%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW542_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 01:30:47 PM UTC 2026
% Result : Theorem 4.19s 1.54s
% Output : Refutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 74 ( 8 unt; 0 typ; 7 def)
% Number of atoms : 188 ( 24 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 216 ( 102 ~; 93 |; 4 &)
% ( 5 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 27 ( 25 usr; 6 prp; 0-3 aty)
% Number of functors : 29 ( 29 usr; 6 con; 0-5 aty)
% Number of variables : 80 ( 0 sgn 80 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
a1: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
huffma1450048681e_tree: $tType > $tType ).
tff(type_def_8,type,
int: $tType ).
tff(type_def_9,type,
nat: $tType ).
tff(type_def_10,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_1,type,
huffma675207370phabet:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > fun(X0,bool) ) ).
tff(func_def_2,type,
huffma1134658180e_cost:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_3,type,
huffma410068972_depth:
!>[X0: $tType] : ( ( huffma1450048681e_tree(X0) * X0 ) > nat ) ).
tff(func_def_4,type,
huffma1352802255e_freq:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > fun(X0,nat) ) ).
tff(func_def_5,type,
huffma945805758height:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_6,type,
huffma1401021291ibling:
!>[X0: $tType] : ( ( huffma1450048681e_tree(X0) * X0 ) > X0 ) ).
tff(func_def_7,type,
huffma1146269203erNode:
!>[X0: $tType] : ( ( nat * huffma1450048681e_tree(X0) * huffma1450048681e_tree(X0) ) > huffma1450048681e_tree(X0) ) ).
tff(func_def_8,type,
huffma2021818691e_Leaf:
!>[X0: $tType] : ( ( nat * X0 ) > huffma1450048681e_tree(X0) ) ).
tff(func_def_9,type,
huffma107959123e_case:
!>[X0: $tType,X1: $tType] : ( ( fun(nat,fun(X0,X1)) * fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),X1))) * huffma1450048681e_tree(X0) ) > X1 ) ).
tff(func_def_10,type,
huffma1280178957ee_rec:
!>[X0: $tType,X1: $tType] : ( ( fun(nat,fun(X0,X1)) * fun(nat,fun(huffma1450048681e_tree(X0),fun(huffma1450048681e_tree(X0),fun(X1,fun(X1,X1))))) * huffma1450048681e_tree(X0) ) > X1 ) ).
tff(func_def_11,type,
if:
!>[X0: $tType] : ( ( bool * X0 * X0 ) > X0 ) ).
tff(func_def_12,type,
semiring_1_of_nat:
!>[X0: $tType] : ( nat > X0 ) ).
tff(func_def_13,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_14,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_15,type,
fFalse: bool ).
tff(func_def_16,type,
fTrue: bool ).
tff(func_def_17,type,
a: a1 ).
tff(func_def_18,type,
t_1: huffma1450048681e_tree(a1) ).
tff(func_def_19,type,
t_2: huffma1450048681e_tree(a1) ).
tff(func_def_20,type,
w: nat ).
tff(func_def_21,type,
sK0:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_22,type,
sK1:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > huffma1450048681e_tree(X0) ) ).
tff(func_def_23,type,
sK2:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > huffma1450048681e_tree(X0) ) ).
tff(func_def_24,type,
sK3:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_25,type,
sK4:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > X0 ) ).
tff(func_def_26,type,
sK5:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > X0 ) ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
ord:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
preorder:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
semiring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
linordered_semidom:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
huffma1518433673istent:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > $o ) ).
tff(pred_def_9,type,
huffma1393970616ptimum:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > $o ) ).
tff(pred_def_10,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_11,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_12,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_13,type,
pp: bool > $o ).
tff(pred_def_14,type,
sP6: a1 > $o ).
tff(pred_def_15,type,
sP7: a1 > $o ).
tff(pred_def_16,type,
sP8: a1 > $o ).
tff(pred_def_17,type,
sP9: a1 > $o ).
tff(pred_def_18,type,
sP10: nat > $o ).
tff(pred_def_19,type,
sP11: nat > $o ).
tff(pred_def_20,type,
sP12: nat > $o ).
tff(f5,axiom,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: nat,X3: X0,X4: huffma1450048681e_tree(X0)] :
( ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4))
=> ( ~ member(X0,X3,huffma675207370phabet(X0,X4))
=> ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X4,X1),X3) = huffma1401021291ibling(X0,X1,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_height__gt__0__notin__alphabet__imp__sibling__left) ).
tff(f6,axiom,
! [X0: $tType,X1: nat,X2: huffma1450048681e_tree(X0),X3: X0,X4: huffma1450048681e_tree(X0)] :
( ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4))
=> ( ~ member(X0,X3,huffma675207370phabet(X0,X2))
=> ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,X4),X3) = huffma1401021291ibling(X0,X4,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_height__gt__0__notin__alphabet__imp__sibling__right) ).
tff(f7,axiom,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: nat,X3: X0,X4: huffma1450048681e_tree(X0)] :
( ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4))
=> ( member(X0,X3,huffma675207370phabet(X0,X4))
=> ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X4,X1),X3) = huffma1401021291ibling(X0,X4,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_height__gt__0__in__alphabet__imp__sibling__left) ).
tff(f8,axiom,
! [X0: $tType,X1: nat,X2: huffma1450048681e_tree(X0),X3: X0,X4: huffma1450048681e_tree(X0)] :
( ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4))
=> ( member(X0,X3,huffma675207370phabet(X0,X2))
=> ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,X4),X3) = huffma1401021291ibling(X0,X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_height__gt__0__in__alphabet__imp__sibling__right) ).
tff(f124,axiom,
( ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_1))
| ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f125,conjecture,
( ( member(a1,a,huffma675207370phabet(a1,t_1))
=> ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a) = huffma1401021291ibling(a1,t_1,a) ) )
& ( ~ member(a1,a,huffma675207370phabet(a1,t_1))
=> ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a) = huffma1401021291ibling(a1,t_2,a) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
tff(f126,negated_conjecture,
~ ( ( member(a1,a,huffma675207370phabet(a1,t_1))
=> ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a) = huffma1401021291ibling(a1,t_1,a) ) )
& ( ~ member(a1,a,huffma675207370phabet(a1,t_1))
=> ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a) = huffma1401021291ibling(a1,t_2,a) ) ) ),
inference(negated_conjecture,[status(cth)],[f125]) ).
tff(f129,plain,
( ( ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a) != huffma1401021291ibling(a1,t_1,a) )
& member(a1,a,huffma675207370phabet(a1,t_1)) )
| ( ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a) != huffma1401021291ibling(a1,t_2,a) )
& ~ member(a1,a,huffma675207370phabet(a1,t_1)) ) ),
inference(ennf_transformation,[],[f126]) ).
tff(f131,plain,
! [X0: $tType,X1: nat,X2: huffma1450048681e_tree(X0),X3: X0,X4: huffma1450048681e_tree(X0)] :
( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,X4),X3) = huffma1401021291ibling(X0,X2,X3) )
| ~ member(X0,X3,huffma675207370phabet(X0,X2))
| ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ),
inference(ennf_transformation,[],[f8]) ).
tff(f132,plain,
! [X0: $tType,X1: nat,X2: huffma1450048681e_tree(X0),X3: X0,X4: huffma1450048681e_tree(X0)] :
( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,X4),X3) = huffma1401021291ibling(X0,X2,X3) )
| ~ member(X0,X3,huffma675207370phabet(X0,X2))
| ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ),
inference(flattening,[],[f131]) ).
tff(f133,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: nat,X3: X0,X4: huffma1450048681e_tree(X0)] :
( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X4,X1),X3) = huffma1401021291ibling(X0,X4,X3) )
| ~ member(X0,X3,huffma675207370phabet(X0,X4))
| ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ),
inference(ennf_transformation,[],[f7]) ).
tff(f134,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: nat,X3: X0,X4: huffma1450048681e_tree(X0)] :
( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X4,X1),X3) = huffma1401021291ibling(X0,X4,X3) )
| ~ member(X0,X3,huffma675207370phabet(X0,X4))
| ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ),
inference(flattening,[],[f133]) ).
tff(f135,plain,
! [X0: $tType,X1: nat,X2: huffma1450048681e_tree(X0),X3: X0,X4: huffma1450048681e_tree(X0)] :
( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,X4),X3) = huffma1401021291ibling(X0,X4,X3) )
| member(X0,X3,huffma675207370phabet(X0,X2))
| ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ),
inference(ennf_transformation,[],[f6]) ).
tff(f136,plain,
! [X0: $tType,X1: nat,X2: huffma1450048681e_tree(X0),X3: X0,X4: huffma1450048681e_tree(X0)] :
( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,X4),X3) = huffma1401021291ibling(X0,X4,X3) )
| member(X0,X3,huffma675207370phabet(X0,X2))
| ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ),
inference(flattening,[],[f135]) ).
tff(f137,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: nat,X3: X0,X4: huffma1450048681e_tree(X0)] :
( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X4,X1),X3) = huffma1401021291ibling(X0,X1,X3) )
| member(X0,X3,huffma675207370phabet(X0,X4))
| ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ),
inference(ennf_transformation,[],[f5]) ).
tff(f138,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: nat,X3: X0,X4: huffma1450048681e_tree(X0)] :
( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X4,X1),X3) = huffma1401021291ibling(X0,X1,X3) )
| member(X0,X3,huffma675207370phabet(X0,X4))
| ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ),
inference(flattening,[],[f137]) ).
tff(f158,plain,
( ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_1))
| ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_2)) ),
inference(cnf_transformation,[],[f124]) ).
tff(f160,plain,
( member(a1,a,huffma675207370phabet(a1,t_1))
| ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a) != huffma1401021291ibling(a1,t_2,a) ) ),
inference(cnf_transformation,[],[f129]) ).
tff(f161,plain,
( ( huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a) != huffma1401021291ibling(a1,t_1,a) )
| ~ member(a1,a,huffma675207370phabet(a1,t_1)) ),
inference(cnf_transformation,[],[f129]) ).
tff(f165,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: X0,X1: nat,X4: huffma1450048681e_tree(X0)] :
( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,X4),X3) = huffma1401021291ibling(X0,X2,X3) )
| ~ member(X0,X3,huffma675207370phabet(X0,X2))
| ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ),
inference(cnf_transformation,[],[f132]) ).
tff(f166,plain,
! [X0: $tType,X2: nat,X3: X0,X1: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0)] :
( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X4,X1),X3) = huffma1401021291ibling(X0,X4,X3) )
| ~ member(X0,X3,huffma675207370phabet(X0,X4))
| ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ),
inference(cnf_transformation,[],[f134]) ).
tff(f167,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: X0,X1: nat,X4: huffma1450048681e_tree(X0)] :
( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X1,X2,X4),X3) = huffma1401021291ibling(X0,X4,X3) )
| member(X0,X3,huffma675207370phabet(X0,X2))
| ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ),
inference(cnf_transformation,[],[f136]) ).
tff(f168,plain,
! [X0: $tType,X2: nat,X3: X0,X1: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0)] :
( ( huffma1401021291ibling(X0,huffma1146269203erNode(X0,X2,X4,X1),X3) = huffma1401021291ibling(X0,X1,X3) )
| member(X0,X3,huffma675207370phabet(X0,X4))
| ~ ord_less(nat,zero_zero(nat),huffma945805758height(X0,X4)) ),
inference(cnf_transformation,[],[f138]) ).
tff(f206,definition,
~ sP8(huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a)),
introduced(definition,[new_symbols(definition,[sP8])],[inequality_splitting_name_introduction]) ).
tff(f207,plain,
( sP8(huffma1401021291ibling(a1,t_1,a))
| ~ member(a1,a,huffma675207370phabet(a1,t_1)) ),
inference(inequality_splitting,[],[f161,f206]) ).
tff(f208,definition,
~ sP9(huffma1401021291ibling(a1,huffma1146269203erNode(a1,w,t_1,t_2),a)),
introduced(definition,[new_symbols(definition,[sP9])],[inequality_splitting_name_introduction]) ).
tff(f209,plain,
( member(a1,a,huffma675207370phabet(a1,t_1))
| sP9(huffma1401021291ibling(a1,t_2,a)) ),
inference(inequality_splitting,[],[f160,f208]) ).
tff(f226,definition,
( spl13_1
<=> sP9(huffma1401021291ibling(a1,t_2,a)) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
tff(f228,plain,
( sP9(huffma1401021291ibling(a1,t_2,a))
| ~ spl13_1 ),
inference(avatar_component_clause,[],[f226]) ).
tff(f230,definition,
( spl13_2
<=> member(a1,a,huffma675207370phabet(a1,t_1)) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
tff(f231,plain,
( ~ member(a1,a,huffma675207370phabet(a1,t_1))
| spl13_2 ),
inference(avatar_component_clause,[],[f230]) ).
tff(f232,plain,
( member(a1,a,huffma675207370phabet(a1,t_1))
| ~ spl13_2 ),
inference(avatar_component_clause,[],[f230]) ).
tff(f233,plain,
( spl13_1
| spl13_2 ),
inference(avatar_split_clause,[],[f209,f230,f226]) ).
tff(f235,definition,
( spl13_3
<=> sP8(huffma1401021291ibling(a1,t_1,a)) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
tff(f237,plain,
( sP8(huffma1401021291ibling(a1,t_1,a))
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f235]) ).
tff(f238,plain,
( ~ spl13_2
| spl13_3 ),
inference(avatar_split_clause,[],[f207,f235,f230]) ).
tff(f249,definition,
( spl13_6
<=> ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_2)) ),
introduced(definition,[new_symbols(definition,[spl13_6])],[avatar_definition]) ).
tff(f251,plain,
( ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_2))
| ~ spl13_6 ),
inference(avatar_component_clause,[],[f249]) ).
tff(f253,definition,
( spl13_7
<=> ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_1)) ),
introduced(definition,[new_symbols(definition,[spl13_7])],[avatar_definition]) ).
tff(f255,plain,
( ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_1))
| ~ spl13_7 ),
inference(avatar_component_clause,[],[f253]) ).
tff(f256,plain,
( spl13_6
| spl13_7 ),
inference(avatar_split_clause,[],[f158,f253,f249]) ).
tff(f323,plain,
( ~ sP8(huffma1401021291ibling(a1,t_1,a))
| ~ member(a1,a,huffma675207370phabet(a1,t_1))
| ~ ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_1)) ),
inference(superposition,[],[f206,f166]) ).
tff(f324,plain,
( ~ sP8(huffma1401021291ibling(a1,t_1,a))
| ~ member(a1,a,huffma675207370phabet(a1,t_1))
| ~ ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_2)) ),
inference(superposition,[],[f206,f165]) ).
tff(f327,plain,
( ~ member(a1,a,huffma675207370phabet(a1,t_1))
| ~ ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_2))
| ~ spl13_3 ),
inference(forward_subsumption_resolution,[],[f324,f237]) ).
tff(f328,plain,
( ~ member(a1,a,huffma675207370phabet(a1,t_1))
| ~ ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_1))
| ~ spl13_3 ),
inference(forward_subsumption_resolution,[],[f323,f237]) ).
tff(f329,plain,
( ~ ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_2))
| ~ spl13_2
| ~ spl13_3 ),
inference(forward_subsumption_resolution,[],[f327,f232]) ).
tff(f330,plain,
( ~ ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_1))
| ~ spl13_2
| ~ spl13_3 ),
inference(forward_subsumption_resolution,[],[f328,f232]) ).
tff(f331,plain,
( $false
| ~ spl13_2
| ~ spl13_3
| ~ spl13_6 ),
inference(forward_subsumption_resolution,[],[f329,f251]) ).
tff(f332,plain,
( ~ spl13_2
| ~ spl13_3
| ~ spl13_6 ),
inference(avatar_contradiction_clause,[],[f331]) ).
tff(f333,plain,
( ~ spl13_7
| ~ spl13_2
| ~ spl13_3 ),
inference(avatar_split_clause,[],[f330,f235,f230,f253]) ).
tff(f364,plain,
( ~ sP9(huffma1401021291ibling(a1,t_2,a))
| member(a1,a,huffma675207370phabet(a1,t_1))
| ~ ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_1)) ),
inference(superposition,[],[f208,f168]) ).
tff(f365,plain,
( ~ sP9(huffma1401021291ibling(a1,t_2,a))
| member(a1,a,huffma675207370phabet(a1,t_1))
| ~ ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_2)) ),
inference(superposition,[],[f208,f167]) ).
tff(f369,plain,
( member(a1,a,huffma675207370phabet(a1,t_1))
| ~ ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_2))
| ~ spl13_1 ),
inference(forward_subsumption_resolution,[],[f365,f228]) ).
tff(f370,plain,
( ~ ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_2))
| ~ spl13_1
| spl13_2 ),
inference(forward_subsumption_resolution,[],[f369,f231]) ).
tff(f371,plain,
( $false
| ~ spl13_1
| spl13_2
| ~ spl13_6 ),
inference(forward_subsumption_resolution,[],[f370,f251]) ).
tff(f372,plain,
( ~ spl13_1
| spl13_2
| ~ spl13_6 ),
inference(avatar_contradiction_clause,[],[f371]) ).
tff(f373,plain,
( member(a1,a,huffma675207370phabet(a1,t_1))
| ~ ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_1))
| ~ spl13_1 ),
inference(forward_subsumption_resolution,[],[f364,f228]) ).
tff(f374,plain,
( ~ ord_less(nat,zero_zero(nat),huffma945805758height(a1,t_1))
| ~ spl13_1
| spl13_2 ),
inference(forward_subsumption_resolution,[],[f373,f231]) ).
tff(f375,plain,
( $false
| ~ spl13_1
| spl13_2
| ~ spl13_7 ),
inference(forward_subsumption_resolution,[],[f374,f255]) ).
tff(f376,plain,
( ~ spl13_1
| spl13_2
| ~ spl13_7 ),
inference(avatar_contradiction_clause,[],[f375]) ).
cnf(s1,plain,
( spl13_1
| spl13_2 ),
inference(sat_conversion,[],[f233]) ).
cnf(s2,plain,
( ~ spl13_2
| spl13_3 ),
inference(sat_conversion,[],[f238]) ).
cnf(s4,plain,
( spl13_6
| spl13_7 ),
inference(sat_conversion,[],[f256]) ).
cnf(s16,plain,
( ~ spl13_2
| ~ spl13_3
| ~ spl13_6 ),
inference(sat_conversion,[],[f332]) ).
cnf(s17,plain,
( ~ spl13_2
| ~ spl13_3
| ~ spl13_7 ),
inference(sat_conversion,[],[f333]) ).
cnf(s24,plain,
( ~ spl13_1
| spl13_2
| ~ spl13_6 ),
inference(sat_conversion,[],[f372]) ).
cnf(s25,plain,
( ~ spl13_1
| spl13_2
| ~ spl13_7 ),
inference(sat_conversion,[],[f376]) ).
cnf(s26,plain,
( ~ spl13_3
| ~ spl13_2 ),
inference(rat,[],[s4,s16,s17]) ).
cnf(s27,plain,
~ spl13_2,
inference(rat,[],[s26,s2]) ).
cnf(s28,plain,
spl13_1,
inference(rat,[],[s1,s27]) ).
cnf(s29,plain,
~ spl13_6,
inference(rat,[],[s24,s27,s28]) ).
cnf(s30,plain,
~ spl13_7,
inference(rat,[],[s25,s27,s28]) ).
cnf(s31,plain,
$false,
inference(rat,[],[s4,s30,s29]) ).
tff(f377,plain,
$false,
inference(avatar_sat_refutation,[],[s31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWW542_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.26 % Computer : n011.cluster.edu
% 0.11/0.26 % Model : x86_64 x86_64
% 0.11/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.26 % Memory : 8046.5625MB
% 0.11/0.26 % OS : Linux 6.8.0-71-generic
% 0.11/0.26 % CPULimit : 300
% 0.11/0.26 % WCLimit : 300
% 0.11/0.26 % DateTime : Mon Sep 28 14:18:15 UTC 2026
% 0.11/0.26 % CPUTime :
% 0.11/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.26/0.31 Running first-order theorem proving
% 0.26/0.31 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
% 4.19/1.54 % (3409493)Detected formulas, will run a generic FOF schedule.
% 4.19/1.54 % (3409510)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=2187479324:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.19/1.54 % (3409510)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.19/1.54 % (3409508)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=1962557277:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.19/1.54 % (3409513)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3694197719:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.19/1.54 % (3409509)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=2786948116:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.19/1.54 % (3409512)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2212701053:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.19/1.54 % (3409511)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2676993390:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.19/1.54 % (3409511)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.19/1.54 % (3409511)First to succeed.
% 4.19/1.54 % (3409511)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3409493"
% 4.19/1.54 % (3409512)Also succeeded, but the first one will report.
% 4.19/1.54 % (3409514)dis-21_1_sil=8000:lcm=predicate:random_seed=1389602942: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)
% 4.19/1.54 % (3409513)Also succeeded, but the first one will report.
% 4.19/1.54 % (3409514)Instruction limit reached!
% 4.19/1.54 % (3409514)------------------------------
% 4.19/1.54 % (3409514)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.19/1.54 % (3409514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.19/1.54 % (3409514)CaDiCaL version: 2.1.3
% 4.19/1.54 % (3409514)Termination reason: Instruction limit
% 4.19/1.54 % (3409514)Termination phase: Saturation
% 4.19/1.54 % (3409514)Time elapsed: 0.105 s
% 4.19/1.54 % (3409514)Peak memory usage: 89 MB
% 4.19/1.54 % (3409514)Instructions burned: 130 (million)
% 4.19/1.54 % Exception at run slice level
% 4.19/1.54 User error: GNN currently only supports monomorphic FOL.
% 4.19/1.54 % (3409527)lrs+10_1_sil=8000:sp=occurrence:random_seed=15174369:i=285:sd=3:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/285Mi)
% 4.19/1.54 % (3409527)Also succeeded, but the first one will report.
% 4.19/1.54 % (3409528)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2523876523:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 4.19/1.54 % (3409511)Refutation found. Thanks to Tanya!
% 4.19/1.54 % SZS status Theorem for theBenchmark
% 4.19/1.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.29/1.80 % (3409511)------------------------------
% 0.29/1.80 % (3409511)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.29/1.80 % (3409511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.29/1.80 % (3409511)CaDiCaL version: 2.1.3
% 0.29/1.80 % (3409511)Termination reason: Refutation
% 0.29/1.80 % (3409511)Time elapsed: 0.012 s
% 0.29/1.80 % (3409511)Peak memory usage: 89 MB
% 0.29/1.80 % (3409511)Instructions burned: 9 (million)
% 0.29/1.80 % (3409511)------------------------------
% 0.29/1.80 % (3409511)------------------------------
% 0.29/1.80 % (3409493)Success in time 0.687 s
% 0.29/1.80 % Vampire exiting
%------------------------------------------------------------------------------