%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG006-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 11:47:44 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.42s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 4
% Syntax : Number of formulae : 49 ( 49 unt; 0 def)
% Number of atoms : 49 ( 48 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 112 ( 112 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : difference(X,difference(Y,X)) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : difference(X,difference(X,Y)) = difference(Y,difference(Y,X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : difference(difference(X,Y),Z) = difference(difference(X,Z),difference(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
difference(difference(a,c),b) != difference(difference(a,b),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,plain,
! [X0,X1] : difference(X0,difference(X1,X0)) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f6,plain,
! [X0,X1] : difference(X0,difference(X0,X1)) = difference(X1,difference(X1,X0)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
! [X0,X1,X2] : difference(difference(X0,X1),X2) = difference(difference(X0,X2),difference(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,plain,
difference(difference(a,c),b) != difference(difference(a,b),c),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
! [X0,X1] : difference(difference(X0,X1),X1) = difference(X0,X1),
inference(paramodulation,[status(thm)],[f5,f5]) ).
fof(f20,plain,
! [X0,X1] : difference(difference(X0,X1),difference(X0,X1)) = difference(X1,difference(X1,difference(X0,X1))),
inference(paramodulation,[status(thm)],[f14,f6]) ).
fof(f28,plain,
! [X0,X1] : difference(difference(X0,X0),X1) = difference(X1,difference(X1,difference(X0,X1))),
inference(forward_demodulation,[status(thm)],[f7,f20]) ).
fof(f29,plain,
! [X0,X1] : difference(difference(X0,X0),X1) = difference(X1,X1),
inference(forward_demodulation,[status(thm)],[f5,f28]) ).
fof(f37,plain,
! [X0,X1] : difference(X0,difference(X0,difference(X1,X1))) = difference(difference(X1,X1),difference(X0,X0)),
inference(paramodulation,[status(thm)],[f29,f6]) ).
fof(f45,plain,
! [X0,X1] : difference(difference(X0,X1),X0) = difference(difference(X1,X0),difference(X1,X0)),
inference(paramodulation,[status(thm)],[f29,f7]) ).
fof(f51,plain,
! [X0,X1,X2] : difference(difference(difference(X0,X1),X2),X1) = difference(difference(X0,X1),difference(X2,X1)),
inference(paramodulation,[status(thm)],[f14,f7]) ).
fof(f57,plain,
! [X0,X1,X2] : difference(difference(X0,difference(X1,X1)),X2) = difference(difference(X0,X2),difference(X2,X2)),
inference(paramodulation,[status(thm)],[f29,f7]) ).
fof(f72,plain,
! [X0,X1] : difference(difference(X0,X1),X0) = difference(difference(X1,X1),X0),
inference(forward_demodulation,[status(thm)],[f7,f45]) ).
fof(f76,plain,
! [X0,X1,X2] : difference(difference(difference(X0,X1),X2),X1) = difference(difference(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f7,f51]) ).
fof(f79,plain,
! [X0,X1,X2] : difference(difference(X0,difference(X1,X1)),X2) = difference(difference(X0,X2),X2),
inference(forward_demodulation,[status(thm)],[f7,f57]) ).
fof(f80,plain,
! [X0,X1,X2] : difference(difference(X0,difference(X1,X1)),X2) = difference(X0,X2),
inference(forward_demodulation,[status(thm)],[f14,f79]) ).
fof(f101,plain,
! [X0,X1,X2] : difference(difference(X0,X1),difference(X2,X2)) = difference(X0,difference(X1,difference(X2,X2))),
inference(paramodulation,[status(thm)],[f7,f80]) ).
fof(f131,plain,
! [X0,X1] : difference(X0,difference(X0,difference(X1,X1))) = difference(X1,difference(X1,difference(X0,X0))),
inference(backward_demodulation,[status(thm)],[f101,f37]) ).
fof(f156,plain,
! [X0,X1] : difference(difference(X0,X1),X0) = difference(X0,X0),
inference(paramodulation,[status(thm)],[f29,f72]) ).
fof(f229,plain,
! [X0,X1] : difference(difference(X0,X0),difference(X1,X1)) = difference(difference(X1,X1),difference(X1,X1)),
inference(paramodulation,[status(thm)],[f29,f156]) ).
fof(f239,plain,
! [X0,X1,X2] : difference(difference(difference(X0,X0),difference(X0,X0)),X1) = difference(difference(difference(X0,X0),X2),X1),
inference(paramodulation,[status(thm)],[f156,f80]) ).
fof(f242,plain,
! [X0,X1] : difference(X0,difference(X0,difference(X0,X1))) = difference(difference(X0,X1),difference(X0,X0)),
inference(paramodulation,[status(thm)],[f156,f6]) ).
fof(f253,plain,
! [X0,X1] : difference(X0,difference(X0,difference(X1,X1))) = difference(difference(X1,X1),difference(X1,X1)),
inference(forward_demodulation,[status(thm)],[f101,f229]) ).
fof(f254,plain,
! [X0,X1] : difference(X0,difference(X0,difference(X1,X1))) = difference(difference(X1,X1),X1),
inference(forward_demodulation,[status(thm)],[f7,f253]) ).
fof(f256,plain,
! [X0,X1] : difference(X0,difference(X0,difference(X1,X1))) = difference(X0,X0),
inference(backward_demodulation,[status(thm)],[f259,f131]) ).
fof(f259,plain,
! [X0,X1] : difference(X0,difference(X0,difference(X1,X1))) = difference(X1,X1),
inference(forward_demodulation,[status(thm)],[f156,f254]) ).
fof(f267,plain,
! [X0,X1,X2] : difference(difference(X0,X0),X1) = difference(difference(difference(X0,X0),X2),X1),
inference(forward_demodulation,[status(thm)],[f80,f239]) ).
fof(f272,plain,
! [X0,X1] : difference(X0,difference(X0,difference(X0,X1))) = difference(X0,difference(X1,difference(X0,X0))),
inference(forward_demodulation,[status(thm)],[f101,f242]) ).
fof(f277,plain,
! [X0,X1] : difference(X0,X0) = difference(X1,X1),
inference(forward_demodulation,[status(thm)],[f259,f256]) ).
fof(f294,plain,
! [X0,X1,X2] : difference(difference(X0,X1),X1) = difference(difference(X0,X1),difference(X2,X2)),
inference(paramodulation,[status(thm)],[f277,f7]) ).
fof(f299,plain,
! [X0,X1] : difference(X0,difference(X1,X1)) = X0,
inference(paramodulation,[status(thm)],[f277,f5]) ).
fof(f314,plain,
! [X0,X1,X2] : difference(X0,X1) = difference(difference(X0,X1),difference(X2,X2)),
inference(forward_demodulation,[status(thm)],[f14,f294]) ).
fof(f315,plain,
! [X0,X1] : difference(X0,difference(X0,difference(X0,X1))) = difference(X0,X1),
inference(backward_demodulation,[status(thm)],[f321,f272]) ).
fof(f321,plain,
! [X0,X1,X2] : difference(X0,X1) = difference(X0,difference(X1,difference(X2,X2))),
inference(forward_demodulation,[status(thm)],[f101,f314]) ).
fof(f338,plain,
! [X0,X1,X2] : difference(X0,difference(difference(X1,X1),X2)) = X0,
inference(paramodulation,[status(thm)],[f7,f299]) ).
fof(f1687,plain,
! [X0,X1,X2] : difference(difference(difference(X0,X1),X2),difference(difference(difference(X0,X1),X2),difference(difference(X0,X2),X1))) = difference(difference(difference(X0,X1),X2),X1),
inference(paramodulation,[status(thm)],[f76,f315]) ).
fof(f1688,plain,
! [X0,X1,X2] : difference(difference(difference(X0,X1),X2),difference(difference(X0,X2),X1)) = difference(difference(difference(X0,X2),X1),difference(difference(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f76,f156]) ).
fof(f1769,plain,
! [X0,X1,X2] : difference(difference(difference(X0,X1),X2),difference(difference(difference(X0,X1),X2),difference(difference(X0,X2),X1))) = difference(difference(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f76,f1687]) ).
fof(f1770,plain,
! [X0,X1,X2] : difference(difference(difference(X0,X1),X2),difference(difference(X0,X2),X1)) = difference(difference(difference(X0,X2),difference(X0,X2)),X1),
inference(forward_demodulation,[status(thm)],[f7,f1688]) ).
fof(f1771,plain,
! [X0,X1,X2] : difference(difference(difference(X0,X1),X2),difference(difference(X0,X2),X1)) = difference(difference(difference(X0,X0),X2),X1),
inference(forward_demodulation,[status(thm)],[f7,f1770]) ).
fof(f1772,plain,
! [X0,X1,X2] : difference(difference(difference(X0,X1),X2),difference(difference(X0,X0),X1)) = difference(difference(X0,X2),X1),
inference(backward_demodulation,[status(thm)],[f1775,f1769]) ).
fof(f1775,plain,
! [X0,X1,X2] : difference(difference(difference(X0,X1),X2),difference(difference(X0,X2),X1)) = difference(difference(X0,X0),X1),
inference(forward_demodulation,[status(thm)],[f267,f1771]) ).
fof(f1782,plain,
difference(difference(a,c),b) != difference(difference(a,c),b),
inference(backward_demodulation,[status(thm)],[f1795,f8]) ).
fof(f1795,plain,
! [X0,X1,X2] : difference(difference(X0,X1),X2) = difference(difference(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f338,f1772]) ).
fof(f1806,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1782]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG006-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n018.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 12:54:30 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.42 % Refutation found
% 0.09/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.54/1.66 % Elapsed time: 1.066331 seconds
% 1.54/1.66 % CPU time: 0.324800 seconds
% 1.54/1.66 % Total memory used: 7.200 MB
% 1.54/1.66 % Net memory used: 7.034 MB
%------------------------------------------------------------------------------