%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP088-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 4
% Syntax : Number of formulae : 58 ( 52 unt; 0 def)
% Number of atoms : 73 ( 72 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 38 ( 23 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 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 : 117 ( 117 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : divide(X,divide(Y,divide(Z,divide(X,Y)))) = Z,
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(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(f5,plain,
! [X0,X1,X2] : divide(X0,divide(X1,divide(X2,divide(X0,X1)))) = X2,
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(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)],[f4]) ).
fof(f9,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(backward_demodulation,[status(thm)],[f7,f6]) ).
fof(f11,plain,
! [X0,X1] : multiply(divide(X0,X0),X1) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f7,f9]) ).
fof(f13,plain,
! [X0,X1] : inverse(X0) = divide(multiply(inverse(X1),X1),X0),
inference(paramodulation,[status(thm)],[f9,f7]) ).
fof(f22,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f9,f11]) ).
fof(f23,plain,
( multiply(a4,b4) != multiply(b4,a4)
| 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)],[f22,f8]) ).
fof(f45,plain,
! [X0,X1,X2] : inverse(divide(X0,divide(X1,divide(multiply(inverse(X2),X2),X0)))) = X1,
inference(paramodulation,[status(thm)],[f13,f5]) ).
fof(f52,plain,
! [X0,X1,X2] : divide(X0,inverse(divide(X1,divide(X0,divide(X2,X2))))) = X1,
inference(paramodulation,[status(thm)],[f7,f5]) ).
fof(f68,plain,
! [X0,X1] : inverse(divide(X0,divide(X1,inverse(X0)))) = X1,
inference(forward_demodulation,[status(thm)],[f13,f45]) ).
fof(f69,plain,
! [X0,X1] : inverse(divide(X0,multiply(X1,X0))) = X1,
inference(forward_demodulation,[status(thm)],[f9,f68]) ).
fof(f81,plain,
! [X0,X1,X2] : multiply(X0,divide(X1,divide(X0,divide(X2,X2)))) = X1,
inference(forward_demodulation,[status(thm)],[f9,f52]) ).
fof(f105,plain,
! [X0,X1] : inverse(inverse(multiply(X0,divide(X1,X1)))) = X0,
inference(paramodulation,[status(thm)],[f7,f69]) ).
fof(f107,plain,
! [X0,X1] : inverse(divide(X0,inverse(inverse(X0)))) = divide(X1,X1),
inference(paramodulation,[status(thm)],[f11,f69]) ).
fof(f111,plain,
! [X0,X1] : inverse(multiply(X0,inverse(X0))) = divide(X1,X1),
inference(forward_demodulation,[status(thm)],[f9,f107]) ).
fof(f121,plain,
! [X0,X1,X2] : multiply(X0,inverse(multiply(X1,divide(X2,X2)))) = divide(X0,X1),
inference(paramodulation,[status(thm)],[f105,f9]) ).
fof(f123,plain,
! [X0,X1] : divide(X0,X0) = divide(X1,X1),
inference(paramodulation,[status(thm)],[f111,f111]) ).
fof(f141,plain,
! [X0,X1,X2] : divide(X0,divide(X1,inverse(multiply(X2,inverse(X2))))) = divide(X0,X1),
inference(paramodulation,[status(thm)],[f111,f5]) ).
fof(f144,plain,
! [X0,X1,X2] : divide(X0,divide(X0,divide(X1,inverse(multiply(X2,inverse(X2)))))) = X1,
inference(paramodulation,[status(thm)],[f111,f5]) ).
fof(f151,plain,
! [X0,X1,X2] : divide(X0,multiply(X1,multiply(X2,inverse(X2)))) = divide(X0,X1),
inference(forward_demodulation,[status(thm)],[f9,f141]) ).
fof(f152,plain,
! [X0,X1,X2] : divide(X0,divide(X0,multiply(X1,multiply(X2,inverse(X2))))) = X1,
inference(forward_demodulation,[status(thm)],[f9,f144]) ).
fof(f153,plain,
! [X0,X1] : divide(X0,divide(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f151,f152]) ).
fof(f174,plain,
! [X0,X1,X2] : divide(X0,divide(X1,divide(X2,X2))) = divide(X0,X1),
inference(paramodulation,[status(thm)],[f123,f5]) ).
fof(f198,plain,
! [X0,X1] : multiply(X0,divide(X1,X0)) = X1,
inference(backward_demodulation,[status(thm)],[f174,f81]) ).
fof(f208,plain,
! [X0,X1] : inverse(divide(multiply(inverse(X0),X0),X1)) = X1,
inference(paramodulation,[status(thm)],[f13,f153]) ).
fof(f217,plain,
! [X0,X1,X2] : divide(X0,X1) = divide(X2,divide(X1,divide(X0,X2))),
inference(paramodulation,[status(thm)],[f5,f153]) ).
fof(f219,plain,
! [X0,X1] : divide(X0,multiply(X0,X1)) = inverse(X1),
inference(paramodulation,[status(thm)],[f9,f153]) ).
fof(f231,plain,
! [X0,X1] : multiply(X0,divide(X1,X1)) = X0,
inference(backward_demodulation,[status(thm)],[f269,f105]) ).
fof(f233,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)],[f269,f23]) ).
fof(f269,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f13,f208]) ).
fof(f286,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,X1),
inference(backward_demodulation,[status(thm)],[f231,f121]) ).
fof(f288,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)],[f233]) ).
fof(f411,plain,
! [X0,X1] : inverse(X0) = divide(X1,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f69,f269]) ).
fof(f448,plain,
! [X0,X1] : multiply(divide(X0,X1),X1) = X0,
inference(paramodulation,[status(thm)],[f153,f198]) ).
fof(f449,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X1,X0)) = X1,
inference(paramodulation,[status(thm)],[f9,f198]) ).
fof(f486,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f13,f448]) ).
fof(f491,plain,
! [X0,X1] : multiply(multiply(X0,X1),inverse(X1)) = X0,
inference(paramodulation,[status(thm)],[f9,f448]) ).
fof(f496,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
inference(backward_subsumption_resolution,[status(thm)],[f288,f486]) ).
fof(f497,plain,
! [X0,X1] : divide(multiply(X0,X1),X1) = X0,
inference(forward_demodulation,[status(thm)],[f286,f491]) ).
fof(f509,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(paramodulation,[status(thm)],[f497,f198]) ).
fof(f513,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(backward_subsumption_resolution,[status(thm)],[f496,f509]) ).
fof(f566,plain,
multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
inference(paramodulation,[status(thm)],[f509,f513]) ).
fof(f718,plain,
! [X0,X1] : divide(X0,X1) = inverse(divide(X1,X0)),
inference(paramodulation,[status(thm)],[f198,f219]) ).
fof(f876,plain,
! [X0,X1] : divide(inverse(X0),X1) = inverse(multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f449,f219]) ).
fof(f948,plain,
! [X0,X1,X2] : divide(X0,divide(X1,X2)) = divide(X2,divide(X1,X0)),
inference(paramodulation,[status(thm)],[f217,f153]) ).
fof(f978,plain,
! [X0,X1] : divide(X0,inverse(X1)) = multiply(X1,X0),
inference(paramodulation,[status(thm)],[f411,f153]) ).
fof(f1038,plain,
! [X0,X1,X2] : multiply(X0,divide(X1,X2)) = divide(X0,divide(X2,X1)),
inference(paramodulation,[status(thm)],[f718,f286]) ).
fof(f1058,plain,
! [X0,X1,X2] : divide(X0,divide(X1,X2)) = multiply(X2,divide(X0,X1)),
inference(backward_demodulation,[status(thm)],[f1038,f948]) ).
fof(f1248,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = divide(X0,divide(inverse(X2),X1)),
inference(paramodulation,[status(thm)],[f876,f9]) ).
fof(f1274,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,divide(X0,inverse(X2))),
inference(forward_demodulation,[status(thm)],[f1058,f1248]) ).
fof(f1276,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = multiply(X1,multiply(X2,X0)),
inference(forward_demodulation,[status(thm)],[f978,f1274]) ).
fof(f1277,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f566,f1276]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP088-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n026.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 19:59:51 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.067679 seconds
% 0.13/0.43 % CPU time: 0.299152 seconds
% 0.13/0.43 % Total memory used: 70.639 MB
% 0.13/0.43 % Net memory used: 69.775 MB
%------------------------------------------------------------------------------