%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP095-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 12:32:30 PM UTC 2026
% Result : Unsatisfiable 0.20s 0.57s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 85 ( 75 unt; 0 def)
% Number of atoms : 111 ( 110 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 64 ( 38 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 9 ( 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 : 167 ( 167 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : divide(divide(identity,X),divide(divide(divide(Y,X),Z),Y)) = Z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : multiply(X,Y) = divide(X,divide(identity,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : inverse(X) = divide(identity,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(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(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,X1,X2] : divide(inverse(X0),divide(divide(divide(X1,X0),X2),X1)) = X2,
inference(backward_demodulation,[status(thm)],[f8,f6]) ).
fof(f13,plain,
! [X0] : multiply(identity,X0) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f8,f11]) ).
fof(f15,plain,
! [X0] : multiply(identity,inverse(X0)) = inverse(multiply(identity,X0)),
inference(paramodulation,[status(thm)],[f13,f13]) ).
fof(f16,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,multiply(identity,X1)),
inference(paramodulation,[status(thm)],[f13,f11]) ).
fof(f26,plain,
! [X0,X1,X2] : divide(inverse(X0),multiply(divide(divide(inverse(X1),X0),X2),X1)) = X2,
inference(paramodulation,[status(thm)],[f11,f12]) ).
fof(f28,plain,
! [X0,X1,X2] : divide(inverse(X0),divide(multiply(divide(X1,X0),X2),X1)) = inverse(X2),
inference(paramodulation,[status(thm)],[f11,f12]) ).
fof(f29,plain,
! [X0,X1,X2,X3] : divide(inverse(divide(divide(divide(X0,X1),X2),X0)),divide(divide(X2,X3),inverse(X1))) = X3,
inference(paramodulation,[status(thm)],[f12,f12]) ).
fof(f37,plain,
! [X0,X1,X2,X3] : divide(inverse(divide(divide(divide(X0,X1),X2),X0)),multiply(divide(X2,X3),X1)) = X3,
inference(forward_demodulation,[status(thm)],[f11,f29]) ).
fof(f41,plain,
! [X0,X1,X2] : divide(multiply(identity,X0),multiply(divide(divide(inverse(X1),inverse(X0)),X2),X1)) = X2,
inference(paramodulation,[status(thm)],[f13,f26]) ).
fof(f53,plain,
! [X0,X1,X2] : divide(multiply(identity,X0),multiply(divide(multiply(inverse(X1),X0),X2),X1)) = X2,
inference(forward_demodulation,[status(thm)],[f11,f41]) ).
fof(f79,plain,
identity = inverse(identity),
inference(paramodulation,[status(thm)],[f8,f9]) ).
fof(f81,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(paramodulation,[status(thm)],[f11,f9]) ).
fof(f83,plain,
! [X0,X1] : divide(inverse(X0),divide(identity,X1)) = divide(X1,X0),
inference(paramodulation,[status(thm)],[f9,f12]) ).
fof(f88,plain,
! [X0,X1] : divide(inverse(X0),divide(multiply(identity,X1),X0)) = inverse(X1),
inference(paramodulation,[status(thm)],[f9,f28]) ).
fof(f89,plain,
! [X0,X1] : divide(inverse(X0),divide(divide(identity,X1),X0)) = X1,
inference(paramodulation,[status(thm)],[f9,f12]) ).
fof(f90,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)],[f81,f10]) ).
fof(f92,plain,
! [X0,X1] : divide(inverse(X0),inverse(X1)) = divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f8,f83]) ).
fof(f97,plain,
! [X0,X1,X2] : divide(multiply(identity,X0),multiply(divide(divide(X0,X1),X2),X1)) = X2,
inference(backward_demodulation,[status(thm)],[f98,f53]) ).
fof(f98,plain,
! [X0,X1] : multiply(inverse(X0),X1) = divide(X1,X0),
inference(forward_demodulation,[status(thm)],[f11,f92]) ).
fof(f103,plain,
! [X0,X1] : divide(inverse(X0),divide(inverse(X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f89]) ).
fof(f104,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| divide(a1,a1) != multiply(inverse(b1),b1) ),
inference(forward_demodulation,[status(thm)],[f98,f90]) ).
fof(f105,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)],[f9,f104]) ).
fof(f106,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| identity != divide(b1,b1) ),
inference(forward_demodulation,[status(thm)],[f98,f105]) ).
fof(f107,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)],[f9,f106]) ).
fof(f108,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)],[f107]) ).
fof(f111,plain,
! [X0,X1] : divide(identity,multiply(divide(divide(inverse(X0),identity),X1),X0)) = X1,
inference(paramodulation,[status(thm)],[f79,f26]) ).
fof(f114,plain,
! [X0] : multiply(X0,identity) = divide(X0,identity),
inference(paramodulation,[status(thm)],[f79,f11]) ).
fof(f117,plain,
! [X0,X1] : inverse(multiply(divide(divide(inverse(X0),identity),X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f111]) ).
fof(f120,plain,
! [X0,X1] : inverse(multiply(divide(multiply(inverse(X0),identity),X1),X0)) = X1,
inference(backward_demodulation,[status(thm)],[f114,f117]) ).
fof(f125,plain,
! [X0,X1] : inverse(multiply(divide(divide(identity,X0),X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f98,f120]) ).
fof(f126,plain,
! [X0,X1] : inverse(multiply(divide(inverse(X0),X1),X0)) = X1,
inference(forward_demodulation,[status(thm)],[f8,f125]) ).
fof(f134,plain,
! [X0,X1] : multiply(multiply(identity,X0),X1) = divide(X1,inverse(X0)),
inference(paramodulation,[status(thm)],[f13,f98]) ).
fof(f138,plain,
! [X0,X1] : multiply(multiply(identity,X0),X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f11,f134]) ).
fof(f202,plain,
! [X0,X1,X2,X3] : divide(inverse(divide(multiply(divide(X0,X1),inverse(X2)),X0)),multiply(divide(multiply(identity,X2),X3),X1)) = X3,
inference(paramodulation,[status(thm)],[f16,f37]) ).
fof(f215,plain,
! [X0,X1,X2,X3,X4,X5] : divide(inverse(divide(divide(divide(X0,X1),inverse(divide(divide(divide(X2,X3),X4),X2))),X0)),multiply(X5,X1)) = multiply(divide(X4,X5),X3),
inference(paramodulation,[status(thm)],[f37,f37]) ).
fof(f247,plain,
! [X0,X1,X2,X3,X4,X5] : divide(inverse(divide(multiply(divide(X0,X1),divide(divide(divide(X2,X3),X4),X2)),X0)),multiply(X5,X1)) = multiply(divide(X4,X5),X3),
inference(forward_demodulation,[status(thm)],[f11,f215]) ).
fof(f270,plain,
! [X0] : divide(inverse(identity),multiply(inverse(X0),identity)) = X0,
inference(paramodulation,[status(thm)],[f114,f103]) ).
fof(f275,plain,
! [X0,X1] : divide(inverse(X0),divide(multiply(identity,inverse(X1)),X0)) = multiply(identity,X1),
inference(paramodulation,[status(thm)],[f15,f103]) ).
fof(f278,plain,
! [X0,X1,X2,X3] : divide(inverse(divide(divide(divide(X0,X1),inverse(X2)),X0)),multiply(X3,X1)) = divide(inverse(X3),X2),
inference(paramodulation,[status(thm)],[f103,f37]) ).
fof(f296,plain,
! [X0] : divide(identity,multiply(inverse(X0),identity)) = X0,
inference(forward_demodulation,[status(thm)],[f79,f270]) ).
fof(f297,plain,
! [X0] : inverse(multiply(inverse(X0),identity)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f296]) ).
fof(f298,plain,
! [X0] : inverse(divide(identity,X0)) = X0,
inference(forward_demodulation,[status(thm)],[f98,f297]) ).
fof(f300,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f8,f298]) ).
fof(f310,plain,
! [X0] : inverse(inverse(X0)) = multiply(identity,X0),
inference(forward_demodulation,[status(thm)],[f88,f275]) ).
fof(f311,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(backward_demodulation,[status(thm)],[f335,f108]) ).
fof(f315,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,X1),
inference(backward_demodulation,[status(thm)],[f335,f16]) ).
fof(f323,plain,
! [X0,X1,X2,X3] : divide(inverse(divide(multiply(divide(X0,X1),inverse(X2)),X0)),multiply(divide(X2,X3),X1)) = X3,
inference(backward_demodulation,[status(thm)],[f335,f202]) ).
fof(f327,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(backward_demodulation,[status(thm)],[f335,f138]) ).
fof(f328,plain,
! [X0,X1,X2] : divide(X0,multiply(divide(divide(X0,X1),X2),X1)) = X2,
inference(backward_demodulation,[status(thm)],[f335,f97]) ).
fof(f335,plain,
! [X0] : X0 = multiply(identity,X0),
inference(forward_demodulation,[status(thm)],[f300,f310]) ).
fof(f338,plain,
! [X0,X1,X2,X3] : divide(inverse(X0),divide(divide(divide(X1,X2),X3),X1)) = multiply(divide(X3,X0),X2),
inference(backward_demodulation,[status(thm)],[f343,f247]) ).
fof(f343,plain,
! [X0,X1,X2,X3] : divide(inverse(divide(multiply(divide(X0,X1),X2),X0)),multiply(X3,X1)) = divide(inverse(X3),X2),
inference(forward_demodulation,[status(thm)],[f11,f278]) ).
fof(f347,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(trivial_equality_resolution,[status(thm)],[f311]) ).
fof(f352,plain,
! [X0,X1] : divide(inverse(divide(X0,X1)),inverse(X0)) = X1,
inference(forward_demodulation,[status(thm)],[f343,f323]) ).
fof(f353,plain,
! [X0,X1] : multiply(inverse(divide(X0,X1)),X0) = X1,
inference(forward_demodulation,[status(thm)],[f11,f352]) ).
fof(f354,plain,
! [X0,X1] : divide(X0,divide(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f98,f353]) ).
fof(f363,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(backward_subsumption_resolution,[status(thm)],[f347,f327]) ).
fof(f366,plain,
! [X0,X1] : multiply(divide(X0,X1),X1) = X0,
inference(backward_demodulation,[status(thm)],[f338,f12]) ).
fof(f385,plain,
! [X0,X1] : multiply(X0,X1) = divide(X1,inverse(X0)),
inference(paramodulation,[status(thm)],[f300,f98]) ).
fof(f423,plain,
! [X0,X1] : divide(X0,multiply(X0,X1)) = inverse(X1),
inference(paramodulation,[status(thm)],[f11,f354]) ).
fof(f426,plain,
! [X0,X1] : multiply(X0,divide(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f354,f366]) ).
fof(f519,plain,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(paramodulation,[status(thm)],[f327,f363]) ).
fof(f613,plain,
! [X0,X1] : divide(X0,X1) = inverse(divide(X1,X0)),
inference(paramodulation,[status(thm)],[f426,f423]) ).
fof(f644,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = divide(inverse(X1),X0),
inference(paramodulation,[status(thm)],[f354,f126]) ).
fof(f737,plain,
! [X0,X1,X2] : divide(X0,multiply(inverse(X1),X2)) = multiply(divide(X0,X2),X1),
inference(paramodulation,[status(thm)],[f423,f328]) ).
fof(f777,plain,
! [X0,X1,X2] : divide(X0,divide(X1,X2)) = multiply(divide(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f98,f737]) ).
fof(f1032,plain,
! [X0,X1,X2] : multiply(divide(X0,X1),X2) = divide(X2,divide(X1,X0)),
inference(paramodulation,[status(thm)],[f613,f385]) ).
fof(f1033,plain,
! [X0,X1,X2] : multiply(X0,divide(X1,X2)) = divide(X0,divide(X2,X1)),
inference(paramodulation,[status(thm)],[f613,f315]) ).
fof(f1045,plain,
! [X0,X1,X2] : multiply(X0,divide(X1,X2)) = multiply(divide(X0,X2),X1),
inference(backward_demodulation,[status(thm)],[f1033,f777]) ).
fof(f1072,plain,
! [X0,X1,X2] : multiply(X0,divide(X1,X2)) = divide(X1,divide(X2,X0)),
inference(backward_demodulation,[status(thm)],[f1045,f1032]) ).
fof(f1343,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = divide(X0,divide(inverse(X2),X1)),
inference(paramodulation,[status(thm)],[f644,f11]) ).
fof(f1366,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,divide(X0,inverse(X2))),
inference(forward_demodulation,[status(thm)],[f1072,f1343]) ).
fof(f1368,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X2,X0)),
inference(forward_demodulation,[status(thm)],[f385,f1366]) ).
fof(f1369,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f519,f1368]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP095-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n011.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Sun Sep 20 19:56:55 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.48 % Drodi V4.1.1
% 0.20/0.57 % Refutation found
% 0.20/0.57 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.62 % Elapsed time: 0.142828 seconds
% 0.20/0.62 % CPU time: 0.598421 seconds
% 0.20/0.62 % Total memory used: 50.410 MB
% 0.20/0.62 % Net memory used: 49.746 MB
%------------------------------------------------------------------------------