%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN078+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 : n017.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 03:33:45 PM UTC 2026
% Result : Theorem 2.39s 0.79s
% Output : Proof 2.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 32 ( 8 unt; 0 def)
% Number of atoms : 90 ( 11 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 87 ( 29 ~; 40 |; 12 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 26 ( 0 sgn 10 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
( ! [X] :
( ? [Y] :
( X = f(Y)
& big_p(Y) )
=> big_p(X) )
<=> ! [U] :
( big_p(U)
=> big_p(f(U)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel56) ).
fof(f0_neg,negated_conjecture,
~ ( ! [X] :
( ? [Y] :
( X = f(Y)
& big_p(Y) )
=> big_p(X) )
<=> ! [U] :
( big_p(U)
=> big_p(f(U)) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
( ( ! [U] :
( big_p(f(U))
| ~ big_p(U) )
& ? [X] :
( ~ big_p(X)
& ? [Y] :
( X = f(Y)
& big_p(Y) ) ) )
| ( ? [U] :
( ~ big_p(f(U))
& big_p(U) )
& ! [X] :
( big_p(X)
| ! [Y] :
( X != f(Y)
| ~ big_p(Y) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [Y,X,U] :
( ( ( big_p(f(U))
| ~ big_p(U) )
& ~ big_p(sk1)
& sk1 = f(sk2)
& big_p(sk2) )
| ( ~ big_p(f(sk0))
& big_p(sk0)
& ( big_p(X)
| X != f(Y)
| ~ big_p(Y) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2])],[f0_nnf]) ).
cnf(c3,plain,
( big_p(f(X2))
| ~ big_p(X2)
| big_p(X0)
| X0 != f(X1)
| ~ big_p(X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p43,plain,
( big_p(f(X1))
| ~ big_p(X1)
| big_p(f(X0))
| ~ big_p(X0) ),
inference(equality_resolution,[status(thm)],[c3]) ).
cnf(p47,plain,
( ~ big_p(X0)
| big_p(f(X0))
| ~ big_p(X0) ),
inference(factoring,[status(thm)],[p43]) ).
cnf(p50,plain,
( big_p(f(X0))
| ~ big_p(X0) ),
inference(factoring,[status(thm)],[p47]) ).
cnf(c5,plain,
( sk1 = f(sk2)
| big_p(sk0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c7,plain,
( big_p(f(X2))
| ~ big_p(X2)
| big_p(sk0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c4,plain,
( big_p(sk2)
| big_p(sk0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p12,plain,
( big_p(sk0)
| big_p(f(sk2))
| big_p(sk0) ),
inference(resolution,[status(thm)],[c7,c4]) ).
cnf(p13,plain,
( big_p(f(sk2))
| big_p(sk0) ),
inference(factoring,[status(thm)],[p12]) ).
cnf(p15,plain,
( big_p(sk1)
| big_p(sk0)
| big_p(sk0) ),
inference(superposition,[status(thm)],[c5,p13]) ).
cnf(p17,plain,
( big_p(sk1)
| big_p(sk0) ),
inference(factoring,[status(thm)],[p15]) ).
cnf(c6,plain,
( ~ big_p(sk1)
| big_p(sk0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p18,plain,
( big_p(sk0)
| big_p(sk0) ),
inference(resolution,[status(thm)],[p17,c6]) ).
cnf(p19,plain,
big_p(sk0),
inference(factoring,[status(thm)],[p18]) ).
cnf(p51,plain,
big_p(f(sk0)),
inference(resolution,[status(thm)],[p50,p19]) ).
cnf(c9,plain,
( sk1 = f(sk2)
| ~ big_p(f(sk0)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p54,plain,
sk1 = f(sk2),
inference(resolution,[status(thm)],[p51,c9]) ).
cnf(c0,plain,
( big_p(sk2)
| big_p(X0)
| X0 != f(X1)
| ~ big_p(X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p21,plain,
( big_p(sk2)
| big_p(f(X0))
| ~ big_p(X0) ),
inference(equality_resolution,[status(thm)],[c0]) ).
cnf(p23,plain,
( big_p(sk2)
| big_p(f(sk0)) ),
inference(resolution,[status(thm)],[p21,p19]) ).
cnf(c8,plain,
( big_p(sk2)
| ~ big_p(f(sk0)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p26,plain,
( big_p(sk2)
| big_p(sk2) ),
inference(resolution,[status(thm)],[p23,c8]) ).
cnf(p28,plain,
big_p(sk2),
inference(factoring,[status(thm)],[p26]) ).
cnf(p52,plain,
big_p(f(sk2)),
inference(resolution,[status(thm)],[p50,p28]) ).
cnf(p57,plain,
big_p(sk1),
inference(superposition,[status(thm)],[p54,p52]) ).
cnf(c10,plain,
( ~ big_p(sk1)
| ~ big_p(f(sk0)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p53,plain,
~ big_p(sk1),
inference(resolution,[status(thm)],[p51,c10]) ).
cnf(p59,plain,
$false,
inference(resolution,[status(thm)],[p57,p53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN078+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 00:02:17 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 2.39/0.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.39/0.79 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------