%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ALG007-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 19.12s 2.94s
% Output : CNFRefutation 19.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 39 ( 39 unt; 0 def)
% Number of atoms : 39 ( 38 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 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 : 95 ( 95 !; 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),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
difference(difference(a,b),c) != difference(difference(a,c),difference(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),X1),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,plain,
difference(difference(a,b),c) != difference(difference(a,c),difference(b,c)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f15,plain,
! [X0,X1] : difference(difference(X0,X1),X1) = difference(X0,X1),
inference(paramodulation,[status(thm)],[f5,f5]) ).
fof(f21,plain,
! [X0,X1] : difference(difference(X0,X1),difference(X0,X1)) = difference(X1,difference(X1,difference(X0,X1))),
inference(paramodulation,[status(thm)],[f15,f6]) ).
fof(f29,plain,
! [X0,X1] : difference(difference(X0,X1),difference(X0,X1)) = difference(X1,X1),
inference(forward_demodulation,[status(thm)],[f5,f21]) ).
fof(f33,plain,
! [X0,X1,X2,X3] : difference(difference(difference(X0,X1),X2),X3) = difference(difference(difference(X0,X2),X3),X1),
inference(paramodulation,[status(thm)],[f7,f7]) ).
fof(f36,plain,
! [X0,X1,X2] : difference(difference(X0,difference(X0,X1)),X2) = difference(difference(X1,X2),difference(X1,X0)),
inference(paramodulation,[status(thm)],[f6,f7]) ).
fof(f38,plain,
! [X0,X1,X2] : difference(X0,X1) = difference(difference(X0,X1),difference(X2,X0)),
inference(paramodulation,[status(thm)],[f5,f7]) ).
fof(f47,plain,
! [X0,X1,X2] : difference(X0,difference(X0,difference(X1,X2))) = difference(difference(X1,X2),difference(difference(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f7,f6]) ).
fof(f50,plain,
! [X0,X1,X2] : difference(X0,difference(difference(X1,X0),X2)) = X0,
inference(paramodulation,[status(thm)],[f7,f5]) ).
fof(f83,plain,
! [X0,X1,X2] : difference(X0,difference(X0,difference(difference(X1,X0),X2))) = difference(difference(difference(X1,X0),X2),difference(difference(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f50,f29]) ).
fof(f103,plain,
! [X0,X1,X2] : difference(X0,X0) = difference(difference(difference(X1,X0),X2),difference(difference(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f50,f83]) ).
fof(f104,plain,
! [X0,X1] : difference(X0,X0) = difference(X1,X1),
inference(forward_demodulation,[status(thm)],[f29,f103]) ).
fof(f125,plain,
! [X0,X1] : difference(X0,difference(X1,X1)) = X0,
inference(paramodulation,[status(thm)],[f104,f50]) ).
fof(f127,plain,
! [X0,X1,X2] : difference(difference(X0,X1),X0) = difference(difference(X2,X2),X1),
inference(paramodulation,[status(thm)],[f104,f7]) ).
fof(f162,plain,
! [X0,X1] : difference(difference(X0,X0),X1) = difference(X0,X0),
inference(paramodulation,[status(thm)],[f125,f5]) ).
fof(f167,plain,
! [X0,X1,X2] : difference(difference(X0,X1),X0) = difference(X2,X2),
inference(backward_demodulation,[status(thm)],[f162,f127]) ).
fof(f252,plain,
! [X0,X1,X2] : difference(X0,difference(X0,difference(X0,X1))) = difference(difference(X0,X1),difference(X2,X2)),
inference(paramodulation,[status(thm)],[f167,f6]) ).
fof(f283,plain,
! [X0,X1] : difference(X0,difference(X0,difference(X0,X1))) = difference(X0,X1),
inference(forward_demodulation,[status(thm)],[f125,f252]) ).
fof(f361,plain,
! [X0,X1] : difference(X0,difference(X1,difference(X1,X0))) = difference(X0,X1),
inference(paramodulation,[status(thm)],[f6,f283]) ).
fof(f384,plain,
! [X0,X1,X2] : difference(difference(X0,X1),difference(X0,difference(X0,X2))) = difference(difference(X0,X2),X1),
inference(paramodulation,[status(thm)],[f283,f7]) ).
fof(f435,plain,
! [X0,X1,X2,X3] : difference(difference(X0,X1),X2) = difference(difference(difference(X0,X1),X2),difference(X3,X0)),
inference(paramodulation,[status(thm)],[f5,f33]) ).
fof(f1054,plain,
! [X0,X1,X2] : difference(X0,difference(X0,X1)) = difference(difference(X1,difference(X2,X0)),difference(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f38]) ).
fof(f3425,plain,
! [X0,X1,X2] : difference(difference(X0,X1),difference(difference(X2,difference(X2,X0)),X1)) = difference(difference(X0,X2),difference(difference(X0,difference(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f36,f47]) ).
fof(f7589,plain,
! [X0,X1,X2] : difference(X0,difference(X0,difference(X1,X2))) = difference(difference(difference(X0,difference(X0,X1)),X2),difference(difference(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f36,f1054]) ).
fof(f7986,plain,
! [X0,X1,X2] : difference(difference(X0,X1),difference(difference(X2,difference(X2,X0)),X1)) = difference(difference(X0,X2),difference(X0,difference(X0,difference(X1,X2)))),
inference(backward_demodulation,[status(thm)],[f8027,f3425]) ).
fof(f8027,plain,
! [X0,X1,X2] : difference(X0,difference(X0,difference(X1,X2))) = difference(difference(X0,difference(X0,X1)),X2),
inference(forward_demodulation,[status(thm)],[f435,f7589]) ).
fof(f8654,plain,
! [X0,X1,X2] : difference(difference(X0,X1),difference(X2,difference(X2,difference(X0,X1)))) = difference(difference(X0,X2),difference(X0,difference(X0,difference(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f8027,f7986]) ).
fof(f8655,plain,
! [X0,X1,X2] : difference(difference(X0,X1),X2) = difference(difference(X0,X2),difference(X0,difference(X0,difference(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f361,f8654]) ).
fof(f8656,plain,
! [X0,X1,X2] : difference(difference(X0,X1),X2) = difference(difference(X0,difference(X1,X2)),X2),
inference(forward_demodulation,[status(thm)],[f384,f8655]) ).
fof(f8659,plain,
difference(difference(a,b),c) != difference(difference(a,b),c),
inference(backward_demodulation,[status(thm)],[f8685,f8]) ).
fof(f8685,plain,
! [X0,X1,X2] : difference(difference(X0,X1),X2) = difference(difference(X0,X2),difference(X1,X2)),
inference(forward_demodulation,[status(thm)],[f7,f8656]) ).
fof(f9056,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f8659]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG007-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.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 : Mon Sep 21 12:53:46 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 19.12/2.94 % Refutation found
% 19.12/2.94 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 19.12/2.94 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 15.67/4.21 % Elapsed time: 3.615448 seconds
% 15.67/4.21 % CPU time: 16.683001 seconds
% 15.67/4.21 % Total memory used: 103.730 MB
% 15.67/4.21 % Net memory used: 100.599 MB
%------------------------------------------------------------------------------