%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP092-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 0.02s 0.33s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% 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 : 5 ( 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 : 108 ( 108 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : divide(divide(X,Y),divide(divide(X,Z),Y)) = Z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : multiply(X,Y) = divide(X,divide(divide(Z,Z),Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Z] : inverse(X) = divide(divide(Z,Z),X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] : identity = divide(X,X),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : divide(divide(X0,X1),divide(divide(X0,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(f56,plain,
! [X0,X1,X2,X3] : divide(X0,divide(divide(divide(X1,X2),X3),divide(divide(X1,X0),X2))) = X3,
inference(paramodulation,[status(thm)],[f6,f6]) ).
fof(f57,plain,
! [X0,X1] : divide(inverse(X0),divide(divide(identity,X1),X0)) = X1,
inference(paramodulation,[status(thm)],[f12,f6]) ).
fof(f61,plain,
! [X0,X1] : divide(identity,divide(divide(X0,X1),X0)) = X1,
inference(paramodulation,[status(thm)],[f9,f6]) ).
fof(f66,plain,
! [X0,X1] : divide(divide(X0,divide(X0,X1)),identity) = X1,
inference(paramodulation,[status(thm)],[f9,f6]) ).
fof(f72,plain,
! [X0,X1] : divide(divide(X0,X1),divide(identity,X1)) = X0,
inference(paramodulation,[status(thm)],[f9,f6]) ).
fof(f73,plain,
! [X0,X1] : divide(inverse(X0),divide(inverse(X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f12,f57]) ).
fof(f79,plain,
! [X0,X1] : inverse(divide(divide(X0,X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f12,f61]) ).
fof(f83,plain,
! [X0,X1] : multiply(divide(X0,divide(X0,X1)),identity) = X1,
inference(forward_demodulation,[status(thm)],[f34,f66]) ).
fof(f87,plain,
! [X0,X1] : divide(divide(X0,X1),inverse(X1)) = X0,
inference(forward_demodulation,[status(thm)],[f12,f72]) ).
fof(f88,plain,
! [X0,X1] : multiply(divide(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f11,f87]) ).
fof(f89,plain,
! [X0,X1,X2] : multiply(X0,divide(divide(X1,X0),X2)) = divide(X1,X2),
inference(paramodulation,[status(thm)],[f6,f88]) ).
fof(f94,plain,
! [X0] : multiply(identity,X0) = X0,
inference(paramodulation,[status(thm)],[f9,f88]) ).
fof(f98,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(backward_demodulation,[status(thm)],[f94,f32]) ).
fof(f100,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,X1),
inference(backward_demodulation,[status(thm)],[f94,f16]) ).
fof(f104,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(trivial_equality_resolution,[status(thm)],[f98]) ).
fof(f111,plain,
! [X0] : divide(X0,identity) = X0,
inference(paramodulation,[status(thm)],[f9,f56]) ).
fof(f112,plain,
! [X0,X1,X2,X3] : divide(X0,divide(X1,divide(divide(X2,X0),X3))) = divide(divide(X2,X1),X3),
inference(paramodulation,[status(thm)],[f6,f56]) ).
fof(f122,plain,
! [X0,X1,X2] : divide(X0,divide(divide(identity,X1),divide(divide(X2,X0),X2))) = X1,
inference(paramodulation,[status(thm)],[f9,f56]) ).
fof(f140,plain,
! [X0] : multiply(X0,identity) = X0,
inference(backward_demodulation,[status(thm)],[f111,f34]) ).
fof(f158,plain,
! [X0,X1] : divide(divide(X0,divide(identity,X1)),X0) = X1,
inference(forward_demodulation,[status(thm)],[f112,f122]) ).
fof(f159,plain,
! [X0,X1] : divide(divide(X0,inverse(X1)),X0) = X1,
inference(forward_demodulation,[status(thm)],[f12,f158]) ).
fof(f160,plain,
! [X0,X1] : divide(multiply(X0,X1),X0) = X1,
inference(forward_demodulation,[status(thm)],[f11,f159]) ).
fof(f177,plain,
! [X0,X1] : divide(X0,divide(X0,X1)) = X1,
inference(backward_demodulation,[status(thm)],[f140,f83]) ).
fof(f187,plain,
! [X0,X1] : multiply(X0,divide(inverse(X0),X1)) = inverse(X1),
inference(paramodulation,[status(thm)],[f73,f88]) ).
fof(f256,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(paramodulation,[status(thm)],[f160,f88]) ).
fof(f261,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(backward_subsumption_resolution,[status(thm)],[f104,f256]) ).
fof(f271,plain,
! [X0,X1] : divide(X0,multiply(X0,X1)) = inverse(X1),
inference(paramodulation,[status(thm)],[f11,f177]) ).
fof(f321,plain,
! [X0,X1] : inverse(divide(X0,X1)) = divide(X1,X0),
inference(paramodulation,[status(thm)],[f177,f79]) ).
fof(f355,plain,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(paramodulation,[status(thm)],[f256,f261]) ).
fof(f423,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = divide(inverse(X1),X0),
inference(paramodulation,[status(thm)],[f11,f321]) ).
fof(f425,plain,
! [X0,X1,X2] : multiply(X0,divide(X1,X2)) = divide(X0,divide(X2,X1)),
inference(paramodulation,[status(thm)],[f321,f100]) ).
fof(f476,plain,
! [X0,X1,X2] : divide(X0,divide(X1,X2)) = inverse(divide(divide(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f89,f271]) ).
fof(f488,plain,
! [X0,X1,X2] : multiply(X0,divide(X1,X2)) = inverse(divide(divide(X2,X0),X1)),
inference(forward_demodulation,[status(thm)],[f425,f476]) ).
fof(f489,plain,
! [X0,X1,X2] : multiply(X0,divide(X1,X2)) = divide(X1,divide(X2,X0)),
inference(forward_demodulation,[status(thm)],[f321,f488]) ).
fof(f657,plain,
! [X0,X1] : divide(X0,inverse(X1)) = inverse(divide(inverse(X0),X1)),
inference(paramodulation,[status(thm)],[f187,f271]) ).
fof(f674,plain,
! [X0,X1] : multiply(X0,X1) = inverse(divide(inverse(X0),X1)),
inference(forward_demodulation,[status(thm)],[f11,f657]) ).
fof(f675,plain,
! [X0,X1] : multiply(X0,X1) = divide(X1,inverse(X0)),
inference(forward_demodulation,[status(thm)],[f321,f674]) ).
fof(f824,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = divide(X0,divide(inverse(X2),X1)),
inference(paramodulation,[status(thm)],[f423,f11]) ).
fof(f845,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,divide(X0,inverse(X2))),
inference(forward_demodulation,[status(thm)],[f489,f824]) ).
fof(f847,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X2,X0)),
inference(forward_demodulation,[status(thm)],[f675,f845]) ).
fof(f848,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f355,f847]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP092-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.29 % Computer : n012.cluster.edu
% 0.02/0.29 % Model : x86_64 x86_64
% 0.02/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.29 % Memory : 8046.5625MB
% 0.02/0.29 % OS : Linux 6.8.0-71-generic
% 0.02/0.29 % CPULimit : 300
% 0.02/0.29 % WCLimit : 300
% 0.02/0.29 % DateTime : Sun Sep 20 19:56:51 UTC 2026
% 0.02/0.29 % CPUTime :
% 0.02/0.30 % Drodi V4.1.1
% 0.02/0.33 % Refutation found
% 0.02/0.33 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.02/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.02/0.34 % Elapsed time: 0.042158 seconds
% 0.02/0.34 % CPU time: 0.160912 seconds
% 0.02/0.34 % Total memory used: 70.149 MB
% 0.02/0.34 % Net memory used: 69.391 MB
%------------------------------------------------------------------------------