(double_divide(identity,double_divide(inverse(X0),inverse(identity)))) = X0,
inference(forward_demodulation,[status(thm)],[f8,f301]) ).
fof(f315,plain,
! [X0] : multiply(double_divide(inverse(X0),inverse(identity)),identity) = X0,
inference(forward_demodulation,[status(thm)],[f40,f314]) ).
fof(f370,plain,
! [X0] : double_divide(double_divide(identity,X0),multiply(inverse(identity),identity)) = X0,
inference(paramodulation,[status(thm)],[f9,f80]) ).
fof(f382,plain,
! [X0] : double_divide(double_divide(identity,X0),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f75,f370]) ).
fof(f440,plain,
double_divide(identity,inverse(identity)) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f382]) ).
fof(f462,plain,
identity = inverse(identity),
inference(forward_demodulation,[status(thm)],[f9,f440]) ).
fof(f472,plain,
! [X0] : double_divide(double_divide(identity,X0),identity) = X0,
inference(backward_demodulation,[status(thm)],[f462,f382]) ).
fof(f480,plain,
! [X0] : multiply(double_divide(inverse(X0),identity),identity) = X0,
inference(backward_demodulation,[status(thm)],[f462,f315]) ).
fof(f492,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,X0),double_divide(double_divide(double_divide(X1,X2),identity),double_divide(X0,X2))) = X1,
inference(backward_demodulation,[status(thm)],[f462,f51]) ).
fof(f494,plain,
! [X0] : inverse(double_divide(identity,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f472]) ).
fof(f495,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[status(thm)],[f40,f494]) ).
fof(f506,plain,
! [X0] : multiply(inverse(inverse(X0)),identity) = X0,
inference(forward_demodulation,[status(thm)],[f8,f480]) ).
fof(f519,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,X0),double_divide(inverse(double_divide(X1,X2)),double_divide(X0,X2))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f492]) ).
fof(f520,plain,
! [X0,X1,X2] : double_divide(double_divide(identity,X0),double_divide(multiply(X1,X2),double_divide(X0,X1))) = X2,
inference(forward_demodulation,[status(thm)],[f40,f519]) ).
fof(f537,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f495,f506]) ).
fof(f540,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = double_divide(X1,X0),
inference(paramodulation,[status(thm)],[f40,f537]) ).
fof(f542,plain,
! [X0] : identity = double_divide(inverse(X0),X0),
inference(paramodulation,[status(thm)],[f537,f9]) ).
fof(f615,plain,
inverse(sF2_fnc) = double_divide(sF3_fnc,a3),
inference(paramodulation,[status(thm)],[f14,f540]) ).
fof(f616,plain,
inverse(sF1_fnc) = double_divide(b3,a3),
inference(paramodulation,[status(thm)],[f11,f540]) ).
fof(f618,plain,
! [X0] : inverse(X0) = double_divide(identity,X0),
inference(paramodulation,[status(thm)],[f495,f540]) ).
fof(f657,plain,
! [X0,X1,X2] : double_divide(inverse(X0),double_divide(multiply(X1,X2),double_divide(X0,X1))) = X2,
inference(forward_demodulation,[status(thm)],[f618,f520]) ).
fof(f664,plain,
! [X0] : double_divide(inverse(X0),double_divide(sF3_fnc,double_divide(X0,b3))) = c3,
inference(paramodulation,[status(thm)],[f13,f657]) ).
fof(f673,plain,
! [X0,X1] : double_divide(inverse(inverse(X0)),double_divide(multiply(X0,X1),identity)) = X1,
inference(paramodulation,[status(thm)],[f542,f657]) ).
fof(f694,plain,
! [X0,X1] : double_divide(X0,double_divide(multiply(X0,X1),identity)) = X1,
inference(forward_demodulation,[status(thm)],[f537,f673]) ).
fof(f695,plain,
! [X0,X1] : double_divide(X0,inverse(multiply(X0,X1))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f694]) ).
fof(f696,plain,
! [X0,X1] : double_divide(X0,double_divide(X1,X0)) = X1,
inference(forward_demodulation,[status(thm)],[f540,f695]) ).
fof(f905,plain,
! [X0,X1] : double_divide(double_divide(X0,X1),X0) = X1,
inference(paramodulation,[status(thm)],[f696,f696]) ).
fof(f920,plain,
double_divide(inverse(sF1_fnc),b3) = a3,
inference(paramodulation,[status(thm)],[f616,f905]) ).
fof(f940,plain,
! [X0,X1] : multiply(X0,double_divide(X0,X1)) = inverse(X1),
inference(paramodulation,[status(thm)],[f905,f40]) ).
fof(f1037,plain,
double_divide(inverse(inverse(sF1_fnc)),double_divide(sF3_fnc,a3)) = c3,
inference(paramodulation,[status(thm)],[f920,f664]) ).
fof(f1045,plain,
double_divide(sF1_fnc,double_divide(sF3_fnc,a3)) = c3,
inference(forward_demodulation,[status(thm)],[f537,f1037]) ).
fof(f1046,plain,
double_divide(sF1_fnc,inverse(sF2_fnc)) = c3,
inference(forward_demodulation,[status(thm)],[f615,f1045]) ).
fof(f1339,plain,
multiply(sF1_fnc,c3) = inverse(inverse(sF2_fnc)),
inference(paramodulation,[status(thm)],[f1046,f940]) ).
fof(f1347,plain,
sF0_fnc = inverse(inverse(sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f12,f1339]) ).
fof(f1348,plain,
sF0_fnc = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f537,f1347]) ).
fof(f1349,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1348,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP495-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n016.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Sun Sep 20 20:19:23 UTC 2026
% 0.10/0.34 % CPUTime :
% 0.10/0.35 % Drodi V4.1.1
% 0.13/0.36 % Refutation found
% 0.13/0.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.38 % Elapsed time: 0.026987 seconds
% 0.13/0.38 % CPU time: 0.069827 seconds
% 0.13/0.38 % Total memory used: 3.679 MB
% 0.13/0.38 % Net memory used: 3.515 MB
%------------------------------------------------------------------------------