%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN377+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 09:37:44 AM UTC 2026
% Result : Theorem 0.18s 5.49s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 4 unt; 0 def)
% Number of atoms : 105 ( 0 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 133 ( 47 ~; 63 |; 17 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 60 ( 15 sgn 36 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2128,conjecture,
( ! [X] :
( big_p(X)
<=> ! [Y] : big_p(Y) )
<=> ( ? [X] : big_p(X)
<=> ! [Y] : big_p(Y) ) ),
file('theBenchmark.p',x2128) ).
fof(x2128_neg,negated_conjecture,
~ ( ! [X] :
( big_p(X)
<=> ! [Y] : big_p(Y) )
<=> ( ? [X] : big_p(X)
<=> ! [Y] : big_p(Y) ) ),
inference(assume_negation,[status(cth)],[x2128]) ).
fof(nnf_1,plain,
( ( ( ( ? [Y] : ~ big_p(Y)
| ! [X] : ~ big_p(X) )
& ( ! [X11] : big_p(X11)
| ? [X10] : big_p(X10) ) )
| ? [X7] :
( ( ? [X9] : ~ big_p(X9)
| ~ big_p(X7) )
& ( ! [X8] : big_p(X8)
| big_p(X7) ) ) )
& ( ( ( ? [X6] : ~ big_p(X6)
| ? [X5] : big_p(X5) )
& ( ! [X4] : big_p(X4)
| ! [X3] : ~ big_p(X3) ) )
| ! [X0] :
( ( ? [X2] : ~ big_p(X2)
| big_p(X0) )
& ( ! [X1] : big_p(X1)
| ~ big_p(X0) ) ) ) ),
inference(fof_nnf,[status(thm)],[x2128_neg]) ).
fof(sk_x2128_neg_sk,plain,
( ( ( ( ~ big_p(sK3)
| ! [X] : ~ big_p(X) )
& ( ! [X11] : big_p(X11)
| big_p(sK1) ) )
| ( ( ~ big_p(sK2)
| ~ big_p(sK0) )
& ( ! [X8] : big_p(X8)
| big_p(sK0) ) ) )
& ( ( ( ~ big_p(sK6)
| big_p(sK5) )
& ( ! [X4] : big_p(X4)
| ! [X3] : ~ big_p(X3) ) )
| ! [X0] :
( ( ~ big_p(sK4(X0))
| big_p(X0) )
& ( ! [X1] : big_p(X1)
| ~ big_p(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK0,sK2,sK1,sK3]),skolemize(X2,sK4(X0)),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X7,sK0),skolemize(X9,sK2),skolemize(X10,sK1),skolemize(Y,sK3)],[nnf_1]) ).
fof(sk_x2128_neg,plain,
( ! [VAR_0] :
( ~ big_p(sK3)
| ~ big_p(VAR_0)
| ~ big_p(sK2)
| ~ big_p(sK0) )
& ! [VAR_0] :
( big_p(VAR_0)
| big_p(sK1)
| ~ big_p(sK2)
| ~ big_p(sK0) )
& ! [VAR_0,VAR_1] :
( ~ big_p(sK3)
| ~ big_p(VAR_1)
| big_p(VAR_0)
| big_p(sK0) )
& ! [VAR_0,VAR_1] :
( big_p(VAR_1)
| big_p(sK1)
| big_p(VAR_0)
| big_p(sK0) )
& ! [VAR_0] :
( ~ big_p(sK6)
| big_p(sK5)
| ~ big_p(sK4(VAR_0))
| big_p(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( big_p(VAR_2)
| ~ big_p(VAR_1)
| ~ big_p(sK4(VAR_0))
| big_p(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ big_p(sK6)
| big_p(sK5)
| big_p(VAR_1)
| ~ big_p(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( big_p(VAR_3)
| ~ big_p(VAR_2)
| big_p(VAR_1)
| ~ big_p(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_x2128_neg_sk]) ).
cnf(c_2,negated_conjecture,
( big_p(D)
| ~ big_p(C)
| big_p(B)
| ~ big_p(A) ),
inference(split_conjunct,[status(thm)],[sk_x2128_neg]) ).
cnf(c_3,negated_conjecture,
( big_p(B)
| big_p(sK1)
| big_p(A)
| big_p(sK0) ),
inference(split_conjunct,[status(thm)],[sk_x2128_neg]) ).
cnf(c_4,negated_conjecture,
( ~ big_p(sK3)
| ~ big_p(A)
| ~ big_p(sK2)
| ~ big_p(sK0) ),
inference(split_conjunct,[status(thm)],[sk_x2128_neg]) ).
cnf(c_5,plain,
( big_p(C)
| big_p(B)
| ~ big_p(A) ),
inference(factor,[status(thm)],[c_2]) ).
cnf(c_7,plain,
( big_p(A)
| big_p(sK1)
| big_p(sK0) ),
inference(factor,[status(thm)],[c_3]) ).
cnf(c_8,plain,
( ~ big_p(sK3)
| ~ big_p(sK2)
| ~ big_p(sK0) ),
inference(factor,[status(thm)],[c_4]) ).
cnf(c_9,plain,
( big_p(B)
| ~ big_p(A) ),
inference(factor,[status(thm)],[c_5]) ).
cnf(c_10,plain,
( big_p(sK1)
| big_p(sK0) ),
inference(factor,[status(thm)],[c_7]) ).
cnf(c_11,plain,
( big_p(A)
| big_p(sK0) ),
inference(resolve,[status(thm)],[c_10,c_9]) ).
cnf(c_12,plain,
big_p(sK0),
inference(factor,[status(thm)],[c_11]) ).
cnf(c_13,plain,
( ~ big_p(sK3)
| ~ big_p(sK2) ),
inference(resolve,[status(thm)],[c_12,c_8]) ).
cnf(c_14,plain,
big_p(A),
inference(resolve,[status(thm)],[c_12,c_9]) ).
cnf(c_16,plain,
~ big_p(sK3),
inference(resolve,[status(thm)],[c_14,c_13]) ).
cnf(c_15,plain,
$false,
inference(resolve,[status(thm)],[c_14,c_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN377+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/5.46 % Computer : n005.cluster.edu
% 0.18/5.46 % Model : x86_64 x86_64
% 0.18/5.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.46 % Memory : 8046.5625MB
% 0.18/5.46 % OS : Linux 6.8.0-71-generic
% 0.18/5.46 % CPULimit : 300
% 0.18/5.46 % WCLimit : 300
% 0.18/5.46 % DateTime : Sat Sep 26 17:39:08 UTC 2026
% 0.18/5.46 % CPUTime :
% 0.18/5.47 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/5.47 % Process 2671377 was started by sandbox2 on n005,
% 0.18/5.47 % Sat Sep 26 17:39:08 2026
% 0.18/5.47 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/5.47
% 0.18/5.47 % From the command line: assign(max_seconds, 300).
% 0.18/5.49
% 0.18/5.49 % SZS status Theorem for theBenchmark
% 0.18/5.49
% 0.18/5.49 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.18/5.49 % Length of proof is 14.
% 0.18/5.49 % Level of proof is 7.
% 0.18/5.49 % Maximum clause weight is 8.000.
% 0.18/5.49 % Given clauses 4.
% 0.18/5.49
% 0.18/5.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------