%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN375+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 0.04s 20.55s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 20 ( 4 unt; 0 def)
% Number of atoms : 108 ( 0 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 137 ( 49 ~; 65 |; 17 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 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 : 61 ( 16 sgn 34 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2126,conjecture,
( ! [X] :
( big_p(X)
<=> ? [Y] : big_p(Y) )
<=> ( ! [X] : big_p(X)
<=> ? [Y] : big_p(Y) ) ),
file('theBenchmark.p',x2126) ).
fof(x2126_neg,negated_conjecture,
~ ( ! [X] :
( big_p(X)
<=> ? [Y] : big_p(Y) )
<=> ( ! [X] : big_p(X)
<=> ? [Y] : big_p(Y) ) ),
inference(assume_negation,[status(cth)],[x2126]) ).
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)],[x2126_neg]) ).
fof(sk_x2126_neg_sk,plain,
( ( ( ( ! [Y] : ~ big_p(Y)
| ~ big_p(sK3) )
& ( big_p(sK2)
| ! [X10] : big_p(X10) ) )
| ( ( ! [X9] : ~ big_p(X9)
| ~ big_p(sK0) )
& ( big_p(sK1)
| big_p(sK0) ) ) )
& ( ( ( ! [X6] : ~ big_p(X6)
| ! [X5] : big_p(X5) )
& ( big_p(sK6)
| ~ big_p(sK5) ) )
| ! [X0] :
( ( ! [X2] : ~ big_p(X2)
| big_p(X0) )
& ( big_p(sK4(X0))
| ~ big_p(X0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK0,sK1,sK2,sK3]),skolemize(X1,sK4(X0)),skolemize(X3,sK5),skolemize(X4,sK6),skolemize(X7,sK0),skolemize(X8,sK1),skolemize(X11,sK2),skolemize(X,sK3)],[nnf_1]) ).
fof(sk_x2126_neg,plain,
( ! [VAR_0,VAR_1] :
( ~ big_p(VAR_1)
| ~ big_p(sK3)
| ~ big_p(VAR_0)
| ~ big_p(sK0) )
& ! [VAR_0,VAR_1] :
( big_p(sK2)
| big_p(VAR_1)
| ~ big_p(VAR_0)
| ~ big_p(sK0) )
& ! [VAR_0] :
( ~ big_p(VAR_0)
| ~ big_p(sK3)
| big_p(sK1)
| big_p(sK0) )
& ! [VAR_0] :
( big_p(sK2)
| big_p(VAR_0)
| big_p(sK1)
| big_p(sK0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ big_p(VAR_3)
| big_p(VAR_2)
| ~ big_p(VAR_1)
| 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] :
( ~ big_p(VAR_2)
| big_p(VAR_1)
| big_p(sK4(VAR_0))
| ~ big_p(VAR_0) )
& ! [VAR_0] :
( big_p(sK6)
| ~ big_p(sK5)
| big_p(sK4(VAR_0))
| ~ big_p(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_x2126_neg_sk]) ).
cnf(c_5,negated_conjecture,
( ~ big_p(D)
| big_p(C)
| ~ big_p(B)
| big_p(A) ),
inference(split_conjunct,[status(thm)],[sk_x2126_neg]) ).
cnf(c_6,negated_conjecture,
( big_p(sK2)
| big_p(A)
| big_p(sK1)
| big_p(sK0) ),
inference(split_conjunct,[status(thm)],[sk_x2126_neg]) ).
cnf(c_7,negated_conjecture,
( ~ big_p(B)
| ~ big_p(sK3)
| ~ big_p(A)
| ~ big_p(sK0) ),
inference(split_conjunct,[status(thm)],[sk_x2126_neg]) ).
cnf(c_13,plain,
( ~ big_p(C)
| ~ big_p(B)
| big_p(A) ),
inference(factor,[status(thm)],[c_5]) ).
cnf(c_15,plain,
( big_p(sK2)
| big_p(sK1)
| big_p(sK0) ),
inference(factor,[status(thm)],[c_6]) ).
cnf(c_16,plain,
( ~ big_p(A)
| ~ big_p(sK3)
| ~ big_p(sK0) ),
inference(factor,[status(thm)],[c_7]) ).
cnf(c_19,plain,
( ~ big_p(B)
| big_p(A) ),
inference(factor,[status(thm)],[c_13]) ).
cnf(c_20,plain,
( ~ big_p(sK3)
| ~ big_p(sK0) ),
inference(factor,[status(thm)],[c_16]) ).
cnf(c_21,plain,
( big_p(sK1)
| big_p(sK0)
| big_p(A) ),
inference(resolve,[status(thm)],[c_19,c_15]) ).
cnf(c_22,plain,
( big_p(sK1)
| big_p(sK0) ),
inference(factor,[status(thm)],[c_21]) ).
cnf(c_23,plain,
( big_p(A)
| big_p(sK0) ),
inference(resolve,[status(thm)],[c_22,c_19]) ).
cnf(c_24,plain,
big_p(sK0),
inference(factor,[status(thm)],[c_23]) ).
cnf(c_25,plain,
~ big_p(sK3),
inference(resolve,[status(thm)],[c_24,c_20]) ).
cnf(c_26,plain,
~ big_p(A),
inference(resolve,[status(thm)],[c_19,c_25]) ).
cnf(c_27,plain,
$false,
inference(resolve,[status(thm)],[c_26,c_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYN375+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/20.54 % Computer : n012.cluster.edu
% 0.04/20.54 % Model : x86_64 x86_64
% 0.04/20.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/20.54 % Memory : 8046.5625MB
% 0.04/20.54 % OS : Linux 6.8.0-71-generic
% 0.04/20.54 % CPULimit : 300
% 0.04/20.54 % WCLimit : 300
% 0.04/20.54 % DateTime : Sat Sep 26 17:38:58 UTC 2026
% 0.04/20.54 % CPUTime :
% 0.04/20.54 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/20.54 % Process 1149748 was started by sandbox on n012,
% 0.04/20.54 % Sat Sep 26 17:38:58 2026
% 0.04/20.54 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.04/20.54
% 0.04/20.54 % From the command line: assign(max_seconds, 300).
% 0.04/20.55
% 0.04/20.55 % SZS status Theorem for theBenchmark
% 0.04/20.55
% 0.04/20.55 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.04/20.55 % Length of proof is 16.
% 0.04/20.55 % Level of proof is 10.
% 0.04/20.55 % Maximum clause weight is 8.000.
% 0.04/20.55 % Given clauses 5.
% 0.04/20.55
% 0.04/20.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------