%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP065-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 0.10s 0.50s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 4
% Syntax : Number of formulae : 61 ( 56 unt; 0 def)
% Number of atoms : 69 ( 68 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 15 ~; 8 |; 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 127 ( 127 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : divide(divide(divide(X,X),divide(X,divide(Y,divide(divide(divide(X,X),X),Z)))),Z) = Y,
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,negated_conjecture,
( 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(f5,plain,
! [X0,X1,X2] : divide(divide(divide(X0,X0),divide(X0,divide(X1,divide(divide(divide(X0,X0),X0),X2)))),X2) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f6,plain,
! [X0,X1,X2] : multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
! [X0,X1] : inverse(X0) = divide(divide(X1,X1),X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,plain,
( 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)],[f4]) ).
fof(f9,plain,
! [X0,X1,X2] : divide(inverse(divide(X0,divide(X1,divide(divide(divide(X0,X0),X0),X2)))),X2) = X1,
inference(backward_demodulation,[status(thm)],[f7,f5]) ).
fof(f10,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(backward_demodulation,[status(thm)],[f7,f6]) ).
fof(f11,plain,
! [X0,X1,X2] : divide(inverse(divide(X0,divide(X1,divide(inverse(X0),X2)))),X2) = X1,
inference(forward_demodulation,[status(thm)],[f7,f9]) ).
fof(f12,plain,
! [X0,X1] : inverse(X0) = divide(inverse(divide(X1,X1)),X0),
inference(paramodulation,[status(thm)],[f7,f7]) ).
fof(f13,plain,
! [X0,X1] : multiply(divide(X0,X0),X1) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f7,f10]) ).
fof(f16,plain,
! [X0,X1,X2] : multiply(inverse(divide(X0,divide(X1,divide(inverse(X0),inverse(X2))))),X2) = X1,
inference(paramodulation,[status(thm)],[f10,f11]) ).
fof(f17,plain,
! [X0,X1,X2] : divide(inverse(inverse(divide(X0,divide(inverse(divide(X1,X1)),X2)))),X2) = X0,
inference(paramodulation,[status(thm)],[f7,f11]) ).
fof(f18,plain,
! [X0,X1,X2,X3] : divide(inverse(divide(X0,X1)),X2) = inverse(divide(X3,divide(X1,divide(inverse(X3),divide(inverse(X0),X2))))),
inference(paramodulation,[status(thm)],[f11,f11]) ).
fof(f23,plain,
! [X0,X1,X2] : multiply(inverse(divide(X0,divide(X1,multiply(inverse(X0),X2)))),X2) = X1,
inference(forward_demodulation,[status(thm)],[f10,f16]) ).
fof(f24,plain,
! [X0,X1] : divide(inverse(inverse(divide(X0,inverse(X1)))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f12,f17]) ).
fof(f25,plain,
! [X0,X1] : divide(inverse(inverse(multiply(X0,X1))),X1) = X0,
inference(forward_demodulation,[status(thm)],[f10,f24]) ).
fof(f30,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f10,f13]) ).
fof(f31,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(backward_demodulation,[status(thm)],[f30,f8]) ).
fof(f58,plain,
! [X0,X1] : divide(inverse(inverse(inverse(inverse(X0)))),X0) = multiply(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f30,f25]) ).
fof(f61,plain,
! [X0,X1,X2] : divide(inverse(divide(X0,X1)),X2) = inverse(inverse(multiply(X1,divide(inverse(X0),X2)))),
inference(paramodulation,[status(thm)],[f25,f11]) ).
fof(f63,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f58,f58]) ).
fof(f65,plain,
! [X0,X1] : divide(inverse(inverse(inverse(inverse(X0)))),X0) = divide(inverse(inverse(inverse(inverse(X1)))),X1),
inference(paramodulation,[status(thm)],[f58,f58]) ).
fof(f72,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| inverse(inverse(a2)) != a2 ),
inference(backward_subsumption_resolution,[status(thm)],[f31,f63]) ).
fof(f78,plain,
! [X0,X1,X2] : multiply(inverse(divide(X0,X1)),X2) = inverse(inverse(multiply(X1,multiply(inverse(X0),X2)))),
inference(paramodulation,[status(thm)],[f25,f23]) ).
fof(f84,plain,
! [X0,X1,X2] : divide(inverse(inverse(X0)),X1) = inverse(divide(X2,divide(X0,multiply(inverse(X2),X1)))),
inference(paramodulation,[status(thm)],[f23,f25]) ).
fof(f94,plain,
! [X0,X1] : multiply(divide(inverse(inverse(X0)),X1),X1) = X0,
inference(backward_demodulation,[status(thm)],[f84,f23]) ).
fof(f202,plain,
! [X0] : inverse(inverse(inverse(inverse(X0)))) = X0,
inference(paramodulation,[status(thm)],[f13,f94]) ).
fof(f225,plain,
! [X0,X1] : divide(inverse(inverse(inverse(inverse(X0)))),X0) = divide(X1,X1),
inference(backward_demodulation,[status(thm)],[f202,f65]) ).
fof(f233,plain,
! [X0,X1] : divide(X0,X0) = divide(X1,X1),
inference(forward_demodulation,[status(thm)],[f202,f225]) ).
fof(f236,plain,
! [X0,X1] : inverse(divide(X0,X0)) = divide(X1,X1),
inference(paramodulation,[status(thm)],[f7,f233]) ).
fof(f274,plain,
! [X0,X1] : multiply(X0,inverse(inverse(inverse(X1)))) = divide(X0,X1),
inference(paramodulation,[status(thm)],[f202,f10]) ).
fof(f319,plain,
! [X0,X1,X2,X3] : divide(inverse(divide(X0,divide(inverse(X1),divide(inverse(X0),X2)))),X2) = inverse(divide(X1,divide(X3,X3))),
inference(paramodulation,[status(thm)],[f233,f18]) ).
fof(f362,plain,
! [X0,X1] : inverse(X0) = inverse(divide(X0,divide(X1,X1))),
inference(forward_demodulation,[status(thm)],[f11,f319]) ).
fof(f580,plain,
! [X0,X1,X2] : multiply(X0,divide(X1,X1)) = divide(X0,divide(X2,X2)),
inference(paramodulation,[status(thm)],[f236,f10]) ).
fof(f903,plain,
! [X0,X1,X2] : divide(inverse(inverse(divide(X0,divide(X1,X1)))),divide(X2,X2)) = X0,
inference(paramodulation,[status(thm)],[f580,f25]) ).
fof(f953,plain,
! [X0,X1] : divide(inverse(inverse(X0)),divide(X1,X1)) = X0,
inference(forward_demodulation,[status(thm)],[f362,f903]) ).
fof(f967,plain,
! [X0,X1] : X0 = multiply(X0,divide(X1,X1)),
inference(paramodulation,[status(thm)],[f25,f953]) ).
fof(f968,plain,
! [X0,X1] : multiply(inverse(inverse(X0)),divide(X1,X1)) = X0,
inference(paramodulation,[status(thm)],[f580,f953]) ).
fof(f1001,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,X1),
inference(backward_demodulation,[status(thm)],[f1051,f274]) ).
fof(f1002,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2 ),
inference(backward_demodulation,[status(thm)],[f1051,f72]) ).
fof(f1003,plain,
! [X0,X1] : divide(multiply(X0,X1),X1) = X0,
inference(backward_demodulation,[status(thm)],[f1051,f25]) ).
fof(f1038,plain,
! [X0,X1,X2] : multiply(inverse(divide(X0,X1)),X2) = multiply(X1,multiply(inverse(X0),X2)),
inference(backward_demodulation,[status(thm)],[f1051,f78]) ).
fof(f1039,plain,
! [X0,X1,X2] : divide(inverse(divide(X0,X1)),X2) = multiply(X1,divide(inverse(X0),X2)),
inference(backward_demodulation,[status(thm)],[f1051,f61]) ).
fof(f1051,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f967,f968]) ).
fof(f1101,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(trivial_equality_resolution,[status(thm)],[f1002]) ).
fof(f1118,plain,
! [X0,X1] : inverse(X0) = multiply(X1,divide(inverse(X1),X0)),
inference(backward_demodulation,[status(thm)],[f1039,f12]) ).
fof(f1226,plain,
! [X0,X1] : multiply(multiply(X0,inverse(X1)),X1) = X0,
inference(paramodulation,[status(thm)],[f10,f1003]) ).
fof(f1234,plain,
! [X0,X1] : multiply(divide(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f1001,f1226]) ).
fof(f1631,plain,
! [X0,X1] : inverse(X0) = multiply(inverse(X1),divide(X1,X0)),
inference(paramodulation,[status(thm)],[f1051,f1118]) ).
fof(f1944,plain,
! [X0,X1] : inverse(inverse(X0)) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f10,f1631]) ).
fof(f1963,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f1051,f1944]) ).
fof(f1990,plain,
! [X0,X1] : divide(X0,multiply(X1,X0)) = inverse(X1),
inference(paramodulation,[status(thm)],[f1963,f1003]) ).
fof(f2013,plain,
! [X0,X1] : divide(X0,X1) = inverse(divide(X1,X0)),
inference(paramodulation,[status(thm)],[f1234,f1990]) ).
fof(f2037,plain,
! [X0,X1,X2] : multiply(divide(X0,X1),X2) = multiply(X0,multiply(inverse(X1),X2)),
inference(backward_demodulation,[status(thm)],[f2013,f1038]) ).
fof(f2464,plain,
! [X0,X1,X2] : multiply(divide(X0,inverse(X1)),X2) = multiply(X0,multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f1051,f2037]) ).
fof(f2536,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(backward_demodulation,[status(thm)],[f2540,f1101]) ).
fof(f2540,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(forward_demodulation,[status(thm)],[f10,f2464]) ).
fof(f2606,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f2536]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP065-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:02:13 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.50 % Refutation found
% 0.10/0.50 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.57/0.54 % Elapsed time: 0.149242 seconds
% 0.57/0.54 % CPU time: 0.977634 seconds
% 0.57/0.54 % Total memory used: 85.086 MB
% 0.57/0.54 % Net memory used: 82.966 MB
%------------------------------------------------------------------------------