%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN376+1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.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 4.11s 0.96s
% Output : Proof 4.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 17 ( 11 unt; 0 def)
% Number of atoms : 35 ( 8 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 32 ( 14 ~; 8 |; 6 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-4 aty)
% Number of variables : 19 ( 6 sgn 8 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
( ? [X] :
! [Y] :
( big_p(Y)
<=> big_p(X) )
=> ( ! [X] : ~ big_p(X)
| ! [X] : big_p(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x2127) ).
fof(f0_neg,negated_conjecture,
~ ( ? [X] :
! [Y] :
( big_p(Y)
<=> big_p(X) )
=> ( ! [X] : ~ big_p(X)
| ! [X] : big_p(X) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
( ? [X] : big_p(X)
& ? [X] : ~ big_p(X)
& ? [X] :
! [Y] :
( ( ~ big_p(X)
| big_p(Y) )
& ( big_p(X)
| ~ big_p(Y) ) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [Y] :
( big_p(sk2)
& ~ big_p(sk1)
& ( ~ big_p(sk0)
| big_p(Y) )
& ( big_p(sk0)
| ~ big_p(Y) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f0_nnf]) ).
cnf(c0,plain,
( big_p(sk0)
| ~ big_p(X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,negated_conjecture,
ifeq(big_p(X0),true,big_p(sk0),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(c3,plain,
big_p(sk2),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi2,negated_conjecture,
big_p(sk2) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h0,plain,
big_p(sk0) = true,
inference(hyper_resolution,[status(thm)],[hi0,hi2]) ).
cnf(c1,plain,
( ~ big_p(sk0)
| big_p(X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi1,negated_conjecture,
ifeq(big_p(sk0),true,big_p(X0),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t0,plain,
big_p(X1) = true,
inference(hyper_resolution,[status(thm)],[hi1,h0]) ).
cnf(t7,plain,
big_p(X1) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(c2,plain,
~ big_p(sk1),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(goal_0,negated_conjecture,
big_p(sk1) != true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t7]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN376+1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.35 % Computer : n018.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 25 01:03:50 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.11/0.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.11/0.96 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------