%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN375+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 : n013.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 4.01s 1.08s
% Output : Proof 4.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 19 ( 4 unt; 0 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 89 ( 32 ~; 35 |; 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 : 36 ( 8 sgn 13 !; 11 ?)
% 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',x2126) ).
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(Y)
| big_p(X) )
& ( big_p(sk6)
| ~ big_p(sk5) )
& ( ( big_p(sk4)
& ~ big_p(sk3) )
| ( ~ big_p(Y)
& big_p(sk3) ) ) )
| ( ( ( big_p(sk2)
& ~ big_p(sk1) )
| ( ~ big_p(Y)
& big_p(X) ) )
& ( ~ big_p(Y)
| big_p(X) )
& ( big_p(sk0(X))
| ~ big_p(X) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3,sk4,sk5,sk6])],[f0_nnf]) ).
cnf(c26,plain,
( ~ big_p(sk3)
| ~ big_p(X1)
| ~ big_p(sk1)
| ~ big_p(X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p55,plain,
( ~ big_p(sk3)
| ~ big_p(sk1)
| ~ big_p(X0) ),
inference(factoring,[status(thm)],[c26]) ).
cnf(p58,plain,
( ~ big_p(sk3)
| ~ big_p(sk1) ),
inference(factoring,[status(thm)],[p55]) ).
cnf(c19,plain,
( big_p(sk4)
| big_p(sk3)
| big_p(sk2)
| big_p(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p50,plain,
( big_p(sk4)
| big_p(sk3)
| big_p(sk2) ),
inference(factoring,[status(thm)],[c19]) ).
cnf(c11,plain,
( ~ big_p(X1)
| big_p(X0)
| ~ big_p(X1)
| big_p(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p47,plain,
( ~ big_p(X1)
| ~ big_p(X1)
| big_p(X0) ),
inference(factoring,[status(thm)],[c11]) ).
cnf(p49,plain,
( ~ big_p(X1)
| big_p(X0) ),
inference(factoring,[status(thm)],[p47]) ).
cnf(p51,plain,
( big_p(X0)
| big_p(sk3)
| big_p(sk2) ),
inference(resolution,[status(thm)],[p50,p49]) ).
cnf(p52,plain,
( big_p(sk3)
| big_p(sk2) ),
inference(factoring,[status(thm)],[p51]) ).
cnf(p53,plain,
( big_p(X0)
| big_p(sk2) ),
inference(resolution,[status(thm)],[p52,p49]) ).
cnf(p56,plain,
big_p(sk2),
inference(factoring,[status(thm)],[p53]) ).
cnf(p57,plain,
big_p(X0),
inference(resolution,[status(thm)],[p56,p49]) ).
cnf(p59,plain,
~ big_p(sk3),
inference(resolution,[status(thm)],[p58,p57]) ).
cnf(p60,plain,
$false,
inference(resolution,[status(thm)],[p59,p57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN375+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 01:00:36 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.01/1.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.01/1.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------