%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ133+1 : 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 : 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 : Tue Sep 29 12:31:40 PM UTC 2026
% Result : Theorem 10.54s 2.47s
% Output : Refutation 11.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 25
% Syntax : Number of formulae : 154 ( 27 unt; 16 def)
% Number of atoms : 521 ( 86 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 654 ( 287 ~; 282 |; 56 &)
% ( 21 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 19 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 111 ( 0 sgn 103 !; 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(f14,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(f15,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,[],[f14]) ).
fof(f16,plain,
( ~ queens_q
& queens_p
& ! [X0] : q(X0) = p(perm(X0)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f17,plain,
( ~ queens_q
& queens_p
& ! [X0] : q(X0) = p(perm(X0)) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0] :
( ( le(s(n0),perm(X0))
& le(perm(X0),n) )
| ~ le(s(n0),X0)
| ~ le(X0,n) ),
inference(ennf_transformation,[],[f6]) ).
fof(f19,plain,
! [X0] :
( ( le(s(n0),perm(X0))
& le(perm(X0),n) )
| ~ le(s(n0),X0)
| ~ le(X0,n) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( le(X0,X2)
| ~ le(X0,X1)
| ~ le(X1,X2) ),
inference(ennf_transformation,[],[f8]) ).
fof(f21,plain,
! [X0,X1,X2] :
( le(X0,X2)
| ~ le(X0,X1)
| ~ le(X1,X2) ),
inference(flattening,[],[f20]) ).
fof(f22,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,[],[f15]) ).
fof(f23,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,[],[f22]) ).
fof(f24,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)],[f23]) ).
fof(f25,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(f26,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(f27,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(f28,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(f29,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(f31,plain,
( queens_q
| le(s(perm(sK1)),perm(sK0))
| ~ le(s(sK0),sK1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f33,plain,
( queens_q
| le(sK1,n) ),
inference(cnf_transformation,[],[f24]) ).
fof(f34,plain,
( queens_q
| le(s(sK0),sK1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f35,plain,
( queens_q
| le(sK0,n) ),
inference(cnf_transformation,[],[f24]) ).
fof(f36,plain,
( queens_q
| le(s(n0),sK0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f37,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,[],[f24]) ).
fof(f38,plain,
! [X0] : q(X0) = p(perm(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f39,plain,
queens_p,
inference(cnf_transformation,[],[f17]) ).
fof(f40,plain,
~ queens_q,
inference(cnf_transformation,[],[f17]) ).
fof(f41,plain,
! [X0] :
( ~ le(s(n0),X0)
| le(perm(X0),n)
| ~ le(X0,n) ),
inference(cnf_transformation,[],[f19]) ).
fof(f42,plain,
! [X0] :
( le(s(n0),perm(X0))
| ~ le(s(n0),X0)
| ~ le(X0,n) ),
inference(cnf_transformation,[],[f19]) ).
fof(f43,plain,
! [X0,X1] : minus(X1,X0) = minus(perm(X0),perm(X1)),
inference(cnf_transformation,[],[f7]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ~ le(X1,X2)
| ~ le(X0,X1)
| le(X0,X2) ),
inference(cnf_transformation,[],[f21]) ).
fof(f45,plain,
! [X0] : le(X0,s(X0)),
inference(cnf_transformation,[],[f9]) ).
fof(f46,plain,
! [X2,X3,X0,X1] :
( plus(X0,X1) != plus(X2,X3)
| minus(X0,X2) = minus(X3,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( minus(X0,X2) != minus(X3,X1)
| plus(X0,X1) = plus(X2,X3) ),
inference(cnf_transformation,[],[f25]) ).
fof(f48,plain,
! [X2,X3,X0,X1] :
( minus(X0,X1) != minus(X2,X3)
| minus(X0,X2) = minus(X1,X3) ),
inference(cnf_transformation,[],[f26]) ).
fof(f51,definition,
( spl2_1
<=> le(s(sK0),sK1) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f52,plain,
( le(s(sK0),sK1)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f55,definition,
( spl2_2
<=> le(s(perm(sK1)),perm(sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f57,plain,
( le(s(perm(sK1)),perm(sK0))
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f59,definition,
( spl2_3
<=> queens_q ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f62,plain,
( ~ spl2_1
| spl2_2
| spl2_3 ),
inference(avatar_split_clause,[],[f31,f59,f55,f51]) ).
fof(f65,definition,
( spl2_4
<=> le(sK1,n) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f67,plain,
( le(sK1,n)
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f65]) ).
fof(f68,plain,
( spl2_4
| spl2_3 ),
inference(avatar_split_clause,[],[f33,f59,f65]) ).
fof(f69,plain,
( spl2_1
| spl2_3 ),
inference(avatar_split_clause,[],[f34,f59,f51]) ).
fof(f71,definition,
( spl2_5
<=> le(sK0,n) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f73,plain,
( le(sK0,n)
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f71]) ).
fof(f74,plain,
( spl2_5
| spl2_3 ),
inference(avatar_split_clause,[],[f35,f59,f71]) ).
fof(f76,definition,
( spl2_6
<=> le(s(n0),sK0) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f78,plain,
( le(s(n0),sK0)
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f76]) ).
fof(f79,plain,
( spl2_6
| spl2_3 ),
inference(avatar_split_clause,[],[f36,f59,f76]) ).
fof(f81,definition,
( spl2_7
<=> minus(q(sK0),sK0) = minus(q(sK1),sK1) ),
introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition]) ).
fof(f83,plain,
( minus(q(sK0),sK0) = minus(q(sK1),sK1)
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f85,definition,
( spl2_8
<=> plus(q(sK0),sK0) = plus(q(sK1),sK1) ),
introduced(definition,[new_symbols(definition,[spl2_8])],[avatar_definition]) ).
fof(f87,plain,
( plus(q(sK0),sK0) = plus(q(sK1),sK1)
| ~ spl2_8 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f89,definition,
( spl2_9
<=> q(sK0) = q(sK1) ),
introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition]) ).
fof(f91,plain,
( q(sK0) = q(sK1)
| ~ spl2_9 ),
inference(avatar_component_clause,[],[f89]) ).
fof(f92,plain,
( spl2_7
| spl2_8
| spl2_9
| spl2_3 ),
inference(avatar_split_clause,[],[f37,f59,f89,f85,f81]) ).
fof(f94,definition,
( spl2_10
<=> queens_p ),
introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition]) ).
fof(f98,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(f99,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,[],[f98]) ).
fof(f100,plain,
( ~ spl2_10
| spl2_11 ),
inference(avatar_split_clause,[],[f27,f98,f94]) ).
fof(f102,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(f103,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,[],[f102]) ).
fof(f104,plain,
( ~ spl2_10
| spl2_12 ),
inference(avatar_split_clause,[],[f28,f102,f94]) ).
fof(f106,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(f107,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,[],[f106]) ).
fof(f108,plain,
( ~ spl2_10
| spl2_13 ),
inference(avatar_split_clause,[],[f29,f106,f94]) ).
fof(f109,plain,
spl2_10,
inference(avatar_split_clause,[],[f39,f94]) ).
fof(f110,plain,
~ spl2_3,
inference(avatar_split_clause,[],[f40,f59]) ).
fof(f111,plain,
( le(perm(sK0),n)
| ~ spl2_5
| ~ spl2_6 ),
inference(unit_resulting_resolution,[],[f41,f73,f78]) ).
fof(f113,plain,
( minus(q(sK0),q(sK1)) = minus(sK1,sK0)
| ~ spl2_8 ),
inference(unit_resulting_resolution,[],[f46,f87]) ).
fof(f123,plain,
! [X2,X3,X0,X1] :
( minus(X0,X1) != minus(X2,X3)
| plus(X2,perm(X0)) = plus(X3,perm(X1)) ),
inference(superposition,[],[f47,f43]) ).
fof(f130,plain,
! [X2,X3,X0,X1] :
( minus(X0,X1) != minus(X2,X3)
| minus(X2,perm(X1)) = minus(X3,perm(X0)) ),
inference(superposition,[],[f48,f43]) ).
fof(f133,plain,
( ! [X0,X1] :
( p(X1) != q(X0)
| ~ le(X1,n)
| ~ le(s(perm(X0)),X1)
| ~ le(perm(X0),n)
| ~ le(s(n0),perm(X0)) )
| ~ spl2_13 ),
inference(superposition,[],[f107,f38]) ).
fof(f139,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,[],[f99,f38]) ).
fof(f144,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,[],[f103,f38]) ).
fof(f149,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,[],[f139,f38]) ).
fof(f152,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,[],[f144,f38]) ).
fof(f219,plain,
( le(perm(sK1),perm(sK0))
| ~ spl2_2 ),
inference(unit_resulting_resolution,[],[f44,f45,f57]) ).
fof(f223,plain,
( le(sK0,sK1)
| ~ spl2_1 ),
inference(unit_resulting_resolution,[],[f44,f45,f52]) ).
fof(f1466,definition,
( spl2_34
<=> le(s(n0),perm(sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_34])],[avatar_definition]) ).
fof(f1467,plain,
( le(s(n0),perm(sK1))
| ~ spl2_34 ),
inference(avatar_component_clause,[],[f1466]) ).
fof(f1468,plain,
( ~ le(s(n0),perm(sK1))
| spl2_34 ),
inference(avatar_component_clause,[],[f1466]) ).
fof(f1470,definition,
( spl2_35
<=> le(perm(sK1),n) ),
introduced(definition,[new_symbols(definition,[spl2_35])],[avatar_definition]) ).
fof(f1471,plain,
( le(perm(sK1),n)
| ~ spl2_35 ),
inference(avatar_component_clause,[],[f1470]) ).
fof(f1472,plain,
( ~ le(perm(sK1),n)
| spl2_35 ),
inference(avatar_component_clause,[],[f1470]) ).
fof(f2300,plain,
( ~ le(perm(sK0),n)
| ~ spl2_2
| spl2_35 ),
inference(unit_resulting_resolution,[],[f44,f219,f1472]) ).
fof(f2310,plain,
( $false
| ~ spl2_2
| ~ spl2_5
| ~ spl2_6
| spl2_35 ),
inference(forward_subsumption_resolution,[],[f2300,f111]) ).
fof(f2311,plain,
( ~ spl2_2
| ~ spl2_5
| ~ spl2_6
| spl2_35 ),
inference(avatar_contradiction_clause,[],[f2310]) ).
fof(f2312,plain,
( ! [X0] :
( p(X0) != q(sK0)
| ~ le(X0,n)
| ~ le(s(perm(sK1)),X0)
| ~ le(perm(sK1),n)
| ~ le(s(n0),perm(sK1)) )
| ~ spl2_9
| ~ spl2_13 ),
inference(superposition,[],[f133,f91]) ).
fof(f2429,definition,
( spl2_80
<=> ! [X0] :
( p(X0) != q(sK0)
| ~ le(s(perm(sK1)),X0)
| ~ le(X0,n) ) ),
introduced(definition,[new_symbols(definition,[spl2_80])],[avatar_definition]) ).
fof(f2430,plain,
( ! [X0] :
( p(X0) != q(sK0)
| ~ le(s(perm(sK1)),X0)
| ~ le(X0,n) )
| ~ spl2_80 ),
inference(avatar_component_clause,[],[f2429]) ).
fof(f2431,plain,
( ~ spl2_34
| ~ spl2_35
| spl2_80
| ~ spl2_9
| ~ spl2_13 ),
inference(avatar_split_clause,[],[f2312,f106,f89,f2429,f1470,f1466]) ).
fof(f2458,plain,
( minus(q(sK0),perm(sK0)) = minus(q(sK1),perm(sK1))
| ~ spl2_8 ),
inference(unit_resulting_resolution,[],[f130,f113]) ).
fof(f2508,plain,
( ~ le(s(n0),sK1)
| ~ spl2_4
| spl2_34 ),
inference(unit_resulting_resolution,[],[f42,f67,f1468]) ).
fof(f2617,plain,
( ~ le(sK0,sK1)
| ~ spl2_4
| ~ spl2_6
| spl2_34 ),
inference(unit_resulting_resolution,[],[f44,f78,f2508]) ).
fof(f2627,plain,
( $false
| ~ spl2_1
| ~ spl2_4
| ~ spl2_6
| spl2_34 ),
inference(forward_subsumption_resolution,[],[f2617,f223]) ).
fof(f2628,plain,
( ~ spl2_1
| ~ spl2_4
| ~ spl2_6
| spl2_34 ),
inference(avatar_contradiction_clause,[],[f2627]) ).
fof(f2899,plain,
( ~ le(perm(sK0),n)
| ~ spl2_2
| ~ spl2_8
| ~ spl2_11
| ~ spl2_34
| ~ spl2_35 ),
inference(unit_resulting_resolution,[],[f149,f1471,f1467,f57,f2458]) ).
fof(f2946,plain,
( $false
| ~ spl2_2
| ~ spl2_5
| ~ spl2_6
| ~ spl2_8
| ~ spl2_11
| ~ spl2_34
| ~ spl2_35 ),
inference(forward_subsumption_resolution,[],[f2899,f111]) ).
fof(f2947,plain,
( ~ spl2_2
| ~ spl2_5
| ~ spl2_6
| ~ spl2_8
| ~ spl2_11
| ~ spl2_34
| ~ spl2_35 ),
inference(avatar_contradiction_clause,[],[f2946]) ).
fof(f2960,plain,
( ~ le(perm(sK0),n)
| ~ spl2_2
| ~ spl2_80 ),
inference(unit_resulting_resolution,[],[f2430,f57,f38]) ).
fof(f2970,plain,
( $false
| ~ spl2_2
| ~ spl2_5
| ~ spl2_6
| ~ spl2_80 ),
inference(forward_subsumption_resolution,[],[f2960,f111]) ).
fof(f2971,plain,
( ~ spl2_2
| ~ spl2_5
| ~ spl2_6
| ~ spl2_80 ),
inference(avatar_contradiction_clause,[],[f2970]) ).
fof(f2976,plain,
( minus(q(sK0),q(sK1)) = minus(sK0,sK1)
| ~ spl2_7 ),
inference(unit_resulting_resolution,[],[f48,f83]) ).
fof(f3012,plain,
( plus(q(sK0),perm(sK0)) = plus(q(sK1),perm(sK1))
| ~ spl2_7 ),
inference(unit_resulting_resolution,[],[f123,f2976]) ).
fof(f4083,plain,
( ~ le(perm(sK0),n)
| ~ spl2_2
| ~ spl2_7
| ~ spl2_12
| ~ spl2_34
| ~ spl2_35 ),
inference(unit_resulting_resolution,[],[f152,f1471,f1467,f57,f3012]) ).
fof(f4116,plain,
( $false
| ~ spl2_2
| ~ spl2_5
| ~ spl2_6
| ~ spl2_7
| ~ spl2_12
| ~ spl2_34
| ~ spl2_35 ),
inference(forward_subsumption_resolution,[],[f4083,f111]) ).
fof(f4117,plain,
( ~ spl2_2
| ~ spl2_5
| ~ spl2_6
| ~ spl2_7
| ~ spl2_12
| ~ spl2_34
| ~ spl2_35 ),
inference(avatar_contradiction_clause,[],[f4116]) ).
cnf(s1,plain,
( ~ spl2_1
| spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f62]) ).
cnf(s3,plain,
( spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f68]) ).
cnf(s4,plain,
( spl2_1
| spl2_3 ),
inference(sat_conversion,[],[f69]) ).
cnf(s5,plain,
( spl2_3
| spl2_5 ),
inference(sat_conversion,[],[f74]) ).
cnf(s6,plain,
( spl2_3
| spl2_6 ),
inference(sat_conversion,[],[f79]) ).
cnf(s7,plain,
( spl2_3
| spl2_7
| spl2_8
| spl2_9 ),
inference(sat_conversion,[],[f92]) ).
cnf(s8,plain,
( ~ spl2_10
| spl2_11 ),
inference(sat_conversion,[],[f100]) ).
cnf(s9,plain,
( ~ spl2_10
| spl2_12 ),
inference(sat_conversion,[],[f104]) ).
cnf(s10,plain,
( ~ spl2_10
| spl2_13 ),
inference(sat_conversion,[],[f108]) ).
cnf(s11,plain,
spl2_10,
inference(sat_conversion,[],[f109]) ).
cnf(s12,plain,
~ spl2_3,
inference(sat_conversion,[],[f110]) ).
cnf(s65,plain,
( ~ spl2_2
| ~ spl2_5
| ~ spl2_6
| spl2_35 ),
inference(sat_conversion,[],[f2311]) ).
cnf(s89,plain,
( ~ spl2_9
| ~ spl2_13
| ~ spl2_34
| ~ spl2_35
| spl2_80 ),
inference(sat_conversion,[],[f2431]) ).
cnf(s95,plain,
( ~ spl2_1
| ~ spl2_4
| ~ spl2_6
| spl2_34 ),
inference(sat_conversion,[],[f2628]) ).
cnf(s105,plain,
( ~ spl2_2
| ~ spl2_5
| ~ spl2_6
| ~ spl2_8
| ~ spl2_11
| ~ spl2_34
| ~ spl2_35 ),
inference(sat_conversion,[],[f2947]) ).
cnf(s111,plain,
( ~ spl2_2
| ~ spl2_5
| ~ spl2_6
| ~ spl2_80 ),
inference(sat_conversion,[],[f2971]) ).
cnf(s228,plain,
( ~ spl2_2
| ~ spl2_5
| ~ spl2_6
| ~ spl2_7
| ~ spl2_12
| ~ spl2_34
| ~ spl2_35 ),
inference(sat_conversion,[],[f4117]) ).
cnf(s229,plain,
spl2_13,
inference(rat,[],[s10,s11]) ).
cnf(s230,plain,
spl2_12,
inference(rat,[],[s9,s11]) ).
cnf(s231,plain,
spl2_11,
inference(rat,[],[s8,s11]) ).
cnf(s232,plain,
( spl2_7
| spl2_8
| spl2_9 ),
inference(rat,[],[s7,s12]) ).
cnf(s233,plain,
spl2_6,
inference(rat,[],[s6,s12]) ).
cnf(s234,plain,
spl2_5,
inference(rat,[],[s5,s12]) ).
cnf(s235,plain,
spl2_1,
inference(rat,[],[s4,s12]) ).
cnf(s236,plain,
spl2_4,
inference(rat,[],[s3,s12]) ).
cnf(s237,plain,
spl2_34,
inference(rat,[],[s95,s235,s233,s236]) ).
cnf(s238,plain,
spl2_2,
inference(rat,[],[s1,s12,s235]) ).
cnf(s240,plain,
~ spl2_80,
inference(rat,[],[s111,s234,s233,s238]) ).
cnf(s241,plain,
spl2_35,
inference(rat,[],[s65,s234,s233,s238]) ).
cnf(s243,plain,
~ spl2_9,
inference(rat,[],[s89,s240,s237,s229,s241]) ).
cnf(s244,plain,
~ spl2_7,
inference(rat,[],[s228,s238,s237,s230,s234,s233,s241]) ).
cnf(s245,plain,
~ spl2_8,
inference(rat,[],[s105,s238,s237,s231,s234,s233,s241]) ).
cnf(s246,plain,
$false,
inference(rat,[],[s232,s243,s245,s244]) ).
fof(f4122,plain,
$false,
inference(avatar_sat_refutation,[],[s246]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ133+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n006.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 22:44:40 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 10.54/2.47 % (3401541)Detected formulas, will run a generic FOF schedule.
% 10.54/2.47 % (3401589)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=2860233389:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 10.54/2.47 % (3401594)dis-21_1_sil=8000:lcm=predicate:random_seed=4077633079: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)
% 10.54/2.47 % (3401592)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2489467033:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 10.54/2.47 % (3401587)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=361793675:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 10.54/2.47 % (3401590)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3099057125:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 10.54/2.47 % (3401590)Refutation not found, incomplete strategy
% 10.54/2.47 % (3401590)------------------------------
% 10.54/2.47 % (3401590)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.54/2.47 % (3401590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.54/2.47 % (3401590)CaDiCaL version: 2.1.3
% 10.54/2.47 % (3401590)Termination reason: Refutation not found, incomplete strategy
% 10.54/2.47 % (3401590)Time elapsed: 0.004 s
% 10.54/2.47 % (3401590)Peak memory usage: 89 MB
% 10.54/2.47 % (3401590)Instructions burned: 2 (million)
% 10.54/2.47 % (3401593)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4126728208:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 10.54/2.47 % (3401588)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=2330305726:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 10.54/2.47 % (3401594)Instruction limit reached!
% 10.54/2.47 % (3401594)------------------------------
% 10.54/2.47 % (3401594)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.54/2.47 % (3401594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.54/2.47 % (3401594)CaDiCaL version: 2.1.3
% 10.54/2.47 % (3401594)Termination reason: Instruction limit
% 10.54/2.47 % (3401594)Termination phase: Saturation
% 10.54/2.47 % (3401594)Time elapsed: 0.141 s
% 10.54/2.47 % (3401594)Peak memory usage: 89 MB
% 10.54/2.47 % (3401594)Instructions burned: 129 (million)
% 10.54/2.47 % (3401592)Instruction limit reached!
% 10.54/2.47 % (3401592)------------------------------
% 10.54/2.47 % (3401592)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.54/2.47 % (3401592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.54/2.47 % (3401592)CaDiCaL version: 2.1.3
% 10.54/2.47 % (3401592)Termination reason: Instruction limit
% 10.54/2.47 % (3401592)Termination phase: Saturation
% 10.54/2.47 % (3401592)Time elapsed: 0.106 s
% 10.54/2.47 % (3401592)Peak memory usage: 88 MB
% 10.54/2.47 % (3401592)Instructions burned: 119 (million)
% 10.54/2.47 % (3401593)Instruction limit reached!
% 10.54/2.47 % (3401593)------------------------------
% 10.54/2.47 % (3401593)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.54/2.47 % (3401593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.54/2.47 % (3401593)CaDiCaL version: 2.1.3
% 10.54/2.47 % (3401593)Termination reason: Instruction limit
% 10.54/2.47 % (3401593)Termination phase: Saturation
% 10.54/2.47 % (3401593)Time elapsed: 0.141 s
% 10.54/2.47 % (3401593)Peak memory usage: 89 MB
% 10.54/2.47 % (3401593)Instructions burned: 139 (million)
% 10.54/2.47 % (3401607)lrs+10_1_sil=8000:sp=occurrence:random_seed=529931082:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 10.54/2.47 % (3401608)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3300336676:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 10.54/2.47 % (3401590)------------------------------
% 10.54/2.47 % (3401590)------------------------------
% 10.54/2.47 % (3401609)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3861270148:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 10.54/2.47 % (3401608)Instruction limit reached!
% 10.54/2.47 % (3401608)------------------------------
% 10.54/2.47 % (3401608)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.54/2.47 % (3401608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.54/2.47 % (3401608)CaDiCaL version: 2.1.3
% 10.54/2.47 % (3401608)Termination reason: Instruction limit
% 10.54/2.47 % (3401608)Termination phase: Saturation
% 10.54/2.47 % (3401608)Time elapsed: 0.157 s
% 10.54/2.47 % (3401608)Peak memory usage: 90 MB
% 10.54/2.47 % (3401608)Instructions burned: 158 (million)
% 10.54/2.47 % (3401607)Instruction limit reached!
% 10.54/2.47 % (3401607)------------------------------
% 10.54/2.47 % (3401607)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.54/2.47 % (3401607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.54/2.47 % (3401607)CaDiCaL version: 2.1.3
% 10.54/2.47 % (3401607)Termination reason: Instruction limit
% 10.54/2.47 % (3401607)Termination phase: Saturation
% 10.54/2.47 % (3401607)Time elapsed: 0.276 s
% 10.54/2.47 % (3401607)Peak memory usage: 90 MB
% 10.54/2.47 % (3401607)Instructions burned: 285 (million)
% 10.54/2.47 % (3401616)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=182343968:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 10.54/2.47 % (3401609)Instruction limit reached!
% 10.54/2.47 % (3401609)------------------------------
% 10.54/2.47 % (3401609)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.54/2.47 % (3401609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.54/2.47 % (3401609)CaDiCaL version: 2.1.3
% 10.54/2.47 % (3401609)Termination reason: Instruction limit
% 10.54/2.47 % (3401609)Termination phase: Saturation
% 10.54/2.47 % (3401609)Time elapsed: 0.284 s
% 10.54/2.47 % (3401609)Peak memory usage: 90 MB
% 10.54/2.47 % (3401609)Instructions burned: 325 (million)
% 10.54/2.47 % (3401620)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2451630834:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2991 on theBenchmark for (2991ds/294Mi)
% 10.54/2.47 % (3401621)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1380982406:i=2350_2991 on theBenchmark for (2991ds/2350Mi)
% 10.54/2.47 % (3401616)First to succeed.
% 10.54/2.47 % (3401616)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3401541"
% 10.54/2.47 % (3401589)Also succeeded, but the first one will report.
% 10.54/2.47 % (3401625)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3900595777:cts=off:i=113:fsr=off:ss=included:sgt=4_2990 on theBenchmark for (2990ds/113Mi)
% 10.54/2.47 % (3401620)Instruction limit reached!
% 10.54/2.47 % (3401620)------------------------------
% 10.54/2.47 % (3401620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.54/2.47 % (3401620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.54/2.47 % (3401620)CaDiCaL version: 2.1.3
% 10.54/2.47 % (3401620)Termination reason: Instruction limit
% 10.54/2.47 % (3401620)Termination phase: Saturation
% 10.54/2.47 % (3401620)Time elapsed: 0.264 s
% 10.54/2.47 % (3401620)Peak memory usage: 89 MB
% 10.54/2.47 % (3401620)Instructions burned: 294 (million)
% 10.54/2.47 % (3401625)Instruction limit reached!
% 10.54/2.47 % (3401625)------------------------------
% 10.54/2.47 % (3401625)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.54/2.47 % (3401625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.54/2.47 % (3401625)CaDiCaL version: 2.1.3
% 10.54/2.47 % (3401625)Termination reason: Instruction limit
% 10.54/2.47 % (3401625)Termination phase: Saturation
% 10.54/2.47 % (3401625)Time elapsed: 0.103 s
% 10.54/2.47 % (3401625)Peak memory usage: 89 MB
% 10.54/2.47 % (3401625)Instructions burned: 113 (million)
% 10.54/2.47 % (3401616)Refutation found. Thanks to Tanya!
% 10.54/2.47 % SZS status Theorem for theBenchmark
% 10.54/2.47 % SZS output start Proof for theBenchmark
% See solution above
% 11.58/2.79 % (3401616)------------------------------
% 11.58/2.79 % (3401616)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 11.58/2.79 % (3401616)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 11.58/2.79 % (3401616)CaDiCaL version: 2.1.3
% 11.58/2.79 % (3401616)Termination reason: Refutation
% 11.58/2.79 % (3401616)Time elapsed: 0.182 s
% 11.58/2.79 % (3401616)Peak memory usage: 91 MB
% 11.58/2.79 % (3401616)Instructions burned: 191 (million)
% 11.58/2.79 % (3401616)------------------------------
% 11.58/2.79 % (3401616)------------------------------
% 11.58/2.79 % (3401541)Success in time 1.537 s
% 11.58/2.79 % Vampire exiting
%------------------------------------------------------------------------------