%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN726+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.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 4.57s 1.15s
% Output : Proof 4.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 30 ( 9 unt; 0 def)
% Number of atoms : 98 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 97 ( 29 ~; 40 |; 20 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 84 ( 7 sgn 41 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f0,conjecture,
( ! [X,Y] : q(X,Y)
| ( ( ! [X,Y] :
( q(X,Y)
| p(X,Y) )
& ! [X,Y] :
( q(X,Y)
=> q(Y,X) )
& ! [X,Y,Z] :
( ( q(Y,Z)
& q(X,Y) )
=> q(X,Z) )
& ! [X,Y,Z] :
( ( p(Y,Z)
& p(X,Y) )
=> p(X,Z) ) )
=> ! [X,Y] : p(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm400) ).
fof(f0_neg,negated_conjecture,
~ ( ! [X,Y] : q(X,Y)
| ( ( ! [X,Y] :
( q(X,Y)
| p(X,Y) )
& ! [X,Y] :
( q(X,Y)
=> q(Y,X) )
& ! [X,Y,Z] :
( ( q(Y,Z)
& q(X,Y) )
=> q(X,Z) )
& ! [X,Y,Z] :
( ( p(Y,Z)
& p(X,Y) )
=> p(X,Z) ) )
=> ! [X,Y] : p(X,Y) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
( ? [X,Y] : ~ q(X,Y)
& ? [X,Y] : ~ p(X,Y)
& ! [X,Y] :
( q(X,Y)
| p(X,Y) )
& ! [X,Y] :
( q(Y,X)
| ~ q(X,Y) )
& ! [X,Y,Z] :
( q(X,Z)
| ~ q(Y,Z)
| ~ q(X,Y) )
& ! [X,Y,Z] :
( p(X,Z)
| ~ p(Y,Z)
| ~ p(X,Y) ) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
! [X,Y,Z] :
( ~ q(sk2,sk3)
& ~ p(sk0,sk1)
& ( q(X,Y)
| p(X,Y) )
& ( q(Y,X)
| ~ q(X,Y) )
& ( q(X,Z)
| ~ q(Y,Z)
| ~ q(X,Y) )
& ( p(X,Z)
| ~ p(Y,Z)
| ~ p(X,Y) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3])],[f0_nnf]) ).
cnf(c1,plain,
( q(X0,X2)
| ~ q(X1,X2)
| ~ q(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c3,plain,
( q(X0,X1)
| p(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(c2,plain,
( q(X1,X0)
| ~ q(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p7,plain,
( q(X1,X0)
| p(X0,X1) ),
inference(resolution,[status(thm)],[c3,c2]) ).
cnf(p13,plain,
( p(X0,X2)
| q(X2,X1)
| ~ q(X0,X1) ),
inference(resolution,[status(thm)],[c1,p7]) ).
cnf(p17,plain,
( p(X2,X1)
| p(X2,X0)
| q(X0,X1) ),
inference(resolution,[status(thm)],[p13,c3]) ).
cnf(c5,plain,
~ q(sk2,sk3),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p69,plain,
( p(X0,sk3)
| p(X0,sk2) ),
inference(resolution,[status(thm)],[p17,c5]) ).
cnf(c0,plain,
( p(X0,X2)
| ~ p(X1,X2)
| ~ p(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p113,plain,
( p(X0,X1)
| ~ p(sk3,X1)
| p(X0,sk2) ),
inference(resolution,[status(thm)],[p69,c0]) ).
cnf(p525,plain,
( ~ p(sk3,sk2)
| p(X0,sk2) ),
inference(factoring,[status(thm)],[p113]) ).
cnf(p12,plain,
( p(X2,X0)
| q(X2,X1)
| ~ q(X0,X1) ),
inference(resolution,[status(thm)],[c1,c3]) ).
cnf(p16,plain,
( p(X1,X2)
| p(X0,X2)
| q(X0,X1) ),
inference(resolution,[status(thm)],[p12,p7]) ).
cnf(p45,plain,
( p(sk3,X0)
| p(sk2,X0) ),
inference(resolution,[status(thm)],[p16,c5]) ).
cnf(p6,plain,
p(sk2,sk3),
inference(resolution,[status(thm)],[c3,c5]) ).
cnf(p8,plain,
( p(sk2,X0)
| ~ p(sk3,X0) ),
inference(resolution,[status(thm)],[p6,c0]) ).
cnf(p84,plain,
( p(sk2,X0)
| p(sk2,X0) ),
inference(resolution,[status(thm)],[p45,p8]) ).
cnf(p115,plain,
p(sk2,X0),
inference(factoring,[status(thm)],[p84]) ).
cnf(p9,plain,
p(sk3,sk2),
inference(resolution,[status(thm)],[p7,c5]) ).
cnf(p10,plain,
( p(sk3,X0)
| ~ p(sk2,X0) ),
inference(resolution,[status(thm)],[p9,c0]) ).
cnf(p127,plain,
p(sk3,X0),
inference(resolution,[status(thm)],[p115,p10]) ).
cnf(p536,plain,
p(X0,sk2),
inference(resolution,[status(thm)],[p525,p127]) ).
cnf(p559,plain,
( p(X1,X0)
| ~ p(sk2,X0) ),
inference(resolution,[status(thm)],[p536,c0]) ).
cnf(p564,plain,
p(X0,X1),
inference(resolution,[status(thm)],[p559,p115]) ).
cnf(c4,plain,
~ p(sk0,sk1),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p565,plain,
$false,
inference(resolution,[status(thm)],[p564,c4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN726+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n006.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 02:11:40 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.57/1.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.57/1.15 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------