%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT250_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 : n013.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 12:37:20 PM UTC 2026
% Result : Theorem 3.60s 1.65s
% Output : Refutation 5.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 11 ~; 8 |; 0 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 14 usr; 1 prp; 0-5 aty)
% Number of functors : 59 ( 59 usr; 13 con; 0-6 aty)
% Number of variables : 27 ( 27 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
arrow_411405190le_alt: $tType ).
tff(type_def_6,type,
arrow_159774573e_indi: $tType ).
tff(type_def_7,type,
bool: $tType ).
tff(type_def_8,type,
nat: $tType ).
tff(type_def_9,type,
fun: ( $tType * $tType ) > $tType ).
tff(type_def_10,type,
product_prod: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
arrow_1985332922le_Lin: fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool) ).
tff(func_def_1,type,
arrow_610318064e_Prof: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),bool) ).
tff(func_def_2,type,
arrow_1158827142_above: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_3,type,
arrow_319942042_below: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_4,type,
arrow_276188178_mkbot: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_5,type,
arrow_424895264_mktop: ( fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_6,type,
combb:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * fun(X2,X0) ) > fun(X2,X1) ) ).
tff(func_def_7,type,
combc:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * X1 ) > fun(X0,X2) ) ).
tff(func_def_8,type,
combi:
!>[X0: $tType] : fun(X0,X0) ).
tff(func_def_9,type,
combk:
!>[X0: $tType,X1: $tType] : fun(X0,fun(X1,X0)) ).
tff(func_def_10,type,
finite_card:
!>[X0: $tType] : ( fun(X0,bool) > nat ) ).
tff(func_def_11,type,
pi:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,bool) * fun(X0,fun(X1,bool)) ) > fun(fun(X0,X1),bool) ) ).
tff(func_def_12,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_13,type,
if:
!>[X0: $tType] : fun(bool,fun(X0,fun(X0,X0))) ).
tff(func_def_14,type,
ord_less:
!>[X0: $tType] : fun(X0,fun(X0,bool)) ).
tff(func_def_15,type,
top_top:
!>[X0: $tType] : X0 ).
tff(func_def_16,type,
product_Pair:
!>[X0: $tType,X1: $tType] : ( ( X0 * X1 ) > product_prod(X0,X1) ) ).
tff(func_def_17,type,
product_prod_rec:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).
tff(func_def_18,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_19,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_20,type,
fFalse: bool ).
tff(func_def_21,type,
fTrue: bool ).
tff(func_def_22,type,
f: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ).
tff(func_def_23,type,
lab: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_24,type,
lba: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_25,type,
a: arrow_411405190le_alt ).
tff(func_def_26,type,
b: arrow_411405190le_alt ).
tff(func_def_27,type,
h: fun(arrow_159774573e_indi,nat) ).
tff(func_def_28,type,
sK2: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_29,type,
sK3: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).
tff(func_def_30,type,
sK4: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).
tff(func_def_31,type,
sK5: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).
tff(func_def_32,type,
sK6: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).
tff(func_def_33,type,
sK7: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).
tff(func_def_34,type,
sK8: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).
tff(func_def_35,type,
sK9: ( fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_411405190le_alt * arrow_411405190le_alt ) > arrow_159774573e_indi ).
tff(func_def_36,type,
sK10: ( arrow_159774573e_indi * fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ) > fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ).
tff(func_def_37,type,
sK11: ( arrow_159774573e_indi * fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ) > arrow_411405190le_alt ).
tff(func_def_38,type,
sK12: ( arrow_159774573e_indi * fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ) > arrow_411405190le_alt ).
tff(func_def_39,type,
sK13: ( arrow_411405190le_alt * arrow_411405190le_alt ) > fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_40,type,
sK14:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_41,type,
sK15:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).
tff(func_def_42,type,
sK16:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).
tff(func_def_43,type,
sK17: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_44,type,
sK18: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_45,type,
sK19:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,fun(X0,bool)) * fun(X1,X0) * fun(X1,bool) ) > X1 ) ).
tff(func_def_46,type,
sK20:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > product_prod(X0,X1) ) ).
tff(func_def_47,type,
sK21:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X0 ) ).
tff(func_def_48,type,
sK22:
!>[X0: $tType,X1: $tType] : ( fun(product_prod(X0,X1),bool) > X1 ) ).
tff(func_def_49,type,
sK23:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,bool) * fun(X0,X1) * fun(X0,bool) ) > X0 ) ).
tff(func_def_50,type,
sK24:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X1,X0),bool) * fun(product_prod(X1,X0),bool) ) > X1 ) ).
tff(func_def_51,type,
sK25:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X1,X0),bool) * fun(product_prod(X1,X0),bool) ) > X0 ) ).
tff(func_def_52,type,
sK26:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,bool) * fun(X1,X0) ) > X1 ) ).
tff(func_def_53,type,
sK27:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,bool) * fun(X1,X0) ) > X1 ) ).
tff(func_def_54,type,
sK28:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_55,type,
sK29:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(func_def_56,type,
sK30:
!>[X0: $tType,X1: $tType] : ( fun(X1,X0) > X1 ) ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
ord:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
top:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
order:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
preorder:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
arrow_1958449194le_IIA: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) > $o ).
tff(pred_def_8,type,
arrow_987702531ctator: ( fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) * arrow_159774573e_indi ) > $o ).
tff(pred_def_9,type,
arrow_2069624013nimity: fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) > $o ).
tff(pred_def_10,type,
inj_on:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * fun(X0,bool) ) > $o ) ).
tff(pred_def_11,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_12,type,
pp: bool > $o ).
tff(pred_def_13,type,
sP0: ( arrow_411405190le_alt * arrow_411405190le_alt * fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).
tff(pred_def_14,type,
sP1: ( arrow_411405190le_alt * arrow_411405190le_alt * fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).
tff(f1,axiom,
member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),lab,arrow_1985332922le_Lin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0__096Lab_A_058_ALin_096) ).
tff(f4,axiom,
member(fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),f,pi(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_610318064e_Prof,aa(fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool),fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool),fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1985332922le_Lin))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_assms_I1_J) ).
tff(f7,axiom,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin)
=> member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combk(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi),X0),arrow_610318064e_Prof) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_const__Lin__Prof) ).
tff(f43,axiom,
! [X0: $tType,X1: $tType,X2: X0,X3: fun(X1,bool),X4: fun(X0,bool),X5: fun(X0,X1)] :
( member(fun(X0,X1),X5,pi(X0,X1,X4,aa(fun(X1,bool),fun(X0,fun(X1,bool)),combk(fun(X1,bool),X0),X3)))
=> ( member(X0,X2,X4)
=> member(X1,aa(X0,X1,X5,X2),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_funcset__mem) ).
tff(f125,conjecture,
member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combk(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi),lab)),arrow_1985332922le_Lin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f126,negated_conjecture,
~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combk(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi),lab)),arrow_1985332922le_Lin),
inference(negated_conjecture,[status(cth)],[f125]) ).
tff(f127,plain,
~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combk(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi),lab)),arrow_1985332922le_Lin),
inference(flattening,[],[f126]) ).
tff(f131,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combk(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi),X0),arrow_610318064e_Prof)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin) ),
inference(ennf_transformation,[],[f7]) ).
tff(f170,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: fun(X1,bool),X4: fun(X0,bool),X5: fun(X0,X1)] :
( member(X1,aa(X0,X1,X5,X2),X3)
| ~ member(X0,X2,X4)
| ~ member(fun(X0,X1),X5,pi(X0,X1,X4,aa(fun(X1,bool),fun(X0,fun(X1,bool)),combk(fun(X1,bool),X0),X3))) ),
inference(ennf_transformation,[],[f43]) ).
tff(f171,plain,
! [X0: $tType,X1: $tType,X2: X0,X3: fun(X1,bool),X4: fun(X0,bool),X5: fun(X0,X1)] :
( member(X1,aa(X0,X1,X5,X2),X3)
| ~ member(X0,X2,X4)
| ~ member(fun(X0,X1),X5,pi(X0,X1,X4,aa(fun(X1,bool),fun(X0,fun(X1,bool)),combk(fun(X1,bool),X0),X3))) ),
inference(flattening,[],[f170]) ).
tff(f287,plain,
member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),lab,arrow_1985332922le_Lin),
inference(cnf_transformation,[],[f1]) ).
tff(f290,plain,
member(fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),f,pi(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_610318064e_Prof,aa(fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool),fun(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool)),combk(fun(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),bool),fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))),arrow_1985332922le_Lin))),
inference(cnf_transformation,[],[f4]) ).
tff(f293,plain,
! [X0: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)] :
( member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combk(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi),X0),arrow_610318064e_Prof)
| ~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,arrow_1985332922le_Lin) ),
inference(cnf_transformation,[],[f131]) ).
tff(f394,plain,
! [X1: $tType,X0: $tType,X2: X0,X3: fun(X1,bool),X4: fun(X0,bool),X5: fun(X0,X1)] :
( ~ member(fun(X0,X1),X5,pi(X0,X1,X4,aa(fun(X1,bool),fun(X0,fun(X1,bool)),combk(fun(X1,bool),X0),X3)))
| ~ member(X0,X2,X4)
| member(X1,aa(X0,X1,X5,X2),X3) ),
inference(cnf_transformation,[],[f171]) ).
tff(f502,plain,
~ member(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),aa(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),f,aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combk(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi),lab)),arrow_1985332922le_Lin),
inference(cnf_transformation,[],[f127]) ).
tff(f529,plain,
member(fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),aa(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),combk(fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),arrow_159774573e_indi),lab),arrow_610318064e_Prof),
inference(unit_resulting_resolution,[],[f293,f287]) ).
tff(f1046,plain,
$false,
inference(unit_resulting_resolution,[],[f394,f529,f502,f290]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT250_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 % Computer : n013.cluster.edu
% 0.12/0.42 % Model : x86_64 x86_64
% 0.12/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.42 % Memory : 8046.5625MB
% 0.12/0.42 % OS : Linux 6.8.0-71-generic
% 0.12/0.42 % CPULimit : 300
% 0.12/0.42 % WCLimit : 300
% 0.12/0.42 % DateTime : Mon Sep 28 00:01:37 UTC 2026
% 0.12/0.42 % CPUTime :
% 0.12/0.42 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.46 Running first-order theorem proving
% 0.12/0.46 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
% 3.60/1.65 % (679825)Detected formulas, will run a generic FOF schedule.
% 3.60/1.65 % (679925)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1373837002:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.60/1.65 % (679925)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.60/1.65 % (679925)Refutation not found, incomplete strategy
% 3.60/1.65 % (679925)------------------------------
% 3.60/1.65 % (679925)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.65 % (679925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.65 % (679925)CaDiCaL version: 2.1.3
% 3.60/1.65 % (679925)Termination reason: Refutation not found, incomplete strategy
% 3.60/1.65 % (679925)Time elapsed: 0.003 s
% 3.60/1.65 % (679925)Peak memory usage: 88 MB
% 3.60/1.65 % (679925)Instructions burned: 6 (million)
% 3.60/1.65 % (679926)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3427953003:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.60/1.65 % (679924)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=3746915666:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.60/1.65 % (679927)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1552308576:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.60/1.65 % (679928)dis-21_1_sil=8000:lcm=predicate:random_seed=4248461848: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)
% 3.60/1.65 % (679923)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=2860359366:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.60/1.65 % (679922)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=2935445244:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.60/1.65 % (679924)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.60/1.65 % (679928)Instruction limit reached!
% 3.60/1.65 % (679928)------------------------------
% 3.60/1.65 % (679928)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.65 % (679928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.65 % (679928)CaDiCaL version: 2.1.3
% 3.60/1.65 % (679928)Termination reason: Instruction limit
% 3.60/1.65 % (679928)Termination phase: Saturation
% 3.60/1.65 % (679928)Time elapsed: 0.059 s
% 3.60/1.65 % (679928)Peak memory usage: 89 MB
% 3.60/1.65 % (679928)Instructions burned: 135 (million)
% 3.60/1.65 % (679926)Instruction limit reached!
% 3.60/1.65 % (679926)------------------------------
% 3.60/1.65 % (679926)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.65 % (679926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.65 % (679926)CaDiCaL version: 2.1.3
% 3.60/1.65 % (679926)Termination reason: Instruction limit
% 3.60/1.65 % (679926)Termination phase: Saturation
% 3.60/1.65 % (679926)Time elapsed: 0.068 s
% 3.60/1.65 % (679926)Peak memory usage: 88 MB
% 3.60/1.65 % (679926)Instructions burned: 119 (million)
% 3.60/1.65 % (679927)Instruction limit reached!
% 3.60/1.65 % (679927)------------------------------
% 3.60/1.65 % (679927)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.65 % (679927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.65 % (679927)CaDiCaL version: 2.1.3
% 3.60/1.65 % (679927)Termination reason: Instruction limit
% 3.60/1.65 % (679927)Termination phase: Saturation
% 3.60/1.65 % (679927)Time elapsed: 0.090 s
% 3.60/1.65 % (679927)Peak memory usage: 89 MB
% 3.60/1.65 % (679927)Instructions burned: 139 (million)
% 3.60/1.65 % (679925)------------------------------
% 3.60/1.65 % (679925)------------------------------
% 3.60/1.65 % (679959)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=460266235:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 3.60/1.65 % (679943)lrs+10_1_sil=8000:sp=occurrence:random_seed=1844091275:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.60/1.65 % (679959)First to succeed.
% 3.60/1.65 % (679959)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-679825"
% 3.60/1.65 % (679949)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2378235030:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.60/1.65 % (679949)Refutation not found, incomplete strategy
% 3.60/1.65 % (679949)------------------------------
% 3.60/1.65 % (679949)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.65 % (679949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.65 % (679949)CaDiCaL version: 2.1.3
% 3.60/1.65 % (679949)Termination reason: Refutation not found, incomplete strategy
% 3.60/1.65 % (679949)Time elapsed: 0.017 s
% 3.60/1.65 % (679949)Peak memory usage: 89 MB
% 3.60/1.65 % (679949)Instructions burned: 15 (million)
% 3.60/1.65 % (679951)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2620286038:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.60/1.65 % (679951)Also succeeded, but the first one will report.
% 3.60/1.65 % Exception at run slice level
% 3.60/1.65 User error: GNN currently only supports monomorphic FOL.
% 3.60/1.65 % Exception at run slice level
% 3.60/1.65 User error: GNN currently only supports monomorphic FOL.
% 3.60/1.65 % (679959)Refutation found. Thanks to Tanya!
% 3.60/1.65 % SZS status Theorem for theBenchmark
% 3.60/1.65 % SZS output start Proof for theBenchmark
% See solution above
% 5.82/1.83 % (679959)------------------------------
% 5.82/1.83 % (679959)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.82/1.83 % (679959)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.82/1.83 % (679959)CaDiCaL version: 2.1.3
% 5.82/1.83 % (679959)Termination reason: Refutation
% 5.82/1.83 % (679959)Time elapsed: 0.039 s
% 5.82/1.83 % (679959)Peak memory usage: 90 MB
% 5.82/1.83 % (679959)Instructions burned: 73 (million)
% 5.82/1.83 % (679959)------------------------------
% 5.82/1.83 % (679959)------------------------------
% 5.82/1.83 % (679825)Success in time 0.751 s
% 5.82/1.83 % Vampire exiting
%------------------------------------------------------------------------------