%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP482-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 12:34:29 PM UTC 2026
% Result : Unsatisfiable 0.25s 0.75s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 5
% Syntax : Number of formulae : 58 ( 58 unt; 0 def)
% Number of atoms : 58 ( 57 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 144 ( 144 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C,D] : double_divide(double_divide(double_divide(A,double_divide(B,identity)),double_divide(double_divide(C,double_divide(D,double_divide(D,identity))),double_divide(A,identity))),B) = C,
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,X3] : double_divide(double_divide(double_divide(X0,double_divide(X1,identity)),double_divide(double_divide(X2,double_divide(X3,double_divide(X3,identity))),double_divide(X0,identity))),X1) = X2,
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(f20,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,double_divide(X1,identity)),X2),X1) = double_divide(double_divide(X2,double_divide(X3,double_divide(X3,identity))),double_divide(double_divide(X0,identity),identity)),
inference(paramodulation,[status(thm)],[f6,f6]) ).
fof(f21,plain,
! [X0,X1,X2,X3,X4,X5] : double_divide(double_divide(double_divide(X0,double_divide(X1,identity)),double_divide(X2,double_divide(X0,identity))),X1) = double_divide(double_divide(X3,double_divide(double_divide(X4,double_divide(X4,identity)),identity)),double_divide(double_divide(X2,double_divide(X5,double_divide(X5,identity))),double_divide(X3,identity))),
inference(paramodulation,[status(thm)],[f6,f6]) ).
fof(f31,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,double_divide(X1,identity)),X2),X1) = double_divide(double_divide(X2,double_divide(X3,double_divide(X3,identity))),multiply(identity,X0)),
inference(forward_demodulation,[status(thm)],[f7,f20]) ).
fof(f32,plain,
! [X0,X1,X2,X3,X4,X5] : double_divide(double_divide(double_divide(X0,double_divide(X1,identity)),double_divide(X2,double_divide(X0,identity))),X1) = double_divide(double_divide(X3,multiply(double_divide(X4,identity),X4)),double_divide(double_divide(X2,double_divide(X5,double_divide(X5,identity))),double_divide(X3,identity))),
inference(forward_demodulation,[status(thm)],[f7,f21]) ).
fof(f411,plain,
! [X0,X1] : multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f417,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,double_divide(X1,identity)),double_divide(double_divide(X2,double_divide(X3,double_divide(X3,identity))),inverse(X0))),X1) = X2,
inference(backward_demodulation,[status(thm)],[f8,f6]) ).
fof(f438,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,inverse(X1)),double_divide(double_divide(X2,double_divide(X3,double_divide(X3,identity))),inverse(X0))),X1) = X2,
inference(forward_demodulation,[status(thm)],[f8,f417]) ).
fof(f439,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,inverse(X1)),double_divide(double_divide(X2,double_divide(X3,inverse(X3))),inverse(X0))),X1) = X2,
inference(forward_demodulation,[status(thm)],[f8,f438]) ).
fof(f440,plain,
! [X0,X1,X2] : double_divide(double_divide(double_divide(X0,inverse(X1)),double_divide(double_divide(X2,identity),inverse(X0))),X1) = X2,
inference(forward_demodulation,[status(thm)],[f9,f439]) ).
fof(f441,plain,
! [X0,X1,X2] : double_divide(double_divide(double_divide(X0,inverse(X1)),double_divide(inverse(X2),inverse(X0))),X1) = X2,
inference(forward_demodulation,[status(thm)],[f8,f440]) ).
fof(f442,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f411]) ).
fof(f443,plain,
! [X0] : multiply(inverse(X0),X0) = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f411]) ).
fof(f449,plain,
! [X0] : identity = double_divide(inverse(X0),multiply(identity,X0)),
inference(paramodulation,[status(thm)],[f442,f9]) ).
fof(f525,plain,
! [X0,X1] : double_divide(double_divide(double_divide(inverse(X0),inverse(X1)),identity),X1) = X0,
inference(paramodulation,[status(thm)],[f9,f441]) ).
fof(f540,plain,
! [X0,X1] : double_divide(inverse(double_divide(inverse(X0),inverse(X1))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f8,f525]) ).
fof(f541,plain,
! [X0,X1] : double_divide(multiply(inverse(X0),inverse(X1)),X0) = X1,
inference(forward_demodulation,[status(thm)],[f411,f540]) ).
fof(f543,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,inverse(X1)),X2),X1) = double_divide(double_divide(X2,double_divide(X3,double_divide(X3,identity))),multiply(identity,X0)),
inference(forward_demodulation,[status(thm)],[f8,f31]) ).
fof(f544,plain,
! [X0,X1,X2,X3] : double_divide(double_divide(double_divide(X0,inverse(X1)),X2),X1) = double_divide(double_divide(X2,double_divide(X3,inverse(X3))),multiply(identity,X0)),
inference(forward_demodulation,[status(thm)],[f8,f543]) ).
fof(f545,plain,
! [X0,X1,X2] : double_divide(double_divide(double_divide(X0,inverse(X1)),X2),X1) = double_divide(double_divide(X2,identity),multiply(identity,X0)),
inference(forward_demodulation,[status(thm)],[f9,f544]) ).
fof(f546,plain,
! [X0,X1] : double_divide(inverse(double_divide(inverse(X0),inverse(X1))),multiply(identity,X1)) = X0,
inference(backward_demodulation,[status(thm)],[f547,f441]) ).
fof(f547,plain,
! [X0,X1,X2] : double_divide(double_divide(double_divide(X0,inverse(X1)),X2),X1) = double_divide(inverse(X2),multiply(identity,X0)),
inference(forward_demodulation,[status(thm)],[f8,f545]) ).
fof(f563,plain,
! [X0,X1] : double_divide(multiply(inverse(X0),inverse(X1)),multiply(identity,X0)) = X1,
inference(forward_demodulation,[status(thm)],[f411,f546]) ).
fof(f590,plain,
! [X0] : double_divide(inverse(identity),inverse(X0)) = X0,
inference(paramodulation,[status(thm)],[f443,f541]) ).
fof(f604,plain,
identity = inverse(identity),
inference(paramodulation,[status(thm)],[f9,f590]) ).
fof(f614,plain,
! [X0] : double_divide(identity,inverse(X0)) = X0,
inference(backward_demodulation,[status(thm)],[f604,f590]) ).
fof(f617,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(backward_demodulation,[status(thm)],[f604,f443]) ).
fof(f658,plain,
! [X0,X1,X2,X3,X4,X5] : double_divide(double_divide(double_divide(X0,inverse(X1)),double_divide(X2,double_divide(X0,identity))),X1) = double_divide(double_divide(X3,multiply(double_divide(X4,identity),X4)),double_divide(double_divide(X2,double_divide(X5,double_divide(X5,identity))),double_divide(X3,identity))),
inference(forward_demodulation,[status(thm)],[f8,f32]) ).
fof(f659,plain,
! [X0,X1,X2,X3,X4] : double_divide(inverse(double_divide(X0,double_divide(X1,identity))),multiply(identity,X1)) = double_divide(double_divide(X2,multiply(double_divide(X3,identity),X3)),double_divide(double_divide(X0,double_divide(X4,double_divide(X4,identity))),double_divide(X2,identity))),
inference(forward_demodulation,[status(thm)],[f547,f658]) ).
fof(f660,plain,
! [X0,X1,X2,X3,X4] : double_divide(multiply(double_divide(X0,identity),X1),multiply(identity,X0)) = double_divide(double_divide(X2,multiply(double_divide(X3,identity),X3)),double_divide(double_divide(X1,double_divide(X4,double_divide(X4,identity))),double_divide(X2,identity))),
inference(forward_demodulation,[status(thm)],[f411,f659]) ).
fof(f661,plain,
! [X0,X1,X2,X3,X4] : double_divide(multiply(inverse(X0),X1),multiply(identity,X0)) = double_divide(double_divide(X2,multiply(double_divide(X3,identity),X3)),double_divide(double_divide(X1,double_divide(X4,double_divide(X4,identity))),double_divide(X2,identity))),
inference(forward_demodulation,[status(thm)],[f8,f660]) ).
fof(f662,plain,
! [X0,X1,X2,X3,X4] : double_divide(multiply(inverse(X0),X1),multiply(identity,X0)) = double_divide(double_divide(X2,multiply(inverse(X3),X3)),double_divide(double_divide(X1,double_divide(X4,double_divide(X4,identity))),double_divide(X2,identity))),
inference(forward_demodulation,[status(thm)],[f8,f661]) ).
fof(f663,plain,
! [X0,X1,X2,X3] : double_divide(multiply(inverse(X0),X1),multiply(identity,X0)) = double_divide(double_divide(X2,identity),double_divide(double_divide(X1,double_divide(X3,double_divide(X3,identity))),double_divide(X2,identity))),
inference(forward_demodulation,[status(thm)],[f617,f662]) ).
fof(f664,plain,
! [X0,X1,X2,X3] : double_divide(multiply(inverse(X0),X1),multiply(identity,X0)) = double_divide(inverse(X2),double_divide(double_divide(X1,double_divide(X3,double_divide(X3,identity))),double_divide(X2,identity))),
inference(forward_demodulation,[status(thm)],[f8,f663]) ).
fof(f665,plain,
! [X0,X1,X2,X3] : double_divide(multiply(inverse(X0),X1),multiply(identity,X0)) = double_divide(inverse(X2),double_divide(double_divide(X1,double_divide(X3,inverse(X3))),double_divide(X2,identity))),
inference(forward_demodulation,[status(thm)],[f8,f664]) ).
fof(f666,plain,
! [X0,X1,X2] : double_divide(multiply(inverse(X0),X1),multiply(identity,X0)) = double_divide(inverse(X2),double_divide(double_divide(X1,identity),double_divide(X2,identity))),
inference(forward_demodulation,[status(thm)],[f9,f665]) ).
fof(f667,plain,
! [X0,X1,X2] : double_divide(multiply(inverse(X0),X1),multiply(identity,X0)) = double_divide(inverse(X2),double_divide(inverse(X1),double_divide(X2,identity))),
inference(forward_demodulation,[status(thm)],[f8,f666]) ).
fof(f668,plain,
! [X0,X1,X2] : double_divide(multiply(inverse(X0),X1),multiply(identity,X0)) = double_divide(inverse(X2),double_divide(inverse(X1),inverse(X2))),
inference(forward_demodulation,[status(thm)],[f8,f667]) ).
fof(f729,plain,
! [X0] : multiply(inverse(X0),identity) = inverse(X0),
inference(paramodulation,[status(thm)],[f614,f411]) ).
fof(f756,plain,
! [X0,X1] : double_divide(inverse(X0),multiply(identity,X0)) = double_divide(inverse(X1),double_divide(inverse(identity),inverse(X1))),
inference(paramodulation,[status(thm)],[f729,f668]) ).
fof(f763,plain,
! [X0] : identity = double_divide(inverse(X0),double_divide(inverse(identity),inverse(X0))),
inference(forward_demodulation,[status(thm)],[f449,f756]) ).
fof(f764,plain,
! [X0] : identity = double_divide(inverse(X0),double_divide(identity,inverse(X0))),
inference(forward_demodulation,[status(thm)],[f604,f763]) ).
fof(f765,plain,
! [X0] : identity = double_divide(inverse(X0),X0),
inference(forward_demodulation,[status(thm)],[f614,f764]) ).
fof(f772,plain,
! [X0,X1] : double_divide(multiply(inverse(X0),inverse(X1)),multiply(identity,X0)) = double_divide(inverse(X1),identity),
inference(paramodulation,[status(thm)],[f765,f668]) ).
fof(f780,plain,
! [X0] : X0 = double_divide(inverse(X0),identity),
inference(forward_demodulation,[status(thm)],[f563,f772]) ).
fof(f781,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f8,f780]) ).
fof(f782,plain,
! [X0] : X0 = multiply(identity,X0),
inference(forward_demodulation,[status(thm)],[f442,f781]) ).
fof(f793,plain,
a2 != a2,
inference(backward_demodulation,[status(thm)],[f782,f10]) ).
fof(f801,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f793]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP482-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.70 % Computer : n003.cluster.edu
% 0.20/0.70 % Model : x86_64 x86_64
% 0.20/0.70 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.70 % Memory : 8046.5625MB
% 0.20/0.70 % OS : Linux 6.8.0-71-generic
% 0.20/0.70 % CPULimit : 300
% 0.20/0.70 % WCLimit : 300
% 0.20/0.70 % DateTime : Sun Sep 20 20:16:01 UTC 2026
% 0.20/0.71 % CPUTime :
% 0.25/0.73 % Drodi V4.1.1
% 0.25/0.75 % Refutation found
% 0.25/0.75 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.25/0.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.25/0.82 % Elapsed time: 0.080144 seconds
% 0.25/0.82 % CPU time: 0.146329 seconds
% 0.25/0.82 % Total memory used: 5.033 MB
% 0.25/0.82 % Net memory used: 4.931 MB
%------------------------------------------------------------------------------