%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP574-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 12:34:42 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 6
% Syntax : Number of formulae : 61 ( 61 unt; 1 def)
% Number of atoms : 61 ( 60 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 78 ( 78 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : double_divide(double_divide(A,double_divide(double_divide(B,double_divide(C,A)),double_divide(C,identity))),double_divide(identity,identity)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = double_divide(double_divide(B,A),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : inverse(A) = double_divide(A,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : identity = double_divide(A,inverse(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
multiply(identity,a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X2,X0)),double_divide(X2,identity))),double_divide(identity,identity)) = 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(identity,a2) != a2,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,definition,
sF0_fnc = multiply(identity,a2),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f12,plain,
sF0_fnc != a2,
inference(definition_folding,[],[f10,f11]) ).
fof(f25,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(double_divide(X2,X3),X0)),multiply(X3,X2))),double_divide(identity,identity)) = X1,
inference(paramodulation,[status(thm)],[f7,f6]) ).
fof(f251,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(double_divide(X2,X3),X0)),multiply(X3,X2))),inverse(identity)) = X1,
inference(backward_demodulation,[status(thm)],[f8,f25]) ).
fof(f255,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X2,X0)),double_divide(X2,identity))),inverse(identity)) = X1,
inference(backward_demodulation,[status(thm)],[f8,f6]) ).
fof(f258,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f267,plain,
! [X0,X1,X2] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(X2,X0)),inverse(X2))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f255]) ).
fof(f269,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f258]) ).
fof(f270,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f258]) ).
fof(f273,plain,
sF0_fnc = inverse(inverse(a2)),
inference(backward_demodulation,[status(thm)],[f270,f11]) ).
fof(f275,plain,
identity = double_divide(inverse(a2),sF0_fnc),
inference(paramodulation,[status(thm)],[f273,f9]) ).
fof(f294,plain,
! [X0] : double_divide(double_divide(sF0_fnc,double_divide(double_divide(X0,identity),inverse(inverse(a2)))),inverse(identity)) = X0,
inference(paramodulation,[status(thm)],[f275,f267]) ).
fof(f295,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),double_divide(double_divide(X1,identity),inverse(X0))),inverse(identity)) = X1,
inference(paramodulation,[status(thm)],[f9,f267]) ).
fof(f304,plain,
! [X0] : double_divide(double_divide(sF0_fnc,double_divide(inverse(X0),inverse(inverse(a2)))),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f294]) ).
fof(f305,plain,
! [X0] : double_divide(double_divide(sF0_fnc,double_divide(inverse(X0),sF0_fnc)),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f273,f304]) ).
fof(f306,plain,
! [X0,X1] : double_divide(double_divide(inverse(X0),double_divide(inverse(X1),inverse(X0))),inverse(identity)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f295]) ).
fof(f357,plain,
double_divide(double_divide(sF0_fnc,identity),inverse(identity)) = a2,
inference(paramodulation,[status(thm)],[f275,f305]) ).
fof(f365,plain,
double_divide(inverse(sF0_fnc),inverse(identity)) = a2,
inference(forward_demodulation,[status(thm)],[f8,f357]) ).
fof(f430,plain,
! [X0] : double_divide(double_divide(inverse(inverse(X0)),identity),inverse(identity)) = X0,
inference(paramodulation,[status(thm)],[f9,f306]) ).
fof(f443,plain,
! [X0] : double_divide(inverse(inverse(inverse(X0))),inverse(identity)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f430]) ).
fof(f451,plain,
! [X0] : double_divide(double_divide(inverse(identity),X0),inverse(identity)) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f443,f306]) ).
fof(f562,plain,
! [X0] : X0 = inverse(inverse(double_divide(inverse(X0),inverse(identity)))),
inference(paramodulation,[status(thm)],[f306,f451]) ).
fof(f565,plain,
double_divide(identity,inverse(identity)) = inverse(inverse(inverse(inverse(identity)))),
inference(paramodulation,[status(thm)],[f9,f451]) ).
fof(f577,plain,
! [X0] : X0 = inverse(multiply(inverse(identity),inverse(X0))),
inference(forward_demodulation,[status(thm)],[f258,f562]) ).
fof(f581,plain,
identity = inverse(inverse(inverse(inverse(identity)))),
inference(forward_demodulation,[status(thm)],[f9,f565]) ).
fof(f607,plain,
double_divide(identity,inverse(identity)) = inverse(identity),
inference(paramodulation,[status(thm)],[f581,f443]) ).
fof(f621,plain,
identity = inverse(identity),
inference(forward_demodulation,[status(thm)],[f9,f607]) ).
fof(f633,plain,
! [X0] : X0 = inverse(multiply(identity,inverse(X0))),
inference(backward_demodulation,[status(thm)],[f621,f577]) ).
fof(f634,plain,
! [X0] : double_divide(double_divide(inverse(identity),X0),identity) = inverse(inverse(X0)),
inference(backward_demodulation,[status(thm)],[f621,f451]) ).
fof(f647,plain,
double_divide(inverse(sF0_fnc),identity) = a2,
inference(backward_demodulation,[status(thm)],[f621,f365]) ).
fof(f651,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(backward_demodulation,[status(thm)],[f621,f269]) ).
fof(f655,plain,
! [X0] : X0 = inverse(inverse(inverse(inverse(X0)))),
inference(forward_demodulation,[status(thm)],[f270,f633]) ).
fof(f656,plain,
! [X0] : inverse(double_divide(inverse(identity),X0)) = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f8,f634]) ).
fof(f657,plain,
! [X0] : multiply(X0,inverse(identity)) = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f258,f656]) ).
fof(f658,plain,
! [X0] : multiply(X0,identity) = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f621,f657]) ).
fof(f685,plain,
inverse(inverse(sF0_fnc)) = a2,
inference(forward_demodulation,[status(thm)],[f8,f647]) ).
fof(f714,plain,
! [X0] : multiply(X0,inverse(inverse(inverse(X0)))) = identity,
inference(paramodulation,[status(thm)],[f655,f651]) ).
fof(f731,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(X0,double_divide(double_divide(X1,double_divide(double_divide(X2,X3),X0)),multiply(X3,X2))),identity) = X1,
inference(forward_demodulation,[status(thm)],[f621,f251]) ).
fof(f732,plain,
! [X0,X1,X2,X3] : inverse(double_divide(X0,double_divide(double_divide(X1,double_divide(double_divide(X2,X3),X0)),multiply(X3,X2)))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f731]) ).
fof(f733,plain,
! [X0,X1,X2,X3] : multiply(double_divide(double_divide(X0,double_divide(double_divide(X1,X2),X3)),multiply(X2,X1)),X3) = X0,
inference(forward_demodulation,[status(thm)],[f258,f732]) ).
fof(f739,plain,
! [X0,X1,X2] : multiply(double_divide(double_divide(X0,double_divide(identity,X1)),multiply(inverse(X2),X2)),X1) = X0,
inference(paramodulation,[status(thm)],[f9,f733]) ).
fof(f749,plain,
! [X0,X1] : multiply(double_divide(double_divide(X0,double_divide(identity,X1)),identity),X1) = X0,
inference(forward_demodulation,[status(thm)],[f651,f739]) ).
fof(f750,plain,
! [X0,X1] : multiply(inverse(double_divide(X0,double_divide(identity,X1))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f8,f749]) ).
fof(f751,plain,
! [X0,X1] : multiply(multiply(double_divide(identity,X0),X1),X0) = X1,
inference(forward_demodulation,[status(thm)],[f258,f750]) ).
fof(f1173,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(inverse(double_divide(identity,X0)))),
inference(paramodulation,[status(thm)],[f714,f751]) ).
fof(f1184,plain,
! [X0] : inverse(inverse(X0)) = inverse(inverse(inverse(double_divide(identity,X0)))),
inference(forward_demodulation,[status(thm)],[f270,f1173]) ).
fof(f1185,plain,
! [X0] : inverse(inverse(X0)) = inverse(inverse(multiply(X0,identity))),
inference(forward_demodulation,[status(thm)],[f258,f1184]) ).
fof(f1186,plain,
! [X0] : inverse(inverse(X0)) = inverse(inverse(inverse(inverse(X0)))),
inference(forward_demodulation,[status(thm)],[f658,f1185]) ).
fof(f1187,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f655,f1186]) ).
fof(f1202,plain,
sF0_fnc = a2,
inference(backward_demodulation,[status(thm)],[f1187,f685]) ).
fof(f1217,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1202,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP574-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:19:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.42 % Elapsed time: 0.039443 seconds
% 0.10/0.42 % CPU time: 0.171458 seconds
% 0.10/0.42 % Total memory used: 8.686 MB
% 0.10/0.42 % Net memory used: 8.582 MB
%------------------------------------------------------------------------------