%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP068-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 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 12:32:26 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.40s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 5
% Syntax : Number of formulae : 69 ( 63 unt; 0 def)
% Number of atoms : 79 ( 78 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 18 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 143 ( 143 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : divide(X,divide(divide(divide(identity,Y),Z),divide(divide(divide(X,X),X),Z))) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : multiply(X,Y) = divide(X,divide(identity,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : inverse(X) = divide(identity,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(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,plain,
! [X0,X1,X2] : divide(X0,divide(divide(divide(identity,X1),X2),divide(divide(divide(X0,X0),X0),X2))) = X1,
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(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
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,X1,X2] : divide(X0,divide(divide(inverse(X1),X2),divide(divide(divide(X0,X0),X0),X2))) = X1,
inference(backward_demodulation,[status(thm)],[f8,f6]) ).
fof(f13,plain,
! [X0,X1,X2] : divide(X0,divide(divide(inverse(X1),X2),divide(divide(identity,X0),X2))) = X1,
inference(forward_demodulation,[status(thm)],[f9,f12]) ).
fof(f14,plain,
! [X0,X1,X2] : divide(X0,divide(divide(inverse(X1),X2),divide(inverse(X0),X2))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f13]) ).
fof(f15,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f9,f8]) ).
fof(f17,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f11]) ).
fof(f18,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(paramodulation,[status(thm)],[f9,f11]) ).
fof(f19,plain,
! [X0] : multiply(X0,identity) = divide(X0,identity),
inference(paramodulation,[status(thm)],[f15,f11]) ).
fof(f22,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2
| multiply(inverse(a1),a1) != identity ),
inference(backward_demodulation,[status(thm)],[f17,f10]) ).
fof(f23,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f18,f22]) ).
fof(f24,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2 ),
inference(trivial_equality_resolution,[status(thm)],[f23]) ).
fof(f41,plain,
! [X0] : divide(X0,identity) = X0,
inference(paramodulation,[status(thm)],[f9,f14]) ).
fof(f43,plain,
! [X0,X1] : divide(X0,divide(multiply(inverse(X1),identity),divide(inverse(X0),identity))) = X1,
inference(paramodulation,[status(thm)],[f19,f14]) ).
fof(f44,plain,
! [X0,X1,X2] : divide(X0,divide(multiply(inverse(X1),X2),divide(inverse(X0),inverse(X2)))) = X1,
inference(paramodulation,[status(thm)],[f11,f14]) ).
fof(f45,plain,
! [X0,X1] : divide(X0,divide(identity,divide(inverse(X0),inverse(X1)))) = X1,
inference(paramodulation,[status(thm)],[f9,f14]) ).
fof(f47,plain,
! [X0,X1,X2,X3] : divide(X0,divide(divide(inverse(X1),divide(divide(inverse(X2),X3),divide(inverse(inverse(X0)),X3))),X2)) = X1,
inference(paramodulation,[status(thm)],[f14,f14]) ).
fof(f57,plain,
! [X0] : multiply(X0,identity) = X0,
inference(forward_demodulation,[status(thm)],[f19,f41]) ).
fof(f58,plain,
! [X0,X1] : divide(X0,divide(inverse(X1),divide(inverse(X0),identity))) = X1,
inference(forward_demodulation,[status(thm)],[f57,f43]) ).
fof(f59,plain,
! [X0,X1] : divide(X0,divide(inverse(X1),multiply(inverse(X0),identity))) = X1,
inference(forward_demodulation,[status(thm)],[f19,f58]) ).
fof(f60,plain,
! [X0,X1] : divide(X0,divide(inverse(X1),inverse(X0))) = X1,
inference(forward_demodulation,[status(thm)],[f57,f59]) ).
fof(f61,plain,
! [X0,X1] : divide(X0,multiply(inverse(X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f11,f60]) ).
fof(f62,plain,
! [X0,X1,X2] : divide(X0,divide(multiply(inverse(X1),X2),multiply(inverse(X0),X2))) = X1,
inference(forward_demodulation,[status(thm)],[f11,f44]) ).
fof(f63,plain,
! [X0,X1] : divide(X0,inverse(divide(inverse(X0),inverse(X1)))) = X1,
inference(forward_demodulation,[status(thm)],[f8,f45]) ).
fof(f64,plain,
! [X0,X1] : multiply(X0,divide(inverse(X0),inverse(X1))) = X1,
inference(forward_demodulation,[status(thm)],[f11,f63]) ).
fof(f65,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[status(thm)],[f11,f64]) ).
fof(f85,plain,
! [X0] : inverse(multiply(inverse(X0),identity)) = X0,
inference(paramodulation,[status(thm)],[f8,f61]) ).
fof(f93,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(backward_demodulation,[status(thm)],[f96,f24]) ).
fof(f94,plain,
! [X0,X1,X2,X3] : divide(X0,divide(divide(inverse(X1),divide(divide(inverse(X2),X3),divide(X0,X3))),X2)) = X1,
inference(backward_demodulation,[status(thm)],[f96,f47]) ).
fof(f96,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f57,f85]) ).
fof(f102,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(trivial_equality_resolution,[status(thm)],[f93]) ).
fof(f105,plain,
! [X0,X1] : divide(X0,multiply(X1,X0)) = inverse(X1),
inference(paramodulation,[status(thm)],[f96,f61]) ).
fof(f109,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,X1),
inference(paramodulation,[status(thm)],[f96,f11]) ).
fof(f143,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(paramodulation,[status(thm)],[f96,f65]) ).
fof(f173,plain,
! [X0,X1] : divide(multiply(X0,X1),X1) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f143,f105]) ).
fof(f176,plain,
! [X0,X1] : divide(multiply(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f96,f173]) ).
fof(f178,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X1)),X1) = X0,
inference(paramodulation,[status(thm)],[f11,f176]) ).
fof(f188,plain,
! [X0,X1] : multiply(divide(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f109,f178]) ).
fof(f204,plain,
! [X0,X1] : divide(X0,X1) = inverse(divide(X1,X0)),
inference(paramodulation,[status(thm)],[f188,f105]) ).
fof(f227,plain,
! [X0,X1] : divide(inverse(X0),X1) = inverse(multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f11,f204]) ).
fof(f230,plain,
! [X0,X1,X2] : multiply(X0,divide(X1,X2)) = divide(X0,divide(X2,X1)),
inference(paramodulation,[status(thm)],[f204,f109]) ).
fof(f241,plain,
! [X0,X1,X2,X3] : divide(X0,divide(inverse(multiply(divide(divide(inverse(X1),X2),divide(X0,X2)),X3)),X1)) = X3,
inference(backward_demodulation,[status(thm)],[f227,f94]) ).
fof(f246,plain,
! [X0,X1,X2] : multiply(X0,divide(multiply(inverse(X0),X1),multiply(inverse(X2),X1))) = X2,
inference(backward_demodulation,[status(thm)],[f230,f62]) ).
fof(f261,plain,
! [X0,X1,X2,X3] : multiply(X0,divide(X1,inverse(multiply(divide(divide(inverse(X1),X2),divide(X0,X2)),X3)))) = X3,
inference(forward_demodulation,[status(thm)],[f230,f241]) ).
fof(f262,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X1,multiply(divide(divide(inverse(X1),X2),divide(X0,X2)),X3))) = X3,
inference(forward_demodulation,[status(thm)],[f11,f261]) ).
fof(f263,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X1,multiply(multiply(divide(inverse(X1),X2),divide(X2,X0)),X3))) = X3,
inference(forward_demodulation,[status(thm)],[f230,f262]) ).
fof(f264,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X1,multiply(multiply(inverse(multiply(X2,X1)),divide(X2,X0)),X3))) = X3,
inference(forward_demodulation,[status(thm)],[f227,f263]) ).
fof(f298,plain,
! [X0,X1] : multiply(inverse(X0),X1) = inverse(multiply(inverse(X1),X0)),
inference(paramodulation,[status(thm)],[f11,f227]) ).
fof(f489,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X1,X2)) = multiply(inverse(multiply(inverse(multiply(X3,X1)),divide(X3,X0))),X2),
inference(paramodulation,[status(thm)],[f65,f264]) ).
fof(f533,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X1,X2)) = multiply(multiply(inverse(divide(X3,X0)),multiply(X3,X1)),X2),
inference(forward_demodulation,[status(thm)],[f298,f489]) ).
fof(f535,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X1,X2)) = multiply(multiply(divide(X0,X3),multiply(X3,X1)),X2),
inference(forward_demodulation,[status(thm)],[f204,f533]) ).
fof(f616,plain,
! [X0,X1,X2] : multiply(X0,X1) = divide(multiply(inverse(inverse(X0)),X2),multiply(inverse(X1),X2)),
inference(paramodulation,[status(thm)],[f246,f65]) ).
fof(f665,plain,
! [X0,X1,X2] : multiply(X0,X1) = divide(multiply(X0,X2),multiply(inverse(X1),X2)),
inference(forward_demodulation,[status(thm)],[f96,f616]) ).
fof(f842,plain,
! [X0,X1,X2] : multiply(X0,X1) = divide(multiply(X0,inverse(X2)),divide(inverse(X1),X2)),
inference(paramodulation,[status(thm)],[f109,f665]) ).
fof(f888,plain,
! [X0,X1,X2] : multiply(X0,X1) = multiply(multiply(X0,inverse(X2)),divide(X2,inverse(X1))),
inference(forward_demodulation,[status(thm)],[f230,f842]) ).
fof(f889,plain,
! [X0,X1,X2] : multiply(X0,X1) = multiply(divide(X0,X2),divide(X2,inverse(X1))),
inference(forward_demodulation,[status(thm)],[f109,f888]) ).
fof(f896,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(multiply(X0,X1),X2),
inference(backward_demodulation,[status(thm)],[f898,f535]) ).
fof(f898,plain,
! [X0,X1,X2] : multiply(X0,X1) = multiply(divide(X0,X2),multiply(X2,X1)),
inference(forward_demodulation,[status(thm)],[f11,f889]) ).
fof(f944,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(backward_demodulation,[status(thm)],[f896,f102]) ).
fof(f961,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f944]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP068-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 19:58:16 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.40 % Refutation found
% 0.08/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.44 % Elapsed time: 0.066991 seconds
% 0.08/0.44 % CPU time: 0.284047 seconds
% 0.08/0.44 % Total memory used: 42.782 MB
% 0.08/0.44 % Net memory used: 42.595 MB
%------------------------------------------------------------------------------