%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ133_2 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 3.81s 1.40s
% Output : Refutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 52
% Syntax : Number of formulae : 192 ( 40 unt; 0 typ; 47 def)
% Number of atoms : 659 ( 139 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 733 ( 266 ~; 340 |; 72 &)
% ( 41 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number arithmetic : 768 ( 213 atm; 335 fun; 157 num; 63 var)
% Number of types : 1 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 42 ( 38 usr; 39 prp; 0-2 aty)
% Number of functors : 21 ( 17 usr; 15 con; 0-2 aty)
% Number of variables : 63 ( 55 !; 8 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
q: $int > $int ).
tff(func_def_1,type,
p: $int > $int ).
tff(func_def_2,type,
n: $int ).
tff(func_def_3,type,
perm: $int > $int ).
tff(func_def_8,type,
sK0: $int ).
tff(func_def_9,type,
sK1: $int ).
tff(func_def_10,type,
sF2: $int ).
tff(func_def_11,type,
sF3: $int ).
tff(func_def_12,type,
sF4: $int ).
tff(func_def_13,type,
sF5: $int ).
tff(func_def_14,type,
sF6: $int ).
tff(func_def_15,type,
sF7: $int ).
tff(func_def_16,type,
sF8: $int ).
tff(func_def_17,type,
sF9: $int ).
tff(func_def_18,type,
sF10: $int ).
tff(func_def_19,type,
sF11: $int ).
tff(func_def_20,type,
sF12: $int ).
tff(f1,axiom,
( queens_p
=> ! [X0: $int,X1: $int] :
( ( $lesseq(X0,n)
& $lesseq(X1,n)
& $lesseq($sum(1,X0),X1)
& $lesseq(1,X0) )
=> ( ( p(X0) != p(X1) )
& ( $sum(p(X0),X0) != $sum(p(X1),X1) )
& ( $difference(p(X0),X0) != $difference(p(X1),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',queens_p) ).
tff(f2,axiom,
! [X0: $int] : ( perm(X0) = $difference($sum(1,n),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',permutation) ).
tff(f3,axiom,
( ! [X1: $int,X0: $int] :
( ( $lesseq(X1,n)
& $lesseq(X0,n)
& ( $lesseq($sum(1,X0),X1)
<=> $lesseq($sum(1,perm(X1)),perm(X0)) )
& $lesseq($sum(1,X0),X1)
& $lesseq(1,X0) )
=> ( ( $sum(q(X0),X0) != $sum(q(X1),X1) )
& ( q(X0) != q(X1) )
& ( $difference(q(X0),X0) != $difference(q(X1),X1) ) ) )
=> queens_q ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',queens_q) ).
tff(f4,conjecture,
( ( ! [X0: $int] : ( q(X0) = p(perm(X0)) )
& queens_p )
=> queens_q ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',queens_sym) ).
tff(f5,negated_conjecture,
~ ( ( ! [X0: $int] : ( q(X0) = p(perm(X0)) )
& queens_p )
=> queens_q ),
inference(negated_conjecture,[status(cth)],[f4]) ).
tff(f6,axiom,
! [X0: $int] :
( ( $lesseq(X0,n)
& $lesseq(1,X0) )
=> ( $lesseq(perm(X0),n)
& $lesseq(1,perm(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',permutation_range) ).
tff(f8,plain,
( ! [X1: $int,X0: $int] :
( ( ~ $less(n,X1)
& ~ $less(n,X0)
& ( ~ $less(X1,$sum(1,X0))
<=> ~ $less(perm(X0),$sum(1,perm(X1))) )
& ~ $less(X1,$sum(1,X0))
& ~ $less(X0,1) )
=> ( ( $sum(q(X0),X0) != $sum(q(X1),X1) )
& ( q(X0) != q(X1) )
& ( $sum(q(X1),$uminus(X1)) != $sum(q(X0),$uminus(X0)) ) ) )
=> queens_q ),
inference(theory_normalization,[],[f3]) ).
tff(f9,plain,
! [X0: $int] :
( ( ~ $less(n,X0)
& ~ $less(X0,1) )
=> ( ~ $less(n,perm(X0))
& ~ $less(perm(X0),1) ) ),
inference(theory_normalization,[],[f6]) ).
tff(f10,plain,
! [X0: $int] : ( perm(X0) = $sum($sum(1,n),$uminus(X0)) ),
inference(theory_normalization,[],[f2]) ).
tff(f12,plain,
( queens_p
=> ! [X0: $int,X1: $int] :
( ( ~ $less(X0,1)
& ~ $less(n,X0)
& ~ $less(n,X1)
& ~ $less(X1,$sum(1,X0)) )
=> ( ( $sum(p(X0),X0) != $sum(p(X1),X1) )
& ( p(X0) != p(X1) )
& ( $sum(p(X1),$uminus(X1)) != $sum(p(X0),$uminus(X0)) ) ) ) ),
inference(theory_normalization,[],[f1]) ).
tff(f13,plain,
( ! [X1: $int,X0: $int] :
( ( ~ $less(X1,1)
& ~ $less(n,X1)
& ( ~ $less(perm(X1),$sum(1,perm(X0)))
<=> ~ $less(X0,$sum(1,X1)) )
& ~ $less(n,X0)
& ~ $less(X0,$sum(1,X1)) )
=> ( ( $sum(q(X0),X0) != $sum(q(X1),X1) )
& ( q(X0) != q(X1) )
& ( $sum(q(X1),$uminus(X1)) != $sum(q(X0),$uminus(X0)) ) ) )
=> queens_q ),
inference(rectify,[],[f8]) ).
tff(f15,plain,
! [X0: $int] :
( ( ~ $less(n,perm(X0))
& ~ $less(perm(X0),1) )
| $less(n,X0)
| $less(X0,1) ),
inference(ennf_transformation,[],[f9]) ).
tff(f16,plain,
! [X0: $int] :
( $less(X0,1)
| $less(n,X0)
| ( ~ $less(n,perm(X0))
& ~ $less(perm(X0),1) ) ),
inference(flattening,[],[f15]) ).
tff(f17,plain,
( ! [X0: $int,X1: $int] :
( ( ( $sum(p(X0),X0) != $sum(p(X1),X1) )
& ( p(X0) != p(X1) )
& ( $sum(p(X1),$uminus(X1)) != $sum(p(X0),$uminus(X0)) ) )
| $less(X0,1)
| $less(n,X0)
| $less(n,X1)
| $less(X1,$sum(1,X0)) )
| ~ queens_p ),
inference(ennf_transformation,[],[f12]) ).
tff(f18,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(n,X0)
| $less(n,X1)
| $less(X0,1)
| ( ( $sum(p(X0),X0) != $sum(p(X1),X1) )
& ( p(X0) != p(X1) )
& ( $sum(p(X1),$uminus(X1)) != $sum(p(X0),$uminus(X0)) ) ) )
| ~ queens_p ),
inference(flattening,[],[f17]) ).
tff(f19,plain,
( queens_q
| ? [X1: $int,X0: $int] :
( ( ( $sum(q(X0),X0) = $sum(q(X1),X1) )
| ( q(X0) = q(X1) )
| ( $sum(q(X1),$uminus(X1)) = $sum(q(X0),$uminus(X0)) ) )
& ~ $less(X1,1)
& ~ $less(n,X1)
& ( ~ $less(perm(X1),$sum(1,perm(X0)))
<=> ~ $less(X0,$sum(1,X1)) )
& ~ $less(n,X0)
& ~ $less(X0,$sum(1,X1)) ) ),
inference(ennf_transformation,[],[f13]) ).
tff(f20,plain,
( queens_q
| ? [X0: $int,X1: $int] :
( ~ $less(n,X0)
& ( ( $sum(q(X0),X0) = $sum(q(X1),X1) )
| ( q(X0) = q(X1) )
| ( $sum(q(X1),$uminus(X1)) = $sum(q(X0),$uminus(X0)) ) )
& ~ $less(X1,1)
& ~ $less(n,X1)
& ( ~ $less(perm(X1),$sum(1,perm(X0)))
<=> ~ $less(X0,$sum(1,X1)) )
& ~ $less(X0,$sum(1,X1)) ) ),
inference(flattening,[],[f19]) ).
tff(f21,plain,
( ~ queens_q
& ! [X0: $int] : ( q(X0) = p(perm(X0)) )
& queens_p ),
inference(ennf_transformation,[],[f5]) ).
tff(f22,plain,
( ~ queens_q
& queens_p
& ! [X0: $int] : ( q(X0) = p(perm(X0)) ) ),
inference(flattening,[],[f21]) ).
tff(f24,plain,
( queens_q
| ? [X0: $int,X1: $int] :
( ~ $less(n,X0)
& ( ( $sum(q(X0),X0) = $sum(q(X1),X1) )
| ( q(X0) = q(X1) )
| ( $sum(q(X1),$uminus(X1)) = $sum(q(X0),$uminus(X0)) ) )
& ~ $less(X1,1)
& ~ $less(n,X1)
& ( ~ $less(perm(X1),$sum(1,perm(X0)))
| $less(X0,$sum(1,X1)) )
& ( ~ $less(X0,$sum(1,X1))
| $less(perm(X1),$sum(1,perm(X0))) )
& ~ $less(X0,$sum(1,X1)) ) ),
inference(nnf_transformation,[],[f20]) ).
tff(f25,plain,
( queens_q
| ? [X0: $int,X1: $int] :
( ~ $less(n,X0)
& ( ( $sum(q(X0),X0) = $sum(q(X1),X1) )
| ( q(X0) = q(X1) )
| ( $sum(q(X1),$uminus(X1)) = $sum(q(X0),$uminus(X0)) ) )
& ~ $less(X1,1)
& ~ $less(n,X1)
& ( ~ $less(perm(X1),$sum(1,perm(X0)))
| $less(X0,$sum(1,X1)) )
& ( ~ $less(X0,$sum(1,X1))
| $less(perm(X1),$sum(1,perm(X0))) )
& ~ $less(X0,$sum(1,X1)) ) ),
inference(flattening,[],[f24]) ).
tff(f26,plain,
( queens_q
| ( ~ $less(n,sK0)
& ( ( $sum(q(sK1),sK1) = $sum(q(sK0),sK0) )
| ( q(sK1) = q(sK0) )
| ( $sum(q(sK0),$uminus(sK0)) = $sum(q(sK1),$uminus(sK1)) ) )
& ~ $less(sK1,1)
& ~ $less(n,sK1)
& ( ~ $less(perm(sK1),$sum(1,perm(sK0)))
| $less(sK0,$sum(1,sK1)) )
& ( ~ $less(sK0,$sum(1,sK1))
| $less(perm(sK1),$sum(1,perm(sK0))) )
& ~ $less(sK0,$sum(1,sK1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f25]) ).
tff(f27,plain,
! [X0: $int] :
( $less(X0,1)
| $less(n,X0)
| ~ $less(perm(X0),1) ),
inference(cnf_transformation,[],[f16]) ).
tff(f28,plain,
! [X0: $int] :
( $less(X0,1)
| $less(n,X0)
| ~ $less(n,perm(X0)) ),
inference(cnf_transformation,[],[f16]) ).
tff(f30,plain,
( ~ $less(sK0,$sum(1,sK1))
| queens_q ),
inference(cnf_transformation,[],[f26]) ).
tff(f32,plain,
( queens_q
| ~ $less(perm(sK1),$sum(1,perm(sK0)))
| $less(sK0,$sum(1,sK1)) ),
inference(cnf_transformation,[],[f26]) ).
tff(f33,plain,
( ~ $less(n,sK1)
| queens_q ),
inference(cnf_transformation,[],[f26]) ).
tff(f34,plain,
( queens_q
| ~ $less(sK1,1) ),
inference(cnf_transformation,[],[f26]) ).
tff(f35,plain,
( queens_q
| ( $sum(q(sK1),sK1) = $sum(q(sK0),sK0) )
| ( q(sK1) = q(sK0) )
| ( $sum(q(sK0),$uminus(sK0)) = $sum(q(sK1),$uminus(sK1)) ) ),
inference(cnf_transformation,[],[f26]) ).
tff(f36,plain,
( queens_q
| ~ $less(n,sK0) ),
inference(cnf_transformation,[],[f26]) ).
tff(f37,plain,
! [X0: $int] : ( perm(X0) = $sum($sum(1,n),$uminus(X0)) ),
inference(cnf_transformation,[],[f10]) ).
tff(f38,plain,
! [X0: $int] : ( q(X0) = p(perm(X0)) ),
inference(cnf_transformation,[],[f22]) ).
tff(f39,plain,
queens_p,
inference(cnf_transformation,[],[f22]) ).
tff(f40,plain,
~ queens_q,
inference(cnf_transformation,[],[f22]) ).
tff(f41,plain,
! [X0: $int,X1: $int] :
( $less(X0,1)
| $less(n,X0)
| $less(X1,$sum(1,X0))
| ( $sum(p(X1),$uminus(X1)) != $sum(p(X0),$uminus(X0)) )
| $less(n,X1)
| ~ queens_p ),
inference(cnf_transformation,[],[f18]) ).
tff(f42,plain,
! [X0: $int,X1: $int] :
( ~ queens_p
| $less(n,X0)
| $less(n,X1)
| ( p(X0) != p(X1) )
| $less(X0,1)
| $less(X1,$sum(1,X0)) ),
inference(cnf_transformation,[],[f18]) ).
tff(f43,plain,
! [X0: $int,X1: $int] :
( $less(n,X1)
| $less(X0,1)
| ( $sum(p(X0),X0) != $sum(p(X1),X1) )
| $less(n,X0)
| $less(X1,$sum(1,X0))
| ~ queens_p ),
inference(cnf_transformation,[],[f18]) ).
tff(f44,plain,
! [X0: $int] : ( q(X0) = p($sum($sum(1,n),$uminus(X0))) ),
inference(definition_unfolding,[],[f38,f37]) ).
tff(f45,plain,
! [X0: $int] :
( ~ $less(n,$sum($sum(1,n),$uminus(X0)))
| $less(X0,1)
| $less(n,X0) ),
inference(definition_unfolding,[],[f28,f37]) ).
tff(f46,plain,
! [X0: $int] :
( ~ $less($sum($sum(1,n),$uminus(X0)),1)
| $less(X0,1)
| $less(n,X0) ),
inference(definition_unfolding,[],[f27,f37]) ).
tff(f48,plain,
( queens_q
| ( $sum(p($sum($sum(1,n),$uminus(sK0))),sK0) = $sum(p($sum($sum(1,n),$uminus(sK1))),sK1) )
| ( p($sum($sum(1,n),$uminus(sK0))) = p($sum($sum(1,n),$uminus(sK1))) )
| ( $sum(p($sum($sum(1,n),$uminus(sK0))),$uminus(sK0)) = $sum(p($sum($sum(1,n),$uminus(sK1))),$uminus(sK1)) ) ),
inference(definition_unfolding,[],[f35,f44,f44,f44,f44,f44,f44]) ).
tff(f49,plain,
( queens_q
| ~ $less($sum($sum(1,n),$uminus(sK1)),$sum(1,$sum($sum(1,n),$uminus(sK0))))
| $less(sK0,$sum(1,sK1)) ),
inference(definition_unfolding,[],[f32,f37,f37]) ).
tff(f51,definition,
sF2 = $sum(1,n),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f52,plain,
$sum(1,n) = sF2,
inference(reorient_equations,[],[f51]) ).
tff(f53,definition,
sF3 = $uminus(sK0),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f54,plain,
$uminus(sK0) = sF3,
inference(reorient_equations,[],[f53]) ).
tff(f55,definition,
sF4 = $sum(sF2,sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
tff(f56,plain,
$sum(sF2,sF3) = sF4,
inference(reorient_equations,[],[f55]) ).
tff(f57,definition,
sF5 = p(sF4),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
tff(f58,plain,
p(sF4) = sF5,
inference(reorient_equations,[],[f57]) ).
tff(f59,definition,
sF6 = $sum(sF5,sK0),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
tff(f60,plain,
$sum(sF5,sK0) = sF6,
inference(reorient_equations,[],[f59]) ).
tff(f61,definition,
sF7 = $uminus(sK1),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
tff(f62,plain,
$uminus(sK1) = sF7,
inference(reorient_equations,[],[f61]) ).
tff(f63,definition,
sF8 = $sum(sF2,sF7),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
tff(f64,plain,
$sum(sF2,sF7) = sF8,
inference(reorient_equations,[],[f63]) ).
tff(f65,definition,
sF9 = p(sF8),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
tff(f66,definition,
sF10 = $sum(sF9,sK1),
introduced(definition,[new_symbols(definition,[sF10])],[function_definition]) ).
tff(f67,plain,
$sum(sF9,sK1) = sF10,
inference(reorient_equations,[],[f66]) ).
tff(f68,definition,
sF11 = $sum(sF5,sF3),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
tff(f69,definition,
sF12 = $sum(sF9,sF7),
introduced(definition,[new_symbols(definition,[sF12])],[function_definition]) ).
tff(f70,plain,
( queens_q
| ( sF11 = sF12 )
| ( sF9 = sF5 )
| ( sF6 = sF10 ) ),
inference(definition_folding,[],[f48,f69,f62,f65,f64,f62,f52,f68,f54,f58,f56,f54,f52,f65,f64,f62,f52,f58,f56,f54,f52,f67,f65,f64,f62,f52,f60,f58,f56,f54,f52]) ).
tff(f72,definition,
( spl13_1
<=> queens_q ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
tff(f76,definition,
( spl13_2
<=> $less(sK1,1) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
tff(f78,plain,
( ~ $less(sK1,1)
| spl13_2 ),
inference(avatar_component_clause,[],[f76]) ).
tff(f79,plain,
( spl13_1
| ~ spl13_2 ),
inference(avatar_split_clause,[],[f34,f76,f72]) ).
tff(f81,definition,
( spl13_3
<=> $less(n,sK0) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
tff(f83,plain,
( ~ $less(n,sK0)
| spl13_3 ),
inference(avatar_component_clause,[],[f81]) ).
tff(f84,plain,
( spl13_1
| ~ spl13_3 ),
inference(avatar_split_clause,[],[f36,f81,f72]) ).
tff(f86,definition,
( spl13_4
<=> ( sF11 = $sum(sF5,sF3) ) ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
tff(f89,plain,
spl13_4,
inference(avatar_split_clause,[],[f68,f86]) ).
tff(f91,definition,
( spl13_5
<=> queens_p ),
introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition]) ).
tff(f94,plain,
spl13_5,
inference(avatar_split_clause,[],[f39,f91]) ).
tff(f96,definition,
( spl13_6
<=> ( $sum(sF9,sK1) = sF10 ) ),
introduced(definition,[new_symbols(definition,[spl13_6])],[avatar_definition]) ).
tff(f99,plain,
spl13_6,
inference(avatar_split_clause,[],[f67,f96]) ).
tff(f101,definition,
( spl13_7
<=> ( sF12 = $sum(sF9,sF7) ) ),
introduced(definition,[new_symbols(definition,[spl13_7])],[avatar_definition]) ).
tff(f103,plain,
( ( sF12 = $sum(sF9,sF7) )
| ~ spl13_7 ),
inference(avatar_component_clause,[],[f101]) ).
tff(f104,plain,
spl13_7,
inference(avatar_split_clause,[],[f69,f101]) ).
tff(f106,definition,
( spl13_8
<=> ( $uminus(sK0) = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl13_8])],[avatar_definition]) ).
tff(f108,plain,
( ( $uminus(sK0) = sF3 )
| ~ spl13_8 ),
inference(avatar_component_clause,[],[f106]) ).
tff(f109,plain,
spl13_8,
inference(avatar_split_clause,[],[f54,f106]) ).
tff(f111,definition,
( spl13_9
<=> ( p(sF4) = sF5 ) ),
introduced(definition,[new_symbols(definition,[spl13_9])],[avatar_definition]) ).
tff(f113,plain,
( ( p(sF4) = sF5 )
| ~ spl13_9 ),
inference(avatar_component_clause,[],[f111]) ).
tff(f114,plain,
spl13_9,
inference(avatar_split_clause,[],[f58,f111]) ).
tff(f116,definition,
( spl13_10
<=> ! [X0: $int,X1: $int] :
( $less(X0,1)
| $less(n,X1)
| ( $sum(p(X1),$uminus(X1)) != $sum(p(X0),$uminus(X0)) )
| $less(X1,$sum(1,X0))
| $less(n,X0) ) ),
introduced(definition,[new_symbols(definition,[spl13_10])],[avatar_definition]) ).
tff(f117,plain,
( ! [X0: $int,X1: $int] :
( ( $sum(p(X1),$uminus(X1)) != $sum(p(X0),$uminus(X0)) )
| $less(n,X1)
| $less(X1,$sum(1,X0))
| $less(n,X0)
| $less(X0,1) )
| ~ spl13_10 ),
inference(avatar_component_clause,[],[f116]) ).
tff(f118,plain,
( spl13_10
| ~ spl13_5 ),
inference(avatar_split_clause,[],[f41,f91,f116]) ).
tff(f120,definition,
( spl13_11
<=> ( $sum(sF2,sF3) = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl13_11])],[avatar_definition]) ).
tff(f122,plain,
( ( $sum(sF2,sF3) = sF4 )
| ~ spl13_11 ),
inference(avatar_component_clause,[],[f120]) ).
tff(f123,plain,
spl13_11,
inference(avatar_split_clause,[],[f56,f120]) ).
tff(f125,definition,
( spl13_12
<=> ! [X0: $int,X1: $int] :
( $less(n,X0)
| $less(X1,$sum(1,X0))
| $less(X0,1)
| ( p(X0) != p(X1) )
| $less(n,X1) ) ),
introduced(definition,[new_symbols(definition,[spl13_12])],[avatar_definition]) ).
tff(f126,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| ( p(X0) != p(X1) )
| $less(n,X0)
| $less(X0,1)
| $less(n,X1) )
| ~ spl13_12 ),
inference(avatar_component_clause,[],[f125]) ).
tff(f127,plain,
( spl13_12
| ~ spl13_5 ),
inference(avatar_split_clause,[],[f42,f91,f125]) ).
tff(f129,definition,
( spl13_13
<=> ! [X0: $int,X1: $int] :
( $less(n,X1)
| $less(X1,$sum(1,X0))
| $less(n,X0)
| ( $sum(p(X0),X0) != $sum(p(X1),X1) )
| $less(X0,1) ) ),
introduced(definition,[new_symbols(definition,[spl13_13])],[avatar_definition]) ).
tff(f130,plain,
( ! [X0: $int,X1: $int] :
( ( $sum(p(X0),X0) != $sum(p(X1),X1) )
| $less(X1,$sum(1,X0))
| $less(X0,1)
| $less(n,X1)
| $less(n,X0) )
| ~ spl13_13 ),
inference(avatar_component_clause,[],[f129]) ).
tff(f131,plain,
( ~ spl13_5
| spl13_13 ),
inference(avatar_split_clause,[],[f43,f129,f91]) ).
tff(f133,definition,
( spl13_14
<=> ( $uminus(sK1) = sF7 ) ),
introduced(definition,[new_symbols(definition,[spl13_14])],[avatar_definition]) ).
tff(f135,plain,
( ( $uminus(sK1) = sF7 )
| ~ spl13_14 ),
inference(avatar_component_clause,[],[f133]) ).
tff(f136,plain,
spl13_14,
inference(avatar_split_clause,[],[f62,f133]) ).
tff(f138,definition,
( spl13_15
<=> $less(sK0,$sum(1,sK1)) ),
introduced(definition,[new_symbols(definition,[spl13_15])],[avatar_definition]) ).
tff(f141,plain,
( spl13_1
| ~ spl13_15 ),
inference(avatar_split_clause,[],[f30,f138,f72]) ).
tff(f143,definition,
( spl13_16
<=> $less(n,sK1) ),
introduced(definition,[new_symbols(definition,[spl13_16])],[avatar_definition]) ).
tff(f145,plain,
( ~ $less(n,sK1)
| spl13_16 ),
inference(avatar_component_clause,[],[f143]) ).
tff(f146,plain,
( spl13_1
| ~ spl13_16 ),
inference(avatar_split_clause,[],[f33,f143,f72]) ).
tff(f148,definition,
( spl13_17
<=> $less($sum($sum(1,n),$uminus(sK1)),$sum(1,$sum($sum(1,n),$uminus(sK0)))) ),
introduced(definition,[new_symbols(definition,[spl13_17])],[avatar_definition]) ).
tff(f150,plain,
( ~ $less($sum($sum(1,n),$uminus(sK1)),$sum(1,$sum($sum(1,n),$uminus(sK0))))
| spl13_17 ),
inference(avatar_component_clause,[],[f148]) ).
tff(f151,plain,
( ~ spl13_17
| spl13_1
| spl13_15 ),
inference(avatar_split_clause,[],[f49,f138,f72,f148]) ).
tff(f153,definition,
( spl13_18
<=> ( $sum(sF2,sF7) = sF8 ) ),
introduced(definition,[new_symbols(definition,[spl13_18])],[avatar_definition]) ).
tff(f155,plain,
( ( $sum(sF2,sF7) = sF8 )
| ~ spl13_18 ),
inference(avatar_component_clause,[],[f153]) ).
tff(f156,plain,
spl13_18,
inference(avatar_split_clause,[],[f64,f153]) ).
tff(f158,definition,
( spl13_19
<=> ( sF9 = p(sF8) ) ),
introduced(definition,[new_symbols(definition,[spl13_19])],[avatar_definition]) ).
tff(f160,plain,
( ( sF9 = p(sF8) )
| ~ spl13_19 ),
inference(avatar_component_clause,[],[f158]) ).
tff(f161,plain,
spl13_19,
inference(avatar_split_clause,[],[f65,f158]) ).
tff(f163,definition,
( spl13_20
<=> ( $sum(sF5,sK0) = sF6 ) ),
introduced(definition,[new_symbols(definition,[spl13_20])],[avatar_definition]) ).
tff(f166,plain,
spl13_20,
inference(avatar_split_clause,[],[f60,f163]) ).
tff(f168,definition,
( spl13_21
<=> ( sF9 = sF5 ) ),
introduced(definition,[new_symbols(definition,[spl13_21])],[avatar_definition]) ).
tff(f172,definition,
( spl13_22
<=> ( sF11 = sF12 ) ),
introduced(definition,[new_symbols(definition,[spl13_22])],[avatar_definition]) ).
tff(f174,plain,
( ( sF11 = sF12 )
| ~ spl13_22 ),
inference(avatar_component_clause,[],[f172]) ).
tff(f176,definition,
( spl13_23
<=> ( sF6 = sF10 ) ),
introduced(definition,[new_symbols(definition,[spl13_23])],[avatar_definition]) ).
tff(f179,plain,
( spl13_21
| spl13_22
| spl13_1
| spl13_23 ),
inference(avatar_split_clause,[],[f70,f176,f72,f172,f168]) ).
tff(f180,plain,
~ spl13_1,
inference(avatar_split_clause,[],[f40,f72]) ).
tff(f183,definition,
( spl13_24
<=> ( $sum(1,n) = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl13_24])],[avatar_definition]) ).
tff(f185,plain,
( ( $sum(1,n) = sF2 )
| ~ spl13_24 ),
inference(avatar_component_clause,[],[f183]) ).
tff(f186,plain,
spl13_24,
inference(avatar_split_clause,[],[f52,f183]) ).
tff(f193,plain,
( ( sF12 = $sum(sF9,$uminus(sK1)) )
| ~ spl13_7
| ~ spl13_14 ),
inference(forward_demodulation,[],[f103,f135]) ).
tff(f195,definition,
( spl13_26
<=> ( sF12 = $sum(sF9,$uminus(sK1)) ) ),
introduced(definition,[new_symbols(definition,[spl13_26])],[avatar_definition]) ).
tff(f197,plain,
( ( sF12 = $sum(sF9,$uminus(sK1)) )
| ~ spl13_26 ),
inference(avatar_component_clause,[],[f195]) ).
tff(f198,plain,
( spl13_26
| ~ spl13_7
| ~ spl13_14 ),
inference(avatar_split_clause,[],[f193,f133,f101,f195]) ).
tff(f199,plain,
( ( sF8 = $sum(sF2,$uminus(sK1)) )
| ~ spl13_14
| ~ spl13_18 ),
inference(forward_demodulation,[],[f155,f135]) ).
tff(f201,definition,
( spl13_27
<=> ( sF8 = $sum(sF2,$uminus(sK1)) ) ),
introduced(definition,[new_symbols(definition,[spl13_27])],[avatar_definition]) ).
tff(f203,plain,
( ( sF8 = $sum(sF2,$uminus(sK1)) )
| ~ spl13_27 ),
inference(avatar_component_clause,[],[f201]) ).
tff(f204,plain,
( spl13_27
| ~ spl13_14
| ~ spl13_18 ),
inference(avatar_split_clause,[],[f199,f153,f133,f201]) ).
tff(f211,plain,
( ( $sum($sum(1,n),sF3) = sF4 )
| ~ spl13_11
| ~ spl13_24 ),
inference(superposition,[],[f122,f185]) ).
tff(f213,definition,
( spl13_29
<=> ( $sum($sum(1,n),sF3) = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl13_29])],[avatar_definition]) ).
tff(f215,plain,
( ( $sum($sum(1,n),sF3) = sF4 )
| ~ spl13_29 ),
inference(avatar_component_clause,[],[f213]) ).
tff(f216,plain,
( spl13_29
| ~ spl13_11
| ~ spl13_24 ),
inference(avatar_split_clause,[],[f211,f183,f120,f213]) ).
tff(f217,plain,
( ( sF11 = $sum(sF9,$uminus(sK1)) )
| ~ spl13_22
| ~ spl13_26 ),
inference(forward_demodulation,[],[f197,f174]) ).
tff(f219,definition,
( spl13_30
<=> ( sF11 = $sum(sF9,$uminus(sK1)) ) ),
introduced(definition,[new_symbols(definition,[spl13_30])],[avatar_definition]) ).
tff(f222,plain,
( spl13_30
| ~ spl13_22
| ~ spl13_26 ),
inference(avatar_split_clause,[],[f217,f195,f172,f219]) ).
tff(f237,plain,
( ( $sum($sum(1,n),$uminus(sK1)) = sF8 )
| ~ spl13_24
| ~ spl13_27 ),
inference(forward_demodulation,[],[f203,f185]) ).
tff(f239,definition,
( spl13_33
<=> ( $sum($sum(1,n),$uminus(sK1)) = sF8 ) ),
introduced(definition,[new_symbols(definition,[spl13_33])],[avatar_definition]) ).
tff(f241,plain,
( ( $sum($sum(1,n),$uminus(sK1)) = sF8 )
| ~ spl13_33 ),
inference(avatar_component_clause,[],[f239]) ).
tff(f242,plain,
( spl13_33
| ~ spl13_24
| ~ spl13_27 ),
inference(avatar_split_clause,[],[f237,f201,f183,f239]) ).
tff(f243,plain,
( $less(n,sK0)
| ~ $less(n,$sum($sum(1,n),sF3))
| $less(sK0,1)
| ~ spl13_8 ),
inference(superposition,[],[f45,f108]) ).
tff(f244,plain,
( $less(n,sK1)
| $less(sK1,1)
| ~ $less(n,sF8)
| ~ spl13_33 ),
inference(superposition,[],[f45,f241]) ).
tff(f245,plain,
( ~ $less(n,sF8)
| $less(sK1,1)
| spl13_16
| ~ spl13_33 ),
inference(forward_subsumption_resolution,[],[f244,f145]) ).
tff(f246,plain,
( $less(sK0,1)
| ~ $less(n,$sum($sum(1,n),sF3))
| spl13_3
| ~ spl13_8 ),
inference(forward_subsumption_resolution,[],[f243,f83]) ).
tff(f247,plain,
( ~ $less(n,sF8)
| spl13_2
| spl13_16
| ~ spl13_33 ),
inference(forward_subsumption_resolution,[],[f245,f78]) ).
tff(f248,plain,
( $less(sK0,1)
| ~ $less(n,sF4)
| spl13_3
| ~ spl13_8
| ~ spl13_29 ),
inference(forward_demodulation,[],[f246,f215]) ).
tff(f250,definition,
( spl13_34
<=> $less(n,sF8) ),
introduced(definition,[new_symbols(definition,[spl13_34])],[avatar_definition]) ).
tff(f252,plain,
( ~ $less(n,sF8)
| spl13_34 ),
inference(avatar_component_clause,[],[f250]) ).
tff(f253,plain,
( ~ spl13_34
| spl13_2
| spl13_16
| ~ spl13_33 ),
inference(avatar_split_clause,[],[f247,f239,f143,f76,f250]) ).
tff(f255,definition,
( spl13_35
<=> $less(n,sF4) ),
introduced(definition,[new_symbols(definition,[spl13_35])],[avatar_definition]) ).
tff(f257,plain,
( ~ $less(n,sF4)
| spl13_35 ),
inference(avatar_component_clause,[],[f255]) ).
tff(f259,definition,
( spl13_36
<=> $less(sK0,1) ),
introduced(definition,[new_symbols(definition,[spl13_36])],[avatar_definition]) ).
tff(f262,plain,
( ~ spl13_35
| spl13_36
| spl13_3
| ~ spl13_8
| ~ spl13_29 ),
inference(avatar_split_clause,[],[f248,f213,f106,f81,f259,f255]) ).
tff(f263,plain,
( $less(sK0,1)
| ~ $less($sum($sum(1,n),sF3),1)
| $less(n,sK0)
| ~ spl13_8 ),
inference(superposition,[],[f46,f108]) ).
tff(f266,plain,
( ~ $less($sum($sum(1,n),sF3),1)
| $less(sK0,1)
| spl13_3
| ~ spl13_8 ),
inference(forward_subsumption_resolution,[],[f263,f83]) ).
tff(f268,plain,
( $less(sK0,1)
| ~ $less(sF4,1)
| spl13_3
| ~ spl13_8
| ~ spl13_29 ),
inference(forward_demodulation,[],[f266,f215]) ).
tff(f275,definition,
( spl13_38
<=> $less(sF4,1) ),
introduced(definition,[new_symbols(definition,[spl13_38])],[avatar_definition]) ).
tff(f277,plain,
( ~ $less(sF4,1)
| spl13_38 ),
inference(avatar_component_clause,[],[f275]) ).
tff(f278,plain,
( ~ spl13_38
| spl13_36
| spl13_3
| ~ spl13_8
| ~ spl13_29 ),
inference(avatar_split_clause,[],[f268,f213,f106,f81,f259,f275]) ).
tff(f279,plain,
( ~ $less($sum($sum(1,n),$uminus(sK1)),$sum(1,$sum($sum(1,n),sF3)))
| ~ spl13_8
| spl13_17 ),
inference(forward_demodulation,[],[f150,f108]) ).
tff(f280,plain,
( ~ $less($sum($sum(1,n),$uminus(sK1)),$sum(1,sF4))
| ~ spl13_8
| spl13_17
| ~ spl13_29 ),
inference(forward_demodulation,[],[f279,f215]) ).
tff(f281,plain,
( ~ $less(sF8,$sum(1,sF4))
| ~ spl13_8
| spl13_17
| ~ spl13_29
| ~ spl13_33 ),
inference(forward_demodulation,[],[f280,f241]) ).
tff(f283,definition,
( spl13_39
<=> $less(sF8,$sum(1,sF4)) ),
introduced(definition,[new_symbols(definition,[spl13_39])],[avatar_definition]) ).
tff(f285,plain,
( ~ $less(sF8,$sum(1,sF4))
| spl13_39 ),
inference(avatar_component_clause,[],[f283]) ).
tff(f286,plain,
( ~ spl13_39
| ~ spl13_8
| spl13_17
| ~ spl13_29
| ~ spl13_33 ),
inference(avatar_split_clause,[],[f281,f239,f213,f148,f106,f283]) ).
tff(f294,plain,
( ( p(sF4) != p(sF8) )
| $less(n,sF4)
| $less(n,sF8)
| $less(sF4,1)
| ~ spl13_12
| spl13_39 ),
inference(resolution,[],[f126,f285]) ).
tff(f295,plain,
( $less(n,sF8)
| $less(sF4,1)
| ( p(sF4) != p(sF8) )
| ~ spl13_12
| spl13_35
| spl13_39 ),
inference(forward_subsumption_resolution,[],[f294,f257]) ).
tff(f297,plain,
( $less(sF4,1)
| ( p(sF4) != p(sF8) )
| ~ spl13_12
| spl13_34
| spl13_35
| spl13_39 ),
inference(forward_subsumption_resolution,[],[f295,f252]) ).
tff(f299,plain,
( ( p(sF4) != p(sF8) )
| ~ spl13_12
| spl13_34
| spl13_35
| spl13_38
| spl13_39 ),
inference(forward_subsumption_resolution,[],[f297,f277]) ).
tff(f301,plain,
( ( p(sF4) != sF9 )
| ~ spl13_12
| ~ spl13_19
| spl13_34
| spl13_35
| spl13_38
| spl13_39 ),
inference(forward_demodulation,[],[f299,f160]) ).
tff(f310,plain,
( ( sF9 != sF5 )
| ~ spl13_9
| ~ spl13_12
| ~ spl13_19
| spl13_34
| spl13_35
| spl13_38
| spl13_39 ),
inference(forward_demodulation,[],[f301,f113]) ).
tff(f311,plain,
( ~ spl13_21
| ~ spl13_9
| ~ spl13_12
| ~ spl13_19
| spl13_34
| spl13_35
| spl13_38
| spl13_39 ),
inference(avatar_split_clause,[],[f310,f283,f275,f255,f250,f158,f125,f111,f168]) ).
tff(f313,plain,
( ! [X0: $int] :
( $less(n,sF4)
| $less(sF4,1)
| $less(n,X0)
| $less(X0,$sum(1,sF4))
| ( $sum(p(X0),X0) != $sum(sF5,sF4) ) )
| ~ spl13_9
| ~ spl13_13 ),
inference(superposition,[],[f130,f113]) ).
tff(f320,plain,
( ! [X0: $int] :
( $less(n,X0)
| $less(sF4,1)
| $less(X0,$sum(1,sF4))
| ( $sum(p(X0),X0) != $sum(sF5,sF4) ) )
| ~ spl13_9
| ~ spl13_13
| spl13_35 ),
inference(forward_subsumption_resolution,[],[f313,f257]) ).
tff(f323,plain,
( ! [X0: $int] :
( ( $sum(p(X0),X0) != $sum(sF5,sF4) )
| $less(X0,$sum(1,sF4))
| $less(n,X0) )
| ~ spl13_9
| ~ spl13_13
| spl13_35
| spl13_38 ),
inference(forward_subsumption_resolution,[],[f320,f277]) ).
tff(f328,plain,
( ! [X0: $int] :
( ( $sum(sF5,$uminus(sF4)) != $sum(p(X0),$uminus(X0)) )
| $less(X0,$sum(1,sF4))
| $less(n,X0)
| $less(sF4,1)
| $less(n,sF4) )
| ~ spl13_9
| ~ spl13_10 ),
inference(superposition,[],[f117,f113]) ).
tff(f338,plain,
( ! [X0: $int] :
( ( $sum(sF5,$uminus(sF4)) != $sum(p(X0),$uminus(X0)) )
| $less(n,sF4)
| $less(X0,$sum(1,sF4))
| $less(n,X0) )
| ~ spl13_9
| ~ spl13_10
| spl13_38 ),
inference(forward_subsumption_resolution,[],[f328,f277]) ).
tff(f344,plain,
( ! [X0: $int] :
( ( $sum(sF5,$uminus(sF4)) != $sum(p(X0),$uminus(X0)) )
| $less(n,X0)
| $less(X0,$sum(1,sF4)) )
| ~ spl13_9
| ~ spl13_10
| spl13_35
| spl13_38 ),
inference(forward_subsumption_resolution,[],[f338,f257]) ).
tff(f378,plain,
( $less(sF8,$sum(1,sF4))
| $less(n,sF8)
| ( $sum(sF9,sF8) != $sum(sF5,sF4) )
| ~ spl13_9
| ~ spl13_13
| ~ spl13_19
| spl13_35
| spl13_38 ),
inference(superposition,[],[f323,f160]) ).
tff(f381,plain,
( $less(n,sF8)
| ( $sum(sF9,sF8) != $sum(sF5,sF4) )
| ~ spl13_9
| ~ spl13_13
| ~ spl13_19
| spl13_35
| spl13_38
| spl13_39 ),
inference(forward_subsumption_resolution,[],[f378,f285]) ).
tff(f387,plain,
( ( $sum(sF9,sF8) != $sum(sF5,sF4) )
| ~ spl13_9
| ~ spl13_13
| ~ spl13_19
| spl13_34
| spl13_35
| spl13_38
| spl13_39 ),
inference(forward_subsumption_resolution,[],[f381,f252]) ).
tff(f389,definition,
( spl13_47
<=> ( $sum(sF9,sF8) = $sum(sF5,sF4) ) ),
introduced(definition,[new_symbols(definition,[spl13_47])],[avatar_definition]) ).
tff(f392,plain,
( ~ spl13_47
| ~ spl13_9
| ~ spl13_13
| ~ spl13_19
| spl13_34
| spl13_35
| spl13_38
| spl13_39 ),
inference(avatar_split_clause,[],[f387,f283,f275,f255,f250,f158,f129,f111,f389]) ).
tff(f415,definition,
( spl13_50
<=> ( $sum(sF9,$uminus(sF8)) = $sum(sF5,$uminus(sF4)) ) ),
introduced(definition,[new_symbols(definition,[spl13_50])],[avatar_definition]) ).
tff(f450,plain,
( $less(sF8,$sum(1,sF4))
| $less(n,sF8)
| ( $sum(sF9,$uminus(sF8)) != $sum(sF5,$uminus(sF4)) )
| ~ spl13_9
| ~ spl13_10
| ~ spl13_19
| spl13_35
| spl13_38 ),
inference(superposition,[],[f344,f160]) ).
tff(f452,plain,
( ( $sum(sF9,$uminus(sF8)) != $sum(sF5,$uminus(sF4)) )
| $less(n,sF8)
| ~ spl13_9
| ~ spl13_10
| ~ spl13_19
| spl13_35
| spl13_38
| spl13_39 ),
inference(forward_subsumption_resolution,[],[f450,f285]) ).
tff(f453,plain,
( ( $sum(sF9,$uminus(sF8)) != $sum(sF5,$uminus(sF4)) )
| ~ spl13_9
| ~ spl13_10
| ~ spl13_19
| spl13_34
| spl13_35
| spl13_38
| spl13_39 ),
inference(forward_subsumption_resolution,[],[f452,f252]) ).
tff(f454,plain,
( ~ spl13_50
| ~ spl13_9
| ~ spl13_10
| ~ spl13_19
| spl13_34
| spl13_35
| spl13_38
| spl13_39 ),
inference(avatar_split_clause,[],[f453,f283,f275,f255,f250,f158,f116,f111,f415]) ).
tff(f455,plain,
$false,
inference(avatar_smt_refutation,[],[f454,f392,f311,f286,f278,f262,f253,f242,f222,f216,f204,f198,f186,f180,f179,f166,f161,f156,f151,f146,f141,f136,f131,f127,f123,f118,f114,f109,f104,f99,f94,f89,f84,f79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ133_2 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n005.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 22:44:47 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 3.81/1.40 % (255168)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.81/1.40 % (255274)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1458483615:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.81/1.40 % (255274)Instruction limit reached!
% 3.81/1.40 % (255274)------------------------------
% 3.81/1.40 % (255274)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.40 % (255274)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.40 % (255274)CaDiCaL version: 2.1.3
% 3.81/1.40 % (255274)Termination reason: Instruction limit
% 3.81/1.40 % (255274)Termination phase: Saturation
% 3.81/1.40 % (255274)Time elapsed: 0.020 s
% 3.81/1.40 % (255274)Peak memory usage: 116 MB
% 3.81/1.40 % (255274)Instructions burned: 13 (million)
% 3.81/1.40 % (255276)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1160298938:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.81/1.40 % (255277)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3654668201:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.81/1.40 % (255275)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=4084524831:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.81/1.40 % (255278)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1212542904:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.81/1.40 % (255280)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3369379469:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.81/1.40 % (255279)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=79935508:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.81/1.40 % (255278)Instruction limit reached!
% 3.81/1.40 % (255278)------------------------------
% 3.81/1.40 % (255278)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.40 % (255278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.40 % (255278)CaDiCaL version: 2.1.3
% 3.81/1.40 % (255278)Termination reason: Instruction limit
% 3.81/1.40 % (255278)Termination phase: Saturation
% 3.81/1.40 % (255278)Time elapsed: 0.004 s
% 3.81/1.40 % (255278)Peak memory usage: 89 MB
% 3.81/1.40 % (255278)Instructions burned: 5 (million)
% 3.81/1.40 % (255277)Instruction limit reached!
% 3.81/1.40 % (255277)------------------------------
% 3.81/1.40 % (255277)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.40 % (255277)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.40 % (255277)CaDiCaL version: 2.1.3
% 3.81/1.40 % (255277)Termination reason: Instruction limit
% 3.81/1.40 % (255277)Termination phase: Saturation
% 3.81/1.40 % (255277)Time elapsed: 0.005 s
% 3.81/1.40 % (255277)Peak memory usage: 88 MB
% 3.81/1.40 % (255277)Instructions burned: 8 (million)
% 3.81/1.40 % (255279)Refutation not found, incomplete strategy
% 3.81/1.40 % (255279)------------------------------
% 3.81/1.40 % (255279)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.40 % (255279)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.40 % (255279)CaDiCaL version: 2.1.3
% 3.81/1.40 % (255279)Termination reason: Refutation not found, incomplete strategy
% 3.81/1.40 % (255279)Time elapsed: 0.043 s
% 3.81/1.40 % (255279)Peak memory usage: 116 MB
% 3.81/1.40 % (255279)Instructions burned: 12 (million)
% 3.81/1.40 % (255280)Instruction limit reached!
% 3.81/1.40 % (255280)------------------------------
% 3.81/1.40 % (255280)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.40 % (255280)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.40 % (255280)CaDiCaL version: 2.1.3
% 3.81/1.40 % (255280)Termination reason: Instruction limit
% 3.81/1.40 % (255280)Termination phase: Saturation
% 3.81/1.40 % (255280)Time elapsed: 0.054 s
% 3.81/1.40 % (255280)Peak memory usage: 116 MB
% 3.81/1.40 % (255280)Instructions burned: 33 (million)
% 3.81/1.40 % (255275)First to succeed.
% 3.81/1.40 % (255275)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-255168"
% 3.81/1.40 % (255276)Instruction limit reached!
% 3.81/1.40 % (255276)------------------------------
% 3.81/1.40 % (255276)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.40 % (255276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.40 % (255276)CaDiCaL version: 2.1.3
% 3.81/1.40 % (255276)Termination reason: Instruction limit
% 3.81/1.40 % (255276)Termination phase: Saturation
% 3.81/1.40 % (255276)Time elapsed: 0.143 s
% 3.81/1.40 % (255276)Peak memory usage: 113 MB
% 3.81/1.40 % (255276)Instructions burned: 202 (million)
% 3.81/1.40 % (255286)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=242710764:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.81/1.40 % (255286)Refutation not found, incomplete strategy
% 3.81/1.40 % (255286)------------------------------
% 3.81/1.40 % (255286)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.40 % (255286)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.40 % (255286)CaDiCaL version: 2.1.3
% 3.81/1.40 % (255286)Termination reason: Refutation not found, incomplete strategy
% 3.81/1.40 % (255286)Time elapsed: 0.002 s
% 3.81/1.40 % (255286)Peak memory usage: 89 MB
% 3.81/1.40 % (255286)Instructions burned: 3 (million)
% 3.81/1.40 % (255293)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=2710370563:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.81/1.40 % (255294)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=1750373566:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 3.81/1.40 % (255294)Instruction limit reached!
% 3.81/1.40 % (255294)------------------------------
% 3.81/1.40 % (255294)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.40 % (255294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.40 % (255294)CaDiCaL version: 2.1.3
% 3.81/1.40 % (255294)Termination reason: Instruction limit
% 3.81/1.40 % (255294)Termination phase: Saturation
% 3.81/1.40 % (255294)Time elapsed: 0.011 s
% 3.81/1.40 % (255294)Peak memory usage: 90 MB
% 3.81/1.40 % (255294)Instructions burned: 18 (million)
% 3.81/1.40 % (255293)Instruction limit reached!
% 3.81/1.40 % (255293)------------------------------
% 3.81/1.40 % (255293)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.40 % (255293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.40 % (255293)CaDiCaL version: 2.1.3
% 3.81/1.40 % (255293)Termination reason: Instruction limit
% 3.81/1.40 % (255293)Termination phase: Saturation
% 3.81/1.40 % (255293)Time elapsed: 0.023 s
% 3.81/1.40 % (255293)Peak memory usage: 88 MB
% 3.81/1.40 % (255293)Instructions burned: 30 (million)
% 3.81/1.40 % (255316)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=2432478974:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 3.81/1.40 % (255316)Instruction limit reached!
% 3.81/1.40 % (255316)------------------------------
% 3.81/1.40 % (255316)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.40 % (255316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.40 % (255316)CaDiCaL version: 2.1.3
% 3.81/1.40 % (255316)Termination reason: Instruction limit
% 3.81/1.40 % (255316)Termination phase: Saturation
% 3.81/1.40 % (255316)Time elapsed: 0.019 s
% 3.81/1.40 % (255316)Peak memory usage: 89 MB
% 3.81/1.40 % (255316)Instructions burned: 25 (million)
% 3.81/1.40 % (255279)------------------------------
% 3.81/1.40 % (255279)------------------------------
% 3.81/1.40 % (255286)------------------------------
% 3.81/1.40 % (255286)------------------------------
% 3.81/1.40 % (255328)ott+1010_8_to=lpo:sil=128000:si=on:norm_ineq=on:sp=unary_frequency:sos=on:gve=cautious:spb=goal_then_units:uwa=alasca_main_floor:tha=some:random_seed=402201514:i=27:canc=cautious:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/27Mi)
% 3.81/1.40 % (255328)Refutation not found, incomplete strategy
% 3.81/1.40 % (255328)------------------------------
% 3.81/1.40 % (255328)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.40 % (255328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.40 % (255328)CaDiCaL version: 2.1.3
% 3.81/1.40 % (255328)Termination reason: Refutation not found, incomplete strategy
% 3.81/1.40 % (255328)Time elapsed: 0.005 s
% 3.81/1.40 % (255328)Peak memory usage: 90 MB
% 3.81/1.40 % (255328)Instructions burned: 5 (million)
% 3.81/1.40 % (255345)dis+1002_24_to=kbo:sil=128000:si=on:random_seed=597269130:i=85:gtgl=4:rtra=on:gtg=exists_sym_2996 on theBenchmark for (2996ds/85Mi)
% 3.81/1.40 % (255275)Refutation found. Thanks to Tanya!
% 3.81/1.40 % SZS status Theorem for theBenchmark
% 3.81/1.40 % SZS output start Proof for theBenchmark
% See solution above
% 3.81/1.50 % (255275)------------------------------
% 3.81/1.50 % (255275)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.81/1.50 % (255275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.81/1.50 % (255275)CaDiCaL version: 2.1.3
% 3.81/1.50 % (255275)Termination reason: Refutation
% 3.81/1.50 % (255275)Time elapsed: 0.091 s
% 3.81/1.50 % (255275)Peak memory usage: 117 MB
% 3.81/1.50 % (255275)Instructions burned: 76 (million)
% 3.81/1.50 % (255275)------------------------------
% 3.81/1.50 % (255275)------------------------------
% 3.81/1.50 % (255168)Success in time 0.523 s
% 3.81/1.50 % Vampire exiting
%------------------------------------------------------------------------------