%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN084+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 : Fri Sep 25 03:33:46 PM UTC 2026
% Result : Theorem 3.83s 1.04s
% Output : Proof 0.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 1
% Syntax : Number of formulae : 66 ( 9 unt; 0 def)
% Number of atoms : 234 ( 0 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 265 ( 97 ~; 138 |; 24 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 33 ( 0 sgn 8 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,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('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel62) ).
fof(f0_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(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,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) ) )
| ( ? [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) ) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [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) )
& ~ big_p(f(f(sk1)))
& ( big_p(f(sk1))
| ~ big_p(sk1) )
& big_p(a) )
| ( ( ( ~ big_p(f(f(sk0)))
& big_p(f(sk0))
& big_p(a) )
| ( ~ big_p(f(f(sk0)))
& ~ big_p(sk0)
& big_p(a) ) )
& ( big_p(f(f(X)))
| ( ~ big_p(f(X))
& big_p(X) )
| ~ big_p(a) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f0_nnf]) ).
cnf(c9,plain,
( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a)
| big_p(f(f(X0)))
| ~ big_p(f(X0))
| ~ big_p(a) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p185,plain,
( ~ big_p(f(X0))
| ~ big_p(a)
| big_p(f(f(X0)))
| ~ big_p(f(X0))
| ~ big_p(a) ),
inference(factoring,[status(thm)],[c9]) ).
cnf(p187,plain,
( ~ big_p(a)
| big_p(f(f(X0)))
| ~ big_p(f(X0))
| ~ big_p(a) ),
inference(factoring,[status(thm)],[p185]) ).
cnf(p188,plain,
( big_p(f(f(X0)))
| ~ big_p(f(X0))
| ~ big_p(a) ),
inference(factoring,[status(thm)],[p187]) ).
cnf(c10,plain,
( big_p(a)
| big_p(a)
| big_p(a) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p55,plain,
( big_p(a)
| big_p(a) ),
inference(factoring,[status(thm)],[c10]) ).
cnf(p56,plain,
big_p(a),
inference(factoring,[status(thm)],[p55]) ).
cnf(p189,plain,
( big_p(f(f(X0)))
| ~ big_p(f(X0)) ),
inference(resolution,[status(thm)],[p188,p56]) ).
cnf(c54,plain,
( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a)
| ~ big_p(f(f(sk0)))
| ~ big_p(f(f(sk0))) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p132,plain,
( big_p(f(f(X0)))
| ~ big_p(f(X0))
| ~ big_p(a)
| ~ big_p(f(f(sk0))) ),
inference(factoring,[status(thm)],[c54]) ).
cnf(c3,plain,
( big_p(f(f(X1)))
| big_p(X1)
| ~ big_p(a)
| big_p(f(f(X0)))
| big_p(X0)
| ~ big_p(a) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p74,plain,
( big_p(X0)
| ~ big_p(a)
| big_p(f(f(X0)))
| big_p(X0)
| ~ big_p(a) ),
inference(factoring,[status(thm)],[c3]) ).
cnf(p75,plain,
( big_p(X0)
| big_p(f(f(X0)))
| big_p(X0)
| ~ big_p(a) ),
inference(factoring,[status(thm)],[p74]) ).
cnf(p77,plain,
( big_p(f(f(X0)))
| big_p(X0)
| ~ big_p(a) ),
inference(factoring,[status(thm)],[p75]) ).
cnf(p78,plain,
( big_p(f(f(X0)))
| big_p(X0) ),
inference(resolution,[status(thm)],[p77,p56]) ).
cnf(p134,plain,
( big_p(sk0)
| big_p(f(f(X0)))
| ~ big_p(f(X0))
| ~ big_p(a) ),
inference(resolution,[status(thm)],[p132,p78]) ).
cnf(p137,plain,
( big_p(sk0)
| big_p(f(f(X0)))
| ~ big_p(f(X0)) ),
inference(resolution,[status(thm)],[p134,p56]) ).
cnf(c51,plain,
( big_p(f(sk1))
| ~ big_p(sk1)
| ~ big_p(f(f(sk0)))
| ~ big_p(f(f(sk0))) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p62,plain,
( big_p(f(sk1))
| ~ big_p(sk1)
| ~ big_p(f(f(sk0))) ),
inference(factoring,[status(thm)],[c51]) ).
cnf(p82,plain,
( big_p(f(sk1))
| ~ big_p(sk1)
| big_p(sk0) ),
inference(resolution,[status(thm)],[p78,p62]) ).
cnf(c52,plain,
( ~ big_p(f(f(sk1)))
| ~ big_p(f(f(sk0)))
| ~ big_p(f(f(sk0))) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p57,plain,
( ~ big_p(f(f(sk1)))
| ~ big_p(f(f(sk0))) ),
inference(factoring,[status(thm)],[c52]) ).
cnf(p79,plain,
( ~ big_p(f(f(sk1)))
| big_p(sk0) ),
inference(resolution,[status(thm)],[p78,p57]) ).
cnf(p85,plain,
( big_p(sk1)
| big_p(sk0) ),
inference(resolution,[status(thm)],[p79,p78]) ).
cnf(p87,plain,
( big_p(sk0)
| big_p(f(sk1))
| big_p(sk0) ),
inference(resolution,[status(thm)],[p82,p85]) ).
cnf(p88,plain,
( big_p(f(sk1))
| big_p(sk0) ),
inference(factoring,[status(thm)],[p87]) ).
cnf(p139,plain,
( big_p(sk0)
| big_p(sk0)
| big_p(f(f(sk1))) ),
inference(resolution,[status(thm)],[p137,p88]) ).
cnf(p141,plain,
( big_p(sk0)
| big_p(f(f(sk1))) ),
inference(factoring,[status(thm)],[p139]) ).
cnf(p143,plain,
( big_p(sk0)
| big_p(sk0) ),
inference(resolution,[status(thm)],[p141,p79]) ).
cnf(p144,plain,
big_p(sk0),
inference(factoring,[status(thm)],[p143]) ).
cnf(c34,plain,
( big_p(f(f(X1)))
| ~ big_p(f(X1))
| ~ big_p(a)
| big_p(f(sk0))
| ~ big_p(sk0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p147,plain,
( big_p(f(f(X0)))
| ~ big_p(f(X0))
| ~ big_p(a)
| big_p(f(sk0)) ),
inference(resolution,[status(thm)],[p144,c34]) ).
cnf(p164,plain,
( big_p(f(f(X0)))
| ~ big_p(f(X0))
| big_p(f(sk0)) ),
inference(resolution,[status(thm)],[p147,p56]) ).
cnf(c32,plain,
( ~ big_p(f(f(sk1)))
| big_p(f(sk0))
| ~ big_p(sk0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p145,plain,
( ~ big_p(f(f(sk1)))
| big_p(f(sk0)) ),
inference(resolution,[status(thm)],[p144,c32]) ).
cnf(p148,plain,
( big_p(sk1)
| big_p(f(sk0)) ),
inference(resolution,[status(thm)],[p145,p78]) ).
cnf(c7,plain,
( ~ big_p(f(f(sk1)))
| big_p(f(f(X0)))
| ~ big_p(f(X0))
| ~ big_p(a) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p60,plain,
( ~ big_p(f(f(sk1)))
| big_p(f(f(X0)))
| ~ big_p(f(X0)) ),
inference(resolution,[status(thm)],[c7,p56]) ).
cnf(p149,plain,
( ~ big_p(f(f(sk1)))
| big_p(f(f(sk0)))
| big_p(sk1) ),
inference(resolution,[status(thm)],[p148,p60]) ).
cnf(p150,plain,
( big_p(sk1)
| big_p(f(f(sk0)))
| big_p(sk1) ),
inference(resolution,[status(thm)],[p149,p78]) ).
cnf(p151,plain,
( big_p(f(f(sk0)))
| big_p(sk1) ),
inference(factoring,[status(thm)],[p150]) ).
cnf(p152,plain,
( ~ big_p(f(f(sk1)))
| big_p(sk1) ),
inference(resolution,[status(thm)],[p151,p57]) ).
cnf(p155,plain,
( big_p(sk1)
| big_p(sk1) ),
inference(resolution,[status(thm)],[p152,p78]) ).
cnf(p156,plain,
big_p(sk1),
inference(factoring,[status(thm)],[p155]) ).
cnf(c31,plain,
( big_p(f(sk1))
| ~ big_p(sk1)
| big_p(f(sk0))
| ~ big_p(sk0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p146,plain,
( big_p(f(sk1))
| ~ big_p(sk1)
| big_p(f(sk0)) ),
inference(resolution,[status(thm)],[p144,c31]) ).
cnf(p159,plain,
( big_p(f(sk1))
| big_p(f(sk0)) ),
inference(resolution,[status(thm)],[p156,p146]) ).
cnf(p166,plain,
( big_p(f(sk0))
| big_p(f(f(sk1)))
| big_p(f(sk0)) ),
inference(resolution,[status(thm)],[p164,p159]) ).
cnf(p170,plain,
( big_p(f(f(sk1)))
| big_p(f(sk0)) ),
inference(factoring,[status(thm)],[p166]) ).
cnf(p172,plain,
( big_p(f(sk0))
| big_p(f(sk0)) ),
inference(resolution,[status(thm)],[p170,p145]) ).
cnf(p173,plain,
big_p(f(sk0)),
inference(factoring,[status(thm)],[p172]) ).
cnf(p191,plain,
big_p(f(f(sk0))),
inference(resolution,[status(thm)],[p189,p173]) ).
cnf(p193,plain,
~ big_p(f(f(sk1))),
inference(resolution,[status(thm)],[p191,p57]) ).
cnf(c6,plain,
( big_p(f(sk1))
| ~ big_p(sk1)
| big_p(f(f(X0)))
| ~ big_p(f(X0))
| ~ big_p(a) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p67,plain,
( big_p(f(sk1))
| ~ big_p(sk1)
| big_p(f(f(X0)))
| ~ big_p(f(X0)) ),
inference(resolution,[status(thm)],[c6,p56]) ).
cnf(p175,plain,
( big_p(f(sk1))
| ~ big_p(sk1)
| big_p(f(f(sk0))) ),
inference(resolution,[status(thm)],[p173,p67]) ).
cnf(p176,plain,
( big_p(f(sk1))
| big_p(f(f(sk0))) ),
inference(resolution,[status(thm)],[p175,p156]) ).
cnf(p178,plain,
( big_p(f(sk1))
| ~ big_p(sk1)
| big_p(f(sk1)) ),
inference(resolution,[status(thm)],[p176,p62]) ).
cnf(p181,plain,
( ~ big_p(sk1)
| big_p(f(sk1)) ),
inference(factoring,[status(thm)],[p178]) ).
cnf(p182,plain,
big_p(f(sk1)),
inference(resolution,[status(thm)],[p181,p156]) ).
cnf(p192,plain,
big_p(f(f(sk1))),
inference(resolution,[status(thm)],[p189,p182]) ).
cnf(p196,plain,
$false,
inference(resolution,[status(thm)],[p193,p192]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN084+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.03/0.36 % Computer : n020.cluster.edu
% 0.03/0.36 % Model : x86_64 x86_64
% 0.03/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.36 % Memory : 8046.5625MB
% 0.03/0.36 % OS : Linux 6.8.0-71-generic
% 0.03/0.36 % CPULimit : 300
% 0.03/0.36 % WCLimit : 300
% 0.03/0.36 % DateTime : Fri Sep 25 00:09:18 UTC 2026
% 0.03/0.36 % CPUTime :
% 0.03/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.83/1.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.83/1.04 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------