%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV125^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:37:51 AM UTC 2026
% Result : Theorem 4.20s 1.02s
% Output : Refutation 4.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 61
% Number of leaves : 24
% Syntax : Number of formulae : 545 ( 24 unt; 0 typ; 23 def)
% Number of atoms : 7732 (1882 equ; 0 cnn)
% Maximal formula atoms : 14 ( 14 avg)
% Number of connectives : 11848 (1110 ~;2461 |; 430 &;6610 @)
% ( 23 <=>; 453 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 2270 (2270 >; 0 *; 0 +; 0 <<)
% Number of symbols : 99 ( 94 usr; 29 con; 0-5 aty)
% ( 574 !!; 187 ??; 0 @@+; 0 @@-)
% Number of variables : 2015 ( 0 sgn 898 !; 13 ?;2015 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
vIMP: $o > $o > $o ).
thf(func_def_3,type,
vAND: $o > $o > $o ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_11,type,
sK0: ( a > a > $o ) > $o ).
thf(func_def_12,type,
sK1: ( a > a > $o ) > $o ).
thf(func_def_15,type,
sK2: a ).
thf(func_def_16,type,
sK3: a ).
thf(func_def_17,type,
sK4: a > a > $o ).
thf(func_def_18,type,
sK5: a > a > $o ).
thf(func_def_19,type,
sK6: ( a > a > $o ) > a ).
thf(func_def_20,type,
sK7: ( a > a > $o ) > a ).
thf(func_def_21,type,
sK8: ( a > a > $o ) > a ).
thf(func_def_22,type,
sK9: ( a > a > $o ) > a ).
thf(func_def_23,type,
sK10: ( a > a > $o ) > a > a > $o ).
thf(func_def_24,type,
sK11: ( a > a > $o ) > a > a > $o ).
thf(func_def_25,type,
sK12: ( a > a > $o ) > a > a > $o ).
thf(func_def_26,type,
sK13: ( a > a > $o ) > a > a > $o ).
thf(func_def_27,type,
sK14: ( a > a > $o ) > a > a > $o ).
thf(func_def_28,type,
sK15: ( a > a > $o ) > a > a > $o ).
thf(func_def_30,type,
sK17: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_31,type,
sK18: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_32,type,
sK19: a > a > ( a > a > $o ) > a > a > $o ).
thf(func_def_33,type,
sK20: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_34,type,
sK21: a > ( a > a > ( a > a > $o ) > $o ) > a > a > a > $o ).
thf(func_def_35,type,
sK22: a > ( a > a > $o ) > a > a > a > $o ).
thf(func_def_36,type,
sK23: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_37,type,
sK24: ( a > a > $o ) > ( a > a > $o ) > a > a > $o ).
thf(func_def_38,type,
sK25: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_39,type,
sK26: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_40,type,
sK27: a > ( a > a > ( a > a > $o ) > $o ) > a > a > a > $o ).
thf(func_def_41,type,
sK28: ( a > a > ( a > a > $o ) > $o ) > ( a > a > $o ) > a ).
thf(func_def_42,type,
sK29: ( a > a > ( a > a > $o ) > $o ) > ( a > a > $o ) > a ).
thf(func_def_43,type,
sK30: ( a > a > ( a > a > $o ) > $o ) > ( a > a > $o ) > a > a > $o ).
thf(func_def_44,type,
sK31: ( a > a > ( a > a > $o ) > $o ) > ( a > a > $o ) > a > a > $o ).
thf(func_def_45,type,
sK32: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_46,type,
sK33: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_47,type,
sK34: a > a > ( a > a > $o ) > a > a > $o ).
thf(func_def_48,type,
sK35: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_49,type,
sK36: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_50,type,
sK37: ( a > a > ( a > a > $o ) > $o ) > ( a > a > $o ) > a ).
thf(func_def_51,type,
sK38: ( a > a > ( a > a > $o ) > $o ) > ( a > a > $o ) > a > a > $o ).
thf(func_def_52,type,
sK39: ( a > a > ( a > a > $o ) > $o ) > ( a > a > $o ) > a > a > $o ).
thf(func_def_53,type,
sK40: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_54,type,
sK41: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_55,type,
sK42: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_56,type,
sK43: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_57,type,
sK44: a > a > ( a > a > $o ) > a > a > $o ).
thf(func_def_58,type,
sK45: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_59,type,
sK46: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_60,type,
sK47: a > a > ( a > a > $o ) > a > a > $o ).
thf(func_def_61,type,
sK48: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_62,type,
sK49: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_63,type,
sK50: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_64,type,
sK51: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_65,type,
sK52: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_66,type,
sK53: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_67,type,
sK54: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_68,type,
sK55: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_69,type,
sK56: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_70,type,
sK57: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_71,type,
sK58: a > a > ( a > a > $o ) > a > a > $o ).
thf(func_def_72,type,
sK59: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(func_def_73,type,
sK60: ( a > a > $o ) > ( a > a > $o ) > a ).
thf(f1,conjecture,
! [X1: ( a > a > $o ) > $o,X0: ( a > a > $o ) > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ? [X7: a > a > $o] :
( ? [X8: a > a > $o] :
( ( X7
= ( ^ [X9: a,X10: a] :
! [X11: a > a > $o] :
( ( ! [X12: a,X13: a] :
( ( X8 @ X12 @ X13 )
=> ( X11 @ X12 @ X13 ) )
& ( X0 @ X11 ) )
=> ( X11 @ X9 @ X10 ) ) ) )
& ( X1 @ X8 ) )
& ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ( X0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ? [X7: a > a > $o] :
( ( X1 @ X7 )
& ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ( X0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM254_pme) ).
thf(f2,negated_conjecture,
~ ! [X1: ( a > a > $o ) > $o,X0: ( a > a > $o ) > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ? [X7: a > a > $o] :
( ? [X8: a > a > $o] :
( ( X7
= ( ^ [X9: a,X10: a] :
! [X11: a > a > $o] :
( ( ! [X12: a,X13: a] :
( ( X8 @ X12 @ X13 )
=> ( X11 @ X12 @ X13 ) )
& ( X0 @ X11 ) )
=> ( X11 @ X9 @ X10 ) ) ) )
& ( X1 @ X8 ) )
& ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ( X0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X6: a,X5: a] :
( ? [X7: a > a > $o] :
( ( X1 @ X7 )
& ( X7 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) )
& ( X0 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: ( a > a > $o ) > $o,X1: ( a > a > $o ) > $o] :
( ( ^ [X2: a,X3: a] :
! [X4: a > a > $o] :
( ( ! [X5: a,X6: a] :
( ? [X7: a > a > $o] :
( ? [X8: a > a > $o] :
( ( X7
= ( ^ [X9: a,X10: a] :
! [X11: a > a > $o] :
( ( ! [X12: a,X13: a] :
( ( X8 @ X12 @ X13 )
=> ( X11 @ X12 @ X13 ) )
& ( X1 @ X11 ) )
=> ( X11 @ X9 @ X10 ) ) ) )
& ( X0 @ X8 ) )
& ( X7 @ X6 @ X5 ) )
=> ( X4 @ X6 @ X5 ) )
& ( X1 @ X4 ) )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X14: a,X15: a] :
! [X16: a > a > $o] :
( ( ! [X17: a,X18: a] :
( ? [X19: a > a > $o] :
( ( X0 @ X19 )
& ( X19 @ X18 @ X17 ) )
=> ( X16 @ X18 @ X17 ) )
& ( X1 @ X16 ) )
=> ( X16 @ X14 @ X15 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: ( a > a > $o ) > $o,X1: ( a > a > $o ) > $o] :
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X1 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y5 @ Y3 @ Y4 )
& ( ?? @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( X0 @ Y6 )
& ( Y5
= ( ^ [Y7: a,Y8: a] :
( !! @ ( a > a > $o )
@ ^ [Y9: a > a > $o] :
( ( ( X1 @ Y9 )
& ( !! @ a
@ ^ [Y10: a] :
( !! @ a
@ ^ [Y11: a] :
( ( Y6 @ Y11 @ Y10 )
=> ( Y9 @ Y11 @ Y10 ) ) ) ) )
=> ( Y9 @ Y7 @ Y8 ) ) ) ) ) ) ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X1 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y5 @ Y3 @ Y4 )
& ( X0 @ Y5 ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X1: ( a > a > $o ) > $o,X0: ( a > a > $o ) > $o] :
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X1 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y5 @ Y3 @ Y4 )
& ( ?? @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( X0 @ Y6 )
& ( Y5
= ( ^ [Y7: a,Y8: a] :
( !! @ ( a > a > $o )
@ ^ [Y9: a > a > $o] :
( ( ( X1 @ Y9 )
& ( !! @ a
@ ^ [Y10: a] :
( !! @ a
@ ^ [Y11: a] :
( ( Y6 @ Y11 @ Y10 )
=> ( Y9 @ Y11 @ Y10 ) ) ) ) )
=> ( Y9 @ Y7 @ Y8 ) ) ) ) ) ) ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X1 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y5 @ Y3 @ Y4 )
& ( X0 @ Y5 ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: ( a > a > $o ) > $o,X1: ( a > a > $o ) > $o] :
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y5 @ Y3 @ Y4 )
& ( X1 @ Y5 ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( X0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y5 @ Y3 @ Y4 )
& ( ?? @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( X1 @ Y6 )
& ( Y5
= ( ^ [Y7: a,Y8: a] :
( !! @ ( a > a > $o )
@ ^ [Y9: a > a > $o] :
( ( ( X0 @ Y9 )
& ( !! @ a
@ ^ [Y10: a] :
( !! @ a
@ ^ [Y11: a] :
( ( Y6 @ Y11 @ Y10 )
=> ( Y9 @ Y11 @ Y10 ) ) ) ) )
=> ( Y9 @ Y7 @ Y8 ) ) ) ) ) ) ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y5 @ Y3 @ Y4 )
& ( ?? @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( sK1 @ Y6 )
& ( Y5
= ( ^ [Y7: a,Y8: a] :
( !! @ ( a > a > $o )
@ ^ [Y9: a > a > $o] :
( ( ( sK0 @ Y9 )
& ( !! @ a
@ ^ [Y10: a] :
( !! @ a
@ ^ [Y11: a] :
( ( Y6 @ Y11 @ Y10 )
=> ( Y9 @ Y11 @ Y10 ) ) ) ) )
=> ( Y9 @ Y7 @ Y8 ) ) ) ) ) ) ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y5 @ Y3 @ Y4 )
& ( sK1 @ Y5 ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f6]) ).
thf(f8,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y5 @ Y3 @ Y4 )
& ( ?? @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( sK1 @ Y6 )
& ( Y5
= ( ^ [Y7: a,Y8: a] :
( !! @ ( a > a > $o )
@ ^ [Y9: a > a > $o] :
( ( ( sK0 @ Y9 )
& ( !! @ a
@ ^ [Y10: a] :
( !! @ a
@ ^ [Y11: a] :
( ( Y6 @ Y11 @ Y10 )
=> ( Y9 @ Y11 @ Y10 ) ) ) ) )
=> ( Y9 @ Y7 @ Y8 ) ) ) ) ) ) ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y5 @ Y3 @ Y4 )
& ( sK1 @ Y5 ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y5 @ Y3 @ Y4 )
& ( ?? @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( sK1 @ Y6 )
& ( Y5
= ( ^ [Y7: a,Y8: a] :
( !! @ ( a > a > $o )
@ ^ [Y9: a > a > $o] :
( ( ( sK0 @ Y9 )
& ( !! @ a
@ ^ [Y10: a] :
( !! @ a
@ ^ [Y11: a] :
( ( Y6 @ Y11 @ Y10 )
=> ( Y9 @ Y11 @ Y10 ) ) ) ) )
=> ( Y9 @ Y7 @ Y8 ) ) ) ) ) ) ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK2 )
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( Y5 @ Y3 @ Y4 )
& ( sK1 @ Y5 ) ) )
=> ( Y2 @ Y3 @ Y4 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK2 ) ),
inference(negative_extensionality,[],[f8]) ).
thf(f12,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( Y4 @ Y2 @ Y3 )
& ( sK1 @ Y4 ) ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK2 @ Y0 ) ) ) )
!= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( Y4 @ Y2 @ Y3 )
& ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( sK1 @ Y5 )
& ( Y4
= ( ^ [Y6: a,Y7: a] :
( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( sK0 @ Y8 )
& ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y5 @ Y10 @ Y9 )
=> ( Y8 @ Y10 @ Y9 ) ) ) ) )
=> ( Y8 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f11]) ).
thf(f13,plain,
( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( Y4 @ Y2 @ Y3 )
& ( sK1 @ Y4 ) ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK2 @ Y0 ) ) )
@ sK3 )
!= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( Y4 @ Y2 @ Y3 )
& ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( sK1 @ Y5 )
& ( Y4
= ( ^ [Y6: a,Y7: a] :
( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( sK0 @ Y8 )
& ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y5 @ Y10 @ Y9 )
=> ( Y8 @ Y10 @ Y9 ) ) ) ) )
=> ( Y8 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK2 @ Y0 ) ) )
@ sK3 ) ),
inference(negative_extensionality,[],[f12]) ).
thf(f14,plain,
( ( $true
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( Y4 @ Y2 @ Y3 )
& ( sK1 @ Y4 ) ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK2 @ Y0 ) ) )
@ sK3 ) )
| ( $true
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( Y4 @ Y2 @ Y3 )
& ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( sK1 @ Y5 )
& ( Y4
= ( ^ [Y6: a,Y7: a] :
( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( sK0 @ Y8 )
& ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y5 @ Y10 @ Y9 )
=> ( Y8 @ Y10 @ Y9 ) ) ) ) )
=> ( Y8 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK2 @ Y0 ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f13]) ).
thf(f15,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( Y4 @ Y2 @ Y3 )
& ( sK1 @ Y4 ) ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK2 @ Y0 ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( Y4 @ Y2 @ Y3 )
& ( ?? @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( sK1 @ Y5 )
& ( Y4
= ( ^ [Y6: a,Y7: a] :
( !! @ ( a > a > $o )
@ ^ [Y8: a > a > $o] :
( ( ( sK0 @ Y8 )
& ( !! @ a
@ ^ [Y9: a] :
( !! @ a
@ ^ [Y10: a] :
( ( Y5 @ Y10 @ Y9 )
=> ( Y8 @ Y10 @ Y9 ) ) ) ) )
=> ( Y8 @ Y6 @ Y7 ) ) ) ) ) ) ) ) )
=> ( Y1 @ Y2 @ Y3 ) ) ) ) )
=> ( Y1 @ sK2 @ Y0 ) ) )
@ sK3 ) ) ),
inference(xor_proxy_clausification,[],[f13]) ).
thf(f16,plain,
( ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y3 @ Y1 @ Y2 )
& ( sK1 @ Y3 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) )
| ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y3 @ Y1 @ Y2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( sK1 @ Y4 )
& ( Y3
= ( ^ [Y5: a,Y6: a] :
( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( sK0 @ Y7 )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y4 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) ) ) ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ) ),
inference(beta-eta_normalization,[],[f15]) ).
thf(f17,plain,
( ( ( ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y3 @ Y1 @ Y2 )
& ( sK1 @ Y3 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) )
@ sK4 )
= $false )
| ( $false
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y3 @ Y1 @ Y2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( sK1 @ Y4 )
& ( Y3
= ( ^ [Y5: a,Y6: a] :
( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( sK0 @ Y7 )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y4 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) ) ) ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y3 @ Y1 @ Y2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( sK1 @ Y4 )
& ( Y3
= ( ^ [Y5: a,Y6: a] :
( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( sK0 @ Y7 )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y4 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) ) ) ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) )
@ sK5 ) )
| ( ( ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y3 @ Y1 @ Y2 )
& ( sK1 @ Y3 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) )
@ sK4 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f17]) ).
thf(f19,plain,
( ( ( ( ( sK0 @ sK5 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK1 @ Y3 )
& ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( sK0 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) )
=> ( sK5 @ sK2 @ sK3 ) )
= $false )
| ( $false
= ( ( ( sK0 @ sK4 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( sK1 @ Y2 ) ) )
=> ( sK4 @ Y0 @ Y1 ) ) ) ) )
=> ( sK4 @ sK2 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f20,plain,
( ( $false
= ( sK5 @ sK2 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK4 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( sK1 @ Y2 ) ) )
=> ( sK4 @ Y0 @ Y1 ) ) ) ) )
=> ( sK4 @ sK2 @ sK3 ) ) ) ),
inference(imp_proxy_clausification,[],[f19]) ).
thf(f21,plain,
( ( ( ( sK0 @ sK5 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK1 @ Y3 )
& ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( sK0 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
=> ( sK5 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ( $false
= ( ( ( sK0 @ sK4 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( sK1 @ Y2 ) ) )
=> ( sK4 @ Y0 @ Y1 ) ) ) ) )
=> ( sK4 @ sK2 @ sK3 ) ) ) ),
inference(imp_proxy_clausification,[],[f19]) ).
thf(f22,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK1 @ Y3 )
& ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( sK0 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
=> ( sK5 @ Y0 @ Y1 ) ) ) )
= $true )
| ( $false
= ( ( ( sK0 @ sK4 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( sK1 @ Y2 ) ) )
=> ( sK4 @ Y0 @ Y1 ) ) ) ) )
=> ( sK4 @ sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( $false
= ( ( ( sK0 @ sK4 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( sK1 @ Y2 ) ) )
=> ( sK4 @ Y0 @ Y1 ) ) ) ) )
=> ( sK4 @ sK2 @ sK3 ) ) ) ),
inference(and_proxy_clausification,[],[f21]) ).
thf(f24,plain,
( ( $false
= ( sK4 @ sK2 @ sK3 ) )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(imp_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( ( ( sK0 @ sK4 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( sK1 @ Y2 ) ) )
=> ( sK4 @ Y0 @ Y1 ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f23]) ).
thf(f26,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( sK1 @ Y2 ) ) )
=> ( sK4 @ Y0 @ Y1 ) ) ) )
= $true )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(and_proxy_clausification,[],[f25]) ).
thf(f27,plain,
( ( ( sK0 @ sK5 )
= $true )
| ( ( sK0 @ sK4 )
= $true ) ),
inference(and_proxy_clausification,[],[f25]) ).
thf(f28,plain,
! [X1: a] :
( ( ( sK0 @ sK5 )
= $true )
| ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( sK1 @ Y2 ) ) )
=> ( sK4 @ Y0 @ Y1 ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f26]) ).
thf(f29,plain,
! [X1: a] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ X1 @ Y0 )
& ( sK1 @ Y1 ) ) )
=> ( sK4 @ X1 @ Y0 ) ) )
= $true )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,plain,
! [X2: a,X1: a] :
( ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ X1 @ Y0 )
& ( sK1 @ Y1 ) ) )
=> ( sK4 @ X1 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f29]) ).
thf(f31,plain,
! [X2: a,X1: a] :
( ( ( sK0 @ sK5 )
= $true )
| ( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X1 @ X2 )
& ( sK1 @ Y0 ) ) )
=> ( sK4 @ X1 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f30]) ).
thf(f32,plain,
! [X2: a,X1: a] :
( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X1 @ X2 )
& ( sK1 @ Y0 ) ) )
= $false )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( ( sK0 @ sK5 )
= $true ) ),
inference(imp_proxy_clausification,[],[f31]) ).
thf(f33,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( ( sK0 @ sK5 )
= $true )
| ( $false
= ( ^ [Y0: a > a > $o] :
( ( Y0 @ X1 @ X2 )
& ( sK1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( sK4 @ X1 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f32]) ).
thf(f34,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( ( ( X3 @ X1 @ X2 )
& ( sK1 @ X3 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f35,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( ( sK0 @ sK5 )
= $true )
| ( ( X3 @ X1 @ X2 )
= $false )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( $false
= ( sK1 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f34]) ).
thf(f36,plain,
! [X1: a] :
( ( $false
= ( ( ( sK0 @ sK4 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( sK1 @ Y2 ) ) )
=> ( sK4 @ Y0 @ Y1 ) ) ) ) )
=> ( sK4 @ sK2 @ sK3 ) ) )
| ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK1 @ Y3 )
& ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( sK0 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
=> ( sK5 @ Y0 @ Y1 ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f22]) ).
thf(f37,plain,
! [X1: a] :
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK1 @ Y3 )
& ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( sK0 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
=> ( sK5 @ Y0 @ Y1 ) ) )
@ X1 )
= $true )
| ( $false
= ( sK4 @ sK2 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f36]) ).
thf(f38,plain,
! [X1: a] :
( ( ( ( sK0 @ sK4 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( sK1 @ Y2 ) ) )
=> ( sK4 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK1 @ Y3 )
& ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( sK0 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
=> ( sK5 @ Y0 @ Y1 ) ) )
@ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f36]) ).
thf(f39,plain,
! [X1: a] :
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK1 @ Y3 )
& ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( sK0 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
=> ( sK5 @ Y0 @ Y1 ) ) )
@ X1 )
= $true )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( sK1 @ Y2 ) ) )
=> ( sK4 @ Y0 @ Y1 ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f38]) ).
thf(f40,plain,
! [X1: a] :
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK1 @ Y3 )
& ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( sK0 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
=> ( sK5 @ Y0 @ Y1 ) ) )
@ X1 )
= $true )
| ( ( sK0 @ sK4 )
= $true ) ),
inference(and_proxy_clausification,[],[f38]) ).
thf(f41,plain,
! [X1: a] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ X1 @ Y0 )
& ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( sK1 @ Y2 )
& ( Y1
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( sK0 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( sK5 @ X1 @ Y0 ) ) )
= $true )
| ( ( sK0 @ sK4 )
= $true ) ),
inference(beta-eta_normalization,[],[f40]) ).
thf(f42,plain,
! [X2: a,X1: a] :
( ( ( sK0 @ sK4 )
= $true )
| ( ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ X1 @ Y0 )
& ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( sK1 @ Y2 )
& ( Y1
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( sK0 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( sK5 @ X1 @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f41]) ).
thf(f43,plain,
! [X2: a,X1: a] :
( ( ( sK0 @ sK4 )
= $true )
| ( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X1 @ X2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK1 @ Y1 )
& ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( sK5 @ X1 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f42]) ).
thf(f44,plain,
! [X2: a,X1: a] :
( ( ( sK0 @ sK4 )
= $true )
| ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X1 @ X2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK1 @ Y1 )
& ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
= $false )
| ( ( sK5 @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f43]) ).
thf(f45,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( ( sK0 @ sK4 )
= $true )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( $false
= ( ^ [Y0: a > a > $o] :
( ( Y0 @ X1 @ X2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK1 @ Y1 )
& ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f44]) ).
thf(f46,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( ( sK5 @ X1 @ X2 )
= $true )
| ( $false
= ( ( X3 @ X1 @ X2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( sK1 @ Y0 )
& ( X3
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ) ) )
| ( ( sK0 @ sK4 )
= $true ) ),
inference(beta-eta_normalization,[],[f45]) ).
thf(f47,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( X3 @ X1 @ X2 )
= $false )
| ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( sK1 @ Y0 )
& ( X3
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false )
| ( ( sK0 @ sK4 )
= $true ) ),
inference(and_proxy_clausification,[],[f46]) ).
thf(f48,plain,
! [X2: a,X3: a > a > $o,X1: a,X4: a > a > $o] :
( ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( sK0 @ sK4 )
= $true )
| ( ( X3 @ X1 @ X2 )
= $false )
| ( $false
= ( ^ [Y0: a > a > $o] :
( ( sK1 @ Y0 )
& ( X3
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f47]) ).
thf(f49,plain,
! [X2: a,X3: a > a > $o,X1: a,X4: a > a > $o] :
( ( ( X3 @ X1 @ X2 )
= $false )
| ( ( ( sK1 @ X4 )
& ( X3
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
= $false )
| ( ( sK0 @ sK4 )
= $true )
| ( ( sK5 @ X1 @ X2 )
= $true ) ),
inference(beta-eta_normalization,[],[f48]) ).
thf(f50,plain,
! [X2: a,X3: a > a > $o,X1: a,X4: a > a > $o] :
( ( ( sK0 @ sK4 )
= $true )
| ( ( sK1 @ X4 )
= $false )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( X3 @ X1 @ X2 )
= $false )
| ( $false
= ( X3
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f49]) ).
thf(f51,plain,
! [X2: a,X3: a > a > $o,X1: a,X4: a > a > $o] :
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= X3 )
| ( ( sK1 @ X4 )
= $false )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( X3 @ X1 @ X2 )
= $false )
| ( ( sK0 @ sK4 )
= $true ) ),
inference(equality_proxy_clausification,[],[f50]) ).
thf(f52,plain,
! [X2: a,X1: a] :
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( sK1 @ Y2 ) ) )
=> ( sK4 @ Y0 @ Y1 ) ) )
@ X2 )
= $true )
| ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK1 @ Y3 )
& ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( sK0 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
=> ( sK5 @ Y0 @ Y1 ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f39]) ).
thf(f53,plain,
! [X2: a,X1: a] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ X1 @ Y0 )
& ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( sK1 @ Y2 )
& ( Y1
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( sK0 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( sK5 @ X1 @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ X2 @ Y0 )
& ( sK1 @ Y1 ) ) )
=> ( sK4 @ X2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f52]) ).
thf(f54,plain,
! [X2: a,X3: a,X1: a] :
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ X2 @ Y0 )
& ( sK1 @ Y1 ) ) )
=> ( sK4 @ X2 @ Y0 ) ) ) )
| ( ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ X1 @ Y0 )
& ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( sK1 @ Y2 )
& ( Y1
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( sK0 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( sK5 @ X1 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f53]) ).
thf(f55,plain,
! [X2: a,X3: a,X1: a,X4: a] :
( ( ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ X2 @ Y0 )
& ( sK1 @ Y1 ) ) )
=> ( sK4 @ X2 @ Y0 ) )
@ X4 )
= $true )
| ( ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ X1 @ Y0 )
& ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( sK1 @ Y2 )
& ( Y1
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( sK0 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( sK5 @ X1 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f54]) ).
thf(f56,plain,
! [X2: a,X3: a,X1: a,X4: a] :
( ( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X1 @ X3 )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK1 @ Y1 )
& ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( sK5 @ X1 @ X3 ) )
= $true )
| ( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X2 @ X4 )
& ( sK1 @ Y0 ) ) )
=> ( sK4 @ X2 @ X4 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f55]) ).
thf(f57,plain,
! [X2: a,X3: a,X1: a,X4: a] :
( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X1 @ X3 )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK1 @ Y1 )
& ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
= $false )
| ( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X2 @ X4 )
& ( sK1 @ Y0 ) ) )
=> ( sK4 @ X2 @ X4 ) )
= $true )
| ( $true
= ( sK5 @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f56]) ).
thf(f58,plain,
! [X2: a,X3: a,X1: a,X4: a,X5: a > a > $o] :
( ( ( ^ [Y0: a > a > $o] :
( ( Y0 @ X1 @ X3 )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK1 @ Y1 )
& ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) )
@ X5 )
= $false )
| ( $true
= ( sK5 @ X1 @ X3 ) )
| ( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X2 @ X4 )
& ( sK1 @ Y0 ) ) )
=> ( sK4 @ X2 @ X4 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f57]) ).
thf(f59,plain,
! [X2: a,X3: a,X1: a,X4: a,X5: a > a > $o] :
( ( ( sK4 @ X2 @ X4 )
= $true )
| ( $true
= ( sK5 @ X1 @ X3 ) )
| ( ( ^ [Y0: a > a > $o] :
( ( Y0 @ X1 @ X3 )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK1 @ Y1 )
& ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) )
@ X5 )
= $false )
| ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X2 @ X4 )
& ( sK1 @ Y0 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f58]) ).
thf(f60,plain,
! [X2: a,X3: a,X1: a,X6: a > a > $o,X4: a,X5: a > a > $o] :
( ( ( ^ [Y0: a > a > $o] :
( ( Y0 @ X2 @ X4 )
& ( sK1 @ Y0 ) )
@ X6 )
= $false )
| ( ( ^ [Y0: a > a > $o] :
( ( Y0 @ X1 @ X3 )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK1 @ Y1 )
& ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) )
@ X5 )
= $false )
| ( $true
= ( sK5 @ X1 @ X3 ) )
| ( ( sK4 @ X2 @ X4 )
= $true ) ),
inference(pi_proxy_clausification,[],[f59]) ).
thf(f61,plain,
! [X2: a,X3: a,X1: a,X6: a > a > $o,X4: a,X5: a > a > $o] :
( ( $true
= ( sK5 @ X1 @ X3 ) )
| ( ( ( X6 @ X2 @ X4 )
& ( sK1 @ X6 ) )
= $false )
| ( ( ( X5 @ X1 @ X3 )
& ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( sK1 @ Y0 )
& ( X5
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $false )
| ( ( sK4 @ X2 @ X4 )
= $true ) ),
inference(beta-eta_normalization,[],[f60]) ).
thf(f62,plain,
! [X2: a,X3: a,X1: a,X6: a > a > $o,X4: a,X5: a > a > $o] :
( ( $true
= ( sK5 @ X1 @ X3 ) )
| ( ( ( X5 @ X1 @ X3 )
& ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( sK1 @ Y0 )
& ( X5
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $false )
| ( ( sK1 @ X6 )
= $false )
| ( ( sK4 @ X2 @ X4 )
= $true )
| ( ( X6 @ X2 @ X4 )
= $false ) ),
inference(and_proxy_clausification,[],[f61]) ).
thf(f63,plain,
! [X2: a,X3: a,X1: a,X6: a > a > $o,X4: a,X5: a > a > $o] :
( ( ( sK4 @ X2 @ X4 )
= $true )
| ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( sK1 @ Y0 )
& ( X5
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false )
| ( ( sK1 @ X6 )
= $false )
| ( $false
= ( X5 @ X1 @ X3 ) )
| ( $true
= ( sK5 @ X1 @ X3 ) )
| ( ( X6 @ X2 @ X4 )
= $false ) ),
inference(and_proxy_clausification,[],[f62]) ).
thf(f64,plain,
! [X2: a,X3: a,X1: a,X6: a > a > $o,X7: a > a > $o,X4: a,X5: a > a > $o] :
( ( $false
= ( X5 @ X1 @ X3 ) )
| ( ( sK4 @ X2 @ X4 )
= $true )
| ( ( X6 @ X2 @ X4 )
= $false )
| ( ( ^ [Y0: a > a > $o] :
( ( sK1 @ Y0 )
& ( X5
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
@ X7 )
= $false )
| ( $true
= ( sK5 @ X1 @ X3 ) )
| ( ( sK1 @ X6 )
= $false ) ),
inference(pi_proxy_clausification,[],[f63]) ).
thf(f65,plain,
! [X2: a,X3: a,X1: a,X6: a > a > $o,X7: a > a > $o,X4: a,X5: a > a > $o] :
( ( ( sK1 @ X6 )
= $false )
| ( $false
= ( ( sK1 @ X7 )
& ( X5
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X7 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
| ( $false
= ( X5 @ X1 @ X3 ) )
| ( ( X6 @ X2 @ X4 )
= $false )
| ( ( sK4 @ X2 @ X4 )
= $true )
| ( $true
= ( sK5 @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f66,plain,
! [X2: a,X3: a,X1: a,X6: a > a > $o,X7: a > a > $o,X4: a,X5: a > a > $o] :
( ( ( X5
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X7 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( $true
= ( sK5 @ X1 @ X3 ) )
| ( ( sK4 @ X2 @ X4 )
= $true )
| ( ( X6 @ X2 @ X4 )
= $false )
| ( $false
= ( X5 @ X1 @ X3 ) )
| ( ( sK1 @ X7 )
= $false )
| ( ( sK1 @ X6 )
= $false ) ),
inference(and_proxy_clausification,[],[f65]) ).
thf(f67,plain,
! [X2: a,X3: a,X1: a,X6: a > a > $o,X7: a > a > $o,X4: a,X5: a > a > $o] :
( ( ( sK4 @ X2 @ X4 )
= $true )
| ( ( sK1 @ X6 )
= $false )
| ( ( X6 @ X2 @ X4 )
= $false )
| ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X7 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= X5 )
| ( $true
= ( sK5 @ X1 @ X3 ) )
| ( ( sK1 @ X7 )
= $false )
| ( $false
= ( X5 @ X1 @ X3 ) ) ),
inference(equality_proxy_clausification,[],[f66]) ).
thf(f68,plain,
! [X1: a] :
( ( $false
= ( sK4 @ sK2 @ sK3 ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ X1 @ Y0 )
& ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( sK1 @ Y2 )
& ( Y1
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( sK0 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( sK5 @ X1 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f37]) ).
thf(f69,plain,
! [X2: a,X1: a] :
( ( ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ X1 @ Y0 )
& ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( sK1 @ Y2 )
& ( Y1
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( sK0 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( sK5 @ X1 @ Y0 ) )
@ X2 )
= $true )
| ( $false
= ( sK4 @ sK2 @ sK3 ) ) ),
inference(pi_proxy_clausification,[],[f68]) ).
thf(f70,plain,
! [X2: a,X1: a] :
( ( $false
= ( sK4 @ sK2 @ sK3 ) )
| ( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X1 @ X2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK1 @ Y1 )
& ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( sK5 @ X1 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f69]) ).
thf(f71,plain,
! [X2: a,X1: a] :
( ( ( sK5 @ X1 @ X2 )
= $true )
| ( $false
= ( sK4 @ sK2 @ sK3 ) )
| ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X1 @ X2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK1 @ Y1 )
& ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f70]) ).
thf(f72,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( $false
= ( ^ [Y0: a > a > $o] :
( ( Y0 @ X1 @ X2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK1 @ Y1 )
& ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) )
@ X3 ) )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( $false
= ( sK4 @ sK2 @ sK3 ) ) ),
inference(pi_proxy_clausification,[],[f71]) ).
thf(f73,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( $false
= ( ( X3 @ X1 @ X2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( sK1 @ Y0 )
& ( X3
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ) ) )
| ( $false
= ( sK4 @ sK2 @ sK3 ) )
| ( ( sK5 @ X1 @ X2 )
= $true ) ),
inference(beta-eta_normalization,[],[f72]) ).
thf(f74,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( X3 @ X1 @ X2 )
= $false )
| ( $false
= ( sK4 @ sK2 @ sK3 ) )
| ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( sK1 @ Y0 )
& ( X3
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f73]) ).
thf(f75,plain,
! [X2: a,X3: a > a > $o,X1: a,X4: a > a > $o] :
( ( $false
= ( sK4 @ sK2 @ sK3 ) )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( X3 @ X1 @ X2 )
= $false )
| ( $false
= ( ^ [Y0: a > a > $o] :
( ( sK1 @ Y0 )
& ( X3
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f74]) ).
thf(f76,plain,
! [X2: a,X3: a > a > $o,X1: a,X4: a > a > $o] :
( ( $false
= ( sK4 @ sK2 @ sK3 ) )
| ( ( X3 @ X1 @ X2 )
= $false )
| ( ( ( sK1 @ X4 )
& ( X3
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
= $false )
| ( ( sK5 @ X1 @ X2 )
= $true ) ),
inference(beta-eta_normalization,[],[f75]) ).
thf(f77,plain,
! [X2: a,X3: a > a > $o,X1: a,X4: a > a > $o] :
( ( ( sK5 @ X1 @ X2 )
= $true )
| ( $false
= ( X3
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
| ( $false
= ( sK4 @ sK2 @ sK3 ) )
| ( ( sK1 @ X4 )
= $false )
| ( ( X3 @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f76]) ).
thf(f78,plain,
! [X2: a,X3: a > a > $o,X1: a,X4: a > a > $o] :
( ( ( X3 @ X1 @ X2 )
= $false )
| ( $false
= ( sK4 @ sK2 @ sK3 ) )
| ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= X3 )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( sK1 @ X4 )
= $false ) ),
inference(equality_proxy_clausification,[],[f77]) ).
thf(f79,plain,
( ( $false
= ( sK4 @ sK2 @ sK3 ) )
| ( $false
= ( sK5 @ sK2 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f20]) ).
thf(f80,plain,
( ( $false
= ( sK5 @ sK2 @ sK3 ) )
| ( ( ( sK0 @ sK4 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( sK1 @ Y2 ) ) )
=> ( sK4 @ Y0 @ Y1 ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f20]) ).
thf(f81,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( sK1 @ Y2 ) ) )
=> ( sK4 @ Y0 @ Y1 ) ) ) )
= $true )
| ( $false
= ( sK5 @ sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f80]) ).
thf(f82,plain,
( ( ( sK0 @ sK4 )
= $true )
| ( $false
= ( sK5 @ sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f80]) ).
thf(f83,plain,
! [X1: a] :
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( sK1 @ Y2 ) ) )
=> ( sK4 @ Y0 @ Y1 ) ) )
@ X1 )
= $true )
| ( $false
= ( sK5 @ sK2 @ sK3 ) ) ),
inference(pi_proxy_clausification,[],[f81]) ).
thf(f84,plain,
! [X1: a] :
( ( $false
= ( sK5 @ sK2 @ sK3 ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ X1 @ Y0 )
& ( sK1 @ Y1 ) ) )
=> ( sK4 @ X1 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f83]) ).
thf(f85,plain,
! [X2: a,X1: a] :
( ( $true
= ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ X1 @ Y0 )
& ( sK1 @ Y1 ) ) )
=> ( sK4 @ X1 @ Y0 ) )
@ X2 ) )
| ( $false
= ( sK5 @ sK2 @ sK3 ) ) ),
inference(pi_proxy_clausification,[],[f84]) ).
thf(f86,plain,
! [X2: a,X1: a] :
( ( $false
= ( sK5 @ sK2 @ sK3 ) )
| ( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X1 @ X2 )
& ( sK1 @ Y0 ) ) )
=> ( sK4 @ X1 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f85]) ).
thf(f87,plain,
! [X2: a,X1: a] :
( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ X1 @ X2 )
& ( sK1 @ Y0 ) ) )
= $false )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( $false
= ( sK5 @ sK2 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f86]) ).
thf(f88,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( $false
= ( sK5 @ sK2 @ sK3 ) )
| ( $false
= ( ^ [Y0: a > a > $o] :
( ( Y0 @ X1 @ X2 )
& ( sK1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( sK4 @ X1 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f87]) ).
thf(f89,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( $true
= ( sK4 @ X1 @ X2 ) )
| ( ( ( X3 @ X1 @ X2 )
& ( sK1 @ X3 ) )
= $false )
| ( $false
= ( sK5 @ sK2 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f88]) ).
thf(f90,plain,
! [X2: a,X3: a > a > $o,X1: a] :
( ( $true
= ( sK4 @ X1 @ X2 ) )
| ( $false
= ( sK1 @ X3 ) )
| ( $false
= ( sK5 @ sK2 @ sK3 ) )
| ( ( X3 @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f89]) ).
thf(f91,plain,
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y3 @ Y1 @ Y2 )
& ( sK1 @ Y3 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) ) )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y3 @ Y1 @ Y2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( sK1 @ Y4 )
& ( Y3
= ( ^ [Y5: a,Y6: a] :
( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( sK0 @ Y7 )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y4 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) ) ) ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f14]) ).
thf(f92,plain,
! [X1: a > a > $o] :
( ( ( ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y3 @ Y1 @ Y2 )
& ( sK1 @ Y3 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) )
@ X1 )
= $true )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y3 @ Y1 @ Y2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( sK1 @ Y4 )
& ( Y3
= ( ^ [Y5: a,Y6: a] :
( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( sK0 @ Y7 )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y4 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) ) ) ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f91]) ).
thf(f93,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y3 @ Y1 @ Y2 )
& ( ?? @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( sK1 @ Y4 )
& ( Y3
= ( ^ [Y5: a,Y6: a] :
( !! @ ( a > a > $o )
@ ^ [Y7: a > a > $o] :
( ( ( sK0 @ Y7 )
& ( !! @ a
@ ^ [Y8: a] :
( !! @ a
@ ^ [Y9: a] :
( ( Y4 @ Y9 @ Y8 )
=> ( Y7 @ Y9 @ Y8 ) ) ) ) )
=> ( Y7 @ Y5 @ Y6 ) ) ) ) ) ) ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) )
@ X2 )
= $true )
| ( ( ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( Y3 @ Y1 @ Y2 )
& ( sK1 @ Y3 ) ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
=> ( Y0 @ sK2 @ sK3 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f92]) ).
thf(f94,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( ( ( sK0 @ X2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK1 @ Y3 )
& ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( sK0 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
=> ( X2 @ sK2 @ sK3 ) )
= $true )
| ( ( ( ( sK0 @ X1 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( sK1 @ Y2 ) ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK2 @ sK3 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f93]) ).
thf(f95,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( ( sK0 @ X2 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK1 @ Y3 )
& ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( sK0 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( ( ( ( sK0 @ X1 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( sK1 @ Y2 ) ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK2 @ sK3 ) )
= $true )
| ( $true
= ( X2 @ sK2 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f94]) ).
thf(f96,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK1 @ Y3 )
& ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( sK0 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
=> ( X2 @ Y0 @ Y1 ) ) ) ) )
| ( ( ( ( sK0 @ X1 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( sK1 @ Y2 ) ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK2 @ sK3 ) )
= $true )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f95]) ).
thf(f97,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK1 @ Y3 )
& ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( sK0 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
=> ( X2 @ Y0 @ Y1 ) ) )
@ ( sK6 @ X2 ) )
= $false )
| ( ( ( ( sK0 @ X1 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( sK1 @ Y2 ) ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) )
=> ( X1 @ sK2 @ sK3 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f96]) ).
thf(f98,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK1 @ Y3 )
& ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( sK0 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
=> ( X2 @ Y0 @ Y1 ) ) )
@ ( sK6 @ X2 ) )
= $false )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( ( sK0 @ X1 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( sK1 @ Y2 ) ) )
=> ( X1 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f97]) ).
thf(f99,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK1 @ Y3 )
& ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( sK0 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
=> ( X2 @ Y0 @ Y1 ) ) )
@ ( sK6 @ X2 ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( sK1 @ Y2 ) ) )
=> ( X1 @ Y0 @ Y1 ) ) ) )
= $false )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f98]) ).
thf(f100,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( ?? @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( sK1 @ Y3 )
& ( Y2
= ( ^ [Y4: a,Y5: a] :
( !! @ ( a > a > $o )
@ ^ [Y6: a > a > $o] :
( ( ( sK0 @ Y6 )
& ( !! @ a
@ ^ [Y7: a] :
( !! @ a
@ ^ [Y8: a] :
( ( Y3 @ Y8 @ Y7 )
=> ( Y6 @ Y8 @ Y7 ) ) ) ) )
=> ( Y6 @ Y4 @ Y5 ) ) ) ) ) ) ) ) )
=> ( X2 @ Y0 @ Y1 ) ) )
@ ( sK6 @ X2 ) )
= $false )
| ( $false
= ( sK0 @ X1 ) )
| ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( Y2 @ Y0 @ Y1 )
& ( sK1 @ Y2 ) ) )
=> ( X1 @ Y0 @ Y1 ) ) )
@ ( sK7 @ X1 ) )
= $false )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f99]) ).
thf(f101,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $false
= ( sK0 @ X2 ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ ( sK7 @ X1 ) @ Y0 )
& ( sK1 @ Y1 ) ) )
=> ( X1 @ ( sK7 @ X1 ) @ Y0 ) ) )
= $false )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ ( sK6 @ X2 ) @ Y0 )
& ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( sK1 @ Y2 )
& ( Y1
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( sK0 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( X2 @ ( sK6 @ X2 ) @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f100]) ).
thf(f102,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ ( sK7 @ X1 ) @ Y0 )
& ( sK1 @ Y1 ) ) )
=> ( X1 @ ( sK7 @ X1 ) @ Y0 ) )
@ ( sK8 @ X1 ) )
= $false )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ ( sK6 @ X2 ) @ Y0 )
& ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( sK1 @ Y2 )
& ( Y1
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( sK0 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( X2 @ ( sK6 @ X2 ) @ Y0 ) ) ) )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f101]) ).
thf(f103,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ ( sK6 @ X2 ) @ Y0 )
& ( ?? @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( sK1 @ Y2 )
& ( Y1
= ( ^ [Y3: a,Y4: a] :
( !! @ ( a > a > $o )
@ ^ [Y5: a > a > $o] :
( ( ( sK0 @ Y5 )
& ( !! @ a
@ ^ [Y6: a] :
( !! @ a
@ ^ [Y7: a] :
( ( Y2 @ Y7 @ Y6 )
=> ( Y5 @ Y7 @ Y6 ) ) ) ) )
=> ( Y5 @ Y3 @ Y4 ) ) ) ) ) ) ) ) )
=> ( X2 @ ( sK6 @ X2 ) @ Y0 ) )
@ ( sK9 @ X2 ) )
= $false )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X1 ) )
| ( ( ^ [Y0: a] :
( ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( Y1 @ ( sK7 @ X1 ) @ Y0 )
& ( sK1 @ Y1 ) ) )
=> ( X1 @ ( sK7 @ X1 ) @ Y0 ) )
@ ( sK8 @ X1 ) )
= $false )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f102]) ).
thf(f104,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
& ( sK1 @ Y0 ) ) )
=> ( X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) ) ) )
| ( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK1 @ Y1 )
& ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( X2 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f103]) ).
thf(f105,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( ( X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
= $false )
| ( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK1 @ Y1 )
& ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( X2 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) ) )
= $false )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f104]) ).
thf(f106,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( $true
= ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
& ( sK1 @ Y0 ) ) ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK1 @ Y1 )
& ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( X2 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) ) )
= $false )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f104]) ).
thf(f107,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
& ( sK1 @ Y0 ) )
@ ( sK10 @ X1 ) )
= $true )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK1 @ Y1 )
& ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
=> ( X2 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) ) )
= $false )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f106]) ).
thf(f108,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $false
= ( sK0 @ X1 ) )
| ( ( ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
& ( sK1 @ Y0 ) )
@ ( sK10 @ X1 ) )
= $true )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( X2 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) )
= $false )
| ( $true
= ( X1 @ sK2 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f107]) ).
thf(f109,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK1 @ Y1 )
& ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
= $true )
| ( ( ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
& ( sK1 @ Y0 ) )
@ ( sK10 @ X1 ) )
= $true )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f107]) ).
thf(f110,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $true
= ( ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK1 @ Y1 )
& ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) )
@ ( sK11 @ X2 ) ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( ( ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
& ( sK1 @ Y0 ) )
@ ( sK10 @ X1 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f109]) ).
thf(f111,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( ( sK10 @ X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
& ( sK1 @ ( sK10 @ X1 ) ) )
= $true )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( ( sK11 @ X2 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) )
& ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( sK1 @ Y0 )
& ( ( sK11 @ X2 )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f110]) ).
thf(f112,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( ( sK11 @ X2 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) )
& ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( sK1 @ Y0 )
& ( ( sK11 @ X2 )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( sK1 @ ( sK10 @ X1 ) ) ) ),
inference(and_proxy_clausification,[],[f111]) ).
thf(f113,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( ( ( sK11 @ X2 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) )
& ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( sK1 @ Y0 )
& ( ( sK11 @ X2 )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $true )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X1 ) )
| ( ( sK10 @ X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f111]) ).
thf(f114,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( sK10 @ X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
= $true )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( $true
= ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( sK1 @ Y0 )
& ( ( sK11 @ X2 )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f113]) ).
thf(f115,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( ( sK11 @ X2 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) )
= $true )
| ( $false
= ( sK0 @ X1 ) )
| ( ( sK10 @ X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
= $true )
| ( $true
= ( X2 @ sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f113]) ).
thf(f116,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $false
= ( sK0 @ X2 ) )
| ( $false
= ( sK0 @ X1 ) )
| ( ( ^ [Y0: a > a > $o] :
( ( sK1 @ Y0 )
& ( ( sK11 @ X2 )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
@ ( sK12 @ X2 ) )
= $true )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( ( sK10 @ X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
= $true )
| ( $true
= ( X2 @ sK2 @ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f114]) ).
thf(f117,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( ( sK10 @ X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
= $true )
| ( ( ( sK1 @ ( sK12 @ X2 ) )
& ( ( sK11 @ X2 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK12 @ X2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f116]) ).
thf(f118,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( ( sK11 @ X2 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK12 @ X2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( ( sK10 @ X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
= $true )
| ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f117]) ).
thf(f119,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( ( sK10 @ X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
= $true )
| ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( sK1 @ ( sK12 @ X2 ) ) ) ),
inference(and_proxy_clausification,[],[f117]) ).
thf(f120,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( sK10 @ X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
= $true )
| ( $false
= ( sK0 @ X2 ) )
| ( ( sK11 @ X2 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK12 @ X2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) ) ),
inference(equality_proxy_clausification,[],[f118]) ).
thf(f121,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( sK1 @ Y0 )
& ( ( sK11 @ X2 )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( $true
= ( sK1 @ ( sK10 @ X1 ) ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f112]) ).
thf(f122,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( sK1 @ ( sK10 @ X1 ) ) )
| ( $false
= ( sK0 @ X2 ) )
| ( ( sK11 @ X2 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) )
= $true )
| ( $true
= ( X1 @ sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f112]) ).
thf(f123,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $true
= ( sK1 @ ( sK10 @ X1 ) ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( ^ [Y0: a > a > $o] :
( ( sK1 @ Y0 )
& ( ( sK11 @ X2 )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
@ ( sK13 @ X2 ) ) )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f121]) ).
thf(f124,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( ( sK1 @ ( sK13 @ X2 ) )
& ( ( sK11 @ X2 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK13 @ X2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( $true
= ( sK1 @ ( sK10 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f123]) ).
thf(f125,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( sK1 @ ( sK10 @ X1 ) ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( ( ( sK11 @ X2 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK13 @ X2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
= $true ) ),
inference(and_proxy_clausification,[],[f124]) ).
thf(f126,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( sK1 @ ( sK13 @ X2 ) ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( sK1 @ ( sK10 @ X1 ) ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f124]) ).
thf(f127,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK13 @ X2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( sK11 @ X2 ) )
| ( $true
= ( sK1 @ ( sK10 @ X1 ) ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) ) ),
inference(equality_proxy_clausification,[],[f125]) ).
thf(f128,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( ( sK10 @ X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
& ( sK1 @ ( sK10 @ X1 ) ) )
= $true )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( ( X2 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) )
= $false )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f108]) ).
thf(f129,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( sK1 @ ( sK10 @ X1 ) ) )
| ( ( X2 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) )
= $false )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f128]) ).
thf(f130,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( X2 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) )
= $false )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( sK10 @ X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
= $true )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f128]) ).
thf(f131,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X1 ) )
| ( ( X2 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) )
= $false )
| ( $false
= ( sK0 @ X2 ) )
| ( ( X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f105]) ).
thf(f132,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( ( X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
= $false )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X1 ) )
| ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK1 @ Y1 )
& ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f105]) ).
thf(f133,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( ^ [Y0: a > a > $o] :
( ( Y0 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) )
& ( ?? @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( sK1 @ Y1 )
& ( Y0
= ( ^ [Y2: a,Y3: a] :
( !! @ ( a > a > $o )
@ ^ [Y4: a > a > $o] :
( ( ( sK0 @ Y4 )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( Y1 @ Y6 @ Y5 )
=> ( Y4 @ Y6 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 @ Y3 ) ) ) ) ) ) ) )
@ ( sK14 @ X2 ) )
= $true )
| ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f132]) ).
thf(f134,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
= $false )
| ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( ( sK14 @ X2 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) )
& ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( sK1 @ Y0 )
& ( ( sK14 @ X2 )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) ) ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f133]) ).
thf(f135,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $false
= ( sK0 @ X1 ) )
| ( ( ?? @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( sK1 @ Y0 )
& ( ( sK14 @ X2 )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) ) )
= $true )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( ( X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
= $false )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f134]) ).
thf(f136,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( sK14 @ X2 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) )
= $true )
| ( $false
= ( sK0 @ X2 ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( ( X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f134]) ).
thf(f137,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( ^ [Y0: a > a > $o] :
( ( sK1 @ Y0 )
& ( ( sK14 @ X2 )
= ( ^ [Y1: a,Y2: a] :
( !! @ ( a > a > $o )
@ ^ [Y3: a > a > $o] :
( ( ( sK0 @ Y3 )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 @ Y2 ) ) ) ) ) )
@ ( sK15 @ X2 ) )
= $true )
| ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
= $false )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f135]) ).
thf(f138,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
= $false )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X1 ) )
| ( ( ( sK1 @ ( sK15 @ X2 ) )
& ( ( sK14 @ X2 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK15 @ X2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) )
= $true )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f137]) ).
thf(f139,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( ( ( sK14 @ X2 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK15 @ X2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( ( X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
= $false )
| ( $false
= ( sK0 @ X2 ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f138]) ).
thf(f140,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( ( X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
= $false )
| ( $false
= ( sK0 @ X1 ) )
| ( ( sK1 @ ( sK15 @ X2 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f138]) ).
thf(f141,plain,
! [X2: a > a > $o,X1: a > a > $o] :
( ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( ( X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
= $false )
| ( $false
= ( sK0 @ X1 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( ( sK14 @ X2 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK15 @ X2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) ) ),
inference(equality_proxy_clausification,[],[f139]) ).
thf(f143,definition,
( spl16_1
<=> ( ( sK0 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
thf(f145,plain,
( ( ( sK0 @ sK5 )
= $true )
| ~ spl16_1 ),
inference(avatar_component_clause,[],[f143]) ).
thf(f147,definition,
( spl16_2
<=> ( ( sK0 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
thf(f149,plain,
( ( ( sK0 @ sK4 )
= $true )
| ~ spl16_2 ),
inference(avatar_component_clause,[],[f147]) ).
thf(f150,plain,
( spl16_1
| spl16_2 ),
inference(avatar_split_clause,[],[f27,f147,f143]) ).
thf(f152,definition,
( spl16_3
<=> ! [X2: a,X1: a,X3: a > a > $o] :
( ( ( X3 @ X1 @ X2 )
= $false )
| ( $false
= ( sK1 @ X3 ) )
| ( $true
= ( sK4 @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_3])],[avatar_definition]) ).
thf(f153,plain,
( ! [X2: a,X3: a > a > $o,X1: a] :
( ( $true
= ( sK4 @ X1 @ X2 ) )
| ( ( X3 @ X1 @ X2 )
= $false )
| ( $false
= ( sK1 @ X3 ) ) )
| ~ spl16_3 ),
inference(avatar_component_clause,[],[f152]) ).
thf(f154,plain,
( spl16_3
| spl16_1 ),
inference(avatar_split_clause,[],[f35,f143,f152]) ).
thf(f156,definition,
( spl16_4
<=> ( $false
= ( sK4 @ sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_4])],[avatar_definition]) ).
thf(f158,plain,
( ( $false
= ( sK4 @ sK2 @ sK3 ) )
| ~ spl16_4 ),
inference(avatar_component_clause,[],[f156]) ).
thf(f159,plain,
( spl16_1
| spl16_4 ),
inference(avatar_split_clause,[],[f24,f156,f143]) ).
thf(f161,definition,
( spl16_5
<=> ! [X4: a > a > $o,X3: a > a > $o,X2: a,X1: a] :
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= X3 )
| ( ( X3 @ X1 @ X2 )
= $false )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( sK1 @ X4 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl16_5])],[avatar_definition]) ).
thf(f162,plain,
( ! [X2: a,X3: a > a > $o,X1: a,X4: a > a > $o] :
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X4 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= X3 )
| ( ( X3 @ X1 @ X2 )
= $false )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( sK1 @ X4 )
= $false ) )
| ~ spl16_5 ),
inference(avatar_component_clause,[],[f161]) ).
thf(f163,plain,
( spl16_5
| spl16_2 ),
inference(avatar_split_clause,[],[f51,f147,f161]) ).
thf(f164,plain,
( spl16_5
| spl16_3 ),
inference(avatar_split_clause,[],[f67,f152,f161]) ).
thf(f165,plain,
( spl16_4
| spl16_5 ),
inference(avatar_split_clause,[],[f78,f161,f156]) ).
thf(f167,definition,
( spl16_6
<=> ( $false
= ( sK5 @ sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_6])],[avatar_definition]) ).
thf(f169,plain,
( ( $false
= ( sK5 @ sK2 @ sK3 ) )
| ~ spl16_6 ),
inference(avatar_component_clause,[],[f167]) ).
thf(f170,plain,
( spl16_2
| spl16_6 ),
inference(avatar_split_clause,[],[f82,f167,f147]) ).
thf(f171,plain,
( spl16_6
| spl16_3 ),
inference(avatar_split_clause,[],[f90,f152,f167]) ).
thf(f172,plain,
( spl16_6
| spl16_4 ),
inference(avatar_split_clause,[],[f79,f156,f167]) ).
thf(f174,definition,
( spl16_7
<=> ! [X1: a > a > $o] :
( ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( ( sK10 @ X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
= $true )
| ( $false
= ( sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_7])],[avatar_definition]) ).
thf(f175,plain,
( ! [X1: a > a > $o] :
( ( ( sK10 @ X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
= $true )
| ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) ) )
| ~ spl16_7 ),
inference(avatar_component_clause,[],[f174]) ).
thf(f177,definition,
( spl16_8
<=> ! [X2: a > a > $o] :
( ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( sK11 @ X2 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl16_8])],[avatar_definition]) ).
thf(f178,plain,
( ! [X2: a > a > $o] :
( ( ( sK11 @ X2 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) )
= $true )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) ) )
| ~ spl16_8 ),
inference(avatar_component_clause,[],[f177]) ).
thf(f179,plain,
( spl16_7
| spl16_8 ),
inference(avatar_split_clause,[],[f115,f177,f174]) ).
thf(f181,definition,
( spl16_9
<=> ! [X2: a > a > $o] :
( ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( sK1 @ ( sK12 @ X2 ) ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_9])],[avatar_definition]) ).
thf(f182,plain,
( ! [X2: a > a > $o] :
( ( $true
= ( sK1 @ ( sK12 @ X2 ) ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) ) )
| ~ spl16_9 ),
inference(avatar_component_clause,[],[f181]) ).
thf(f183,plain,
( spl16_7
| spl16_9 ),
inference(avatar_split_clause,[],[f119,f181,f174]) ).
thf(f185,definition,
( spl16_10
<=> ! [X2: a > a > $o] :
( ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( sK11 @ X2 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK12 @ X2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
| ( $false
= ( sK0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_10])],[avatar_definition]) ).
thf(f186,plain,
( ! [X2: a > a > $o] :
( ( ( sK11 @ X2 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK12 @ X2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) ) )
| ~ spl16_10 ),
inference(avatar_component_clause,[],[f185]) ).
thf(f187,plain,
( spl16_7
| spl16_10 ),
inference(avatar_split_clause,[],[f120,f185,f174]) ).
thf(f189,definition,
( spl16_11
<=> ! [X1: a > a > $o] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( $true
= ( sK1 @ ( sK10 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_11])],[avatar_definition]) ).
thf(f190,plain,
( ! [X1: a > a > $o] :
( ( $true
= ( sK1 @ ( sK10 @ X1 ) ) )
| ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( X1 @ sK2 @ sK3 ) ) )
| ~ spl16_11 ),
inference(avatar_component_clause,[],[f189]) ).
thf(f191,plain,
( spl16_8
| spl16_11 ),
inference(avatar_split_clause,[],[f122,f189,f177]) ).
thf(f193,definition,
( spl16_12
<=> ! [X2: a > a > $o] :
( ( $true
= ( sK1 @ ( sK13 @ X2 ) ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_12])],[avatar_definition]) ).
thf(f194,plain,
( ! [X2: a > a > $o] :
( ( $true
= ( sK1 @ ( sK13 @ X2 ) ) )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) ) )
| ~ spl16_12 ),
inference(avatar_component_clause,[],[f193]) ).
thf(f195,plain,
( spl16_11
| spl16_12 ),
inference(avatar_split_clause,[],[f126,f193,f189]) ).
thf(f197,definition,
( spl16_13
<=> ! [X2: a > a > $o] :
( ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK13 @ X2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( sK11 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_13])],[avatar_definition]) ).
thf(f198,plain,
( ! [X2: a > a > $o] :
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK13 @ X2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
= ( sK11 @ X2 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) ) )
| ~ spl16_13 ),
inference(avatar_component_clause,[],[f197]) ).
thf(f199,plain,
( spl16_11
| spl16_13 ),
inference(avatar_split_clause,[],[f127,f197,f189]) ).
thf(f201,definition,
( spl16_14
<=> ! [X2: a > a > $o] :
( ( ( X2 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) )
= $false )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_14])],[avatar_definition]) ).
thf(f202,plain,
( ! [X2: a > a > $o] :
( ( ( X2 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) )
= $false )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) ) )
| ~ spl16_14 ),
inference(avatar_component_clause,[],[f201]) ).
thf(f203,plain,
( spl16_7
| spl16_14 ),
inference(avatar_split_clause,[],[f130,f201,f174]) ).
thf(f204,plain,
( spl16_11
| spl16_14 ),
inference(avatar_split_clause,[],[f129,f201,f189]) ).
thf(f206,definition,
( spl16_15
<=> ! [X2: a > a > $o] :
( ( ( sK14 @ X2 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) )
= $true )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_15])],[avatar_definition]) ).
thf(f207,plain,
( ! [X2: a > a > $o] :
( ( ( sK14 @ X2 @ ( sK6 @ X2 ) @ ( sK9 @ X2 ) )
= $true )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) ) )
| ~ spl16_15 ),
inference(avatar_component_clause,[],[f206]) ).
thf(f209,definition,
( spl16_16
<=> ! [X1: a > a > $o] :
( ( $false
= ( sK0 @ X1 ) )
| ( ( X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
= $false )
| ( $true
= ( X1 @ sK2 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_16])],[avatar_definition]) ).
thf(f210,plain,
( ! [X1: a > a > $o] :
( ( ( X1 @ ( sK7 @ X1 ) @ ( sK8 @ X1 ) )
= $false )
| ( $true
= ( X1 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X1 ) ) )
| ~ spl16_16 ),
inference(avatar_component_clause,[],[f209]) ).
thf(f211,plain,
( spl16_15
| spl16_16 ),
inference(avatar_split_clause,[],[f136,f209,f206]) ).
thf(f213,definition,
( spl16_17
<=> ! [X2: a > a > $o] :
( ( $false
= ( sK0 @ X2 ) )
| ( ( sK1 @ ( sK15 @ X2 ) )
= $true )
| ( $true
= ( X2 @ sK2 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_17])],[avatar_definition]) ).
thf(f214,plain,
( ! [X2: a > a > $o] :
( ( ( sK1 @ ( sK15 @ X2 ) )
= $true )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) ) )
| ~ spl16_17 ),
inference(avatar_component_clause,[],[f213]) ).
thf(f215,plain,
( spl16_17
| spl16_16 ),
inference(avatar_split_clause,[],[f140,f209,f213]) ).
thf(f217,definition,
( spl16_18
<=> ! [X2: a > a > $o] :
( ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( sK14 @ X2 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK15 @ X2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
| ( $false
= ( sK0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_18])],[avatar_definition]) ).
thf(f218,plain,
( ! [X2: a > a > $o] :
( ( ( sK14 @ X2 )
= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK15 @ X2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) ) )
| ~ spl16_18 ),
inference(avatar_component_clause,[],[f217]) ).
thf(f219,plain,
( spl16_18
| spl16_16 ),
inference(avatar_split_clause,[],[f141,f209,f217]) ).
thf(f220,plain,
( spl16_14
| spl16_16 ),
inference(avatar_split_clause,[],[f131,f209,f201]) ).
thf(f231,plain,
( ! [X0: a > a > $o] :
( ( ( sK0 @ sK4 )
= $false )
| ( $false = $true )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ( ( sK1 @ X0 )
= $false )
| ( ( X0 @ ( sK7 @ sK4 ) @ ( sK8 @ sK4 ) )
= $false ) )
| ~ spl16_3
| ~ spl16_16 ),
inference(superposition,[],[f153,f210]) ).
thf(f232,plain,
( ! [X0: a > a > $o] :
( ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ( ( X0 @ ( sK7 @ sK4 ) @ ( sK8 @ sK4 ) )
= $false )
| ( ( sK0 @ sK4 )
= $false )
| ( ( sK1 @ X0 )
= $false ) )
| ~ spl16_3
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f231]) ).
thf(f234,plain,
( ! [X0: a > a > $o] :
( ( ( sK1 @ X0 )
= $false )
| ( ( sK0 @ sK4 )
= $false )
| ( $false = $true )
| ( ( X0 @ ( sK7 @ sK4 ) @ ( sK8 @ sK4 ) )
= $false ) )
| ~ spl16_3
| ~ spl16_4
| ~ spl16_16 ),
inference(forward_demodulation,[],[f232,f158]) ).
thf(f235,plain,
( ! [X0: a > a > $o] :
( ( ( sK1 @ X0 )
= $false )
| ( ( sK0 @ sK4 )
= $false )
| ( ( X0 @ ( sK7 @ sK4 ) @ ( sK8 @ sK4 ) )
= $false ) )
| ~ spl16_3
| ~ spl16_4
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f234]) ).
thf(f238,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ ( sK7 @ sK4 ) @ ( sK8 @ sK4 ) )
= $false )
| ( ( sK1 @ X0 )
= $false )
| ( $false = $true ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_16 ),
inference(forward_demodulation,[],[f235,f149]) ).
thf(f239,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ ( sK7 @ sK4 ) @ ( sK8 @ sK4 ) )
= $false )
| ( ( sK1 @ X0 )
= $false ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f238]) ).
thf(f247,plain,
( ( $false
= ( sK1 @ ( sK10 @ sK4 ) ) )
| ( $false = $true )
| ( ( sK0 @ sK4 )
= $false )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_7
| ~ spl16_16 ),
inference(superposition,[],[f239,f175]) ).
thf(f248,plain,
( ( ( sK0 @ sK4 )
= $false )
| ( $false
= ( sK1 @ ( sK10 @ sK4 ) ) )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_7
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f247]) ).
thf(f250,plain,
( ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ( $false
= ( sK1 @ ( sK10 @ sK4 ) ) )
| ( $false = $true )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_7
| ~ spl16_16 ),
inference(forward_demodulation,[],[f248,f149]) ).
thf(f251,plain,
( ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ( $false
= ( sK1 @ ( sK10 @ sK4 ) ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_7
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f250]) ).
thf(f254,plain,
( ( $false = $true )
| ( $false
= ( sK1 @ ( sK10 @ sK4 ) ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_7
| ~ spl16_16 ),
inference(forward_demodulation,[],[f251,f158]) ).
thf(f255,plain,
( ( $false
= ( sK1 @ ( sK10 @ sK4 ) ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_7
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f254]) ).
thf(f259,plain,
( ( $false = $true )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ( ( sK0 @ sK4 )
= $false )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_7
| ~ spl16_11
| ~ spl16_16 ),
inference(superposition,[],[f190,f255]) ).
thf(f260,plain,
( ( ( sK0 @ sK4 )
= $false )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_7
| ~ spl16_11
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f259]) ).
thf(f262,plain,
( ( $false = $true )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_7
| ~ spl16_11
| ~ spl16_16 ),
inference(forward_demodulation,[],[f260,f149]) ).
thf(f263,plain,
( ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_7
| ~ spl16_11
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f262]) ).
thf(f266,plain,
( ( $false = $true )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_7
| ~ spl16_11
| ~ spl16_16 ),
inference(forward_demodulation,[],[f263,f158]) ).
thf(f267,plain,
( $false
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_7
| ~ spl16_11
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f266]) ).
thf(f268,plain,
( ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_7
| ~ spl16_11
| ~ spl16_16 ),
inference(avatar_contradiction_clause,[],[f267]) ).
thf(f297,plain,
( ! [X2: a > a > $o,X3: a] :
( ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK13 @ X2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X3 )
= ( sK11 @ X2 @ X3 ) )
| ( $false
= ( sK0 @ X2 ) ) )
| ~ spl16_13 ),
inference(argument_congruence,[],[f198]) ).
thf(f298,plain,
( ! [X2: a > a > $o,X3: a] :
( ( ( sK11 @ X2 @ X3 )
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK13 @ X2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ X3 @ Y0 ) ) ) ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) ) )
| ~ spl16_13 ),
inference(beta-eta_normalization,[],[f297]) ).
thf(f299,plain,
( ! [X2: a > a > $o,X3: a,X4: a] :
( ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( ( sK11 @ X2 @ X3 @ X4 )
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK13 @ X2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ X3 @ Y0 ) ) )
@ X4 ) ) )
| ~ spl16_13 ),
inference(argument_congruence,[],[f298]) ).
thf(f301,plain,
( ! [X2: a > a > $o,X3: a,X4: a] :
( ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK13 @ X2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ X3 @ Y0 ) ) )
@ X4 ) )
| ( $false
= ( sK11 @ X2 @ X3 @ X4 ) ) )
| ~ spl16_13 ),
inference(iff_proxy_clausification,[],[f299]) ).
thf(f302,plain,
( ! [X2: a > a > $o,X3: a,X4: a] :
( ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK11 @ X2 @ X3 @ X4 ) )
| ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK13 @ X2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ X3 @ X4 ) ) ) )
| ( $false
= ( sK0 @ X2 ) ) )
| ~ spl16_13 ),
inference(beta-eta_normalization,[],[f301]) ).
thf(f303,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( $false
= ( sK11 @ X2 @ X3 @ X4 ) )
| ( ( ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK13 @ X2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ X3 @ X4 ) )
@ X5 )
= $true )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) ) )
| ~ spl16_13 ),
inference(pi_proxy_clausification,[],[f302]) ).
thf(f304,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( ( ( sK0 @ X5 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK13 @ X2 @ Y1 @ Y0 )
=> ( X5 @ Y1 @ Y0 ) ) ) ) )
=> ( X5 @ X3 @ X4 ) ) )
| ( $false
= ( sK11 @ X2 @ X3 @ X4 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) ) )
| ~ spl16_13 ),
inference(beta-eta_normalization,[],[f303]) ).
thf(f305,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK11 @ X2 @ X3 @ X4 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( ( X5 @ X3 @ X4 )
= $true )
| ( ( ( sK0 @ X5 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK13 @ X2 @ Y1 @ Y0 )
=> ( X5 @ Y1 @ Y0 ) ) ) ) )
= $false ) )
| ~ spl16_13 ),
inference(imp_proxy_clausification,[],[f304]) ).
thf(f306,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( ( sK0 @ X5 )
= $false )
| ( ( X5 @ X3 @ X4 )
= $true )
| ( $false
= ( sK11 @ X2 @ X3 @ X4 ) )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK13 @ X2 @ Y1 @ Y0 )
=> ( X5 @ Y1 @ Y0 ) ) ) )
= $false )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) ) )
| ~ spl16_13 ),
inference(and_proxy_clausification,[],[f305]) ).
thf(f307,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( X5 @ X3 @ X4 )
= $true )
| ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK13 @ X2 @ Y1 @ Y0 )
=> ( X5 @ Y1 @ Y0 ) ) )
@ ( sK17 @ X5 @ X2 ) ) )
| ( $false
= ( sK11 @ X2 @ X3 @ X4 ) )
| ( ( sK0 @ X5 )
= $false ) )
| ~ spl16_13 ),
inference(sigma_proxy_clausification,[],[f306]) ).
thf(f308,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK13 @ X2 @ Y0 @ ( sK17 @ X5 @ X2 ) )
=> ( X5 @ Y0 @ ( sK17 @ X5 @ X2 ) ) ) ) )
| ( $false
= ( sK0 @ X2 ) )
| ( ( sK0 @ X5 )
= $false )
| ( ( X5 @ X3 @ X4 )
= $true )
| ( $false
= ( sK11 @ X2 @ X3 @ X4 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) ) )
| ~ spl16_13 ),
inference(beta-eta_normalization,[],[f307]) ).
thf(f309,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( ( X5 @ X3 @ X4 )
= $true )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK11 @ X2 @ X3 @ X4 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( ( sK0 @ X5 )
= $false )
| ( ( ^ [Y0: a] :
( ( sK13 @ X2 @ Y0 @ ( sK17 @ X5 @ X2 ) )
=> ( X5 @ Y0 @ ( sK17 @ X5 @ X2 ) ) )
@ ( sK18 @ X5 @ X2 ) )
= $false ) )
| ~ spl16_13 ),
inference(sigma_proxy_clausification,[],[f308]) ).
thf(f310,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( sK0 @ X5 )
= $false )
| ( ( X5 @ X3 @ X4 )
= $true )
| ( $false
= ( sK11 @ X2 @ X3 @ X4 ) )
| ( $false
= ( ( sK13 @ X2 @ ( sK18 @ X5 @ X2 ) @ ( sK17 @ X5 @ X2 ) )
=> ( X5 @ ( sK18 @ X5 @ X2 ) @ ( sK17 @ X5 @ X2 ) ) ) )
| ( $false
= ( sK0 @ X2 ) ) )
| ~ spl16_13 ),
inference(beta-eta_normalization,[],[f309]) ).
thf(f311,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( $false
= ( X5 @ ( sK18 @ X5 @ X2 ) @ ( sK17 @ X5 @ X2 ) ) )
| ( ( sK0 @ X5 )
= $false )
| ( $false
= ( sK11 @ X2 @ X3 @ X4 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( ( X5 @ X3 @ X4 )
= $true ) )
| ~ spl16_13 ),
inference(imp_proxy_clausification,[],[f310]) ).
thf(f312,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( ( sK13 @ X2 @ ( sK18 @ X5 @ X2 ) @ ( sK17 @ X5 @ X2 ) )
= $true )
| ( ( sK0 @ X5 )
= $false )
| ( $false
= ( sK11 @ X2 @ X3 @ X4 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( ( X5 @ X3 @ X4 )
= $true ) )
| ~ spl16_13 ),
inference(imp_proxy_clausification,[],[f310]) ).
thf(f353,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( ( sK0 @ X0 )
= $false )
| ( ( sK0 @ sK4 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $true
= ( sK4 @ X2 @ X3 ) )
| ( ( sK1 @ X1 )
= $false )
| ( $false
= ( X1 @ ( sK18 @ sK4 @ X0 ) @ ( sK17 @ sK4 @ X0 ) ) )
| ( ( sK11 @ X0 @ X2 @ X3 )
= $false )
| ( $false = $true ) )
| ~ spl16_3
| ~ spl16_13 ),
inference(superposition,[],[f153,f311]) ).
thf(f357,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( ( sK11 @ X0 @ X2 @ X3 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK0 @ sK4 )
= $false )
| ( $true
= ( sK4 @ X2 @ X3 ) )
| ( ( sK0 @ X0 )
= $false )
| ( $false
= ( X1 @ ( sK18 @ sK4 @ X0 ) @ ( sK17 @ sK4 @ X0 ) ) )
| ( ( sK1 @ X1 )
= $false ) )
| ~ spl16_3
| ~ spl16_13 ),
inference(trivial_inequality_removal,[],[f353]) ).
thf(f361,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( $false = $true )
| ( ( sK0 @ X0 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $true
= ( sK4 @ X2 @ X3 ) )
| ( $false
= ( X1 @ ( sK18 @ sK4 @ X0 ) @ ( sK17 @ sK4 @ X0 ) ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( sK11 @ X0 @ X2 @ X3 )
= $false ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_13 ),
inference(forward_demodulation,[],[f357,f149]) ).
thf(f362,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( $false
= ( X1 @ ( sK18 @ sK4 @ X0 ) @ ( sK17 @ sK4 @ X0 ) ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK11 @ X0 @ X2 @ X3 )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( $true
= ( sK4 @ X2 @ X3 ) ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_13 ),
inference(trivial_inequality_removal,[],[f361]) ).
thf(f381,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK0 @ sK4 )
= $false )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $true
= ( sK4 @ X3 @ X4 ) )
| ( ( sK1 @ ( sK13 @ X0 ) )
= $false )
| ( $false
= ( sK11 @ X0 @ X3 @ X4 ) )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $false = $true ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_13 ),
inference(superposition,[],[f362,f312]) ).
thf(f386,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( sK0 @ X0 )
= $false )
| ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( $true
= ( sK4 @ X3 @ X4 ) )
| ( ( sK1 @ ( sK13 @ X0 ) )
= $false )
| ( $false = $true )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( ( sK0 @ sK4 )
= $false )
| ( $false
= ( sK11 @ X0 @ X3 @ X4 ) ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_13 ),
inference(duplicate_literal_removal,[],[f381]) ).
thf(f387,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( ( sK1 @ ( sK13 @ X0 ) )
= $false )
| ( $false
= ( sK11 @ X0 @ X3 @ X4 ) )
| ( ( sK0 @ sK4 )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( $true
= ( sK4 @ X3 @ X4 ) ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_13 ),
inference(trivial_inequality_removal,[],[f386]) ).
thf(f396,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $false = $true )
| ( $false
= ( sK11 @ X0 @ X3 @ X4 ) )
| ( ( sK0 @ X0 )
= $false )
| ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( ( sK1 @ ( sK13 @ X0 ) )
= $false )
| ( $true
= ( sK4 @ X3 @ X4 ) )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $true
= ( sK4 @ X1 @ X2 ) ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_13 ),
inference(forward_demodulation,[],[f387,f149]) ).
thf(f397,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $false
= ( sK11 @ X0 @ X3 @ X4 ) )
| ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( ( sK1 @ ( sK13 @ X0 ) )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( $true
= ( sK4 @ X3 @ X4 ) ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_13 ),
inference(trivial_inequality_removal,[],[f396]) ).
thf(f402,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( $true
= ( sK4 @ X1 @ X2 ) )
| ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( ( sK1 @ ( sK13 @ X0 ) )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( $false != $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_13 ),
inference(equality_factoring,[],[f397]) ).
thf(f405,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( sK0 @ X0 )
= $false )
| ( ( sK1 @ ( sK13 @ X0 ) )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( $false != $false ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_13 ),
inference(duplicate_literal_removal,[],[f402]) ).
thf(f406,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK1 @ ( sK13 @ X0 ) )
= $false )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( ( X0 @ sK2 @ sK3 )
= $true ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_13 ),
inference(trivial_inequality_removal,[],[f405]) ).
thf(f409,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $false = $true )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK1 @ ( sK13 @ X0 ) )
= $false )
| ( $true
= ( sK4 @ ( sK6 @ X0 ) @ ( sK9 @ X0 ) ) ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_8
| ~ spl16_13 ),
inference(superposition,[],[f406,f178]) ).
thf(f411,plain,
( ! [X0: a > a > $o] :
( ( ( sK0 @ X0 )
= $false )
| ( $true
= ( sK4 @ ( sK6 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( ( sK1 @ ( sK13 @ X0 ) )
= $false )
| ( $false = $true )
| ( ( X0 @ sK2 @ sK3 )
= $true ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_8
| ~ spl16_13 ),
inference(duplicate_literal_removal,[],[f409]) ).
thf(f412,plain,
( ! [X0: a > a > $o] :
( ( $true
= ( sK4 @ ( sK6 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK1 @ ( sK13 @ X0 ) )
= $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_8
| ~ spl16_13 ),
inference(trivial_inequality_removal,[],[f411]) ).
thf(f415,plain,
( ( ( sK0 @ sK4 )
= $false )
| ( $false = $true )
| ( $false
= ( sK1 @ ( sK13 @ sK4 ) ) )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ( ( sK0 @ sK4 )
= $false )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_8
| ~ spl16_13
| ~ spl16_14 ),
inference(superposition,[],[f412,f202]) ).
thf(f420,plain,
( ( $false
= ( sK1 @ ( sK13 @ sK4 ) ) )
| ( $false = $true )
| ( ( sK0 @ sK4 )
= $false )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_8
| ~ spl16_13
| ~ spl16_14 ),
inference(duplicate_literal_removal,[],[f415]) ).
thf(f421,plain,
( ( ( sK0 @ sK4 )
= $false )
| ( $false
= ( sK1 @ ( sK13 @ sK4 ) ) )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_8
| ~ spl16_13
| ~ spl16_14 ),
inference(trivial_inequality_removal,[],[f420]) ).
thf(f427,plain,
( ( $false
= ( sK1 @ ( sK13 @ sK4 ) ) )
| ( $false = $true )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_8
| ~ spl16_13
| ~ spl16_14 ),
inference(forward_demodulation,[],[f421,f149]) ).
thf(f428,plain,
( ( $false
= ( sK1 @ ( sK13 @ sK4 ) ) )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_8
| ~ spl16_13
| ~ spl16_14 ),
inference(trivial_inequality_removal,[],[f427]) ).
thf(f435,plain,
( ( $false
= ( sK1 @ ( sK13 @ sK4 ) ) )
| ( $false = $true )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_8
| ~ spl16_13
| ~ spl16_14 ),
inference(forward_demodulation,[],[f428,f158]) ).
thf(f436,plain,
( ( $false
= ( sK1 @ ( sK13 @ sK4 ) ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_8
| ~ spl16_13
| ~ spl16_14 ),
inference(trivial_inequality_removal,[],[f435]) ).
thf(f442,definition,
( spl16_19
<=> ( $false
= ( sK1 @ ( sK13 @ sK4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_19])],[avatar_definition]) ).
thf(f444,plain,
( ( $false
= ( sK1 @ ( sK13 @ sK4 ) ) )
| ~ spl16_19 ),
inference(avatar_component_clause,[],[f442]) ).
thf(f450,plain,
( spl16_19
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_8
| ~ spl16_13
| ~ spl16_14 ),
inference(avatar_split_clause,[],[f436,f201,f197,f177,f156,f152,f147,f442]) ).
thf(f494,plain,
( ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ( ( sK0 @ sK4 )
= $false )
| ( $false = $true )
| ~ spl16_12
| ~ spl16_19 ),
inference(superposition,[],[f194,f444]) ).
thf(f496,plain,
( ( ( sK0 @ sK4 )
= $false )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ~ spl16_12
| ~ spl16_19 ),
inference(trivial_inequality_removal,[],[f494]) ).
thf(f499,plain,
( ( $false = $true )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ~ spl16_2
| ~ spl16_12
| ~ spl16_19 ),
inference(forward_demodulation,[],[f496,f149]) ).
thf(f500,plain,
( ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ~ spl16_2
| ~ spl16_12
| ~ spl16_19 ),
inference(trivial_inequality_removal,[],[f499]) ).
thf(f501,plain,
( ( $false = $true )
| ~ spl16_2
| ~ spl16_4
| ~ spl16_12
| ~ spl16_19 ),
inference(forward_demodulation,[],[f500,f158]) ).
thf(f502,plain,
( $false
| ~ spl16_2
| ~ spl16_4
| ~ spl16_12
| ~ spl16_19 ),
inference(trivial_inequality_removal,[],[f501]) ).
thf(f503,plain,
( ~ spl16_2
| ~ spl16_4
| ~ spl16_12
| ~ spl16_19 ),
inference(avatar_contradiction_clause,[],[f502]) ).
thf(f505,definition,
( spl16_21
<=> ( ( sK0 @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl16_21])],[avatar_definition]) ).
thf(f507,plain,
( ( ( sK0 @ sK4 )
= $false )
| ~ spl16_21 ),
inference(avatar_component_clause,[],[f505]) ).
thf(f580,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( X0 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X1
@ X2 )
= $false )
| ( ( sK1 @ X0 )
= $false )
| ( ( sK5 @ X1 @ X2 )
= $true ) )
| ~ spl16_5 ),
inference(equality_resolution,[],[f162]) ).
thf(f583,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( sK1 @ X0 )
= $false )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( X0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ X1 @ X2 ) ) )
= $false ) )
| ~ spl16_5 ),
inference(beta-eta_normalization,[],[f580]) ).
thf(f584,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( sK1 @ X0 )
= $false )
| ( $false
= ( ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( X0 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ X1 @ X2 ) )
@ ( sK22 @ X1 @ X0 @ X2 ) ) )
| ( ( sK5 @ X1 @ X2 )
= $true ) )
| ~ spl16_5 ),
inference(sigma_proxy_clausification,[],[f583]) ).
thf(f585,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( ( ( sK0 @ ( sK22 @ X1 @ X0 @ X2 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( X0 @ Y1 @ Y0 )
=> ( sK22 @ X1 @ X0 @ X2 @ Y1 @ Y0 ) ) ) ) )
=> ( sK22 @ X1 @ X0 @ X2 @ X1 @ X2 ) )
= $false )
| ( ( sK1 @ X0 )
= $false )
| ( ( sK5 @ X1 @ X2 )
= $true ) )
| ~ spl16_5 ),
inference(beta-eta_normalization,[],[f584]) ).
thf(f586,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( sK22 @ X1 @ X0 @ X2 @ X1 @ X2 )
= $false )
| ( ( sK1 @ X0 )
= $false )
| ( ( sK5 @ X1 @ X2 )
= $true ) )
| ~ spl16_5 ),
inference(imp_proxy_clausification,[],[f585]) ).
thf(f587,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( sK1 @ X0 )
= $false )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( $true
= ( ( sK0 @ ( sK22 @ X1 @ X0 @ X2 ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( X0 @ Y1 @ Y0 )
=> ( sK22 @ X1 @ X0 @ X2 @ Y1 @ Y0 ) ) ) ) ) ) )
| ~ spl16_5 ),
inference(imp_proxy_clausification,[],[f585]) ).
thf(f588,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( X0 @ Y1 @ Y0 )
=> ( sK22 @ X1 @ X0 @ X2 @ Y1 @ Y0 ) ) ) )
= $true )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( sK1 @ X0 )
= $false ) )
| ~ spl16_5 ),
inference(and_proxy_clausification,[],[f587]) ).
thf(f590,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a] :
( ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( sK1 @ X0 )
= $false )
| ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( X0 @ Y1 @ Y0 )
=> ( sK22 @ X1 @ X0 @ X2 @ Y1 @ Y0 ) ) )
@ X3 )
= $true ) )
| ~ spl16_5 ),
inference(pi_proxy_clausification,[],[f588]) ).
thf(f591,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a] :
( ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( X0 @ Y0 @ X3 )
=> ( sK22 @ X1 @ X0 @ X2 @ Y0 @ X3 ) ) )
= $true )
| ( ( sK1 @ X0 )
= $false ) )
| ~ spl16_5 ),
inference(beta-eta_normalization,[],[f590]) ).
thf(f592,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( ^ [Y0: a] :
( ( X0 @ Y0 @ X3 )
=> ( sK22 @ X1 @ X0 @ X2 @ Y0 @ X3 ) )
@ X4 )
= $true )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( sK1 @ X0 )
= $false ) )
| ~ spl16_5 ),
inference(pi_proxy_clausification,[],[f591]) ).
thf(f593,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( sK1 @ X0 )
= $false )
| ( ( ( X0 @ X4 @ X3 )
=> ( sK22 @ X1 @ X0 @ X2 @ X4 @ X3 ) )
= $true )
| ( ( sK5 @ X1 @ X2 )
= $true ) )
| ~ spl16_5 ),
inference(beta-eta_normalization,[],[f592]) ).
thf(f594,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $true
= ( sK22 @ X1 @ X0 @ X2 @ X4 @ X3 ) )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( X0 @ X4 @ X3 )
= $false )
| ( ( sK1 @ X0 )
= $false ) )
| ~ spl16_5 ),
inference(imp_proxy_clausification,[],[f593]) ).
thf(f603,plain,
( ! [X2: a,X0: a,X1: a > a > $o] :
( ( ( sK1 @ X1 )
= $false )
| ( $true
= ( sK5 @ X0 @ X2 ) )
| ( $false
= ( X1 @ X0 @ X2 ) )
| ( $true
= ( sK5 @ X0 @ X2 ) )
| ( ( sK1 @ X1 )
= $false )
| ( $false = $true ) )
| ~ spl16_5 ),
inference(superposition,[],[f586,f594]) ).
thf(f612,plain,
( ! [X2: a,X0: a,X1: a > a > $o] :
( ( ( sK1 @ X1 )
= $false )
| ( $false
= ( X1 @ X0 @ X2 ) )
| ( $false = $true )
| ( $true
= ( sK5 @ X0 @ X2 ) ) )
| ~ spl16_5 ),
inference(duplicate_literal_removal,[],[f603]) ).
thf(f613,plain,
( ! [X2: a,X0: a,X1: a > a > $o] :
( ( $true
= ( sK5 @ X0 @ X2 ) )
| ( $false
= ( X1 @ X0 @ X2 ) )
| ( ( sK1 @ X1 )
= $false ) )
| ~ spl16_5 ),
inference(trivial_inequality_removal,[],[f612]) ).
thf(f628,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ ( sK7 @ sK5 ) @ ( sK8 @ sK5 ) )
= $false )
| ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ( $false = $true )
| ( ( sK1 @ X0 )
= $false ) )
| ~ spl16_5
| ~ spl16_16 ),
inference(superposition,[],[f613,f210]) ).
thf(f632,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( ( sK0 @ sK5 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK0 @ X0 )
= $false )
| ( ( X1 @ ( sK18 @ sK5 @ X0 ) @ ( sK17 @ sK5 @ X0 ) )
= $false )
| ( ( sK5 @ X2 @ X3 )
= $true )
| ( ( sK1 @ X1 )
= $false )
| ( ( sK11 @ X0 @ X2 @ X3 )
= $false )
| ( $false = $true ) )
| ~ spl16_5
| ~ spl16_13 ),
inference(superposition,[],[f613,f311]) ).
thf(f642,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ ( sK7 @ sK5 ) @ ( sK8 @ sK5 ) )
= $false )
| ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( ( sK1 @ X0 )
= $false ) )
| ~ spl16_5
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f628]) ).
thf(f647,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( ( sK11 @ X0 @ X2 @ X3 )
= $false )
| ( ( sK0 @ sK5 )
= $false )
| ( ( X1 @ ( sK18 @ sK5 @ X0 ) @ ( sK17 @ sK5 @ X0 ) )
= $false )
| ( ( sK5 @ X2 @ X3 )
= $true )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK1 @ X1 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true ) )
| ~ spl16_5
| ~ spl16_13 ),
inference(trivial_inequality_removal,[],[f632]) ).
thf(f655,plain,
( ! [X0: a > a > $o] :
( ( ( sK0 @ sK5 )
= $false )
| ( $false = $true )
| ( ( sK1 @ X0 )
= $false )
| ( ( X0 @ ( sK7 @ sK5 ) @ ( sK8 @ sK5 ) )
= $false ) )
| ~ spl16_5
| ~ spl16_6
| ~ spl16_16 ),
inference(forward_demodulation,[],[f642,f169]) ).
thf(f656,plain,
( ! [X0: a > a > $o] :
( ( ( sK1 @ X0 )
= $false )
| ( ( sK0 @ sK5 )
= $false )
| ( ( X0 @ ( sK7 @ sK5 ) @ ( sK8 @ sK5 ) )
= $false ) )
| ~ spl16_5
| ~ spl16_6
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f655]) ).
thf(f659,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( ( sK1 @ X1 )
= $false )
| ( $false = $true )
| ( ( sK11 @ X0 @ X2 @ X3 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( X1 @ ( sK18 @ sK5 @ X0 ) @ ( sK17 @ sK5 @ X0 ) )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK5 @ X2 @ X3 )
= $true ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_13 ),
inference(forward_demodulation,[],[f647,f145]) ).
thf(f660,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( ( X1 @ ( sK18 @ sK5 @ X0 ) @ ( sK17 @ sK5 @ X0 ) )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK5 @ X2 @ X3 )
= $true )
| ( ( sK1 @ X1 )
= $false )
| ( ( sK11 @ X0 @ X2 @ X3 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_13 ),
inference(trivial_inequality_removal,[],[f659]) ).
thf(f667,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ ( sK7 @ sK5 ) @ ( sK8 @ sK5 ) )
= $false )
| ( ( sK1 @ X0 )
= $false )
| ( $false = $true ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_16 ),
inference(forward_demodulation,[],[f656,f145]) ).
thf(f668,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ ( sK7 @ sK5 ) @ ( sK8 @ sK5 ) )
= $false )
| ( ( sK1 @ X0 )
= $false ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f667]) ).
thf(f681,plain,
( ( $false
= ( sK1 @ ( sK10 @ sK5 ) ) )
| ( $false = $true )
| ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_7
| ~ spl16_16 ),
inference(superposition,[],[f175,f668]) ).
thf(f688,plain,
( ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( sK1 @ ( sK10 @ sK5 ) ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_7
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f681]) ).
thf(f699,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( sK1 @ ( sK10 @ sK5 ) ) )
| ( $false = $true )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_7
| ~ spl16_16 ),
inference(forward_demodulation,[],[f688,f169]) ).
thf(f700,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( sK1 @ ( sK10 @ sK5 ) ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_7
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f699]) ).
thf(f703,plain,
( ( $false
= ( sK1 @ ( sK10 @ sK5 ) ) )
| ( $false = $true )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_7
| ~ spl16_16 ),
inference(forward_demodulation,[],[f700,f145]) ).
thf(f704,plain,
( ( $false
= ( sK1 @ ( sK10 @ sK5 ) ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_7
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f703]) ).
thf(f833,definition,
( spl16_27
<=> ( $false
= ( sK1 @ ( sK13 @ sK5 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_27])],[avatar_definition]) ).
thf(f834,plain,
( ( $false
!= ( sK1 @ ( sK13 @ sK5 ) ) )
| spl16_27 ),
inference(avatar_component_clause,[],[f833]) ).
thf(f835,plain,
( ( $false
= ( sK1 @ ( sK13 @ sK5 ) ) )
| ~ spl16_27 ),
inference(avatar_component_clause,[],[f833]) ).
thf(f842,plain,
( ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $false = $true )
| ~ spl16_12
| ~ spl16_27 ),
inference(superposition,[],[f835,f194]) ).
thf(f845,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ~ spl16_12
| ~ spl16_27 ),
inference(trivial_inequality_removal,[],[f842]) ).
thf(f848,plain,
( ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ( $false = $true )
| ~ spl16_1
| ~ spl16_12
| ~ spl16_27 ),
inference(forward_demodulation,[],[f845,f145]) ).
thf(f849,plain,
( ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ~ spl16_1
| ~ spl16_12
| ~ spl16_27 ),
inference(trivial_inequality_removal,[],[f848]) ).
thf(f850,plain,
( ( $false = $true )
| ~ spl16_1
| ~ spl16_6
| ~ spl16_12
| ~ spl16_27 ),
inference(forward_demodulation,[],[f849,f169]) ).
thf(f851,plain,
( $false
| ~ spl16_1
| ~ spl16_6
| ~ spl16_12
| ~ spl16_27 ),
inference(trivial_inequality_removal,[],[f850]) ).
thf(f852,plain,
( ~ spl16_1
| ~ spl16_6
| ~ spl16_12
| ~ spl16_27 ),
inference(avatar_contradiction_clause,[],[f851]) ).
thf(f915,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $false = $true )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK1 @ ( sK13 @ X0 ) )
= $false )
| ( $false
= ( sK11 @ X0 @ X3 @ X4 ) )
| ( ( sK5 @ X3 @ X4 )
= $true )
| ( ( sK0 @ sK5 )
= $false ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_13 ),
inference(superposition,[],[f660,f312]) ).
thf(f931,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( ( sK5 @ X3 @ X4 )
= $true )
| ( ( sK0 @ sK5 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( sK0 @ X0 )
= $false )
| ( $false = $true )
| ( $false
= ( sK11 @ X0 @ X3 @ X4 ) )
| ( ( sK1 @ ( sK13 @ X0 ) )
= $false ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_13 ),
inference(duplicate_literal_removal,[],[f915]) ).
thf(f932,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( sK0 @ X0 )
= $false )
| ( ( sK5 @ X3 @ X4 )
= $true )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $false
= ( sK11 @ X0 @ X3 @ X4 ) )
| ( ( sK1 @ ( sK13 @ X0 ) )
= $false )
| ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( sK11 @ X0 @ X1 @ X2 ) ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_13 ),
inference(trivial_inequality_removal,[],[f931]) ).
thf(f948,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( sK1 @ ( sK13 @ X0 ) )
= $false )
| ( ( sK5 @ X3 @ X4 )
= $true )
| ( $false
= ( sK11 @ X0 @ X3 @ X4 ) )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( sK0 @ X0 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( $false = $true ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_13 ),
inference(forward_demodulation,[],[f932,f145]) ).
thf(f949,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $false
= ( sK11 @ X0 @ X3 @ X4 ) )
| ( ( sK5 @ X3 @ X4 )
= $true )
| ( ( sK1 @ ( sK13 @ X0 ) )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( X0 @ sK2 @ sK3 )
= $true ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_13 ),
inference(trivial_inequality_removal,[],[f948]) ).
thf(f954,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK1 @ ( sK13 @ X0 ) )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $false != $false )
| ( ( sK5 @ X1 @ X2 )
= $true ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_13 ),
inference(equality_factoring,[],[f949]) ).
thf(f957,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( ( sK0 @ X0 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( $false != $false )
| ( ( sK1 @ ( sK13 @ X0 ) )
= $false ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_13 ),
inference(duplicate_literal_removal,[],[f954]) ).
thf(f958,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK1 @ ( sK13 @ X0 ) )
= $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_13 ),
inference(trivial_inequality_removal,[],[f957]) ).
thf(f961,plain,
( ! [X0: a > a > $o] :
( ( ( sK0 @ X0 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK1 @ ( sK13 @ X0 ) )
= $false )
| ( $false = $true )
| ( ( sK0 @ X0 )
= $false )
| ( $true
= ( sK5 @ ( sK6 @ X0 ) @ ( sK9 @ X0 ) ) ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_8
| ~ spl16_13 ),
inference(superposition,[],[f958,f178]) ).
thf(f963,plain,
( ! [X0: a > a > $o] :
( ( ( sK0 @ X0 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $false = $true )
| ( ( sK1 @ ( sK13 @ X0 ) )
= $false )
| ( $true
= ( sK5 @ ( sK6 @ X0 ) @ ( sK9 @ X0 ) ) ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_8
| ~ spl16_13 ),
inference(duplicate_literal_removal,[],[f961]) ).
thf(f964,plain,
( ! [X0: a > a > $o] :
( ( $true
= ( sK5 @ ( sK6 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( ( sK1 @ ( sK13 @ X0 ) )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_8
| ~ spl16_13 ),
inference(trivial_inequality_removal,[],[f963]) ).
thf(f970,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $false = $true )
| ( $false
= ( sK1 @ ( sK13 @ sK5 ) ) )
| ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_8
| ~ spl16_13
| ~ spl16_14 ),
inference(superposition,[],[f202,f964]) ).
thf(f979,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( sK1 @ ( sK13 @ sK5 ) ) )
| ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ( $false = $true )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_8
| ~ spl16_13
| ~ spl16_14 ),
inference(duplicate_literal_removal,[],[f970]) ).
thf(f980,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ( $false
= ( sK1 @ ( sK13 @ sK5 ) ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_8
| ~ spl16_13
| ~ spl16_14 ),
inference(trivial_inequality_removal,[],[f979]) ).
thf(f984,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_8
| ~ spl16_13
| ~ spl16_14
| spl16_27 ),
inference(forward_subsumption_resolution,[],[f980,f834]) ).
thf(f991,plain,
( ( $false = $true )
| ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_8
| ~ spl16_13
| ~ spl16_14
| spl16_27 ),
inference(forward_demodulation,[],[f984,f145]) ).
thf(f992,plain,
( ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_8
| ~ spl16_13
| ~ spl16_14
| spl16_27 ),
inference(trivial_inequality_removal,[],[f991]) ).
thf(f1000,plain,
( ( $false = $true )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_8
| ~ spl16_13
| ~ spl16_14
| spl16_27 ),
inference(forward_demodulation,[],[f992,f169]) ).
thf(f1001,plain,
( $false
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_8
| ~ spl16_13
| ~ spl16_14
| spl16_27 ),
inference(trivial_inequality_removal,[],[f1000]) ).
thf(f1002,plain,
( ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_8
| ~ spl16_13
| ~ spl16_14
| spl16_27 ),
inference(avatar_contradiction_clause,[],[f1001]) ).
thf(f1006,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $false = $true )
| ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_7
| ~ spl16_11
| ~ spl16_16 ),
inference(superposition,[],[f704,f190]) ).
thf(f1010,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_7
| ~ spl16_11
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f1006]) ).
thf(f1013,plain,
( ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ( $false = $true )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_7
| ~ spl16_11
| ~ spl16_16 ),
inference(forward_demodulation,[],[f1010,f145]) ).
thf(f1014,plain,
( ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_7
| ~ spl16_11
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f1013]) ).
thf(f1015,plain,
( ( $false = $true )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_7
| ~ spl16_11
| ~ spl16_16 ),
inference(forward_demodulation,[],[f1014,f169]) ).
thf(f1016,plain,
( $false
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_7
| ~ spl16_11
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f1015]) ).
thf(f1017,plain,
( ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_7
| ~ spl16_11
| ~ spl16_16 ),
inference(avatar_contradiction_clause,[],[f1016]) ).
thf(f1095,plain,
( ! [X2: a > a > $o,X3: a] :
( ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK12 @ X2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X3 )
= ( sK11 @ X2 @ X3 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) ) )
| ~ spl16_10 ),
inference(argument_congruence,[],[f186]) ).
thf(f1096,plain,
( ! [X2: a > a > $o,X3: a] :
( ( ( sK11 @ X2 @ X3 )
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK12 @ X2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ X3 @ Y0 ) ) ) ) )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) ) )
| ~ spl16_10 ),
inference(beta-eta_normalization,[],[f1095]) ).
thf(f1109,plain,
( ! [X2: a > a > $o,X3: a,X4: a] :
( ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK12 @ X2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ X3 @ Y0 ) ) )
@ X4 )
= ( sK11 @ X2 @ X3 @ X4 ) ) )
| ~ spl16_10 ),
inference(argument_congruence,[],[f1096]) ).
thf(f1110,plain,
( ! [X2: a > a > $o,X3: a,X4: a] :
( ( $true
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK12 @ X2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ X3 @ Y0 ) ) )
@ X4 ) )
| ( $false
= ( sK11 @ X2 @ X3 @ X4 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) ) )
| ~ spl16_10 ),
inference(iff_proxy_clausification,[],[f1109]) ).
thf(f1124,plain,
( ! [X2: a > a > $o,X3: a,X4: a] :
( ( $false
= ( sK11 @ X2 @ X3 @ X4 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK12 @ X2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ X3 @ X4 ) ) )
= $true )
| ( $true
= ( X2 @ sK2 @ sK3 ) ) )
| ~ spl16_10 ),
inference(beta-eta_normalization,[],[f1110]) ).
thf(f1125,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK11 @ X2 @ X3 @ X4 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( ( ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK12 @ X2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ X3 @ X4 ) )
@ X5 )
= $true ) )
| ~ spl16_10 ),
inference(pi_proxy_clausification,[],[f1124]) ).
thf(f1126,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( $false
= ( sK11 @ X2 @ X3 @ X4 ) )
| ( ( ( ( sK0 @ X5 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK12 @ X2 @ Y1 @ Y0 )
=> ( X5 @ Y1 @ Y0 ) ) ) ) )
=> ( X5 @ X3 @ X4 ) )
= $true ) )
| ~ spl16_10 ),
inference(beta-eta_normalization,[],[f1125]) ).
thf(f1127,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( ( ( sK0 @ X5 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK12 @ X2 @ Y1 @ Y0 )
=> ( X5 @ Y1 @ Y0 ) ) ) ) )
= $false )
| ( $false
= ( sK11 @ X2 @ X3 @ X4 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( X5 @ X3 @ X4 )
= $true ) )
| ~ spl16_10 ),
inference(imp_proxy_clausification,[],[f1126]) ).
thf(f1128,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( ( X5 @ X3 @ X4 )
= $true )
| ( ( sK0 @ X5 )
= $false )
| ( $false
= ( sK11 @ X2 @ X3 @ X4 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK12 @ X2 @ Y1 @ Y0 )
=> ( X5 @ Y1 @ Y0 ) ) ) ) ) )
| ~ spl16_10 ),
inference(and_proxy_clausification,[],[f1127]) ).
thf(f1129,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( X5 @ X3 @ X4 )
= $true )
| ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK12 @ X2 @ Y1 @ Y0 )
=> ( X5 @ Y1 @ Y0 ) ) )
@ ( sK35 @ X5 @ X2 ) )
= $false )
| ( ( sK0 @ X5 )
= $false )
| ( $false
= ( sK0 @ X2 ) )
| ( $false
= ( sK11 @ X2 @ X3 @ X4 ) ) )
| ~ spl16_10 ),
inference(sigma_proxy_clausification,[],[f1128]) ).
thf(f1130,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK12 @ X2 @ Y0 @ ( sK35 @ X5 @ X2 ) )
=> ( X5 @ Y0 @ ( sK35 @ X5 @ X2 ) ) ) )
= $false )
| ( $false
= ( sK11 @ X2 @ X3 @ X4 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( ( X5 @ X3 @ X4 )
= $true )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( sK0 @ X5 )
= $false ) )
| ~ spl16_10 ),
inference(beta-eta_normalization,[],[f1129]) ).
thf(f1131,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( $false
= ( sK0 @ X2 ) )
| ( $false
= ( sK11 @ X2 @ X3 @ X4 ) )
| ( ( X5 @ X3 @ X4 )
= $true )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( ^ [Y0: a] :
( ( sK12 @ X2 @ Y0 @ ( sK35 @ X5 @ X2 ) )
=> ( X5 @ Y0 @ ( sK35 @ X5 @ X2 ) ) )
@ ( sK36 @ X5 @ X2 ) ) )
| ( ( sK0 @ X5 )
= $false ) )
| ~ spl16_10 ),
inference(sigma_proxy_clausification,[],[f1130]) ).
thf(f1132,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( ( X5 @ X3 @ X4 )
= $true )
| ( ( ( sK12 @ X2 @ ( sK36 @ X5 @ X2 ) @ ( sK35 @ X5 @ X2 ) )
=> ( X5 @ ( sK36 @ X5 @ X2 ) @ ( sK35 @ X5 @ X2 ) ) )
= $false )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( sK0 @ X5 )
= $false )
| ( $false
= ( sK11 @ X2 @ X3 @ X4 ) )
| ( $false
= ( sK0 @ X2 ) ) )
| ~ spl16_10 ),
inference(beta-eta_normalization,[],[f1131]) ).
thf(f1133,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( ( X5 @ ( sK36 @ X5 @ X2 ) @ ( sK35 @ X5 @ X2 ) )
= $false )
| ( ( sK0 @ X5 )
= $false )
| ( $false
= ( sK11 @ X2 @ X3 @ X4 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( ( X5 @ X3 @ X4 )
= $true ) )
| ~ spl16_10 ),
inference(imp_proxy_clausification,[],[f1132]) ).
thf(f1134,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( ( sK12 @ X2 @ ( sK36 @ X5 @ X2 ) @ ( sK35 @ X5 @ X2 ) )
= $true )
| ( $false
= ( sK11 @ X2 @ X3 @ X4 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( ( X5 @ X3 @ X4 )
= $true )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( sK0 @ X5 )
= $false ) )
| ~ spl16_10 ),
inference(imp_proxy_clausification,[],[f1132]) ).
thf(f1215,plain,
( ! [X2: a,X3: a > a > $o,X0: a > a > $o,X1: a] :
( ( $false = $true )
| ( $false
= ( X3 @ ( sK36 @ sK4 @ X0 ) @ ( sK35 @ sK4 @ X0 ) ) )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( $false
= ( sK1 @ X3 ) )
| ( ( sK0 @ sK4 )
= $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl16_3
| ~ spl16_10 ),
inference(superposition,[],[f1133,f153]) ).
thf(f1220,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( ( sK0 @ X0 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK0 @ sK5 )
= $false )
| ( ( sK1 @ X1 )
= $false )
| ( $false = $true )
| ( $false
= ( X1 @ ( sK36 @ sK5 @ X0 ) @ ( sK35 @ sK5 @ X0 ) ) )
| ( ( sK5 @ X2 @ X3 )
= $true )
| ( ( sK11 @ X0 @ X2 @ X3 )
= $false ) )
| ~ spl16_5
| ~ spl16_10 ),
inference(superposition,[],[f613,f1133]) ).
thf(f1223,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( $false
= ( X1 @ ( sK36 @ sK5 @ X0 ) @ ( sK35 @ sK5 @ X0 ) ) )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK11 @ X0 @ X2 @ X3 )
= $false )
| ( ( sK5 @ X2 @ X3 )
= $true )
| ( ( sK0 @ sK5 )
= $false )
| ( ( sK1 @ X1 )
= $false ) )
| ~ spl16_5
| ~ spl16_10 ),
inference(trivial_inequality_removal,[],[f1220]) ).
thf(f1231,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK1 @ X1 )
= $false )
| ( ( sK11 @ X0 @ X2 @ X3 )
= $false )
| ( ( sK5 @ X2 @ X3 )
= $true )
| ( ( sK0 @ X0 )
= $false )
| ( $false = $true )
| ( $false
= ( X1 @ ( sK36 @ sK5 @ X0 ) @ ( sK35 @ sK5 @ X0 ) ) ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_10 ),
inference(forward_demodulation,[],[f1223,f145]) ).
thf(f1232,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( $false
= ( X1 @ ( sK36 @ sK5 @ X0 ) @ ( sK35 @ sK5 @ X0 ) ) )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK5 @ X2 @ X3 )
= $true )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK11 @ X0 @ X2 @ X3 )
= $false )
| ( ( sK1 @ X1 )
= $false ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_10 ),
inference(trivial_inequality_removal,[],[f1231]) ).
thf(f1259,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK1 @ ( sK12 @ X0 ) )
= $false )
| ( $false
= ( sK11 @ X0 @ X3 @ X4 ) )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( sK0 @ sK5 )
= $false )
| ( $false = $true )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK5 @ X3 @ X4 )
= $true )
| ( ( sK0 @ X0 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_10 ),
inference(superposition,[],[f1232,f1134]) ).
thf(f1270,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( sK5 @ X3 @ X4 )
= $true )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( $false = $true )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK1 @ ( sK12 @ X0 ) )
= $false )
| ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( sK11 @ X0 @ X3 @ X4 ) )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_10 ),
inference(duplicate_literal_removal,[],[f1259]) ).
thf(f1271,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( sK5 @ X3 @ X4 )
= $true )
| ( ( sK0 @ sK5 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $false
= ( sK11 @ X0 @ X3 @ X4 ) )
| ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( ( sK1 @ ( sK12 @ X0 ) )
= $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_10 ),
inference(trivial_inequality_removal,[],[f1270]) ).
thf(f1274,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( ( sK0 @ X0 )
= $false )
| ( $false
= ( sK11 @ X0 @ X3 @ X4 ) )
| ( ( sK5 @ X3 @ X4 )
= $true )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( sK1 @ ( sK12 @ X0 ) )
= $false )
| ( $false = $true ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_10 ),
inference(forward_demodulation,[],[f1271,f145]) ).
thf(f1275,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $false
= ( sK11 @ X0 @ X3 @ X4 ) )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( ( sK5 @ X3 @ X4 )
= $true )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK1 @ ( sK12 @ X0 ) )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_10 ),
inference(trivial_inequality_removal,[],[f1274]) ).
thf(f1280,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( $false != $false )
| ( ( sK1 @ ( sK12 @ X0 ) )
= $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_10 ),
inference(equality_factoring,[],[f1275]) ).
thf(f1283,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( sK0 @ X0 )
= $false )
| ( $false != $false )
| ( ( sK1 @ ( sK12 @ X0 ) )
= $false )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $false
= ( sK11 @ X0 @ X1 @ X2 ) ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_10 ),
inference(duplicate_literal_removal,[],[f1280]) ).
thf(f1284,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK1 @ ( sK12 @ X0 ) )
= $false )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_10 ),
inference(trivial_inequality_removal,[],[f1283]) ).
thf(f1287,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $false = $true )
| ( $true
= ( sK5 @ ( sK6 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK1 @ ( sK12 @ X0 ) )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_8
| ~ spl16_10 ),
inference(superposition,[],[f1284,f178]) ).
thf(f1289,plain,
( ! [X0: a > a > $o] :
( ( $false = $true )
| ( ( sK1 @ ( sK12 @ X0 ) )
= $false )
| ( $true
= ( sK5 @ ( sK6 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( ( sK0 @ X0 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_8
| ~ spl16_10 ),
inference(duplicate_literal_removal,[],[f1287]) ).
thf(f1290,plain,
( ! [X0: a > a > $o] :
( ( $true
= ( sK5 @ ( sK6 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( ( sK1 @ ( sK12 @ X0 ) )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_8
| ~ spl16_10 ),
inference(trivial_inequality_removal,[],[f1289]) ).
thf(f1293,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ( $false = $true )
| ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ( ( sK1 @ ( sK12 @ sK5 ) )
= $false )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_8
| ~ spl16_10
| ~ spl16_14 ),
inference(superposition,[],[f1290,f202]) ).
thf(f1301,plain,
( ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ( $false = $true )
| ( ( sK1 @ ( sK12 @ sK5 ) )
= $false )
| ( ( sK0 @ sK5 )
= $false )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_8
| ~ spl16_10
| ~ spl16_14 ),
inference(duplicate_literal_removal,[],[f1293]) ).
thf(f1302,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( ( sK1 @ ( sK12 @ sK5 ) )
= $false )
| ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_8
| ~ spl16_10
| ~ spl16_14 ),
inference(trivial_inequality_removal,[],[f1301]) ).
thf(f1307,plain,
( ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ( ( sK1 @ ( sK12 @ sK5 ) )
= $false )
| ( $false = $true )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_8
| ~ spl16_10
| ~ spl16_14 ),
inference(forward_demodulation,[],[f1302,f145]) ).
thf(f1308,plain,
( ( ( sK1 @ ( sK12 @ sK5 ) )
= $false )
| ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_8
| ~ spl16_10
| ~ spl16_14 ),
inference(trivial_inequality_removal,[],[f1307]) ).
thf(f1311,plain,
( ( ( sK1 @ ( sK12 @ sK5 ) )
= $false )
| ( $false = $true )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_8
| ~ spl16_10
| ~ spl16_14 ),
inference(forward_demodulation,[],[f1308,f169]) ).
thf(f1312,plain,
( ( ( sK1 @ ( sK12 @ sK5 ) )
= $false )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_8
| ~ spl16_10
| ~ spl16_14 ),
inference(trivial_inequality_removal,[],[f1311]) ).
thf(f1366,plain,
( ( $false = $true )
| ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ( ( sK0 @ sK5 )
= $false )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_8
| ~ spl16_9
| ~ spl16_10
| ~ spl16_14 ),
inference(superposition,[],[f182,f1312]) ).
thf(f1368,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_8
| ~ spl16_9
| ~ spl16_10
| ~ spl16_14 ),
inference(trivial_inequality_removal,[],[f1366]) ).
thf(f1371,plain,
( ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ( $false = $true )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_8
| ~ spl16_9
| ~ spl16_10
| ~ spl16_14 ),
inference(forward_demodulation,[],[f1368,f145]) ).
thf(f1372,plain,
( ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_8
| ~ spl16_9
| ~ spl16_10
| ~ spl16_14 ),
inference(trivial_inequality_removal,[],[f1371]) ).
thf(f1376,plain,
( ( $false = $true )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_8
| ~ spl16_9
| ~ spl16_10
| ~ spl16_14 ),
inference(forward_demodulation,[],[f1372,f169]) ).
thf(f1377,plain,
( $false
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_8
| ~ spl16_9
| ~ spl16_10
| ~ spl16_14 ),
inference(trivial_inequality_removal,[],[f1376]) ).
thf(f1378,plain,
( ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_8
| ~ spl16_9
| ~ spl16_10
| ~ spl16_14 ),
inference(avatar_contradiction_clause,[],[f1377]) ).
thf(f1443,plain,
( ! [X2: a > a > $o,X3: a] :
( ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > a > $o )
@ ^ [Y2: a > a > $o] :
( ( ( sK0 @ Y2 )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( sK15 @ X2 @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ X3 )
= ( sK14 @ X2 @ X3 ) ) )
| ~ spl16_18 ),
inference(argument_congruence,[],[f218]) ).
thf(f1444,plain,
( ! [X2: a > a > $o,X3: a] :
( ( ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK15 @ X2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ X3 @ Y0 ) ) ) )
= ( sK14 @ X2 @ X3 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) ) )
| ~ spl16_18 ),
inference(beta-eta_normalization,[],[f1443]) ).
thf(f1463,plain,
( ! [X2: a > a > $o,X3: a,X4: a] :
( ( ( sK14 @ X2 @ X3 @ X4 )
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK15 @ X2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ X3 @ Y0 ) ) )
@ X4 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) ) )
| ~ spl16_18 ),
inference(argument_congruence,[],[f1444]) ).
thf(f1465,plain,
( ! [X2: a > a > $o,X3: a,X4: a] :
( ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $true
= ( ^ [Y0: a] :
( !! @ ( a > a > $o )
@ ^ [Y1: a > a > $o] :
( ( ( sK0 @ Y1 )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( sK15 @ X2 @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) ) ) )
=> ( Y1 @ X3 @ Y0 ) ) )
@ X4 ) )
| ( ( sK14 @ X2 @ X3 @ X4 )
= $false ) )
| ~ spl16_18 ),
inference(iff_proxy_clausification,[],[f1463]) ).
thf(f1466,plain,
( ! [X2: a > a > $o,X3: a,X4: a] :
( ( $true
= ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK15 @ X2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ X3 @ X4 ) ) ) )
| ( $false
= ( sK0 @ X2 ) )
| ( ( sK14 @ X2 @ X3 @ X4 )
= $false )
| ( $true
= ( X2 @ sK2 @ sK3 ) ) )
| ~ spl16_18 ),
inference(beta-eta_normalization,[],[f1465]) ).
thf(f1467,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( ( sK14 @ X2 @ X3 @ X4 )
= $false )
| ( ( ^ [Y0: a > a > $o] :
( ( ( sK0 @ Y0 )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( sK15 @ X2 @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
=> ( Y0 @ X3 @ X4 ) )
@ X5 )
= $true )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) ) )
| ~ spl16_18 ),
inference(pi_proxy_clausification,[],[f1466]) ).
thf(f1468,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( ( ( ( sK0 @ X5 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK15 @ X2 @ Y1 @ Y0 )
=> ( X5 @ Y1 @ Y0 ) ) ) ) )
=> ( X5 @ X3 @ X4 ) )
= $true )
| ( ( sK14 @ X2 @ X3 @ X4 )
= $false ) )
| ~ spl16_18 ),
inference(beta-eta_normalization,[],[f1467]) ).
thf(f1469,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( $false
= ( ( sK0 @ X5 )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK15 @ X2 @ Y1 @ Y0 )
=> ( X5 @ Y1 @ Y0 ) ) ) ) ) )
| ( ( sK14 @ X2 @ X3 @ X4 )
= $false )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( X5 @ X3 @ X4 )
= $true ) )
| ~ spl16_18 ),
inference(imp_proxy_clausification,[],[f1468]) ).
thf(f1470,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( $false
= ( sK0 @ X2 ) )
| ( ( X5 @ X3 @ X4 )
= $true )
| ( ( sK0 @ X5 )
= $false )
| ( $false
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK15 @ X2 @ Y1 @ Y0 )
=> ( X5 @ Y1 @ Y0 ) ) ) ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( sK14 @ X2 @ X3 @ X4 )
= $false ) )
| ~ spl16_18 ),
inference(and_proxy_clausification,[],[f1469]) ).
thf(f1471,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( $false
= ( sK0 @ X2 ) )
| ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK15 @ X2 @ Y1 @ Y0 )
=> ( X5 @ Y1 @ Y0 ) ) )
@ ( sK42 @ X5 @ X2 ) )
= $false )
| ( ( X5 @ X3 @ X4 )
= $true )
| ( ( sK0 @ X5 )
= $false )
| ( ( sK14 @ X2 @ X3 @ X4 )
= $false ) )
| ~ spl16_18 ),
inference(sigma_proxy_clausification,[],[f1470]) ).
thf(f1472,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( ( sK14 @ X2 @ X3 @ X4 )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( ( sK15 @ X2 @ Y0 @ ( sK42 @ X5 @ X2 ) )
=> ( X5 @ Y0 @ ( sK42 @ X5 @ X2 ) ) ) )
= $false )
| ( $false
= ( sK0 @ X2 ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( X5 @ X3 @ X4 )
= $true )
| ( ( sK0 @ X5 )
= $false ) )
| ~ spl16_18 ),
inference(beta-eta_normalization,[],[f1471]) ).
thf(f1473,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( ( X5 @ X3 @ X4 )
= $true )
| ( $false
= ( sK0 @ X2 ) )
| ( ( sK0 @ X5 )
= $false )
| ( ( sK14 @ X2 @ X3 @ X4 )
= $false )
| ( $false
= ( ^ [Y0: a] :
( ( sK15 @ X2 @ Y0 @ ( sK42 @ X5 @ X2 ) )
=> ( X5 @ Y0 @ ( sK42 @ X5 @ X2 ) ) )
@ ( sK43 @ X5 @ X2 ) ) )
| ( $true
= ( X2 @ sK2 @ sK3 ) ) )
| ~ spl16_18 ),
inference(sigma_proxy_clausification,[],[f1472]) ).
thf(f1474,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( ( ( sK15 @ X2 @ ( sK43 @ X5 @ X2 ) @ ( sK42 @ X5 @ X2 ) )
=> ( X5 @ ( sK43 @ X5 @ X2 ) @ ( sK42 @ X5 @ X2 ) ) )
= $false )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( sK0 @ X5 )
= $false )
| ( ( sK14 @ X2 @ X3 @ X4 )
= $false )
| ( $false
= ( sK0 @ X2 ) )
| ( ( X5 @ X3 @ X4 )
= $true ) )
| ~ spl16_18 ),
inference(beta-eta_normalization,[],[f1473]) ).
thf(f1475,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( $false
= ( X5 @ ( sK43 @ X5 @ X2 ) @ ( sK42 @ X5 @ X2 ) ) )
| ( ( sK14 @ X2 @ X3 @ X4 )
= $false )
| ( ( sK0 @ X5 )
= $false )
| ( $true
= ( X2 @ sK2 @ sK3 ) )
| ( ( X5 @ X3 @ X4 )
= $true )
| ( $false
= ( sK0 @ X2 ) ) )
| ~ spl16_18 ),
inference(imp_proxy_clausification,[],[f1474]) ).
thf(f1476,plain,
( ! [X2: a > a > $o,X3: a,X4: a,X5: a > a > $o] :
( ( $true
= ( sK15 @ X2 @ ( sK43 @ X5 @ X2 ) @ ( sK42 @ X5 @ X2 ) ) )
| ( ( sK0 @ X5 )
= $false )
| ( ( sK14 @ X2 @ X3 @ X4 )
= $false )
| ( $false
= ( sK0 @ X2 ) )
| ( ( X5 @ X3 @ X4 )
= $true )
| ( $true
= ( X2 @ sK2 @ sK3 ) ) )
| ~ spl16_18 ),
inference(imp_proxy_clausification,[],[f1474]) ).
thf(f1494,plain,
( ! [X2: a,X3: a > a > $o,X0: a > a > $o,X1: a] :
( ( ( sK0 @ X0 )
= $false )
| ( ( X3 @ ( sK43 @ sK4 @ X0 ) @ ( sK42 @ sK4 @ X0 ) )
= $false )
| ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( $false
= ( sK1 @ X3 ) )
| ( $false = $true )
| ( ( sK0 @ sK4 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true ) )
| ~ spl16_3
| ~ spl16_18 ),
inference(superposition,[],[f1475,f153]) ).
thf(f1495,plain,
( ! [X2: a,X3: a > a > $o,X0: a > a > $o,X1: a] :
( ( ( sK0 @ X0 )
= $false )
| ( ( X3 @ ( sK43 @ sK5 @ X0 ) @ ( sK42 @ sK5 @ X0 ) )
= $false )
| ( ( sK0 @ sK5 )
= $false )
| ( $false = $true )
| ( $false
= ( sK1 @ X3 ) )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK14 @ X0 @ X1 @ X2 )
= $false ) )
| ~ spl16_5
| ~ spl16_18 ),
inference(superposition,[],[f1475,f613]) ).
thf(f1502,plain,
( ! [X2: a,X3: a > a > $o,X0: a > a > $o,X1: a] :
( ( ( sK0 @ X0 )
= $false )
| ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( sK1 @ X3 ) )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( X3 @ ( sK43 @ sK5 @ X0 ) @ ( sK42 @ sK5 @ X0 ) )
= $false ) )
| ~ spl16_5
| ~ spl16_18 ),
inference(trivial_inequality_removal,[],[f1495]) ).
thf(f1506,plain,
( ! [X2: a,X3: a > a > $o,X0: a > a > $o,X1: a] :
( ( $false
= ( sK1 @ X3 ) )
| ( ( X3 @ ( sK43 @ sK4 @ X0 ) @ ( sK42 @ sK4 @ X0 ) )
= $false )
| ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK0 @ X0 )
= $false )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( ( sK0 @ sK4 )
= $false ) )
| ~ spl16_3
| ~ spl16_18 ),
inference(trivial_inequality_removal,[],[f1494]) ).
thf(f1507,plain,
( ! [X2: a,X3: a > a > $o,X0: a > a > $o,X1: a] :
( ( $false
= ( sK1 @ X3 ) )
| ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( $false = $true )
| ( ( X3 @ ( sK43 @ sK5 @ X0 ) @ ( sK42 @ sK5 @ X0 ) )
= $false ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_18 ),
inference(forward_demodulation,[],[f1502,f145]) ).
thf(f1508,plain,
( ! [X2: a,X3: a > a > $o,X0: a > a > $o,X1: a] :
( ( ( X3 @ ( sK43 @ sK5 @ X0 ) @ ( sK42 @ sK5 @ X0 ) )
= $false )
| ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( $false
= ( sK1 @ X3 ) )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_18 ),
inference(trivial_inequality_removal,[],[f1507]) ).
thf(f1597,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( sK5 @ X3 @ X4 )
= $true )
| ( ( sK0 @ X0 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK14 @ X0 @ X3 @ X4 )
= $false )
| ( ( sK0 @ sK5 )
= $false )
| ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( $false
= ( sK1 @ ( sK15 @ X0 ) ) )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $false = $true ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_18 ),
inference(superposition,[],[f1508,f1476]) ).
thf(f1608,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $false = $true )
| ( ( sK5 @ X3 @ X4 )
= $true )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( sK14 @ X0 @ X3 @ X4 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK0 @ sK5 )
= $false )
| ( $false
= ( sK1 @ ( sK15 @ X0 ) ) )
| ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_18 ),
inference(duplicate_literal_removal,[],[f1597]) ).
thf(f1609,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK14 @ X0 @ X3 @ X4 )
= $false )
| ( $false
= ( sK1 @ ( sK15 @ X0 ) ) )
| ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( ( sK5 @ X3 @ X4 )
= $true )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK0 @ sK5 )
= $false ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_18 ),
inference(trivial_inequality_removal,[],[f1608]) ).
thf(f1612,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $false = $true )
| ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK5 @ X3 @ X4 )
= $true )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( $false
= ( sK1 @ ( sK15 @ X0 ) ) )
| ( ( sK14 @ X0 @ X3 @ X4 )
= $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_18 ),
inference(forward_demodulation,[],[f1609,f145]) ).
thf(f1613,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( sK14 @ X0 @ X3 @ X4 )
= $false )
| ( $false
= ( sK1 @ ( sK15 @ X0 ) ) )
| ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK5 @ X3 @ X4 )
= $true )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( X0 @ sK2 @ sK3 )
= $true ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_18 ),
inference(trivial_inequality_removal,[],[f1612]) ).
thf(f1666,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( sK0 @ X0 )
= $false )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $false
= ( sK1 @ ( sK15 @ X0 ) ) )
| ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( $false != $false )
| ( ( sK5 @ X1 @ X2 )
= $true ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_18 ),
inference(equality_factoring,[],[f1613]) ).
thf(f1677,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( $false != $false )
| ( $false
= ( sK1 @ ( sK15 @ X0 ) ) ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_18 ),
inference(duplicate_literal_removal,[],[f1666]) ).
thf(f1678,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( $false
= ( sK1 @ ( sK15 @ X0 ) ) )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK5 @ X1 @ X2 )
= $true )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_18 ),
inference(trivial_inequality_removal,[],[f1677]) ).
thf(f1679,plain,
( ! [X0: a > a > $o] :
( ( ( sK0 @ X0 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $true
= ( sK5 @ ( sK6 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $false
= ( sK1 @ ( sK15 @ X0 ) ) )
| ( $false = $true )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_15
| ~ spl16_18 ),
inference(superposition,[],[f1678,f207]) ).
thf(f1690,plain,
( ! [X0: a > a > $o] :
( ( $true
= ( sK5 @ ( sK6 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $false = $true )
| ( $false
= ( sK1 @ ( sK15 @ X0 ) ) )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_15
| ~ spl16_18 ),
inference(duplicate_literal_removal,[],[f1679]) ).
thf(f1691,plain,
( ! [X0: a > a > $o] :
( ( $true
= ( sK5 @ ( sK6 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( ( sK0 @ X0 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $false
= ( sK1 @ ( sK15 @ X0 ) ) ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_15
| ~ spl16_18 ),
inference(trivial_inequality_removal,[],[f1690]) ).
thf(f1697,plain,
( ( $false
= ( sK1 @ ( sK15 @ sK5 ) ) )
| ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ( $false = $true )
| ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ( ( sK0 @ sK5 )
= $false )
| ( ( sK0 @ sK5 )
= $false )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_14
| ~ spl16_15
| ~ spl16_18 ),
inference(superposition,[],[f1691,f202]) ).
thf(f1705,plain,
( ( $false
= ( sK1 @ ( sK15 @ sK5 ) ) )
| ( $false = $true )
| ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ( ( sK0 @ sK5 )
= $false )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_14
| ~ spl16_15
| ~ spl16_18 ),
inference(duplicate_literal_removal,[],[f1697]) ).
thf(f1706,plain,
( ( $false
= ( sK1 @ ( sK15 @ sK5 ) ) )
| ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_14
| ~ spl16_15
| ~ spl16_18 ),
inference(trivial_inequality_removal,[],[f1705]) ).
thf(f1711,plain,
( ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ( $false = $true )
| ( $false
= ( sK1 @ ( sK15 @ sK5 ) ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_14
| ~ spl16_15
| ~ spl16_18 ),
inference(forward_demodulation,[],[f1706,f145]) ).
thf(f1712,plain,
( ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ( $false
= ( sK1 @ ( sK15 @ sK5 ) ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_14
| ~ spl16_15
| ~ spl16_18 ),
inference(trivial_inequality_removal,[],[f1711]) ).
thf(f1715,plain,
( ( $false = $true )
| ( $false
= ( sK1 @ ( sK15 @ sK5 ) ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_14
| ~ spl16_15
| ~ spl16_18 ),
inference(forward_demodulation,[],[f1712,f169]) ).
thf(f1716,plain,
( ( $false
= ( sK1 @ ( sK15 @ sK5 ) ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_14
| ~ spl16_15
| ~ spl16_18 ),
inference(trivial_inequality_removal,[],[f1715]) ).
thf(f1719,plain,
( ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ( $false = $true )
| ( ( sK0 @ sK5 )
= $false )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_14
| ~ spl16_15
| ~ spl16_17
| ~ spl16_18 ),
inference(superposition,[],[f1716,f214]) ).
thf(f1721,plain,
( ( ( sK0 @ sK5 )
= $false )
| ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_14
| ~ spl16_15
| ~ spl16_17
| ~ spl16_18 ),
inference(trivial_inequality_removal,[],[f1719]) ).
thf(f1723,plain,
( ( $false = $true )
| ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_14
| ~ spl16_15
| ~ spl16_17
| ~ spl16_18 ),
inference(forward_demodulation,[],[f1721,f145]) ).
thf(f1724,plain,
( ( $true
= ( sK5 @ sK2 @ sK3 ) )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_14
| ~ spl16_15
| ~ spl16_17
| ~ spl16_18 ),
inference(trivial_inequality_removal,[],[f1723]) ).
thf(f1727,plain,
( ( $false = $true )
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_14
| ~ spl16_15
| ~ spl16_17
| ~ spl16_18 ),
inference(forward_demodulation,[],[f1724,f169]) ).
thf(f1728,plain,
( $false
| ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_14
| ~ spl16_15
| ~ spl16_17
| ~ spl16_18 ),
inference(trivial_inequality_removal,[],[f1727]) ).
thf(f1729,plain,
( ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_14
| ~ spl16_15
| ~ spl16_17
| ~ spl16_18 ),
inference(avatar_contradiction_clause,[],[f1728]) ).
thf(f1755,plain,
( ( $false = $true )
| ~ spl16_2
| ~ spl16_21 ),
inference(forward_demodulation,[],[f149,f507]) ).
thf(f1756,plain,
( $false
| ~ spl16_2
| ~ spl16_21 ),
inference(trivial_inequality_removal,[],[f1755]) ).
thf(f1757,plain,
( ~ spl16_2
| ~ spl16_21 ),
inference(avatar_contradiction_clause,[],[f1756]) ).
thf(f1772,definition,
( spl16_38
<=> ! [X0: a > a > $o,X3: a,X2: a,X1: a > a > $o] :
( ( $true
= ( sK4 @ X2 @ X3 ) )
| ( ( sK1 @ X1 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK14 @ X0 @ X2 @ X3 )
= $false )
| ( $false
= ( X1 @ ( sK43 @ sK4 @ X0 ) @ ( sK42 @ sK4 @ X0 ) ) )
| ( ( sK0 @ X0 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl16_38])],[avatar_definition]) ).
thf(f1773,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a > a > $o] :
( ( $false
= ( X1 @ ( sK43 @ sK4 @ X0 ) @ ( sK42 @ sK4 @ X0 ) ) )
| ( ( sK1 @ X1 )
= $false )
| ( $true
= ( sK4 @ X2 @ X3 ) )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK14 @ X0 @ X2 @ X3 )
= $false ) )
| ~ spl16_38 ),
inference(avatar_component_clause,[],[f1772]) ).
thf(f1776,plain,
( spl16_38
| spl16_21
| ~ spl16_3
| ~ spl16_18 ),
inference(avatar_split_clause,[],[f1506,f217,f152,f505,f1772]) ).
thf(f1856,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $false
= ( sK1 @ ( sK15 @ X0 ) ) )
| ( ( sK14 @ X0 @ X3 @ X4 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( $true
= ( sK4 @ X3 @ X4 ) )
| ( $false = $true )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( ( sK0 @ X0 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK0 @ sK4 )
= $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl16_18
| ~ spl16_38 ),
inference(superposition,[],[f1476,f1773]) ).
thf(f1863,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( $false
= ( sK1 @ ( sK15 @ X0 ) ) )
| ( $true
= ( sK4 @ X3 @ X4 ) )
| ( ( sK14 @ X0 @ X3 @ X4 )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( $false = $true )
| ( ( sK0 @ sK4 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $true
= ( sK4 @ X1 @ X2 ) ) )
| ~ spl16_18
| ~ spl16_38 ),
inference(duplicate_literal_removal,[],[f1856]) ).
thf(f1864,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $false
= ( sK1 @ ( sK15 @ X0 ) ) )
| ( ( sK0 @ X0 )
= $false )
| ( $true
= ( sK4 @ X3 @ X4 ) )
| ( ( sK14 @ X0 @ X3 @ X4 )
= $false )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK0 @ sK4 )
= $false ) )
| ~ spl16_18
| ~ spl16_38 ),
inference(trivial_inequality_removal,[],[f1863]) ).
thf(f1876,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $true
= ( sK4 @ X3 @ X4 ) )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( ( sK14 @ X0 @ X3 @ X4 )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( $false
= ( sK1 @ ( sK15 @ X0 ) ) )
| ( $false = $true )
| ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true ) )
| ~ spl16_2
| ~ spl16_18
| ~ spl16_38 ),
inference(forward_demodulation,[],[f1864,f149]) ).
thf(f1877,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( sK14 @ X0 @ X3 @ X4 )
= $false )
| ( $true
= ( sK4 @ X3 @ X4 ) )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( $false
= ( sK1 @ ( sK15 @ X0 ) ) )
| ( ( X0 @ sK2 @ sK3 )
= $true ) )
| ~ spl16_2
| ~ spl16_18
| ~ spl16_38 ),
inference(trivial_inequality_removal,[],[f1876]) ).
thf(f1888,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( $false != $false )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( $false
= ( sK1 @ ( sK15 @ X0 ) ) )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl16_2
| ~ spl16_18
| ~ spl16_38 ),
inference(equality_factoring,[],[f1877]) ).
thf(f1894,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( $false != $false )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( $false
= ( sK1 @ ( sK15 @ X0 ) ) )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl16_2
| ~ spl16_18
| ~ spl16_38 ),
inference(duplicate_literal_removal,[],[f1888]) ).
thf(f1895,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( sK14 @ X0 @ X1 @ X2 )
= $false )
| ( $false
= ( sK1 @ ( sK15 @ X0 ) ) )
| ( ( sK0 @ X0 )
= $false )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( ( X0 @ sK2 @ sK3 )
= $true ) )
| ~ spl16_2
| ~ spl16_18
| ~ spl16_38 ),
inference(trivial_inequality_removal,[],[f1894]) ).
thf(f1901,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( $false
= ( sK1 @ ( sK15 @ X0 ) ) )
| ( $false = $true )
| ( $true
= ( sK4 @ ( sK6 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( ( X0 @ sK2 @ sK3 )
= $true ) )
| ~ spl16_2
| ~ spl16_15
| ~ spl16_18
| ~ spl16_38 ),
inference(superposition,[],[f1895,f207]) ).
thf(f1912,plain,
( ! [X0: a > a > $o] :
( ( $true
= ( sK4 @ ( sK6 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( ( sK0 @ X0 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $false = $true )
| ( $false
= ( sK1 @ ( sK15 @ X0 ) ) ) )
| ~ spl16_2
| ~ spl16_15
| ~ spl16_18
| ~ spl16_38 ),
inference(duplicate_literal_removal,[],[f1901]) ).
thf(f1913,plain,
( ! [X0: a > a > $o] :
( ( $true
= ( sK4 @ ( sK6 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( $false
= ( sK1 @ ( sK15 @ X0 ) ) )
| ( ( sK0 @ X0 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true ) )
| ~ spl16_2
| ~ spl16_15
| ~ spl16_18
| ~ spl16_38 ),
inference(trivial_inequality_removal,[],[f1912]) ).
thf(f1923,plain,
( ( ( sK1 @ ( sK15 @ sK4 ) )
= $false )
| ( $false = $true )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ( ( sK0 @ sK4 )
= $false )
| ( ( sK0 @ sK4 )
= $false )
| ~ spl16_2
| ~ spl16_14
| ~ spl16_15
| ~ spl16_18
| ~ spl16_38 ),
inference(superposition,[],[f202,f1913]) ).
thf(f1927,plain,
( ( $false = $true )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ( ( sK0 @ sK4 )
= $false )
| ( ( sK1 @ ( sK15 @ sK4 ) )
= $false )
| ~ spl16_2
| ~ spl16_14
| ~ spl16_15
| ~ spl16_18
| ~ spl16_38 ),
inference(duplicate_literal_removal,[],[f1923]) ).
thf(f1928,plain,
( ( ( sK0 @ sK4 )
= $false )
| ( ( sK1 @ ( sK15 @ sK4 ) )
= $false )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ~ spl16_2
| ~ spl16_14
| ~ spl16_15
| ~ spl16_18
| ~ spl16_38 ),
inference(trivial_inequality_removal,[],[f1927]) ).
thf(f1937,plain,
( ( $false = $true )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ( ( sK1 @ ( sK15 @ sK4 ) )
= $false )
| ~ spl16_2
| ~ spl16_14
| ~ spl16_15
| ~ spl16_18
| ~ spl16_38 ),
inference(forward_demodulation,[],[f1928,f149]) ).
thf(f1938,plain,
( ( ( sK1 @ ( sK15 @ sK4 ) )
= $false )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ~ spl16_2
| ~ spl16_14
| ~ spl16_15
| ~ spl16_18
| ~ spl16_38 ),
inference(trivial_inequality_removal,[],[f1937]) ).
thf(f1945,plain,
( ( $false = $true )
| ( ( sK1 @ ( sK15 @ sK4 ) )
= $false )
| ~ spl16_2
| ~ spl16_4
| ~ spl16_14
| ~ spl16_15
| ~ spl16_18
| ~ spl16_38 ),
inference(forward_demodulation,[],[f1938,f158]) ).
thf(f1946,plain,
( ( ( sK1 @ ( sK15 @ sK4 ) )
= $false )
| ~ spl16_2
| ~ spl16_4
| ~ spl16_14
| ~ spl16_15
| ~ spl16_18
| ~ spl16_38 ),
inference(trivial_inequality_removal,[],[f1945]) ).
thf(f1950,definition,
( spl16_46
<=> ( ( sK1 @ ( sK15 @ sK4 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl16_46])],[avatar_definition]) ).
thf(f1952,plain,
( ( ( sK1 @ ( sK15 @ sK4 ) )
= $false )
| ~ spl16_46 ),
inference(avatar_component_clause,[],[f1950]) ).
thf(f1955,plain,
( spl16_46
| ~ spl16_2
| ~ spl16_4
| ~ spl16_14
| ~ spl16_15
| ~ spl16_18
| ~ spl16_38 ),
inference(avatar_split_clause,[],[f1946,f1772,f217,f206,f201,f156,f147,f1950]) ).
thf(f1988,plain,
( ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ( $false = $true )
| ( ( sK0 @ sK4 )
= $false )
| ~ spl16_17
| ~ spl16_46 ),
inference(superposition,[],[f1952,f214]) ).
thf(f1990,plain,
( ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ( ( sK0 @ sK4 )
= $false )
| ~ spl16_17
| ~ spl16_46 ),
inference(trivial_inequality_removal,[],[f1988]) ).
thf(f1992,plain,
( ( $false = $true )
| ( ( sK0 @ sK4 )
= $false )
| ~ spl16_4
| ~ spl16_17
| ~ spl16_46 ),
inference(forward_demodulation,[],[f1990,f158]) ).
thf(f1993,plain,
( ( ( sK0 @ sK4 )
= $false )
| ~ spl16_4
| ~ spl16_17
| ~ spl16_46 ),
inference(trivial_inequality_removal,[],[f1992]) ).
thf(f1996,plain,
( spl16_21
| ~ spl16_4
| ~ spl16_17
| ~ spl16_46 ),
inference(avatar_split_clause,[],[f1993,f1950,f213,f156,f505]) ).
thf(f2050,plain,
( ! [X2: a,X3: a > a > $o,X0: a > a > $o,X1: a] :
( ( ( sK0 @ sK4 )
= $false )
| ( $false
= ( X3 @ ( sK36 @ sK4 @ X0 ) @ ( sK35 @ sK4 @ X0 ) ) )
| ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK0 @ X0 )
= $false )
| ( $false
= ( sK1 @ X3 ) )
| ( $true
= ( sK4 @ X1 @ X2 ) ) )
| ~ spl16_3
| ~ spl16_10 ),
inference(trivial_inequality_removal,[],[f1215]) ).
thf(f2114,plain,
( ! [X2: a,X3: a > a > $o,X0: a > a > $o,X1: a] :
( ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $false = $true )
| ( $false
= ( X3 @ ( sK36 @ sK4 @ X0 ) @ ( sK35 @ sK4 @ X0 ) ) )
| ( ( sK0 @ X0 )
= $false )
| ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( $false
= ( sK1 @ X3 ) )
| ( $true
= ( sK4 @ X1 @ X2 ) ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_10 ),
inference(forward_demodulation,[],[f2050,f149]) ).
thf(f2115,plain,
( ! [X2: a,X3: a > a > $o,X0: a > a > $o,X1: a] :
( ( $false
= ( X3 @ ( sK36 @ sK4 @ X0 ) @ ( sK35 @ sK4 @ X0 ) ) )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( ( sK0 @ X0 )
= $false )
| ( $false
= ( sK1 @ X3 ) )
| ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( ( X0 @ sK2 @ sK3 )
= $true ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_10 ),
inference(trivial_inequality_removal,[],[f2114]) ).
thf(f2821,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( $false
= ( sK11 @ X0 @ X3 @ X4 ) )
| ( ( sK0 @ X0 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK0 @ X0 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( $true
= ( sK4 @ X3 @ X4 ) )
| ( ( sK0 @ sK4 )
= $false )
| ( ( sK1 @ ( sK12 @ X0 ) )
= $false )
| ( $false = $true ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_10 ),
inference(superposition,[],[f1134,f2115]) ).
thf(f2830,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( ( sK0 @ sK4 )
= $false )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( ( sK0 @ X0 )
= $false )
| ( $false = $true )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $false
= ( sK11 @ X0 @ X3 @ X4 ) )
| ( $true
= ( sK4 @ X3 @ X4 ) )
| ( ( sK1 @ ( sK12 @ X0 ) )
= $false ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_10 ),
inference(duplicate_literal_removal,[],[f2821]) ).
thf(f2831,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $true
= ( sK4 @ X3 @ X4 ) )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK1 @ ( sK12 @ X0 ) )
= $false )
| ( $false
= ( sK11 @ X0 @ X3 @ X4 ) )
| ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK0 @ sK4 )
= $false ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_10 ),
inference(trivial_inequality_removal,[],[f2830]) ).
thf(f2840,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $false
= ( sK11 @ X0 @ X3 @ X4 ) )
| ( $true
= ( sK4 @ X3 @ X4 ) )
| ( $false = $true )
| ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( ( sK0 @ X0 )
= $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK1 @ ( sK12 @ X0 ) )
= $false )
| ( $true
= ( sK4 @ X1 @ X2 ) ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_10 ),
inference(forward_demodulation,[],[f2831,f149]) ).
thf(f2841,plain,
( ! [X2: a,X3: a,X0: a > a > $o,X1: a,X4: a] :
( ( $false
= ( sK11 @ X0 @ X3 @ X4 ) )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( $true
= ( sK4 @ X3 @ X4 ) )
| ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( ( sK1 @ ( sK12 @ X0 ) )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( $true
= ( sK4 @ X1 @ X2 ) ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_10 ),
inference(trivial_inequality_removal,[],[f2840]) ).
thf(f2852,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( ( sK0 @ X0 )
= $false )
| ( ( sK1 @ ( sK12 @ X0 ) )
= $false )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( $false != $false )
| ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( ( X0 @ sK2 @ sK3 )
= $true ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_10 ),
inference(equality_factoring,[],[f2841]) ).
thf(f2859,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( ( sK1 @ ( sK12 @ X0 ) )
= $false )
| ( $false != $false )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_10 ),
inference(duplicate_literal_removal,[],[f2852]) ).
thf(f2860,plain,
( ! [X2: a,X0: a > a > $o,X1: a] :
( ( $false
= ( sK11 @ X0 @ X1 @ X2 ) )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK0 @ X0 )
= $false )
| ( $true
= ( sK4 @ X1 @ X2 ) )
| ( ( sK1 @ ( sK12 @ X0 ) )
= $false ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_10 ),
inference(trivial_inequality_removal,[],[f2859]) ).
thf(f2865,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK1 @ ( sK12 @ X0 ) )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( $false = $true )
| ( $true
= ( sK4 @ ( sK6 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_8
| ~ spl16_10 ),
inference(superposition,[],[f2860,f178]) ).
thf(f2874,plain,
( ! [X0: a > a > $o] :
( ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK0 @ X0 )
= $false )
| ( $true
= ( sK4 @ ( sK6 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( ( sK1 @ ( sK12 @ X0 ) )
= $false )
| ( $false = $true ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_8
| ~ spl16_10 ),
inference(duplicate_literal_removal,[],[f2865]) ).
thf(f2875,plain,
( ! [X0: a > a > $o] :
( ( $true
= ( sK4 @ ( sK6 @ X0 ) @ ( sK9 @ X0 ) ) )
| ( ( X0 @ sK2 @ sK3 )
= $true )
| ( ( sK1 @ ( sK12 @ X0 ) )
= $false )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_8
| ~ spl16_10 ),
inference(trivial_inequality_removal,[],[f2874]) ).
thf(f2884,plain,
( ( $false
= ( sK1 @ ( sK12 @ sK4 ) ) )
| ( ( sK0 @ sK4 )
= $false )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ( $false = $true )
| ( ( sK0 @ sK4 )
= $false )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_8
| ~ spl16_10
| ~ spl16_14 ),
inference(superposition,[],[f2875,f202]) ).
thf(f2891,plain,
( ( $false
= ( sK1 @ ( sK12 @ sK4 ) ) )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ( $false = $true )
| ( ( sK0 @ sK4 )
= $false )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_8
| ~ spl16_10
| ~ spl16_14 ),
inference(duplicate_literal_removal,[],[f2884]) ).
thf(f2892,plain,
( ( ( sK0 @ sK4 )
= $false )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ( $false
= ( sK1 @ ( sK12 @ sK4 ) ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_8
| ~ spl16_10
| ~ spl16_14 ),
inference(trivial_inequality_removal,[],[f2891]) ).
thf(f2903,plain,
( ( $false
= ( sK1 @ ( sK12 @ sK4 ) ) )
| ( $false = $true )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_8
| ~ spl16_10
| ~ spl16_14 ),
inference(forward_demodulation,[],[f2892,f149]) ).
thf(f2904,plain,
( ( $false
= ( sK1 @ ( sK12 @ sK4 ) ) )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_8
| ~ spl16_10
| ~ spl16_14 ),
inference(trivial_inequality_removal,[],[f2903]) ).
thf(f2907,plain,
( ( $false = $true )
| ( $false
= ( sK1 @ ( sK12 @ sK4 ) ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_8
| ~ spl16_10
| ~ spl16_14 ),
inference(forward_demodulation,[],[f2904,f158]) ).
thf(f2908,plain,
( ( $false
= ( sK1 @ ( sK12 @ sK4 ) ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_8
| ~ spl16_10
| ~ spl16_14 ),
inference(trivial_inequality_removal,[],[f2907]) ).
thf(f2911,plain,
( ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ( ( sK0 @ sK4 )
= $false )
| ( $false = $true )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_8
| ~ spl16_9
| ~ spl16_10
| ~ spl16_14 ),
inference(superposition,[],[f2908,f182]) ).
thf(f2914,plain,
( ( ( sK0 @ sK4 )
= $false )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_8
| ~ spl16_9
| ~ spl16_10
| ~ spl16_14 ),
inference(trivial_inequality_removal,[],[f2911]) ).
thf(f2917,plain,
( ( $false = $true )
| ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_8
| ~ spl16_9
| ~ spl16_10
| ~ spl16_14 ),
inference(forward_demodulation,[],[f2914,f149]) ).
thf(f2918,plain,
( ( $true
= ( sK4 @ sK2 @ sK3 ) )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_8
| ~ spl16_9
| ~ spl16_10
| ~ spl16_14 ),
inference(trivial_inequality_removal,[],[f2917]) ).
thf(f2920,plain,
( ( $false = $true )
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_8
| ~ spl16_9
| ~ spl16_10
| ~ spl16_14 ),
inference(forward_demodulation,[],[f2918,f158]) ).
thf(f2921,plain,
( $false
| ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_8
| ~ spl16_9
| ~ spl16_10
| ~ spl16_14 ),
inference(trivial_inequality_removal,[],[f2920]) ).
thf(f2922,plain,
( ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_8
| ~ spl16_9
| ~ spl16_10
| ~ spl16_14 ),
inference(avatar_contradiction_clause,[],[f2921]) ).
cnf(s1,plain,
( spl16_1
| spl16_2 ),
inference(sat_conversion,[],[f150]) ).
cnf(s2,plain,
( spl16_1
| spl16_3 ),
inference(sat_conversion,[],[f154]) ).
cnf(s3,plain,
( spl16_1
| spl16_4 ),
inference(sat_conversion,[],[f159]) ).
cnf(s4,plain,
( spl16_2
| spl16_5 ),
inference(sat_conversion,[],[f163]) ).
cnf(s5,plain,
( spl16_3
| spl16_5 ),
inference(sat_conversion,[],[f164]) ).
cnf(s6,plain,
( spl16_4
| spl16_5 ),
inference(sat_conversion,[],[f165]) ).
cnf(s7,plain,
( spl16_2
| spl16_6 ),
inference(sat_conversion,[],[f170]) ).
cnf(s8,plain,
( spl16_3
| spl16_6 ),
inference(sat_conversion,[],[f171]) ).
cnf(s9,plain,
( spl16_4
| spl16_6 ),
inference(sat_conversion,[],[f172]) ).
cnf(s10,plain,
( spl16_7
| spl16_8 ),
inference(sat_conversion,[],[f179]) ).
cnf(s11,plain,
( spl16_7
| spl16_9 ),
inference(sat_conversion,[],[f183]) ).
cnf(s12,plain,
( spl16_7
| spl16_10 ),
inference(sat_conversion,[],[f187]) ).
cnf(s13,plain,
( spl16_8
| spl16_11 ),
inference(sat_conversion,[],[f191]) ).
cnf(s14,plain,
( spl16_11
| spl16_12 ),
inference(sat_conversion,[],[f195]) ).
cnf(s15,plain,
( spl16_11
| spl16_13 ),
inference(sat_conversion,[],[f199]) ).
cnf(s16,plain,
( spl16_7
| spl16_14 ),
inference(sat_conversion,[],[f203]) ).
cnf(s17,plain,
( spl16_11
| spl16_14 ),
inference(sat_conversion,[],[f204]) ).
cnf(s18,plain,
( spl16_15
| spl16_16 ),
inference(sat_conversion,[],[f211]) ).
cnf(s19,plain,
( spl16_16
| spl16_17 ),
inference(sat_conversion,[],[f215]) ).
cnf(s20,plain,
( spl16_16
| spl16_18 ),
inference(sat_conversion,[],[f219]) ).
cnf(s21,plain,
( spl16_14
| spl16_16 ),
inference(sat_conversion,[],[f220]) ).
cnf(s22,plain,
( ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_7
| ~ spl16_11
| ~ spl16_16 ),
inference(sat_conversion,[],[f268]) ).
cnf(s24,plain,
( ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_8
| ~ spl16_13
| ~ spl16_14
| spl16_19 ),
inference(sat_conversion,[],[f450]) ).
cnf(s27,plain,
( ~ spl16_2
| ~ spl16_4
| ~ spl16_12
| ~ spl16_19 ),
inference(sat_conversion,[],[f503]) ).
cnf(s40,plain,
( ~ spl16_1
| ~ spl16_6
| ~ spl16_12
| ~ spl16_27 ),
inference(sat_conversion,[],[f852]) ).
cnf(s42,plain,
( ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_8
| ~ spl16_13
| ~ spl16_14
| spl16_27 ),
inference(sat_conversion,[],[f1002]) ).
cnf(s43,plain,
( ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_7
| ~ spl16_11
| ~ spl16_16 ),
inference(sat_conversion,[],[f1017]) ).
cnf(s51,plain,
( ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_8
| ~ spl16_9
| ~ spl16_10
| ~ spl16_14 ),
inference(sat_conversion,[],[f1378]) ).
cnf(s52,plain,
( ~ spl16_1
| ~ spl16_5
| ~ spl16_6
| ~ spl16_14
| ~ spl16_15
| ~ spl16_17
| ~ spl16_18 ),
inference(sat_conversion,[],[f1729]) ).
cnf(s60,plain,
( ~ spl16_2
| ~ spl16_21 ),
inference(sat_conversion,[],[f1757]) ).
cnf(s66,plain,
( ~ spl16_3
| ~ spl16_18
| spl16_21
| spl16_38 ),
inference(sat_conversion,[],[f1776]) ).
cnf(s95,plain,
( ~ spl16_2
| ~ spl16_4
| ~ spl16_14
| ~ spl16_15
| ~ spl16_18
| ~ spl16_38
| spl16_46 ),
inference(sat_conversion,[],[f1955]) ).
cnf(s101,plain,
( ~ spl16_4
| ~ spl16_17
| spl16_21
| ~ spl16_46 ),
inference(sat_conversion,[],[f1996]) ).
cnf(s109,plain,
( ~ spl16_2
| ~ spl16_3
| ~ spl16_4
| ~ spl16_8
| ~ spl16_9
| ~ spl16_10
| ~ spl16_14 ),
inference(sat_conversion,[],[f2922]) ).
cnf(s110,plain,
( spl16_7
| spl16_1 ),
inference(rat,[],[s109,s10,s11,s12,s16,s3,s2,s1]) ).
cnf(s111,plain,
( spl16_14
| spl16_1 ),
inference(rat,[],[s22,s17,s21,s3,s2,s1,s110]) ).
cnf(s112,plain,
( spl16_16
| spl16_1 ),
inference(rat,[],[s95,s101,s66,s18,s19,s20,s3,s2,s60,s1,s111]) ).
cnf(s113,plain,
spl16_1,
inference(rat,[],[s27,s24,s13,s14,s15,s22,s112,s111,s110,s1,s2,s3]) ).
cnf(s114,plain,
( spl16_16
| ~ spl16_14
| ~ spl16_4
| ~ spl16_3
| ~ spl16_2 ),
inference(rat,[],[s95,s101,s66,s18,s19,s20,s60]) ).
cnf(s115,plain,
( ~ spl16_14
| ~ spl16_7
| ~ spl16_4
| ~ spl16_3
| ~ spl16_2 ),
inference(rat,[],[s27,s24,s13,s14,s15,s22,s114]) ).
cnf(s116,plain,
( ~ spl16_7
| ~ spl16_4
| ~ spl16_2
| ~ spl16_3 ),
inference(rat,[],[s22,s17,s21,s115]) ).
cnf(s117,plain,
( ~ spl16_4
| ~ spl16_3
| ~ spl16_2 ),
inference(rat,[],[s109,s10,s11,s12,s16,s116]) ).
cnf(s118,plain,
( spl16_16
| ~ spl16_14
| spl16_4 ),
inference(rat,[],[s52,s18,s19,s20,s9,s6,s113]) ).
cnf(s119,plain,
( ~ spl16_14
| ~ spl16_7
| spl16_4 ),
inference(rat,[],[s40,s42,s13,s14,s15,s43,s118,s9,s6,s113]) ).
cnf(s120,plain,
( ~ spl16_7
| spl16_4 ),
inference(rat,[],[s43,s17,s21,s119,s9,s6,s113]) ).
cnf(s121,plain,
spl16_4,
inference(rat,[],[s51,s10,s11,s12,s16,s120,s6,s9,s113]) ).
cnf(s122,plain,
( spl16_16
| ~ spl16_14
| spl16_3 ),
inference(rat,[],[s52,s18,s19,s20,s8,s5,s113]) ).
cnf(s123,plain,
( ~ spl16_14
| ~ spl16_7
| spl16_3 ),
inference(rat,[],[s40,s42,s13,s14,s15,s43,s122,s8,s5,s113]) ).
cnf(s124,plain,
( ~ spl16_7
| spl16_3 ),
inference(rat,[],[s43,s17,s21,s123,s8,s5,s113]) ).
cnf(s125,plain,
spl16_3,
inference(rat,[],[s51,s10,s11,s12,s16,s124,s5,s8,s113]) ).
cnf(s126,plain,
~ spl16_2,
inference(rat,[],[s117,s121,s125]) ).
cnf(s127,plain,
spl16_6,
inference(rat,[],[s7,s126]) ).
cnf(s128,plain,
spl16_5,
inference(rat,[],[s4,s126]) ).
cnf(s129,plain,
( spl16_16
| ~ spl16_14 ),
inference(rat,[],[s52,s18,s19,s20,s113,s128,s127]) ).
cnf(s130,plain,
( ~ spl16_14
| ~ spl16_7 ),
inference(rat,[],[s40,s42,s13,s14,s15,s43,s129,s113,s127,s128]) ).
cnf(s131,plain,
~ spl16_7,
inference(rat,[],[s43,s17,s21,s130,s113,s128,s127]) ).
cnf(s132,plain,
spl16_14,
inference(rat,[],[s16,s131]) ).
cnf(s133,plain,
spl16_10,
inference(rat,[],[s12,s131]) ).
cnf(s134,plain,
spl16_9,
inference(rat,[],[s11,s131]) ).
cnf(s135,plain,
spl16_8,
inference(rat,[],[s10,s131]) ).
cnf(s137,plain,
$false,
inference(rat,[],[s51,s132,s135,s127,s128,s113,s134,s133]) ).
thf(f2923,plain,
$false,
inference(avatar_sat_refutation,[],[s137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV125^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n011.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Tue Sep 29 15:12:31 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running higher-order theorem proving
% 0.06/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.79/0.37 % (206285)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.79/0.37 % (206293)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2813854991:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.79/0.37 % (206296)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.79/0.37 % (206296)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.79/0.37 % (206290)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1947304641:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.79/0.37 % (206291)lrs+10_16_si=on:nwc=1.5:random_seed=809101878:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.79/0.37 % (206295)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3349310149:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.79/0.37 % (206292)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=921720169:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.79/0.37 % (206294)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=821607984:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.79/0.37 % (206296)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2407146470:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.79/0.37 % (206292)Instruction limit reached!
% 0.79/0.37 % (206292)------------------------------
% 0.79/0.37 % (206292)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.37 % (206292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.37 % (206292)CaDiCaL version: 2.1.3
% 0.79/0.37 % (206292)Termination reason: Instruction limit
% 0.79/0.37 % (206292)Termination phase: Saturation
% 0.79/0.37 % (206292)Time elapsed: 0.002 s
% 0.79/0.37 % (206292)Peak memory usage: 12 MB
% 0.79/0.37 % (206292)Instructions burned: 3 (million)
% 0.79/0.37 % (206291)Instruction limit reached!
% 0.79/0.37 % (206291)------------------------------
% 0.79/0.37 % (206291)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.37 % (206291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.37 % (206291)CaDiCaL version: 2.1.3
% 0.79/0.37 % (206291)Termination reason: Instruction limit
% 0.79/0.37 % (206291)Termination phase: Saturation
% 0.79/0.37 % (206291)Time elapsed: 0.011 s
% 0.79/0.37 % (206291)Peak memory usage: 12 MB
% 0.79/0.37 % (206291)Instructions burned: 20 (million)
% 0.79/0.37 % (206294)Instruction limit reached!
% 0.79/0.37 % (206294)------------------------------
% 0.79/0.37 % (206294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.37 % (206294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.37 % (206294)CaDiCaL version: 2.1.3
% 0.79/0.37 % (206294)Termination reason: Instruction limit
% 0.79/0.37 % (206294)Termination phase: Saturation
% 0.79/0.37 % (206294)Time elapsed: 0.012 s
% 0.79/0.37 % (206294)Peak memory usage: 12 MB
% 0.79/0.37 % (206294)Instructions burned: 24 (million)
% 0.79/0.37 % (206304)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2968679672:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.79/0.37 % (206304)Instruction limit reached!
% 0.79/0.37 % (206304)------------------------------
% 0.79/0.37 % (206304)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.37 % (206304)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.37 % (206304)CaDiCaL version: 2.1.3
% 0.79/0.37 % (206304)Termination reason: Instruction limit
% 0.79/0.37 % (206304)Termination phase: Saturation
% 0.79/0.37 % (206304)Time elapsed: 0.002 s
% 0.79/0.37 % (206304)Peak memory usage: 12 MB
% 0.79/0.37 % (206304)Instructions burned: 3 (million)
% 0.79/0.37 % (206306)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.79/0.37 % (206305)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1578328531:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.79/0.41 % (206306)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3414735381:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.79/0.41 % (206305)Instruction limit reached!
% 0.79/0.41 % (206305)------------------------------
% 0.79/0.41 % (206305)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.41 % (206305)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.41 % (206305)CaDiCaL version: 2.1.3
% 0.79/0.41 % (206305)Termination reason: Instruction limit
% 0.79/0.41 % (206305)Termination phase: Saturation
% 0.79/0.41 % (206305)Time elapsed: 0.003 s
% 0.79/0.41 % (206305)Peak memory usage: 12 MB
% 0.79/0.41 % (206305)Instructions burned: 5 (million)
% 0.79/0.41 % (206306)Instruction limit reached!
% 0.79/0.41 % (206306)------------------------------
% 0.79/0.41 % (206306)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.41 % (206306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.41 % (206306)CaDiCaL version: 2.1.3
% 0.79/0.41 % (206306)Termination reason: Instruction limit
% 0.79/0.41 % (206306)Termination phase: Saturation
% 0.79/0.41 % (206306)Time elapsed: 0.004 s
% 0.79/0.41 % (206306)Peak memory usage: 12 MB
% 0.79/0.41 % (206306)Instructions burned: 7 (million)
% 0.79/0.41 % (206295)Instruction limit reached!
% 0.79/0.41 % (206295)------------------------------
% 0.79/0.41 % (206295)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.41 % (206295)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.41 % (206295)CaDiCaL version: 2.1.3
% 0.79/0.41 % (206295)Termination reason: Instruction limit
% 0.79/0.41 % (206295)Termination phase: Saturation
% 0.79/0.41 % (206295)Time elapsed: 0.038 s
% 0.79/0.41 % (206295)Peak memory usage: 13 MB
% 0.79/0.41 % (206295)Instructions burned: 76 (million)
% 0.79/0.41 % (206308)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3508177285:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.79/0.41 % (206290)Instruction limit reached!
% 0.79/0.41 % (206290)------------------------------
% 0.79/0.41 % (206290)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.41 % (206290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.41 % (206290)CaDiCaL version: 2.1.3
% 0.79/0.41 % (206290)Termination reason: Instruction limit
% 0.79/0.41 % (206290)Termination phase: Saturation
% 0.79/0.41 % (206290)Time elapsed: 0.048 s
% 0.79/0.41 % (206290)Peak memory usage: 13 MB
% 0.79/0.41 % (206290)Instructions burned: 88 (million)
% 0.79/0.41 % (206311)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.79/0.41 % (206311)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.79/0.41 % (206308)Instruction limit reached!
% 0.79/0.41 % (206308)------------------------------
% 0.79/0.41 % (206308)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.41 % (206308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.41 % (206308)CaDiCaL version: 2.1.3
% 0.79/0.41 % (206308)Termination reason: Instruction limit
% 0.79/0.41 % (206308)Termination phase: Saturation
% 0.79/0.41 % (206308)Time elapsed: 0.006 s
% 0.79/0.41 % (206308)Peak memory usage: 12 MB
% 0.79/0.41 % (206308)Instructions burned: 12 (million)
% 0.79/0.41 % (206311)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3891954470:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.79/0.41 % (206312)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1370067440:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.79/0.41 % (206313)lrs+10_1_si=on:cs=on:random_seed=428315456:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.79/0.41 % (206313)Instruction limit reached!
% 0.79/0.41 % (206313)------------------------------
% 0.79/0.41 % (206313)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.44 % (206313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.44 % (206313)CaDiCaL version: 2.1.3
% 0.79/0.44 % (206313)Termination reason: Instruction limit
% 0.79/0.44 % (206313)Termination phase: Saturation
% 0.79/0.44 % (206313)Time elapsed: 0.005 s
% 0.79/0.44 % (206313)Peak memory usage: 12 MB
% 0.79/0.44 % (206313)Instructions burned: 9 (million)
% 0.79/0.44 % (206315)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.79/0.44 % (206311)Instruction limit reached!
% 0.79/0.44 % (206311)------------------------------
% 0.79/0.44 % (206311)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.44 % (206311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.44 % (206311)CaDiCaL version: 2.1.3
% 0.79/0.44 % (206311)Termination reason: Instruction limit
% 0.79/0.44 % (206311)Termination phase: Saturation
% 0.79/0.44 % (206311)Time elapsed: 0.013 s
% 0.79/0.44 % (206311)Peak memory usage: 12 MB
% 0.79/0.44 % (206311)Instructions burned: 29 (million)
% 0.79/0.44 % (206315)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=1906818714:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.79/0.44 % (206316)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3762189642:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.79/0.44 % (206315)Instruction limit reached!
% 0.79/0.44 % (206315)------------------------------
% 0.79/0.44 % (206315)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.44 % (206315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.44 % (206315)CaDiCaL version: 2.1.3
% 0.79/0.44 % (206315)Termination reason: Instruction limit
% 0.79/0.44 % (206315)Termination phase: Saturation
% 0.79/0.44 % (206315)Time elapsed: 0.002 s
% 0.79/0.44 % (206315)Peak memory usage: 11 MB
% 0.79/0.44 % (206315)Instructions burned: 3 (million)
% 0.79/0.44 % (206316)Refutation not found, incomplete strategy
% 0.79/0.44 % (206316)------------------------------
% 0.79/0.44 % (206316)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.44 % (206316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.44 % (206316)CaDiCaL version: 2.1.3
% 0.79/0.44 % (206316)Termination reason: Refutation not found, incomplete strategy
% 0.79/0.44 % (206316)Time elapsed: 0.011 s
% 0.79/0.44 % (206316)Peak memory usage: 12 MB
% 0.79/0.44 % (206316)Instructions burned: 21 (million)
% 0.79/0.44 % (206320)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2061063347:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.79/0.44 % (206316)------------------------------
% 0.79/0.44 % (206316)------------------------------
% 0.79/0.44 % (206296)Instruction limit reached!
% 0.79/0.44 % (206296)------------------------------
% 0.79/0.44 % (206296)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.44 % (206296)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.44 % (206296)CaDiCaL version: 2.1.3
% 0.79/0.44 % (206296)Termination reason: Instruction limit
% 0.79/0.44 % (206296)Termination phase: Saturation
% 0.79/0.44 % (206296)Time elapsed: 0.082 s
% 0.79/0.44 % (206296)Peak memory usage: 13 MB
% 0.79/0.44 % (206296)Instructions burned: 157 (million)
% 0.79/0.44 % (206324)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=2100747014:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.79/0.44 % (206323)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2661037117:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.79/0.44 % (206324)Instruction limit reached!
% 0.79/0.44 % (206324)------------------------------
% 0.79/0.44 % (206324)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.44 % (206324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.44 % (206324)CaDiCaL version: 2.1.3
% 0.79/0.44 % (206324)Termination reason: Instruction limit
% 0.79/0.44 % (206324)Termination phase: Saturation
% 0.79/0.44 % (206324)Time elapsed: 0.007 s
% 0.79/0.44 % (206324)Peak memory usage: 12 MB
% 0.79/0.44 % (206324)Instructions burned: 14 (million)
% 1.51/0.49 % (206312)Instruction limit reached!
% 1.51/0.49 % (206312)------------------------------
% 1.51/0.49 % (206312)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.49 % (206326)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1946757955:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.51/0.49 % (206312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.49 % (206312)CaDiCaL version: 2.1.3
% 1.51/0.49 % (206312)Termination reason: Instruction limit
% 1.51/0.49 % (206312)Termination phase: Saturation
% 1.51/0.49 % (206312)Time elapsed: 0.045 s
% 1.51/0.49 % (206312)Peak memory usage: 12 MB
% 1.51/0.49 % (206312)Instructions burned: 88 (million)
% 1.51/0.49 % (206327)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2089017698:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.51/0.49 % (206323)Instruction limit reached!
% 1.51/0.49 % (206323)------------------------------
% 1.51/0.49 % (206323)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.49 % (206323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.49 % (206323)CaDiCaL version: 2.1.3
% 1.51/0.49 % (206323)Termination reason: Instruction limit
% 1.51/0.49 % (206323)Termination phase: Saturation
% 1.51/0.49 % (206323)Time elapsed: 0.014 s
% 1.51/0.49 % (206323)Peak memory usage: 12 MB
% 1.51/0.49 % (206323)Instructions burned: 25 (million)
% 1.51/0.49 % (206327)Instruction limit reached!
% 1.51/0.49 % (206327)------------------------------
% 1.51/0.49 % (206327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.49 % (206327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.49 % (206327)CaDiCaL version: 2.1.3
% 1.51/0.49 % (206327)Termination reason: Instruction limit
% 1.51/0.49 % (206327)Termination phase: Saturation
% 1.51/0.49 % (206327)Time elapsed: 0.007 s
% 1.51/0.49 % (206327)Peak memory usage: 12 MB
% 1.51/0.49 % (206327)Instructions burned: 14 (million)
% 1.51/0.49 % (206330)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1013107419:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.51/0.49 % (206330)Instruction limit reached!
% 1.51/0.49 % (206330)------------------------------
% 1.51/0.49 % (206330)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.49 % (206330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.49 % (206330)CaDiCaL version: 2.1.3
% 1.51/0.49 % (206330)Termination reason: Instruction limit
% 1.51/0.49 % (206330)Termination phase: Saturation
% 1.51/0.49 % (206330)Time elapsed: 0.002 s
% 1.51/0.49 % (206330)Peak memory usage: 12 MB
% 1.51/0.49 % (206330)Instructions burned: 3 (million)
% 1.51/0.49 % (206332)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2606203378:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.51/0.49 % (206334)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2978757168:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.51/0.49 % (206335)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=751610719:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.51/0.49 % (206337)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 1.51/0.49 % (206337)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.51/0.49 % (206332)Instruction limit reached!
% 1.51/0.49 % (206332)------------------------------
% 1.51/0.49 % (206332)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.49 % (206332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.49 % (206332)CaDiCaL version: 2.1.3
% 1.51/0.49 % (206332)Termination reason: Instruction limit
% 1.51/0.49 % (206332)Termination phase: Saturation
% 1.51/0.49 % (206332)Time elapsed: 0.015 s
% 1.51/0.49 % (206332)Peak memory usage: 12 MB
% 1.51/0.49 % (206332)Instructions burned: 28 (million)
% 1.51/0.49 % (206334)Instruction limit reached!
% 1.51/0.49 % (206334)------------------------------
% 1.51/0.49 % (206334)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.54 % (206334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.54 % (206334)CaDiCaL version: 2.1.3
% 1.51/0.54 % (206334)Termination reason: Instruction limit
% 1.51/0.54 % (206334)Termination phase: Saturation
% 1.51/0.54 % (206334)Time elapsed: 0.012 s
% 1.51/0.54 % (206334)Peak memory usage: 11 MB
% 1.51/0.54 % (206334)Instructions burned: 23 (million)
% 1.51/0.54 % (206337)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=584106913:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.51/0.54 % (206337)Instruction limit reached!
% 1.51/0.54 % (206337)------------------------------
% 1.51/0.54 % (206337)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.54 % (206337)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.54 % (206337)CaDiCaL version: 2.1.3
% 1.51/0.54 % (206337)Termination reason: Instruction limit
% 1.51/0.54 % (206337)Termination phase: Saturation
% 1.51/0.54 % (206337)Time elapsed: 0.008 s
% 1.51/0.54 % (206337)Peak memory usage: 12 MB
% 1.51/0.54 % (206337)Instructions burned: 14 (million)
% 1.51/0.54 % (206341)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.51/0.54 % (206341)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=1518964934:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.51/0.54 % (206342)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=2555196819:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.51/0.54 % (206342)Refutation not found, incomplete strategy
% 1.51/0.54 % (206342)------------------------------
% 1.51/0.54 % (206342)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.54 % (206342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.54 % (206342)CaDiCaL version: 2.1.3
% 1.51/0.54 % (206342)Termination reason: Refutation not found, incomplete strategy
% 1.51/0.54 % (206342)Time elapsed: 0.004 s
% 1.51/0.54 % (206342)Peak memory usage: 12 MB
% 1.51/0.54 % (206342)Instructions burned: 7 (million)
% 1.51/0.54 % (206341)Instruction limit reached!
% 1.51/0.54 % (206341)------------------------------
% 1.51/0.54 % (206341)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.54 % (206341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.54 % (206341)CaDiCaL version: 2.1.3
% 1.51/0.54 % (206341)Termination reason: Instruction limit
% 1.51/0.54 % (206341)Termination phase: Saturation
% 1.51/0.54 % (206341)Time elapsed: 0.005 s
% 1.51/0.54 % (206341)Peak memory usage: 12 MB
% 1.51/0.54 % (206341)Instructions burned: 10 (million)
% 1.51/0.54 % (206342)------------------------------
% 1.51/0.54 % (206342)------------------------------
% 1.51/0.54 % (206335)Instruction limit reached!
% 1.51/0.54 % (206335)------------------------------
% 1.51/0.54 % (206335)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.54 % (206335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.54 % (206335)CaDiCaL version: 2.1.3
% 1.51/0.54 % (206335)Termination reason: Instruction limit
% 1.51/0.54 % (206335)Termination phase: Saturation
% 1.51/0.54 % (206335)Time elapsed: 0.033 s
% 1.51/0.54 % (206335)Peak memory usage: 12 MB
% 1.51/0.54 % (206335)Instructions burned: 62 (million)
% 1.51/0.54 % (206344)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=687409839:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.51/0.54 % (206293)Instruction limit reached!
% 1.51/0.54 % (206293)------------------------------
% 1.51/0.54 % (206293)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.51/0.54 % (206293)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.51/0.54 % (206293)CaDiCaL version: 2.1.3
% 1.51/0.54 % (206293)Termination reason: Instruction limit
% 1.51/0.54 % (206293)Termination phase: Saturation
% 1.51/0.54 % (206293)Time elapsed: 0.176 s
% 1.51/0.54 % (206293)Peak memory usage: 15 MB
% 1.51/0.54 % (206293)Instructions burned: 635 (million)
% 1.51/0.54 % (206344)Instruction limit reached!
% 1.51/0.54 % (206344)------------------------------
% 1.51/0.54 % (206344)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.61 % (206344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.61 % (206344)CaDiCaL version: 2.1.3
% 2.24/0.61 % (206344)Termination reason: Instruction limit
% 2.24/0.61 % (206344)Termination phase: Saturation
% 2.24/0.61 % (206344)Time elapsed: 0.004 s
% 2.24/0.61 % (206344)Peak memory usage: 12 MB
% 2.24/0.61 % (206344)Instructions burned: 8 (million)
% 2.24/0.61 % (206347)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=516879953:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 2.24/0.61 % (206348)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=545577185:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.24/0.61 % (206349)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=739950386:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 2.24/0.61 % (206347)Refutation not found, incomplete strategy
% 2.24/0.61 % (206347)------------------------------
% 2.24/0.61 % (206347)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.61 % (206347)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.61 % (206347)CaDiCaL version: 2.1.3
% 2.24/0.61 % (206347)Termination reason: Refutation not found, incomplete strategy
% 2.24/0.61 % (206347)Time elapsed: 0.004 s
% 2.24/0.61 % (206347)Peak memory usage: 12 MB
% 2.24/0.61 % (206347)Instructions burned: 6 (million)
% 2.24/0.61 % (206351)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=1681144863:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.24/0.61 % (206347)------------------------------
% 2.24/0.61 % (206347)------------------------------
% 2.24/0.61 % (206352)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=4250606580:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.24/0.61 % (206348)Instruction limit reached!
% 2.24/0.61 % (206348)------------------------------
% 2.24/0.61 % (206348)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.61 % (206348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.61 % (206348)CaDiCaL version: 2.1.3
% 2.24/0.61 % (206348)Termination reason: Instruction limit
% 2.24/0.61 % (206348)Termination phase: Saturation
% 2.24/0.61 % (206348)Time elapsed: 0.011 s
% 2.24/0.61 % (206348)Peak memory usage: 12 MB
% 2.24/0.61 % (206348)Instructions burned: 20 (million)
% 2.24/0.61 % (206357)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3120539503:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.24/0.61 % (206359)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.24/0.61 % (206359)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3638639052:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.24/0.61 % (206320)Instruction limit reached!
% 2.24/0.61 % (206320)------------------------------
% 2.24/0.61 % (206320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.61 % (206320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.61 % (206320)CaDiCaL version: 2.1.3
% 2.24/0.61 % (206320)Termination reason: Instruction limit
% 2.24/0.61 % (206320)Termination phase: Saturation
% 2.24/0.61 % (206320)Time elapsed: 0.131 s
% 2.24/0.61 % (206320)Peak memory usage: 13 MB
% 2.24/0.61 % (206320)Instructions burned: 251 (million)
% 2.24/0.61 % (206359)Instruction limit reached!
% 2.24/0.61 % (206359)------------------------------
% 2.24/0.61 % (206359)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.61 % (206359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.61 % (206359)CaDiCaL version: 2.1.3
% 2.24/0.61 % (206359)Termination reason: Instruction limit
% 2.24/0.61 % (206359)Termination phase: Saturation
% 2.24/0.61 % (206359)Time elapsed: 0.004 s
% 2.24/0.61 % (206359)Peak memory usage: 12 MB
% 2.24/0.61 % (206359)Instructions burned: 7 (million)
% 2.24/0.61 % (206351)Instruction limit reached!
% 2.24/0.61 % (206351)------------------------------
% 2.24/0.61 % (206351)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.61 % (206351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.71 % (206351)CaDiCaL version: 2.1.3
% 2.85/0.71 % (206351)Termination reason: Instruction limit
% 2.85/0.71 % (206351)Termination phase: Saturation
% 2.85/0.71 % (206351)Time elapsed: 0.038 s
% 2.85/0.71 % (206351)Peak memory usage: 13 MB
% 2.85/0.71 % (206351)Instructions burned: 147 (million)
% 2.85/0.71 % (206357)Instruction limit reached!
% 2.85/0.71 % (206357)------------------------------
% 2.85/0.71 % (206357)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.85/0.71 % (206357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.71 % (206357)CaDiCaL version: 2.1.3
% 2.85/0.71 % (206357)Termination reason: Instruction limit
% 2.85/0.71 % (206357)Termination phase: Saturation
% 2.85/0.71 % (206357)Time elapsed: 0.022 s
% 2.85/0.71 % (206357)Peak memory usage: 12 MB
% 2.85/0.71 % (206357)Instructions burned: 42 (million)
% 2.85/0.71 % (206364)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.85/0.71 % (206362)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=686795836:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.85/0.71 % (206364)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=4039554725:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.85/0.71 % (206363)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=3403080799:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.85/0.71 % (206364)Instruction limit reached!
% 2.85/0.71 % (206364)------------------------------
% 2.85/0.71 % (206364)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.85/0.71 % (206364)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.71 % (206364)CaDiCaL version: 2.1.3
% 2.85/0.71 % (206364)Termination reason: Instruction limit
% 2.85/0.71 % (206364)Termination phase: Saturation
% 2.85/0.71 % (206364)Time elapsed: 0.002 s
% 2.85/0.71 % (206364)Peak memory usage: 12 MB
% 2.85/0.71 % (206364)Instructions burned: 7 (million)
% 2.85/0.71 % (206365)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=3881452565:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.85/0.71 % (206365)Refutation not found, incomplete strategy
% 2.85/0.71 % (206365)------------------------------
% 2.85/0.71 % (206365)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.85/0.71 % (206365)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.71 % (206365)CaDiCaL version: 2.1.3
% 2.85/0.71 % (206365)Termination reason: Refutation not found, incomplete strategy
% 2.85/0.71 % (206365)Time elapsed: 0.003 s
% 2.85/0.71 % (206365)Peak memory usage: 12 MB
% 2.85/0.71 % (206365)Instructions burned: 5 (million)
% 2.85/0.71 % (206365)------------------------------
% 2.85/0.71 % (206365)------------------------------
% 2.85/0.71 % (206369)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=1558076945:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.85/0.71 % (206326)Instruction limit reached!
% 2.85/0.71 % (206326)------------------------------
% 2.85/0.71 % (206326)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.85/0.71 % (206326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.71 % (206326)CaDiCaL version: 2.1.3
% 2.85/0.71 % (206326)Termination reason: Instruction limit
% 2.85/0.71 % (206326)Termination phase: Saturation
% 2.85/0.71 % (206326)Time elapsed: 0.163 s
% 2.85/0.71 % (206326)Peak memory usage: 13 MB
% 2.85/0.71 % (206326)Instructions burned: 328 (million)
% 2.85/0.71 % (206369)Instruction limit reached!
% 2.85/0.71 % (206369)------------------------------
% 2.85/0.71 % (206369)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.85/0.71 % (206369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.71 % (206369)CaDiCaL version: 2.1.3
% 2.85/0.71 % (206369)Termination reason: Instruction limit
% 2.85/0.71 % (206369)Termination phase: Saturation
% 2.85/0.71 % (206369)Time elapsed: 0.012 s
% 2.85/0.71 % (206369)Peak memory usage: 13 MB
% 2.85/0.71 % (206369)Instructions burned: 19 (million)
% 2.85/0.71 % (206371)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=3946846183:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 2.85/0.79 % (206373)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=3203820187:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2997 on theBenchmark for (2997ds/853Mi)
% 2.85/0.79 % (206375)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=2084878523:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 2.85/0.79 % (206352)Instruction limit reached!
% 2.85/0.79 % (206352)------------------------------
% 2.85/0.79 % (206352)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.85/0.79 % (206352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.79 % (206352)CaDiCaL version: 2.1.3
% 2.85/0.79 % (206352)Termination reason: Instruction limit
% 2.85/0.79 % (206352)Termination phase: Saturation
% 2.85/0.79 % (206352)Time elapsed: 0.101 s
% 2.85/0.79 % (206352)Peak memory usage: 13 MB
% 2.85/0.79 % (206352)Instructions burned: 194 (million)
% 2.85/0.79 % (206378)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=2682116750:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 2.85/0.79 % (206375)Instruction limit reached!
% 2.85/0.79 % (206375)------------------------------
% 2.85/0.79 % (206375)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.85/0.79 % (206375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.79 % (206375)CaDiCaL version: 2.1.3
% 2.85/0.79 % (206375)Termination reason: Instruction limit
% 2.85/0.79 % (206375)Termination phase: Saturation
% 2.85/0.79 % (206375)Time elapsed: 0.026 s
% 2.85/0.79 % (206375)Peak memory usage: 12 MB
% 2.85/0.79 % (206375)Instructions burned: 45 (million)
% 2.85/0.79 % (206362)Instruction limit reached!
% 2.85/0.79 % (206362)------------------------------
% 2.85/0.79 % (206362)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.85/0.79 % (206362)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.79 % (206362)CaDiCaL version: 2.1.3
% 2.85/0.79 % (206362)Termination reason: Instruction limit
% 2.85/0.79 % (206362)Termination phase: Saturation
% 2.85/0.79 % (206362)Time elapsed: 0.085 s
% 2.85/0.79 % (206362)Peak memory usage: 13 MB
% 2.85/0.79 % (206362)Instructions burned: 181 (million)
% 2.85/0.79 % (206363)Instruction limit reached!
% 2.85/0.79 % (206363)------------------------------
% 2.85/0.79 % (206363)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.85/0.79 % (206363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.79 % (206363)CaDiCaL version: 2.1.3
% 2.85/0.79 % (206363)Termination reason: Instruction limit
% 2.85/0.79 % (206363)Termination phase: Saturation
% 2.85/0.79 % (206363)Time elapsed: 0.088 s
% 2.85/0.79 % (206363)Peak memory usage: 13 MB
% 2.85/0.79 % (206363)Instructions burned: 169 (million)
% 2.85/0.79 % (206380)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=2679906800:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 2.85/0.79 % (206381)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 2.85/0.79 % (206381)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=1651701594:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 2.85/0.79 % (206382)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3891350451:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 2.85/0.79 % (206380)Instruction limit reached!
% 2.85/0.79 % (206380)------------------------------
% 2.85/0.79 % (206380)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.85/0.79 % (206380)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.85/0.79 % (206380)CaDiCaL version: 2.1.3
% 2.85/0.79 % (206380)Termination reason: Instruction limit
% 2.85/0.79 % (206380)Termination phase: Saturation
% 2.85/0.79 % (206380)Time elapsed: 0.011 s
% 2.85/0.79 % (206380)Peak memory usage: 12 MB
% 4.20/0.91 % (206380)Instructions burned: 22 (million)
% 4.20/0.91 % (206382)Instruction limit reached!
% 4.20/0.91 % (206382)------------------------------
% 4.20/0.91 % (206382)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/0.91 % (206382)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/0.91 % (206382)CaDiCaL version: 2.1.3
% 4.20/0.91 % (206382)Termination reason: Instruction limit
% 4.20/0.91 % (206382)Termination phase: Saturation
% 4.20/0.91 % (206382)Time elapsed: 0.007 s
% 4.20/0.91 % (206382)Peak memory usage: 12 MB
% 4.20/0.91 % (206382)Instructions burned: 14 (million)
% 4.20/0.91 % (206386)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=3784697975:i=66:s2at=3:nm=2:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/66Mi)
% 4.20/0.91 % (206387)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=1823672401:i=51:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/51Mi)
% 4.20/0.91 % (206386)Instruction limit reached!
% 4.20/0.91 % (206386)------------------------------
% 4.20/0.91 % (206386)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/0.91 % (206386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/0.91 % (206386)CaDiCaL version: 2.1.3
% 4.20/0.91 % (206386)Termination reason: Instruction limit
% 4.20/0.91 % (206386)Termination phase: Saturation
% 4.20/0.91 % (206386)Time elapsed: 0.033 s
% 4.20/0.91 % (206386)Peak memory usage: 13 MB
% 4.20/0.91 % (206386)Instructions burned: 66 (million)
% 4.20/0.91 % (206387)Instruction limit reached!
% 4.20/0.91 % (206387)------------------------------
% 4.20/0.91 % (206387)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/0.91 % (206387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/0.91 % (206387)CaDiCaL version: 2.1.3
% 4.20/0.91 % (206387)Termination reason: Instruction limit
% 4.20/0.91 % (206387)Termination phase: Saturation
% 4.20/0.91 % (206387)Time elapsed: 0.027 s
% 4.20/0.91 % (206387)Peak memory usage: 12 MB
% 4.20/0.91 % (206387)Instructions burned: 51 (million)
% 4.20/0.91 % (206390)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=2241708880:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/31Mi)
% 4.20/0.91 % (206391)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=3205958555:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 4.20/0.91 % (206390)Refutation not found, incomplete strategy
% 4.20/0.91 % (206390)------------------------------
% 4.20/0.91 % (206390)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/0.91 % (206390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/0.91 % (206390)CaDiCaL version: 2.1.3
% 4.20/0.91 % (206390)Termination reason: Refutation not found, incomplete strategy
% 4.20/0.91 % (206390)Time elapsed: 0.004 s
% 4.20/0.91 % (206390)Peak memory usage: 12 MB
% 4.20/0.91 % (206390)Instructions burned: 7 (million)
% 4.20/0.91 % (206390)------------------------------
% 4.20/0.91 % (206390)------------------------------
% 4.20/0.91 % (206381)Instruction limit reached!
% 4.20/0.91 % (206381)------------------------------
% 4.20/0.91 % (206381)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/0.91 % (206381)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/0.91 % (206381)CaDiCaL version: 2.1.3
% 4.20/0.91 % (206381)Termination reason: Instruction limit
% 4.20/0.91 % (206381)Termination phase: Saturation
% 4.20/0.91 % (206381)Time elapsed: 0.091 s
% 4.20/0.91 % (206381)Peak memory usage: 12 MB
% 4.20/0.91 % (206381)Instructions burned: 200 (million)
% 4.20/0.91 % (206373)Instruction limit reached!
% 4.20/0.91 % (206373)------------------------------
% 4.20/0.91 % (206373)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/0.91 % (206373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/0.91 % (206373)CaDiCaL version: 2.1.3
% 4.20/0.91 % (206373)Termination reason: Instruction limit
% 4.20/0.91 % (206373)Termination phase: Saturation
% 4.20/0.91 % (206373)Time elapsed: 0.155 s
% 4.20/0.91 % (206373)Peak memory usage: 14 MB
% 4.20/0.91 % (206373)Instructions burned: 854 (million)
% 4.20/0.91 % (206394)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=2426140388:cond=on:i=34:hud=10:nm=10:rtra=on_2995 on theBenchmark for (2995ds/34Mi)
% 4.20/1.01 % (206396)WARNING Broken Constraint: if sine_generality_threshold(60) has been set then sine_selection(off) is not equal to off
% 4.20/1.01 % (206396)dis+21_1_to=lpo:sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:bsr=on:random_seed=764904905:i=180:hud=16:bd=all:fsr=off:rtra=on:sgt=60:ntd=on_2995 on theBenchmark for (2995ds/180Mi)
% 4.20/1.01 % (206396)Refutation not found, incomplete strategy
% 4.20/1.01 % (206396)------------------------------
% 4.20/1.01 % (206396)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/1.01 % (206396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.01 % (206396)CaDiCaL version: 2.1.3
% 4.20/1.01 % (206396)Termination reason: Refutation not found, incomplete strategy
% 4.20/1.01 % (206396)Time elapsed: 0.002 s
% 4.20/1.01 % (206396)Peak memory usage: 12 MB
% 4.20/1.01 % (206396)Instructions burned: 7 (million)
% 4.20/1.01 % (206396)------------------------------
% 4.20/1.01 % (206396)------------------------------
% 4.20/1.01 % (206395)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=2257401076:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 4.20/1.01 % (206371)Instruction limit reached!
% 4.20/1.01 % (206371)------------------------------
% 4.20/1.01 % (206371)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/1.01 % (206371)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.01 % (206371)CaDiCaL version: 2.1.3
% 4.20/1.01 % (206371)Termination reason: Instruction limit
% 4.20/1.01 % (206371)Termination phase: Saturation
% 4.20/1.01 % (206371)Time elapsed: 0.184 s
% 4.20/1.01 % (206371)Peak memory usage: 15 MB
% 4.20/1.01 % (206371)Instructions burned: 317 (million)
% 4.20/1.01 % (206394)Instruction limit reached!
% 4.20/1.01 % (206394)------------------------------
% 4.20/1.01 % (206394)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/1.01 % (206394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.01 % (206394)CaDiCaL version: 2.1.3
% 4.20/1.01 % (206394)Termination reason: Instruction limit
% 4.20/1.01 % (206394)Termination phase: Saturation
% 4.20/1.01 % (206394)Time elapsed: 0.017 s
% 4.20/1.01 % (206394)Peak memory usage: 12 MB
% 4.20/1.01 % (206394)Instructions burned: 35 (million)
% 4.20/1.01 % (206399)lrs+1002_1_sil=128000:si=on:uwa=off:random_seed=615112319:st=2:i=246:sd=3:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/246Mi)
% 4.20/1.01 % (206401)lrs+10_7_sil=128000:tgt=full:si=on:lma=off:uwa=off:nwc=1:sac=on:random_seed=2510970025:cond=on:i=96:bd=all:rtra=on_2995 on theBenchmark for (2995ds/96Mi)
% 4.20/1.01 % (206402)lrs+10_1_sil=128000:si=on:sos=on:urr=on:random_seed=4001278277:i=427:sd=1:rtra=on:ss=axioms_2995 on theBenchmark for (2995ds/427Mi)
% 4.20/1.01 % (206395)Instruction limit reached!
% 4.20/1.01 % (206395)------------------------------
% 4.20/1.01 % (206395)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/1.01 % (206395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.01 % (206395)CaDiCaL version: 2.1.3
% 4.20/1.01 % (206395)Termination reason: Instruction limit
% 4.20/1.01 % (206395)Termination phase: Saturation
% 4.20/1.01 % (206395)Time elapsed: 0.033 s
% 4.20/1.01 % (206395)Peak memory usage: 12 MB
% 4.20/1.01 % (206395)Instructions burned: 67 (million)
% 4.20/1.01 % (206391)Instruction limit reached!
% 4.20/1.01 % (206391)------------------------------
% 4.20/1.01 % (206391)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/1.01 % (206391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.01 % (206391)CaDiCaL version: 2.1.3
% 4.20/1.01 % (206391)Termination reason: Instruction limit
% 4.20/1.01 % (206391)Termination phase: Saturation
% 4.20/1.01 % (206391)Time elapsed: 0.073 s
% 4.20/1.01 % (206391)Peak memory usage: 13 MB
% 4.20/1.01 % (206391)Instructions burned: 138 (million)
% 4.20/1.01 % (206406)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3745864803:st=3:s2a=on:i=874:sd=3:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/874Mi)
% 4.20/1.01 % (206407)dis+1010_4_sas=cadical:si=on:cbe=off:nwc=20:random_seed=3587012919:st=6:s2a=on:i=515:sd=2:nm=2:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/515Mi)
% 4.20/1.01 % (206401)Instruction limit reached!
% 4.20/1.01 % (206401)------------------------------
% 4.20/1.01 % (206401)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/1.02 % (206401)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.02 % (206401)CaDiCaL version: 2.1.3
% 4.20/1.02 % (206401)Termination reason: Instruction limit
% 4.20/1.02 % (206401)Termination phase: Saturation
% 4.20/1.02 % (206401)Time elapsed: 0.051 s
% 4.20/1.02 % (206401)Peak memory usage: 12 MB
% 4.20/1.02 % (206401)Instructions burned: 97 (million)
% 4.20/1.02 % (206410)lrs+1002_1_cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:random_seed=3772843615:st=1.5:i=130:rtra=on:ss=axioms_2994 on theBenchmark for (2994ds/130Mi)
% 4.20/1.02 % (206378)Instruction limit reached!
% 4.20/1.02 % (206378)------------------------------
% 4.20/1.02 % (206378)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/1.02 % (206378)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.02 % (206378)CaDiCaL version: 2.1.3
% 4.20/1.02 % (206378)Termination reason: Instruction limit
% 4.20/1.02 % (206378)Termination phase: Saturation
% 4.20/1.02 % (206378)Time elapsed: 0.241 s
% 4.20/1.02 % (206378)Peak memory usage: 15 MB
% 4.20/1.02 % (206378)Instructions burned: 481 (million)
% 4.20/1.02 % (206412)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=1901429887:i=44:ep=R:rtra=on:ntd=on_2994 on theBenchmark for (2994ds/44Mi)
% 4.20/1.02 % (206412)Instruction limit reached!
% 4.20/1.02 % (206412)------------------------------
% 4.20/1.02 % (206412)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/1.02 % (206412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.02 % (206412)CaDiCaL version: 2.1.3
% 4.20/1.02 % (206412)Termination reason: Instruction limit
% 4.20/1.02 % (206412)Termination phase: Saturation
% 4.20/1.02 % (206412)Time elapsed: 0.024 s
% 4.20/1.02 % (206412)Peak memory usage: 12 MB
% 4.20/1.02 % (206412)Instructions burned: 46 (million)
% 4.20/1.02 % (206399)Instruction limit reached!
% 4.20/1.02 % (206399)------------------------------
% 4.20/1.02 % (206399)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/1.02 % (206399)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.02 % (206399)CaDiCaL version: 2.1.3
% 4.20/1.02 % (206399)Termination reason: Instruction limit
% 4.20/1.02 % (206399)Termination phase: Saturation
% 4.20/1.02 % (206399)Time elapsed: 0.131 s
% 4.20/1.02 % (206399)Peak memory usage: 14 MB
% 4.20/1.02 % (206399)Instructions burned: 248 (million)
% 4.20/1.02 % (206410)Instruction limit reached!
% 4.20/1.02 % (206410)------------------------------
% 4.20/1.02 % (206410)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/1.02 % (206410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.02 % (206410)CaDiCaL version: 2.1.3
% 4.20/1.02 % (206410)Termination reason: Instruction limit
% 4.20/1.02 % (206410)Termination phase: Saturation
% 4.20/1.02 % (206410)Time elapsed: 0.067 s
% 4.20/1.02 % (206410)Peak memory usage: 12 MB
% 4.20/1.02 % (206410)Instructions burned: 131 (million)
% 4.20/1.02 % (206414)lrs+1010_8:1_sil=128000:fde=unused:e2e=on:si=on:sos=on:urr=on:uwa=one_side_constant:fd=off:random_seed=4234211427:s2a=on:i=571:nm=16:rtra=on_2993 on theBenchmark for (2993ds/571Mi)
% 4.20/1.02 % (206415)dis+1010_8_to=lpo:sil=128000:tgt=ground:si=on:sp=reverse_frequency:cbe=off:uwa=off:random_seed=947045403:i=450:rtra=on:ixr=off:ntd=on_2993 on theBenchmark for (2993ds/450Mi)
% 4.20/1.02 % (206414)Refutation not found, incomplete strategy
% 4.20/1.02 % (206414)------------------------------
% 4.20/1.02 % (206414)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/1.02 % (206414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.02 % (206414)CaDiCaL version: 2.1.3
% 4.20/1.02 % (206414)Termination reason: Refutation not found, incomplete strategy
% 4.20/1.02 % (206414)Time elapsed: 0.010 s
% 4.20/1.02 % (206414)Peak memory usage: 12 MB
% 4.20/1.02 % (206414)Instructions burned: 18 (million)
% 4.20/1.02 % (206414)------------------------------
% 4.20/1.02 % (206414)------------------------------
% 4.20/1.02 % (206416)lrs+10_5:1_to=lpo:sil=128000:si=on:uwa=one_side_interpreted:random_seed=1819740238:cts=off:i=95:piset=pi_sigma:bd=all:rtra=on:ntd=on_2993 on theBenchmark for (2993ds/95Mi)
% 4.20/1.02 % (206419)lrs+1003_1_sil=128000:drc=off:cnfonf=lazy_pi_sigma_gen:si=on:uwa=one_side_interpreted:fd=off:rp=on:sac=on:random_seed=3649111086:s2a=on:i=65:add=on:bd=preordered:ins=10:rtra=on_2993 on theBenchmark for (2993ds/65Mi)
% 4.20/1.02 % (206402)Instruction limit reached!
% 4.20/1.02 % (206402)------------------------------
% 4.20/1.02 % (206402)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/1.02 % (206402)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.02 % (206402)CaDiCaL version: 2.1.3
% 4.20/1.02 % (206402)Termination reason: Instruction limit
% 4.20/1.02 % (206402)Termination phase: Saturation
% 4.20/1.02 % (206402)Time elapsed: 0.198 s
% 4.20/1.02 % (206402)Peak memory usage: 14 MB
% 4.20/1.02 % (206402)Instructions burned: 428 (million)
% 4.20/1.02 % (206416)Instruction limit reached!
% 4.20/1.02 % (206416)------------------------------
% 4.20/1.02 % (206416)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/1.02 % (206416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.02 % (206416)CaDiCaL version: 2.1.3
% 4.20/1.02 % (206416)Termination reason: Instruction limit
% 4.20/1.02 % (206416)Termination phase: Saturation
% 4.20/1.02 % (206416)Time elapsed: 0.051 s
% 4.20/1.02 % (206416)Peak memory usage: 12 MB
% 4.20/1.02 % (206416)Instructions burned: 96 (million)
% 4.20/1.02 % (206419)Instruction limit reached!
% 4.20/1.02 % (206419)------------------------------
% 4.20/1.02 % (206419)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/1.02 % (206419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.02 % (206419)CaDiCaL version: 2.1.3
% 4.20/1.02 % (206419)Termination reason: Instruction limit
% 4.20/1.02 % (206419)Termination phase: Saturation
% 4.20/1.02 % (206419)Time elapsed: 0.035 s
% 4.20/1.02 % (206419)Peak memory usage: 12 MB
% 4.20/1.02 % (206419)Instructions burned: 65 (million)
% 4.20/1.02 % (206422)dis+1010_2:1_slsqr=2,1:to=lpo:plsq=on:cnfonf=lazy_pi_sigma_gen:si=on:sp=reverse_arity:acc=on:uwa=hol:fd=preordered:s2agt=16:flr=on:pe=on:slsq=on:random_seed=717990602:uwa_fpi=on:avsq=on:s2a=on:cond=fast:i=105:s2at=1.5:aac=none:fgj=on:piset=and:hud=3:fsr=off:rtra=on:er=filter:rawr=on_2992 on theBenchmark for (2992ds/105Mi)
% 4.20/1.02 % (206423)dis+10_4:1_sfv=off:to=kbo:fde=unused:cnfonf=off:sas=cadical:e2e=on:si=on:sp=occurrence:acc=on:uwa=off:fd=preordered:foolp=on:random_seed=3308543680:hsq=on:hsqr=16,1:s2a=on:i=5755:piset=or:nm=32:rtra=on:ss=axioms:c=on:sgt=8:rawr=on_2992 on theBenchmark for (2992ds/5755Mi)
% 4.20/1.02 % (206424)lrs+10_1_sil=128000:drc=off:si=on:fs=off:urr=on:uwa=one_side_constant:random_seed=3411399028:st=10:i=375:sd=1:bd=all:fsr=off:rtra=on:ss=axioms_2992 on theBenchmark for (2992ds/375Mi)
% 4.20/1.02 % (206423)Refutation not found, incomplete strategy
% 4.20/1.02 % (206423)------------------------------
% 4.20/1.02 % (206423)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/1.02 % (206423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.02 % (206423)CaDiCaL version: 2.1.3
% 4.20/1.02 % (206423)Termination reason: Refutation not found, incomplete strategy
% 4.20/1.02 % (206423)Time elapsed: 0.004 s
% 4.20/1.02 % (206423)Peak memory usage: 12 MB
% 4.20/1.02 % (206423)Instructions burned: 6 (million)
% 4.20/1.02 % (206423)------------------------------
% 4.20/1.02 % (206423)------------------------------
% 4.20/1.02 % (206428)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=356206700:s2a=on:i=495:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2992 on theBenchmark for (2992ds/495Mi)
% 4.20/1.02 % (206415) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-206285-206415"...
% 4.20/1.02 % (206407)Instruction limit reached!
% 4.20/1.02 % (206407)------------------------------
% 4.20/1.02 % (206407)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/1.02 % (206407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.02 % (206407)CaDiCaL version: 2.1.3
% 4.20/1.02 % (206407)Termination reason: Instruction limit
% 4.20/1.02 % (206407)Termination phase: Saturation
% 4.20/1.02 % (206407)Time elapsed: 0.235 s
% 4.20/1.02 % (206407)Peak memory usage: 15 MB
% 4.20/1.02 % (206407)Instructions burned: 516 (million)
% 4.20/1.02 % (206422)Instruction limit reached!
% 4.20/1.02 % (206422)------------------------------
% 4.20/1.02 % (206422)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/1.02 % (206422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.02 % (206422)CaDiCaL version: 2.1.3
% 4.20/1.02 % (206422)Termination reason: Instruction limit
% 4.20/1.02 % (206422)Termination phase: Saturation
% 4.20/1.02 % (206422)Time elapsed: 0.050 s
% 4.20/1.02 % (206422)Peak memory usage: 13 MB
% 4.20/1.02 % (206422)Instructions burned: 107 (million)
% 4.20/1.02 % (206415)...printing done.
% 4.20/1.02 % (206415)Refutation found. Thanks to Tanya!
% 4.20/1.02 % SZS status Theorem for theBenchmark
% 4.20/1.02 % SZS output start Proof for theBenchmark
% See solution above
% 4.20/1.03 % (206415)------------------------------
% 4.20/1.03 % (206415)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.20/1.03 % (206415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.20/1.03 % (206415)CaDiCaL version: 2.1.3
% 4.20/1.03 % (206415)Termination reason: Refutation
% 4.20/1.03 % (206415)Time elapsed: 0.130 s
% 4.20/1.03 % (206415)Peak memory usage: 14 MB
% 4.20/1.03 % (206415)Instructions burned: 467 (million)
% 4.20/1.03 % (206285)Success in time 0.783 s
% 4.20/1.03 % Vampire exiting
%------------------------------------------------------------------------------