%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP096-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 3
% Syntax : Number of formulae : 63 ( 57 unt; 0 def)
% Number of atoms : 76 ( 75 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 35 ( 22 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 169 ( 169 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : divide(divide(X,inverse(divide(Y,divide(X,Z)))),Z) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : multiply(X,Y) = divide(X,inverse(Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,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(f4,plain,
! [X0,X1,X2] : divide(divide(X0,inverse(divide(X1,divide(X0,X2)))),X2) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f6,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)],[f3]) ).
fof(f7,plain,
! [X0,X1,X2] : divide(multiply(X0,divide(X1,divide(X0,X2))),X2) = X1,
inference(backward_demodulation,[status(thm)],[f5,f4]) ).
fof(f8,plain,
! [X0,X1,X2] : multiply(multiply(X0,divide(X1,divide(X0,inverse(X2)))),X2) = X1,
inference(paramodulation,[status(thm)],[f5,f7]) ).
fof(f9,plain,
! [X0,X1,X2,X3] : divide(multiply(X0,X1),X2) = multiply(X3,divide(X1,divide(X3,divide(X0,X2)))),
inference(paramodulation,[status(thm)],[f7,f7]) ).
fof(f10,plain,
! [X0,X1,X2,X3] : divide(multiply(multiply(X0,divide(X1,divide(X0,X2))),divide(X3,X1)),X2) = X3,
inference(paramodulation,[status(thm)],[f7,f7]) ).
fof(f13,plain,
! [X0,X1,X2] : multiply(multiply(X0,divide(X1,multiply(X0,X2))),X2) = X1,
inference(forward_demodulation,[status(thm)],[f5,f8]) ).
fof(f16,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),X2) = multiply(X3,divide(X1,divide(X3,multiply(X0,X2)))),
inference(paramodulation,[status(thm)],[f7,f13]) ).
fof(f19,plain,
! [X0,X1,X2,X3,X4] : divide(multiply(X0,X1),X2) = multiply(multiply(X3,divide(X4,divide(X3,divide(X0,X2)))),divide(X1,X4)),
inference(paramodulation,[status(thm)],[f7,f9]) ).
fof(f22,plain,
! [X0,X1,X2] : divide(divide(multiply(X0,X1),X2),divide(X0,X2)) = X1,
inference(paramodulation,[status(thm)],[f9,f7]) ).
fof(f25,plain,
! [X0,X1,X2,X3] : divide(multiply(X0,X1),X2) = multiply(divide(multiply(X0,X3),X2),divide(X1,X3)),
inference(forward_demodulation,[status(thm)],[f9,f19]) ).
fof(f28,plain,
! [X0,X1,X2] : divide(multiply(multiply(X0,X1),X2),divide(X0,inverse(X2))) = X1,
inference(paramodulation,[status(thm)],[f5,f22]) ).
fof(f39,plain,
! [X0,X1,X2] : divide(multiply(multiply(X0,X1),X2),multiply(X0,X2)) = X1,
inference(forward_demodulation,[status(thm)],[f5,f28]) ).
fof(f48,plain,
! [X0,X1,X2] : divide(X0,divide(multiply(X1,X0),multiply(X1,X2))) = X2,
inference(paramodulation,[status(thm)],[f39,f22]) ).
fof(f65,plain,
! [X0,X1,X2,X3,X4,X5] : divide(multiply(multiply(X0,divide(X1,divide(X0,X2))),X3),X2) = multiply(multiply(X4,divide(X5,divide(X4,X1))),divide(X3,X5)),
inference(paramodulation,[status(thm)],[f10,f10]) ).
fof(f68,plain,
! [X0,X1,X2,X3] : divide(multiply(multiply(X0,divide(inverse(X1),divide(X0,X2))),multiply(X3,X1)),X2) = X3,
inference(paramodulation,[status(thm)],[f5,f10]) ).
fof(f71,plain,
! [X0,X1,X2,X3,X4] : multiply(multiply(X0,X1),X2) = multiply(multiply(X3,divide(X4,divide(X3,multiply(X0,X2)))),divide(X1,X4)),
inference(paramodulation,[status(thm)],[f10,f13]) ).
fof(f89,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),X2) = multiply(multiply(multiply(X0,X3),X2),divide(X1,X3)),
inference(forward_demodulation,[status(thm)],[f16,f71]) ).
fof(f136,plain,
! [X0,X1,X2,X3] : divide(multiply(multiply(X0,X1),X2),multiply(X0,X3)) = multiply(X1,divide(X2,X3)),
inference(paramodulation,[status(thm)],[f48,f9]) ).
fof(f137,plain,
! [X0,X1,X2] : divide(multiply(multiply(X0,X1),X2),multiply(X0,X2)) = X1,
inference(paramodulation,[status(thm)],[f48,f7]) ).
fof(f145,plain,
! [X0,X1] : multiply(X0,divide(X1,X1)) = X0,
inference(forward_demodulation,[status(thm)],[f136,f137]) ).
fof(f159,plain,
! [X0,X1,X2] : divide(X0,divide(multiply(X1,X0),X1)) = divide(X2,X2),
inference(paramodulation,[status(thm)],[f145,f48]) ).
fof(f161,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),divide(X2,X2)) = multiply(X3,divide(X1,divide(X3,X0))),
inference(paramodulation,[status(thm)],[f145,f16]) ).
fof(f166,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(multiply(X0,X2),X1),
inference(backward_demodulation,[status(thm)],[f184,f16]) ).
fof(f167,plain,
! [X0,X1,X2] : divide(multiply(X0,X1),X2) = multiply(divide(X0,X2),X1),
inference(backward_demodulation,[status(thm)],[f184,f9]) ).
fof(f168,plain,
! [X0,X1,X2] : divide(multiply(multiply(X0,X1),divide(X2,X1)),X0) = X2,
inference(backward_demodulation,[status(thm)],[f184,f10]) ).
fof(f170,plain,
! [X0,X1,X2] : divide(multiply(multiply(X0,inverse(X1)),multiply(X2,X1)),X0) = X2,
inference(backward_demodulation,[status(thm)],[f184,f68]) ).
fof(f177,plain,
! [X0,X1,X2,X3,X4] : divide(multiply(multiply(X0,divide(X1,divide(X0,X2))),X3),X2) = multiply(multiply(X1,X4),divide(X3,X4)),
inference(backward_demodulation,[status(thm)],[f184,f65]) ).
fof(f184,plain,
! [X0,X1,X2] : multiply(X0,X1) = multiply(X2,divide(X1,divide(X2,X0))),
inference(forward_demodulation,[status(thm)],[f145,f161]) ).
fof(f208,plain,
! [X0,X1,X2] : divide(X0,multiply(divide(X1,X1),X0)) = divide(X2,X2),
inference(backward_demodulation,[status(thm)],[f167,f159]) ).
fof(f212,plain,
! [X0,X1,X2] : multiply(divide(multiply(X0,X1),X0),divide(X2,X1)) = X2,
inference(forward_demodulation,[status(thm)],[f167,f168]) ).
fof(f213,plain,
! [X0,X1] : divide(multiply(X0,X1),X0) = X1,
inference(forward_demodulation,[status(thm)],[f25,f212]) ).
fof(f214,plain,
! [X0,X1] : multiply(divide(X0,X0),X1) = X1,
inference(forward_demodulation,[status(thm)],[f167,f213]) ).
fof(f216,plain,
! [X0,X1,X2] : multiply(divide(multiply(X0,inverse(X1)),X0),multiply(X2,X1)) = X2,
inference(forward_demodulation,[status(thm)],[f167,f170]) ).
fof(f217,plain,
! [X0,X1,X2] : multiply(multiply(divide(X0,X0),inverse(X1)),multiply(X2,X1)) = X2,
inference(forward_demodulation,[status(thm)],[f167,f216]) ).
fof(f218,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X1,X0)) = X1,
inference(forward_demodulation,[status(thm)],[f214,f217]) ).
fof(f235,plain,
! [X0,X1,X2,X3,X4] : multiply(divide(multiply(X0,divide(X1,divide(X0,X2))),X2),X3) = multiply(multiply(X1,X4),divide(X3,X4)),
inference(forward_demodulation,[status(thm)],[f167,f177]) ).
fof(f236,plain,
! [X0,X1,X2] : multiply(X0,X1) = multiply(multiply(X0,X2),divide(X1,X2)),
inference(forward_demodulation,[status(thm)],[f7,f235]) ).
fof(f287,plain,
! [X0,X1] : divide(X0,X0) = divide(X1,X1),
inference(forward_demodulation,[status(thm)],[f214,f208]) ).
fof(f298,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = X1,
inference(paramodulation,[status(thm)],[f5,f214]) ).
fof(f299,plain,
! [X0,X1,X2] : multiply(divide(X0,multiply(divide(X1,X1),X2)),X2) = X0,
inference(paramodulation,[status(thm)],[f214,f13]) ).
fof(f303,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| a2 != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(backward_demodulation,[status(thm)],[f298,f6]) ).
fof(f305,plain,
! [X0,X1] : multiply(divide(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f214,f299]) ).
fof(f307,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(trivial_equality_resolution,[status(thm)],[f303]) ).
fof(f429,plain,
! [X0,X1,X2] : multiply(X0,X1) = multiply(multiply(divide(X2,X2),X1),X0),
inference(paramodulation,[status(thm)],[f214,f166]) ).
fof(f468,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(backward_subsumption_resolution,[status(thm)],[f307,f469]) ).
fof(f469,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(forward_demodulation,[status(thm)],[f214,f429]) ).
fof(f486,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X1,multiply(X0,X2)),
inference(paramodulation,[status(thm)],[f166,f469]) ).
fof(f512,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(multiply(X2,X0),X1),
inference(paramodulation,[status(thm)],[f469,f166]) ).
fof(f532,plain,
! [X0,X1,X2,X3] : multiply(multiply(X0,X1),X2) = multiply(X2,multiply(multiply(X0,X3),divide(X1,X3))),
inference(backward_demodulation,[status(thm)],[f486,f89]) ).
fof(f534,plain,
( multiply(b3,multiply(a3,c3)) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(backward_demodulation,[status(thm)],[f486,f468]) ).
fof(f576,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X2,X1)),
inference(forward_demodulation,[status(thm)],[f486,f512]) ).
fof(f597,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(multiply(X0,X3),divide(X2,X3))),
inference(forward_demodulation,[status(thm)],[f576,f532]) ).
fof(f598,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X0,X2)),
inference(forward_demodulation,[status(thm)],[f236,f597]) ).
fof(f599,plain,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
inference(forward_subsumption_resolution,[status(thm)],[f534,f598]) ).
fof(f645,plain,
! [X0,X1] : multiply(inverse(X0),X1) = divide(X1,X0),
inference(paramodulation,[status(thm)],[f305,f218]) ).
fof(f657,plain,
multiply(inverse(a1),a1) != divide(b1,b1),
inference(backward_demodulation,[status(thm)],[f645,f599]) ).
fof(f680,plain,
divide(a1,a1) != divide(b1,b1),
inference(forward_demodulation,[status(thm)],[f645,f657]) ).
fof(f681,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f680,f287]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP096-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 19:56:57 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.41 % Refutation found
% 0.14/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.062206 seconds
% 0.14/0.43 % CPU time: 0.275264 seconds
% 0.14/0.43 % Total memory used: 70.308 MB
% 0.14/0.43 % Net memory used: 69.265 MB
%------------------------------------------------------------------------------