%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN374+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 : n004.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 0.10s 5.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 23 ( 4 unt; 0 def)
% Number of atoms : 117 ( 0 equ)
% Maximal formula atoms : 32 ( 5 avg)
% Number of connectives : 146 ( 52 ~; 71 |; 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 : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 62 ( 16 sgn 32 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(x2125,conjecture,
( ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
<=> ( ? [X] : big_p(X)
<=> ! [Y] : big_p(Y) ) ),
file('theBenchmark.p',x2125) ).
fof(x2125_neg,negated_conjecture,
~ ( ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
<=> ( ? [X] : big_p(X)
<=> ! [Y] : big_p(Y) ) ),
inference(assume_negation,[status(cth)],[x2125]) ).
fof(nnf_1,plain,
( ( ( ( ? [Y] : ~ big_p(Y)
| ! [X] : ~ big_p(X) )
& ( ! [X9] : big_p(X9)
| ? [X8] : big_p(X8) ) )
| ! [X6] :
? [X7] :
( ( ~ big_p(X7)
| ~ big_p(X6) )
& ( big_p(X7)
| big_p(X6) ) ) )
& ( ( ( ? [X5] : ~ big_p(X5)
| ? [X4] : big_p(X4) )
& ( ! [X3] : big_p(X3)
| ! [X2] : ~ big_p(X2) ) )
| ? [X0] :
! [X1] :
( ( ~ big_p(X1)
| big_p(X0) )
& ( big_p(X1)
| ~ big_p(X0) ) ) ) ),
inference(fof_nnf,[status(thm)],[x2125_neg]) ).
fof(sk_x2125_neg_sk,plain,
( ( ( ( ~ big_p(sK3)
| ! [X] : ~ big_p(X) )
& ( ! [X9] : big_p(X9)
| big_p(sK2) ) )
| ! [X6] :
( ( ~ big_p(sK1(X6))
| ~ big_p(X6) )
& ( big_p(sK1(X6))
| big_p(X6) ) ) )
& ( ( ( ~ big_p(sK5)
| big_p(sK4) )
& ( ! [X3] : big_p(X3)
| ! [X2] : ~ big_p(X2) ) )
| ! [X1] :
( ( ~ big_p(X1)
| big_p(sK0) )
& ( big_p(X1)
| ~ big_p(sK0) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK4,sK5,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X7,sK1(X6)),skolemize(X8,sK2),skolemize(Y,sK3)],[nnf_1]) ).
fof(sk_x2125_neg,plain,
( ! [VAR_0,VAR_1] :
( ~ big_p(sK3)
| ~ big_p(VAR_1)
| ~ big_p(sK1(VAR_0))
| ~ big_p(VAR_0) )
& ! [VAR_0,VAR_1] :
( big_p(VAR_1)
| big_p(sK2)
| ~ big_p(sK1(VAR_0))
| ~ big_p(VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ big_p(sK3)
| ~ big_p(VAR_1)
| big_p(sK1(VAR_0))
| big_p(VAR_0) )
& ! [VAR_0,VAR_1] :
( big_p(VAR_1)
| big_p(sK2)
| big_p(sK1(VAR_0))
| big_p(VAR_0) )
& ! [VAR_0] :
( ~ big_p(sK5)
| big_p(sK4)
| ~ big_p(VAR_0)
| big_p(sK0) )
& ! [VAR_0,VAR_1,VAR_2] :
( big_p(VAR_2)
| ~ big_p(VAR_1)
| ~ big_p(VAR_0)
| big_p(sK0) )
& ! [VAR_0] :
( ~ big_p(sK5)
| big_p(sK4)
| big_p(VAR_0)
| ~ big_p(sK0) )
& ! [VAR_0,VAR_1,VAR_2] :
( big_p(VAR_2)
| ~ big_p(VAR_1)
| big_p(VAR_0)
| ~ big_p(sK0) ) ),
inference(cnf_transformation,[status(thm)],[sk_x2125_neg_sk]) ).
cnf(c_2,negated_conjecture,
( big_p(C)
| ~ big_p(B)
| big_p(A)
| ~ big_p(sK0) ),
inference(split_conjunct,[status(thm)],[sk_x2125_neg]) ).
cnf(c_3,negated_conjecture,
( big_p(C)
| ~ big_p(B)
| ~ big_p(A)
| big_p(sK0) ),
inference(split_conjunct,[status(thm)],[sk_x2125_neg]) ).
cnf(c_4,negated_conjecture,
( big_p(B)
| big_p(sK2)
| big_p(sK1(A))
| big_p(A) ),
inference(split_conjunct,[status(thm)],[sk_x2125_neg]) ).
cnf(c_7,negated_conjecture,
( ~ big_p(sK3)
| ~ big_p(B)
| ~ big_p(sK1(A))
| ~ big_p(A) ),
inference(split_conjunct,[status(thm)],[sk_x2125_neg]) ).
cnf(c_8,plain,
( big_p(B)
| big_p(A)
| ~ big_p(sK0) ),
inference(factor,[status(thm)],[c_2]) ).
cnf(c_10,plain,
( ~ big_p(B)
| ~ big_p(A)
| big_p(sK0) ),
inference(factor,[status(thm)],[c_3]) ).
cnf(c_13,plain,
( big_p(sK2)
| big_p(sK1(A))
| big_p(A) ),
inference(factor,[status(thm)],[c_4]) ).
cnf(c_16,plain,
( ~ big_p(sK3)
| ~ big_p(sK1(A))
| ~ big_p(A) ),
inference(factor,[status(thm)],[c_7]) ).
cnf(c_17,plain,
( big_p(A)
| ~ big_p(sK0) ),
inference(factor,[status(thm)],[c_8]) ).
cnf(c_18,plain,
( ~ big_p(A)
| big_p(sK0) ),
inference(factor,[status(thm)],[c_10]) ).
cnf(c_20,plain,
( ~ big_p(sK1(sK3))
| ~ big_p(sK3) ),
inference(factor,[status(thm)],[c_16]) ).
cnf(c_21,plain,
( big_p(sK2)
| big_p(A)
| big_p(sK0) ),
inference(resolve,[status(thm)],[c_18,c_13]) ).
cnf(c_22,plain,
( big_p(sK2)
| big_p(sK0) ),
inference(factor,[status(thm)],[c_21]) ).
cnf(c_26,plain,
( big_p(sK0)
| big_p(sK0) ),
inference(resolve,[status(thm)],[c_22,c_18]) ).
cnf(c_23,plain,
big_p(sK0),
inference(copy,[status(thm)],[c_26]) ).
cnf(c_24,plain,
big_p(A),
inference(resolve,[status(thm)],[c_23,c_17]) ).
cnf(c_27,plain,
~ big_p(sK1(sK3)),
inference(resolve,[status(thm)],[c_24,c_20]) ).
cnf(c_25,plain,
$false,
inference(resolve,[status(thm)],[c_24,c_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN374+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n004.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Sat Sep 26 17:38:57 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.37 % Process 2258946 was started by sandbox on n004,
% 0.10/5.37 % Sat Sep 26 17:38:57 2026
% 0.10/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.37
% 0.10/5.37 % From the command line: assign(max_seconds, 300).
% 0.10/5.38
% 0.10/5.38 % SZS status Theorem for theBenchmark
% 0.10/5.38
% 0.10/5.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/5.38 % Length of proof is 17.
% 0.10/5.38 % Level of proof is 8.
% 0.10/5.38 % Maximum clause weight is 9.000.
% 0.10/5.38 % Given clauses 9.
% 0.10/5.38
% 0.10/5.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------