%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN078+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 : n011.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 09:36:59 AM UTC 2026
% Result : Theorem 0.18s 0.45s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 27 ( 8 unt; 0 def)
% Number of atoms : 89 ( 18 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 96 ( 34 ~; 40 |; 16 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 25 ( 0 sgn 13 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel56,conjecture,
( ! [X] :
( ? [Y] :
( X = f(Y)
& big_p(Y) )
=> big_p(X) )
<=> ! [U] :
( big_p(U)
=> big_p(f(U)) ) ),
file('theBenchmark.p',pel56) ).
fof(pel56_neg,negated_conjecture,
~ ( ! [X] :
( ? [Y] :
( X = f(Y)
& big_p(Y) )
=> big_p(X) )
<=> ! [U] :
( big_p(U)
=> big_p(f(U)) ) ),
inference(assume_negation,[status(cth)],[pel56]) ).
fof(nnf_1,plain,
( ( ? [U] :
( ~ big_p(f(U))
& big_p(U) )
| ? [X] :
( ~ big_p(X)
& ? [Y] :
( f(Y) = X
& big_p(Y) ) ) )
& ( ! [X2] :
( big_p(f(X2))
| ~ big_p(X2) )
| ! [X0] :
( big_p(X0)
| ! [X1] :
( f(X1) != X0
| ~ big_p(X1) ) ) ) ),
inference(fof_nnf,[status(thm)],[pel56_neg]) ).
fof(sk_pel56_neg_sk,plain,
( ( ( ~ big_p(f(sK1))
& big_p(sK1) )
| ( ~ big_p(sK2)
& f(sK0) = sK2
& big_p(sK0) ) )
& ( ! [X2] :
( big_p(f(X2))
| ~ big_p(X2) )
| ! [X0] :
( big_p(X0)
| ! [X1] :
( f(X1) != X0
| ~ big_p(X1) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK1]),skolemize(X,sK2),skolemize(Y,sK0),skolemize(U,sK1)],[nnf_1]) ).
fof(sk_pel56_neg,plain,
( ( ~ big_p(f(sK1))
| ~ big_p(sK2) )
& ( big_p(sK1)
| ~ big_p(sK2) )
& ( ~ big_p(f(sK1))
| f(sK0) = sK2 )
& ( big_p(sK1)
| f(sK0) = sK2 )
& ( ~ big_p(f(sK1))
| big_p(sK0) )
& ( big_p(sK1)
| big_p(sK0) )
& ! [VAR_0,VAR_1,VAR_2] :
( big_p(f(VAR_2))
| ~ big_p(VAR_2)
| big_p(VAR_1)
| f(VAR_0) != VAR_1
| ~ big_p(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_pel56_neg_sk]) ).
cnf(c_2,negated_conjecture,
( big_p(f(C))
| ~ big_p(C)
| big_p(B)
| f(A) != B
| ~ big_p(A) ),
inference(split_conjunct,[status(thm)],[sk_pel56_neg]) ).
cnf(c_3,negated_conjecture,
( big_p(sK1)
| big_p(sK0) ),
inference(split_conjunct,[status(thm)],[sk_pel56_neg]) ).
cnf(c_4,negated_conjecture,
( ~ big_p(f(sK1))
| big_p(sK0) ),
inference(split_conjunct,[status(thm)],[sk_pel56_neg]) ).
cnf(c_5,negated_conjecture,
( big_p(sK1)
| f(sK0) = sK2 ),
inference(split_conjunct,[status(thm)],[sk_pel56_neg]) ).
cnf(c_6,negated_conjecture,
( ~ big_p(f(sK1))
| f(sK0) = sK2 ),
inference(split_conjunct,[status(thm)],[sk_pel56_neg]) ).
cnf(c_7,negated_conjecture,
( big_p(sK1)
| ~ big_p(sK2) ),
inference(split_conjunct,[status(thm)],[sk_pel56_neg]) ).
cnf(c_8,negated_conjecture,
( ~ big_p(f(sK1))
| ~ big_p(sK2) ),
inference(split_conjunct,[status(thm)],[sk_pel56_neg]) ).
cnf(c_9,plain,
( big_p(f(A))
| big_p(B)
| f(A) != B
| ~ big_p(A) ),
inference(factor,[status(thm)],[c_2]) ).
cnf(c_25,plain,
( big_p(f(A))
| f(A) != f(A)
| ~ big_p(A) ),
inference(factor,[status(thm)],[c_9]) ).
cnf(c_11,plain,
( big_p(f(A))
| ~ big_p(A) ),
inference(copy,[status(thm)],[c_25]) ).
cnf(c_12,plain,
( f(sK0) = sK2
| big_p(f(sK1)) ),
inference(resolve,[status(thm)],[c_11,c_5]) ).
cnf(c_13,plain,
( big_p(sK0)
| big_p(f(sK1)) ),
inference(resolve,[status(thm)],[c_11,c_3]) ).
cnf(c_26,negated_conjecture,
( f(sK0) = sK2
| f(sK0) = sK2 ),
inference(resolve,[status(thm)],[c_12,c_6]) ).
cnf(c_16,negated_conjecture,
f(sK0) = sK2,
inference(copy,[status(thm)],[c_26]) ).
cnf(c_27,negated_conjecture,
( big_p(sK0)
| big_p(sK0) ),
inference(resolve,[status(thm)],[c_13,c_4]) ).
cnf(c_19,negated_conjecture,
big_p(sK0),
inference(copy,[status(thm)],[c_27]) ).
cnf(c_28,plain,
big_p(f(sK0)),
inference(resolve,[status(thm)],[c_19,c_11]) ).
cnf(c_20,plain,
big_p(sK2),
inference(paramod,[status(thm)],[c_16,c_28]) ).
cnf(c_21,negated_conjecture,
~ big_p(f(sK1)),
inference(resolve,[status(thm)],[c_20,c_8]) ).
cnf(c_22,negated_conjecture,
big_p(sK1),
inference(resolve,[status(thm)],[c_20,c_7]) ).
cnf(c_29,negated_conjecture,
~ big_p(sK1),
inference(resolve,[status(thm)],[c_11,c_21]) ).
cnf(c_24,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_22,c_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN078+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n011.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 17:09:59 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 1120139 was started by sandbox2 on n011,
% 0.18/0.44 % Sat Sep 26 17:09:59 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.44
% 0.18/0.44 % From the command line: assign(max_seconds, 300).
% 0.18/0.45
% 0.18/0.45 % SZS status Theorem for theBenchmark
% 0.18/0.45
% 0.18/0.45 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.18/0.45 % Length of proof is 18.
% 0.18/0.45 % Level of proof is 8.
% 0.18/0.45 % Maximum clause weight is 13.000.
% 0.18/0.45 % Given clauses 13.
% 0.18/0.45
% 0.18/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------