%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN084-2 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 09:37:01 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.37s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 10 unt; 0 def)
% Number of atoms : 90 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 79 ( 31 ~; 48 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 6 ( 0 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel62_1,axiom,
big_p(a),
file('theBenchmark.p',pel62_1) ).
cnf(c_1,plain,
big_p(a),
inference(clausify,[status(thm)],[pel62_1]) ).
fof(pel62_2,axiom,
! [VAR_0] :
( ~ big_p(a)
| big_p(VAR_0)
| big_p(f(f(VAR_0))) ),
file('theBenchmark.p',pel62_2) ).
cnf(c_2,plain,
( ~ big_p(a)
| big_p(A)
| big_p(f(f(A))) ),
inference(clausify,[status(thm)],[pel62_2]) ).
cnf(c_3,plain,
( big_p(A)
| big_p(f(f(A))) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(pel62_3,axiom,
! [VAR_0] :
( ~ big_p(a)
| ~ big_p(f(VAR_0))
| big_p(f(f(VAR_0))) ),
file('theBenchmark.p',pel62_3) ).
cnf(c_4,plain,
( ~ big_p(a)
| ~ big_p(f(A))
| big_p(f(f(A))) ),
inference(clausify,[status(thm)],[pel62_3]) ).
cnf(c_5,plain,
( ~ big_p(f(A))
| big_p(f(f(A))) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
fof(pel62_4,axiom,
( ~ big_p(f(f(sk2)))
| ~ big_p(f(f(sk1))) ),
file('theBenchmark.p',pel62_4) ).
cnf(c_6,plain,
( ~ big_p(f(f(sk2)))
| ~ big_p(f(f(sk1))) ),
inference(clausify,[status(thm)],[pel62_4]) ).
fof(pel62_5,axiom,
( ~ big_p(sk2)
| ~ big_p(sk1)
| big_p(f(sk2))
| big_p(f(sk1)) ),
file('theBenchmark.p',pel62_5) ).
cnf(c_7,plain,
( ~ big_p(sk2)
| ~ big_p(sk1)
| big_p(f(sk2))
| big_p(f(sk1)) ),
inference(clausify,[status(thm)],[pel62_5]) ).
fof(pel62_6,axiom,
( ~ big_p(f(f(sk2)))
| ~ big_p(sk1)
| big_p(f(sk1)) ),
file('theBenchmark.p',pel62_6) ).
cnf(c_8,plain,
( ~ big_p(f(f(sk2)))
| ~ big_p(sk1)
| big_p(f(sk1)) ),
inference(clausify,[status(thm)],[pel62_6]) ).
fof(pel62_7,axiom,
( ~ big_p(f(f(sk1)))
| ~ big_p(sk2)
| big_p(f(sk2)) ),
file('theBenchmark.p',pel62_7) ).
cnf(c_9,plain,
( ~ big_p(f(f(sk1)))
| ~ big_p(sk2)
| big_p(f(sk2)) ),
inference(clausify,[status(thm)],[pel62_7]) ).
cnf(c_11,plain,
( big_p(sk2)
| ~ big_p(f(f(sk1))) ),
inference(resolve,[status(thm)],[c_6,c_3]) ).
cnf(c_12,plain,
( big_p(sk2)
| ~ big_p(sk1)
| big_p(f(sk1)) ),
inference(resolve,[status(thm)],[c_8,c_3]) ).
cnf(c_13,plain,
( big_p(sk1)
| ~ big_p(sk2)
| big_p(f(sk2)) ),
inference(resolve,[status(thm)],[c_9,c_3]) ).
cnf(c_15,plain,
( big_p(sk1)
| big_p(sk2) ),
inference(resolve,[status(thm)],[c_11,c_3]) ).
cnf(c_36,plain,
( big_p(sk1)
| big_p(sk1)
| big_p(f(sk2)) ),
inference(resolve,[status(thm)],[c_13,c_15]) ).
cnf(c_16,plain,
( big_p(sk1)
| big_p(f(sk2)) ),
inference(copy,[status(thm)],[c_36]) ).
cnf(c_18,plain,
( big_p(f(f(sk2)))
| big_p(sk1) ),
inference(resolve,[status(thm)],[c_16,c_5]) ).
cnf(c_19,plain,
( ~ big_p(f(f(sk1)))
| big_p(sk1) ),
inference(resolve,[status(thm)],[c_18,c_6]) ).
cnf(c_37,plain,
( big_p(sk1)
| big_p(sk1) ),
inference(resolve,[status(thm)],[c_19,c_3]) ).
cnf(c_21,plain,
big_p(sk1),
inference(copy,[status(thm)],[c_37]) ).
cnf(c_22,plain,
( big_p(sk2)
| big_p(f(sk1)) ),
inference(resolve,[status(thm)],[c_21,c_12]) ).
cnf(c_23,plain,
( ~ big_p(f(f(sk2)))
| big_p(f(sk1)) ),
inference(resolve,[status(thm)],[c_21,c_8]) ).
cnf(c_24,plain,
( ~ big_p(sk2)
| big_p(f(sk2))
| big_p(f(sk1)) ),
inference(resolve,[status(thm)],[c_21,c_7]) ).
cnf(c_26,plain,
( big_p(f(f(sk1)))
| big_p(sk2) ),
inference(resolve,[status(thm)],[c_22,c_5]) ).
cnf(c_38,plain,
( big_p(sk2)
| big_p(sk2) ),
inference(resolve,[status(thm)],[c_26,c_11]) ).
cnf(c_27,plain,
big_p(sk2),
inference(copy,[status(thm)],[c_38]) ).
cnf(c_28,plain,
( big_p(f(sk2))
| big_p(f(sk1)) ),
inference(resolve,[status(thm)],[c_27,c_24]) ).
cnf(c_29,plain,
( ~ big_p(f(f(sk1)))
| big_p(f(sk2)) ),
inference(resolve,[status(thm)],[c_27,c_9]) ).
cnf(c_30,plain,
( big_p(f(f(sk2)))
| big_p(f(sk1)) ),
inference(resolve,[status(thm)],[c_28,c_5]) ).
cnf(c_39,plain,
( big_p(f(sk1))
| big_p(f(sk1)) ),
inference(resolve,[status(thm)],[c_30,c_23]) ).
cnf(c_31,plain,
big_p(f(sk1)),
inference(copy,[status(thm)],[c_39]) ).
cnf(c_32,plain,
big_p(f(f(sk1))),
inference(resolve,[status(thm)],[c_31,c_5]) ).
cnf(c_33,plain,
big_p(f(sk2)),
inference(resolve,[status(thm)],[c_32,c_29]) ).
cnf(c_34,plain,
~ big_p(f(f(sk2))),
inference(resolve,[status(thm)],[c_32,c_6]) ).
cnf(c_40,plain,
big_p(f(f(sk2))),
inference(resolve,[status(thm)],[c_33,c_5]) ).
cnf(c_35,plain,
$false,
inference(resolve,[status(thm)],[c_34,c_40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN084-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.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 : Sat Sep 26 17:15:16 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1368105 was started by sandbox on n016,
% 0.09/0.36 % Sat Sep 26 17:15:16 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.09/0.37
% 0.09/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.37
% 0.09/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.37 % Length of proof is 30.
% 0.09/0.37 % Level of proof is 16.
% 0.09/0.37 % Maximum clause weight is 10.000.
% 0.09/0.37 % Given clauses 27.
% 0.09/0.37
% 0.09/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------