%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : BOO075-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 : Sun Sep 27 06:55:14 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.43s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 2
% Syntax : Number of formulae : 25 ( 25 unt; 0 def)
% Number of atoms : 25 ( 24 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 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 : 51 ( 5 sgn 3 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sh_1,axiom,
! [VAR_0,VAR_1,VAR_2] : nand(nand(VAR_0,nand(nand(VAR_1,VAR_0),VAR_0)),nand(VAR_1,nand(VAR_2,VAR_0))) = VAR_1,
file('theBenchmark.p',sh_1) ).
cnf(c_1,plain,
nand(nand(A,nand(nand(B,A),A)),nand(B,nand(C,A))) = B,
inference(clausify,[status(thm)],[sh_1]) ).
fof(prove_meredith_2_basis_1,axiom,
nand(nand(a,a),nand(b,a)) != a,
file('theBenchmark.p',prove_meredith_2_basis_1) ).
cnf(c_2,plain,
nand(nand(a,a),nand(b,a)) != a,
inference(clausify,[status(thm)],[prove_meredith_2_basis_1]) ).
cnf(c_3,plain,
nand(nand(nand(A,nand(B,C)),nand(A,nand(A,nand(B,C)))),nand(nand(C,nand(nand(A,C),C)),nand(D,nand(A,nand(B,C))))) = nand(C,nand(nand(A,C),C)),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_4,plain,
nand(nand(nand(A,nand(B,C)),nand(nand(D,nand(A,nand(B,C))),nand(A,nand(B,C)))),nand(D,A)) = D,
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_5,plain,
nand(nand(nand(A,B),nand(nand(nand(B,nand(nand(C,B),B)),nand(A,B)),nand(A,B))),C) = nand(B,nand(nand(C,B),B)),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_62,plain,
nand(nand(A,nand(nand(B,nand(nand(C,nand(nand(A,C),C)),nand(A,nand(D,C)))),nand(nand(C,nand(nand(A,C),C)),nand(A,nand(D,C))))),nand(B,nand(C,nand(nand(A,C),C)))) = B,
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_63,plain,
nand(nand(A,nand(nand(B,A),nand(nand(C,nand(nand(A,C),C)),nand(A,nand(D,C))))),nand(B,nand(C,nand(nand(A,C),C)))) = B,
inference(paramod,[status(thm)],[c_1,c_62]) ).
cnf(c_8,plain,
nand(nand(A,nand(nand(B,A),A)),nand(B,nand(C,nand(nand(A,C),C)))) = B,
inference(paramod,[status(thm)],[c_1,c_63]) ).
cnf(c_9,plain,
nand(nand(A,nand(nand(nand(B,nand(nand(B,B),B)),A),A)),B) = nand(B,nand(nand(B,B),B)),
inference(paramod,[status(thm)],[c_1,c_8]) ).
cnf(c_64,plain,
nand(nand(nand(A,nand(nand(A,A),A)),nand(A,nand(A,nand(nand(A,A),A)))),A) = nand(A,nand(nand(A,A),A)),
inference(paramod,[status(thm)],[c_8,c_3]) ).
cnf(c_65,plain,
nand(A,A) = nand(A,nand(nand(A,A),A)),
inference(paramod,[status(thm)],[c_8,c_64]) ).
cnf(c_11,plain,
nand(A,nand(nand(A,A),A)) = nand(A,A),
inference(copy,[status(thm)],[c_65]) ).
cnf(c_66,plain,
nand(nand(A,nand(nand(nand(B,B),A),A)),B) = nand(B,nand(nand(B,B),B)),
inference(paramod,[status(thm)],[c_11,c_9]) ).
cnf(c_14,plain,
nand(nand(A,nand(nand(nand(B,B),A),A)),B) = nand(B,B),
inference(paramod,[status(thm)],[c_11,c_66]) ).
cnf(c_67,plain,
nand(nand(A,nand(nand(A,A),A)),nand(A,A)) = A,
inference(paramod,[status(thm)],[c_11,c_1]) ).
cnf(c_17,plain,
nand(nand(A,A),nand(A,A)) = A,
inference(paramod,[status(thm)],[c_11,c_67]) ).
cnf(c_68,plain,
nand(nand(nand(A,B),nand(nand(nand(A,B),nand(A,B)),nand(A,B))),nand(nand(A,B),nand(A,B))) = nand(B,nand(nand(nand(nand(A,B),nand(A,B)),B),B)),
inference(paramod,[status(thm)],[c_14,c_5]) ).
cnf(c_69,plain,
nand(nand(nand(A,B),nand(A,B)),nand(nand(A,B),nand(A,B))) = nand(B,nand(nand(nand(nand(A,B),nand(A,B)),B),B)),
inference(paramod,[status(thm)],[c_11,c_68]) ).
cnf(c_70,plain,
nand(A,B) = nand(B,nand(nand(nand(nand(A,B),nand(A,B)),B),B)),
inference(paramod,[status(thm)],[c_17,c_69]) ).
cnf(c_49,plain,
nand(A,nand(nand(nand(nand(B,A),nand(B,A)),A),A)) = nand(B,A),
inference(copy,[status(thm)],[c_70]) ).
cnf(c_71,plain,
nand(nand(A,nand(nand(A,A),A)),nand(B,A)) = A,
inference(paramod,[status(thm)],[c_49,c_1]) ).
cnf(c_60,plain,
nand(nand(A,A),nand(B,A)) = A,
inference(paramod,[status(thm)],[c_11,c_71]) ).
cnf(c_61,plain,
$false,
inference(resolve,[status(thm)],[c_60,c_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO075-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % 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 22:45:06 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 2868852 was started by sandbox on n002,
% 0.10/0.38 % Sat Sep 26 22:45:06 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.43
% 0.10/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.43
% 0.10/0.43 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.10/0.43 % Length of proof is 13.
% 0.10/0.43 % Level of proof is 7.
% 0.10/0.43 % Maximum clause weight is 97.000.
% 0.10/0.43 % Given clauses 16.
% 0.10/0.43
% 0.10/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------