%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN084+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 : n007.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 09:37:01 AM UTC 2026
% Result : Theorem 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 1
% Syntax : Number of formulae : 44 ( 9 unt; 0 def)
% Number of atoms : 182 ( 0 equ)
% Maximal formula atoms : 33 ( 4 avg)
% Number of connectives : 208 ( 70 ~; 102 |; 30 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 28 ( 0 sgn 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(pel62,conjecture,
( ! [X] :
( ( ( big_p(X)
=> big_p(f(X)) )
& big_p(a) )
=> big_p(f(f(X))) )
<=> ! [X1] :
( ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a) ) ) ),
file('theBenchmark.p',pel62) ).
fof(pel62_neg,negated_conjecture,
~ ( ! [X] :
( ( ( big_p(X)
=> big_p(f(X)) )
& big_p(a) )
=> big_p(f(f(X))) )
<=> ! [X1] :
( ( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a) )
& ( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a) ) ) ),
inference(assume_negation,[status(cth)],[pel62]) ).
fof(nnf_1,plain,
( ( ? [X1] :
( ( ~ big_p(f(f(X1)))
& big_p(f(X1))
& big_p(a) )
| ( ~ big_p(f(f(X1)))
& ~ big_p(X1)
& big_p(a) ) )
| ? [X] :
( ~ big_p(f(f(X)))
& ( big_p(f(X))
| ~ big_p(X) )
& big_p(a) ) )
& ( ! [X2] :
( ( big_p(f(f(X2)))
| ~ big_p(f(X2))
| ~ big_p(a) )
& ( big_p(f(f(X2)))
| big_p(X2)
| ~ big_p(a) ) )
| ! [X0] :
( big_p(f(f(X0)))
| ( ~ big_p(f(X0))
& big_p(X0) )
| ~ big_p(a) ) ) ),
inference(fof_nnf,[status(thm)],[pel62_neg]) ).
fof(sk_pel62_neg_sk,plain,
( ( ( ~ big_p(f(f(sK1)))
& big_p(f(sK1))
& big_p(a) )
| ( ~ big_p(f(f(sK1)))
& ~ big_p(sK1)
& big_p(a) )
| ( ~ big_p(f(f(sK0)))
& ( big_p(f(sK0))
| ~ big_p(sK0) )
& big_p(a) ) )
& ( ! [X2] :
( ( big_p(f(f(X2)))
| ~ big_p(f(X2))
| ~ big_p(a) )
& ( big_p(f(f(X2)))
| big_p(X2)
| ~ big_p(a) ) )
| ! [X0] :
( big_p(f(f(X0)))
| ( ~ big_p(f(X0))
& big_p(X0) )
| ~ big_p(a) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(X1,sK1)],[nnf_1]) ).
fof(sk_pel62_neg,plain,
( ( ~ big_p(f(f(sK1)))
| ~ big_p(f(f(sK0))) )
& ( big_p(f(sK1))
| ~ big_p(sK1)
| ~ big_p(f(f(sK0))) )
& ( ~ big_p(f(f(sK1)))
| big_p(f(sK0))
| ~ big_p(sK0) )
& ( big_p(f(sK1))
| ~ big_p(sK1)
| big_p(f(sK0))
| ~ big_p(sK0) )
& big_p(a)
& ! [VAR_0,VAR_1] :
( big_p(f(f(VAR_1)))
| ~ big_p(f(VAR_1))
| big_p(f(f(VAR_0)))
| ~ big_p(f(VAR_0))
| ~ big_p(a) )
& ! [VAR_0,VAR_1] :
( big_p(f(f(VAR_1)))
| big_p(VAR_1)
| big_p(f(f(VAR_0)))
| ~ big_p(f(VAR_0))
| ~ big_p(a) )
& ! [VAR_0,VAR_1] :
( big_p(f(f(VAR_1)))
| ~ big_p(f(VAR_1))
| big_p(f(f(VAR_0)))
| big_p(VAR_0)
| ~ big_p(a) )
& ! [VAR_0,VAR_1] :
( big_p(f(f(VAR_1)))
| big_p(VAR_1)
| big_p(f(f(VAR_0)))
| big_p(VAR_0)
| ~ big_p(a) ) ),
inference(cnf_transformation,[status(thm)],[sk_pel62_neg_sk]) ).
cnf(c_2,negated_conjecture,
( big_p(f(f(B)))
| big_p(B)
| big_p(f(f(A)))
| big_p(A)
| ~ big_p(a) ),
inference(split_conjunct,[status(thm)],[sk_pel62_neg]) ).
cnf(c_4,negated_conjecture,
( big_p(f(f(B)))
| ~ big_p(f(B))
| big_p(f(f(A)))
| ~ big_p(f(A))
| ~ big_p(a) ),
inference(split_conjunct,[status(thm)],[sk_pel62_neg]) ).
cnf(c_5,negated_conjecture,
big_p(a),
inference(split_conjunct,[status(thm)],[sk_pel62_neg]) ).
cnf(c_6,negated_conjecture,
( big_p(f(sK1))
| ~ big_p(sK1)
| big_p(f(sK0))
| ~ big_p(sK0) ),
inference(split_conjunct,[status(thm)],[sk_pel62_neg]) ).
cnf(c_7,negated_conjecture,
( ~ big_p(f(f(sK1)))
| big_p(f(sK0))
| ~ big_p(sK0) ),
inference(split_conjunct,[status(thm)],[sk_pel62_neg]) ).
cnf(c_8,negated_conjecture,
( big_p(f(sK1))
| ~ big_p(sK1)
| ~ big_p(f(f(sK0))) ),
inference(split_conjunct,[status(thm)],[sk_pel62_neg]) ).
cnf(c_9,negated_conjecture,
( ~ big_p(f(f(sK1)))
| ~ big_p(f(f(sK0))) ),
inference(split_conjunct,[status(thm)],[sk_pel62_neg]) ).
cnf(c_37,plain,
( big_p(f(f(A)))
| big_p(f(f(A)))
| big_p(A)
| ~ big_p(a) ),
inference(factor,[status(thm)],[c_2]) ).
cnf(c_38,plain,
( big_p(f(f(A)))
| big_p(A)
| ~ big_p(a) ),
inference(copy,[status(thm)],[c_37]) ).
cnf(c_10,negated_conjecture,
( big_p(f(f(A)))
| big_p(A) ),
inference(resolve,[status(thm)],[c_5,c_38]) ).
cnf(c_39,plain,
( big_p(f(f(A)))
| big_p(f(f(A)))
| ~ big_p(f(A))
| ~ big_p(a) ),
inference(factor,[status(thm)],[c_4]) ).
cnf(c_40,plain,
( big_p(f(f(A)))
| ~ big_p(f(A))
| ~ big_p(a) ),
inference(copy,[status(thm)],[c_39]) ).
cnf(c_11,negated_conjecture,
( big_p(f(f(A)))
| ~ big_p(f(A)) ),
inference(resolve,[status(thm)],[c_5,c_40]) ).
cnf(c_12,plain,
( ~ big_p(f(f(sK0)))
| big_p(sK1) ),
inference(resolve,[status(thm)],[c_10,c_9]) ).
cnf(c_13,plain,
( big_p(f(sK1))
| ~ big_p(sK1)
| big_p(sK0) ),
inference(resolve,[status(thm)],[c_10,c_8]) ).
cnf(c_14,plain,
( big_p(f(sK0))
| ~ big_p(sK0)
| big_p(sK1) ),
inference(resolve,[status(thm)],[c_10,c_7]) ).
cnf(c_16,plain,
( big_p(sK0)
| big_p(sK1) ),
inference(resolve,[status(thm)],[c_12,c_10]) ).
cnf(c_41,plain,
( big_p(sK0)
| big_p(f(sK1))
| big_p(sK0) ),
inference(resolve,[status(thm)],[c_13,c_16]) ).
cnf(c_17,plain,
( big_p(f(sK1))
| big_p(sK0) ),
inference(copy,[status(thm)],[c_41]) ).
cnf(c_18,plain,
( big_p(f(f(sK1)))
| big_p(sK0) ),
inference(resolve,[status(thm)],[c_17,c_11]) ).
cnf(c_20,plain,
( ~ big_p(f(f(sK0)))
| big_p(sK0) ),
inference(resolve,[status(thm)],[c_18,c_9]) ).
cnf(c_42,plain,
( big_p(sK0)
| big_p(sK0) ),
inference(resolve,[status(thm)],[c_20,c_10]) ).
cnf(c_21,plain,
big_p(sK0),
inference(copy,[status(thm)],[c_42]) ).
cnf(c_22,plain,
( big_p(f(sK0))
| big_p(sK1) ),
inference(resolve,[status(thm)],[c_21,c_14]) ).
cnf(c_23,negated_conjecture,
( ~ big_p(f(f(sK1)))
| big_p(f(sK0)) ),
inference(resolve,[status(thm)],[c_21,c_7]) ).
cnf(c_24,negated_conjecture,
( big_p(f(sK1))
| ~ big_p(sK1)
| big_p(f(sK0)) ),
inference(resolve,[status(thm)],[c_21,c_6]) ).
cnf(c_25,plain,
( big_p(f(f(sK0)))
| big_p(sK1) ),
inference(resolve,[status(thm)],[c_22,c_11]) ).
cnf(c_43,plain,
( big_p(sK1)
| big_p(sK1) ),
inference(resolve,[status(thm)],[c_25,c_12]) ).
cnf(c_26,plain,
big_p(sK1),
inference(copy,[status(thm)],[c_43]) ).
cnf(c_27,negated_conjecture,
( big_p(f(sK1))
| big_p(f(sK0)) ),
inference(resolve,[status(thm)],[c_26,c_24]) ).
cnf(c_28,negated_conjecture,
( big_p(f(sK1))
| ~ big_p(f(f(sK0))) ),
inference(resolve,[status(thm)],[c_26,c_8]) ).
cnf(c_30,plain,
( big_p(f(f(sK1)))
| big_p(f(sK0)) ),
inference(resolve,[status(thm)],[c_27,c_11]) ).
cnf(c_44,negated_conjecture,
( big_p(f(sK0))
| big_p(f(sK0)) ),
inference(resolve,[status(thm)],[c_30,c_23]) ).
cnf(c_32,negated_conjecture,
big_p(f(sK0)),
inference(copy,[status(thm)],[c_44]) ).
cnf(c_33,plain,
big_p(f(f(sK0))),
inference(resolve,[status(thm)],[c_32,c_11]) ).
cnf(c_34,negated_conjecture,
big_p(f(sK1)),
inference(resolve,[status(thm)],[c_33,c_28]) ).
cnf(c_35,negated_conjecture,
~ big_p(f(f(sK1))),
inference(resolve,[status(thm)],[c_33,c_9]) ).
cnf(c_45,negated_conjecture,
big_p(f(f(sK1))),
inference(resolve,[status(thm)],[c_34,c_11]) ).
cnf(c_36,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_35,c_45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN084+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 17:08:24 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 41870 was started by sandbox2 on n007,
% 0.10/0.37 % Sat Sep 26 17:08:24 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.39
% 0.10/0.39 % SZS status Theorem for theBenchmark
% 0.10/0.39
% 0.10/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.39 % Length of proof is 31.
% 0.10/0.39 % Level of proof is 17.
% 0.10/0.39 % Maximum clause weight is 16.000.
% 0.10/0.39 % Given clauses 26.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------