%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN724+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 03:35:34 PM UTC 2026
% Result : Theorem 5.03s 1.14s
% Output : Proof 5.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 1
% Syntax : Number of formulae : 25 ( 6 unt; 0 def)
% Number of atoms : 89 ( 0 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 103 ( 39 ~; 40 |; 18 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 12 ( 0 sgn 7 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
( ! [X] :
( r(X)
=> s(X) )
<=> ! [X] :
( ( s(X)
& r(X) )
<=> r(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm31) ).
fof(f0_neg,negated_conjecture,
~ ( ! [X] :
( r(X)
=> s(X) )
<=> ! [X] :
( ( s(X)
& r(X) )
<=> r(X) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
( ( ! [X] :
( ( ~ r(X)
| ( s(X)
& r(X) ) )
& ( r(X)
| ~ s(X)
| ~ r(X) ) )
& ? [X] :
( ~ s(X)
& r(X) ) )
| ( ? [X] :
( ( r(X)
& ( ~ s(X)
| ~ r(X) ) )
| ( ~ r(X)
& s(X)
& r(X) ) )
& ! [X] :
( s(X)
| ~ r(X) ) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [X] :
( ( ( ~ r(X)
| ( s(X)
& r(X) ) )
& ( r(X)
| ~ s(X)
| ~ r(X) )
& ~ s(sk1)
& r(sk1) )
| ( ( ( r(sk0)
& ( ~ s(sk0)
| ~ r(sk0) ) )
| ( ~ r(sk0)
& s(sk0)
& r(sk0) ) )
& ( s(X)
| ~ r(X) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f0_nnf]) ).
cnf(c26,plain,
( ~ s(sk1)
| ~ s(sk0)
| ~ r(sk0)
| ~ r(sk0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p48,plain,
( ~ s(sk1)
| ~ s(sk0)
| ~ r(sk0) ),
inference(factoring,[status(thm)],[c26]) ).
cnf(c4,plain,
( ~ r(X0)
| s(X0)
| s(X0)
| ~ r(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p37,plain,
( s(X0)
| s(X0)
| ~ r(X0) ),
inference(factoring,[status(thm)],[c4]) ).
cnf(p39,plain,
( s(X0)
| ~ r(X0) ),
inference(factoring,[status(thm)],[p37]) ).
cnf(c10,plain,
( r(sk1)
| r(sk0)
| r(sk0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p35,plain,
( r(sk1)
| r(sk0) ),
inference(factoring,[status(thm)],[c10]) ).
cnf(p40,plain,
( r(sk0)
| s(sk1) ),
inference(resolution,[status(thm)],[p39,p35]) ).
cnf(c11,plain,
( ~ s(sk1)
| r(sk0)
| r(sk0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p36,plain,
( ~ s(sk1)
| r(sk0) ),
inference(factoring,[status(thm)],[c11]) ).
cnf(p41,plain,
( r(sk0)
| r(sk0) ),
inference(resolution,[status(thm)],[p40,p36]) ).
cnf(p42,plain,
r(sk0),
inference(factoring,[status(thm)],[p41]) ).
cnf(p49,plain,
( ~ s(sk1)
| ~ s(sk0) ),
inference(resolution,[status(thm)],[p48,p42]) ).
cnf(p43,plain,
s(sk0),
inference(resolution,[status(thm)],[p42,p39]) ).
cnf(p50,plain,
~ s(sk1),
inference(resolution,[status(thm)],[p49,p43]) ).
cnf(c25,plain,
( r(sk1)
| ~ s(sk0)
| ~ r(sk0)
| ~ r(sk0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p44,plain,
( r(sk1)
| ~ s(sk0)
| ~ r(sk0) ),
inference(factoring,[status(thm)],[c25]) ).
cnf(p45,plain,
( r(sk1)
| ~ s(sk0) ),
inference(resolution,[status(thm)],[p44,p42]) ).
cnf(p46,plain,
r(sk1),
inference(resolution,[status(thm)],[p45,p43]) ).
cnf(p47,plain,
s(sk1),
inference(resolution,[status(thm)],[p46,p39]) ).
cnf(p51,plain,
$false,
inference(resolution,[status(thm)],[p50,p47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN724+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.39 % Computer : n003.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Fri Sep 25 02:13:06 UTC 2026
% 0.10/0.40 % CPUTime :
% 0.10/0.40 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.03/1.14 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.03/1.14 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------