%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HWV052-1.001.001 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 07:34:36 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 21 unt; 0 def)
% Number of atoms : 68 ( 67 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 6 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 35 ( 5 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(bit_domain,axiom,
! [VAR_0] :
( VAR_0 = i
| VAR_0 = o ),
file('theBenchmark.p',bit_domain) ).
cnf(c_1,plain,
( A = i
| A = o ),
inference(clausify,[status(thm)],[bit_domain]) ).
cnf(c_80,plain,
( A = i
| o = A ),
inference(copy,[status(thm)],[c_1]) ).
cnf(c_2,plain,
( i = A
| o = A ),
inference(copy,[status(thm)],[c_80]) ).
fof(bit_inverse,axiom,
! [VAR_0] : inv(VAR_0) != VAR_0,
file('theBenchmark.p',bit_inverse) ).
cnf(c_3,plain,
inv(A) != A,
inference(clausify,[status(thm)],[bit_inverse]) ).
fof(unpack1,axiom,
! [VAR_0] : unpack1(VAR_0,pack1(VAR_0)) = VAR_0,
file('theBenchmark.p',unpack1) ).
cnf(c_4,plain,
unpack1(A,pack1(A)) = A,
inference(clausify,[status(thm)],[unpack1]) ).
fof(unpack1_01,axiom,
! [VAR_0] : unpack1(inv(VAR_0),pack1(VAR_0)) = VAR_0,
file('theBenchmark.p',unpack1_01) ).
cnf(c_5,plain,
unpack1(inv(A),pack1(A)) = A,
inference(clausify,[status(thm)],[unpack1_01]) ).
fof(unpack1_02,axiom,
! [VAR_0] : unpack1(VAR_0,inv(pack1(VAR_0))) = VAR_0,
file('theBenchmark.p',unpack1_02) ).
cnf(c_6,plain,
unpack1(A,inv(pack1(A))) = A,
inference(clausify,[status(thm)],[unpack1_02]) ).
cnf(c_7,plain,
( i = B
| A = B
| i = A ),
inference(paramod,[status(thm)],[c_2,c_2]) ).
cnf(c_81,plain,
( i = A
| A = o ),
inference(copy,[status(thm)],[c_2]) ).
cnf(c_82,plain,
i = inv(o),
inference(resolve,[status(thm)],[c_3,c_81]) ).
cnf(c_8,plain,
inv(o) = i,
inference(copy,[status(thm)],[c_82]) ).
cnf(c_83,plain,
( unpack1(A,o) = A
| i = pack1(A) ),
inference(paramod,[status(thm)],[c_2,c_4]) ).
cnf(c_10,plain,
( unpack1(A,o) = A
| pack1(A) = i ),
inference(copy,[status(thm)],[c_83]) ).
cnf(c_84,plain,
( unpack1(inv(A),o) = A
| i = pack1(A) ),
inference(paramod,[status(thm)],[c_2,c_5]) ).
cnf(c_12,plain,
( unpack1(inv(A),o) = A
| pack1(A) = i ),
inference(copy,[status(thm)],[c_84]) ).
cnf(c_85,plain,
A != inv(A),
inference(copy,[status(thm)],[c_3]) ).
cnf(c_15,plain,
( i = A
| inv(i) = A ),
inference(resolve,[status(thm)],[c_7,c_85]) ).
cnf(c_86,plain,
i != o,
inference(paramod,[status(thm)],[c_8,c_3]) ).
cnf(c_37,plain,
o != i,
inference(copy,[status(thm)],[c_86]) ).
cnf(c_38,plain,
unpack1(i,pack1(o)) = o,
inference(paramod,[status(thm)],[c_8,c_5]) ).
cnf(c_41,plain,
( unpack1(A,pack1(o)) = o
| i = B
| A = B ),
inference(paramod,[status(thm)],[c_7,c_38]) ).
cnf(c_87,plain,
( inv(i) = o
| i = unpack1(i,pack1(o)) ),
inference(paramod,[status(thm)],[c_15,c_38]) ).
cnf(c_88,plain,
( inv(i) = o
| i = o ),
inference(paramod,[status(thm)],[c_38,c_87]) ).
cnf(c_89,plain,
( inv(i) = o
| o = i ),
inference(copy,[status(thm)],[c_88]) ).
cnf(c_56,plain,
inv(i) = o,
inference(resolve,[status(thm)],[c_37,c_89]) ).
cnf(c_90,plain,
( unpack1(A,inv(i)) = A
| unpack1(A,o) = A ),
inference(paramod,[status(thm)],[c_10,c_6]) ).
cnf(c_91,plain,
( unpack1(A,o) = A
| unpack1(A,o) = A ),
inference(paramod,[status(thm)],[c_56,c_90]) ).
cnf(c_62,plain,
unpack1(A,o) = A,
inference(copy,[status(thm)],[c_91]) ).
cnf(c_92,plain,
( inv(A) = A
| pack1(A) = i ),
inference(paramod,[status(thm)],[c_62,c_12]) ).
cnf(c_64,plain,
pack1(A) = i,
inference(resolve,[status(thm)],[c_3,c_92]) ).
cnf(c_67,plain,
( unpack1(A,i) = o
| i = B
| A = B ),
inference(paramod,[status(thm)],[c_64,c_41]) ).
cnf(c_77,plain,
unpack1(A,i) = A,
inference(paramod,[status(thm)],[c_64,c_4]) ).
cnf(c_93,plain,
( unpack1(i,i) = o
| i = A ),
inference(factor,[status(thm)],[c_67]) ).
cnf(c_94,plain,
( i = o
| i = A ),
inference(paramod,[status(thm)],[c_77,c_93]) ).
cnf(c_95,plain,
( o = i
| i = A ),
inference(copy,[status(thm)],[c_94]) ).
cnf(c_78,plain,
i = A,
inference(resolve,[status(thm)],[c_37,c_95]) ).
cnf(c_96,plain,
i != o,
inference(copy,[status(thm)],[c_37]) ).
cnf(c_79,plain,
$false,
inference(resolve,[status(thm)],[c_78,c_96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWV052-1.001.001 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.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 : Fri Sep 25 16:20:41 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.36 % Process 3322527 was started by sandbox2 on n006,
% 0.14/0.36 % Fri Sep 25 16:20:41 2026
% 0.14/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.37
% 0.14/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.39
% 0.14/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.39
% 0.14/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/0.39 % Length of proof is 21.
% 0.14/0.39 % Level of proof is 9.
% 0.14/0.39 % Maximum clause weight is 12.000.
% 0.14/0.39 % Given clauses 11.
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------