%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HWC001-1 : TPTP v9.3.1. Bugfixed v1.1.1.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 07:32:06 AM UTC 2026
% Result : Unsatisfiable 0.14s 5.60s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 44 unt; 0 def)
% Number of atoms : 68 ( 10 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 17 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 68 ( 1 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(nand_definition,axiom,
! [VAR_0,VAR_1] : nand(VAR_0,VAR_1) = not(and(VAR_0,VAR_1)),
file('theBenchmark.p',nand_definition) ).
cnf(c_1,plain,
nand(A,B) = not(and(A,B)),
inference(clausify,[status(thm)],[nand_definition]) ).
fof(and_definition1,axiom,
! [VAR_0] : and(VAR_0,n0) = n0,
file('theBenchmark.p',and_definition1) ).
cnf(c_2,plain,
and(A,n0) = n0,
inference(clausify,[status(thm)],[and_definition1]) ).
fof(and_definition2,axiom,
! [VAR_0] : and(VAR_0,n1) = VAR_0,
file('theBenchmark.p',and_definition2) ).
cnf(c_3,plain,
and(A,n1) = A,
inference(clausify,[status(thm)],[and_definition2]) ).
fof(not_definition1,axiom,
not(n0) = n1,
file('theBenchmark.p',not_definition1) ).
cnf(c_4,plain,
not(n0) = n1,
inference(clausify,[status(thm)],[not_definition1]) ).
fof(not_definition2,axiom,
not(n1) = n0,
file('theBenchmark.p',not_definition2) ).
cnf(c_5,plain,
not(n1) = n0,
inference(clausify,[status(thm)],[not_definition2]) ).
fof(nand_table_definition,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5,VAR_6,VAR_7] :
( output(nand(VAR_0,VAR_4),nand(VAR_1,VAR_5),nand(VAR_2,VAR_6),nand(VAR_3,VAR_7))
| ~ output(VAR_4,VAR_5,VAR_6,VAR_7)
| ~ output(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',nand_table_definition) ).
cnf(c_6,plain,
( output(nand(A,E),nand(B,F),nand(C,V6),nand(D,V7))
| ~ output(E,F,V6,V7)
| ~ output(A,B,C,D) ),
inference(clausify,[status(thm)],[nand_table_definition]) ).
cnf(c_18,plain,
( output(not(and(A,E)),nand(B,F),nand(C,V6),nand(D,V7))
| ~ output(E,F,V6,V7)
| ~ output(A,B,C,D) ),
inference(paramod,[status(thm)],[c_1,c_6]) ).
cnf(c_19,plain,
( output(not(and(A,E)),not(and(B,F)),nand(C,V6),nand(D,V7))
| ~ output(E,F,V6,V7)
| ~ output(A,B,C,D) ),
inference(paramod,[status(thm)],[c_1,c_18]) ).
cnf(c_20,plain,
( output(not(and(A,E)),not(and(B,F)),not(and(C,V6)),nand(D,V7))
| ~ output(E,F,V6,V7)
| ~ output(A,B,C,D) ),
inference(paramod,[status(thm)],[c_1,c_19]) ).
cnf(c_7,plain,
( output(not(and(A,E)),not(and(B,F)),not(and(C,V6)),not(and(D,V7)))
| ~ output(E,F,V6,V7)
| ~ output(A,B,C,D) ),
inference(paramod,[status(thm)],[c_1,c_20]) ).
fof(input1,axiom,
output(n0,n0,n1,n1),
file('theBenchmark.p',input1) ).
cnf(c_8,plain,
output(n0,n0,n1,n1),
inference(clausify,[status(thm)],[input1]) ).
fof(input2,axiom,
output(n0,n1,n0,n1),
file('theBenchmark.p',input2) ).
cnf(c_9,plain,
output(n0,n1,n0,n1),
inference(clausify,[status(thm)],[input2]) ).
fof(prove_cannot_make_or,axiom,
~ output(n0,n1,n1,n1),
file('theBenchmark.p',prove_cannot_make_or) ).
cnf(c_10,plain,
~ output(n0,n1,n1,n1),
inference(clausify,[status(thm)],[prove_cannot_make_or]) ).
cnf(c_21,plain,
( output(not(and(n0,A)),not(and(n0,B)),not(and(n1,C)),not(and(n1,D)))
| ~ output(A,B,C,D) ),
inference(resolve,[status(thm)],[c_7,c_8]) ).
cnf(c_22,plain,
output(not(and(n0,n0)),not(and(n0,n0)),not(and(n1,n1)),not(and(n1,n1))),
inference(resolve,[status(thm)],[c_21,c_8]) ).
cnf(c_23,plain,
output(not(n0),not(and(n0,n0)),not(and(n1,n1)),not(and(n1,n1))),
inference(paramod,[status(thm)],[c_2,c_22]) ).
cnf(c_24,plain,
output(n1,not(and(n0,n0)),not(and(n1,n1)),not(and(n1,n1))),
inference(paramod,[status(thm)],[c_4,c_23]) ).
cnf(c_25,plain,
output(n1,not(n0),not(and(n1,n1)),not(and(n1,n1))),
inference(paramod,[status(thm)],[c_2,c_24]) ).
cnf(c_26,plain,
output(n1,n1,not(and(n1,n1)),not(and(n1,n1))),
inference(paramod,[status(thm)],[c_4,c_25]) ).
cnf(c_27,plain,
output(n1,n1,not(n1),not(and(n1,n1))),
inference(paramod,[status(thm)],[c_3,c_26]) ).
cnf(c_28,plain,
output(n1,n1,n0,not(and(n1,n1))),
inference(paramod,[status(thm)],[c_5,c_27]) ).
cnf(c_29,plain,
output(n1,n1,n0,not(n1)),
inference(paramod,[status(thm)],[c_3,c_28]) ).
cnf(c_11,plain,
output(n1,n1,n0,n0),
inference(paramod,[status(thm)],[c_5,c_29]) ).
cnf(c_30,plain,
( output(not(and(n0,A)),not(and(n1,B)),not(and(n0,C)),not(and(n1,D)))
| ~ output(A,B,C,D) ),
inference(resolve,[status(thm)],[c_7,c_9]) ).
cnf(c_31,plain,
output(not(and(n0,n0)),not(and(n1,n1)),not(and(n0,n0)),not(and(n1,n1))),
inference(resolve,[status(thm)],[c_30,c_9]) ).
cnf(c_32,plain,
output(not(n0),not(and(n1,n1)),not(and(n0,n0)),not(and(n1,n1))),
inference(paramod,[status(thm)],[c_2,c_31]) ).
cnf(c_33,plain,
output(n1,not(and(n1,n1)),not(and(n0,n0)),not(and(n1,n1))),
inference(paramod,[status(thm)],[c_4,c_32]) ).
cnf(c_34,plain,
output(n1,not(n1),not(and(n0,n0)),not(and(n1,n1))),
inference(paramod,[status(thm)],[c_3,c_33]) ).
cnf(c_35,plain,
output(n1,n0,not(and(n0,n0)),not(and(n1,n1))),
inference(paramod,[status(thm)],[c_5,c_34]) ).
cnf(c_36,plain,
output(n1,n0,not(n0),not(and(n1,n1))),
inference(paramod,[status(thm)],[c_2,c_35]) ).
cnf(c_37,plain,
output(n1,n0,n1,not(and(n1,n1))),
inference(paramod,[status(thm)],[c_4,c_36]) ).
cnf(c_38,plain,
output(n1,n0,n1,not(n1)),
inference(paramod,[status(thm)],[c_3,c_37]) ).
cnf(c_12,plain,
output(n1,n0,n1,n0),
inference(paramod,[status(thm)],[c_5,c_38]) ).
cnf(c_39,plain,
( output(not(and(n1,A)),not(and(n1,B)),not(and(n0,C)),not(and(n0,D)))
| ~ output(A,B,C,D) ),
inference(resolve,[status(thm)],[c_7,c_11]) ).
cnf(c_40,plain,
output(not(and(n1,n1)),not(and(n1,n0)),not(and(n0,n1)),not(and(n0,n0))),
inference(resolve,[status(thm)],[c_39,c_12]) ).
cnf(c_41,plain,
output(not(n1),not(and(n1,n0)),not(and(n0,n1)),not(and(n0,n0))),
inference(paramod,[status(thm)],[c_3,c_40]) ).
cnf(c_42,plain,
output(n0,not(and(n1,n0)),not(and(n0,n1)),not(and(n0,n0))),
inference(paramod,[status(thm)],[c_5,c_41]) ).
cnf(c_43,plain,
output(n0,not(n0),not(and(n0,n1)),not(and(n0,n0))),
inference(paramod,[status(thm)],[c_2,c_42]) ).
cnf(c_44,plain,
output(n0,n1,not(and(n0,n1)),not(and(n0,n0))),
inference(paramod,[status(thm)],[c_4,c_43]) ).
cnf(c_45,plain,
output(n0,n1,not(n0),not(and(n0,n0))),
inference(paramod,[status(thm)],[c_3,c_44]) ).
cnf(c_46,plain,
output(n0,n1,n1,not(and(n0,n0))),
inference(paramod,[status(thm)],[c_4,c_45]) ).
cnf(c_47,plain,
output(n0,n1,n1,not(n0)),
inference(paramod,[status(thm)],[c_2,c_46]) ).
cnf(c_16,plain,
output(n0,n1,n1,n1),
inference(paramod,[status(thm)],[c_4,c_47]) ).
cnf(c_17,plain,
$false,
inference(resolve,[status(thm)],[c_16,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWC001-1 : TPTP v9.3.1. Bugfixed v1.1.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/5.58 % Computer : n013.cluster.edu
% 0.11/5.58 % Model : x86_64 x86_64
% 0.11/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.58 % Memory : 8046.5625MB
% 0.11/5.58 % OS : Linux 6.8.0-71-generic
% 0.11/5.58 % CPULimit : 300
% 0.11/5.58 % WCLimit : 300
% 0.11/5.58 % DateTime : Fri Sep 25 15:58:21 UTC 2026
% 0.11/5.58 % CPUTime :
% 0.11/5.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.58 % Process 788019 was started by sandbox on n013,
% 0.11/5.58 % Fri Sep 25 15:58:21 2026
% 0.11/5.58 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/5.58
% 0.11/5.58 % From the command line: assign(max_seconds, 300).
% 0.14/5.60
% 0.14/5.60 % SZS status Unsatisfiable for theBenchmark
% 0.14/5.60
% 0.14/5.60 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/5.60 % Length of proof is 14.
% 0.14/5.60 % Level of proof is 4.
% 0.14/5.60 % Maximum clause weight is 27.000.
% 0.14/5.60 % Given clauses 11.
% 0.14/5.60
% 0.14/5.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------