%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN082+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 : n001.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 09:37:00 AM UTC 2026
% Result : Theorem 0.08s 0.37s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 20 ( 5 unt; 0 def)
% Number of atoms : 63 ( 0 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 70 ( 27 ~; 28 |; 11 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 19 ( 0 sgn 11 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel60,conjecture,
! [X] :
( big_f(X,f(X))
<=> ? [Y] :
( big_f(X,Y)
& ! [Z] :
( big_f(Z,Y)
=> big_f(Z,f(X)) ) ) ),
file('theBenchmark.p',pel60) ).
fof(pel60_neg,negated_conjecture,
~ ! [X] :
( big_f(X,f(X))
<=> ? [Y] :
( big_f(X,Y)
& ! [Z] :
( big_f(Z,Y)
=> big_f(Z,f(X)) ) ) ),
inference(assume_negation,[status(cth)],[pel60]) ).
fof(nnf_1,plain,
? [X] :
( ( ! [Y] :
( ~ big_f(X,Y)
| ? [Z] :
( ~ big_f(Z,f(X))
& big_f(Z,Y) ) )
| ~ big_f(X,f(X)) )
& ( ? [X0] :
( big_f(X,X0)
& ! [X1] :
( big_f(X1,f(X))
| ~ big_f(X1,X0) ) )
| big_f(X,f(X)) ) ),
inference(fof_nnf,[status(thm)],[pel60_neg]) ).
fof(sk_pel60_neg_sk,plain,
( ( ! [Y] :
( ~ big_f(sK0,Y)
| ( ~ big_f(sK2(Y),f(sK0))
& big_f(sK2(Y),Y) ) )
| ~ big_f(sK0,f(sK0)) )
& ( ( big_f(sK0,sK1)
& ! [X1] :
( big_f(X1,f(sK0))
| ~ big_f(X1,sK1) ) )
| big_f(sK0,f(sK0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X,sK0),skolemize(X0,sK1),skolemize(Z,sK2(Y))],[nnf_1]) ).
fof(sk_pel60_neg,plain,
( ! [VAR_0] :
( ~ big_f(sK0,VAR_0)
| ~ big_f(sK2(VAR_0),f(sK0))
| ~ big_f(sK0,f(sK0)) )
& ! [VAR_0] :
( ~ big_f(sK0,VAR_0)
| big_f(sK2(VAR_0),VAR_0)
| ~ big_f(sK0,f(sK0)) )
& ( big_f(sK0,sK1)
| big_f(sK0,f(sK0)) )
& ! [VAR_0] :
( big_f(VAR_0,f(sK0))
| ~ big_f(VAR_0,sK1)
| big_f(sK0,f(sK0)) ) ),
inference(cnf_transformation,[status(thm)],[sk_pel60_neg_sk]) ).
cnf(c_2,negated_conjecture,
( big_f(A,f(sK0))
| ~ big_f(A,sK1)
| big_f(sK0,f(sK0)) ),
inference(split_conjunct,[status(thm)],[sk_pel60_neg]) ).
cnf(c_3,negated_conjecture,
( big_f(sK0,sK1)
| big_f(sK0,f(sK0)) ),
inference(split_conjunct,[status(thm)],[sk_pel60_neg]) ).
cnf(c_4,negated_conjecture,
( ~ big_f(sK0,A)
| big_f(sK2(A),A)
| ~ big_f(sK0,f(sK0)) ),
inference(split_conjunct,[status(thm)],[sk_pel60_neg]) ).
cnf(c_5,negated_conjecture,
( ~ big_f(sK0,A)
| ~ big_f(sK2(A),f(sK0))
| ~ big_f(sK0,f(sK0)) ),
inference(split_conjunct,[status(thm)],[sk_pel60_neg]) ).
cnf(c_6,plain,
( ~ big_f(sK0,sK1)
| big_f(sK0,f(sK0)) ),
inference(factor,[status(thm)],[c_2]) ).
cnf(c_7,plain,
( big_f(sK2(f(sK0)),f(sK0))
| ~ big_f(sK0,f(sK0)) ),
inference(factor,[status(thm)],[c_4]) ).
cnf(c_8,plain,
( ~ big_f(sK2(f(sK0)),f(sK0))
| ~ big_f(sK0,f(sK0)) ),
inference(factor,[status(thm)],[c_5]) ).
cnf(c_10,plain,
( big_f(sK0,sK1)
| big_f(sK2(f(sK0)),f(sK0)) ),
inference(resolve,[status(thm)],[c_7,c_3]) ).
cnf(c_11,plain,
( ~ big_f(sK0,f(sK0))
| big_f(sK0,sK1) ),
inference(resolve,[status(thm)],[c_10,c_8]) ).
cnf(c_16,negated_conjecture,
( big_f(sK0,sK1)
| big_f(sK0,sK1) ),
inference(resolve,[status(thm)],[c_11,c_3]) ).
cnf(c_12,negated_conjecture,
big_f(sK0,sK1),
inference(copy,[status(thm)],[c_16]) ).
cnf(c_13,plain,
big_f(sK0,f(sK0)),
inference(resolve,[status(thm)],[c_12,c_6]) ).
cnf(c_14,plain,
~ big_f(sK2(f(sK0)),f(sK0)),
inference(resolve,[status(thm)],[c_13,c_8]) ).
cnf(c_17,plain,
big_f(sK2(f(sK0)),f(sK0)),
inference(resolve,[status(thm)],[c_13,c_7]) ).
cnf(c_15,plain,
$false,
inference(resolve,[status(thm)],[c_14,c_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN082+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 17:15:43 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 2293192 was started by sandbox2 on n001,
% 0.08/0.36 % Sat Sep 26 17:15:43 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.08/0.37
% 0.08/0.37 % SZS status Theorem for theBenchmark
% 0.08/0.37
% 0.08/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.08/0.37 % Length of proof is 14.
% 0.08/0.37 % Level of proof is 8.
% 0.08/0.37 % Maximum clause weight is 12.000.
% 0.08/0.37 % Given clauses 10.
% 0.08/0.37
% 0.08/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------