%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT192_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 : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:37:12 PM UTC 2026
% Result : Theorem 4.06s 1.20s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 15
% Syntax : Number of formulae : 99 ( 23 unt; 0 typ; 4 def)
% Number of atoms : 321 ( 25 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 386 ( 164 ~; 172 |; 30 &)
% ( 9 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 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 : 14 ( 12 usr; 5 prp; 0-6 aty)
% Number of functors : 65 ( 65 usr; 7 con; 0-7 aty)
% Number of variables : 137 ( 0 sgn 126 !; 11 ?; 137 :)
% 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,
fun: ( $tType * $tType ) > $tType ).
tff(type_def_9,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_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_2,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_3,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_4,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_5,type,
combk:
!>[X0: $tType,X1: $tType] : ( X0 > fun(X1,X0) ) ).
tff(func_def_6,type,
order_215145569der_on:
!>[X0: $tType] : ( fun(X0,bool) > fun(fun(product_prod(X0,X0),bool),bool) ) ).
tff(func_def_7,type,
top_top:
!>[X0: $tType] : X0 ).
tff(func_def_8,type,
product_Pair:
!>[X0: $tType,X1: $tType] : fun(X0,fun(X1,product_prod(X0,X1))) ).
tff(func_def_9,type,
product_apfst:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * product_prod(X0,X2) ) > product_prod(X1,X2) ) ).
tff(func_def_10,type,
product_apsnd:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * product_prod(X2,X0) ) > product_prod(X2,X1) ) ).
tff(func_def_11,type,
product_curry:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X0,X1),X2) > fun(X0,fun(X1,X2)) ) ).
tff(func_def_12,type,
produc1605651328_split:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2)) ).
tff(func_def_13,type,
product_prod_case:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2)) ).
tff(func_def_14,type,
product_prod_rec:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).
tff(func_def_15,type,
product_scomp:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( ( fun(X0,product_prod(X1,X2)) * fun(X1,fun(X2,X3)) ) > fun(X0,X3) ) ).
tff(func_def_16,type,
inv_image:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X0),bool) * fun(X1,X0) ) > fun(product_prod(X1,X1),bool) ) ).
tff(func_def_17,type,
collect:
!>[X0: $tType] : ( fun(X0,bool) > fun(X0,bool) ) ).
tff(func_def_18,type,
lex_prod:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X0),bool) * fun(product_prod(X1,X1),bool) ) > fun(product_prod(product_prod(X0,X1),product_prod(X0,X1)),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(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,
p: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) ).
tff(func_def_24,type,
a: arrow_411405190le_alt ).
tff(func_def_25,type,
b: arrow_411405190le_alt ).
tff(func_def_26,type,
i: arrow_159774573e_indi ).
tff(func_def_27,type,
sK0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) > arrow_159774573e_indi ).
tff(func_def_28,type,
sK1: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)) > arrow_159774573e_indi ).
tff(func_def_29,type,
sK2:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_30,type,
sK3:
!>[X0: $tType] : ( ( fun(product_prod(X0,X0),bool) * fun(X0,bool) ) > X0 ) ).
tff(func_def_31,type,
sK4:
!>[X0: $tType] : ( ( fun(product_prod(X0,X0),bool) * fun(X0,bool) ) > X0 ) ).
tff(func_def_32,type,
sK5:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_33,type,
sK6:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_34,type,
sK7:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_35,type,
sK8:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_36,type,
sK9:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_37,type,
sK10:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > X0 ) ).
tff(func_def_38,type,
sK11:
!>[X0: $tType] : X0 ).
tff(func_def_39,type,
sK12:
!>[X0: $tType] : ( fun(X0,bool) > X0 ) ).
tff(func_def_40,type,
sK13:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_41,type,
sK14:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X0 ) ).
tff(func_def_42,type,
sK15:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X1 ) ).
tff(func_def_43,type,
sK16:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X2 ) ).
tff(func_def_44,type,
sK17:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X3 ) ).
tff(func_def_45,type,
sK18:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X0 ) ).
tff(func_def_46,type,
sK19:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X1 ) ).
tff(func_def_47,type,
sK20:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X2 ) ).
tff(func_def_48,type,
sK21:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X3 ) ).
tff(func_def_49,type,
sK22:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,X4)))) > X4 ) ).
tff(func_def_50,type,
sK23:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X0 ) ).
tff(func_def_51,type,
sK24:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X1 ) ).
tff(func_def_52,type,
sK25:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X2 ) ).
tff(func_def_53,type,
sK26:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X3 ) ).
tff(func_def_54,type,
sK27:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X4 ) ).
tff(func_def_55,type,
sK28:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: $tType,X5: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,product_prod(X3,product_prod(X4,X5))))) > X5 ) ).
tff(func_def_56,type,
sK29:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X0 ) ).
tff(func_def_57,type,
sK30:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X1 ) ).
tff(func_def_58,type,
sK31:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X2 ) ).
tff(func_def_59,type,
sK32:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_60,type,
sK33:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_61,type,
sK34:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_62,type,
sK35:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(pred_def_1,type,
top:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
in_rel:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X1),bool) * X0 * X1 ) > $o ) ).
tff(pred_def_3,type,
inv_imagep:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,fun(X0,bool)) * fun(X1,X0) * X1 * X1 ) > $o ) ).
tff(pred_def_4,type,
irrefl:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).
tff(pred_def_5,type,
total_on:
!>[X0: $tType] : ( ( fun(X0,bool) * fun(product_prod(X0,X0),bool) ) > $o ) ).
tff(pred_def_6,type,
trans:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).
tff(pred_def_7,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_8,type,
pp: bool > $o ).
tff(f1,axiom,
! [X0: $tType,X5: fun(product_prod(X0,X0),bool)] :
( irrefl(X0,X5)
<=> ! [X6: X0] : ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X6),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_irrefl__def) ).
tff(f3,axiom,
! [X0: $tType,X1: X0] : member(X0,X1,top_top(fun(X0,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_UNIV__I) ).
tff(f4,axiom,
! [X0: $tType,X1: X0] : member(X0,X1,top_top(fun(X0,bool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_iso__tuple__UNIV__I) ).
tff(f7,axiom,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( total_on(X0,X2,X1)
<=> ! [X3: X0] :
( member(X0,X3,X2)
=> ! [X4: X0] :
( member(X0,X4,X2)
=> ( ( X3 != X4 )
=> ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_total__on__def) ).
tff(f9,axiom,
! [X0: $tType,X1: X0,X2: X0,X3: X0,X4: fun(product_prod(X0,X0),bool)] :
( trans(X0,X4)
=> ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X2),X4)
=> ( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X1),X4)
=> member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X1),X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_transD) ).
tff(f19,axiom,
! [X0: $tType,X1: fun(X0,bool)] :
( ! [X2: X0] : member(X0,X2,X1)
=> ( top_top(fun(X0,bool)) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_UNIV__eq__I) ).
tff(f89,axiom,
! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
( ! [X1: arrow_159774573e_indi] :
( trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
& irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
& total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1)) )
=> ( trans(arrow_411405190le_alt,f(X0))
& irrefl(arrow_411405190le_alt,f(X0))
& total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),f(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f90,axiom,
! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
( ! [X1: arrow_159774573e_indi] :
( trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
& irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
& total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1)) )
=> ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( ( X2 != X3 )
=> ( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,i))
=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X3),f(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(f91,axiom,
! [X0: arrow_159774573e_indi] :
( trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
& irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0))
& total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
tff(f92,axiom,
member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b),f(p)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
tff(f93,conjecture,
member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
tff(f94,negated_conjecture,
~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)),
inference(negated_conjecture,[status(cth)],[f93]) ).
tff(f95,plain,
~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)),
inference(flattening,[],[f94]) ).
tff(f96,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( irrefl(X0,X1)
<=> ! [X2: X0] : ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X2),X1) ),
inference(rectify,[],[f1]) ).
tff(f98,plain,
! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
( ( trans(arrow_411405190le_alt,f(X0))
& irrefl(arrow_411405190le_alt,f(X0))
& total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),f(X0)) )
| ? [X1: arrow_159774573e_indi] :
( ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
| ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1)) ) ),
inference(ennf_transformation,[],[f89]) ).
tff(f99,plain,
! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
( ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X3),f(X0))
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,i))
| ( X2 = X3 ) )
| ? [X1: arrow_159774573e_indi] :
( ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
| ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1)) ) ),
inference(ennf_transformation,[],[f90]) ).
tff(f100,plain,
! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
( ! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X3),f(X0))
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X2),X3),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,i))
| ( X2 = X3 ) )
| ? [X1: arrow_159774573e_indi] :
( ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1))
| ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X1)) ) ),
inference(flattening,[],[f99]) ).
tff(f101,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( total_on(X0,X2,X1)
<=> ! [X3: X0] :
( ! [X4: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1)
| ( X3 = X4 )
| ~ member(X0,X4,X2) )
| ~ member(X0,X3,X2) ) ),
inference(ennf_transformation,[],[f7]) ).
tff(f102,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( total_on(X0,X2,X1)
<=> ! [X3: X0] :
( ! [X4: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1)
| ( X3 = X4 )
| ~ member(X0,X4,X2) )
| ~ member(X0,X3,X2) ) ),
inference(flattening,[],[f101]) ).
tff(f105,plain,
! [X0: $tType,X1: X0,X2: X0,X3: X0,X4: fun(product_prod(X0,X0),bool)] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X1),X4)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X1),X4)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X2),X4)
| ~ trans(X0,X4) ),
inference(ennf_transformation,[],[f9]) ).
tff(f106,plain,
! [X0: $tType,X1: X0,X2: X0,X3: X0,X4: fun(product_prod(X0,X0),bool)] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X1),X4)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X1),X4)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X2),X4)
| ~ trans(X0,X4) ),
inference(flattening,[],[f105]) ).
tff(f109,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( top_top(fun(X0,bool)) = X1 )
| ? [X2: X0] : ~ member(X0,X2,X1) ),
inference(ennf_transformation,[],[f19]) ).
tff(f118,plain,
! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
( ( trans(arrow_411405190le_alt,f(X0))
& irrefl(arrow_411405190le_alt,f(X0))
& total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),f(X0)) )
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK0(X0)))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK0(X0)))
| ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK0(X0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f98]) ).
tff(f119,plain,
! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
( ! [X1: arrow_411405190le_alt,X2: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),f(X0))
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,i))
| ( X1 = X2 ) )
| ? [X3: arrow_159774573e_indi] :
( ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X3))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X3))
| ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,X3)) ) ),
inference(rectify,[],[f100]) ).
tff(f120,plain,
! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
( ! [X1: arrow_411405190le_alt,X2: arrow_411405190le_alt] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),f(X0))
| ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,i))
| ( X1 = X2 ) )
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK1(X0)))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK1(X0)))
| ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK1(X0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0))],[f119]) ).
tff(f121,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( ( irrefl(X0,X1)
| ? [X2: X0] : member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X2),X1) )
& ( ! [X2: X0] : ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X2),X1)
| ~ irrefl(X0,X1) ) ),
inference(nnf_transformation,[],[f96]) ).
tff(f122,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( ( irrefl(X0,X1)
| ? [X2: X0] : member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X2),X1) )
& ( ! [X3: X0] : ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X3),X1)
| ~ irrefl(X0,X1) ) ),
inference(rectify,[],[f121]) ).
tff(f123,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool)] :
( ( irrefl(X0,X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK2(X0,X1)),sK2(X0,X1)),X1) )
& ( ! [X3: X0] : ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X3),X1)
| ~ irrefl(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f122]) ).
tff(f124,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ( total_on(X0,X2,X1)
| ? [X3: X0] :
( ? [X4: X0] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
& ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1)
& ( X3 != X4 )
& member(X0,X4,X2) )
& member(X0,X3,X2) ) )
& ( ! [X3: X0] :
( ! [X4: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1)
| ( X3 = X4 )
| ~ member(X0,X4,X2) )
| ~ member(X0,X3,X2) )
| ~ total_on(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f102]) ).
tff(f125,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ( total_on(X0,X2,X1)
| ? [X3: X0] :
( ? [X4: X0] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X4),X1)
& ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X4),X3),X1)
& ( X3 != X4 )
& member(X0,X4,X2) )
& member(X0,X3,X2) ) )
& ( ! [X5: X0] :
( ! [X6: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X6),X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X5),X1)
| ( X5 = X6 )
| ~ member(X0,X6,X2) )
| ~ member(X0,X5,X2) )
| ~ total_on(X0,X2,X1) ) ),
inference(rectify,[],[f124]) ).
tff(f126,plain,
! [X0: $tType,X1: fun(product_prod(X0,X0),bool),X2: fun(X0,bool)] :
( ( total_on(X0,X2,X1)
| ( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK3(X0,X1,X2)),sK4(X0,X1,X2)),X1)
& ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),sK4(X0,X1,X2)),sK3(X0,X1,X2)),X1)
& ( sK3(X0,X1,X2) != sK4(X0,X1,X2) )
& member(X0,sK4(X0,X1,X2),X2)
& member(X0,sK3(X0,X1,X2),X2) ) )
& ( ! [X5: X0] :
( ! [X6: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X6),X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X5),X1)
| ( X5 = X6 )
| ~ member(X0,X6,X2) )
| ~ member(X0,X5,X2) )
| ~ total_on(X0,X2,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X3,sK3(X0,X1,X2)),skolemize(X4,sK4(X0,X1,X2))],[f125]) ).
tff(f132,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( top_top(fun(X0,bool)) = X1 )
| ~ member(X0,sK12(X0,X1),X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X2,sK12(X0,X1))],[f109]) ).
tff(f143,plain,
! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK0(X0)))
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK0(X0)))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK0(X0)))
| irrefl(arrow_411405190le_alt,f(X0)) ),
inference(cnf_transformation,[],[f118]) ).
tff(f144,plain,
! [X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool))] :
( ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK0(X0)))
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK0(X0)))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK0(X0)))
| trans(arrow_411405190le_alt,f(X0)) ),
inference(cnf_transformation,[],[f118]) ).
tff(f145,plain,
! [X2: arrow_411405190le_alt,X0: fun(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool)),X1: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,i))
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),X1),X2),f(X0))
| ( X1 = X2 )
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK1(X0)))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK1(X0)))
| ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),X0,sK1(X0))) ),
inference(cnf_transformation,[],[f120]) ).
tff(f146,plain,
! [X0: arrow_159774573e_indi] : total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),
inference(cnf_transformation,[],[f91]) ).
tff(f147,plain,
! [X0: arrow_159774573e_indi] : irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),
inference(cnf_transformation,[],[f91]) ).
tff(f148,plain,
! [X0: arrow_159774573e_indi] : trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X0)),
inference(cnf_transformation,[],[f91]) ).
tff(f149,plain,
member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b),f(p)),
inference(cnf_transformation,[],[f92]) ).
tff(f150,plain,
~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),b),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)),
inference(cnf_transformation,[],[f95]) ).
tff(f151,plain,
! [X0: $tType,X3: X0,X1: fun(product_prod(X0,X0),bool)] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X3),X1)
| ~ irrefl(X0,X1) ),
inference(cnf_transformation,[],[f123]) ).
tff(f153,plain,
! [X0: $tType,X2: fun(X0,bool),X1: fun(product_prod(X0,X0),bool),X6: X0,X5: X0] :
( member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X6),X5),X1)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X5),X6),X1)
| ( X5 = X6 )
| ~ member(X0,X6,X2)
| ~ member(X0,X5,X2)
| ~ total_on(X0,X2,X1) ),
inference(cnf_transformation,[],[f126]) ).
tff(f162,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0,X4: fun(product_prod(X0,X0),bool)] :
( ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X2),X4)
| ~ member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X2),X1),X4)
| member(product_prod(X0,X0),aa(X0,product_prod(X0,X0),aa(X0,fun(X0,product_prod(X0,X0)),product_Pair(X0,X0),X3),X1),X4)
| ~ trans(X0,X4) ),
inference(cnf_transformation,[],[f106]) ).
tff(f168,plain,
! [X0: $tType,X1: fun(X0,bool)] :
( ( top_top(fun(X0,bool)) = X1 )
| ~ member(X0,sK12(X0,X1),X1) ),
inference(cnf_transformation,[],[f132]) ).
tff(f169,plain,
! [X0: $tType,X1: X0] : member(X0,X1,top_top(fun(X0,bool))),
inference(cnf_transformation,[],[f4]) ).
tff(f170,plain,
! [X0: $tType,X1: X0] : member(X0,X1,top_top(fun(X0,bool))),
inference(cnf_transformation,[],[f3]) ).
tff(f185,plain,
! [X0: fun(arrow_411405190le_alt,bool)] :
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))
| ( a = b )
| ~ member(arrow_411405190le_alt,a,X0)
| ~ member(arrow_411405190le_alt,b,X0)
| ~ total_on(arrow_411405190le_alt,X0,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)) ),
inference(resolution,[],[f150,f153]) ).
tff(f187,definition,
( spl36_1
<=> ! [X0: fun(arrow_411405190le_alt,bool)] :
( ~ member(arrow_411405190le_alt,a,X0)
| ~ total_on(arrow_411405190le_alt,X0,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))
| ~ member(arrow_411405190le_alt,b,X0) ) ),
introduced(definition,[new_symbols(definition,[spl36_1])],[avatar_definition]) ).
tff(f188,plain,
( ! [X0: fun(arrow_411405190le_alt,bool)] :
( ~ total_on(arrow_411405190le_alt,X0,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))
| ~ member(arrow_411405190le_alt,a,X0)
| ~ member(arrow_411405190le_alt,b,X0) )
| ~ spl36_1 ),
inference(avatar_component_clause,[],[f187]) ).
tff(f190,definition,
( spl36_2
<=> ( a = b ) ),
introduced(definition,[new_symbols(definition,[spl36_2])],[avatar_definition]) ).
tff(f191,plain,
( ( a != b )
| spl36_2 ),
inference(avatar_component_clause,[],[f190]) ).
tff(f192,plain,
( ( a = b )
| ~ spl36_2 ),
inference(avatar_component_clause,[],[f190]) ).
tff(f194,definition,
( spl36_3
<=> member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i)) ),
introduced(definition,[new_symbols(definition,[spl36_3])],[avatar_definition]) ).
tff(f196,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,i))
| ~ spl36_3 ),
inference(avatar_component_clause,[],[f194]) ).
tff(f197,plain,
( spl36_1
| spl36_2
| spl36_3 ),
inference(avatar_split_clause,[],[f185,f194,f190,f187]) ).
tff(f201,plain,
! [X0: fun(arrow_411405190le_alt,bool),X1: arrow_159774573e_indi] :
( total_on(arrow_411405190le_alt,X0,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,X1))
| ~ member(arrow_411405190le_alt,sK12(arrow_411405190le_alt,X0),X0) ),
inference(superposition,[],[f146,f168]) ).
tff(f204,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),a),f(p))
| ~ spl36_2 ),
inference(superposition,[],[f149,f192]) ).
tff(f207,plain,
( ~ irrefl(arrow_411405190le_alt,f(p))
| ~ spl36_2 ),
inference(resolution,[],[f204,f151]) ).
tff(f210,plain,
( ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK0(p)))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK0(p)))
| irrefl(arrow_411405190le_alt,f(p)) ),
inference(resolution,[],[f143,f146]) ).
tff(f211,plain,
( ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK0(p)))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK0(p)))
| irrefl(arrow_411405190le_alt,f(p))
| ~ member(arrow_411405190le_alt,sK12(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),top_top(fun(arrow_411405190le_alt,bool))) ),
inference(resolution,[],[f143,f201]) ).
tff(f213,plain,
( ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK0(p)))
| irrefl(arrow_411405190le_alt,f(p))
| ~ member(arrow_411405190le_alt,sK12(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),top_top(fun(arrow_411405190le_alt,bool))) ),
inference(forward_subsumption_resolution,[],[f211,f148]) ).
tff(f214,plain,
( ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK0(p)))
| irrefl(arrow_411405190le_alt,f(p)) ),
inference(forward_subsumption_resolution,[],[f210,f148]) ).
tff(f215,plain,
( irrefl(arrow_411405190le_alt,f(p))
| ~ member(arrow_411405190le_alt,sK12(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),top_top(fun(arrow_411405190le_alt,bool))) ),
inference(forward_subsumption_resolution,[],[f213,f147]) ).
tff(f216,plain,
irrefl(arrow_411405190le_alt,f(p)),
inference(forward_subsumption_resolution,[],[f214,f147]) ).
tff(f217,plain,
( ~ member(arrow_411405190le_alt,sK12(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),top_top(fun(arrow_411405190le_alt,bool)))
| ~ spl36_2 ),
inference(forward_subsumption_resolution,[],[f215,f207]) ).
tff(f220,plain,
( $false
| ~ spl36_2 ),
inference(forward_subsumption_resolution,[],[f217,f170]) ).
tff(f221,plain,
~ spl36_2,
inference(avatar_contradiction_clause,[],[f220]) ).
tff(f223,definition,
( spl36_4
<=> trans(arrow_411405190le_alt,f(p)) ),
introduced(definition,[new_symbols(definition,[spl36_4])],[avatar_definition]) ).
tff(f224,plain,
( trans(arrow_411405190le_alt,f(p))
| ~ spl36_4 ),
inference(avatar_component_clause,[],[f223]) ).
tff(f225,plain,
( ~ trans(arrow_411405190le_alt,f(p))
| spl36_4 ),
inference(avatar_component_clause,[],[f223]) ).
tff(f236,plain,
( ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK0(p)))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK0(p)))
| trans(arrow_411405190le_alt,f(p))
| ~ member(arrow_411405190le_alt,sK12(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),top_top(fun(arrow_411405190le_alt,bool))) ),
inference(resolution,[],[f144,f201]) ).
tff(f238,plain,
( ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK0(p)))
| trans(arrow_411405190le_alt,f(p))
| ~ member(arrow_411405190le_alt,sK12(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),top_top(fun(arrow_411405190le_alt,bool))) ),
inference(forward_subsumption_resolution,[],[f236,f148]) ).
tff(f240,plain,
( trans(arrow_411405190le_alt,f(p))
| ~ member(arrow_411405190le_alt,sK12(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),top_top(fun(arrow_411405190le_alt,bool))) ),
inference(forward_subsumption_resolution,[],[f238,f147]) ).
tff(f242,plain,
( ~ member(arrow_411405190le_alt,sK12(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool))),top_top(fun(arrow_411405190le_alt,bool)))
| spl36_4 ),
inference(forward_subsumption_resolution,[],[f240,f225]) ).
tff(f245,plain,
( $false
| spl36_4 ),
inference(forward_subsumption_resolution,[],[f242,f170]) ).
tff(f246,plain,
spl36_4,
inference(avatar_contradiction_clause,[],[f245]) ).
tff(f259,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),f(p))
| ( a = b )
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK1(p)))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK1(p)))
| ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK1(p)))
| ~ spl36_3 ),
inference(resolution,[],[f145,f196]) ).
tff(f269,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),f(p))
| ~ trans(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK1(p)))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK1(p)))
| ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK1(p)))
| spl36_2
| ~ spl36_3 ),
inference(forward_subsumption_resolution,[],[f259,f191]) ).
tff(f270,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),f(p))
| ~ irrefl(arrow_411405190le_alt,aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK1(p)))
| ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK1(p)))
| spl36_2
| ~ spl36_3 ),
inference(forward_subsumption_resolution,[],[f269,f148]) ).
tff(f271,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),f(p))
| ~ total_on(arrow_411405190le_alt,top_top(fun(arrow_411405190le_alt,bool)),aa(arrow_159774573e_indi,fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool),p,sK1(p)))
| spl36_2
| ~ spl36_3 ),
inference(forward_subsumption_resolution,[],[f270,f147]) ).
tff(f272,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),a),f(p))
| spl36_2
| ~ spl36_3 ),
inference(forward_subsumption_resolution,[],[f271,f146]) ).
tff(f274,plain,
( ! [X0: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),X0),f(p))
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),X0),f(p))
| ~ trans(arrow_411405190le_alt,f(p)) )
| spl36_2
| ~ spl36_3 ),
inference(resolution,[],[f272,f162]) ).
tff(f275,plain,
( ! [X0: arrow_411405190le_alt] :
( ~ member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),a),X0),f(p))
| member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),X0),f(p)) )
| spl36_2
| ~ spl36_3
| ~ spl36_4 ),
inference(forward_subsumption_resolution,[],[f274,f224]) ).
tff(f277,plain,
( member(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt),aa(arrow_411405190le_alt,fun(arrow_411405190le_alt,product_prod(arrow_411405190le_alt,arrow_411405190le_alt)),product_Pair(arrow_411405190le_alt,arrow_411405190le_alt),b),b),f(p))
| spl36_2
| ~ spl36_3
| ~ spl36_4 ),
inference(resolution,[],[f275,f149]) ).
tff(f280,plain,
( ~ irrefl(arrow_411405190le_alt,f(p))
| spl36_2
| ~ spl36_3
| ~ spl36_4 ),
inference(resolution,[],[f277,f151]) ).
tff(f283,plain,
( $false
| spl36_2
| ~ spl36_3
| ~ spl36_4 ),
inference(forward_subsumption_resolution,[],[f280,f216]) ).
tff(f284,plain,
( spl36_2
| ~ spl36_3
| ~ spl36_4 ),
inference(avatar_contradiction_clause,[],[f283]) ).
tff(f285,plain,
( ~ member(arrow_411405190le_alt,a,top_top(fun(arrow_411405190le_alt,bool)))
| ~ member(arrow_411405190le_alt,b,top_top(fun(arrow_411405190le_alt,bool)))
| ~ spl36_1 ),
inference(resolution,[],[f188,f146]) ).
tff(f287,plain,
( ~ member(arrow_411405190le_alt,b,top_top(fun(arrow_411405190le_alt,bool)))
| ~ spl36_1 ),
inference(forward_subsumption_resolution,[],[f285,f169]) ).
tff(f288,plain,
( $false
| ~ spl36_1 ),
inference(forward_subsumption_resolution,[],[f287,f170]) ).
tff(f289,plain,
~ spl36_1,
inference(avatar_contradiction_clause,[],[f288]) ).
cnf(s1,plain,
( spl36_1
| spl36_2
| spl36_3 ),
inference(sat_conversion,[],[f197]) ).
cnf(s3,plain,
~ spl36_2,
inference(sat_conversion,[],[f221]) ).
cnf(s7,plain,
spl36_4,
inference(sat_conversion,[],[f246]) ).
cnf(s8,plain,
( spl36_2
| ~ spl36_3
| ~ spl36_4 ),
inference(sat_conversion,[],[f284]) ).
cnf(s9,plain,
~ spl36_1,
inference(sat_conversion,[],[f289]) ).
cnf(s12,plain,
~ spl36_3,
inference(rat,[],[s8,s7,s3]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s1,s12,s3,s9]) ).
tff(f290,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SCT192_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n005.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 23:58:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.47/1.20 % (304771)Detected formulas, will run a generic FOF schedule.
% 3.47/1.20 % (304790)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=281826217:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.47/1.20 % (304791)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=3296660294:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.47/1.20 % (304794)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2294422188:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.47/1.20 % (304792)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=1230947357:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.47/1.20 % (304793)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3227154016:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.47/1.20 % (304793)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.47/1.20 % (304792)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.47/1.20 % (304796)dis-21_1_sil=8000:lcm=predicate:random_seed=589528732: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)
% 3.47/1.20 % (304793)First to succeed.
% 3.47/1.20 % (304795)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=935519601:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.47/1.20 % (304793)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-304771"
% 3.47/1.20 % (304794)Also succeeded, but the first one will report.
% 3.47/1.20 % (304796)Instruction limit reached!
% 3.47/1.20 % (304796)------------------------------
% 3.47/1.20 % (304796)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.20 % (304796)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.20 % (304796)CaDiCaL version: 2.1.3
% 3.47/1.20 % (304796)Termination reason: Instruction limit
% 3.47/1.20 % (304796)Termination phase: Saturation
% 3.47/1.20 % (304796)Time elapsed: 0.086 s
% 3.47/1.20 % (304796)Peak memory usage: 90 MB
% 3.47/1.20 % (304796)Instructions burned: 131 (million)
% 3.47/1.20 % (304795)Instruction limit reached!
% 3.47/1.20 % (304795)------------------------------
% 3.47/1.20 % (304795)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.20 % (304795)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.20 % (304795)CaDiCaL version: 2.1.3
% 3.47/1.20 % (304795)Termination reason: Instruction limit
% 3.47/1.20 % (304795)Termination phase: Saturation
% 3.47/1.20 % (304795)Time elapsed: 0.135 s
% 3.47/1.20 % (304795)Peak memory usage: 89 MB
% 3.47/1.20 % (304795)Instructions burned: 139 (million)
% 3.47/1.20 % Exception at run slice level
% 3.47/1.20 User error: GNN currently only supports monomorphic FOL.
% 3.47/1.20 % (304811)lrs+10_1_sil=32000:urr=on:br=off:random_seed=264705242:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 3.47/1.20 % (304811)Refutation not found, incomplete strategy
% 3.47/1.20 % (304811)------------------------------
% 4.06/1.20 % (304811)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.06/1.20 % (304811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.06/1.20 % (304811)CaDiCaL version: 2.1.3
% 4.06/1.20 % (304811)Termination reason: Refutation not found, incomplete strategy
% 4.06/1.20 % (304811)Time elapsed: 0.003 s
% 4.06/1.20 % (304811)Peak memory usage: 88 MB
% 4.06/1.20 % (304811)Instructions burned: 4 (million)
% 4.06/1.20 % (304812)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2168567602:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 4.06/1.20 % (304793)Refutation found. Thanks to Tanya!
% 4.06/1.20 % SZS status Theorem for theBenchmark
% 4.06/1.20 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/1.30 % (304793)------------------------------
% 0.16/1.30 % (304793)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/1.30 % (304793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/1.30 % (304793)CaDiCaL version: 2.1.3
% 0.16/1.30 % (304793)Termination reason: Refutation
% 0.16/1.30 % (304793)Time elapsed: 0.024 s
% 0.16/1.30 % (304793)Peak memory usage: 90 MB
% 0.16/1.30 % (304793)Instructions burned: 22 (million)
% 0.16/1.30 % (304793)------------------------------
% 0.16/1.30 % (304793)------------------------------
% 0.16/1.30 % (304771)Success in time 0.538 s
% 0.16/1.30 % Vampire exiting
%------------------------------------------------------------------------------