%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO109+1 : TPTP v9.3.1. Released v3.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 : Sun Sep 27 06:55:16 AM UTC 2026
% Result : Theorem 227.86s 30.21s
% Output : CNFRefutation 227.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 3
% Syntax : Number of formulae : 80 ( 43 unt; 0 def)
% Number of atoms : 119 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 80 ( 41 ~; 37 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 267 ( 45 sgn 11 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(wajsbergs_axiom,axiom,
! [A,B,C,D] : p(nand(nand(A,nand(B,C)),nand(nand(nand(D,C),nand(nand(A,D),nand(A,D))),nand(A,nand(A,B))))),
file('theBenchmark.p',wajsbergs_axiom) ).
fof(modus_ponens_for_nand,axiom,
! [P,Q,R] :
( ( p(P)
& p(nand(P,nand(Q,R))) )
=> p(R) ),
file('theBenchmark.p',modus_ponens_for_nand) ).
fof(tautology,conjecture,
! [A,B] : p(nand(nand(A,nand(B,B)),nand(nand(nand(B,B),nand(nand(A,A),nand(A,A))),nand(nand(B,B),nand(nand(A,A),nand(A,A)))))),
file('theBenchmark.p',tautology) ).
fof(tautology_neg,negated_conjecture,
~ ! [A,B] : p(nand(nand(A,nand(B,B)),nand(nand(nand(B,B),nand(nand(A,A),nand(A,A))),nand(nand(B,B),nand(nand(A,A),nand(A,A)))))),
inference(assume_negation,[status(cth)],[tautology]) ).
cnf(c_4,plain,
p(nand(nand(A,nand(B,C)),nand(nand(nand(D,C),nand(nand(A,D),nand(A,D))),nand(A,nand(A,B))))),
inference(clausify,[status(thm)],[wajsbergs_axiom]) ).
cnf(c_5,plain,
( p(C)
| ~ p(A)
| ~ p(nand(A,nand(B,C))) ),
inference(clausify,[status(thm)],[modus_ponens_for_nand]) ).
fof(nnf_3,plain,
? [A,B] : ~ p(nand(nand(A,nand(B,B)),nand(nand(nand(B,B),nand(nand(A,A),nand(A,A))),nand(nand(B,B),nand(nand(A,A),nand(A,A)))))),
inference(fof_nnf,[status(thm)],[tautology_neg]) ).
fof(sk_tautology_neg,plain,
~ p(nand(nand(sK0,nand(sK1,sK1)),nand(nand(nand(sK1,sK1),nand(nand(sK0,sK0),nand(sK0,sK0))),nand(nand(sK1,sK1),nand(nand(sK0,sK0),nand(sK0,sK0)))))),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK0),skolemize(B,sK1)],[nnf_3]) ).
cnf(c_6,negated_conjecture,
~ p(nand(nand(sK0,nand(sK1,sK1)),nand(nand(nand(sK1,sK1),nand(nand(sK0,sK0),nand(sK0,sK0))),nand(nand(sK1,sK1),nand(nand(sK0,sK0),nand(sK0,sK0)))))),
inference(split_conjunct,[status(thm)],[sk_tautology_neg]) ).
cnf(c_15129,plain,
( p(nand(A,nand(A,B)))
| ~ p(nand(A,nand(B,C))) ),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_7,plain,
p(nand(nand(A,nand(B,C)),nand(nand(A,nand(B,C)),nand(nand(D,C),nand(nand(A,D),nand(A,D)))))),
inference(resolve,[status(thm)],[c_15129,c_4]) ).
cnf(c_15130,plain,
( p(nand(nand(D,C),nand(nand(A,D),nand(A,D))))
| ~ p(nand(A,nand(B,C))) ),
inference(resolve,[status(thm)],[c_5,c_7]) ).
cnf(c_8,plain,
p(nand(nand(A,nand(nand(B,C),nand(nand(D,B),nand(D,B)))),nand(nand(nand(D,nand(E,C)),A),nand(nand(D,nand(E,C)),A)))),
inference(resolve,[status(thm)],[c_15130,c_7]) ).
cnf(c_15131,plain,
( p(nand(A,nand(A,B)))
| ~ p(nand(A,nand(B,C))) ),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_9,plain,
p(nand(nand(A,nand(B,C)),nand(nand(A,nand(B,C)),nand(A,nand(B,C))))),
inference(resolve,[status(thm)],[c_15131,c_7]) ).
cnf(c_15132,plain,
( p(nand(nand(D,C),nand(nand(A,D),nand(A,D))))
| ~ p(nand(A,nand(B,C))) ),
inference(resolve,[status(thm)],[c_5,c_7]) ).
cnf(c_10,plain,
p(nand(nand(A,nand(B,nand(B,C))),nand(nand(nand(B,nand(C,D)),A),nand(nand(B,nand(C,D)),A)))),
inference(resolve,[status(thm)],[c_15132,c_4]) ).
cnf(c_15133,plain,
( p(nand(nand(D,C),nand(nand(A,D),nand(A,D))))
| ~ p(nand(A,nand(B,C))) ),
inference(resolve,[status(thm)],[c_5,c_7]) ).
cnf(c_11,plain,
p(nand(nand(A,nand(B,nand(C,D))),nand(nand(nand(B,nand(C,D)),A),nand(nand(B,nand(C,D)),A)))),
inference(resolve,[status(thm)],[c_15133,c_9]) ).
cnf(c_15134,plain,
( p(nand(nand(D,C),nand(nand(A,D),nand(A,D))))
| ~ p(nand(A,nand(B,C))) ),
inference(resolve,[status(thm)],[c_5,c_7]) ).
cnf(c_12,plain,
p(nand(nand(A,nand(nand(B,nand(C,D)),E)),nand(nand(nand(E,nand(B,nand(B,C))),A),nand(nand(E,nand(B,nand(B,C))),A)))),
inference(resolve,[status(thm)],[c_15134,c_10]) ).
cnf(c_15135,plain,
( p(nand(A,nand(A,B)))
| ~ p(nand(A,nand(B,C))) ),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_13,plain,
p(nand(nand(A,nand(B,nand(B,C))),nand(nand(A,nand(B,nand(B,C))),nand(nand(B,nand(C,D)),A)))),
inference(resolve,[status(thm)],[c_15135,c_10]) ).
cnf(c_15136,plain,
( p(nand(nand(B,nand(C,D)),A))
| ~ p(nand(A,nand(B,nand(C,D)))) ),
inference(resolve,[status(thm)],[c_5,c_11]) ).
cnf(c_14,plain,
p(nand(nand(nand(nand(A,nand(B,C)),D),nand(nand(A,nand(B,C)),D)),nand(D,nand(A,nand(B,C))))),
inference(resolve,[status(thm)],[c_15136,c_11]) ).
cnf(c_15137,plain,
( p(nand(A,nand(A,B)))
| ~ p(nand(A,nand(B,C))) ),
inference(resolve,[status(thm)],[c_5,c_4]) ).
cnf(c_16,plain,
p(nand(nand(A,nand(B,nand(C,D))),nand(nand(A,nand(B,nand(C,D))),nand(nand(B,nand(C,D)),A)))),
inference(resolve,[status(thm)],[c_15137,c_11]) ).
cnf(c_15138,plain,
( p(nand(nand(B,nand(C,D)),A))
| ~ p(nand(A,nand(B,nand(C,D)))) ),
inference(resolve,[status(thm)],[c_5,c_11]) ).
cnf(c_18,plain,
p(nand(nand(nand(A,nand(B,C)),nand(A,nand(B,C))),nand(A,nand(B,C)))),
inference(resolve,[status(thm)],[c_15138,c_9]) ).
cnf(c_15139,plain,
( p(nand(nand(B,nand(C,D)),A))
| ~ p(nand(A,nand(B,nand(B,C)))) ),
inference(resolve,[status(thm)],[c_5,c_10]) ).
cnf(c_22,plain,
p(nand(nand(A,nand(B,C)),nand(nand(A,nand(A,B)),nand(A,nand(A,B))))),
inference(resolve,[status(thm)],[c_15139,c_18]) ).
cnf(c_15140,plain,
( p(nand(nand(D,nand(E,C)),A))
| ~ p(nand(A,nand(nand(B,C),nand(nand(D,B),nand(D,B))))) ),
inference(resolve,[status(thm)],[c_5,c_8]) ).
cnf(c_23,plain,
p(nand(nand(A,nand(B,C)),nand(nand(nand(D,C),nand(nand(A,D),nand(A,D))),nand(nand(D,C),nand(nand(A,D),nand(A,D)))))),
inference(resolve,[status(thm)],[c_15140,c_18]) ).
cnf(c_15141,plain,
( p(nand(A,nand(A,B)))
| ~ p(nand(A,nand(B,C))) ),
inference(resolve,[status(thm)],[c_5,c_22]) ).
cnf(c_26,plain,
p(nand(nand(A,nand(B,C)),nand(nand(A,nand(B,C)),nand(A,nand(A,B))))),
inference(resolve,[status(thm)],[c_15141,c_22]) ).
cnf(c_15142,plain,
( p(nand(nand(B,nand(C,D)),A))
| ~ p(nand(A,nand(B,nand(C,D)))) ),
inference(resolve,[status(thm)],[c_5,c_11]) ).
cnf(c_27,plain,
p(nand(nand(nand(A,nand(A,B)),nand(A,nand(A,B))),nand(A,nand(B,C)))),
inference(resolve,[status(thm)],[c_15142,c_22]) ).
cnf(c_15143,plain,
( p(nand(nand(B,nand(C,D)),A))
| ~ p(nand(A,nand(B,nand(B,C)))) ),
inference(resolve,[status(thm)],[c_5,c_13]) ).
cnf(c_35,plain,
p(nand(nand(nand(A,nand(A,nand(A,A))),nand(A,B)),nand(A,nand(A,nand(A,A))))),
inference(resolve,[status(thm)],[c_15143,c_13]) ).
cnf(c_15144,plain,
( p(nand(A,nand(A,B)))
| ~ p(nand(A,nand(B,C))) ),
inference(resolve,[status(thm)],[c_5,c_26]) ).
cnf(c_38,plain,
p(nand(nand(nand(nand(A,nand(B,C)),D),nand(nand(A,nand(B,C)),D)),nand(nand(nand(nand(A,nand(B,C)),D),nand(nand(A,nand(B,C)),D)),D))),
inference(resolve,[status(thm)],[c_15144,c_14]) ).
cnf(c_15145,plain,
( p(nand(nand(D,nand(E,C)),A))
| ~ p(nand(A,nand(nand(B,C),nand(nand(D,B),nand(D,B))))) ),
inference(resolve,[status(thm)],[c_5,c_8]) ).
cnf(c_41,plain,
p(nand(nand(A,nand(B,C)),nand(nand(nand(nand(A,D),nand(A,D)),nand(D,C)),nand(nand(nand(A,D),nand(A,D)),nand(D,C))))),
inference(resolve,[status(thm)],[c_15145,c_14]) ).
cnf(c_15146,plain,
( p(nand(nand(D,nand(E,C)),A))
| ~ p(nand(A,nand(nand(B,C),nand(nand(D,B),nand(D,B))))) ),
inference(resolve,[status(thm)],[c_5,c_8]) ).
cnf(c_43,plain,
p(nand(nand(A,nand(B,C)),nand(nand(nand(D,C),nand(nand(D,C),nand(A,D))),nand(nand(D,C),nand(nand(D,C),nand(A,D)))))),
inference(resolve,[status(thm)],[c_15146,c_27]) ).
cnf(c_15147,plain,
( p(nand(nand(D,C),nand(nand(A,D),nand(A,D))))
| ~ p(nand(A,nand(B,C))) ),
inference(resolve,[status(thm)],[c_5,c_7]) ).
cnf(c_44,plain,
p(nand(nand(A,nand(B,C)),nand(nand(nand(nand(D,nand(D,B)),nand(D,nand(D,B))),A),nand(nand(nand(D,nand(D,B)),nand(D,nand(D,B))),A)))),
inference(resolve,[status(thm)],[c_15147,c_27]) ).
cnf(c_15148,plain,
( p(nand(nand(B,nand(C,D)),A))
| ~ p(nand(A,nand(B,nand(C,D)))) ),
inference(resolve,[status(thm)],[c_5,c_16]) ).
cnf(c_94,plain,
p(nand(nand(A,nand(A,nand(A,A))),nand(nand(A,nand(A,nand(A,A))),nand(A,B)))),
inference(resolve,[status(thm)],[c_15148,c_35]) ).
cnf(c_15149,plain,
( p(nand(nand(E,nand(B,nand(B,C))),A))
| ~ p(nand(A,nand(nand(B,nand(C,D)),E))) ),
inference(resolve,[status(thm)],[c_5,c_12]) ).
cnf(c_128,plain,
p(nand(nand(nand(A,B),nand(A,nand(A,A))),nand(A,nand(A,nand(A,A))))),
inference(resolve,[status(thm)],[c_15149,c_94]) ).
cnf(c_15150,plain,
( p(nand(nand(B,nand(C,D)),A))
| ~ p(nand(A,nand(B,nand(B,C)))) ),
inference(resolve,[status(thm)],[c_5,c_13]) ).
cnf(c_133,plain,
p(nand(nand(A,nand(nand(A,A),B)),nand(nand(A,C),nand(A,nand(A,A))))),
inference(resolve,[status(thm)],[c_15150,c_128]) ).
cnf(c_15151,plain,
( p(nand(nand(B,nand(C,D)),A))
| ~ p(nand(A,nand(B,nand(C,D)))) ),
inference(resolve,[status(thm)],[c_5,c_16]) ).
cnf(c_138,plain,
p(nand(nand(nand(A,B),nand(A,nand(A,A))),nand(A,nand(nand(A,A),C)))),
inference(resolve,[status(thm)],[c_15151,c_133]) ).
cnf(c_15152,plain,
( p(nand(nand(D,C),nand(nand(A,D),nand(A,D))))
| ~ p(nand(A,nand(B,C))) ),
inference(resolve,[status(thm)],[c_5,c_23]) ).
cnf(c_202,plain,
p(nand(nand(A,nand(nand(nand(B,C),nand(B,C)),nand(C,D))),nand(nand(nand(B,nand(E,D)),A),nand(nand(B,nand(E,D)),A)))),
inference(resolve,[status(thm)],[c_15152,c_41]) ).
cnf(c_15153,plain,
( p(nand(nand(nand(D,nand(D,B)),nand(D,nand(D,B))),A))
| ~ p(nand(A,nand(B,C))) ),
inference(resolve,[status(thm)],[c_5,c_44]) ).
cnf(c_286,plain,
p(nand(nand(nand(A,nand(A,B)),nand(A,nand(A,B))),nand(nand(B,C),nand(B,nand(B,B))))),
inference(resolve,[status(thm)],[c_15153,c_138]) ).
cnf(c_15154,plain,
( p(D)
| ~ p(nand(nand(nand(A,nand(B,C)),D),nand(nand(A,nand(B,C)),D))) ),
inference(resolve,[status(thm)],[c_5,c_38]) ).
cnf(c_312,plain,
p(nand(A,nand(A,A))),
inference(resolve,[status(thm)],[c_15154,c_286]) ).
cnf(c_15155,plain,
( p(nand(nand(nand(D,nand(D,B)),nand(D,nand(D,B))),A))
| ~ p(nand(A,nand(B,C))) ),
inference(resolve,[status(thm)],[c_5,c_44]) ).
cnf(c_317,plain,
p(nand(nand(nand(A,nand(A,B)),nand(A,nand(A,B))),B)),
inference(resolve,[status(thm)],[c_15155,c_312]) ).
cnf(c_15156,plain,
( p(nand(nand(D,C),nand(nand(D,C),nand(A,D))))
| ~ p(nand(A,nand(B,C))) ),
inference(resolve,[status(thm)],[c_5,c_43]) ).
cnf(c_318,plain,
p(nand(nand(A,B),nand(nand(A,B),nand(B,A)))),
inference(resolve,[status(thm)],[c_15156,c_312]) ).
cnf(c_15157,plain,
( p(nand(B,A))
| ~ p(nand(A,B)) ),
inference(resolve,[status(thm)],[c_5,c_318]) ).
cnf(c_414,plain,
p(nand(A,nand(nand(B,nand(B,A)),nand(B,nand(B,A))))),
inference(resolve,[status(thm)],[c_15157,c_317]) ).
cnf(c_15158,plain,
( p(nand(nand(D,C),nand(nand(A,D),nand(A,D))))
| ~ p(nand(A,nand(B,C))) ),
inference(resolve,[status(thm)],[c_5,c_23]) ).
cnf(c_493,plain,
p(nand(nand(A,nand(B,nand(B,C))),nand(nand(C,A),nand(C,A)))),
inference(resolve,[status(thm)],[c_15158,c_414]) ).
cnf(c_15159,plain,
( p(nand(B,nand(B,A)))
| ~ p(A) ),
inference(resolve,[status(thm)],[c_5,c_414]) ).
cnf(c_502,plain,
p(nand(A,nand(A,nand(B,nand(B,B))))),
inference(resolve,[status(thm)],[c_15159,c_312]) ).
cnf(c_15160,plain,
( p(nand(nand(nand(A,D),nand(A,D)),nand(D,C)))
| ~ p(nand(A,nand(B,C))) ),
inference(resolve,[status(thm)],[c_5,c_41]) ).
cnf(c_617,plain,
p(nand(nand(nand(A,B),nand(A,B)),nand(B,nand(C,nand(C,C))))),
inference(resolve,[status(thm)],[c_15160,c_502]) ).
cnf(c_15161,plain,
( p(nand(C,A))
| ~ p(nand(A,nand(B,nand(B,C)))) ),
inference(resolve,[status(thm)],[c_5,c_493]) ).
cnf(c_1565,plain,
p(nand(nand(A,A),nand(nand(B,A),nand(B,A)))),
inference(resolve,[status(thm)],[c_15161,c_617]) ).
cnf(c_15162,plain,
( p(nand(nand(nand(A,D),nand(A,D)),nand(D,C)))
| ~ p(nand(A,nand(B,C))) ),
inference(resolve,[status(thm)],[c_5,c_41]) ).
cnf(c_1586,plain,
p(nand(nand(nand(nand(A,A),B),nand(nand(A,A),B)),nand(B,nand(C,A)))),
inference(resolve,[status(thm)],[c_15162,c_1565]) ).
cnf(c_15163,plain,
( p(nand(nand(B,nand(E,D)),A))
| ~ p(nand(A,nand(nand(nand(B,C),nand(B,C)),nand(C,D)))) ),
inference(resolve,[status(thm)],[c_5,c_202]) ).
cnf(c_15127,plain,
p(nand(nand(A,nand(B,C)),nand(nand(nand(C,C),nand(nand(A,D),nand(A,D))),nand(nand(C,C),nand(nand(A,D),nand(A,D)))))),
inference(resolve,[status(thm)],[c_15163,c_1586]) ).
cnf(c_15128,plain,
$false,
inference(resolve,[status(thm)],[c_15127,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO109+1 : TPTP v9.3.1. Released v3.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 22:50:14 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 959881 was started by sandbox2 on n015,
% 0.10/0.37 % Sat Sep 26 22:50:14 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 227.86/30.21
% 227.86/30.21 % given #500 (A,wt=69): 290 p(nand(nand(nand(A,nand(A,B)),nand(A,nand(A,B))),nand(nand(B,nand(B,C)),nand(B,nand(C,D))))). [hyper(5,a,44,a,b,59,a)].
% 227.86/30.21
% 227.86/30.21 % SZS status Theorem for theBenchmark
% 227.86/30.21
% 227.86/30.21 % Proof 1 at 4.51 (+ 1.13) seconds.
% 227.86/30.21 % Length of proof is 42.
% 227.86/30.21 % Level of proof is 19.
% 227.86/30.21 % Maximum clause weight is 99.000.
% 227.86/30.21 % Given clauses 848.
% 227.86/30.21
% 227.86/30.21 % SZS output start CNFRefutation for theBenchmark
% See solution above
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