%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP091-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 12:32:29 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 5
% Syntax : Number of formulae : 62 ( 54 unt; 0 def)
% Number of atoms : 82 ( 81 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 50 ( 30 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 106 ( 106 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : divide(divide(X,divide(divide(X,Y),Z)),Y) = Z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : multiply(X,Y) = divide(X,divide(divide(Z,Z),Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Z] : inverse(X) = divide(divide(Z,Z),X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : identity = divide(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : divide(divide(X0,divide(divide(X0,X1),X2)),X1) = X2,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0,X1,X2] : multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f8,plain,
! [X0,X1] : inverse(X0) = divide(divide(X1,X1),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(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(backward_demodulation,[status(thm)],[f8,f7]) ).
fof(f12,plain,
! [X0] : inverse(X0) = divide(identity,X0),
inference(backward_demodulation,[status(thm)],[f9,f8]) ).
fof(f13,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f12,f11]) ).
fof(f16,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,multiply(identity,X1)),
inference(paramodulation,[status(thm)],[f13,f11]) ).
fof(f23,plain,
identity = inverse(identity),
inference(paramodulation,[status(thm)],[f12,f9]) ).
fof(f25,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(paramodulation,[status(thm)],[f11,f9]) ).
fof(f29,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(backward_demodulation,[status(thm)],[f25,f10]) ).
fof(f30,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| identity != multiply(inverse(b1),b1) ),
inference(forward_demodulation,[status(thm)],[f25,f29]) ).
fof(f31,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f25,f30]) ).
fof(f32,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2 ),
inference(trivial_equality_resolution,[status(thm)],[f31]) ).
fof(f34,plain,
! [X0] : multiply(X0,identity) = divide(X0,identity),
inference(paramodulation,[status(thm)],[f23,f11]) ).
fof(f58,plain,
! [X0,X1,X2] : multiply(divide(X0,divide(divide(X0,inverse(X1)),X2)),X1) = X2,
inference(paramodulation,[status(thm)],[f11,f6]) ).
fof(f60,plain,
! [X0,X1,X2] : divide(divide(X0,X1),divide(divide(X0,X2),X1)) = X2,
inference(paramodulation,[status(thm)],[f6,f6]) ).
fof(f63,plain,
! [X0,X1,X2] : divide(divide(X0,multiply(divide(X0,X1),X2)),X1) = inverse(X2),
inference(paramodulation,[status(thm)],[f11,f6]) ).
fof(f70,plain,
! [X0,X1] : divide(divide(X0,divide(identity,X1)),X0) = X1,
inference(paramodulation,[status(thm)],[f9,f6]) ).
fof(f78,plain,
! [X0,X1,X2] : multiply(divide(X0,divide(multiply(X0,X1),X2)),X1) = X2,
inference(forward_demodulation,[status(thm)],[f11,f58]) ).
fof(f87,plain,
! [X0,X1] : divide(divide(X0,inverse(X1)),X0) = X1,
inference(forward_demodulation,[status(thm)],[f12,f70]) ).
fof(f88,plain,
! [X0,X1] : divide(multiply(X0,X1),X0) = X1,
inference(forward_demodulation,[status(thm)],[f11,f87]) ).
fof(f92,plain,
! [X0] : multiply(multiply(identity,X0),identity) = X0,
inference(paramodulation,[status(thm)],[f34,f88]) ).
fof(f97,plain,
! [X0] : divide(identity,inverse(X0)) = X0,
inference(paramodulation,[status(thm)],[f25,f88]) ).
fof(f105,plain,
! [X0] : multiply(identity,X0) = X0,
inference(backward_demodulation,[status(thm)],[f106,f13]) ).
fof(f106,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f12,f97]) ).
fof(f110,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(backward_demodulation,[status(thm)],[f105,f32]) ).
fof(f112,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,X1),
inference(backward_demodulation,[status(thm)],[f105,f16]) ).
fof(f116,plain,
! [X0] : multiply(X0,identity) = X0,
inference(backward_demodulation,[status(thm)],[f105,f92]) ).
fof(f120,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(trivial_equality_resolution,[status(thm)],[f110]) ).
fof(f123,plain,
! [X0] : X0 = divide(X0,identity),
inference(backward_demodulation,[status(thm)],[f116,f34]) ).
fof(f126,plain,
! [X0,X1] : multiply(divide(X0,X1),X1) = X0,
inference(paramodulation,[status(thm)],[f88,f78]) ).
fof(f166,plain,
! [X0,X1] : divide(divide(X0,multiply(identity,X1)),X0) = inverse(X1),
inference(paramodulation,[status(thm)],[f9,f63]) ).
fof(f174,plain,
! [X0,X1] : divide(divide(X0,X1),X0) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f105,f166]) ).
fof(f178,plain,
! [X0,X1] : X0 = divide(X1,divide(multiply(X1,identity),X0)),
inference(paramodulation,[status(thm)],[f78,f116]) ).
fof(f186,plain,
! [X0,X1] : X0 = divide(X1,divide(X1,X0)),
inference(forward_demodulation,[status(thm)],[f116,f178]) ).
fof(f193,plain,
! [X0,X1] : divide(X0,multiply(divide(X0,identity),X1)) = inverse(X1),
inference(paramodulation,[status(thm)],[f63,f123]) ).
fof(f210,plain,
! [X0,X1] : divide(X0,multiply(X0,X1)) = inverse(X1),
inference(forward_demodulation,[status(thm)],[f123,f193]) ).
fof(f223,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(paramodulation,[status(thm)],[f88,f126]) ).
fof(f237,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(backward_subsumption_resolution,[status(thm)],[f120,f223]) ).
fof(f311,plain,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(paramodulation,[status(thm)],[f223,f237]) ).
fof(f343,plain,
! [X0,X1] : multiply(inverse(X0),X1) = divide(X1,X0),
inference(paramodulation,[status(thm)],[f223,f112]) ).
fof(f381,plain,
! [X0,X1] : divide(X0,X1) = inverse(divide(X1,X0)),
inference(paramodulation,[status(thm)],[f186,f174]) ).
fof(f407,plain,
! [X0,X1] : divide(inverse(X0),X1) = inverse(multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f210,f174]) ).
fof(f422,plain,
! [X0,X1] : multiply(X0,X1) = divide(X1,inverse(X0)),
inference(paramodulation,[status(thm)],[f106,f343]) ).
fof(f460,plain,
! [X0,X1,X2] : divide(X0,divide(X1,X2)) = inverse(divide(divide(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f60,f174]) ).
fof(f496,plain,
! [X0,X1,X2] : divide(X0,divide(X1,X2)) = divide(X2,divide(X1,X0)),
inference(forward_demodulation,[status(thm)],[f381,f460]) ).
fof(f614,plain,
! [X0,X1,X2] : multiply(divide(X0,X1),X2) = divide(X2,divide(X1,X0)),
inference(paramodulation,[status(thm)],[f381,f343]) ).
fof(f615,plain,
! [X0,X1,X2] : multiply(X0,divide(X1,X2)) = divide(X0,divide(X2,X1)),
inference(paramodulation,[status(thm)],[f381,f112]) ).
fof(f638,plain,
! [X0,X1,X2] : divide(X0,divide(X1,X2)) = multiply(divide(X0,X1),X2),
inference(backward_demodulation,[status(thm)],[f614,f496]) ).
fof(f680,plain,
! [X0,X1,X2] : multiply(X0,divide(X1,X2)) = divide(X1,divide(X2,X0)),
inference(backward_demodulation,[status(thm)],[f684,f614]) ).
fof(f684,plain,
! [X0,X1,X2] : multiply(X0,divide(X1,X2)) = multiply(divide(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f615,f638]) ).
fof(f952,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = divide(X0,divide(inverse(X2),X1)),
inference(paramodulation,[status(thm)],[f407,f11]) ).
fof(f991,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,divide(X0,inverse(X2))),
inference(forward_demodulation,[status(thm)],[f680,f952]) ).
fof(f993,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X2,X0)),
inference(forward_demodulation,[status(thm)],[f422,f991]) ).
fof(f994,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f311,f993]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP091-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.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 19:57:24 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.061804 seconds
% 0.12/0.42 % CPU time: 0.254505 seconds
% 0.12/0.42 % Total memory used: 69.405 MB
% 0.12/0.42 % Net memory used: 68.774 MB
%------------------------------------------------------------------------------