%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ133+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:31:41 PM UTC 2026
% Result : Theorem 2.99s 1.39s
% Output : Refutation 4.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 24
% Syntax : Number of formulae : 147 ( 26 unt; 15 def)
% Number of atoms : 499 ( 84 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 622 ( 270 ~; 268 |; 56 &)
% ( 20 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 18 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 102 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
( queens_p
=> ! [X0,X1] :
( ( le(s(n0),X0)
& le(X0,n)
& le(s(X0),X1)
& le(X1,n) )
=> ( p(X0) != p(X1)
& plus(p(X0),X0) != plus(p(X1),X1)
& minus(p(X0),X0) != minus(p(X1),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',queens_p) ).
fof(f3,axiom,
( ! [X0,X1] :
( ( le(s(n0),X0)
& le(X0,n)
& le(s(X0),X1)
& le(X1,n)
& ( le(s(X0),X1)
<=> le(s(perm(X1)),perm(X0)) ) )
=> ( q(X0) != q(X1)
& plus(q(X0),X0) != plus(q(X1),X1)
& minus(q(X0),X0) != minus(q(X1),X1) ) )
=> queens_q ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',queens_q) ).
fof(f4,conjecture,
( ( queens_p
& ! [X0] : q(X0) = p(perm(X0)) )
=> queens_q ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',queens_sym) ).
fof(f5,negated_conjecture,
~ ( ( queens_p
& ! [X0] : q(X0) = p(perm(X0)) )
=> queens_q ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,axiom,
! [X0] :
( ( le(s(n0),X0)
& le(X0,n) )
=> ( le(s(n0),perm(X0))
& le(perm(X0),n) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',permutation_range) ).
fof(f7,axiom,
! [X0,X1] : minus(X1,X0) = minus(perm(X0),perm(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',permutation_another_one) ).
fof(f8,axiom,
! [X0,X1,X2] :
( ( le(X0,X1)
& le(X1,X2) )
=> le(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',le_trans) ).
fof(f9,axiom,
! [X0] : le(X0,s(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',succ_le) ).
fof(f10,axiom,
! [X0,X1,X2,X3] :
( plus(X0,X1) = plus(X2,X3)
<=> minus(X0,X2) = minus(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus1) ).
fof(f11,axiom,
! [X0,X1,X2,X3] :
( minus(X0,X1) = minus(X2,X3)
<=> minus(X0,X2) = minus(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',minus1) ).
fof(f12,plain,
( ! [X0,X1] :
( ( p(X0) != p(X1)
& plus(p(X0),X0) != plus(p(X1),X1)
& minus(p(X0),X0) != minus(p(X1),X1) )
| ~ le(s(n0),X0)
| ~ le(X0,n)
| ~ le(s(X0),X1)
| ~ le(X1,n) )
| ~ queens_p ),
inference(ennf_transformation,[],[f1]) ).
fof(f13,plain,
( ! [X0,X1] :
( ( p(X0) != p(X1)
& plus(p(X0),X0) != plus(p(X1),X1)
& minus(p(X0),X0) != minus(p(X1),X1) )
| ~ le(s(n0),X0)
| ~ le(X0,n)
| ~ le(s(X0),X1)
| ~ le(X1,n) )
| ~ queens_p ),
inference(flattening,[],[f12]) ).
fof(f16,plain,
( queens_q
| ? [X0,X1] :
( ( q(X0) = q(X1)
| plus(q(X0),X0) = plus(q(X1),X1)
| minus(q(X0),X0) = minus(q(X1),X1) )
& le(s(n0),X0)
& le(X0,n)
& le(s(X0),X1)
& le(X1,n)
& ( le(s(X0),X1)
<=> le(s(perm(X1)),perm(X0)) ) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f17,plain,
( queens_q
| ? [X0,X1] :
( ( q(X0) = q(X1)
| plus(q(X0),X0) = plus(q(X1),X1)
| minus(q(X0),X0) = minus(q(X1),X1) )
& le(s(n0),X0)
& le(X0,n)
& le(s(X0),X1)
& le(X1,n)
& ( le(s(X0),X1)
<=> le(s(perm(X1)),perm(X0)) ) ) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
( ~ queens_q
& queens_p
& ! [X0] : q(X0) = p(perm(X0)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f19,plain,
( ~ queens_q
& queens_p
& ! [X0] : q(X0) = p(perm(X0)) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0] :
( ( le(s(n0),perm(X0))
& le(perm(X0),n) )
| ~ le(s(n0),X0)
| ~ le(X0,n) ),
inference(ennf_transformation,[],[f6]) ).
fof(f21,plain,
! [X0] :
( ( le(s(n0),perm(X0))
& le(perm(X0),n) )
| ~ le(s(n0),X0)
| ~ le(X0,n) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( le(X0,X2)
| ~ le(X0,X1)
| ~ le(X1,X2) ),
inference(ennf_transformation,[],[f8]) ).
fof(f23,plain,
! [X0,X1,X2] :
( le(X0,X2)
| ~ le(X0,X1)
| ~ le(X1,X2) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
( queens_q
| ? [X0,X1] :
( ( q(X0) = q(X1)
| plus(q(X0),X0) = plus(q(X1),X1)
| minus(q(X0),X0) = minus(q(X1),X1) )
& le(s(n0),X0)
& le(X0,n)
& le(s(X0),X1)
& le(X1,n)
& ( le(s(X0),X1)
| ~ le(s(perm(X1)),perm(X0)) )
& ( le(s(perm(X1)),perm(X0))
| ~ le(s(X0),X1) ) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f25,plain,
( queens_q
| ? [X0,X1] :
( ( q(X0) = q(X1)
| plus(q(X0),X0) = plus(q(X1),X1)
| minus(q(X0),X0) = minus(q(X1),X1) )
& le(s(n0),X0)
& le(X0,n)
& le(s(X0),X1)
& le(X1,n)
& ( le(s(X0),X1)
| ~ le(s(perm(X1)),perm(X0)) )
& ( le(s(perm(X1)),perm(X0))
| ~ le(s(X0),X1) ) ) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
( queens_q
| ( ( q(sK0) = q(sK1)
| plus(q(sK0),sK0) = plus(q(sK1),sK1)
| minus(q(sK0),sK0) = minus(q(sK1),sK1) )
& le(s(n0),sK0)
& le(sK0,n)
& le(s(sK0),sK1)
& le(sK1,n)
& ( le(s(sK0),sK1)
| ~ le(s(perm(sK1)),perm(sK0)) )
& ( le(s(perm(sK1)),perm(sK0))
| ~ le(s(sK0),sK1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( ( plus(X0,X1) = plus(X2,X3)
| minus(X0,X2) != minus(X3,X1) )
& ( minus(X0,X2) = minus(X3,X1)
| plus(X0,X1) != plus(X2,X3) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( ( minus(X0,X1) = minus(X2,X3)
| minus(X0,X2) != minus(X1,X3) )
& ( minus(X0,X2) = minus(X1,X3)
| minus(X0,X1) != minus(X2,X3) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f29,plain,
! [X0,X1] :
( minus(p(X0),X0) != minus(p(X1),X1)
| ~ le(s(n0),X0)
| ~ le(X0,n)
| ~ le(s(X0),X1)
| ~ le(X1,n)
| ~ queens_p ),
inference(cnf_transformation,[],[f13]) ).
fof(f30,plain,
! [X0,X1] :
( plus(p(X0),X0) != plus(p(X1),X1)
| ~ le(s(n0),X0)
| ~ le(X0,n)
| ~ le(s(X0),X1)
| ~ le(X1,n)
| ~ queens_p ),
inference(cnf_transformation,[],[f13]) ).
fof(f31,plain,
! [X0,X1] :
( p(X0) != p(X1)
| ~ le(s(n0),X0)
| ~ le(X0,n)
| ~ le(s(X0),X1)
| ~ le(X1,n)
| ~ queens_p ),
inference(cnf_transformation,[],[f13]) ).
fof(f33,plain,
( queens_q
| le(s(perm(sK1)),perm(sK0))
| ~ le(s(sK0),sK1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f35,plain,
( queens_q
| le(sK1,n) ),
inference(cnf_transformation,[],[f26]) ).
fof(f36,plain,
( queens_q
| le(s(sK0),sK1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f37,plain,
( queens_q
| le(sK0,n) ),
inference(cnf_transformation,[],[f26]) ).
fof(f38,plain,
( queens_q
| le(s(n0),sK0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f39,plain,
( queens_q
| q(sK0) = q(sK1)
| plus(q(sK0),sK0) = plus(q(sK1),sK1)
| minus(q(sK0),sK0) = minus(q(sK1),sK1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f40,plain,
! [X0] : q(X0) = p(perm(X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f41,plain,
queens_p,
inference(cnf_transformation,[],[f19]) ).
fof(f42,plain,
~ queens_q,
inference(cnf_transformation,[],[f19]) ).
fof(f43,plain,
! [X0] :
( ~ le(s(n0),X0)
| le(perm(X0),n)
| ~ le(X0,n) ),
inference(cnf_transformation,[],[f21]) ).
fof(f44,plain,
! [X0] :
( le(s(n0),perm(X0))
| ~ le(s(n0),X0)
| ~ le(X0,n) ),
inference(cnf_transformation,[],[f21]) ).
fof(f45,plain,
! [X0,X1] : minus(X1,X0) = minus(perm(X0),perm(X1)),
inference(cnf_transformation,[],[f7]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ le(X1,X2)
| ~ le(X0,X1)
| le(X0,X2) ),
inference(cnf_transformation,[],[f23]) ).
fof(f47,plain,
! [X0] : le(X0,s(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( plus(X0,X1) != plus(X2,X3)
| minus(X0,X2) = minus(X3,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f49,plain,
! [X2,X3,X0,X1] :
( minus(X0,X2) != minus(X3,X1)
| plus(X0,X1) = plus(X2,X3) ),
inference(cnf_transformation,[],[f27]) ).
fof(f50,plain,
! [X2,X3,X0,X1] :
( minus(X0,X1) != minus(X2,X3)
| minus(X0,X2) = minus(X1,X3) ),
inference(cnf_transformation,[],[f28]) ).
fof(f53,definition,
( spl2_1
<=> le(s(sK0),sK1) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f54,plain,
( le(s(sK0),sK1)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f57,definition,
( spl2_2
<=> le(s(perm(sK1)),perm(sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f59,plain,
( le(s(perm(sK1)),perm(sK0))
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f61,definition,
( spl2_3
<=> queens_q ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f64,plain,
( ~ spl2_1
| spl2_2
| spl2_3 ),
inference(avatar_split_clause,[],[f33,f61,f57,f53]) ).
fof(f67,definition,
( spl2_4
<=> le(sK1,n) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f69,plain,
( le(sK1,n)
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f70,plain,
( spl2_4
| spl2_3 ),
inference(avatar_split_clause,[],[f35,f61,f67]) ).
fof(f71,plain,
( spl2_1
| spl2_3 ),
inference(avatar_split_clause,[],[f36,f61,f53]) ).
fof(f73,definition,
( spl2_5
<=> le(sK0,n) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f75,plain,
( le(sK0,n)
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f73]) ).
fof(f76,plain,
( spl2_5
| spl2_3 ),
inference(avatar_split_clause,[],[f37,f61,f73]) ).
fof(f78,definition,
( spl2_6
<=> le(s(n0),sK0) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f80,plain,
( le(s(n0),sK0)
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f81,plain,
( spl2_6
| spl2_3 ),
inference(avatar_split_clause,[],[f38,f61,f78]) ).
fof(f83,definition,
( spl2_7
<=> minus(q(sK0),sK0) = minus(q(sK1),sK1) ),
introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition]) ).
fof(f85,plain,
( minus(q(sK0),sK0) = minus(q(sK1),sK1)
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f83]) ).
fof(f87,definition,
( spl2_8
<=> plus(q(sK0),sK0) = plus(q(sK1),sK1) ),
introduced(definition,[new_symbols(definition,[spl2_8])],[avatar_definition]) ).
fof(f89,plain,
( plus(q(sK0),sK0) = plus(q(sK1),sK1)
| ~ spl2_8 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f91,definition,
( spl2_9
<=> q(sK0) = q(sK1) ),
introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition]) ).
fof(f93,plain,
( q(sK0) = q(sK1)
| ~ spl2_9 ),
inference(avatar_component_clause,[],[f91]) ).
fof(f94,plain,
( spl2_7
| spl2_8
| spl2_9
| spl2_3 ),
inference(avatar_split_clause,[],[f39,f61,f91,f87,f83]) ).
fof(f96,definition,
( spl2_10
<=> queens_p ),
introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition]) ).
fof(f100,definition,
( spl2_11
<=> ! [X0,X1] :
( minus(p(X0),X0) != minus(p(X1),X1)
| ~ le(X1,n)
| ~ le(s(X0),X1)
| ~ le(X0,n)
| ~ le(s(n0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl2_11])],[avatar_definition]) ).
fof(f101,plain,
( ! [X0,X1] :
( minus(p(X0),X0) != minus(p(X1),X1)
| ~ le(X1,n)
| ~ le(s(X0),X1)
| ~ le(X0,n)
| ~ le(s(n0),X0) )
| ~ spl2_11 ),
inference(avatar_component_clause,[],[f100]) ).
fof(f102,plain,
( ~ spl2_10
| spl2_11 ),
inference(avatar_split_clause,[],[f29,f100,f96]) ).
fof(f104,definition,
( spl2_12
<=> ! [X0,X1] :
( plus(p(X0),X0) != plus(p(X1),X1)
| ~ le(X1,n)
| ~ le(s(X0),X1)
| ~ le(X0,n)
| ~ le(s(n0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl2_12])],[avatar_definition]) ).
fof(f105,plain,
( ! [X0,X1] :
( plus(p(X0),X0) != plus(p(X1),X1)
| ~ le(X1,n)
| ~ le(s(X0),X1)
| ~ le(X0,n)
| ~ le(s(n0),X0) )
| ~ spl2_12 ),
inference(avatar_component_clause,[],[f104]) ).
fof(f106,plain,
( ~ spl2_10
| spl2_12 ),
inference(avatar_split_clause,[],[f30,f104,f96]) ).
fof(f108,definition,
( spl2_13
<=> ! [X0,X1] :
( p(X0) != p(X1)
| ~ le(X1,n)
| ~ le(s(X0),X1)
| ~ le(X0,n)
| ~ le(s(n0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl2_13])],[avatar_definition]) ).
fof(f109,plain,
( ! [X0,X1] :
( p(X0) != p(X1)
| ~ le(X1,n)
| ~ le(s(X0),X1)
| ~ le(X0,n)
| ~ le(s(n0),X0) )
| ~ spl2_13 ),
inference(avatar_component_clause,[],[f108]) ).
fof(f110,plain,
( ~ spl2_10
| spl2_13 ),
inference(avatar_split_clause,[],[f31,f108,f96]) ).
fof(f111,plain,
spl2_10,
inference(avatar_split_clause,[],[f41,f96]) ).
fof(f112,plain,
~ spl2_3,
inference(avatar_split_clause,[],[f42,f61]) ).
fof(f113,plain,
( le(perm(sK0),n)
| ~ spl2_5
| ~ spl2_6 ),
inference(unit_resulting_resolution,[],[f43,f75,f80]) ).
fof(f116,plain,
( minus(q(sK0),q(sK1)) = minus(sK1,sK0)
| ~ spl2_8 ),
inference(unit_resulting_resolution,[],[f48,f89]) ).
fof(f124,plain,
! [X2,X3,X0,X1] :
( minus(X0,X1) != minus(X2,X3)
| plus(X2,perm(X0)) = plus(X3,perm(X1)) ),
inference(superposition,[],[f49,f45]) ).
fof(f129,plain,
! [X2,X3,X0,X1] :
( minus(X0,X1) != minus(X2,X3)
| minus(X2,perm(X1)) = minus(X3,perm(X0)) ),
inference(superposition,[],[f50,f45]) ).
fof(f133,plain,
( ! [X0,X1] :
( p(X1) != q(X0)
| ~ le(perm(X0),n)
| ~ le(s(X1),perm(X0))
| ~ le(X1,n)
| ~ le(s(n0),X1) )
| ~ spl2_13 ),
inference(superposition,[],[f109,f40]) ).
fof(f138,plain,
( ! [X0,X1] :
( minus(p(X1),X1) != minus(q(X0),perm(X0))
| ~ le(perm(X0),n)
| ~ le(s(X1),perm(X0))
| ~ le(X1,n)
| ~ le(s(n0),X1) )
| ~ spl2_11 ),
inference(superposition,[],[f101,f40]) ).
fof(f143,plain,
( ! [X0,X1] :
( plus(p(X1),X1) != plus(q(X0),perm(X0))
| ~ le(perm(X0),n)
| ~ le(s(X1),perm(X0))
| ~ le(X1,n)
| ~ le(s(n0),X1) )
| ~ spl2_12 ),
inference(superposition,[],[f105,f40]) ).
fof(f146,plain,
( ! [X0,X1] :
( q(X0) != q(X1)
| ~ le(perm(X1),n)
| ~ le(s(perm(X0)),perm(X1))
| ~ le(perm(X0),n)
| ~ le(s(n0),perm(X0)) )
| ~ spl2_13 ),
inference(superposition,[],[f133,f40]) ).
fof(f148,plain,
( ! [X0,X1] :
( minus(q(X0),perm(X0)) != minus(q(X1),perm(X1))
| ~ le(perm(X1),n)
| ~ le(s(perm(X0)),perm(X1))
| ~ le(perm(X0),n)
| ~ le(s(n0),perm(X0)) )
| ~ spl2_11 ),
inference(superposition,[],[f138,f40]) ).
fof(f151,plain,
( ! [X0,X1] :
( plus(q(X0),perm(X0)) != plus(q(X1),perm(X1))
| ~ le(perm(X1),n)
| ~ le(s(perm(X0)),perm(X1))
| ~ le(perm(X0),n)
| ~ le(s(n0),perm(X0)) )
| ~ spl2_12 ),
inference(superposition,[],[f143,f40]) ).
fof(f219,plain,
( le(perm(sK1),perm(sK0))
| ~ spl2_2 ),
inference(unit_resulting_resolution,[],[f46,f47,f59]) ).
fof(f223,plain,
( le(sK0,sK1)
| ~ spl2_1 ),
inference(unit_resulting_resolution,[],[f46,f47,f54]) ).
fof(f515,plain,
( minus(q(sK0),perm(sK0)) = minus(q(sK1),perm(sK1))
| ~ spl2_8 ),
inference(unit_resulting_resolution,[],[f129,f116]) ).
fof(f1099,definition,
( spl2_27
<=> le(s(n0),perm(sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_27])],[avatar_definition]) ).
fof(f1100,plain,
( le(s(n0),perm(sK1))
| ~ spl2_27 ),
inference(avatar_component_clause,[],[f1099]) ).
fof(f1101,plain,
( ~ le(s(n0),perm(sK1))
| spl2_27 ),
inference(avatar_component_clause,[],[f1099]) ).
fof(f1103,definition,
( spl2_28
<=> le(perm(sK1),n) ),
introduced(definition,[new_symbols(definition,[spl2_28])],[avatar_definition]) ).
fof(f1104,plain,
( le(perm(sK1),n)
| ~ spl2_28 ),
inference(avatar_component_clause,[],[f1103]) ).
fof(f1105,plain,
( ~ le(perm(sK1),n)
| spl2_28 ),
inference(avatar_component_clause,[],[f1103]) ).
fof(f1203,plain,
( ~ le(perm(sK0),n)
| ~ spl2_2
| spl2_28 ),
inference(unit_resulting_resolution,[],[f46,f219,f1105]) ).
fof(f1213,plain,
( $false
| ~ spl2_2
| ~ spl2_5
| ~ spl2_6
| spl2_28 ),
inference(forward_subsumption_resolution,[],[f1203,f113]) ).
fof(f1214,plain,
( ~ spl2_2
| ~ spl2_5
| ~ spl2_6
| spl2_28 ),
inference(avatar_contradiction_clause,[],[f1213]) ).
fof(f1989,plain,
( ~ le(s(n0),sK1)
| ~ spl2_4
| spl2_27 ),
inference(unit_resulting_resolution,[],[f44,f69,f1101]) ).
fof(f2005,plain,
( ~ le(s(n0),perm(sK1))
| ~ spl2_2
| ~ spl2_5
| ~ spl2_6
| ~ spl2_8
| ~ spl2_11
| ~ spl2_28 ),
inference(unit_resulting_resolution,[],[f148,f113,f1104,f59,f515]) ).
fof(f2192,plain,
( ~ le(sK0,sK1)
| ~ spl2_4
| ~ spl2_6
| spl2_27 ),
inference(unit_resulting_resolution,[],[f46,f80,f1989]) ).
fof(f2202,plain,
( $false
| ~ spl2_1
| ~ spl2_4
| ~ spl2_6
| spl2_27 ),
inference(forward_subsumption_resolution,[],[f2192,f223]) ).
fof(f2203,plain,
( ~ spl2_1
| ~ spl2_4
| ~ spl2_6
| spl2_27 ),
inference(avatar_contradiction_clause,[],[f2202]) ).
fof(f2205,plain,
( ~ le(s(n0),perm(sK1))
| ~ spl2_2
| ~ spl2_5
| ~ spl2_6
| ~ spl2_9
| ~ spl2_13
| ~ spl2_28 ),
inference(unit_resulting_resolution,[],[f146,f113,f1104,f59,f93]) ).
fof(f2262,plain,
( ~ spl2_27
| ~ spl2_2
| ~ spl2_5
| ~ spl2_6
| ~ spl2_9
| ~ spl2_13
| ~ spl2_28 ),
inference(avatar_split_clause,[],[f2205,f1103,f108,f91,f78,f73,f57,f1099]) ).
fof(f2311,plain,
( ~ spl2_27
| ~ spl2_2
| ~ spl2_5
| ~ spl2_6
| ~ spl2_8
| ~ spl2_11
| ~ spl2_28 ),
inference(avatar_split_clause,[],[f2005,f1103,f100,f87,f78,f73,f57,f1099]) ).
fof(f2367,plain,
( minus(q(sK0),q(sK1)) = minus(sK0,sK1)
| ~ spl2_7 ),
inference(unit_resulting_resolution,[],[f50,f85]) ).
fof(f2414,plain,
( plus(q(sK0),perm(sK0)) = plus(q(sK1),perm(sK1))
| ~ spl2_7 ),
inference(unit_resulting_resolution,[],[f124,f2367]) ).
fof(f3406,plain,
( ~ le(perm(sK0),n)
| ~ spl2_2
| ~ spl2_7
| ~ spl2_12
| ~ spl2_27
| ~ spl2_28 ),
inference(unit_resulting_resolution,[],[f151,f1104,f1100,f59,f2414]) ).
fof(f3438,plain,
( $false
| ~ spl2_2
| ~ spl2_5
| ~ spl2_6
| ~ spl2_7
| ~ spl2_12
| ~ spl2_27
| ~ spl2_28 ),
inference(forward_subsumption_resolution,[],[f3406,f113]) ).
fof(f3439,plain,
( ~ spl2_2
| ~ spl2_5
| ~ spl2_6
| ~ spl2_7
| ~ spl2_12
| ~ spl2_27
| ~ spl2_28 ),
inference(avatar_contradiction_clause,[],[f3438]) ).
cnf(s1,plain,
( ~ spl2_1
| spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f64]) ).
cnf(s3,plain,
( spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f70]) ).
cnf(s4,plain,
( spl2_1
| spl2_3 ),
inference(sat_conversion,[],[f71]) ).
cnf(s5,plain,
( spl2_3
| spl2_5 ),
inference(sat_conversion,[],[f76]) ).
cnf(s6,plain,
( spl2_3
| spl2_6 ),
inference(sat_conversion,[],[f81]) ).
cnf(s7,plain,
( spl2_3
| spl2_7
| spl2_8
| spl2_9 ),
inference(sat_conversion,[],[f94]) ).
cnf(s8,plain,
( ~ spl2_10
| spl2_11 ),
inference(sat_conversion,[],[f102]) ).
cnf(s9,plain,
( ~ spl2_10
| spl2_12 ),
inference(sat_conversion,[],[f106]) ).
cnf(s10,plain,
( ~ spl2_10
| spl2_13 ),
inference(sat_conversion,[],[f110]) ).
cnf(s11,plain,
spl2_10,
inference(sat_conversion,[],[f111]) ).
cnf(s12,plain,
~ spl2_3,
inference(sat_conversion,[],[f112]) ).
cnf(s48,plain,
( ~ spl2_2
| ~ spl2_5
| ~ spl2_6
| spl2_28 ),
inference(sat_conversion,[],[f1214]) ).
cnf(s92,plain,
( ~ spl2_1
| ~ spl2_4
| ~ spl2_6
| spl2_27 ),
inference(sat_conversion,[],[f2203]) ).
cnf(s93,plain,
( ~ spl2_2
| ~ spl2_5
| ~ spl2_6
| ~ spl2_9
| ~ spl2_13
| ~ spl2_27
| ~ spl2_28 ),
inference(sat_conversion,[],[f2262]) ).
cnf(s106,plain,
( ~ spl2_2
| ~ spl2_5
| ~ spl2_6
| ~ spl2_8
| ~ spl2_11
| ~ spl2_27
| ~ spl2_28 ),
inference(sat_conversion,[],[f2311]) ).
cnf(s209,plain,
( ~ spl2_2
| ~ spl2_5
| ~ spl2_6
| ~ spl2_7
| ~ spl2_12
| ~ spl2_27
| ~ spl2_28 ),
inference(sat_conversion,[],[f3439]) ).
cnf(s210,plain,
spl2_13,
inference(rat,[],[s10,s11]) ).
cnf(s211,plain,
spl2_12,
inference(rat,[],[s9,s11]) ).
cnf(s212,plain,
spl2_11,
inference(rat,[],[s8,s11]) ).
cnf(s213,plain,
( spl2_7
| spl2_8
| spl2_9 ),
inference(rat,[],[s7,s12]) ).
cnf(s214,plain,
spl2_6,
inference(rat,[],[s6,s12]) ).
cnf(s215,plain,
spl2_5,
inference(rat,[],[s5,s12]) ).
cnf(s216,plain,
spl2_1,
inference(rat,[],[s4,s12]) ).
cnf(s217,plain,
spl2_4,
inference(rat,[],[s3,s12]) ).
cnf(s218,plain,
spl2_27,
inference(rat,[],[s92,s216,s214,s217]) ).
cnf(s219,plain,
spl2_2,
inference(rat,[],[s1,s12,s216]) ).
cnf(s220,plain,
spl2_28,
inference(rat,[],[s48,s215,s214,s219]) ).
cnf(s221,plain,
~ spl2_7,
inference(rat,[],[s209,s219,s218,s211,s215,s214,s220]) ).
cnf(s222,plain,
~ spl2_8,
inference(rat,[],[s106,s219,s218,s212,s215,s214,s220]) ).
cnf(s223,plain,
~ spl2_9,
inference(rat,[],[s93,s219,s218,s210,s215,s214,s220]) ).
cnf(s224,plain,
$false,
inference(rat,[],[s213,s223,s222,s221]) ).
fof(f3444,plain,
$false,
inference(avatar_sat_refutation,[],[s224]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ133+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sun Sep 27 22:47:42 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.99/1.39 % (3285237)Detected formulas, will run a generic FOF schedule.
% 2.99/1.39 % (3285245)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2519137072:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.99/1.39 % (3285245)Refutation not found, incomplete strategy
% 2.99/1.39 % (3285245)------------------------------
% 2.99/1.39 % (3285245)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.39 % (3285245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.39 % (3285245)CaDiCaL version: 2.1.3
% 2.99/1.39 % (3285245)Termination reason: Refutation not found, incomplete strategy
% 2.99/1.39 % (3285245)Time elapsed: 0.001 s
% 2.99/1.39 % (3285245)Peak memory usage: 89 MB
% 2.99/1.39 % (3285245)Instructions burned: 2 (million)
% 2.99/1.39 % (3285247)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1454433925:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.99/1.39 % (3285243)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=3291549534:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.99/1.39 % (3285244)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=1788221667:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.99/1.39 % (3285242)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=1349732054:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.99/1.39 % (3285246)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1686391574:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.99/1.39 % (3285248)dis-21_1_sil=8000:lcm=predicate:random_seed=460105232: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)
% 2.99/1.39 % (3285246)Instruction limit reached!
% 2.99/1.39 % (3285246)------------------------------
% 2.99/1.39 % (3285246)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.39 % (3285246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.39 % (3285246)CaDiCaL version: 2.1.3
% 2.99/1.39 % (3285246)Termination reason: Instruction limit
% 2.99/1.39 % (3285246)Termination phase: Saturation
% 2.99/1.39 % (3285246)Time elapsed: 0.067 s
% 2.99/1.39 % (3285246)Peak memory usage: 88 MB
% 2.99/1.39 % (3285246)Instructions burned: 120 (million)
% 2.99/1.39 % (3285247)Instruction limit reached!
% 2.99/1.39 % (3285247)------------------------------
% 2.99/1.39 % (3285247)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.39 % (3285247)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.39 % (3285247)CaDiCaL version: 2.1.3
% 2.99/1.39 % (3285247)Termination reason: Instruction limit
% 2.99/1.39 % (3285247)Termination phase: Saturation
% 2.99/1.39 % (3285247)Time elapsed: 0.083 s
% 2.99/1.39 % (3285247)Peak memory usage: 89 MB
% 2.99/1.39 % (3285247)Instructions burned: 139 (million)
% 2.99/1.39 % (3285248)Instruction limit reached!
% 2.99/1.39 % (3285248)------------------------------
% 2.99/1.39 % (3285248)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.39 % (3285248)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.39 % (3285248)CaDiCaL version: 2.1.3
% 2.99/1.39 % (3285248)Termination reason: Instruction limit
% 2.99/1.39 % (3285248)Termination phase: Saturation
% 2.99/1.39 % (3285248)Time elapsed: 0.084 s
% 2.99/1.39 % (3285248)Peak memory usage: 89 MB
% 2.99/1.39 % (3285248)Instructions burned: 129 (million)
% 2.99/1.39 % (3285245)------------------------------
% 2.99/1.39 % (3285245)------------------------------
% 2.99/1.39 % (3285256)lrs+10_1_sil=8000:sp=occurrence:random_seed=1297137339:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.99/1.39 % (3285259)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=732877701:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 2.99/1.39 % (3285257)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3268822339:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.99/1.39 % (3285258)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2116373848:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.99/1.39 % (3285259)First to succeed.
% 2.99/1.39 % (3285259)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3285237"
% 2.99/1.39 % (3285257)Instruction limit reached!
% 2.99/1.39 % (3285257)------------------------------
% 2.99/1.39 % (3285257)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.39 % (3285257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.39 % (3285257)CaDiCaL version: 2.1.3
% 2.99/1.39 % (3285257)Termination reason: Instruction limit
% 2.99/1.39 % (3285257)Termination phase: Saturation
% 2.99/1.39 % (3285257)Time elapsed: 0.090 s
% 2.99/1.39 % (3285257)Peak memory usage: 89 MB
% 2.99/1.39 % (3285257)Instructions burned: 158 (million)
% 2.99/1.39 % (3285256)Instruction limit reached!
% 2.99/1.39 % (3285256)------------------------------
% 2.99/1.39 % (3285256)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.99/1.39 % (3285256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.99/1.39 % (3285256)CaDiCaL version: 2.1.3
% 2.99/1.39 % (3285256)Termination reason: Instruction limit
% 2.99/1.39 % (3285256)Termination phase: Saturation
% 2.99/1.39 % (3285256)Time elapsed: 0.171 s
% 2.99/1.39 % (3285256)Peak memory usage: 91 MB
% 2.99/1.39 % (3285256)Instructions burned: 285 (million)
% 2.99/1.39 % (3285259)Refutation found. Thanks to Tanya!
% 2.99/1.39 % SZS status Theorem for theBenchmark
% 2.99/1.39 % SZS output start Proof for theBenchmark
% See solution above
% 4.41/1.58 % (3285259)------------------------------
% 4.41/1.58 % (3285259)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.41/1.58 % (3285259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.41/1.58 % (3285259)CaDiCaL version: 2.1.3
% 4.41/1.58 % (3285259)Termination reason: Refutation
% 4.41/1.58 % (3285259)Time elapsed: 0.052 s
% 4.41/1.58 % (3285259)Peak memory usage: 91 MB
% 4.41/1.58 % (3285259)Instructions burned: 161 (million)
% 4.41/1.58 % (3285259)------------------------------
% 4.41/1.58 % (3285259)------------------------------
% 4.41/1.58 % (3285237)Success in time 0.545 s
% 4.41/1.58 % Vampire exiting
%------------------------------------------------------------------------------