%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP550-1 : 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 12:34:39 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.37s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 38 unt; 0 def)
% Number of atoms : 38 ( 37 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 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 : 43 ( 43 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : divide(divide(identity,A),divide(divide(divide(B,A),C),B)) = C,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : multiply(A,B) = divide(A,divide(identity,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : inverse(A) = divide(identity,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : identity = divide(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : divide(divide(identity,X0),divide(divide(divide(X1,X0),X2),X1)) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,divide(identity,X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0] : inverse(X0) = divide(identity,X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f9,plain,
! [X0] : identity = divide(X0,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f10,plain,
multiply(multiply(inverse(b2),b2),a2) != a2,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(forward_demodulation,[status(thm)],[f8,f7]) ).
fof(f16,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f15]) ).
fof(f18,plain,
! [X0] : multiply(identity,inverse(X0)) = inverse(multiply(identity,X0)),
inference(paramodulation,[status(thm)],[f16,f16]) ).
fof(f26,plain,
identity = inverse(identity),
inference(paramodulation,[status(thm)],[f8,f9]) ).
fof(f28,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(paramodulation,[status(thm)],[f15,f9]) ).
fof(f33,plain,
! [X0] : multiply(X0,identity) = divide(X0,identity),
inference(paramodulation,[status(thm)],[f26,f15]) ).
fof(f40,plain,
multiply(identity,a2) != a2,
inference(backward_demodulation,[status(thm)],[f28,f10]) ).
fof(f42,plain,
! [X0] : identity = multiply(multiply(identity,inverse(X0)),multiply(identity,X0)),
inference(paramodulation,[status(thm)],[f18,f28]) ).
fof(f100,plain,
! [X0,X1,X2] : divide(inverse(X0),divide(divide(divide(X1,X0),X2),X1)) = X2,
inference(forward_demodulation,[status(thm)],[f8,f6]) ).
fof(f108,plain,
! [X0,X1] : divide(inverse(X0),divide(identity,X1)) = divide(X1,X0),
inference(paramodulation,[status(thm)],[f9,f100]) ).
fof(f117,plain,
! [X0,X1] : divide(inverse(X0),inverse(X1)) = divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f8,f108]) ).
fof(f118,plain,
! [X0,X1] : multiply(inverse(X0),X1) = divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f15,f117]) ).
fof(f124,plain,
! [X0] : divide(inverse(X0),identity) = divide(identity,X0),
inference(paramodulation,[status(thm)],[f33,f118]) ).
fof(f125,plain,
! [X0] : multiply(identity,X0) = divide(X0,identity),
inference(paramodulation,[status(thm)],[f26,f118]) ).
fof(f129,plain,
! [X0] : divide(inverse(X0),identity) = inverse(X0),
inference(forward_demodulation,[status(thm)],[f8,f124]) ).
fof(f142,plain,
divide(a2,identity) != a2,
inference(backward_demodulation,[status(thm)],[f125,f40]) ).
fof(f143,plain,
! [X0] : identity = multiply(divide(inverse(X0),identity),multiply(identity,X0)),
inference(backward_demodulation,[status(thm)],[f125,f42]) ).
fof(f147,plain,
! [X0] : divide(X0,identity) = inverse(inverse(X0)),
inference(backward_demodulation,[status(thm)],[f125,f16]) ).
fof(f150,plain,
! [X0] : identity = multiply(inverse(X0),multiply(identity,X0)),
inference(forward_demodulation,[status(thm)],[f129,f143]) ).
fof(f151,plain,
! [X0] : identity = divide(multiply(identity,X0),X0),
inference(forward_demodulation,[status(thm)],[f118,f150]) ).
fof(f152,plain,
! [X0] : identity = divide(divide(X0,identity),X0),
inference(forward_demodulation,[status(thm)],[f125,f151]) ).
fof(f170,plain,
! [X0] : divide(inverse(identity),divide(identity,X0)) = X0,
inference(paramodulation,[status(thm)],[f152,f100]) ).
fof(f183,plain,
! [X0] : divide(identity,divide(identity,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f26,f170]) ).
fof(f184,plain,
! [X0] : inverse(divide(identity,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f183]) ).
fof(f185,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f184]) ).
fof(f186,plain,
! [X0] : divide(X0,identity) = X0,
inference(forward_demodulation,[status(thm)],[f147,f185]) ).
fof(f190,plain,
a2 != a2,
inference(backward_demodulation,[status(thm)],[f186,f142]) ).
fof(f203,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f190]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP550-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n026.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:19:07 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.37 % Refutation found
% 0.09/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.39 % Elapsed time: 0.029696 seconds
% 0.09/0.39 % CPU time: 0.047992 seconds
% 0.09/0.39 % Total memory used: 1.940 MB
% 0.09/0.39 % Net memory used: 1.902 MB
%------------------------------------------------------------------------------