%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO075-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 12:06:39 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 2
% Syntax : Number of formulae : 24 ( 24 unt; 0 def)
% Number of atoms : 24 ( 23 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 50 ( 50 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : nand(nand(A,nand(nand(B,A),A)),nand(B,nand(C,A))) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
nand(nand(a,a),nand(b,a)) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,plain,
! [X0,X1,X2] : nand(nand(X0,nand(nand(X1,X0),X0)),nand(X1,nand(X2,X0))) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f4,plain,
nand(nand(a,a),nand(b,a)) != a,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0,X1,X2,X3] : nand(nand(nand(X0,nand(X1,X2)),nand(X0,nand(X0,nand(X1,X2)))),nand(nand(X2,nand(nand(X0,X2),X2)),nand(X3,nand(X0,nand(X1,X2))))) = nand(X2,nand(nand(X0,X2),X2)),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f10,plain,
! [X0,X1,X2] : nand(nand(nand(X0,X1),nand(nand(nand(X1,nand(nand(X2,X1),X1)),nand(X0,X1)),nand(X0,X1))),X2) = nand(X1,nand(nand(X2,X1),X1)),
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f11,plain,
! [X0,X1,X2,X3] : nand(nand(nand(X0,nand(X1,X2)),nand(nand(X3,nand(X0,nand(X1,X2))),nand(X0,nand(X1,X2)))),nand(X3,X0)) = X3,
inference(paramodulation,[status(thm)],[f3,f3]) ).
fof(f13,plain,
! [X0,X1,X2,X3] : nand(nand(X0,nand(nand(X1,nand(nand(X2,nand(nand(X0,X2),X2)),nand(X0,nand(X3,X2)))),nand(nand(X2,nand(nand(X0,X2),X2)),nand(X0,nand(X3,X2))))),nand(X1,nand(X2,nand(nand(X0,X2),X2)))) = X1,
inference(paramodulation,[status(thm)],[f3,f11]) ).
fof(f33,plain,
! [X0,X1,X2,X3] : nand(nand(X0,nand(nand(X1,X0),nand(nand(X2,nand(nand(X0,X2),X2)),nand(X0,nand(X3,X2))))),nand(X1,nand(X2,nand(nand(X0,X2),X2)))) = X1,
inference(forward_demodulation,[status(thm)],[f3,f13]) ).
fof(f34,plain,
! [X0,X1,X2] : nand(nand(X0,nand(nand(X1,X0),X0)),nand(X1,nand(X2,nand(nand(X0,X2),X2)))) = X1,
inference(forward_demodulation,[status(thm)],[f3,f33]) ).
fof(f103,plain,
! [X0] : nand(nand(nand(X0,nand(nand(X0,X0),X0)),nand(X0,nand(X0,nand(nand(X0,X0),X0)))),X0) = nand(X0,nand(nand(X0,X0),X0)),
inference(paramodulation,[status(thm)],[f34,f9]) ).
fof(f166,plain,
! [X0] : nand(X0,X0) = nand(X0,nand(nand(X0,X0),X0)),
inference(forward_demodulation,[status(thm)],[f34,f103]) ).
fof(f210,plain,
! [X0,X1] : nand(nand(X0,X0),nand(X0,nand(X1,X0))) = X0,
inference(paramodulation,[status(thm)],[f166,f3]) ).
fof(f213,plain,
! [X0,X1] : nand(nand(nand(X0,nand(nand(X0,X0),X0)),nand(X0,nand(X0,nand(nand(X0,X0),X0)))),nand(nand(X0,nand(nand(X0,X0),X0)),nand(X1,nand(X0,X0)))) = nand(X0,nand(nand(X0,X0),X0)),
inference(paramodulation,[status(thm)],[f166,f9]) ).
fof(f241,plain,
! [X0,X1] : nand(X0,nand(nand(X0,nand(nand(X0,X0),X0)),nand(X1,nand(X0,X0)))) = nand(X0,nand(nand(X0,X0),X0)),
inference(forward_demodulation,[status(thm)],[f34,f213]) ).
fof(f242,plain,
! [X0,X1] : nand(X0,nand(nand(X0,X0),nand(X1,nand(X0,X0)))) = nand(X0,nand(nand(X0,X0),X0)),
inference(forward_demodulation,[status(thm)],[f166,f241]) ).
fof(f243,plain,
! [X0,X1] : nand(X0,nand(nand(X0,X0),nand(X1,nand(X0,X0)))) = nand(X0,X0),
inference(forward_demodulation,[status(thm)],[f166,f242]) ).
fof(f442,plain,
! [X0,X1] : nand(nand(X0,nand(nand(nand(X1,X1),X0),X0)),X1) = nand(X1,X1),
inference(paramodulation,[status(thm)],[f210,f34]) ).
fof(f586,plain,
! [X0,X1] : nand(nand(X0,nand(nand(X1,X0),X0)),nand(X1,X1)) = X1,
inference(paramodulation,[status(thm)],[f243,f34]) ).
fof(f841,plain,
! [X0,X1] : nand(nand(nand(X0,X1),nand(nand(nand(X0,X1),nand(X0,X1)),nand(X0,X1))),nand(nand(X0,X1),nand(X0,X1))) = nand(X1,nand(nand(nand(nand(X0,X1),nand(X0,X1)),X1),X1)),
inference(paramodulation,[status(thm)],[f442,f10]) ).
fof(f924,plain,
! [X0,X1] : nand(X0,X1) = nand(X1,nand(nand(nand(nand(X0,X1),nand(X0,X1)),X1),X1)),
inference(forward_demodulation,[status(thm)],[f586,f841]) ).
fof(f1157,plain,
! [X0,X1] : nand(nand(X0,X0),nand(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f924,f210]) ).
fof(f1299,plain,
a != a,
inference(backward_demodulation,[status(thm)],[f1157,f4]) ).
fof(f1359,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f1299]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO075-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n014.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 : Mon Sep 21 13:52:04 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.14/0.42 % Refutation found
% 0.14/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.71/1.64 % Elapsed time: 1.057678 seconds
% 2.71/1.64 % CPU time: 0.377110 seconds
% 2.71/1.64 % Total memory used: 20.351 MB
% 2.71/1.64 % Net memory used: 20.124 MB
%------------------------------------------------------------------------------