%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN413+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 : n016.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 03:34:38 PM UTC 2026
% Result : Theorem 3.77s 1.08s
% Output : Proof 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 4 unt; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 37 ( 15 ~; 10 |; 8 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 26 ( 3 sgn 12 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
( ! [Z] :
? [Y] :
! [X] :
( f(X,Y)
<=> ( ~ f(X,X)
& f(X,Z) ) )
=> ~ ? [V] :
! [U] : f(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kalish256) ).
fof(f0_neg,negated_conjecture,
~ ( ! [Z] :
? [Y] :
! [X] :
( f(X,Y)
<=> ( ~ f(X,X)
& f(X,Z) ) )
=> ~ ? [V] :
! [U] : f(U,V) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
( ? [V] :
! [U] : f(U,V)
& ! [Z] :
? [Y] :
! [X] :
( ( f(X,X)
| ~ f(X,Z)
| f(X,Y) )
& ( ( ~ f(X,X)
& f(X,Z) )
| ~ f(X,Y) ) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [X,Z,U] :
( f(U,sk1)
& ( f(X,X)
| ~ f(X,Z)
| f(X,sk0(Z)) )
& ( ( ~ f(X,X)
& f(X,Z) )
| ~ f(X,sk0(Z)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f0_nnf]) ).
cnf(c3,plain,
f(X4,sk1),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c2,plain,
( f(X2,X2)
| ~ f(X2,X0)
| f(X2,sk0(X0)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p6,plain,
( f(X0,X0)
| f(X0,sk0(sk1)) ),
inference(resolution,[status(thm)],[c3,c2]) ).
cnf(c1,plain,
( ~ f(X2,X2)
| ~ f(X2,sk0(X0)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p4,plain,
~ f(sk0(X0),sk0(X0)),
inference(factoring,[status(thm)],[c1]) ).
cnf(p10,plain,
f(sk0(X0),sk0(sk1)),
inference(resolution,[status(thm)],[p6,p4]) ).
cnf(p13,plain,
$false,
inference(resolution,[status(thm)],[p10,p4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN413+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n016.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 01:10:58 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.77/1.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.77/1.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------