%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN082+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 0.14s 10.99s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 1
% Syntax : Number of formulae : 21 ( 5 unt; 0 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 61 ( 24 ~; 23 |; 10 &)
% ( 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 : 17 ( 0 sgn 8 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
! [X] :
( big_f(X,f(X))
<=> ? [Y] :
( big_f(X,Y)
& ! [Z] :
( big_f(Z,Y)
=> big_f(Z,f(X)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pel60) ).
fof(f0_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(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
? [X] :
( ( ? [Y] :
( big_f(X,Y)
& ! [Z] :
( big_f(Z,f(X))
| ~ big_f(Z,Y) ) )
& ~ big_f(X,f(X)) )
| ( ! [Y] :
( ~ big_f(X,Y)
| ? [Z] :
( ~ big_f(Z,f(X))
& big_f(Z,Y) ) )
& big_f(X,f(X)) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [Y,Z] :
( ( big_f(sk0,sk2)
& ( big_f(Z,f(sk0))
| ~ big_f(Z,sk2) )
& ~ big_f(sk0,f(sk0)) )
| ( ( ~ big_f(sk0,Y)
| ( ~ big_f(sk1(Y),f(sk0))
& big_f(sk1(Y),Y) ) )
& big_f(sk0,f(sk0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f0_nnf]) ).
cnf(c8,plain,
( big_f(sk0,sk2)
| ~ big_f(sk0,X1)
| ~ big_f(sk1(X1),f(sk0)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c3,plain,
( ~ big_f(sk0,f(sk0))
| ~ big_f(sk0,X1)
| big_f(sk1(X1),X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p11,plain,
( ~ big_f(sk0,f(sk0))
| big_f(sk1(f(sk0)),f(sk0)) ),
inference(factoring,[status(thm)],[c3]) ).
cnf(c2,plain,
( big_f(sk0,sk2)
| big_f(sk0,f(sk0)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p12,plain,
( big_f(sk0,sk2)
| big_f(sk1(f(sk0)),f(sk0)) ),
inference(resolution,[status(thm)],[p11,c2]) ).
cnf(p13,plain,
( big_f(sk0,sk2)
| big_f(sk0,sk2)
| ~ big_f(sk0,f(sk0)) ),
inference(resolution,[status(thm)],[c8,p12]) ).
cnf(p14,plain,
( big_f(sk0,sk2)
| ~ big_f(sk0,f(sk0)) ),
inference(factoring,[status(thm)],[p13]) ).
cnf(p15,plain,
( big_f(sk0,sk2)
| big_f(sk0,sk2) ),
inference(resolution,[status(thm)],[p14,c2]) ).
cnf(p16,plain,
big_f(sk0,sk2),
inference(factoring,[status(thm)],[p15]) ).
cnf(c1,plain,
( big_f(X2,f(sk0))
| ~ big_f(X2,sk2)
| big_f(sk0,f(sk0)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p10,plain,
( ~ big_f(sk0,sk2)
| big_f(sk0,f(sk0)) ),
inference(factoring,[status(thm)],[c1]) ).
cnf(p19,plain,
big_f(sk0,f(sk0)),
inference(resolution,[status(thm)],[p16,p10]) ).
cnf(p22,plain,
big_f(sk1(f(sk0)),f(sk0)),
inference(resolution,[status(thm)],[p19,p11]) ).
cnf(c6,plain,
( ~ big_f(sk0,f(sk0))
| ~ big_f(sk0,X1)
| ~ big_f(sk1(X1),f(sk0)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p23,plain,
( ~ big_f(sk0,f(sk0))
| ~ big_f(sk0,f(sk0)) ),
inference(resolution,[status(thm)],[p22,c6]) ).
cnf(p26,plain,
~ big_f(sk0,f(sk0)),
inference(factoring,[status(thm)],[p23]) ).
cnf(p27,plain,
$false,
inference(resolution,[status(thm)],[p26,p19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN082+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/10.38 % Computer : n020.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Fri Sep 25 00:08:59 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/10.99 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/10.99 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------