%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG025+1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 : Tue Sep 29 09:07:46 AM UTC 2026
% Result : Theorem 1.08s 0.63s
% Output : Refutation 2.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 1
% Syntax : Number of formulae : 37 ( 17 unt; 0 def)
% Number of atoms : 481 ( 480 equ)
% Maximal formula atoms : 72 ( 13 avg)
% Number of connectives : 696 ( 252 ~; 232 |; 212 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 73 ( 12 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,conjecture,
( ( op(e0,e0) = op(e0,e0)
& op(e0,e1) = op(e1,e0)
& op(e0,e2) = op(e2,e0)
& op(e0,e3) = op(e3,e0)
& op(e0,e4) = op(e4,e0)
& op(e0,e5) = op(e5,e0)
& op(e1,e0) = op(e0,e1)
& op(e1,e1) = op(e1,e1)
& op(e1,e2) = op(e2,e1)
& op(e1,e3) = op(e3,e1)
& op(e1,e4) = op(e4,e1)
& op(e1,e5) = op(e5,e1)
& op(e2,e0) = op(e0,e2)
& op(e2,e1) = op(e1,e2)
& op(e2,e2) = op(e2,e2)
& op(e2,e3) = op(e3,e2)
& op(e2,e4) = op(e4,e2)
& op(e2,e5) = op(e5,e2)
& op(e3,e0) = op(e0,e3)
& op(e3,e1) = op(e1,e3)
& op(e3,e2) = op(e2,e3)
& op(e3,e3) = op(e3,e3)
& op(e3,e4) = op(e4,e3)
& op(e3,e5) = op(e5,e3)
& op(e4,e0) = op(e0,e4)
& op(e4,e1) = op(e1,e4)
& op(e4,e2) = op(e2,e4)
& op(e4,e3) = op(e3,e4)
& op(e4,e4) = op(e4,e4)
& op(e4,e5) = op(e5,e4)
& op(e5,e0) = op(e0,e5)
& op(e5,e1) = op(e1,e5)
& op(e5,e2) = op(e2,e5)
& op(e5,e3) = op(e3,e5)
& op(e5,e4) = op(e4,e5)
& op(e5,e5) = op(e5,e5) )
| ~ ( op(e0,e0) = op(e0,e0)
& op(e0,e1) = op(e1,e0)
& op(e0,e2) = op(e2,e0)
& op(e0,e3) = op(e3,e0)
& op(e0,e4) = op(e4,e0)
& op(e0,e5) = op(e5,e0)
& op(e1,e0) = op(e0,e1)
& op(e1,e1) = op(e1,e1)
& op(e1,e2) = op(e2,e1)
& op(e1,e3) = op(e3,e1)
& op(e1,e4) = op(e4,e1)
& op(e1,e5) = op(e5,e1)
& op(e2,e0) = op(e0,e2)
& op(e2,e1) = op(e1,e2)
& op(e2,e2) = op(e2,e2)
& op(e2,e3) = op(e3,e2)
& op(e2,e4) = op(e4,e2)
& op(e2,e5) = op(e5,e2)
& op(e3,e0) = op(e0,e3)
& op(e3,e1) = op(e1,e3)
& op(e3,e2) = op(e2,e3)
& op(e3,e3) = op(e3,e3)
& op(e3,e4) = op(e4,e3)
& op(e3,e5) = op(e5,e3)
& op(e4,e0) = op(e0,e4)
& op(e4,e1) = op(e1,e4)
& op(e4,e2) = op(e2,e4)
& op(e4,e3) = op(e3,e4)
& op(e4,e4) = op(e4,e4)
& op(e4,e5) = op(e5,e4)
& op(e5,e0) = op(e0,e5)
& op(e5,e1) = op(e1,e5)
& op(e5,e2) = op(e2,e5)
& op(e5,e3) = op(e3,e5)
& op(e5,e4) = op(e4,e5)
& op(e5,e5) = op(e5,e5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f13,negated_conjecture,
~ ( ( op(e0,e0) = op(e0,e0)
& op(e0,e1) = op(e1,e0)
& op(e0,e2) = op(e2,e0)
& op(e0,e3) = op(e3,e0)
& op(e0,e4) = op(e4,e0)
& op(e0,e5) = op(e5,e0)
& op(e1,e0) = op(e0,e1)
& op(e1,e1) = op(e1,e1)
& op(e1,e2) = op(e2,e1)
& op(e1,e3) = op(e3,e1)
& op(e1,e4) = op(e4,e1)
& op(e1,e5) = op(e5,e1)
& op(e2,e0) = op(e0,e2)
& op(e2,e1) = op(e1,e2)
& op(e2,e2) = op(e2,e2)
& op(e2,e3) = op(e3,e2)
& op(e2,e4) = op(e4,e2)
& op(e2,e5) = op(e5,e2)
& op(e3,e0) = op(e0,e3)
& op(e3,e1) = op(e1,e3)
& op(e3,e2) = op(e2,e3)
& op(e3,e3) = op(e3,e3)
& op(e3,e4) = op(e4,e3)
& op(e3,e5) = op(e5,e3)
& op(e4,e0) = op(e0,e4)
& op(e4,e1) = op(e1,e4)
& op(e4,e2) = op(e2,e4)
& op(e4,e3) = op(e3,e4)
& op(e4,e4) = op(e4,e4)
& op(e4,e5) = op(e5,e4)
& op(e5,e0) = op(e0,e5)
& op(e5,e1) = op(e1,e5)
& op(e5,e2) = op(e2,e5)
& op(e5,e3) = op(e3,e5)
& op(e5,e4) = op(e4,e5)
& op(e5,e5) = op(e5,e5) )
| ~ ( op(e0,e0) = op(e0,e0)
& op(e0,e1) = op(e1,e0)
& op(e0,e2) = op(e2,e0)
& op(e0,e3) = op(e3,e0)
& op(e0,e4) = op(e4,e0)
& op(e0,e5) = op(e5,e0)
& op(e1,e0) = op(e0,e1)
& op(e1,e1) = op(e1,e1)
& op(e1,e2) = op(e2,e1)
& op(e1,e3) = op(e3,e1)
& op(e1,e4) = op(e4,e1)
& op(e1,e5) = op(e5,e1)
& op(e2,e0) = op(e0,e2)
& op(e2,e1) = op(e1,e2)
& op(e2,e2) = op(e2,e2)
& op(e2,e3) = op(e3,e2)
& op(e2,e4) = op(e4,e2)
& op(e2,e5) = op(e5,e2)
& op(e3,e0) = op(e0,e3)
& op(e3,e1) = op(e1,e3)
& op(e3,e2) = op(e2,e3)
& op(e3,e3) = op(e3,e3)
& op(e3,e4) = op(e4,e3)
& op(e3,e5) = op(e5,e3)
& op(e4,e0) = op(e0,e4)
& op(e4,e1) = op(e1,e4)
& op(e4,e2) = op(e2,e4)
& op(e4,e3) = op(e3,e4)
& op(e4,e4) = op(e4,e4)
& op(e4,e5) = op(e5,e4)
& op(e5,e0) = op(e0,e5)
& op(e5,e1) = op(e1,e5)
& op(e5,e2) = op(e2,e5)
& op(e5,e3) = op(e3,e5)
& op(e5,e4) = op(e4,e5)
& op(e5,e5) = op(e5,e5) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
( ( op(e0,e0) != op(e0,e0)
| op(e0,e1) != op(e1,e0)
| op(e0,e2) != op(e2,e0)
| op(e0,e3) != op(e3,e0)
| op(e0,e4) != op(e4,e0)
| op(e0,e5) != op(e5,e0)
| op(e0,e1) != op(e1,e0)
| op(e1,e1) != op(e1,e1)
| op(e1,e2) != op(e2,e1)
| op(e1,e3) != op(e3,e1)
| op(e1,e4) != op(e4,e1)
| op(e1,e5) != op(e5,e1)
| op(e0,e2) != op(e2,e0)
| op(e1,e2) != op(e2,e1)
| op(e2,e2) != op(e2,e2)
| op(e2,e3) != op(e3,e2)
| op(e2,e4) != op(e4,e2)
| op(e2,e5) != op(e5,e2)
| op(e0,e3) != op(e3,e0)
| op(e1,e3) != op(e3,e1)
| op(e2,e3) != op(e3,e2)
| op(e3,e3) != op(e3,e3)
| op(e3,e4) != op(e4,e3)
| op(e3,e5) != op(e5,e3)
| op(e0,e4) != op(e4,e0)
| op(e1,e4) != op(e4,e1)
| op(e2,e4) != op(e4,e2)
| op(e3,e4) != op(e4,e3)
| op(e4,e4) != op(e4,e4)
| op(e4,e5) != op(e5,e4)
| op(e0,e5) != op(e5,e0)
| op(e1,e5) != op(e5,e1)
| op(e2,e5) != op(e5,e2)
| op(e3,e5) != op(e5,e3)
| op(e4,e5) != op(e5,e4)
| op(e5,e5) != op(e5,e5) )
& op(e0,e0) = op(e0,e0)
& op(e0,e1) = op(e1,e0)
& op(e0,e2) = op(e2,e0)
& op(e0,e3) = op(e3,e0)
& op(e0,e4) = op(e4,e0)
& op(e0,e5) = op(e5,e0)
& op(e1,e0) = op(e0,e1)
& op(e1,e1) = op(e1,e1)
& op(e1,e2) = op(e2,e1)
& op(e1,e3) = op(e3,e1)
& op(e1,e4) = op(e4,e1)
& op(e1,e5) = op(e5,e1)
& op(e2,e0) = op(e0,e2)
& op(e2,e1) = op(e1,e2)
& op(e2,e2) = op(e2,e2)
& op(e2,e3) = op(e3,e2)
& op(e2,e4) = op(e4,e2)
& op(e2,e5) = op(e5,e2)
& op(e3,e0) = op(e0,e3)
& op(e3,e1) = op(e1,e3)
& op(e3,e2) = op(e2,e3)
& op(e3,e3) = op(e3,e3)
& op(e3,e4) = op(e4,e3)
& op(e3,e5) = op(e5,e3)
& op(e4,e0) = op(e0,e4)
& op(e4,e1) = op(e1,e4)
& op(e4,e2) = op(e2,e4)
& op(e4,e3) = op(e3,e4)
& op(e4,e4) = op(e4,e4)
& op(e4,e5) = op(e5,e4)
& op(e5,e0) = op(e0,e5)
& op(e5,e1) = op(e1,e5)
& op(e5,e2) = op(e2,e5)
& op(e5,e3) = op(e3,e5)
& op(e5,e4) = op(e4,e5)
& op(e5,e5) = op(e5,e5) ),
inference(ennf_transformation,[],[f13]) ).
fof(f15,plain,
( ( op(e0,e0) != op(e0,e0)
| op(e0,e1) != op(e1,e0)
| op(e0,e2) != op(e2,e0)
| op(e0,e3) != op(e3,e0)
| op(e0,e4) != op(e4,e0)
| op(e0,e5) != op(e5,e0)
| op(e0,e1) != op(e1,e0)
| op(e1,e1) != op(e1,e1)
| op(e1,e2) != op(e2,e1)
| op(e1,e3) != op(e3,e1)
| op(e1,e4) != op(e4,e1)
| op(e1,e5) != op(e5,e1)
| op(e0,e2) != op(e2,e0)
| op(e1,e2) != op(e2,e1)
| op(e2,e2) != op(e2,e2)
| op(e2,e3) != op(e3,e2)
| op(e2,e4) != op(e4,e2)
| op(e2,e5) != op(e5,e2)
| op(e0,e3) != op(e3,e0)
| op(e1,e3) != op(e3,e1)
| op(e2,e3) != op(e3,e2)
| op(e3,e3) != op(e3,e3)
| op(e3,e4) != op(e4,e3)
| op(e3,e5) != op(e5,e3)
| op(e0,e4) != op(e4,e0)
| op(e1,e4) != op(e4,e1)
| op(e2,e4) != op(e4,e2)
| op(e3,e4) != op(e4,e3)
| op(e4,e4) != op(e4,e4)
| op(e4,e5) != op(e5,e4)
| op(e0,e5) != op(e5,e0)
| op(e1,e5) != op(e5,e1)
| op(e2,e5) != op(e5,e2)
| op(e3,e5) != op(e5,e3)
| op(e4,e5) != op(e5,e4)
| op(e5,e5) != op(e5,e5) )
& op(e0,e0) = op(e0,e0)
& op(e0,e1) = op(e1,e0)
& op(e0,e2) = op(e2,e0)
& op(e0,e3) = op(e3,e0)
& op(e0,e4) = op(e4,e0)
& op(e0,e5) = op(e5,e0)
& op(e1,e0) = op(e0,e1)
& op(e1,e1) = op(e1,e1)
& op(e1,e2) = op(e2,e1)
& op(e1,e3) = op(e3,e1)
& op(e1,e4) = op(e4,e1)
& op(e1,e5) = op(e5,e1)
& op(e2,e0) = op(e0,e2)
& op(e2,e1) = op(e1,e2)
& op(e2,e2) = op(e2,e2)
& op(e2,e3) = op(e3,e2)
& op(e2,e4) = op(e4,e2)
& op(e2,e5) = op(e5,e2)
& op(e3,e0) = op(e0,e3)
& op(e3,e1) = op(e1,e3)
& op(e3,e2) = op(e2,e3)
& op(e3,e3) = op(e3,e3)
& op(e3,e4) = op(e4,e3)
& op(e3,e5) = op(e5,e3)
& op(e4,e0) = op(e0,e4)
& op(e4,e1) = op(e1,e4)
& op(e4,e2) = op(e2,e4)
& op(e4,e3) = op(e3,e4)
& op(e4,e4) = op(e4,e4)
& op(e4,e5) = op(e5,e4)
& op(e5,e0) = op(e0,e5)
& op(e5,e1) = op(e1,e5)
& op(e5,e2) = op(e2,e5)
& op(e5,e3) = op(e3,e5)
& op(e5,e4) = op(e4,e5)
& op(e5,e5) = op(e5,e5) ),
inference(flattening,[],[f14]) ).
fof(f17,plain,
op(e4,e5) = op(e5,e4),
inference(cnf_transformation,[],[f15]) ).
fof(f18,plain,
op(e3,e5) = op(e5,e3),
inference(cnf_transformation,[],[f15]) ).
fof(f19,plain,
op(e2,e5) = op(e5,e2),
inference(cnf_transformation,[],[f15]) ).
fof(f20,plain,
op(e1,e5) = op(e5,e1),
inference(cnf_transformation,[],[f15]) ).
fof(f21,plain,
op(e0,e5) = op(e5,e0),
inference(cnf_transformation,[],[f15]) ).
fof(f24,plain,
op(e3,e4) = op(e4,e3),
inference(cnf_transformation,[],[f15]) ).
fof(f25,plain,
op(e2,e4) = op(e4,e2),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
op(e1,e4) = op(e4,e1),
inference(cnf_transformation,[],[f15]) ).
fof(f27,plain,
op(e0,e4) = op(e4,e0),
inference(cnf_transformation,[],[f15]) ).
fof(f31,plain,
op(e2,e3) = op(e3,e2),
inference(cnf_transformation,[],[f15]) ).
fof(f32,plain,
op(e1,e3) = op(e3,e1),
inference(cnf_transformation,[],[f15]) ).
fof(f33,plain,
op(e0,e3) = op(e3,e0),
inference(cnf_transformation,[],[f15]) ).
fof(f38,plain,
op(e1,e2) = op(e2,e1),
inference(cnf_transformation,[],[f15]) ).
fof(f39,plain,
op(e0,e2) = op(e2,e0),
inference(cnf_transformation,[],[f15]) ).
fof(f45,plain,
op(e0,e1) = op(e1,e0),
inference(cnf_transformation,[],[f15]) ).
fof(f52,plain,
( op(e0,e0) != op(e0,e0)
| op(e0,e1) != op(e1,e0)
| op(e0,e2) != op(e2,e0)
| op(e0,e3) != op(e3,e0)
| op(e0,e4) != op(e4,e0)
| op(e0,e5) != op(e5,e0)
| op(e0,e1) != op(e1,e0)
| op(e1,e1) != op(e1,e1)
| op(e1,e2) != op(e2,e1)
| op(e1,e3) != op(e3,e1)
| op(e1,e4) != op(e4,e1)
| op(e1,e5) != op(e5,e1)
| op(e0,e2) != op(e2,e0)
| op(e1,e2) != op(e2,e1)
| op(e2,e2) != op(e2,e2)
| op(e2,e3) != op(e3,e2)
| op(e2,e4) != op(e4,e2)
| op(e2,e5) != op(e5,e2)
| op(e0,e3) != op(e3,e0)
| op(e1,e3) != op(e3,e1)
| op(e2,e3) != op(e3,e2)
| op(e3,e3) != op(e3,e3)
| op(e3,e4) != op(e4,e3)
| op(e3,e5) != op(e5,e3)
| op(e0,e4) != op(e4,e0)
| op(e1,e4) != op(e4,e1)
| op(e2,e4) != op(e4,e2)
| op(e3,e4) != op(e4,e3)
| op(e4,e4) != op(e4,e4)
| op(e4,e5) != op(e5,e4)
| op(e0,e5) != op(e5,e0)
| op(e1,e5) != op(e5,e1)
| op(e2,e5) != op(e5,e2)
| op(e3,e5) != op(e5,e3)
| op(e4,e5) != op(e5,e4)
| op(e5,e5) != op(e5,e5) ),
inference(cnf_transformation,[],[f15]) ).
fof(f500,plain,
( op(e0,e0) != op(e0,e0)
| op(e0,e1) != op(e1,e0)
| op(e0,e2) != op(e2,e0)
| op(e0,e3) != op(e3,e0)
| op(e0,e4) != op(e4,e0)
| op(e0,e5) != op(e5,e0)
| op(e1,e1) != op(e1,e1)
| op(e1,e2) != op(e2,e1)
| op(e1,e3) != op(e3,e1)
| op(e1,e4) != op(e4,e1)
| op(e1,e5) != op(e5,e1)
| op(e2,e2) != op(e2,e2)
| op(e2,e3) != op(e3,e2)
| op(e2,e4) != op(e4,e2)
| op(e2,e5) != op(e5,e2)
| op(e3,e3) != op(e3,e3)
| op(e3,e4) != op(e4,e3)
| op(e3,e5) != op(e5,e3)
| op(e4,e4) != op(e4,e4)
| op(e4,e5) != op(e5,e4)
| op(e5,e5) != op(e5,e5) ),
inference(duplicate_literal_removal,[],[f52]) ).
fof(f501,plain,
( op(e0,e1) != op(e1,e0)
| op(e0,e2) != op(e2,e0)
| op(e0,e3) != op(e3,e0)
| op(e0,e4) != op(e4,e0)
| op(e0,e5) != op(e5,e0)
| op(e1,e2) != op(e2,e1)
| op(e1,e3) != op(e3,e1)
| op(e1,e4) != op(e4,e1)
| op(e1,e5) != op(e5,e1)
| op(e2,e3) != op(e3,e2)
| op(e2,e4) != op(e4,e2)
| op(e2,e5) != op(e5,e2)
| op(e3,e4) != op(e4,e3)
| op(e3,e5) != op(e5,e3)
| op(e4,e5) != op(e5,e4) ),
inference(trivial_inequality_removal,[],[f500]) ).
fof(f652,plain,
( op(e0,e2) != op(e2,e0)
| op(e0,e3) != op(e3,e0)
| op(e0,e4) != op(e4,e0)
| op(e0,e5) != op(e5,e0)
| op(e1,e2) != op(e2,e1)
| op(e1,e3) != op(e3,e1)
| op(e1,e4) != op(e4,e1)
| op(e1,e5) != op(e5,e1)
| op(e2,e3) != op(e3,e2)
| op(e2,e4) != op(e4,e2)
| op(e2,e5) != op(e5,e2)
| op(e3,e4) != op(e4,e3)
| op(e3,e5) != op(e5,e3)
| op(e4,e5) != op(e5,e4) ),
inference(forward_subsumption_resolution,[],[f501,f45]) ).
fof(f653,plain,
( op(e0,e3) != op(e3,e0)
| op(e0,e4) != op(e4,e0)
| op(e0,e5) != op(e5,e0)
| op(e1,e2) != op(e2,e1)
| op(e1,e3) != op(e3,e1)
| op(e1,e4) != op(e4,e1)
| op(e1,e5) != op(e5,e1)
| op(e2,e3) != op(e3,e2)
| op(e2,e4) != op(e4,e2)
| op(e2,e5) != op(e5,e2)
| op(e3,e4) != op(e4,e3)
| op(e3,e5) != op(e5,e3)
| op(e4,e5) != op(e5,e4) ),
inference(forward_subsumption_resolution,[],[f652,f39]) ).
fof(f654,plain,
( op(e0,e4) != op(e4,e0)
| op(e0,e5) != op(e5,e0)
| op(e1,e2) != op(e2,e1)
| op(e1,e3) != op(e3,e1)
| op(e1,e4) != op(e4,e1)
| op(e1,e5) != op(e5,e1)
| op(e2,e3) != op(e3,e2)
| op(e2,e4) != op(e4,e2)
| op(e2,e5) != op(e5,e2)
| op(e3,e4) != op(e4,e3)
| op(e3,e5) != op(e5,e3)
| op(e4,e5) != op(e5,e4) ),
inference(forward_subsumption_resolution,[],[f653,f33]) ).
fof(f655,plain,
( op(e0,e5) != op(e5,e0)
| op(e1,e2) != op(e2,e1)
| op(e1,e3) != op(e3,e1)
| op(e1,e4) != op(e4,e1)
| op(e1,e5) != op(e5,e1)
| op(e2,e3) != op(e3,e2)
| op(e2,e4) != op(e4,e2)
| op(e2,e5) != op(e5,e2)
| op(e3,e4) != op(e4,e3)
| op(e3,e5) != op(e5,e3)
| op(e4,e5) != op(e5,e4) ),
inference(forward_subsumption_resolution,[],[f654,f27]) ).
fof(f656,plain,
( op(e1,e2) != op(e2,e1)
| op(e1,e3) != op(e3,e1)
| op(e1,e4) != op(e4,e1)
| op(e1,e5) != op(e5,e1)
| op(e2,e3) != op(e3,e2)
| op(e2,e4) != op(e4,e2)
| op(e2,e5) != op(e5,e2)
| op(e3,e4) != op(e4,e3)
| op(e3,e5) != op(e5,e3)
| op(e4,e5) != op(e5,e4) ),
inference(forward_subsumption_resolution,[],[f655,f21]) ).
fof(f657,plain,
( op(e1,e3) != op(e3,e1)
| op(e1,e4) != op(e4,e1)
| op(e1,e5) != op(e5,e1)
| op(e2,e3) != op(e3,e2)
| op(e2,e4) != op(e4,e2)
| op(e2,e5) != op(e5,e2)
| op(e3,e4) != op(e4,e3)
| op(e3,e5) != op(e5,e3)
| op(e4,e5) != op(e5,e4) ),
inference(forward_subsumption_resolution,[],[f656,f38]) ).
fof(f658,plain,
( op(e1,e4) != op(e4,e1)
| op(e1,e5) != op(e5,e1)
| op(e2,e3) != op(e3,e2)
| op(e2,e4) != op(e4,e2)
| op(e2,e5) != op(e5,e2)
| op(e3,e4) != op(e4,e3)
| op(e3,e5) != op(e5,e3)
| op(e4,e5) != op(e5,e4) ),
inference(forward_subsumption_resolution,[],[f657,f32]) ).
fof(f659,plain,
( op(e1,e5) != op(e5,e1)
| op(e2,e3) != op(e3,e2)
| op(e2,e4) != op(e4,e2)
| op(e2,e5) != op(e5,e2)
| op(e3,e4) != op(e4,e3)
| op(e3,e5) != op(e5,e3)
| op(e4,e5) != op(e5,e4) ),
inference(forward_subsumption_resolution,[],[f658,f26]) ).
fof(f660,plain,
( op(e2,e3) != op(e3,e2)
| op(e2,e4) != op(e4,e2)
| op(e2,e5) != op(e5,e2)
| op(e3,e4) != op(e4,e3)
| op(e3,e5) != op(e5,e3)
| op(e4,e5) != op(e5,e4) ),
inference(forward_subsumption_resolution,[],[f659,f20]) ).
fof(f661,plain,
( op(e2,e4) != op(e4,e2)
| op(e2,e5) != op(e5,e2)
| op(e3,e4) != op(e4,e3)
| op(e3,e5) != op(e5,e3)
| op(e4,e5) != op(e5,e4) ),
inference(forward_subsumption_resolution,[],[f660,f31]) ).
fof(f662,plain,
( op(e2,e5) != op(e5,e2)
| op(e3,e4) != op(e4,e3)
| op(e3,e5) != op(e5,e3)
| op(e4,e5) != op(e5,e4) ),
inference(forward_subsumption_resolution,[],[f661,f25]) ).
fof(f663,plain,
( op(e3,e4) != op(e4,e3)
| op(e3,e5) != op(e5,e3)
| op(e4,e5) != op(e5,e4) ),
inference(forward_subsumption_resolution,[],[f662,f19]) ).
fof(f664,plain,
( op(e3,e5) != op(e5,e3)
| op(e4,e5) != op(e5,e4) ),
inference(forward_subsumption_resolution,[],[f663,f24]) ).
fof(f665,plain,
op(e4,e5) != op(e5,e4),
inference(forward_subsumption_resolution,[],[f664,f18]) ).
fof(f666,plain,
$false,
inference(forward_subsumption_resolution,[],[f665,f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ALG025+1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Mon Sep 28 19:18:49 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.13 Running first-order theorem proving
% 0.08/0.13 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.08/0.63 % (3658705)Detected formulas, will run a generic FOF schedule.
% 1.08/0.63 % (3658714)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=7070522:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.08/0.63 % (3658713)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3154039950:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.08/0.63 % (3658716)dis-21_1_sil=8000:lcm=predicate:random_seed=562821277:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 1.08/0.63 % (3658712)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=4182620878:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.08/0.63 % (3658710)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=186652486:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.08/0.63 % (3658711)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=2854425300:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.08/0.63 % (3658715)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2343153432:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.08/0.63 % (3658714)First to succeed.
% 1.08/0.63 % (3658715)Also succeeded, but the first one will report.
% 1.08/0.63 % (3658714)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3658705"
% 1.08/0.63 % (3658713)Also succeeded, but the first one will report.
% 1.08/0.63 % (3658716)Also succeeded, but the first one will report.
% 1.08/0.63 % (3658714)Refutation found. Thanks to Tanya!
% 1.08/0.63 % SZS status Theorem for theBenchmark
% 1.08/0.63 % SZS output start Proof for theBenchmark
% See solution above
% 2.37/0.73 % (3658714)------------------------------
% 2.37/0.73 % (3658714)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.37/0.73 % (3658714)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.37/0.73 % (3658714)CaDiCaL version: 2.1.3
% 2.37/0.73 % (3658714)Termination reason: Refutation
% 2.37/0.73 % (3658714)Time elapsed: 0.007 s
% 2.37/0.73 % (3658714)Peak memory usage: 88 MB
% 2.37/0.73 % (3658714)Instructions burned: 29 (million)
% 2.37/0.73 % (3658714)------------------------------
% 2.37/0.73 % (3658714)------------------------------
% 2.37/0.73 % (3658705)Success in time 0.309 s
% 2.37/0.73 % Vampire exiting
%------------------------------------------------------------------------------