%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW527_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 01:30:45 PM UTC 2026
% Result : Theorem 4.44s 1.30s
% Output : Refutation 5.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 18
% Syntax : Number of formulae : 110 ( 25 unt; 0 typ; 7 def)
% Number of atoms : 390 ( 123 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 508 ( 228 ~; 224 |; 18 &)
% ( 11 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 9 prp; 0-2 aty)
% Number of functors : 42 ( 42 usr; 8 con; 0-5 aty)
% Number of variables : 210 ( 0 sgn 196 !; 14 ?; 210 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
a: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
huffma1450048681e_tree: $tType > $tType ).
tff(type_def_8,type,
nat: $tType ).
tff(type_def_9,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * fun(X2,X0) ) > fun(X2,X1) ) ).
tff(func_def_1,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * X1 ) > fun(X0,X2) ) ).
tff(func_def_2,type,
combk:
!>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).
tff(func_def_3,type,
combs:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * fun(X0,X1) ) > fun(X0,X2) ) ).
tff(func_def_4,type,
huffma675207370phabet:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > fun(X0,bool) ) ).
tff(func_def_5,type,
huffma1146269203erNode:
!>[X0: $tType] : ( ( nat * huffma1450048681e_tree(X0) * huffma1450048681e_tree(X0) ) > huffma1450048681e_tree(X0) ) ).
tff(func_def_6,type,
huffma2021818691e_Leaf:
!>[X0: $tType] : ( ( nat * X0 ) > huffma1450048681e_tree(X0) ) ).
tff(func_def_7,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_8,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_9,type,
inf_inf:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_10,type,
sup_sup:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_11,type,
bot_bot:
!>[X0: $tType] : X0 ).
tff(func_def_12,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_13,type,
insert:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > fun(X0,bool) ) ).
tff(func_def_14,type,
the_elem:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_15,type,
aa1:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_16,type,
fFalse: bool ).
tff(func_def_17,type,
fNot: fun(bool,bool) ).
tff(func_def_18,type,
fTrue: bool ).
tff(func_def_19,type,
fconj: fun(bool,fun(bool,bool)) ).
tff(func_def_20,type,
fdisj: fun(bool,fun(bool,bool)) ).
tff(func_def_21,type,
fequal:
!>[X0: $tType] : fun(X0,fun(X0,bool)) ).
tff(func_def_22,type,
fimplies: fun(bool,fun(bool,bool)) ).
tff(func_def_23,type,
member:
!>[X0: $tType] : fun(X0,fun(fun(X0,bool),bool)) ).
tff(func_def_24,type,
aa: a ).
tff(func_def_25,type,
ta: huffma1450048681e_tree(a) ).
tff(func_def_26,type,
sK0:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_27,type,
sK1:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > huffma1450048681e_tree(X0) ) ).
tff(func_def_28,type,
sK2:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > huffma1450048681e_tree(X0) ) ).
tff(func_def_29,type,
sK3:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > nat ) ).
tff(func_def_30,type,
sK4:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > X0 ) ).
tff(func_def_31,type,
sK5:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > X0 ) ).
tff(func_def_32,type,
sK6:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_33,type,
sK7:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) ) > X0 ) ).
tff(func_def_34,type,
sK8:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(X0,bool) ) > X0 ) ).
tff(func_def_35,type,
sK9:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_36,type,
sK10:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_37,type,
sK11:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_38,type,
sK12:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_39,type,
sK13:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(pred_def_1,type,
bounded_lattice:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
bot:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
lattice:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
semilattice_inf:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
semilattice_sup:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
bounded_lattice_bot:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
huffma1518433673istent:
!>[X0: $tType] : ( huffma1450048681e_tree(X0) > $o ) ).
tff(pred_def_8,type,
pp: bool > $o ).
tff(f4,axiom,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat] :
( huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1))
<=> ( huffma1518433673istent(X0,X2)
& huffma1518433673istent(X0,X1)
& ( inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) = bot_bot(fun(X0,bool)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_consistent_Osimps_I2_J) ).
tff(f44,axiom,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X2,X1) = inf_inf(fun(X0,bool),X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_Int__commute) ).
tff(f47,axiom,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ( inf_inf(fun(X0,bool),X2,X1) = bot_bot(fun(X0,bool)) )
<=> ! [X3: X0] :
( pp(aa1(fun(X0,bool),bool,aa1(X0,fun(fun(X0,bool),bool),member(X0),X3),X2))
=> ! [X4: X0] :
( pp(aa1(fun(X0,bool),bool,aa1(X0,fun(fun(X0,bool),bool),member(X0),X4),X1))
=> ( X3 != X4 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_disjoint__iff__not__equal) ).
tff(f57,axiom,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( ! [X2: nat,X3: X0] : ( X1 != huffma2021818691e_Leaf(X0,X2,X3) )
=> ~ ! [X2: nat,X4: huffma1450048681e_tree(X0),X5: huffma1450048681e_tree(X0)] : ( X1 != huffma1146269203erNode(X0,X2,X4,X5) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_tree_Oexhaust) ).
tff(f77,axiom,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( pp(aa1(fun(X0,bool),bool,aa1(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
<=> pp(aa1(X0,bool,X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
tff(f138,axiom,
huffma1518433673istent(a,ta),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f139,axiom,
! [X0: nat,X1: a,X2: a] :
( ( ta = huffma2021818691e_Leaf(a,X0,X1) )
=> ( ( aa = X2 )
=> pa ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(f140,axiom,
! [X0: nat,X1: huffma1450048681e_tree(a),X2: huffma1450048681e_tree(a),X3: a] :
( huffma1518433673istent(a,X1)
=> ( huffma1518433673istent(a,X2)
=> ( ( inf_inf(fun(a,bool),huffma675207370phabet(a,X1),huffma675207370phabet(a,X2)) = bot_bot(fun(a,bool)) )
=> ( pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),X3),huffma675207370phabet(a,X1)))
=> ( ~ pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),X3),huffma675207370phabet(a,X2)))
=> ( ( ta = huffma1146269203erNode(a,X0,X1,X2) )
=> ( ( aa = X3 )
=> pa ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
tff(f141,axiom,
! [X0: nat,X1: huffma1450048681e_tree(a),X2: huffma1450048681e_tree(a),X3: a] :
( huffma1518433673istent(a,X1)
=> ( huffma1518433673istent(a,X2)
=> ( ( inf_inf(fun(a,bool),huffma675207370phabet(a,X1),huffma675207370phabet(a,X2)) = bot_bot(fun(a,bool)) )
=> ( ~ pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),X3),huffma675207370phabet(a,X1)))
=> ( pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),X3),huffma675207370phabet(a,X2)))
=> ( ( ta = huffma1146269203erNode(a,X0,X1,X2) )
=> ( ( aa = X3 )
=> pa ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
tff(f142,axiom,
! [X0: nat,X1: huffma1450048681e_tree(a),X2: huffma1450048681e_tree(a),X3: a] :
( huffma1518433673istent(a,X1)
=> ( huffma1518433673istent(a,X2)
=> ( ( inf_inf(fun(a,bool),huffma675207370phabet(a,X1),huffma675207370phabet(a,X2)) = bot_bot(fun(a,bool)) )
=> ( ~ pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),X3),huffma675207370phabet(a,X1)))
=> ( ~ pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),X3),huffma675207370phabet(a,X2)))
=> ( ( ta = huffma1146269203erNode(a,X0,X1,X2) )
=> ( ( aa = X3 )
=> pa ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
tff(f143,conjecture,
pa,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_5) ).
tff(f144,negated_conjecture,
~ pa,
inference(negated_conjecture,[status(cth)],[f143]) ).
tff(f145,plain,
~ pa,
inference(flattening,[],[f144]) ).
tff(f146,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( ! [X2: nat,X3: X0] : ( X1 != huffma2021818691e_Leaf(X0,X2,X3) )
=> ~ ! [X4: nat,X5: huffma1450048681e_tree(X0),X6: huffma1450048681e_tree(X0)] : ( huffma1146269203erNode(X0,X4,X5,X6) != X1 ) ),
inference(rectify,[],[f57]) ).
tff(f152,plain,
! [X0: nat,X1: a,X2: a] :
( pa
| ( aa != X2 )
| ( ta != huffma2021818691e_Leaf(a,X0,X1) ) ),
inference(ennf_transformation,[],[f139]) ).
tff(f153,plain,
! [X0: nat,X1: a,X2: a] :
( pa
| ( aa != X2 )
| ( ta != huffma2021818691e_Leaf(a,X0,X1) ) ),
inference(flattening,[],[f152]) ).
tff(f154,plain,
! [X0: nat,X1: huffma1450048681e_tree(a),X2: huffma1450048681e_tree(a),X3: a] :
( pa
| ( aa != X3 )
| ( ta != huffma1146269203erNode(a,X0,X1,X2) )
| pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),X3),huffma675207370phabet(a,X2)))
| ~ pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),X3),huffma675207370phabet(a,X1)))
| ( inf_inf(fun(a,bool),huffma675207370phabet(a,X1),huffma675207370phabet(a,X2)) != bot_bot(fun(a,bool)) )
| ~ huffma1518433673istent(a,X2)
| ~ huffma1518433673istent(a,X1) ),
inference(ennf_transformation,[],[f140]) ).
tff(f155,plain,
! [X0: nat,X1: huffma1450048681e_tree(a),X2: huffma1450048681e_tree(a),X3: a] :
( pa
| ( aa != X3 )
| ( ta != huffma1146269203erNode(a,X0,X1,X2) )
| pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),X3),huffma675207370phabet(a,X2)))
| ~ pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),X3),huffma675207370phabet(a,X1)))
| ( inf_inf(fun(a,bool),huffma675207370phabet(a,X1),huffma675207370phabet(a,X2)) != bot_bot(fun(a,bool)) )
| ~ huffma1518433673istent(a,X2)
| ~ huffma1518433673istent(a,X1) ),
inference(flattening,[],[f154]) ).
tff(f156,plain,
! [X0: nat,X1: huffma1450048681e_tree(a),X2: huffma1450048681e_tree(a),X3: a] :
( pa
| ( aa != X3 )
| ( ta != huffma1146269203erNode(a,X0,X1,X2) )
| ~ pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),X3),huffma675207370phabet(a,X2)))
| pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),X3),huffma675207370phabet(a,X1)))
| ( inf_inf(fun(a,bool),huffma675207370phabet(a,X1),huffma675207370phabet(a,X2)) != bot_bot(fun(a,bool)) )
| ~ huffma1518433673istent(a,X2)
| ~ huffma1518433673istent(a,X1) ),
inference(ennf_transformation,[],[f141]) ).
tff(f157,plain,
! [X0: nat,X1: huffma1450048681e_tree(a),X2: huffma1450048681e_tree(a),X3: a] :
( pa
| ( aa != X3 )
| ( ta != huffma1146269203erNode(a,X0,X1,X2) )
| ~ pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),X3),huffma675207370phabet(a,X2)))
| pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),X3),huffma675207370phabet(a,X1)))
| ( inf_inf(fun(a,bool),huffma675207370phabet(a,X1),huffma675207370phabet(a,X2)) != bot_bot(fun(a,bool)) )
| ~ huffma1518433673istent(a,X2)
| ~ huffma1518433673istent(a,X1) ),
inference(flattening,[],[f156]) ).
tff(f158,plain,
! [X0: nat,X1: huffma1450048681e_tree(a),X2: huffma1450048681e_tree(a),X3: a] :
( pa
| ( aa != X3 )
| ( ta != huffma1146269203erNode(a,X0,X1,X2) )
| pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),X3),huffma675207370phabet(a,X2)))
| pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),X3),huffma675207370phabet(a,X1)))
| ( inf_inf(fun(a,bool),huffma675207370phabet(a,X1),huffma675207370phabet(a,X2)) != bot_bot(fun(a,bool)) )
| ~ huffma1518433673istent(a,X2)
| ~ huffma1518433673istent(a,X1) ),
inference(ennf_transformation,[],[f142]) ).
tff(f159,plain,
! [X0: nat,X1: huffma1450048681e_tree(a),X2: huffma1450048681e_tree(a),X3: a] :
( pa
| ( aa != X3 )
| ( ta != huffma1146269203erNode(a,X0,X1,X2) )
| pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),X3),huffma675207370phabet(a,X2)))
| pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),X3),huffma675207370phabet(a,X1)))
| ( inf_inf(fun(a,bool),huffma675207370phabet(a,X1),huffma675207370phabet(a,X2)) != bot_bot(fun(a,bool)) )
| ~ huffma1518433673istent(a,X2)
| ~ huffma1518433673istent(a,X1) ),
inference(flattening,[],[f158]) ).
tff(f160,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( ? [X4: nat,X5: huffma1450048681e_tree(X0),X6: huffma1450048681e_tree(X0)] : ( huffma1146269203erNode(X0,X4,X5,X6) = X1 )
| ? [X2: nat,X3: X0] : ( huffma2021818691e_Leaf(X0,X2,X3) = X1 ) ),
inference(ennf_transformation,[],[f146]) ).
tff(f169,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ( inf_inf(fun(X0,bool),X2,X1) = bot_bot(fun(X0,bool)) )
<=> ! [X3: X0] :
( ! [X4: X0] :
( ( X3 != X4 )
| ~ pp(aa1(fun(X0,bool),bool,aa1(X0,fun(fun(X0,bool),bool),member(X0),X4),X1)) )
| ~ pp(aa1(fun(X0,bool),bool,aa1(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)) ) ),
inference(ennf_transformation,[],[f47]) ).
tff(f177,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat] :
( ( huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1))
| ~ huffma1518433673istent(X0,X2)
| ~ huffma1518433673istent(X0,X1)
| ( inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) != bot_bot(fun(X0,bool)) ) )
& ( ( huffma1518433673istent(X0,X2)
& huffma1518433673istent(X0,X1)
& ( inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) = bot_bot(fun(X0,bool)) ) )
| ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1)) ) ),
inference(nnf_transformation,[],[f4]) ).
tff(f178,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0),X2: huffma1450048681e_tree(X0),X3: nat] :
( ( huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1))
| ~ huffma1518433673istent(X0,X2)
| ~ huffma1518433673istent(X0,X1)
| ( inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) != bot_bot(fun(X0,bool)) ) )
& ( ( huffma1518433673istent(X0,X2)
& huffma1518433673istent(X0,X1)
& ( inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) = bot_bot(fun(X0,bool)) ) )
| ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1)) ) ),
inference(flattening,[],[f177]) ).
tff(f179,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( ? [X2: nat,X3: huffma1450048681e_tree(X0),X4: huffma1450048681e_tree(X0)] : ( huffma1146269203erNode(X0,X2,X3,X4) = X1 )
| ? [X5: nat,X6: X0] : ( huffma2021818691e_Leaf(X0,X5,X6) = X1 ) ),
inference(rectify,[],[f160]) ).
tff(f180,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( ( huffma1146269203erNode(X0,sK0(X0,X1),sK1(X0,X1),sK2(X0,X1)) = X1 )
| ( huffma2021818691e_Leaf(X0,sK3(X0,X1),sK4(X0,X1)) = X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1)),skolemize(X4,sK2(X0,X1)),skolemize(X5,sK3(X0,X1)),skolemize(X6,sK4(X0,X1))],[f179]) ).
tff(f190,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ( ( inf_inf(fun(X0,bool),X2,X1) = bot_bot(fun(X0,bool)) )
| ? [X3: X0] :
( ? [X4: X0] :
( ( X3 = X4 )
& pp(aa1(fun(X0,bool),bool,aa1(X0,fun(fun(X0,bool),bool),member(X0),X4),X1)) )
& pp(aa1(fun(X0,bool),bool,aa1(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)) ) )
& ( ! [X3: X0] :
( ! [X4: X0] :
( ( X3 != X4 )
| ~ pp(aa1(fun(X0,bool),bool,aa1(X0,fun(fun(X0,bool),bool),member(X0),X4),X1)) )
| ~ pp(aa1(fun(X0,bool),bool,aa1(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)) )
| ( bot_bot(fun(X0,bool)) != inf_inf(fun(X0,bool),X2,X1) ) ) ),
inference(nnf_transformation,[],[f169]) ).
tff(f191,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ( ( inf_inf(fun(X0,bool),X2,X1) = bot_bot(fun(X0,bool)) )
| ? [X3: X0] :
( ? [X4: X0] :
( ( X3 = X4 )
& pp(aa1(fun(X0,bool),bool,aa1(X0,fun(fun(X0,bool),bool),member(X0),X4),X1)) )
& pp(aa1(fun(X0,bool),bool,aa1(X0,fun(fun(X0,bool),bool),member(X0),X3),X2)) ) )
& ( ! [X5: X0] :
( ! [X6: X0] :
( ( X5 != X6 )
| ~ pp(aa1(fun(X0,bool),bool,aa1(X0,fun(fun(X0,bool),bool),member(X0),X6),X1)) )
| ~ pp(aa1(fun(X0,bool),bool,aa1(X0,fun(fun(X0,bool),bool),member(X0),X5),X2)) )
| ( bot_bot(fun(X0,bool)) != inf_inf(fun(X0,bool),X2,X1) ) ) ),
inference(rectify,[],[f190]) ).
tff(f192,plain,
! [X0: $tType,X1: fun(X0,bool),X2: fun(X0,bool)] :
( ( ( inf_inf(fun(X0,bool),X2,X1) = bot_bot(fun(X0,bool)) )
| ( ( sK7(X0,X1,X2) = sK8(X0,X1,X2) )
& pp(aa1(fun(X0,bool),bool,aa1(X0,fun(fun(X0,bool),bool),member(X0),sK8(X0,X1,X2)),X1))
& pp(aa1(fun(X0,bool),bool,aa1(X0,fun(fun(X0,bool),bool),member(X0),sK7(X0,X1,X2)),X2)) ) )
& ( ! [X5: X0] :
( ! [X6: X0] :
( ( X5 != X6 )
| ~ pp(aa1(fun(X0,bool),bool,aa1(X0,fun(fun(X0,bool),bool),member(X0),X6),X1)) )
| ~ pp(aa1(fun(X0,bool),bool,aa1(X0,fun(fun(X0,bool),bool),member(X0),X5),X2)) )
| ( bot_bot(fun(X0,bool)) != inf_inf(fun(X0,bool),X2,X1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X3,sK7(X0,X1,X2)),skolemize(X4,sK8(X0,X1,X2))],[f191]) ).
tff(f207,plain,
! [X0: $tType,X1: fun(X0,bool),X2: X0] :
( ( pp(aa1(fun(X0,bool),bool,aa1(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ pp(aa1(X0,bool,X1,X2)) )
& ( pp(aa1(X0,bool,X1,X2))
| ~ pp(aa1(fun(X0,bool),bool,aa1(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ) ),
inference(nnf_transformation,[],[f77]) ).
tff(f210,plain,
huffma1518433673istent(a,ta),
inference(cnf_transformation,[],[f138]) ).
tff(f211,plain,
! [X2: a,X0: nat,X1: a] :
( pa
| ( aa != X2 )
| ( ta != huffma2021818691e_Leaf(a,X0,X1) ) ),
inference(cnf_transformation,[],[f153]) ).
tff(f212,plain,
! [X2: huffma1450048681e_tree(a),X3: a,X0: nat,X1: huffma1450048681e_tree(a)] :
( pa
| ( aa != X3 )
| ( ta != huffma1146269203erNode(a,X0,X1,X2) )
| pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),X3),huffma675207370phabet(a,X2)))
| ~ pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),X3),huffma675207370phabet(a,X1)))
| ( inf_inf(fun(a,bool),huffma675207370phabet(a,X1),huffma675207370phabet(a,X2)) != bot_bot(fun(a,bool)) )
| ~ huffma1518433673istent(a,X2)
| ~ huffma1518433673istent(a,X1) ),
inference(cnf_transformation,[],[f155]) ).
tff(f213,plain,
! [X2: huffma1450048681e_tree(a),X3: a,X0: nat,X1: huffma1450048681e_tree(a)] :
( pa
| ( aa != X3 )
| ( ta != huffma1146269203erNode(a,X0,X1,X2) )
| ~ pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),X3),huffma675207370phabet(a,X2)))
| pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),X3),huffma675207370phabet(a,X1)))
| ( inf_inf(fun(a,bool),huffma675207370phabet(a,X1),huffma675207370phabet(a,X2)) != bot_bot(fun(a,bool)) )
| ~ huffma1518433673istent(a,X2)
| ~ huffma1518433673istent(a,X1) ),
inference(cnf_transformation,[],[f157]) ).
tff(f214,plain,
! [X2: huffma1450048681e_tree(a),X3: a,X0: nat,X1: huffma1450048681e_tree(a)] :
( pa
| ( aa != X3 )
| ( ta != huffma1146269203erNode(a,X0,X1,X2) )
| pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),X3),huffma675207370phabet(a,X2)))
| pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),X3),huffma675207370phabet(a,X1)))
| ( inf_inf(fun(a,bool),huffma675207370phabet(a,X1),huffma675207370phabet(a,X2)) != bot_bot(fun(a,bool)) )
| ~ huffma1518433673istent(a,X2)
| ~ huffma1518433673istent(a,X1) ),
inference(cnf_transformation,[],[f159]) ).
tff(f215,plain,
~ pa,
inference(cnf_transformation,[],[f145]) ).
tff(f216,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] :
( ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1))
| ( inf_inf(fun(X0,bool),huffma675207370phabet(X0,X2),huffma675207370phabet(X0,X1)) = bot_bot(fun(X0,bool)) ) ),
inference(cnf_transformation,[],[f178]) ).
tff(f217,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] :
( ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1))
| huffma1518433673istent(X0,X1) ),
inference(cnf_transformation,[],[f178]) ).
tff(f218,plain,
! [X0: $tType,X2: huffma1450048681e_tree(X0),X3: nat,X1: huffma1450048681e_tree(X0)] :
( ~ huffma1518433673istent(X0,huffma1146269203erNode(X0,X3,X2,X1))
| huffma1518433673istent(X0,X2) ),
inference(cnf_transformation,[],[f178]) ).
tff(f223,plain,
! [X0: $tType,X1: huffma1450048681e_tree(X0)] :
( ( huffma2021818691e_Leaf(X0,sK3(X0,X1),sK4(X0,X1)) = X1 )
| ( huffma1146269203erNode(X0,sK0(X0,X1),sK1(X0,X1),sK2(X0,X1)) = X1 ) ),
inference(cnf_transformation,[],[f180]) ).
tff(f239,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool)] : ( inf_inf(fun(X0,bool),X2,X1) = inf_inf(fun(X0,bool),X1,X2) ),
inference(cnf_transformation,[],[f44]) ).
tff(f264,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool),X6: X0,X5: X0] :
( ( X5 != X6 )
| ~ pp(aa1(fun(X0,bool),bool,aa1(X0,fun(fun(X0,bool),bool),member(X0),X6),X1))
| ~ pp(aa1(fun(X0,bool),bool,aa1(X0,fun(fun(X0,bool),bool),member(X0),X5),X2))
| ( bot_bot(fun(X0,bool)) != inf_inf(fun(X0,bool),X2,X1) ) ),
inference(cnf_transformation,[],[f192]) ).
tff(f283,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa1(X0,bool,X1,X2))
| ~ pp(aa1(fun(X0,bool),bool,aa1(X0,fun(fun(X0,bool),bool),member(X0),X2),X1)) ),
inference(cnf_transformation,[],[f207]) ).
tff(f284,plain,
! [X0: $tType,X2: X0,X1: fun(X0,bool)] :
( pp(aa1(fun(X0,bool),bool,aa1(X0,fun(fun(X0,bool),bool),member(X0),X2),X1))
| ~ pp(aa1(X0,bool,X1,X2)) ),
inference(cnf_transformation,[],[f207]) ).
tff(f293,plain,
! [X0: nat,X1: a] :
( pa
| ( ta != huffma2021818691e_Leaf(a,X0,X1) ) ),
inference(equality_resolution,[],[f211]) ).
tff(f294,plain,
! [X2: huffma1450048681e_tree(a),X0: nat,X1: huffma1450048681e_tree(a)] :
( pa
| ( ta != huffma1146269203erNode(a,X0,X1,X2) )
| pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),aa),huffma675207370phabet(a,X2)))
| ~ pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),aa),huffma675207370phabet(a,X1)))
| ( inf_inf(fun(a,bool),huffma675207370phabet(a,X1),huffma675207370phabet(a,X2)) != bot_bot(fun(a,bool)) )
| ~ huffma1518433673istent(a,X2)
| ~ huffma1518433673istent(a,X1) ),
inference(equality_resolution,[],[f212]) ).
tff(f295,plain,
! [X2: huffma1450048681e_tree(a),X0: nat,X1: huffma1450048681e_tree(a)] :
( pa
| ( ta != huffma1146269203erNode(a,X0,X1,X2) )
| ~ pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),aa),huffma675207370phabet(a,X2)))
| pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),aa),huffma675207370phabet(a,X1)))
| ( inf_inf(fun(a,bool),huffma675207370phabet(a,X1),huffma675207370phabet(a,X2)) != bot_bot(fun(a,bool)) )
| ~ huffma1518433673istent(a,X2)
| ~ huffma1518433673istent(a,X1) ),
inference(equality_resolution,[],[f213]) ).
tff(f296,plain,
! [X2: huffma1450048681e_tree(a),X0: nat,X1: huffma1450048681e_tree(a)] :
( pa
| ( ta != huffma1146269203erNode(a,X0,X1,X2) )
| pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),aa),huffma675207370phabet(a,X2)))
| pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),aa),huffma675207370phabet(a,X1)))
| ( inf_inf(fun(a,bool),huffma675207370phabet(a,X1),huffma675207370phabet(a,X2)) != bot_bot(fun(a,bool)) )
| ~ huffma1518433673istent(a,X2)
| ~ huffma1518433673istent(a,X1) ),
inference(equality_resolution,[],[f214]) ).
tff(f307,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(X0,bool),X6: X0] :
( ~ pp(aa1(fun(X0,bool),bool,aa1(X0,fun(fun(X0,bool),bool),member(X0),X6),X1))
| ~ pp(aa1(fun(X0,bool),bool,aa1(X0,fun(fun(X0,bool),bool),member(X0),X6),X2))
| ( bot_bot(fun(X0,bool)) != inf_inf(fun(X0,bool),X2,X1) ) ),
inference(equality_resolution,[],[f264]) ).
tff(f311,plain,
! [X2: huffma1450048681e_tree(a),X0: nat,X1: huffma1450048681e_tree(a)] :
( ( inf_inf(fun(a,bool),huffma675207370phabet(a,X1),huffma675207370phabet(a,X2)) != bot_bot(fun(a,bool)) )
| pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),aa),huffma675207370phabet(a,X2)))
| pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),aa),huffma675207370phabet(a,X1)))
| ( ta != huffma1146269203erNode(a,X0,X1,X2) )
| ~ huffma1518433673istent(a,X2)
| ~ huffma1518433673istent(a,X1) ),
inference(forward_subsumption_resolution,[],[f296,f215]) ).
tff(f312,plain,
! [X2: huffma1450048681e_tree(a),X0: nat,X1: huffma1450048681e_tree(a)] :
( pa
| ( ta != huffma1146269203erNode(a,X0,X1,X2) )
| ~ pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),aa),huffma675207370phabet(a,X2)))
| ( inf_inf(fun(a,bool),huffma675207370phabet(a,X1),huffma675207370phabet(a,X2)) != bot_bot(fun(a,bool)) )
| ~ huffma1518433673istent(a,X2)
| ~ huffma1518433673istent(a,X1) ),
inference(forward_subsumption_resolution,[],[f295,f307]) ).
tff(f313,plain,
! [X2: huffma1450048681e_tree(a),X0: nat,X1: huffma1450048681e_tree(a)] :
( pa
| ( ta != huffma1146269203erNode(a,X0,X1,X2) )
| ~ pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),aa),huffma675207370phabet(a,X1)))
| ( inf_inf(fun(a,bool),huffma675207370phabet(a,X1),huffma675207370phabet(a,X2)) != bot_bot(fun(a,bool)) )
| ~ huffma1518433673istent(a,X2)
| ~ huffma1518433673istent(a,X1) ),
inference(forward_subsumption_resolution,[],[f294,f307]) ).
tff(f314,plain,
! [X0: nat,X1: a] : ( ta != huffma2021818691e_Leaf(a,X0,X1) ),
inference(forward_subsumption_resolution,[],[f293,f215]) ).
tff(f315,plain,
! [X2: huffma1450048681e_tree(a),X0: nat,X1: huffma1450048681e_tree(a)] :
( ~ pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),aa),huffma675207370phabet(a,X2)))
| ( ta != huffma1146269203erNode(a,X0,X1,X2) )
| ( inf_inf(fun(a,bool),huffma675207370phabet(a,X1),huffma675207370phabet(a,X2)) != bot_bot(fun(a,bool)) )
| ~ huffma1518433673istent(a,X2)
| ~ huffma1518433673istent(a,X1) ),
inference(forward_subsumption_resolution,[],[f312,f215]) ).
tff(f316,plain,
! [X2: huffma1450048681e_tree(a),X0: nat,X1: huffma1450048681e_tree(a)] :
( ~ pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),aa),huffma675207370phabet(a,X1)))
| ( ta != huffma1146269203erNode(a,X0,X1,X2) )
| ( inf_inf(fun(a,bool),huffma675207370phabet(a,X1),huffma675207370phabet(a,X2)) != bot_bot(fun(a,bool)) )
| ~ huffma1518433673istent(a,X2)
| ~ huffma1518433673istent(a,X1) ),
inference(forward_subsumption_resolution,[],[f313,f215]) ).
tff(f323,plain,
! [X2: nat,X0: huffma1450048681e_tree(a),X1: huffma1450048681e_tree(a)] :
( ( ta != huffma1146269203erNode(a,X2,X1,X0) )
| pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),aa),huffma675207370phabet(a,X0)))
| pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),aa),huffma675207370phabet(a,X1)))
| ( bot_bot(fun(a,bool)) != inf_inf(fun(a,bool),huffma675207370phabet(a,X0),huffma675207370phabet(a,X1)) )
| ~ huffma1518433673istent(a,X0)
| ~ huffma1518433673istent(a,X1) ),
inference(superposition,[],[f311,f239]) ).
tff(f462,plain,
! [X2: huffma1450048681e_tree(a),X0: huffma1450048681e_tree(a),X1: nat] :
( ( ta != huffma1146269203erNode(a,X1,X0,X2) )
| ~ pp(aa1(a,bool,huffma675207370phabet(a,X0),aa))
| ( bot_bot(fun(a,bool)) != inf_inf(fun(a,bool),huffma675207370phabet(a,X0),huffma675207370phabet(a,X2)) )
| ~ huffma1518433673istent(a,X2)
| ~ huffma1518433673istent(a,X0) ),
inference(resolution,[],[f284,f316]) ).
tff(f463,plain,
! [X2: huffma1450048681e_tree(a),X0: huffma1450048681e_tree(a),X1: nat] :
( ( ta != huffma1146269203erNode(a,X1,X2,X0) )
| ~ pp(aa1(a,bool,huffma675207370phabet(a,X0),aa))
| ( bot_bot(fun(a,bool)) != inf_inf(fun(a,bool),huffma675207370phabet(a,X2),huffma675207370phabet(a,X0)) )
| ~ huffma1518433673istent(a,X0)
| ~ huffma1518433673istent(a,X2) ),
inference(resolution,[],[f284,f315]) ).
tff(f483,plain,
! [X0: huffma1450048681e_tree(a)] :
( ( ta != X0 )
| ( huffma1146269203erNode(a,sK0(a,X0),sK1(a,X0),sK2(a,X0)) = X0 ) ),
inference(superposition,[],[f314,f223]) ).
tff(f505,plain,
ta = huffma1146269203erNode(a,sK0(a,ta),sK1(a,ta),sK2(a,ta)),
inference(equality_resolution,[],[f483]) ).
tff(f556,plain,
( ( ta != ta )
| pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),aa),huffma675207370phabet(a,sK2(a,ta))))
| pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),aa),huffma675207370phabet(a,sK1(a,ta))))
| ( bot_bot(fun(a,bool)) != inf_inf(fun(a,bool),huffma675207370phabet(a,sK2(a,ta)),huffma675207370phabet(a,sK1(a,ta))) )
| ~ huffma1518433673istent(a,sK2(a,ta))
| ~ huffma1518433673istent(a,sK1(a,ta)) ),
inference(superposition,[],[f323,f505]) ).
tff(f568,plain,
( ( ta != ta )
| ~ pp(aa1(a,bool,huffma675207370phabet(a,sK1(a,ta)),aa))
| ( bot_bot(fun(a,bool)) != inf_inf(fun(a,bool),huffma675207370phabet(a,sK1(a,ta)),huffma675207370phabet(a,sK2(a,ta))) )
| ~ huffma1518433673istent(a,sK2(a,ta))
| ~ huffma1518433673istent(a,sK1(a,ta)) ),
inference(superposition,[],[f462,f505]) ).
tff(f569,plain,
( ( ta != ta )
| ~ pp(aa1(a,bool,huffma675207370phabet(a,sK2(a,ta)),aa))
| ( bot_bot(fun(a,bool)) != inf_inf(fun(a,bool),huffma675207370phabet(a,sK1(a,ta)),huffma675207370phabet(a,sK2(a,ta))) )
| ~ huffma1518433673istent(a,sK2(a,ta))
| ~ huffma1518433673istent(a,sK1(a,ta)) ),
inference(superposition,[],[f463,f505]) ).
tff(f570,plain,
( ~ huffma1518433673istent(a,ta)
| ( bot_bot(fun(a,bool)) = inf_inf(fun(a,bool),huffma675207370phabet(a,sK1(a,ta)),huffma675207370phabet(a,sK2(a,ta))) ) ),
inference(superposition,[],[f216,f505]) ).
tff(f571,plain,
( ~ huffma1518433673istent(a,ta)
| huffma1518433673istent(a,sK2(a,ta)) ),
inference(superposition,[],[f217,f505]) ).
tff(f572,plain,
( ~ huffma1518433673istent(a,ta)
| huffma1518433673istent(a,sK1(a,ta)) ),
inference(superposition,[],[f218,f505]) ).
tff(f580,plain,
( ~ pp(aa1(a,bool,huffma675207370phabet(a,sK2(a,ta)),aa))
| ( bot_bot(fun(a,bool)) != inf_inf(fun(a,bool),huffma675207370phabet(a,sK1(a,ta)),huffma675207370phabet(a,sK2(a,ta))) )
| ~ huffma1518433673istent(a,sK2(a,ta))
| ~ huffma1518433673istent(a,sK1(a,ta)) ),
inference(trivial_inequality_removal,[],[f569]) ).
tff(f581,plain,
( ~ pp(aa1(a,bool,huffma675207370phabet(a,sK1(a,ta)),aa))
| ( bot_bot(fun(a,bool)) != inf_inf(fun(a,bool),huffma675207370phabet(a,sK1(a,ta)),huffma675207370phabet(a,sK2(a,ta))) )
| ~ huffma1518433673istent(a,sK2(a,ta))
| ~ huffma1518433673istent(a,sK1(a,ta)) ),
inference(trivial_inequality_removal,[],[f568]) ).
tff(f588,plain,
( pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),aa),huffma675207370phabet(a,sK2(a,ta))))
| pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),aa),huffma675207370phabet(a,sK1(a,ta))))
| ( bot_bot(fun(a,bool)) != inf_inf(fun(a,bool),huffma675207370phabet(a,sK2(a,ta)),huffma675207370phabet(a,sK1(a,ta))) )
| ~ huffma1518433673istent(a,sK2(a,ta))
| ~ huffma1518433673istent(a,sK1(a,ta)) ),
inference(trivial_inequality_removal,[],[f556]) ).
tff(f589,plain,
huffma1518433673istent(a,sK1(a,ta)),
inference(forward_subsumption_resolution,[],[f572,f210]) ).
tff(f590,plain,
huffma1518433673istent(a,sK2(a,ta)),
inference(forward_subsumption_resolution,[],[f571,f210]) ).
tff(f591,plain,
bot_bot(fun(a,bool)) = inf_inf(fun(a,bool),huffma675207370phabet(a,sK1(a,ta)),huffma675207370phabet(a,sK2(a,ta))),
inference(forward_subsumption_resolution,[],[f570,f210]) ).
tff(f593,definition,
( spl14_1
<=> huffma1518433673istent(a,sK1(a,ta)) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
tff(f597,definition,
( spl14_2
<=> huffma1518433673istent(a,sK2(a,ta)) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
tff(f601,definition,
( spl14_3
<=> ( bot_bot(fun(a,bool)) = inf_inf(fun(a,bool),huffma675207370phabet(a,sK1(a,ta)),huffma675207370phabet(a,sK2(a,ta))) ) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
tff(f605,definition,
( spl14_4
<=> pp(aa1(a,bool,huffma675207370phabet(a,sK2(a,ta)),aa)) ),
introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition]) ).
tff(f607,plain,
( ~ pp(aa1(a,bool,huffma675207370phabet(a,sK2(a,ta)),aa))
| spl14_4 ),
inference(avatar_component_clause,[],[f605]) ).
tff(f608,plain,
( ~ spl14_1
| ~ spl14_2
| ~ spl14_3
| ~ spl14_4 ),
inference(avatar_split_clause,[],[f580,f605,f601,f597,f593]) ).
tff(f610,definition,
( spl14_5
<=> pp(aa1(a,bool,huffma675207370phabet(a,sK1(a,ta)),aa)) ),
introduced(definition,[new_symbols(definition,[spl14_5])],[avatar_definition]) ).
tff(f612,plain,
( ~ pp(aa1(a,bool,huffma675207370phabet(a,sK1(a,ta)),aa))
| spl14_5 ),
inference(avatar_component_clause,[],[f610]) ).
tff(f613,plain,
( ~ spl14_1
| ~ spl14_2
| ~ spl14_3
| ~ spl14_5 ),
inference(avatar_split_clause,[],[f581,f610,f601,f597,f593]) ).
tff(f645,plain,
( ( bot_bot(fun(a,bool)) != inf_inf(fun(a,bool),huffma675207370phabet(a,sK1(a,ta)),huffma675207370phabet(a,sK2(a,ta))) )
| pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),aa),huffma675207370phabet(a,sK2(a,ta))))
| pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),aa),huffma675207370phabet(a,sK1(a,ta))))
| ~ huffma1518433673istent(a,sK2(a,ta))
| ~ huffma1518433673istent(a,sK1(a,ta)) ),
inference(forward_demodulation,[],[f588,f239]) ).
tff(f646,plain,
spl14_1,
inference(avatar_split_clause,[],[f589,f593]) ).
tff(f647,plain,
spl14_2,
inference(avatar_split_clause,[],[f590,f597]) ).
tff(f648,plain,
spl14_3,
inference(avatar_split_clause,[],[f591,f601]) ).
tff(f670,definition,
( spl14_17
<=> pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),aa),huffma675207370phabet(a,sK1(a,ta)))) ),
introduced(definition,[new_symbols(definition,[spl14_17])],[avatar_definition]) ).
tff(f672,plain,
( pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),aa),huffma675207370phabet(a,sK1(a,ta))))
| ~ spl14_17 ),
inference(avatar_component_clause,[],[f670]) ).
tff(f674,definition,
( spl14_18
<=> pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),aa),huffma675207370phabet(a,sK2(a,ta)))) ),
introduced(definition,[new_symbols(definition,[spl14_18])],[avatar_definition]) ).
tff(f677,plain,
( ~ spl14_1
| ~ spl14_2
| spl14_17
| spl14_18
| ~ spl14_3 ),
inference(avatar_split_clause,[],[f645,f601,f674,f670,f597,f593]) ).
tff(f748,plain,
( ~ pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),aa),huffma675207370phabet(a,sK2(a,ta))))
| spl14_4 ),
inference(resolution,[],[f607,f283]) ).
tff(f751,plain,
( ~ spl14_18
| spl14_4 ),
inference(avatar_split_clause,[],[f748,f605,f674]) ).
tff(f759,plain,
( ~ pp(aa1(fun(a,bool),bool,aa1(a,fun(fun(a,bool),bool),member(a),aa),huffma675207370phabet(a,sK1(a,ta))))
| spl14_5 ),
inference(resolution,[],[f612,f283]) ).
tff(f762,plain,
( $false
| spl14_5
| ~ spl14_17 ),
inference(forward_subsumption_resolution,[],[f759,f672]) ).
tff(f763,plain,
( spl14_5
| ~ spl14_17 ),
inference(avatar_contradiction_clause,[],[f762]) ).
cnf(s1,plain,
( ~ spl14_1
| ~ spl14_2
| ~ spl14_3
| ~ spl14_4 ),
inference(sat_conversion,[],[f608]) ).
cnf(s2,plain,
( ~ spl14_1
| ~ spl14_2
| ~ spl14_3
| ~ spl14_5 ),
inference(sat_conversion,[],[f613]) ).
cnf(s9,plain,
spl14_1,
inference(sat_conversion,[],[f646]) ).
cnf(s10,plain,
spl14_2,
inference(sat_conversion,[],[f647]) ).
cnf(s11,plain,
spl14_3,
inference(sat_conversion,[],[f648]) ).
cnf(s15,plain,
( ~ spl14_1
| ~ spl14_2
| ~ spl14_3
| spl14_17
| spl14_18 ),
inference(sat_conversion,[],[f677]) ).
cnf(s16,plain,
( spl14_4
| ~ spl14_18 ),
inference(sat_conversion,[],[f751]) ).
cnf(s17,plain,
( spl14_5
| ~ spl14_17 ),
inference(sat_conversion,[],[f763]) ).
cnf(s24,plain,
~ spl14_5,
inference(rat,[],[s2,s11,s10,s9]) ).
cnf(s25,plain,
~ spl14_17,
inference(rat,[],[s17,s24]) ).
cnf(s26,plain,
spl14_18,
inference(rat,[],[s15,s9,s10,s11,s25]) ).
cnf(s27,plain,
spl14_4,
inference(rat,[],[s16,s26]) ).
cnf(s28,plain,
$false,
inference(rat,[],[s1,s27,s11,s10,s9]) ).
tff(f764,plain,
$false,
inference(avatar_sat_refutation,[],[s28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW527_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n014.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 14:17:01 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 4.44/1.30 % (1798335)Detected formulas, will run a generic FOF schedule.
% 4.44/1.30 % (1798343)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3589463103:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.44/1.30 % (1798343)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.44/1.30 % (1798343)Instruction limit reached!
% 4.44/1.30 % (1798343)------------------------------
% 4.44/1.30 % (1798343)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.44/1.30 % (1798343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.44/1.30 % (1798343)CaDiCaL version: 2.1.3
% 4.44/1.30 % (1798343)Termination reason: Instruction limit
% 4.44/1.30 % (1798343)Termination phase: Saturation
% 4.44/1.30 % (1798343)Time elapsed: 0.036 s
% 4.44/1.30 % (1798343)Peak memory usage: 89 MB
% 4.44/1.30 % (1798343)Instructions burned: 111 (million)
% 4.44/1.30 % (1798341)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=533340014:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.44/1.30 % (1798342)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=1010480031:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.44/1.30 % (1798340)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=693317511:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.44/1.30 % (1798345)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2424709892:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.44/1.30 % (1798344)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=460592320:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.44/1.30 % (1798346)dis-21_1_sil=8000:lcm=predicate:random_seed=2138268055: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)
% 4.44/1.30 % (1798342)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 4.44/1.30 % (1798344)Instruction limit reached!
% 4.44/1.30 % (1798344)------------------------------
% 4.44/1.30 % (1798344)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.44/1.30 % (1798344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.44/1.30 % (1798344)CaDiCaL version: 2.1.3
% 4.44/1.30 % (1798344)Termination reason: Instruction limit
% 4.44/1.30 % (1798344)Termination phase: Saturation
% 4.44/1.30 % (1798344)Time elapsed: 0.069 s
% 4.44/1.30 % (1798344)Peak memory usage: 89 MB
% 4.44/1.30 % (1798344)Instructions burned: 119 (million)
% 4.44/1.30 % (1798346)Instruction limit reached!
% 4.44/1.30 % (1798346)------------------------------
% 4.44/1.30 % (1798346)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.44/1.30 % (1798346)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.44/1.30 % (1798346)CaDiCaL version: 2.1.3
% 4.44/1.30 % (1798346)Termination reason: Instruction limit
% 4.44/1.30 % (1798346)Termination phase: Saturation
% 4.44/1.30 % (1798346)Time elapsed: 0.073 s
% 4.44/1.30 % (1798346)Peak memory usage: 89 MB
% 4.44/1.30 % (1798346)Instructions burned: 130 (million)
% 4.44/1.30 % (1798354)lrs+10_1_sil=8000:sp=occurrence:random_seed=2736356826:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.44/1.30 % (1798345)Instruction limit reached!
% 4.44/1.30 % (1798345)------------------------------
% 4.44/1.30 % (1798345)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.44/1.30 % (1798345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.44/1.30 % (1798345)CaDiCaL version: 2.1.3
% 4.44/1.30 % (1798345)Termination reason: Instruction limit
% 4.44/1.30 % (1798345)Termination phase: Saturation
% 4.44/1.30 % (1798345)Time elapsed: 0.089 s
% 4.44/1.30 % (1798345)Peak memory usage: 89 MB
% 4.44/1.30 % (1798345)Instructions burned: 139 (million)
% 4.44/1.30 % (1798354)Instruction limit reached!
% 4.44/1.30 % (1798354)------------------------------
% 4.44/1.30 % (1798354)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.44/1.30 % (1798354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.44/1.30 % (1798354)CaDiCaL version: 2.1.3
% 4.44/1.30 % (1798354)Termination reason: Instruction limit
% 4.44/1.30 % (1798354)Termination phase: Saturation
% 4.44/1.30 % (1798354)Time elapsed: 0.091 s
% 4.44/1.30 % (1798354)Peak memory usage: 91 MB
% 4.44/1.30 % (1798354)Instructions burned: 285 (million)
% 4.44/1.30 % (1798356)lrs+1011_1_sil=32000:sp=occurrence:random_seed=832947626:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.44/1.30 % (1798355)lrs+10_1_sil=32000:urr=on:br=off:random_seed=458810019:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.44/1.30 % (1798355)Refutation not found, incomplete strategy
% 4.44/1.30 % (1798355)------------------------------
% 4.44/1.30 % (1798355)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.44/1.30 % (1798355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.44/1.30 % (1798355)CaDiCaL version: 2.1.3
% 4.44/1.30 % (1798355)Termination reason: Refutation not found, incomplete strategy
% 4.44/1.30 % (1798355)Time elapsed: 0.003 s
% 4.44/1.30 % (1798355)Peak memory usage: 89 MB
% 4.44/1.30 % (1798355)Instructions burned: 3 (million)
% 4.44/1.30 % (1798358)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=4109410250:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.44/1.30 % (1798356)First to succeed.
% 4.44/1.30 % (1798356)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1798335"
% 4.44/1.30 % (1798359)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3280800441:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 4.44/1.30 % (1798359)Also succeeded, but the first one will report.
% 4.44/1.30 % (1798358)Instruction limit reached!
% 4.44/1.30 % (1798358)------------------------------
% 4.44/1.30 % (1798358)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.44/1.30 % (1798358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.44/1.30 % (1798358)CaDiCaL version: 2.1.3
% 4.44/1.30 % (1798358)Termination reason: Instruction limit
% 4.44/1.30 % (1798358)Termination phase: Saturation
% 4.44/1.30 % (1798358)Time elapsed: 0.130 s
% 4.44/1.30 % (1798358)Peak memory usage: 90 MB
% 4.44/1.30 % (1798358)Instructions burned: 248 (million)
% 4.44/1.30 % Exception at run slice level% Exception at run slice level
% 4.44/1.30 User error: GNN currently only supports monomorphic FOL.
% 4.44/1.30
% 4.44/1.30 User error: GNN currently only supports monomorphic FOL.
% 4.44/1.30 % Exception at run slice level
% 4.44/1.30 User error: GNN currently only supports monomorphic FOL.
% 4.44/1.30 % (1798355)------------------------------
% 4.44/1.30 % (1798355)------------------------------
% 4.44/1.30 % (1798356)Refutation found. Thanks to Tanya!
% 4.44/1.30 % SZS status Theorem for theBenchmark
% 4.44/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 5.19/1.50 % (1798356)------------------------------
% 5.19/1.50 % (1798356)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.19/1.50 % (1798356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.50 % (1798356)CaDiCaL version: 2.1.3
% 5.19/1.50 % (1798356)Termination reason: Refutation
% 5.19/1.50 % (1798356)Time elapsed: 0.031 s
% 5.19/1.50 % (1798356)Peak memory usage: 90 MB
% 5.19/1.50 % (1798356)Instructions burned: 46 (million)
% 5.19/1.50 % (1798356)------------------------------
% 5.19/1.50 % (1798356)------------------------------
% 5.19/1.50 % (1798335)Success in time 0.641 s
% 5.19/1.50 % Vampire exiting
%------------------------------------------------------------------------------