%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP063-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 12:32:25 PM UTC 2026
% Result : Unsatisfiable 0.12s 5.52s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 4
% Syntax : Number of formulae : 54 ( 49 unt; 0 def)
% Number of atoms : 63 ( 62 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 16 ~; 9 |; 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 : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 110 ( 110 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : divide(X,divide(divide(divide(divide(X,X),Y),Z),divide(divide(divide(X,X),X),Z))) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : multiply(X,Y) = divide(X,divide(divide(Z,Z),Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Z] : inverse(X) = divide(divide(Z,Z),X),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,plain,
! [X0,X1,X2] : divide(X0,divide(divide(divide(divide(X0,X0),X1),X2),divide(divide(divide(X0,X0),X0),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] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(backward_demodulation,[status(thm)],[f7,f6]) ).
fof(f10,plain,
! [X0,X1,X2] : divide(X0,divide(divide(divide(divide(X0,X0),X1),X2),divide(inverse(X0),X2))) = X1,
inference(backward_demodulation,[status(thm)],[f7,f5]) ).
fof(f11,plain,
! [X0,X1,X2] : divide(X0,divide(divide(inverse(X1),X2),divide(inverse(X0),X2))) = X1,
inference(forward_demodulation,[status(thm)],[f7,f10]) ).
fof(f13,plain,
! [X0,X1] : multiply(divide(X0,X0),X1) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f7,f9]) ).
fof(f16,plain,
! [X0,X1] : multiply(inverse(divide(X0,X0)),X1) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f7,f13]) ).
fof(f17,plain,
! [X0,X1] : multiply(multiply(inverse(X0),X0),X1) = inverse(inverse(X1)),
inference(paramodulation,[status(thm)],[f9,f13]) ).
fof(f18,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)],[f17,f8]) ).
fof(f20,plain,
! [X0,X1] : divide(X0,inverse(divide(inverse(X0),inverse(X1)))) = X1,
inference(paramodulation,[status(thm)],[f7,f11]) ).
fof(f22,plain,
! [X0,X1,X2] : divide(X0,divide(multiply(inverse(X1),X2),divide(inverse(X0),inverse(X2)))) = X1,
inference(paramodulation,[status(thm)],[f9,f11]) ).
fof(f28,plain,
! [X0,X1] : multiply(X0,divide(inverse(X0),inverse(X1))) = X1,
inference(forward_demodulation,[status(thm)],[f9,f20]) ).
fof(f29,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(forward_demodulation,[status(thm)],[f9,f28]) ).
fof(f30,plain,
! [X0,X1,X2] : divide(X0,divide(multiply(inverse(X1),X2),multiply(inverse(X0),X2))) = X1,
inference(forward_demodulation,[status(thm)],[f9,f22]) ).
fof(f35,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f29,f29]) ).
fof(f40,plain,
! [X0,X1] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(paramodulation,[status(thm)],[f35,f29]) ).
fof(f71,plain,
! [X0,X1,X2] : inverse(divide(multiply(inverse(X0),X1),multiply(inverse(divide(X2,X2)),X1))) = X0,
inference(paramodulation,[status(thm)],[f7,f30]) ).
fof(f73,plain,
! [X0,X1,X2] : divide(X0,divide(X1,multiply(inverse(X0),multiply(X2,X1)))) = X2,
inference(paramodulation,[status(thm)],[f40,f30]) ).
fof(f74,plain,
! [X0,X1,X2] : divide(X0,divide(X1,multiply(inverse(X0),multiply(inverse(inverse(X2)),X1)))) = X2,
inference(paramodulation,[status(thm)],[f29,f30]) ).
fof(f81,plain,
! [X0,X1] : inverse(divide(multiply(inverse(X0),X1),inverse(inverse(X1)))) = X0,
inference(forward_demodulation,[status(thm)],[f16,f71]) ).
fof(f82,plain,
! [X0,X1] : inverse(multiply(multiply(inverse(X0),X1),inverse(X1))) = X0,
inference(forward_demodulation,[status(thm)],[f9,f81]) ).
fof(f84,plain,
( 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)],[f96,f18]) ).
fof(f96,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f73,f74]) ).
fof(f102,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(trivial_equality_resolution,[status(thm)],[f84]) ).
fof(f112,plain,
! [X0,X1,X2] : divide(inverse(X0),divide(divide(inverse(X1),X2),divide(X0,X2))) = X1,
inference(paramodulation,[status(thm)],[f96,f11]) ).
fof(f114,plain,
! [X0,X1] : multiply(X0,inverse(X1)) = divide(X0,X1),
inference(paramodulation,[status(thm)],[f96,f9]) ).
fof(f116,plain,
! [X0,X1] : inverse(divide(multiply(inverse(X0),X1),X1)) = X0,
inference(backward_demodulation,[status(thm)],[f114,f82]) ).
fof(f121,plain,
! [X0,X1] : inverse(divide(X0,multiply(X1,X0))) = X1,
inference(paramodulation,[status(thm)],[f40,f116]) ).
fof(f140,plain,
! [X0,X1] : inverse(inverse(multiply(X0,divide(X1,X1)))) = X0,
inference(paramodulation,[status(thm)],[f7,f121]) ).
fof(f145,plain,
! [X0,X1] : inverse(X0) = divide(X1,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f121,f96]) ).
fof(f149,plain,
! [X0,X1] : multiply(X0,divide(X1,X1)) = X0,
inference(forward_demodulation,[status(thm)],[f96,f140]) ).
fof(f169,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X1),X1)) = X0,
inference(paramodulation,[status(thm)],[f9,f149]) ).
fof(f224,plain,
! [X0,X1] : inverse(inverse(X0)) = divide(multiply(X0,X1),X1),
inference(paramodulation,[status(thm)],[f40,f145]) ).
fof(f233,plain,
! [X0,X1] : X0 = divide(multiply(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f96,f224]) ).
fof(f237,plain,
! [X0,X1] : X0 = multiply(multiply(X0,inverse(X1)),X1),
inference(paramodulation,[status(thm)],[f9,f233]) ).
fof(f245,plain,
! [X0,X1] : X0 = multiply(divide(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f114,f237]) ).
fof(f262,plain,
! [X0,X1] : inverse(divide(X0,X1)) = divide(X1,X0),
inference(paramodulation,[status(thm)],[f245,f145]) ).
fof(f310,plain,
! [X0,X1] : multiply(inverse(X0),X0) = multiply(inverse(X1),X1),
inference(paramodulation,[status(thm)],[f169,f40]) ).
fof(f316,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(backward_subsumption_resolution,[status(thm)],[f102,f310]) ).
fof(f386,plain,
! [X0,X1] : inverse(multiply(X0,X1)) = divide(inverse(X1),X0),
inference(paramodulation,[status(thm)],[f9,f262]) ).
fof(f542,plain,
! [X0,X1,X2] : multiply(X0,multiply(X1,X2)) = divide(X0,divide(inverse(X2),X1)),
inference(paramodulation,[status(thm)],[f386,f9]) ).
fof(f1145,plain,
! [X0,X1,X2,X3] : multiply(X0,multiply(X1,multiply(X2,X3))) = divide(X0,divide(divide(inverse(X3),X2),X1)),
inference(paramodulation,[status(thm)],[f386,f542]) ).
fof(f1199,plain,
! [X0,X1,X2] : multiply(inverse(X0),multiply(divide(X0,X1),multiply(X1,X2))) = X2,
inference(backward_demodulation,[status(thm)],[f1145,f112]) ).
fof(f1443,plain,
! [X0,X1,X2] : multiply(inverse(inverse(X0)),X1) = multiply(divide(X0,X2),multiply(X2,X1)),
inference(paramodulation,[status(thm)],[f1199,f40]) ).
fof(f1532,plain,
! [X0,X1,X2] : multiply(X0,X1) = multiply(divide(X0,X2),multiply(X2,X1)),
inference(forward_demodulation,[status(thm)],[f96,f1443]) ).
fof(f1539,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(paramodulation,[status(thm)],[f233,f1532]) ).
fof(f1570,plain,
multiply(a3,multiply(b3,c3)) != multiply(a3,multiply(b3,c3)),
inference(backward_demodulation,[status(thm)],[f1539,f316]) ).
fof(f1631,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1570]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP063-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n002.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Sun Sep 20 19:58:52 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.37 % Drodi V4.1.1
% 0.12/5.52 % Refutation found
% 0.12/5.52 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/5.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/5.56 % Elapsed time: 0.181877 seconds
% 0.12/5.56 % CPU time: 1.156802 seconds
% 0.12/5.56 % Total memory used: 84.011 MB
% 0.12/5.56 % Net memory used: 82.774 MB
%------------------------------------------------------------------------------