%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP585-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 12:34:44 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.36s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 7
% Syntax : Number of formulae : 59 ( 59 unt; 4 def)
% Number of atoms : 59 ( 58 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 49 ( 49 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = inverse(double_divide(B,A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2] : double_divide(X0,inverse(double_divide(inverse(double_divide(double_divide(X0,X1),inverse(X2))),X1))) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f6,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f7,definition,
sF1_fnc = inverse(a1),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f8,definition,
sF0_fnc = multiply(sF1_fnc,a1),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f9,definition,
sF3_fnc = inverse(b1),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f10,definition,
sF2_fnc = multiply(sF3_fnc,b1),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f11,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f6,f10,f9,f8,f7]) ).
fof(f12,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,inverse(double_divide(double_divide(X0,X1),inverse(X2))))) = X2,
inference(forward_demodulation,[status(thm)],[f5,f4]) ).
fof(f13,plain,
! [X0,X1,X2] : double_divide(X0,multiply(X1,multiply(inverse(X2),double_divide(X0,X1)))) = X2,
inference(forward_demodulation,[status(thm)],[f5,f12]) ).
fof(f15,plain,
! [X0,X1] : double_divide(X0,multiply(X1,multiply(sF3_fnc,double_divide(X0,X1)))) = b1,
inference(paramodulation,[status(thm)],[f9,f13]) ).
fof(f16,plain,
! [X0,X1] : double_divide(X0,multiply(X1,multiply(sF1_fnc,double_divide(X0,X1)))) = a1,
inference(paramodulation,[status(thm)],[f7,f13]) ).
fof(f17,plain,
! [X0,X1,X2,X3] : double_divide(X0,multiply(multiply(X1,multiply(inverse(X2),double_divide(X0,X1))),multiply(inverse(X3),X2))) = X3,
inference(paramodulation,[status(thm)],[f13,f13]) ).
fof(f18,plain,
! [X0,X1,X2] : multiply(multiply(X0,multiply(inverse(X1),double_divide(X2,X0))),X2) = inverse(X1),
inference(paramodulation,[status(thm)],[f13,f5]) ).
fof(f19,plain,
! [X0,X1] : double_divide(X0,multiply(multiply(X1,multiply(sF3_fnc,double_divide(X0,X1))),multiply(sF3_fnc,b1))) = b1,
inference(paramodulation,[status(thm)],[f15,f15]) ).
fof(f22,plain,
! [X0,X1] : multiply(multiply(X0,multiply(sF3_fnc,double_divide(X1,X0))),X1) = inverse(b1),
inference(paramodulation,[status(thm)],[f15,f5]) ).
fof(f23,plain,
! [X0,X1] : double_divide(X0,multiply(multiply(X1,multiply(sF3_fnc,double_divide(X0,X1))),sF2_fnc)) = b1,
inference(forward_demodulation,[status(thm)],[f10,f19]) ).
fof(f24,plain,
! [X0,X1] : multiply(multiply(X0,multiply(sF3_fnc,double_divide(X1,X0))),X1) = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f9,f22]) ).
fof(f30,plain,
! [X0,X1] : multiply(multiply(X0,multiply(sF1_fnc,double_divide(X1,X0))),X1) = inverse(a1),
inference(paramodulation,[status(thm)],[f16,f5]) ).
fof(f32,plain,
! [X0,X1] : multiply(multiply(X0,multiply(sF1_fnc,double_divide(X1,X0))),X1) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f7,f30]) ).
fof(f73,plain,
! [X0,X1] : double_divide(multiply(inverse(X0),X1),inverse(X1)) = X0,
inference(paramodulation,[status(thm)],[f18,f17]) ).
fof(f93,plain,
double_divide(sF2_fnc,sF3_fnc) = b1,
inference(paramodulation,[status(thm)],[f24,f23]) ).
fof(f123,plain,
multiply(sF3_fnc,sF2_fnc) = inverse(b1),
inference(paramodulation,[status(thm)],[f93,f5]) ).
fof(f127,plain,
multiply(sF3_fnc,sF2_fnc) = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f9,f123]) ).
fof(f131,plain,
! [X0] : double_divide(multiply(sF3_fnc,X0),inverse(X0)) = b1,
inference(paramodulation,[status(thm)],[f9,f73]) ).
fof(f132,plain,
! [X0] : double_divide(multiply(sF1_fnc,X0),inverse(X0)) = a1,
inference(paramodulation,[status(thm)],[f7,f73]) ).
fof(f148,plain,
double_divide(sF3_fnc,inverse(sF2_fnc)) = b1,
inference(paramodulation,[status(thm)],[f127,f131]) ).
fof(f162,plain,
! [X0] : multiply(inverse(X0),multiply(sF3_fnc,X0)) = inverse(b1),
inference(paramodulation,[status(thm)],[f131,f5]) ).
fof(f168,plain,
! [X0] : multiply(inverse(X0),multiply(sF3_fnc,X0)) = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f9,f162]) ).
fof(f178,plain,
multiply(inverse(sF2_fnc),sF3_fnc) = inverse(b1),
inference(paramodulation,[status(thm)],[f148,f5]) ).
fof(f182,plain,
multiply(inverse(sF2_fnc),sF3_fnc) = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f9,f178]) ).
fof(f183,plain,
double_divide(sF3_fnc,inverse(sF3_fnc)) = sF2_fnc,
inference(paramodulation,[status(thm)],[f182,f73]) ).
fof(f196,plain,
multiply(inverse(sF3_fnc),sF3_fnc) = inverse(sF2_fnc),
inference(paramodulation,[status(thm)],[f183,f5]) ).
fof(f200,plain,
double_divide(sF0_fnc,inverse(a1)) = a1,
inference(paramodulation,[status(thm)],[f8,f132]) ).
fof(f213,plain,
! [X0] : multiply(inverse(X0),multiply(sF1_fnc,X0)) = inverse(a1),
inference(paramodulation,[status(thm)],[f132,f5]) ).
fof(f214,plain,
double_divide(sF0_fnc,sF1_fnc) = a1,
inference(forward_demodulation,[status(thm)],[f7,f200]) ).
fof(f218,plain,
! [X0] : multiply(inverse(X0),multiply(sF1_fnc,X0)) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f7,f213]) ).
fof(f228,plain,
multiply(sF1_fnc,sF0_fnc) = inverse(a1),
inference(paramodulation,[status(thm)],[f214,f5]) ).
fof(f231,plain,
multiply(sF1_fnc,sF0_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f7,f228]) ).
fof(f343,plain,
double_divide(sF1_fnc,inverse(sF0_fnc)) = a1,
inference(paramodulation,[status(thm)],[f231,f132]) ).
fof(f358,plain,
multiply(inverse(sF0_fnc),sF1_fnc) = inverse(a1),
inference(paramodulation,[status(thm)],[f343,f5]) ).
fof(f362,plain,
multiply(inverse(sF0_fnc),sF1_fnc) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f7,f358]) ).
fof(f363,plain,
double_divide(sF1_fnc,inverse(sF1_fnc)) = sF0_fnc,
inference(paramodulation,[status(thm)],[f362,f73]) ).
fof(f489,plain,
! [X0] : double_divide(sF3_fnc,inverse(multiply(sF3_fnc,X0))) = X0,
inference(paramodulation,[status(thm)],[f168,f73]) ).
fof(f495,plain,
double_divide(inverse(sF2_fnc),inverse(sF3_fnc)) = sF3_fnc,
inference(paramodulation,[status(thm)],[f196,f73]) ).
fof(f522,plain,
! [X0] : double_divide(sF1_fnc,inverse(multiply(sF1_fnc,X0))) = X0,
inference(paramodulation,[status(thm)],[f218,f73]) ).
fof(f674,plain,
multiply(multiply(inverse(sF3_fnc),multiply(sF1_fnc,sF3_fnc)),inverse(sF2_fnc)) = sF1_fnc,
inference(paramodulation,[status(thm)],[f495,f32]) ).
fof(f675,plain,
multiply(multiply(inverse(sF3_fnc),multiply(sF3_fnc,sF3_fnc)),inverse(sF2_fnc)) = sF3_fnc,
inference(paramodulation,[status(thm)],[f495,f24]) ).
fof(f688,plain,
multiply(sF1_fnc,inverse(sF2_fnc)) = sF1_fnc,
inference(forward_demodulation,[status(thm)],[f218,f674]) ).
fof(f689,plain,
multiply(sF3_fnc,inverse(sF2_fnc)) = sF3_fnc,
inference(forward_demodulation,[status(thm)],[f168,f675]) ).
fof(f950,plain,
double_divide(sF3_fnc,inverse(sF3_fnc)) = inverse(sF2_fnc),
inference(paramodulation,[status(thm)],[f689,f489]) ).
fof(f956,plain,
sF2_fnc = inverse(sF2_fnc),
inference(forward_demodulation,[status(thm)],[f183,f950]) ).
fof(f960,plain,
multiply(sF1_fnc,sF2_fnc) = sF1_fnc,
inference(backward_demodulation,[status(thm)],[f956,f688]) ).
fof(f1671,plain,
double_divide(sF1_fnc,inverse(sF1_fnc)) = sF2_fnc,
inference(paramodulation,[status(thm)],[f960,f522]) ).
fof(f1701,plain,
sF0_fnc = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f363,f1671]) ).
fof(f1702,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1701,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP585-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n004.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sun Sep 20 20:17:20 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 0.11/0.36 % Refutation found
% 0.11/0.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.39 % Elapsed time: 0.039254 seconds
% 0.11/0.39 % CPU time: 0.084744 seconds
% 0.11/0.39 % Total memory used: 4.883 MB
% 0.11/0.39 % Net memory used: 4.856 MB
%------------------------------------------------------------------------------