%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN377+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 03:34:32 PM UTC 2026
% Result : Theorem 3.43s 1.08s
% Output : Proof 3.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 18 ( 4 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 86 ( 31 ~; 33 |; 16 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-1 aty)
% Number of variables : 35 ( 7 sgn 15 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
( ! [X] :
( big_p(X)
<=> ! [Y] : big_p(Y) )
<=> ( ? [X] : big_p(X)
<=> ! [Y] : big_p(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2128) ).
fof(f0_neg,negated_conjecture,
~ ( ! [X] :
( big_p(X)
<=> ! [Y] : big_p(Y) )
<=> ( ? [X] : big_p(X)
<=> ! [Y] : big_p(Y) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
( ( ( ? [Y] : ~ big_p(Y)
| ? [X] : big_p(X) )
& ( ! [Y] : big_p(Y)
| ! [X] : ~ big_p(X) )
& ? [X] :
( ( ! [Y] : big_p(Y)
& ~ big_p(X) )
| ( ? [Y] : ~ big_p(Y)
& big_p(X) ) ) )
| ( ( ( ! [Y] : big_p(Y)
& ! [X] : ~ big_p(X) )
| ( ? [Y] : ~ big_p(Y)
& ? [X] : big_p(X) ) )
& ! [X] :
( ( ? [Y] : ~ big_p(Y)
| big_p(X) )
& ( ! [Y] : big_p(Y)
| ~ big_p(X) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [X,Y] :
( ( ( ~ big_p(sk6)
| big_p(sk5) )
& ( big_p(Y)
| ~ big_p(X) )
& ( ( big_p(Y)
& ~ big_p(sk3) )
| ( ~ big_p(sk4)
& big_p(sk3) ) ) )
| ( ( ( big_p(Y)
& ~ big_p(X) )
| ( ~ big_p(sk2)
& big_p(sk1) ) )
& ( ~ big_p(sk0(X))
| big_p(X) )
& ( big_p(Y)
| ~ big_p(X) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3,sk4,sk5,sk6])],[f0_nnf]) ).
cnf(c19,plain,
( big_p(X1)
| big_p(sk3)
| big_p(X1)
| big_p(sk1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p47,plain,
( big_p(sk3)
| big_p(X0)
| big_p(sk1) ),
inference(factoring,[status(thm)],[c19]) ).
cnf(p52,plain,
( big_p(sk3)
| big_p(sk1) ),
inference(factoring,[status(thm)],[p47]) ).
cnf(c4,plain,
( big_p(X1)
| ~ big_p(X0)
| big_p(X1)
| ~ big_p(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p41,plain,
( big_p(X1)
| big_p(X1)
| ~ big_p(X0) ),
inference(factoring,[status(thm)],[c4]) ).
cnf(p51,plain,
( big_p(X1)
| ~ big_p(X0) ),
inference(factoring,[status(thm)],[p41]) ).
cnf(p53,plain,
( big_p(X0)
| big_p(sk1) ),
inference(resolution,[status(thm)],[p52,p51]) ).
cnf(p54,plain,
big_p(sk1),
inference(factoring,[status(thm)],[p53]) ).
cnf(p55,plain,
big_p(X0),
inference(resolution,[status(thm)],[p54,p51]) ).
cnf(c26,plain,
( ~ big_p(sk3)
| ~ big_p(sk4)
| ~ big_p(X0)
| ~ big_p(sk2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p48,plain,
( ~ big_p(sk3)
| ~ big_p(sk4)
| ~ big_p(sk2) ),
inference(factoring,[status(thm)],[c26]) ).
cnf(p56,plain,
( ~ big_p(sk3)
| ~ big_p(sk4) ),
inference(resolution,[status(thm)],[p55,p48]) ).
cnf(p57,plain,
~ big_p(sk3),
inference(resolution,[status(thm)],[p56,p55]) ).
cnf(p58,plain,
$false,
inference(resolution,[status(thm)],[p57,p55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN377+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n020.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 : Fri Sep 25 01:02:33 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.43/1.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.43/1.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------