%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : HWV052-1.002.001 : 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 0.12s 0.43s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 21 unt; 0 def)
% Number of atoms : 53 ( 52 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 3 ~; 16 |; 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 : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 58 ( 8 sgn 12 !; 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_204,plain,
( A = i
| o = A ),
inference(copy,[status(thm)],[c_1]) ).
cnf(c_2,plain,
( i = A
| o = A ),
inference(copy,[status(thm)],[c_204]) ).
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,VAR_1] : unpack1(VAR_0,VAR_1,pack1(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',unpack1) ).
cnf(c_4,plain,
unpack1(A,B,pack1(A,B)) = A,
inference(clausify,[status(thm)],[unpack1]) ).
fof(unpack1_01,axiom,
! [VAR_0,VAR_1] : unpack1(inv(VAR_0),VAR_1,pack1(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',unpack1_01) ).
cnf(c_5,plain,
unpack1(inv(A),B,pack1(A,B)) = A,
inference(clausify,[status(thm)],[unpack1_01]) ).
fof(unpack1_03,axiom,
! [VAR_0,VAR_1] : unpack1(VAR_0,VAR_1,inv(pack1(VAR_0,VAR_1))) = VAR_0,
file('theBenchmark.p',unpack1_03) ).
cnf(c_7,plain,
unpack1(A,B,inv(pack1(A,B))) = A,
inference(clausify,[status(thm)],[unpack1_03]) ).
fof(unpack2,axiom,
! [VAR_0,VAR_1] : unpack2(VAR_0,VAR_1,pack1(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',unpack2) ).
cnf(c_8,plain,
unpack2(A,B,pack1(A,B)) = B,
inference(clausify,[status(thm)],[unpack2]) ).
fof(unpack2_05,axiom,
! [VAR_0,VAR_1] : unpack2(VAR_0,inv(VAR_1),pack1(VAR_0,VAR_1)) = VAR_1,
file('theBenchmark.p',unpack2_05) ).
cnf(c_10,plain,
unpack2(A,inv(B),pack1(A,B)) = B,
inference(clausify,[status(thm)],[unpack2_05]) ).
cnf(c_205,plain,
( A = i
| o = A ),
inference(copy,[status(thm)],[c_2]) ).
cnf(c_206,plain,
o = inv(i),
inference(resolve,[status(thm)],[c_3,c_205]) ).
cnf(c_14,plain,
inv(i) = o,
inference(copy,[status(thm)],[c_206]) ).
cnf(c_207,plain,
( unpack1(A,B,o) = A
| i = pack1(A,B) ),
inference(paramod,[status(thm)],[c_2,c_4]) ).
cnf(c_18,plain,
( unpack1(A,B,o) = A
| pack1(A,B) = i ),
inference(copy,[status(thm)],[c_207]) ).
cnf(c_208,plain,
( unpack1(inv(A),B,o) = A
| i = pack1(A,B) ),
inference(paramod,[status(thm)],[c_2,c_5]) ).
cnf(c_21,plain,
( unpack1(inv(A),B,o) = A
| pack1(A,B) = i ),
inference(copy,[status(thm)],[c_208]) ).
cnf(c_209,plain,
( unpack2(A,B,i) = B
| o = pack1(A,B) ),
inference(paramod,[status(thm)],[c_2,c_8]) ).
cnf(c_33,plain,
( unpack2(A,B,i) = B
| pack1(A,B) = o ),
inference(copy,[status(thm)],[c_209]) ).
cnf(c_128,plain,
o != i,
inference(paramod,[status(thm)],[c_14,c_3]) ).
cnf(c_210,plain,
( unpack1(A,B,inv(i)) = A
| unpack1(A,B,o) = A ),
inference(paramod,[status(thm)],[c_18,c_7]) ).
cnf(c_211,plain,
( unpack1(A,B,o) = A
| unpack1(A,B,o) = A ),
inference(paramod,[status(thm)],[c_14,c_210]) ).
cnf(c_155,plain,
unpack1(A,B,o) = A,
inference(copy,[status(thm)],[c_211]) ).
cnf(c_212,plain,
( inv(A) = A
| pack1(A,B) = i ),
inference(paramod,[status(thm)],[c_155,c_21]) ).
cnf(c_159,plain,
pack1(A,B) = i,
inference(resolve,[status(thm)],[c_3,c_212]) ).
cnf(c_213,plain,
( unpack2(A,B,i) = B
| i = o ),
inference(paramod,[status(thm)],[c_159,c_33]) ).
cnf(c_214,plain,
( unpack2(A,B,i) = B
| o = i ),
inference(copy,[status(thm)],[c_213]) ).
cnf(c_199,plain,
unpack2(A,B,i) = B,
inference(resolve,[status(thm)],[c_128,c_214]) ).
cnf(c_215,plain,
unpack2(A,inv(B),i) = B,
inference(paramod,[status(thm)],[c_159,c_10]) ).
cnf(c_216,plain,
inv(B) = B,
inference(paramod,[status(thm)],[c_199,c_215]) ).
cnf(c_203,plain,
$false,
inference(resolve,[status(thm)],[c_3,c_216]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : HWV052-1.002.001 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n006.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Fri Sep 25 16:20:57 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 3322926 was started by sandbox2 on n006,
% 0.12/0.38 % Fri Sep 25 16:20:57 2026
% 0.12/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.38
% 0.12/0.38 % From the command line: assign(max_seconds, 300).
% 0.12/0.43
% 0.12/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.43
% 0.12/0.43 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.12/0.43 % Length of proof is 17.
% 0.12/0.43 % Level of proof is 6.
% 0.12/0.43 % Maximum clause weight is 18.000.
% 0.12/0.43 % Given clauses 18.
% 0.12/0.43
% 0.12/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------