%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SCT189_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 : n016.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 3.15s 1.06s
% Output : Refutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 47
% Syntax : Number of formulae : 295 ( 25 unt; 0 typ; 45 def)
% Number of atoms : 1176 ( 340 equ)
% Maximal formula atoms : 53 ( 3 avg)
% Number of connectives : 1478 ( 597 ~; 638 |; 208 &)
% ( 29 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 60 ( 58 usr; 31 prp; 0-5 aty)
% Number of functors : 61 ( 61 usr; 11 con; 0-7 aty)
% Number of variables : 202 ( 0 sgn 180 !; 22 ?; 202 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
arrow_411405190le_alt: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
fun: ( $tType * $tType ) > $tType ).
tff(type_def_8,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,
comp:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * fun(X2,X0) ) > fun(X2,X1) ) ).
tff(func_def_6,type,
product_Pair:
!>[X0: $tType,X1: $tType] : fun(X0,fun(X1,product_prod(X0,X1))) ).
tff(func_def_7,type,
product_apfst:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * product_prod(X0,X2) ) > product_prod(X1,X2) ) ).
tff(func_def_8,type,
product_apsnd:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,X1) * product_prod(X2,X0) ) > product_prod(X2,X1) ) ).
tff(func_def_9,type,
product_curry:
!>[X0: $tType,X1: $tType,X2: $tType] : ( fun(product_prod(X0,X1),X2) > fun(X0,fun(X1,X2)) ) ).
tff(func_def_10,type,
product_fst:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_11,type,
produc1605651328_split:
!>[X0: $tType,X1: $tType,X2: $tType] : fun(fun(X0,fun(X1,X2)),fun(product_prod(X0,X1),X2)) ).
tff(func_def_12,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_13,type,
product_prod_rec:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X0,fun(X1,X2)) * product_prod(X0,X1) ) > X2 ) ).
tff(func_def_14,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_15,type,
product_snd:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_16,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_17,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_18,type,
fFalse: bool ).
tff(func_def_19,type,
fTrue: bool ).
tff(func_def_20,type,
l: fun(product_prod(arrow_411405190le_alt,arrow_411405190le_alt),bool) ).
tff(func_def_21,type,
x: arrow_411405190le_alt ).
tff(func_def_22,type,
y: arrow_411405190le_alt ).
tff(func_def_23,type,
sK6: arrow_411405190le_alt ).
tff(func_def_24,type,
sK7: arrow_411405190le_alt ).
tff(func_def_25,type,
sK8: arrow_411405190le_alt > arrow_411405190le_alt ).
tff(func_def_26,type,
sK9: arrow_411405190le_alt > arrow_411405190le_alt ).
tff(func_def_27,type,
sK10: arrow_411405190le_alt ).
tff(func_def_28,type,
sK11: arrow_411405190le_alt ).
tff(func_def_29,type,
sK12: arrow_411405190le_alt ).
tff(func_def_30,type,
sK13:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(func_def_31,type,
sK14:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,fun(X1,bool))) * X1 ) > X0 ) ).
tff(func_def_32,type,
sK15:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( product_prod(X0,X2) * fun(X0,fun(X2,fun(X1,bool))) * X1 ) > X2 ) ).
tff(func_def_33,type,
sK16:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,fun(X0,bool))) * X0 * product_prod(X2,X1) ) > X2 ) ).
tff(func_def_34,type,
sK17:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( fun(X2,fun(X1,fun(X0,bool))) * X0 * product_prod(X2,X1) ) > X1 ) ).
tff(func_def_35,type,
sK18:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_36,type,
sK19:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_37,type,
sK20:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_38,type,
sK21:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_39,type,
sK22:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X0 ) ).
tff(func_def_40,type,
sK23:
!>[X0: $tType,X1: $tType] : ( product_prod(X0,X1) > X1 ) ).
tff(func_def_41,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))))) > X0 ) ).
tff(func_def_42,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))))) > X1 ) ).
tff(func_def_43,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))))) > X2 ) ).
tff(func_def_44,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))))) > X3 ) ).
tff(func_def_45,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))))) > X4 ) ).
tff(func_def_46,type,
sK29:
!>[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_47,type,
sK30:
!>[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_48,type,
sK31:
!>[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_49,type,
sK32:
!>[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_50,type,
sK33:
!>[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_51,type,
sK34:
!>[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_52,type,
sK35:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X0 ) ).
tff(func_def_53,type,
sK36:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X1 ) ).
tff(func_def_54,type,
sK37:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X2 ) ).
tff(func_def_55,type,
sK38:
!>[X0: $tType,X1: $tType,X2: $tType,X3: $tType] : ( product_prod(X0,product_prod(X1,product_prod(X2,X3))) > X3 ) ).
tff(func_def_56,type,
sK39:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X0 ) ).
tff(func_def_57,type,
sK40:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X1 ) ).
tff(func_def_58,type,
sK41:
!>[X0: $tType,X1: $tType,X2: $tType] : ( product_prod(X0,product_prod(X1,X2)) > X2 ) ).
tff(pred_def_1,type,
in_rel:
!>[X0: $tType,X1: $tType] : ( ( fun(product_prod(X0,X1),bool) * X0 * X1 ) > $o ) ).
tff(pred_def_2,type,
refl:
!>[X0: $tType] : ( fun(product_prod(X0,X0),bool) > $o ) ).
tff(pred_def_3,type,
member:
!>[X0: $tType] : ( ( X0 * fun(X0,bool) ) > $o ) ).
tff(pred_def_4,type,
pp: bool > $o ).
tff(pred_def_5,type,
sP0: ( arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).
tff(pred_def_6,type,
sP1: ( arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).
tff(pred_def_7,type,
sP2: ( arrow_411405190le_alt * arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).
tff(pred_def_8,type,
sP3: ( arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).
tff(pred_def_9,type,
sP4: ( arrow_411405190le_alt * arrow_411405190le_alt ) > $o ).
tff(pred_def_11,type,
sP42: arrow_411405190le_alt > $o ).
tff(pred_def_12,type,
sP43: arrow_411405190le_alt > $o ).
tff(pred_def_13,type,
sP44: arrow_411405190le_alt > $o ).
tff(pred_def_14,type,
sP45: arrow_411405190le_alt > $o ).
tff(pred_def_15,type,
sP46: arrow_411405190le_alt > $o ).
tff(pred_def_16,type,
sP47: arrow_411405190le_alt > $o ).
tff(pred_def_17,type,
sP48: arrow_411405190le_alt > $o ).
tff(pred_def_18,type,
sP49: arrow_411405190le_alt > $o ).
tff(pred_def_19,type,
sP50: arrow_411405190le_alt > $o ).
tff(pred_def_20,type,
sP51: arrow_411405190le_alt > $o ).
tff(pred_def_21,type,
sP52: arrow_411405190le_alt > $o ).
tff(pred_def_22,type,
sP53: arrow_411405190le_alt > $o ).
tff(pred_def_23,type,
sP54: arrow_411405190le_alt > $o ).
tff(pred_def_24,type,
sP55: arrow_411405190le_alt > $o ).
tff(pred_def_25,type,
sP56: arrow_411405190le_alt > $o ).
tff(pred_def_26,type,
sP57: arrow_411405190le_alt > $o ).
tff(pred_def_27,type,
sP58: arrow_411405190le_alt > $o ).
tff(pred_def_28,type,
sP59: arrow_411405190le_alt > $o ).
tff(pred_def_29,type,
sP60: arrow_411405190le_alt > $o ).
tff(f97,axiom,
( ! [X0: arrow_411405190le_alt,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),X0),X1),l)
=> ! [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),l)
=> 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),X0),X2),l) ) )
& ! [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),X0),X0),l)
& ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( X0 != X1 )
=> ( 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),X0),X1),l)
| 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),X0),l) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
tff(f98,conjecture,
( ! [X0: arrow_411405190le_alt,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),X0),X1),l)
| ( X0 = y )
| ( X1 = y )
| ! [X2: arrow_411405190le_alt] :
( ( ( X1 != x )
| ( X2 != y )
| ( X0 = x )
| 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),X0),x),l) )
& ( ~ 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),l)
| ( X2 = y )
| 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),X0),X2),l) )
& ( ( X2 != y )
| ~ 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),x),l)
| ( X0 = x )
| 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),X0),x),l) ) ) )
& ( ( X1 != y )
| ~ 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),X0),x),l)
| ( X0 = y )
| ! [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),x),X2),l)
| ( X2 = y )
| 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),X0),X2),l) ) )
& ( ( X0 != y )
| ~ 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),x),X1),l)
| ( X1 = y )
| ! [X2: arrow_411405190le_alt] :
( ( ( X1 != x )
| ( X2 != y ) )
& ( ~ 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),l)
| ( X2 = y )
| 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),x),X2),l) )
& ( ( X2 != y )
| ~ 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),x),l) ) ) ) )
& ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( X0 = X1 )
| ( ( X0 = x )
& ( X1 = y ) )
| ( 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),X0),X1),l)
& ( X0 != y )
& ( X1 != y ) )
| ( ( X1 = y )
& 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),X0),x),l)
& ( X0 != y ) )
| ( ( X0 = y )
& 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),x),X1),l)
& ( X1 != y ) )
| ( ( X1 = x )
& ( X0 = y ) )
| ( 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),X0),l)
& ( X1 != y )
& ( X0 != y ) )
| ( ( X0 = y )
& 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),x),l)
& ( X1 != y ) )
| ( ( X1 = y )
& 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),x),X0),l)
& ( X0 != y ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
tff(f99,negated_conjecture,
~ ( ! [X0: arrow_411405190le_alt,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),X0),X1),l)
| ( X0 = y )
| ( X1 = y )
| ! [X2: arrow_411405190le_alt] :
( ( ( X1 != x )
| ( X2 != y )
| ( X0 = x )
| 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),X0),x),l) )
& ( ~ 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),l)
| ( X2 = y )
| 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),X0),X2),l) )
& ( ( X2 != y )
| ~ 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),x),l)
| ( X0 = x )
| 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),X0),x),l) ) ) )
& ( ( X1 != y )
| ~ 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),X0),x),l)
| ( X0 = y )
| ! [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),x),X2),l)
| ( X2 = y )
| 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),X0),X2),l) ) )
& ( ( X0 != y )
| ~ 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),x),X1),l)
| ( X1 = y )
| ! [X2: arrow_411405190le_alt] :
( ( ( X1 != x )
| ( X2 != y ) )
& ( ~ 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),l)
| ( X2 = y )
| 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),x),X2),l) )
& ( ( X2 != y )
| ~ 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),x),l) ) ) ) )
& ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( X0 = X1 )
| ( ( X0 = x )
& ( X1 = y ) )
| ( 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),X0),X1),l)
& ( X0 != y )
& ( X1 != y ) )
| ( ( X1 = y )
& 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),X0),x),l)
& ( X0 != y ) )
| ( ( X0 = y )
& 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),x),X1),l)
& ( X1 != y ) )
| ( ( X1 = x )
& ( X0 = y ) )
| ( 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),X0),l)
& ( X1 != y )
& ( X0 != y ) )
| ( ( X0 = y )
& 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),x),l)
& ( X1 != y ) )
| ( ( X1 = y )
& 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),x),X0),l)
& ( X0 != y ) ) ) ),
inference(negated_conjecture,[status(cth)],[f98]) ).
tff(f100,plain,
( ! [X0: arrow_411405190le_alt,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),X0),X1),l)
=> ! [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),l)
=> 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),X0),X2),l) ) )
& ! [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),X3),X3),l)
& ! [X4: arrow_411405190le_alt,X5: arrow_411405190le_alt] :
( ( X4 != X5 )
=> ( 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),X4),X5),l)
| 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),X5),X4),l) ) ) ),
inference(rectify,[],[f97]) ).
tff(f101,plain,
~ ( ! [X0: arrow_411405190le_alt,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),X0),X1),l)
| ( X0 = y )
| ( X1 = y )
| ! [X2: arrow_411405190le_alt] :
( ( ( X1 != x )
| ( X2 != y )
| ( X0 = x )
| 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),X0),x),l) )
& ( ~ 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),l)
| ( X2 = y )
| 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),X0),X2),l) )
& ( ( X2 != y )
| ~ 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),x),l)
| ( X0 = x )
| 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),X0),x),l) ) ) )
& ( ( X1 != y )
| ~ 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),X0),x),l)
| ( X0 = y )
| ! [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),x),X3),l)
| ( y = 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),X0),X3),l) ) )
& ( ( X0 != y )
| ~ 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),x),X1),l)
| ( X1 = y )
| ! [X4: arrow_411405190le_alt] :
( ( ( X1 != x )
| ( y != X4 ) )
& ( ~ 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),X4),l)
| ( y = X4 )
| 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),x),X4),l) )
& ( ( y != X4 )
| ~ 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),x),l) ) ) ) )
& ! [X5: arrow_411405190le_alt,X6: arrow_411405190le_alt] :
( ( X5 = X6 )
| ( ( x = X5 )
& ( y = X6 ) )
| ( 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),X5),X6),l)
& ( y != X5 )
& ( y != X6 ) )
| ( ( y = X6 )
& 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),X5),x),l)
& ( y != X5 ) )
| ( ( y = X5 )
& 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),x),X6),l)
& ( y != X6 ) )
| ( ( x = X6 )
& ( y = X5 ) )
| ( 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),X6),X5),l)
& ( y != X6 )
& ( y != X5 ) )
| ( ( y = X5 )
& 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),X6),x),l)
& ( y != X6 ) )
| ( ( y = X6 )
& 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),x),X5),l)
& ( y != X5 ) ) ) ),
inference(rectify,[],[f99]) ).
tff(f102,plain,
( ! [X0: arrow_411405190le_alt,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),X0),X2),l)
| ~ 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),l) )
| ~ 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),X0),X1),l) )
& ! [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),X3),X3),l)
& ! [X4: arrow_411405190le_alt,X5: 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),X4),X5),l)
| 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),X5),X4),l)
| ( X4 = X5 ) ) ),
inference(ennf_transformation,[],[f100]) ).
tff(f103,plain,
( ! [X0: arrow_411405190le_alt,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),X0),X2),l)
| ~ 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),l) )
| ~ 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),X0),X1),l) )
& ! [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),X3),X3),l)
& ! [X4: arrow_411405190le_alt,X5: 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),X4),X5),l)
| 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),X5),X4),l)
| ( X4 = X5 ) ) ),
inference(flattening,[],[f102]) ).
tff(f104,plain,
( ? [X0: arrow_411405190le_alt,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),X0),X1),l)
& ( y != X0 )
& ( y != X1 )
& ? [X2: arrow_411405190le_alt] :
( ( ( x = X1 )
& ( y = X2 )
& ( x != 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),X0),x),l) )
| ( 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),l)
& ( y != X2 )
& ~ 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),X0),X2),l) )
| ( ( y = X2 )
& 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),x),l)
& ( x != 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),X0),x),l) ) ) )
| ( ( y = X1 )
& 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),X0),x),l)
& ( y != X0 )
& ? [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),x),X3),l)
& ( y != 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),X0),X3),l) ) )
| ( ( y = 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),x),X1),l)
& ( y != X1 )
& ? [X4: arrow_411405190le_alt] :
( ( ( x = X1 )
& ( y = X4 ) )
| ( 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),X4),l)
& ( y != X4 )
& ~ 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),x),X4),l) )
| ( ( y = X4 )
& 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),x),l) ) ) ) )
| ? [X5: arrow_411405190le_alt,X6: arrow_411405190le_alt] :
( ( X5 != X6 )
& ( ( x != X5 )
| ( y != X6 ) )
& ( ~ 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),X5),X6),l)
| ( y = X5 )
| ( y = X6 ) )
& ( ( y != X6 )
| ~ 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),X5),x),l)
| ( y = X5 ) )
& ( ( y != X5 )
| ~ 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),x),X6),l)
| ( y = X6 ) )
& ( ( x != X6 )
| ( y != X5 ) )
& ( ~ 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),X6),X5),l)
| ( y = X6 )
| ( y = X5 ) )
& ( ( y != X5 )
| ~ 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),X6),x),l)
| ( y = X6 ) )
& ( ( y != X6 )
| ~ 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),x),X5),l)
| ( y = X5 ) ) ) ),
inference(ennf_transformation,[],[f101]) ).
tff(f116,definition,
! [X4: arrow_411405190le_alt,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),X4),l)
& ( y != X4 )
& ~ 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),x),X4),l) )
| ~ sP0(X4,X1) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
tff(f117,definition,
! [X2: arrow_411405190le_alt,X1: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
( ( ( y = X2 )
& 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),x),l)
& ( x != 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),X0),x),l) )
| ~ sP1(X2,X1,X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
tff(f118,definition,
! [X1: arrow_411405190le_alt,X2: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
( ( ( x = X1 )
& ( y = X2 )
& ( x != 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),X0),x),l) )
| ~ sP2(X1,X2,X0) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
tff(f119,definition,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( ( y = 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),x),X1),l)
& ( y != X1 )
& ? [X4: arrow_411405190le_alt] :
( ( ( x = X1 )
& ( y = X4 ) )
| sP0(X4,X1)
| ( ( y = X4 )
& 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),x),l) ) ) )
| ~ sP3(X0,X1) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
tff(f120,definition,
! [X1: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
( ( ( y = X1 )
& 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),X0),x),l)
& ( y != X0 )
& ? [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),x),X3),l)
& ( y != 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),X0),X3),l) ) )
| ~ sP4(X1,X0) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
tff(f121,definition,
( ? [X5: arrow_411405190le_alt,X6: arrow_411405190le_alt] :
( ( X5 != X6 )
& ( ( x != X5 )
| ( y != X6 ) )
& ( ~ 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),X5),X6),l)
| ( y = X5 )
| ( y = X6 ) )
& ( ( y != X6 )
| ~ 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),X5),x),l)
| ( y = X5 ) )
& ( ( y != X5 )
| ~ 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),x),X6),l)
| ( y = X6 ) )
& ( ( x != X6 )
| ( y != X5 ) )
& ( ~ 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),X6),X5),l)
| ( y = X6 )
| ( y = X5 ) )
& ( ( y != X5 )
| ~ 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),X6),x),l)
| ( y = X6 ) )
& ( ( y != X6 )
| ~ 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),x),X5),l)
| ( y = X5 ) ) )
| ~ sP5 ),
introduced(definition,[new_symbols(definition,[sP5])],[predicate_definition_introduction]) ).
tff(f122,plain,
( ? [X0: arrow_411405190le_alt,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),X0),X1),l)
& ( y != X0 )
& ( y != X1 )
& ? [X2: arrow_411405190le_alt] :
( sP2(X1,X2,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),l)
& ( y != X2 )
& ~ 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),X0),X2),l) )
| sP1(X2,X1,X0) ) )
| sP4(X1,X0)
| sP3(X0,X1) )
| sP5 ),
inference(definition_folding,[],[f104,f121,f120,f119,f118,f117,f116]) ).
tff(f123,plain,
( ? [X5: arrow_411405190le_alt,X6: arrow_411405190le_alt] :
( ( X5 != X6 )
& ( ( x != X5 )
| ( y != X6 ) )
& ( ~ 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),X5),X6),l)
| ( y = X5 )
| ( y = X6 ) )
& ( ( y != X6 )
| ~ 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),X5),x),l)
| ( y = X5 ) )
& ( ( y != X5 )
| ~ 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),x),X6),l)
| ( y = X6 ) )
& ( ( x != X6 )
| ( y != X5 ) )
& ( ~ 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),X6),X5),l)
| ( y = X6 )
| ( y = X5 ) )
& ( ( y != X5 )
| ~ 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),X6),x),l)
| ( y = X6 ) )
& ( ( y != X6 )
| ~ 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),x),X5),l)
| ( y = X5 ) ) )
| ~ sP5 ),
inference(nnf_transformation,[],[f121]) ).
tff(f124,plain,
( ? [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( X0 != X1 )
& ( ( x != X0 )
| ( y != X1 ) )
& ( ~ 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),X0),X1),l)
| ( y = X0 )
| ( y = X1 ) )
& ( ( y != X1 )
| ~ 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),X0),x),l)
| ( y = X0 ) )
& ( ( y != 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),x),X1),l)
| ( y = X1 ) )
& ( ( x != X1 )
| ( y != 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),X0),l)
| ( y = X1 )
| ( y = X0 ) )
& ( ( y != 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),x),l)
| ( y = X1 ) )
& ( ( y != X1 )
| ~ 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),x),X0),l)
| ( y = X0 ) ) )
| ~ sP5 ),
inference(rectify,[],[f123]) ).
tff(f125,plain,
( ( ( sK6 != sK7 )
& ( ( x != sK6 )
| ( y != sK7 ) )
& ( ~ 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),sK6),sK7),l)
| ( y = sK6 )
| ( y = sK7 ) )
& ( ( y != sK7 )
| ~ 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),sK6),x),l)
| ( y = sK6 ) )
& ( ( y != sK6 )
| ~ 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),x),sK7),l)
| ( y = sK7 ) )
& ( ( x != sK7 )
| ( y != sK6 ) )
& ( ~ 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),sK7),sK6),l)
| ( y = sK7 )
| ( y = sK6 ) )
& ( ( y != sK6 )
| ~ 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),sK7),x),l)
| ( y = sK7 ) )
& ( ( y != sK7 )
| ~ 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),x),sK6),l)
| ( y = sK6 ) ) )
| ~ sP5 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f124]) ).
tff(f126,plain,
! [X1: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
( ( ( y = X1 )
& 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),X0),x),l)
& ( y != X0 )
& ? [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),x),X3),l)
& ( y != 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),X0),X3),l) ) )
| ~ sP4(X1,X0) ),
inference(nnf_transformation,[],[f120]) ).
tff(f127,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( ( y = 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),x),l)
& ( y != X1 )
& ? [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),x),X2),l)
& ( y != X2 )
& ~ 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),l) ) )
| ~ sP4(X0,X1) ),
inference(rectify,[],[f126]) ).
tff(f128,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( ( y = 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),x),l)
& ( y != X1 )
& 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),x),sK8(X1)),l)
& ( y != sK8(X1) )
& ~ 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),sK8(X1)),l) )
| ~ sP4(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(X2,sK8(X1))],[f127]) ).
tff(f129,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( ( y = 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),x),X1),l)
& ( y != X1 )
& ? [X4: arrow_411405190le_alt] :
( ( ( x = X1 )
& ( y = X4 ) )
| sP0(X4,X1)
| ( ( y = X4 )
& 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),x),l) ) ) )
| ~ sP3(X0,X1) ),
inference(nnf_transformation,[],[f119]) ).
tff(f130,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( ( y = 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),x),X1),l)
& ( y != X1 )
& ? [X2: arrow_411405190le_alt] :
( ( ( x = X1 )
& ( y = X2 ) )
| sP0(X2,X1)
| ( ( y = X2 )
& 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),x),l) ) ) )
| ~ sP3(X0,X1) ),
inference(rectify,[],[f129]) ).
tff(f131,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( ( y = 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),x),X1),l)
& ( y != X1 )
& ( ( ( x = X1 )
& ( y = sK9(X1) ) )
| sP0(sK9(X1),X1)
| ( ( y = sK9(X1) )
& 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),x),l) ) ) )
| ~ sP3(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X2,sK9(X1))],[f130]) ).
tff(f132,plain,
! [X1: arrow_411405190le_alt,X2: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
( ( ( x = X1 )
& ( y = X2 )
& ( x != 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),X0),x),l) )
| ~ sP2(X1,X2,X0) ),
inference(nnf_transformation,[],[f118]) ).
tff(f133,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: arrow_411405190le_alt] :
( ( ( x = X0 )
& ( y = X1 )
& ( x != X2 )
& ~ 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),x),l) )
| ~ sP2(X0,X1,X2) ),
inference(rectify,[],[f132]) ).
tff(f134,plain,
! [X2: arrow_411405190le_alt,X1: arrow_411405190le_alt,X0: arrow_411405190le_alt] :
( ( ( y = X2 )
& 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),x),l)
& ( x != 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),X0),x),l) )
| ~ sP1(X2,X1,X0) ),
inference(nnf_transformation,[],[f117]) ).
tff(f135,plain,
! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt,X2: arrow_411405190le_alt] :
( ( ( y = 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),x),l)
& ( x != X2 )
& ~ 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),x),l) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f134]) ).
tff(f136,plain,
! [X4: arrow_411405190le_alt,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),X4),l)
& ( y != X4 )
& ~ 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),x),X4),l) )
| ~ sP0(X4,X1) ),
inference(nnf_transformation,[],[f116]) ).
tff(f137,plain,
! [X0: arrow_411405190le_alt,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),X0),l)
& ( y != 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),x),X0),l) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f136]) ).
tff(f138,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),sK10),sK11),l)
& ( y != sK10 )
& ( y != sK11 )
& ( sP2(sK11,sK12,sK10)
| ( 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),sK11),sK12),l)
& ( y != sK12 )
& ~ 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),sK10),sK12),l) )
| sP1(sK12,sK11,sK10) ) )
| sP4(sK11,sK10)
| sP3(sK10,sK11)
| sP5 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11,sK12]),skolemize(X0,sK10),skolemize(X1,sK11),skolemize(X2,sK12)],[f122]) ).
tff(f153,plain,
! [X4: arrow_411405190le_alt,X5: 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),X5),X4),l)
| 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),X4),X5),l)
| ( X4 = X5 ) ),
inference(cnf_transformation,[],[f103]) ).
tff(f154,plain,
! [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),X3),X3),l),
inference(cnf_transformation,[],[f103]) ).
tff(f155,plain,
! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,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),l)
| 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),X0),X2),l)
| ~ 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),X0),X1),l) ),
inference(cnf_transformation,[],[f103]) ).
tff(f156,plain,
( ( y != sK7 )
| ~ 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),x),sK6),l)
| ( y = sK6 )
| ~ sP5 ),
inference(cnf_transformation,[],[f125]) ).
tff(f157,plain,
( ( y != sK6 )
| ~ 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),sK7),x),l)
| ( y = sK7 )
| ~ sP5 ),
inference(cnf_transformation,[],[f125]) ).
tff(f158,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),sK7),sK6),l)
| ( y = sK7 )
| ( y = sK6 )
| ~ sP5 ),
inference(cnf_transformation,[],[f125]) ).
tff(f159,plain,
( ( x != sK7 )
| ( y != sK6 )
| ~ sP5 ),
inference(cnf_transformation,[],[f125]) ).
tff(f160,plain,
( ( y != sK6 )
| ~ 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),x),sK7),l)
| ( y = sK7 )
| ~ sP5 ),
inference(cnf_transformation,[],[f125]) ).
tff(f161,plain,
( ( y != sK7 )
| ~ 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),sK6),x),l)
| ( y = sK6 )
| ~ sP5 ),
inference(cnf_transformation,[],[f125]) ).
tff(f162,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),sK6),sK7),l)
| ( y = sK6 )
| ( y = sK7 )
| ~ sP5 ),
inference(cnf_transformation,[],[f125]) ).
tff(f163,plain,
( ( x != sK6 )
| ( y != sK7 )
| ~ sP5 ),
inference(cnf_transformation,[],[f125]) ).
tff(f164,plain,
( ( sK6 != sK7 )
| ~ sP5 ),
inference(cnf_transformation,[],[f125]) ).
tff(f165,plain,
! [X0: arrow_411405190le_alt,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),sK8(X1)),l)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f128]) ).
tff(f167,plain,
! [X0: arrow_411405190le_alt,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),x),sK8(X1)),l)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f128]) ).
tff(f169,plain,
! [X0: arrow_411405190le_alt,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),x),l)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f128]) ).
tff(f173,plain,
! [X0: arrow_411405190le_alt,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),x),l)
| sP0(sK9(X1),X1)
| ( x = X1 )
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f131]) ).
tff(f176,plain,
! [X0: arrow_411405190le_alt,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),x),X1),l)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f131]) ).
tff(f178,plain,
! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,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),X2),x),l)
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f133]) ).
tff(f179,plain,
! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ( x != X2 )
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f133]) ).
tff(f181,plain,
! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ sP2(X0,X1,X2)
| ( x = X0 ) ),
inference(cnf_transformation,[],[f133]) ).
tff(f182,plain,
! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,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),X2),x),l)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f135]) ).
tff(f184,plain,
! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,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),x),l)
| ~ sP1(X0,X1,X2) ),
inference(cnf_transformation,[],[f135]) ).
tff(f186,plain,
! [X0: arrow_411405190le_alt,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),x),X0),l)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
tff(f188,plain,
! [X0: arrow_411405190le_alt,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),X0),l)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
tff(f189,plain,
( sP2(sK11,sK12,sK10)
| ~ 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),sK10),sK12),l)
| sP1(sK12,sK11,sK10)
| sP4(sK11,sK10)
| sP3(sK10,sK11)
| sP5 ),
inference(cnf_transformation,[],[f138]) ).
tff(f191,plain,
( sP2(sK11,sK12,sK10)
| 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),sK11),sK12),l)
| sP1(sK12,sK11,sK10)
| sP4(sK11,sK10)
| sP3(sK10,sK11)
| sP5 ),
inference(cnf_transformation,[],[f138]) ).
tff(f194,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),sK10),sK11),l)
| sP4(sK11,sK10)
| sP3(sK10,sK11)
| sP5 ),
inference(cnf_transformation,[],[f138]) ).
tff(f217,definition,
~ sP43(sK6),
introduced(definition,[new_symbols(definition,[sP43])],[inequality_splitting_name_introduction]) ).
tff(f218,plain,
( sP43(sK7)
| ~ sP5 ),
inference(inequality_splitting,[],[f164,f217]) ).
tff(f219,definition,
~ sP44(x),
introduced(definition,[new_symbols(definition,[sP44])],[inequality_splitting_name_introduction]) ).
tff(f220,definition,
~ sP45(y),
introduced(definition,[new_symbols(definition,[sP45])],[inequality_splitting_name_introduction]) ).
tff(f221,plain,
( sP45(sK7)
| sP44(sK6)
| ~ sP5 ),
inference(inequality_splitting,[],[f163,f220,f219]) ).
tff(f222,definition,
~ sP46(y),
introduced(definition,[new_symbols(definition,[sP46])],[inequality_splitting_name_introduction]) ).
tff(f223,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),sK6),x),l)
| sP46(sK7)
| ( y = sK6 )
| ~ sP5 ),
inference(inequality_splitting,[],[f161,f222]) ).
tff(f224,definition,
~ sP47(y),
introduced(definition,[new_symbols(definition,[sP47])],[inequality_splitting_name_introduction]) ).
tff(f225,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),x),sK7),l)
| sP47(sK6)
| ( y = sK7 )
| ~ sP5 ),
inference(inequality_splitting,[],[f160,f224]) ).
tff(f226,definition,
~ sP48(x),
introduced(definition,[new_symbols(definition,[sP48])],[inequality_splitting_name_introduction]) ).
tff(f227,definition,
~ sP49(y),
introduced(definition,[new_symbols(definition,[sP49])],[inequality_splitting_name_introduction]) ).
tff(f228,plain,
( sP49(sK6)
| sP48(sK7)
| ~ sP5 ),
inference(inequality_splitting,[],[f159,f227,f226]) ).
tff(f229,definition,
~ sP50(y),
introduced(definition,[new_symbols(definition,[sP50])],[inequality_splitting_name_introduction]) ).
tff(f230,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),sK7),x),l)
| sP50(sK6)
| ( y = sK7 )
| ~ sP5 ),
inference(inequality_splitting,[],[f157,f229]) ).
tff(f231,definition,
~ sP51(y),
introduced(definition,[new_symbols(definition,[sP51])],[inequality_splitting_name_introduction]) ).
tff(f232,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),x),sK6),l)
| sP51(sK7)
| ( y = sK6 )
| ~ sP5 ),
inference(inequality_splitting,[],[f156,f231]) ).
tff(f239,definition,
~ sP55(x),
introduced(definition,[new_symbols(definition,[sP55])],[inequality_splitting_name_introduction]) ).
tff(f240,plain,
! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ sP2(X0,X1,X2)
| sP55(X2) ),
inference(inequality_splitting,[],[f179,f239]) ).
tff(f255,definition,
( spl61_1
<=> sP5 ),
introduced(definition,[new_symbols(definition,[spl61_1])],[avatar_definition]) ).
tff(f257,plain,
( sP5
| ~ spl61_1 ),
inference(avatar_component_clause,[],[f255]) ).
tff(f259,definition,
( spl61_2
<=> sP3(sK10,sK11) ),
introduced(definition,[new_symbols(definition,[spl61_2])],[avatar_definition]) ).
tff(f261,plain,
( sP3(sK10,sK11)
| ~ spl61_2 ),
inference(avatar_component_clause,[],[f259]) ).
tff(f263,definition,
( spl61_3
<=> sP4(sK11,sK10) ),
introduced(definition,[new_symbols(definition,[spl61_3])],[avatar_definition]) ).
tff(f265,plain,
( sP4(sK11,sK10)
| ~ spl61_3 ),
inference(avatar_component_clause,[],[f263]) ).
tff(f267,definition,
( spl61_4
<=> sP1(sK12,sK11,sK10) ),
introduced(definition,[new_symbols(definition,[spl61_4])],[avatar_definition]) ).
tff(f269,plain,
( sP1(sK12,sK11,sK10)
| ~ spl61_4 ),
inference(avatar_component_clause,[],[f267]) ).
tff(f271,definition,
( spl61_5
<=> 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),sK10),sK12),l) ),
introduced(definition,[new_symbols(definition,[spl61_5])],[avatar_definition]) ).
tff(f273,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),sK10),sK12),l)
| spl61_5 ),
inference(avatar_component_clause,[],[f271]) ).
tff(f275,definition,
( spl61_6
<=> sP2(sK11,sK12,sK10) ),
introduced(definition,[new_symbols(definition,[spl61_6])],[avatar_definition]) ).
tff(f277,plain,
( sP2(sK11,sK12,sK10)
| ~ spl61_6 ),
inference(avatar_component_clause,[],[f275]) ).
tff(f278,plain,
( spl61_1
| spl61_2
| spl61_3
| spl61_4
| ~ spl61_5
| spl61_6 ),
inference(avatar_split_clause,[],[f189,f275,f271,f267,f263,f259,f255]) ).
tff(f285,definition,
( spl61_8
<=> 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),sK11),sK12),l) ),
introduced(definition,[new_symbols(definition,[spl61_8])],[avatar_definition]) ).
tff(f287,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),sK11),sK12),l)
| ~ spl61_8 ),
inference(avatar_component_clause,[],[f285]) ).
tff(f288,plain,
( spl61_1
| spl61_2
| spl61_3
| spl61_4
| spl61_8
| spl61_6 ),
inference(avatar_split_clause,[],[f191,f275,f285,f267,f263,f259,f255]) ).
tff(f300,definition,
( spl61_11
<=> 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),sK10),sK11),l) ),
introduced(definition,[new_symbols(definition,[spl61_11])],[avatar_definition]) ).
tff(f302,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),sK10),sK11),l)
| ~ spl61_11 ),
inference(avatar_component_clause,[],[f300]) ).
tff(f303,plain,
( spl61_1
| spl61_2
| spl61_3
| spl61_11 ),
inference(avatar_split_clause,[],[f194,f300,f263,f259,f255]) ).
tff(f329,plain,
! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,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),x),X0),l)
| ( x = X0 )
| ~ sP2(X1,X2,X0) ),
inference(resolution,[],[f153,f178]) ).
tff(f331,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),sK7),x),l)
| ( x = sK7 )
| sP47(sK6)
| ( y = sK7 )
| ~ sP5 ),
inference(resolution,[],[f153,f225]) ).
tff(f334,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),sK7),sK6),l)
| ( sK6 = sK7 )
| ( y = sK6 )
| ( y = sK7 )
| ~ sP5 ),
inference(resolution,[],[f153,f162]) ).
tff(f335,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),x),sK6),l)
| ( x = sK6 )
| sP46(sK7)
| ( y = sK6 )
| ~ sP5 ),
inference(resolution,[],[f153,f223]) ).
tff(f345,plain,
( ( sK6 = sK7 )
| ( y = sK6 )
| ( y = sK7 )
| ~ sP5 ),
inference(forward_subsumption_resolution,[],[f334,f158]) ).
tff(f349,definition,
( spl61_12
<=> sP50(sK6) ),
introduced(definition,[new_symbols(definition,[spl61_12])],[avatar_definition]) ).
tff(f350,plain,
( ~ sP50(sK6)
| spl61_12 ),
inference(avatar_component_clause,[],[f349]) ).
tff(f351,plain,
( sP50(sK6)
| ~ spl61_12 ),
inference(avatar_component_clause,[],[f349]) ).
tff(f353,definition,
( spl61_13
<=> ( x = sK7 ) ),
introduced(definition,[new_symbols(definition,[spl61_13])],[avatar_definition]) ).
tff(f355,plain,
( ( x = sK7 )
| ~ spl61_13 ),
inference(avatar_component_clause,[],[f353]) ).
tff(f367,definition,
( spl61_16
<=> sP46(sK7) ),
introduced(definition,[new_symbols(definition,[spl61_16])],[avatar_definition]) ).
tff(f368,plain,
( ~ sP46(sK7)
| spl61_16 ),
inference(avatar_component_clause,[],[f367]) ).
tff(f369,plain,
( sP46(sK7)
| ~ spl61_16 ),
inference(avatar_component_clause,[],[f367]) ).
tff(f371,definition,
( spl61_17
<=> ( x = sK6 ) ),
introduced(definition,[new_symbols(definition,[spl61_17])],[avatar_definition]) ).
tff(f372,plain,
( ( x != sK6 )
| spl61_17 ),
inference(avatar_component_clause,[],[f371]) ).
tff(f373,plain,
( ( x = sK6 )
| ~ spl61_17 ),
inference(avatar_component_clause,[],[f371]) ).
tff(f375,definition,
( spl61_18
<=> 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),x),sK6),l) ),
introduced(definition,[new_symbols(definition,[spl61_18])],[avatar_definition]) ).
tff(f376,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),x),sK6),l)
| spl61_18 ),
inference(avatar_component_clause,[],[f375]) ).
tff(f377,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),x),sK6),l)
| ~ spl61_18 ),
inference(avatar_component_clause,[],[f375]) ).
tff(f385,definition,
( spl61_20
<=> sP51(sK7) ),
introduced(definition,[new_symbols(definition,[spl61_20])],[avatar_definition]) ).
tff(f386,plain,
( ~ sP51(sK7)
| spl61_20 ),
inference(avatar_component_clause,[],[f385]) ).
tff(f387,plain,
( sP51(sK7)
| ~ spl61_20 ),
inference(avatar_component_clause,[],[f385]) ).
tff(f394,definition,
( spl61_22
<=> sP47(sK6) ),
introduced(definition,[new_symbols(definition,[spl61_22])],[avatar_definition]) ).
tff(f396,plain,
( sP47(sK6)
| ~ spl61_22 ),
inference(avatar_component_clause,[],[f394]) ).
tff(f398,definition,
( spl61_23
<=> 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),sK7),x),l) ),
introduced(definition,[new_symbols(definition,[spl61_23])],[avatar_definition]) ).
tff(f400,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),sK7),x),l)
| ~ spl61_23 ),
inference(avatar_component_clause,[],[f398]) ).
tff(f405,definition,
( spl61_24
<=> ( sK6 = sK7 ) ),
introduced(definition,[new_symbols(definition,[spl61_24])],[avatar_definition]) ).
tff(f406,plain,
( ( sK6 != sK7 )
| spl61_24 ),
inference(avatar_component_clause,[],[f405]) ).
tff(f407,plain,
( ( sK6 = sK7 )
| ~ spl61_24 ),
inference(avatar_component_clause,[],[f405]) ).
tff(f410,plain,
! [X2: arrow_411405190le_alt,X3: arrow_411405190le_alt,X0: arrow_411405190le_alt,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),X0),X1),l)
| 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),X0),x),l)
| ~ sP1(X2,X1,X3) ),
inference(resolution,[],[f155,f184]) ).
tff(f412,plain,
! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,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),X0),X1),l)
| 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),X0),x),l)
| sP0(sK9(X1),X1)
| ( x = X1 )
| ~ sP3(X2,X1) ),
inference(resolution,[],[f155,f173]) ).
tff(f415,plain,
! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,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),X0),X2),l)
| 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),X0),X1),l)
| ~ sP0(X1,X2) ),
inference(resolution,[],[f155,f188]) ).
tff(f416,plain,
! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,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),X0),sK8(X1)),l)
| ~ 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),X0),x),l)
| ~ sP4(X2,X1) ),
inference(resolution,[],[f155,f167]) ).
tff(f482,plain,
! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,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),x),X0),l)
| ~ sP0(X0,X1)
| ~ sP3(X2,X1) ),
inference(resolution,[],[f415,f176]) ).
tff(f490,plain,
! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ sP3(X2,X1)
| ~ sP0(X0,X1) ),
inference(forward_subsumption_resolution,[],[f482,f186]) ).
tff(f512,definition,
( spl61_25
<=> ! [X0: arrow_411405190le_alt] : ~ sP3(X0,sK11) ),
introduced(definition,[new_symbols(definition,[spl61_25])],[avatar_definition]) ).
tff(f513,plain,
( ! [X0: arrow_411405190le_alt] : ~ sP3(X0,sK11)
| ~ spl61_25 ),
inference(avatar_component_clause,[],[f512]) ).
tff(f515,definition,
( spl61_26
<=> ( x = sK11 ) ),
introduced(definition,[new_symbols(definition,[spl61_26])],[avatar_definition]) ).
tff(f517,plain,
( ( x = sK11 )
| ~ spl61_26 ),
inference(avatar_component_clause,[],[f515]) ).
tff(f527,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),sK7),x),l)
| ( x = sK7 )
| sP47(sK6)
| ( y = sK7 )
| ~ spl61_1 ),
inference(forward_subsumption_resolution,[],[f331,f257]) ).
tff(f529,plain,
( ( sK6 = sK7 )
| ( y = sK6 )
| ( y = sK7 )
| ~ spl61_1 ),
inference(forward_subsumption_resolution,[],[f345,f257]) ).
tff(f537,definition,
( spl61_28
<=> ( y = sK7 ) ),
introduced(definition,[new_symbols(definition,[spl61_28])],[avatar_definition]) ).
tff(f538,plain,
( ( y != sK7 )
| spl61_28 ),
inference(avatar_component_clause,[],[f537]) ).
tff(f539,plain,
( ( y = sK7 )
| ~ spl61_28 ),
inference(avatar_component_clause,[],[f537]) ).
tff(f542,definition,
( spl61_29
<=> ( y = sK6 ) ),
introduced(definition,[new_symbols(definition,[spl61_29])],[avatar_definition]) ).
tff(f544,plain,
( ( y = sK6 )
| ~ spl61_29 ),
inference(avatar_component_clause,[],[f542]) ).
tff(f547,plain,
( spl61_28
| spl61_22
| spl61_13
| spl61_23
| ~ spl61_1 ),
inference(avatar_split_clause,[],[f527,f255,f398,f353,f394,f537]) ).
tff(f549,plain,
( spl61_28
| spl61_29
| spl61_24
| ~ spl61_1 ),
inference(avatar_split_clause,[],[f529,f255,f405,f542,f537]) ).
tff(f575,plain,
( sP55(sK10)
| ~ spl61_6 ),
inference(resolution,[],[f277,f240]) ).
tff(f577,plain,
( ( x = sK11 )
| ~ spl61_6 ),
inference(resolution,[],[f277,f181]) ).
tff(f578,plain,
( spl61_26
| ~ spl61_6 ),
inference(avatar_split_clause,[],[f577,f275,f515]) ).
tff(f580,definition,
( spl61_36
<=> ( x = sK10 ) ),
introduced(definition,[new_symbols(definition,[spl61_36])],[avatar_definition]) ).
tff(f582,plain,
( ( x = sK10 )
| ~ spl61_36 ),
inference(avatar_component_clause,[],[f580]) ).
tff(f617,plain,
( ~ sP48(sK7)
| ~ spl61_13 ),
inference(superposition,[],[f226,f355]) ).
tff(f660,definition,
( spl61_40
<=> 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),sK10),x),l) ),
introduced(definition,[new_symbols(definition,[spl61_40])],[avatar_definition]) ).
tff(f662,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),sK10),x),l)
| ~ spl61_40 ),
inference(avatar_component_clause,[],[f660]) ).
tff(f706,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),X0),sK10),l)
| 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),X0),sK11),l) )
| ~ spl61_11 ),
inference(resolution,[],[f302,f155]) ).
tff(f709,plain,
( ~ sP43(sK7)
| ~ spl61_24 ),
inference(superposition,[],[f217,f407]) ).
tff(f717,definition,
( spl61_43
<=> sP48(sK7) ),
introduced(definition,[new_symbols(definition,[spl61_43])],[avatar_definition]) ).
tff(f718,plain,
( ~ sP48(sK7)
| spl61_43 ),
inference(avatar_component_clause,[],[f717]) ).
tff(f729,plain,
( ~ sP5
| ~ spl61_24 ),
inference(resolution,[],[f709,f218]) ).
tff(f752,plain,
( ! [X0: arrow_411405190le_alt,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),x),sK11),l)
| ( x = sK10 )
| ~ sP2(X0,X1,sK10) )
| ~ spl61_11 ),
inference(resolution,[],[f706,f329]) ).
tff(f757,definition,
( spl61_45
<=> ! [X0: arrow_411405190le_alt] : ~ sP4(X0,sK10) ),
introduced(definition,[new_symbols(definition,[spl61_45])],[avatar_definition]) ).
tff(f758,plain,
( ! [X0: arrow_411405190le_alt] : ~ sP4(X0,sK10)
| ~ spl61_45 ),
inference(avatar_component_clause,[],[f757]) ).
tff(f769,definition,
( spl61_48
<=> ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] : ~ sP1(X0,X1,sK10) ),
introduced(definition,[new_symbols(definition,[spl61_48])],[avatar_definition]) ).
tff(f770,plain,
( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] : ~ sP1(X0,X1,sK10)
| ~ spl61_48 ),
inference(avatar_component_clause,[],[f769]) ).
tff(f772,definition,
( spl61_49
<=> 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),x),sK11),l) ),
introduced(definition,[new_symbols(definition,[spl61_49])],[avatar_definition]) ).
tff(f773,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),x),sK11),l)
| spl61_49 ),
inference(avatar_component_clause,[],[f772]) ).
tff(f774,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),x),sK11),l)
| ~ spl61_49 ),
inference(avatar_component_clause,[],[f772]) ).
tff(f777,definition,
( spl61_50
<=> ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] : ~ sP2(X0,X1,sK10) ),
introduced(definition,[new_symbols(definition,[spl61_50])],[avatar_definition]) ).
tff(f778,plain,
( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] : ~ sP2(X0,X1,sK10)
| ~ spl61_50 ),
inference(avatar_component_clause,[],[f777]) ).
tff(f779,plain,
( spl61_50
| spl61_36
| spl61_49
| ~ spl61_11 ),
inference(avatar_split_clause,[],[f752,f300,f772,f580,f777]) ).
tff(f792,plain,
( ! [X0: arrow_411405190le_alt,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),sK10),x),l)
| ~ sP1(X0,sK11,X1) )
| ~ spl61_11 ),
inference(resolution,[],[f410,f302]) ).
tff(f800,definition,
( spl61_51
<=> ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] : ~ sP1(X0,sK11,X1) ),
introduced(definition,[new_symbols(definition,[spl61_51])],[avatar_definition]) ).
tff(f801,plain,
( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] : ~ sP1(X0,sK11,X1)
| ~ spl61_51 ),
inference(avatar_component_clause,[],[f800]) ).
tff(f802,plain,
( spl61_51
| spl61_40
| ~ spl61_11 ),
inference(avatar_split_clause,[],[f792,f300,f660,f800]) ).
tff(f807,plain,
! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,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),X0),x),l)
| ~ sP4(X1,X0)
| ~ sP4(X2,X0) ),
inference(resolution,[],[f416,f165]) ).
tff(f814,plain,
! [X2: arrow_411405190le_alt,X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] :
( ~ sP4(X2,X0)
| ~ sP4(X1,X0) ),
inference(forward_subsumption_resolution,[],[f807,f169]) ).
tff(f911,plain,
( ! [X0: arrow_411405190le_alt,X1: arrow_411405190le_alt] : ~ sP1(X0,X1,sK10)
| ~ spl61_40 ),
inference(resolution,[],[f662,f182]) ).
tff(f920,plain,
( spl61_48
| ~ spl61_40 ),
inference(avatar_split_clause,[],[f911,f660,f769]) ).
tff(f923,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),x),x),l)
| sP0(sK9(sK11),sK11)
| ( x = sK11 )
| ~ sP3(X0,sK11) )
| ~ spl61_49 ),
inference(resolution,[],[f774,f412]) ).
tff(f929,plain,
( ! [X0: arrow_411405190le_alt] :
( sP0(sK9(sK11),sK11)
| ( x = sK11 )
| ~ sP3(X0,sK11) )
| ~ spl61_49 ),
inference(forward_subsumption_resolution,[],[f923,f154]) ).
tff(f930,plain,
( ! [X0: arrow_411405190le_alt] :
( ( x = sK11 )
| ~ sP3(X0,sK11) )
| ~ spl61_49 ),
inference(forward_subsumption_resolution,[],[f929,f490]) ).
tff(f931,plain,
( spl61_25
| spl61_26
| ~ spl61_49 ),
inference(avatar_split_clause,[],[f930,f772,f515,f512]) ).
tff(f934,plain,
( ! [X0: arrow_411405190le_alt] : ~ sP3(X0,sK11)
| spl61_49 ),
inference(resolution,[],[f773,f176]) ).
tff(f942,plain,
( spl61_25
| spl61_49 ),
inference(avatar_split_clause,[],[f934,f772,f512]) ).
tff(f951,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),x),x),l)
| ~ spl61_26
| ~ spl61_49 ),
inference(forward_demodulation,[],[f774,f517]) ).
tff(f954,plain,
( $false
| ~ spl61_26
| ~ spl61_49 ),
inference(forward_subsumption_resolution,[],[f951,f154]) ).
tff(f955,plain,
( ~ spl61_26
| ~ spl61_49 ),
inference(avatar_contradiction_clause,[],[f954]) ).
tff(f1067,plain,
( ! [X0: arrow_411405190le_alt] : ~ sP4(X0,sK10)
| ~ spl61_3 ),
inference(resolution,[],[f814,f265]) ).
tff(f1068,plain,
( spl61_45
| ~ spl61_3 ),
inference(avatar_split_clause,[],[f1067,f263,f757]) ).
tff(f1069,plain,
( $false
| ~ spl61_4
| ~ spl61_48 ),
inference(forward_subsumption_resolution,[],[f269,f770]) ).
tff(f1070,plain,
( ~ spl61_4
| ~ spl61_48 ),
inference(avatar_contradiction_clause,[],[f1069]) ).
tff(f1078,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),X0),sK11),l)
| 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),X0),sK12),l) )
| ~ spl61_8 ),
inference(resolution,[],[f287,f155]) ).
tff(f1263,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),sK10),sK12),l)
| ~ spl61_8
| ~ spl61_11 ),
inference(resolution,[],[f1078,f302]) ).
tff(f1268,plain,
( $false
| spl61_5
| ~ spl61_8
| ~ spl61_11 ),
inference(forward_subsumption_resolution,[],[f1263,f273]) ).
tff(f1269,plain,
( spl61_5
| ~ spl61_8
| ~ spl61_11 ),
inference(avatar_contradiction_clause,[],[f1268]) ).
tff(f1322,plain,
( $false
| ~ spl61_3
| ~ spl61_45 ),
inference(resolution,[],[f758,f265]) ).
tff(f1323,plain,
( ~ spl61_3
| ~ spl61_45 ),
inference(avatar_contradiction_clause,[],[f1322]) ).
tff(f1324,plain,
( $false
| ~ spl61_4
| ~ spl61_51 ),
inference(forward_subsumption_resolution,[],[f269,f801]) ).
tff(f1325,plain,
( ~ spl61_4
| ~ spl61_51 ),
inference(avatar_contradiction_clause,[],[f1324]) ).
tff(f1344,plain,
( $false
| ~ spl61_6
| ~ spl61_50 ),
inference(forward_subsumption_resolution,[],[f277,f778]) ).
tff(f1345,plain,
( ~ spl61_6
| ~ spl61_50 ),
inference(avatar_contradiction_clause,[],[f1344]) ).
tff(f1346,plain,
( sP55(x)
| ~ spl61_6
| ~ spl61_36 ),
inference(forward_demodulation,[],[f575,f582]) ).
tff(f1369,plain,
( $false
| ~ spl61_6
| ~ spl61_36 ),
inference(forward_subsumption_resolution,[],[f1346,f239]) ).
tff(f1370,plain,
( ~ spl61_6
| ~ spl61_36 ),
inference(avatar_contradiction_clause,[],[f1369]) ).
tff(f1387,plain,
( $false
| ~ spl61_2
| ~ spl61_25 ),
inference(forward_subsumption_resolution,[],[f261,f513]) ).
tff(f1388,plain,
( ~ spl61_2
| ~ spl61_25 ),
inference(avatar_contradiction_clause,[],[f1387]) ).
tff(f1419,plain,
( $false
| ~ spl61_1
| ~ spl61_24 ),
inference(forward_subsumption_resolution,[],[f729,f257]) ).
tff(f1420,plain,
( ~ spl61_1
| ~ spl61_24 ),
inference(avatar_contradiction_clause,[],[f1419]) ).
tff(f1427,plain,
( ~ sP45(sK7)
| ~ spl61_28 ),
inference(superposition,[],[f220,f539]) ).
tff(f1428,plain,
( ~ sP46(sK7)
| ~ spl61_28 ),
inference(superposition,[],[f222,f539]) ).
tff(f1432,plain,
( ~ sP51(sK7)
| ~ spl61_28 ),
inference(superposition,[],[f231,f539]) ).
tff(f1440,plain,
( $false
| ~ spl61_20
| ~ spl61_28 ),
inference(forward_subsumption_resolution,[],[f1432,f387]) ).
tff(f1441,plain,
( ~ spl61_20
| ~ spl61_28 ),
inference(avatar_contradiction_clause,[],[f1440]) ).
tff(f1443,plain,
( $false
| ~ spl61_16
| ~ spl61_28 ),
inference(forward_subsumption_resolution,[],[f1428,f369]) ).
tff(f1444,plain,
( ~ spl61_16
| ~ spl61_28 ),
inference(avatar_contradiction_clause,[],[f1443]) ).
tff(f1454,plain,
( sP44(sK6)
| ~ sP5
| ~ spl61_28 ),
inference(resolution,[],[f1427,f221]) ).
tff(f1455,plain,
( sP44(sK6)
| ~ spl61_1
| ~ spl61_28 ),
inference(forward_subsumption_resolution,[],[f1454,f257]) ).
tff(f1456,plain,
( sP44(x)
| ~ spl61_1
| ~ spl61_17
| ~ spl61_28 ),
inference(forward_demodulation,[],[f1455,f373]) ).
tff(f1457,plain,
( $false
| ~ spl61_1
| ~ spl61_17
| ~ spl61_28 ),
inference(forward_subsumption_resolution,[],[f1456,f219]) ).
tff(f1458,plain,
( ~ spl61_1
| ~ spl61_17
| ~ spl61_28 ),
inference(avatar_contradiction_clause,[],[f1457]) ).
tff(f1459,plain,
( sP51(sK7)
| ( y = sK6 )
| ~ sP5
| ~ spl61_18 ),
inference(resolution,[],[f377,f232]) ).
tff(f1471,plain,
( ( y = sK6 )
| ~ sP5
| ~ spl61_18
| spl61_20 ),
inference(forward_subsumption_resolution,[],[f1459,f386]) ).
tff(f1473,plain,
( ( y = sK6 )
| ~ spl61_1
| ~ spl61_18
| spl61_20 ),
inference(forward_subsumption_resolution,[],[f1471,f257]) ).
tff(f1475,plain,
( ( sK6 = sK7 )
| ~ spl61_1
| ~ spl61_18
| spl61_20
| ~ spl61_28 ),
inference(forward_demodulation,[],[f1473,f539]) ).
tff(f1476,plain,
( $false
| ~ spl61_1
| ~ spl61_18
| spl61_20
| spl61_24
| ~ spl61_28 ),
inference(forward_subsumption_resolution,[],[f1475,f406]) ).
tff(f1477,plain,
( ~ spl61_1
| ~ spl61_18
| spl61_20
| spl61_24
| ~ spl61_28 ),
inference(avatar_contradiction_clause,[],[f1476]) ).
tff(f1479,plain,
( ( x = sK6 )
| sP46(sK7)
| ( y = sK6 )
| ~ sP5
| spl61_18 ),
inference(forward_subsumption_resolution,[],[f335,f376]) ).
tff(f1482,plain,
( sP46(sK7)
| ( y = sK6 )
| ~ sP5
| spl61_17
| spl61_18 ),
inference(forward_subsumption_resolution,[],[f1479,f372]) ).
tff(f1483,plain,
( ( y = sK6 )
| ~ sP5
| spl61_16
| spl61_17
| spl61_18 ),
inference(forward_subsumption_resolution,[],[f1482,f368]) ).
tff(f1484,plain,
( ( y = sK6 )
| ~ spl61_1
| spl61_16
| spl61_17
| spl61_18 ),
inference(forward_subsumption_resolution,[],[f1483,f257]) ).
tff(f1485,plain,
( ( sK6 = sK7 )
| ~ spl61_1
| spl61_16
| spl61_17
| spl61_18
| ~ spl61_28 ),
inference(forward_demodulation,[],[f1484,f539]) ).
tff(f1486,plain,
( $false
| ~ spl61_1
| spl61_16
| spl61_17
| spl61_18
| spl61_24
| ~ spl61_28 ),
inference(forward_subsumption_resolution,[],[f1485,f406]) ).
tff(f1487,plain,
( ~ spl61_1
| spl61_16
| spl61_17
| spl61_18
| spl61_24
| ~ spl61_28 ),
inference(avatar_contradiction_clause,[],[f1486]) ).
tff(f1493,plain,
( ~ sP47(sK6)
| ~ spl61_29 ),
inference(superposition,[],[f224,f544]) ).
tff(f1494,plain,
( ~ sP49(sK6)
| ~ spl61_29 ),
inference(superposition,[],[f227,f544]) ).
tff(f1495,plain,
( ~ sP50(sK6)
| ~ spl61_29 ),
inference(superposition,[],[f229,f544]) ).
tff(f1505,plain,
( $false
| ~ spl61_12
| ~ spl61_29 ),
inference(forward_subsumption_resolution,[],[f1495,f351]) ).
tff(f1506,plain,
( ~ spl61_12
| ~ spl61_29 ),
inference(avatar_contradiction_clause,[],[f1505]) ).
tff(f1507,plain,
( $false
| ~ spl61_22
| ~ spl61_29 ),
inference(forward_subsumption_resolution,[],[f1493,f396]) ).
tff(f1508,plain,
( ~ spl61_22
| ~ spl61_29 ),
inference(avatar_contradiction_clause,[],[f1507]) ).
tff(f1529,plain,
( ~ spl61_43
| ~ spl61_13 ),
inference(avatar_split_clause,[],[f617,f353,f717]) ).
tff(f1580,plain,
( sP50(sK6)
| ( y = sK7 )
| ~ sP5
| ~ spl61_23 ),
inference(resolution,[],[f400,f230]) ).
tff(f1596,plain,
( ( y = sK7 )
| ~ sP5
| spl61_12
| ~ spl61_23 ),
inference(forward_subsumption_resolution,[],[f1580,f350]) ).
tff(f1599,plain,
( ~ sP5
| spl61_12
| ~ spl61_23
| spl61_28 ),
inference(forward_subsumption_resolution,[],[f1596,f538]) ).
tff(f1600,plain,
( $false
| ~ spl61_1
| spl61_12
| ~ spl61_23
| spl61_28 ),
inference(forward_subsumption_resolution,[],[f1599,f257]) ).
tff(f1601,plain,
( ~ spl61_1
| spl61_12
| ~ spl61_23
| spl61_28 ),
inference(avatar_contradiction_clause,[],[f1600]) ).
tff(f1603,plain,
( sP48(sK7)
| ~ sP5
| ~ spl61_29 ),
inference(resolution,[],[f1494,f228]) ).
tff(f1604,plain,
( ~ sP5
| ~ spl61_29
| spl61_43 ),
inference(forward_subsumption_resolution,[],[f1603,f718]) ).
tff(f1605,plain,
( $false
| ~ spl61_1
| ~ spl61_29
| spl61_43 ),
inference(forward_subsumption_resolution,[],[f1604,f257]) ).
tff(f1606,plain,
( ~ spl61_1
| ~ spl61_29
| spl61_43 ),
inference(avatar_contradiction_clause,[],[f1605]) ).
cnf(s1,plain,
( spl61_1
| spl61_2
| spl61_3
| spl61_4
| ~ spl61_5
| spl61_6 ),
inference(sat_conversion,[],[f278]) ).
cnf(s3,plain,
( spl61_1
| spl61_2
| spl61_3
| spl61_4
| spl61_6
| spl61_8 ),
inference(sat_conversion,[],[f288]) ).
cnf(s6,plain,
( spl61_1
| spl61_2
| spl61_3
| spl61_11 ),
inference(sat_conversion,[],[f303]) ).
cnf(s19,plain,
( ~ spl61_1
| spl61_13
| spl61_22
| spl61_23
| spl61_28 ),
inference(sat_conversion,[],[f547]) ).
cnf(s21,plain,
( ~ spl61_1
| spl61_24
| spl61_28
| spl61_29 ),
inference(sat_conversion,[],[f549]) ).
cnf(s28,plain,
( ~ spl61_6
| spl61_26 ),
inference(sat_conversion,[],[f578]) ).
cnf(s44,plain,
( ~ spl61_11
| spl61_36
| spl61_49
| spl61_50 ),
inference(sat_conversion,[],[f779]) ).
cnf(s45,plain,
( ~ spl61_11
| spl61_40
| spl61_51 ),
inference(sat_conversion,[],[f802]) ).
cnf(s50,plain,
( ~ spl61_40
| spl61_48 ),
inference(sat_conversion,[],[f920]) ).
cnf(s51,plain,
( spl61_25
| spl61_26
| ~ spl61_49 ),
inference(sat_conversion,[],[f931]) ).
cnf(s53,plain,
( spl61_25
| spl61_49 ),
inference(sat_conversion,[],[f942]) ).
cnf(s56,plain,
( ~ spl61_26
| ~ spl61_49 ),
inference(sat_conversion,[],[f955]) ).
cnf(s59,plain,
( ~ spl61_3
| spl61_45 ),
inference(sat_conversion,[],[f1068]) ).
cnf(s60,plain,
( ~ spl61_4
| ~ spl61_48 ),
inference(sat_conversion,[],[f1070]) ).
cnf(s81,plain,
( spl61_5
| ~ spl61_8
| ~ spl61_11 ),
inference(sat_conversion,[],[f1269]) ).
cnf(s90,plain,
( ~ spl61_3
| ~ spl61_45 ),
inference(sat_conversion,[],[f1323]) ).
cnf(s91,plain,
( ~ spl61_4
| ~ spl61_51 ),
inference(sat_conversion,[],[f1325]) ).
cnf(s95,plain,
( ~ spl61_6
| ~ spl61_50 ),
inference(sat_conversion,[],[f1345]) ).
cnf(s97,plain,
( ~ spl61_6
| ~ spl61_36 ),
inference(sat_conversion,[],[f1370]) ).
cnf(s99,plain,
( ~ spl61_2
| ~ spl61_25 ),
inference(sat_conversion,[],[f1388]) ).
cnf(s101,plain,
( ~ spl61_1
| ~ spl61_24 ),
inference(sat_conversion,[],[f1420]) ).
cnf(s102,plain,
( ~ spl61_20
| ~ spl61_28 ),
inference(sat_conversion,[],[f1441]) ).
cnf(s104,plain,
( ~ spl61_16
| ~ spl61_28 ),
inference(sat_conversion,[],[f1444]) ).
cnf(s105,plain,
( ~ spl61_1
| ~ spl61_17
| ~ spl61_28 ),
inference(sat_conversion,[],[f1458]) ).
cnf(s106,plain,
( ~ spl61_1
| ~ spl61_18
| spl61_20
| spl61_24
| ~ spl61_28 ),
inference(sat_conversion,[],[f1477]) ).
cnf(s108,plain,
( ~ spl61_1
| spl61_16
| spl61_17
| spl61_18
| spl61_24
| ~ spl61_28 ),
inference(sat_conversion,[],[f1487]) ).
cnf(s109,plain,
( ~ spl61_12
| ~ spl61_29 ),
inference(sat_conversion,[],[f1506]) ).
cnf(s110,plain,
( ~ spl61_22
| ~ spl61_29 ),
inference(sat_conversion,[],[f1508]) ).
cnf(s113,plain,
( ~ spl61_13
| ~ spl61_43 ),
inference(sat_conversion,[],[f1529]) ).
cnf(s115,plain,
( ~ spl61_1
| spl61_12
| ~ spl61_23
| spl61_28 ),
inference(sat_conversion,[],[f1601]) ).
cnf(s116,plain,
( ~ spl61_1
| ~ spl61_29
| spl61_43 ),
inference(sat_conversion,[],[f1606]) ).
cnf(s117,plain,
( ~ spl61_6
| ~ spl61_11 ),
inference(rat,[],[s56,s44,s28,s95,s97]) ).
cnf(s118,plain,
( spl61_4
| spl61_3
| spl61_2
| spl61_1 ),
inference(rat,[],[s81,s3,s1,s117,s6]) ).
cnf(s119,plain,
( spl61_3
| spl61_2
| spl61_1 ),
inference(rat,[],[s50,s45,s60,s91,s118,s6]) ).
cnf(s120,plain,
~ spl61_3,
inference(rat,[],[s59,s90]) ).
cnf(s121,plain,
spl61_25,
inference(rat,[],[s51,s56,s53]) ).
cnf(s122,plain,
~ spl61_2,
inference(rat,[],[s99,s121]) ).
cnf(s123,plain,
spl61_1,
inference(rat,[],[s119,s120,s122]) ).
cnf(s124,plain,
~ spl61_24,
inference(rat,[],[s101,s123]) ).
cnf(s126,plain,
~ spl61_28,
inference(rat,[],[s108,s106,s105,s102,s104,s123,s124]) ).
cnf(s127,plain,
spl61_29,
inference(rat,[],[s21,s123,s124,s126]) ).
cnf(s128,plain,
spl61_43,
inference(rat,[],[s116,s123,s127]) ).
cnf(s129,plain,
~ spl61_22,
inference(rat,[],[s110,s127]) ).
cnf(s130,plain,
~ spl61_12,
inference(rat,[],[s109,s127]) ).
cnf(s131,plain,
~ spl61_13,
inference(rat,[],[s113,s128]) ).
cnf(s135,plain,
~ spl61_23,
inference(rat,[],[s115,s126,s123,s130]) ).
cnf(s136,plain,
$false,
inference(rat,[],[s19,s123,s129,s126,s135,s131]) ).
tff(f1607,plain,
$false,
inference(avatar_sat_refutation,[],[s136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT189_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n016.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 00:03:03 UTC 2026
% 0.14/0.38 % CPUTime :
% 0.14/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 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
% 3.15/1.06 % (3128651)Detected formulas, will run a generic FOF schedule.
% 3.15/1.06 % (3128661)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=519955829:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.15/1.06 % (3128662)dis-21_1_sil=8000:lcm=predicate:random_seed=892212831: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)
% 3.15/1.06 % (3128660)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1524891616:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.15/1.06 % (3128659)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2992340939:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.15/1.06 % (3128656)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=3841178253:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.15/1.06 % (3128657)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=392152873:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.15/1.06 % (3128658)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=2787126969:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.15/1.06 % (3128659)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.15/1.06 % (3128661)Instruction limit reached!
% 3.15/1.06 % (3128661)------------------------------
% 3.15/1.06 % (3128661)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.15/1.06 % (3128661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.15/1.06 % (3128661)CaDiCaL version: 2.1.3
% 3.15/1.06 % (3128661)Termination reason: Instruction limit
% 3.15/1.06 % (3128661)Termination phase: Saturation
% 3.15/1.06 % (3128661)Time elapsed: 0.047 s
% 3.15/1.06 % (3128661)Peak memory usage: 90 MB
% 3.15/1.06 % (3128661)Instructions burned: 141 (million)
% 3.15/1.06 % (3128658)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.15/1.06 % (3128659)First to succeed.
% 3.15/1.06 % (3128659)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3128651"
% 3.15/1.06 % (3128660)Instruction limit reached!
% 3.15/1.06 % (3128660)------------------------------
% 3.15/1.06 % (3128660)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.15/1.06 % (3128660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.15/1.06 % (3128660)CaDiCaL version: 2.1.3
% 3.15/1.06 % (3128660)Termination reason: Instruction limit
% 3.15/1.06 % (3128660)Termination phase: Saturation
% 3.15/1.06 % (3128660)Time elapsed: 0.072 s
% 3.15/1.06 % (3128660)Peak memory usage: 88 MB
% 3.15/1.06 % (3128660)Instructions burned: 119 (million)
% 3.15/1.06 % (3128662)Instruction limit reached!
% 3.15/1.06 % (3128662)------------------------------
% 3.15/1.06 % (3128662)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.15/1.06 % (3128662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.15/1.06 % (3128662)CaDiCaL version: 2.1.3
% 3.15/1.06 % (3128662)Termination reason: Instruction limit
% 3.15/1.06 % (3128662)Termination phase: Saturation
% 3.15/1.06 % (3128662)Time elapsed: 0.077 s
% 3.15/1.06 % (3128662)Peak memory usage: 89 MB
% 3.15/1.06 % (3128662)Instructions burned: 130 (million)
% 3.15/1.06 % (3128670)lrs+10_1_sil=8000:sp=occurrence:random_seed=45770950:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.15/1.06 % (3128671)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2453690190:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.15/1.06 % (3128670)Instruction limit reached!
% 3.15/1.06 % (3128670)------------------------------
% 3.15/1.06 % (3128670)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.15/1.06 % (3128670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.15/1.06 % (3128670)CaDiCaL version: 2.1.3
% 3.15/1.06 % (3128670)Termination reason: Instruction limit
% 3.15/1.06 % (3128670)Termination phase: Saturation
% 3.15/1.06 % (3128670)Time elapsed: 0.098 s
% 3.15/1.06 % (3128670)Peak memory usage: 91 MB
% 3.15/1.06 % (3128670)Instructions burned: 287 (million)
% 3.15/1.06 % (3128672)lrs+1011_1_sil=32000:sp=occurrence:random_seed=252532226:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.15/1.06 % (3128675)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=2894045371:s2a=on:i=248:s2at=1.23:gtg=position_2996 on theBenchmark for (2996ds/248Mi)
% 3.15/1.06 % (3128671)Instruction limit reached!
% 3.15/1.06 % (3128671)------------------------------
% 3.15/1.06 % (3128671)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.15/1.06 % (3128671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.15/1.06 % (3128671)CaDiCaL version: 2.1.3
% 3.15/1.06 % (3128671)Termination reason: Instruction limit
% 3.15/1.06 % (3128671)Termination phase: Saturation
% 3.15/1.06 % (3128671)Time elapsed: 0.093 s
% 3.15/1.06 % (3128671)Peak memory usage: 89 MB
% 3.15/1.06 % (3128671)Instructions burned: 159 (million)
% 3.15/1.06 % (3128659)Refutation found. Thanks to Tanya!
% 3.15/1.06 % SZS status Theorem for theBenchmark
% 3.15/1.06 % SZS output start Proof for theBenchmark
% See solution above
% 3.46/1.15 % (3128659)------------------------------
% 3.46/1.15 % (3128659)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.46/1.15 % (3128659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.46/1.15 % (3128659)CaDiCaL version: 2.1.3
% 3.46/1.15 % (3128659)Termination reason: Refutation
% 3.46/1.15 % (3128659)Time elapsed: 0.054 s
% 3.46/1.15 % (3128659)Peak memory usage: 90 MB
% 3.46/1.15 % (3128659)Instructions burned: 88 (million)
% 3.46/1.15 % (3128659)------------------------------
% 3.46/1.15 % (3128659)------------------------------
% 3.46/1.15 % (3128651)Success in time 0.449 s
% 3.46/1.15 % Vampire exiting
%------------------------------------------------------------------------------