%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO447^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 08:47:43 AM UTC 2026
% Result : Theorem 0.26s 0.33s
% Output : Refutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 34
% Syntax : Number of formulae : 419 ( 83 unt; 0 typ; 21 def)
% Number of atoms : 4519 ( 847 equ; 0 cnn)
% Maximal formula atoms : 12 ( 10 avg)
% Number of connectives : 5878 (1331 ~;1398 |; 13 &;2823 @)
% ( 20 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 272 ( 272 >; 0 *; 0 +; 0 <<)
% Number of symbols : 91 ( 87 usr; 29 con; 0-4 aty)
% ( 271 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 897 ( 0 sgn 193 !; 0 ?; 897 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
rel_s5: $i > $i > $o ).
thf(func_def_33,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
q: $i > $o ).
thf(func_def_37,type,
vNOT: $o > $o ).
thf(func_def_38,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_43,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
vOR: $o > $o > $o ).
thf(func_def_45,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
vIMP: $o > $o > $o ).
thf(func_def_47,type,
vAND: $o > $o > $o ).
thf(func_def_48,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_50,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
sF0: $o ).
thf(func_def_55,type,
sK3: $i > $i ).
thf(func_def_56,type,
sK4: $i > $i ).
thf(func_def_60,type,
sK8: $i > $i ).
thf(func_def_61,type,
sK9: $i > $i ).
thf(func_def_62,type,
sK10: $i > $i ).
thf(func_def_64,type,
sK12: $i > $i ).
thf(func_def_65,type,
sK13: $i > $i ).
thf(func_def_66,type,
sK14: $i > $i ).
thf(func_def_67,type,
sK15: $i > $i ).
thf(func_def_68,type,
sK16: $i > $i ).
thf(func_def_69,type,
sK17: $i > $i ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) )
= mequiv ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X3: $i,X2: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) )
= mbox_s5 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(f33,axiom,
( mdia_s5
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',mdia_s5) ).
thf(f35,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a2) ).
thf(f36,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a3) ).
thf(f37,conjecture,
mvalid @ ( mequiv @ ( mand @ ( mdia_s5 @ p ) @ ( mbox_s5 @ q ) ) @ ( mdia_s5 @ ( mand @ p @ ( mbox_s5 @ q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mand @ ( mdia_s5 @ p ) @ ( mbox_s5 @ q ) ) @ ( mdia_s5 @ ( mand @ p @ ( mbox_s5 @ q ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f39,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f40,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
msymmetric @ rel_s5,
inference(rectify,[],[f36]) ).
thf(f42,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f41]) ).
thf(f43,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f45,plain,
~ ( mvalid @ ( mequiv @ ( mand @ ( mdia_s5 @ p ) @ ( mbox_s5 @ q ) ) @ ( mdia_s5 @ ( mand @ p @ ( mbox_s5 @ q ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f46,plain,
( ( mvalid @ ( mequiv @ ( mand @ ( mdia_s5 @ p ) @ ( mbox_s5 @ q ) ) @ ( mdia_s5 @ ( mand @ p @ ( mbox_s5 @ q ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f45]) ).
thf(f47,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) )
= mbox_s5 ),
inference(rectify,[],[f32]) ).
thf(f48,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f52,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f57,plain,
mtransitive @ rel_s5,
inference(rectify,[],[f35]) ).
thf(f58,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f57]) ).
thf(f77,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f78,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f79,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f78]) ).
thf(f80,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
=> ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f81,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f80]) ).
thf(f84,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X2 )
& ( X0 @ X1 @ X3 ) )
=> ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f85,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f84]) ).
thf(f96,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f99,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f100,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f99]) ).
thf(f101,plain,
( ( mvalid @ ( mequiv @ ( mand @ ( mdia_s5 @ p ) @ ( mbox_s5 @ q ) ) @ ( mdia_s5 @ ( mand @ p @ ( mbox_s5 @ q ) ) ) ) )
!= $true ),
inference(flattening,[],[f46]) ).
thf(f102,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f106,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f79]) ).
thf(f111,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f58]) ).
thf(f112,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f42]) ).
thf(f117,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f122,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f125,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f96]) ).
thf(f126,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f85]) ).
thf(f127,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f77]) ).
thf(f131,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f132,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f134,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f100]) ).
thf(f135,plain,
( ( mvalid @ ( mequiv @ ( mand @ ( mdia_s5 @ p ) @ ( mbox_s5 @ q ) ) @ ( mdia_s5 @ ( mand @ p @ ( mbox_s5 @ q ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f101]) ).
thf(f141,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f102,f122,f106,f122,f122]) ).
thf(f142,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f125,f106,f122]) ).
thf(f144,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f127,f141,f142,f142]) ).
thf(f150,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f117,f122,f132,f122]) ).
thf(f152,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f111,f126]) ).
thf(f153,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
@ rel_s5 )
= $true ),
inference(definition_unfolding,[],[f112,f131]) ).
thf(f154,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ p
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f135,f134,f144,f141,f150,f132,f150,f141,f132]) ).
thf(f155,definition,
( sF0
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ p
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f156,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ p
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) ) ) ) )
= sF0 ),
inference(reorient_equations,[],[f155]) ).
thf(f157,plain,
$true != sF0,
inference(definition_folding,[],[f154,f156]) ).
thf(f158,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y0 @ Y1 )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f159,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y0 @ Y1 )
=> ( rel_s5 @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ X1 @ Y0 )
=> ( rel_s5 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( rel_s5 @ X1 @ Y0 )
=> ( rel_s5 @ Y0 @ X1 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel_s5 @ X1 @ X2 )
=> ( rel_s5 @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X2 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y2 @ Y0 )
& ( rel_s5 @ Y0 @ Y1 ) )
=> ( rel_s5 @ Y2 @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f165,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y2 @ Y0 )
& ( rel_s5 @ Y0 @ Y1 ) )
=> ( rel_s5 @ Y2 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y1 @ X1 )
& ( rel_s5 @ X1 @ Y0 ) )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y1 @ X1 )
& ( rel_s5 @ X1 @ Y0 ) )
=> ( rel_s5 @ Y1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s5 @ Y0 @ X1 )
& ( rel_s5 @ X1 @ X2 ) )
=> ( rel_s5 @ Y0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s5 @ Y0 @ X1 )
& ( rel_s5 @ X1 @ X2 ) )
=> ( rel_s5 @ Y0 @ X2 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( rel_s5 @ X3 @ X1 )
& ( rel_s5 @ X1 @ X2 ) )
=> ( rel_s5 @ X3 @ X2 ) )
= $true ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f171,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s5 @ X3 @ X2 )
= $true )
| ( $false
= ( ( rel_s5 @ X3 @ X1 )
& ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X3 @ X1 ) )
| ( ( rel_s5 @ X3 @ X2 )
= $true )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f171]) ).
thf(f174,plain,
( ( $true = sF0 )
| ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ p
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) ) ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f156]) ).
thf(f175,plain,
( ( $true = sF0 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) )
| ~ ( p @ Y1 ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) )
| ~ ( p @ Y1 ) ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
( ( $true = sF0 )
| ( $false
= ( ^ [Y0: $i] :
~ ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) )
| ~ ( p @ Y1 ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) )
| ~ ( p @ Y1 ) ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( ( $false
= ( ~ ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f176]) ).
thf(f178,plain,
( ( $true
= ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f179,plain,
( ( $true
= ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) ) ) )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) )
= $true )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f178]) ).
thf(f180,plain,
( ( $false
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) ) )
| ( $true = sF0 )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) ) )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) )
= $true )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f182,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) )
= $true )
| ( $true = sF0 )
| ( $false
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f183,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) )
| ( $true = sF0 )
| ( $false
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f184,plain,
( ( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) )
| ( $true = sF0 )
| ( $false
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f185,plain,
( ( $true = sF0 )
| ( $false
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f186,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f185]) ).
thf(f187,plain,
( ( $true = sF0 )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) )
= $true )
| ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f186]) ).
thf(f188,plain,
( ( $true = sF0 )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) )
| ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f189,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true = sF0 )
| ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f188]) ).
thf(f190,plain,
( ( $true = sF0 )
| ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ sK2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f189]) ).
thf(f191,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) )
| ( $true = sF0 )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ sK2 ) ) ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f192,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ sK2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f191]) ).
thf(f193,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ sK2 ) )
| ( $true = sF0 )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) )
@ X1 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X2: $i,X1: $i] :
( ( $true = sF0 )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) )
@ X1 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ sK2 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s5 @ sK1 @ X1 )
| ~ ( p @ X1 ) )
= $true )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ X2 ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK2 )
| ( q @ sK2 ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f194]) ).
thf(f196,plain,
! [X2: $i,X1: $i] :
( ( $true = sF0 )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK2 )
| ( q @ sK2 ) ) )
| ( ( ~ ( p @ X1 ) )
= $true )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ X2 ) ) ) ) ),
inference(or_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( ( ~ ( p @ X1 ) )
= $true )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK2 )
| ( q @ sK2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ X2 ) ) ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ X2 ) ) ) )
| ( $true = sF0 )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK2 )
| ( q @ sK2 ) ) ) ),
inference(not_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 ) ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK2 )
| ( q @ sK2 ) ) )
| ( $true = sF0 )
| ( $true
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ X2 ) ) ) ) ),
inference(or_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ X2 ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK2 )
| ( q @ sK2 ) ) )
| ( $false
= ( p @ X1 ) )
| ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK1 @ sK2 )
| ( q @ sK2 ) ) )
| ( $false
= ( p @ X1 ) )
| ( $true = sF0 )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ X2 ) ) ) )
| ( ( rel_s5 @ sK1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( q @ sK2 ) )
| ( $false
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ X2 ) ) ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f201]) ).
thf(f203,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK2 ) ) )
| ( $false
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ X2 ) ) ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true = sF0 )
| ( $false
= ( p @ X1 ) ) ),
inference(or_proxy_clausification,[],[f201]) ).
thf(f204,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $false
= ( p @ X1 ) )
| ( $true = sF0 )
| ( $true
= ( rel_s5 @ sK1 @ sK2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ X2 ) ) ) ) ),
inference(not_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK2 ) )
| ( $true = sF0 )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $true
= ( rel_s5 @ sK1 @ sK2 ) )
| ( $false
= ( p @ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) ) ) )
= $true )
| ( $true = sF0 )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( ( ~ ( p @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK1 @ sK2 ) )
| ( $true = sF0 )
| ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $false
= ( p @ X1 ) )
| ( ( ~ ( p @ X2 ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) ) )
= $false )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true = sF0 )
| ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $false
= ( p @ X2 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $true = sF0 )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) )
@ ( sK3 @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK2 ) )
| ( $false
= ( p @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f208]) ).
thf(f210,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ X2 @ ( sK3 @ X2 ) )
| ( q @ ( sK3 @ X2 ) ) ) )
| ( $true
= ( rel_s5 @ sK1 @ sK2 ) )
| ( $true = sF0 )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f209]) ).
thf(f211,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK1 @ sK2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true = sF0 )
| ( $false
= ( q @ ( sK3 @ X2 ) ) )
| ( $false
= ( p @ X2 ) )
| ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $false
= ( p @ X1 ) ) ),
inference(or_proxy_clausification,[],[f210]) ).
thf(f212,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ X1 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK2 ) )
| ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $false
= ( p @ X2 ) )
| ( $true = sF0 )
| ( $false
= ( ~ ( rel_s5 @ X2 @ ( sK3 @ X2 ) ) ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f210]) ).
thf(f213,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( ( rel_s5 @ X2 @ ( sK3 @ X2 ) )
= $true )
| ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $true
= ( rel_s5 @ sK1 @ sK2 ) )
| ( $false
= ( p @ X1 ) )
| ( $true = sF0 )
| ( $false
= ( p @ X2 ) ) ),
inference(not_proxy_clausification,[],[f212]) ).
thf(f214,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ X2 ) ) )
| ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $false
= ( q @ sK2 ) )
| ( $false
= ( p @ X1 ) )
| ( $true = sF0 )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f202]) ).
thf(f215,plain,
! [X2: $i,X1: $i] :
( ( $true = sF0 )
| ( $false
= ( q @ sK2 ) )
| ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) ) ) )
= $true )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( ( ~ ( p @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f214]) ).
thf(f216,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) ) )
= $false )
| ( ( ~ ( p @ X2 ) )
= $true )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $true = sF0 )
| ( $false
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f215]) ).
thf(f217,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ X1 ) )
| ( $false
= ( q @ sK2 ) )
| ( ( ~ ( p @ X2 ) )
= $true )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) )
@ ( sK4 @ X2 ) ) )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f216]) ).
thf(f218,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ( q @ Y0 ) )
@ ( sK4 @ X2 ) ) )
| ( $false
= ( p @ X2 ) )
| ( $true = sF0 )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( q @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f217]) ).
thf(f219,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $true = sF0 )
| ( $false
= ( ~ ( rel_s5 @ X2 @ ( sK4 @ X2 ) )
| ( q @ ( sK4 @ X2 ) ) ) )
| ( $false
= ( q @ sK2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( p @ X2 ) ) ),
inference(beta-eta_normalization,[],[f218]) ).
thf(f220,plain,
! [X2: $i,X1: $i] :
( ( $true = sF0 )
| ( $false
= ( q @ sK2 ) )
| ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( q @ ( sK4 @ X2 ) ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f219]) ).
thf(f221,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ X2 @ ( sK4 @ X2 ) ) ) )
| ( $false
= ( p @ X1 ) )
| ( $true = sF0 )
| ( $false
= ( q @ sK2 ) )
| ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $false
= ( p @ X2 ) ) ),
inference(or_proxy_clausification,[],[f219]) ).
thf(f222,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X2 ) )
| ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( q @ sK2 ) )
| ( $true
= ( rel_s5 @ X2 @ ( sK4 @ X2 ) ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f221]) ).
thf(f223,plain,
( ( $true = sF0 )
| ( $false
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f224,plain,
( ( $true = sF0 )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f223]) ).
thf(f225,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) )
= $true )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
= $true )
| ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) )
= $true )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f224]) ).
thf(f226,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) )
= $true )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f225]) ).
thf(f227,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true = sF0 )
| ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f226]) ).
thf(f228,plain,
( ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) )
= $true )
| ( $true = sF0 )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ sK5 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f227]) ).
thf(f229,plain,
( ( $true = sF0 )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ sK5 ) ) ),
inference(not_proxy_clausification,[],[f228]) ).
thf(f230,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) )
= $true )
| ( $true = sF0 )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ sK5 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f229]) ).
thf(f231,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ sK5 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) )
@ X1 )
= $true )
| ( $true = sF0 )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f230]) ).
thf(f233,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) )
@ X1 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ sK5 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f231]) ).
thf(f234,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) )
@ X1 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ sK5 ) )
| ( $true = sF0 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f233]) ).
thf(f235,plain,
! [X2: $i,X1: $i] :
( ( $true = sF0 )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ sK5 ) ) ),
inference(pi_proxy_clausification,[],[f234]) ).
thf(f236,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK1 @ sK5 )
| ( q @ sK5 ) ) )
| ( $true = sF0 )
| ( ( ~ ( rel_s5 @ sK1 @ X1 )
| ~ ( p @ X1 ) )
= $true )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 )
| ( q @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f235]) ).
thf(f237,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK5 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 )
| ( q @ X2 ) ) )
| ( ( ~ ( rel_s5 @ sK1 @ X1 )
| ~ ( p @ X1 ) )
= $true )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f236]) ).
thf(f238,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK1 @ sK5 ) ) )
| ( $true = sF0 )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 )
| ( q @ X2 ) ) )
| ( ( ~ ( rel_s5 @ sK1 @ X1 )
| ~ ( p @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f236]) ).
thf(f239,plain,
! [X2: $i,X1: $i] :
( ( $true = sF0 )
| ( $true
= ( rel_s5 @ sK1 @ sK5 ) )
| ( ( ~ ( rel_s5 @ sK1 @ X1 )
| ~ ( p @ X1 ) )
= $true )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 )
| ( q @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f238]) ).
thf(f240,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true
= ( rel_s5 @ sK1 @ sK5 ) )
| ( $true = sF0 )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 )
| ( q @ X2 ) ) )
| ( ( ~ ( p @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f239]) ).
thf(f241,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 )
| ( q @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true = sF0 )
| ( ( ~ ( p @ X1 ) )
= $true )
| ( $true
= ( rel_s5 @ sK1 @ sK5 ) ) ),
inference(not_proxy_clausification,[],[f240]) ).
thf(f242,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( p @ X1 ) )
= $true )
| ( $true = sF0 )
| ( $true
= ( rel_s5 @ sK1 @ sK5 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 ) ) )
| ( $true
= ( q @ X2 ) ) ),
inference(or_proxy_clausification,[],[f241]) ).
thf(f243,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK5 ) )
| ( $true = sF0 )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 ) ) )
| ( $true
= ( q @ X2 ) ) ),
inference(not_proxy_clausification,[],[f242]) ).
thf(f244,plain,
! [X2: $i,X1: $i] :
( ( $true = sF0 )
| ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK5 ) )
| ( $false
= ( p @ X1 ) )
| ( $true
= ( q @ X2 ) ) ),
inference(not_proxy_clausification,[],[f243]) ).
thf(f245,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 ) ) )
| ( $false
= ( q @ sK5 ) )
| ( $true = sF0 )
| ( ( ~ ( rel_s5 @ sK1 @ X1 )
| ~ ( p @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f237]) ).
thf(f246,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s5 @ sK1 @ X1 )
| ~ ( p @ X1 ) )
= $true )
| ( $true
= ( q @ X2 ) )
| ( $true = sF0 )
| ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $false
= ( q @ sK5 ) ) ),
inference(not_proxy_clausification,[],[f245]) ).
thf(f247,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true
= ( q @ X2 ) )
| ( $true = sF0 )
| ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( ( ~ ( p @ X1 ) )
= $true )
| ( $false
= ( q @ sK5 ) ) ),
inference(or_proxy_clausification,[],[f246]) ).
thf(f248,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $false
= ( q @ sK5 ) )
| ( $true = sF0 )
| ( $true
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( ( ~ ( p @ X1 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f247]) ).
thf(f249,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( q @ sK5 ) )
| ( $true
= ( q @ X2 ) )
| ( $false
= ( p @ X1 ) )
| ( $true = sF0 )
| ( ( rel_s5 @ sK1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f248]) ).
thf(f276,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) )
= $true )
| ( $true = sF0 )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f277,plain,
( ( $true = sF0 )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f276]) ).
thf(f278,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) )
| ( $true = sF0 )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f277]) ).
thf(f279,plain,
( ( $true = sF0 )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) )
@ sK7 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f278]) ).
thf(f280,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) )
@ sK7 ) )
| ( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f279]) ).
thf(f326,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) )
@ sK7 ) )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
= $true )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f280]) ).
thf(f327,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
| ( $true = sF0 )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) )
@ sK7 ) ) ),
inference(not_proxy_clausification,[],[f326]) ).
thf(f328,plain,
( ( $true = sF0 )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) )
@ sK7 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f327]) ).
thf(f329,plain,
( ( $true = sF0 )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) )
@ sK7 ) ) ),
inference(or_proxy_clausification,[],[f327]) ).
thf(f330,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) )
@ sK7 ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f329]) ).
thf(f331,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) )
@ sK7 ) )
| ( $true = sF0 )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f330]) ).
thf(f332,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK1 @ sK7 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ sK7 ) ) ) )
| ( $true = sF0 )
| ( ( ~ ( rel_s5 @ sK1 @ X1 )
| ( q @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f331]) ).
thf(f333,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ sK7 ) ) ) )
| ( ( ~ ( rel_s5 @ sK1 @ X1 )
| ( q @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f332]) ).
thf(f334,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK7 ) ) )
| ( ( ~ ( rel_s5 @ sK1 @ X1 )
| ( q @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f332]) ).
thf(f335,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( ( ~ ( rel_s5 @ sK1 @ X1 )
| ( q @ X1 ) )
= $true )
| ( ( rel_s5 @ sK1 @ sK7 )
= $true ) ),
inference(not_proxy_clausification,[],[f334]) ).
thf(f336,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true = sF0 )
| ( ( rel_s5 @ sK1 @ sK7 )
= $true ) ),
inference(or_proxy_clausification,[],[f335]) ).
thf(f337,plain,
! [X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( q @ X1 ) )
| ( $true = sF0 )
| ( ( rel_s5 @ sK1 @ sK7 )
= $true ) ),
inference(not_proxy_clausification,[],[f336]) ).
thf(f338,plain,
! [X1: $i] :
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ sK7 ) ) ) )
| ( $true = sF0 )
| ( ( ~ ( rel_s5 @ sK1 @ X1 )
| ( q @ X1 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f333]) ).
thf(f339,plain,
! [X1: $i] :
( ( ( ~ ( rel_s5 @ sK1 @ X1 )
| ( q @ X1 ) )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ sK7 ) ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f338]) ).
thf(f340,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ sK7 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f339]) ).
thf(f341,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true = sF0 )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( ~ ( p @ sK7 ) ) ) ),
inference(or_proxy_clausification,[],[f340]) ).
thf(f342,plain,
! [X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true = sF0 )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true
= ( q @ X1 ) ) ),
inference(or_proxy_clausification,[],[f340]) ).
thf(f343,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( q @ X1 ) )
| ( $true = sF0 )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f342]) ).
thf(f344,plain,
! [X2: $i,X1: $i] :
( ( $true = sF0 )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f343]) ).
thf(f345,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $true = sF0 )
| ( $true
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f344]) ).
thf(f346,plain,
! [X2: $i,X1: $i] :
( ( $true = sF0 )
| ( $true
= ( ~ ( rel_s5 @ sK7 @ X2 )
| ( q @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( q @ X1 ) ) ),
inference(beta-eta_normalization,[],[f345]) ).
thf(f347,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK7 @ X2 ) ) )
| ( $true
= ( q @ X2 ) )
| ( $true = sF0 )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f346]) ).
thf(f348,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( rel_s5 @ sK7 @ X2 ) )
| ( $true = sF0 )
| ( $true
= ( q @ X2 ) )
| ( $true
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f347]) ).
thf(f349,plain,
! [X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( ~ ( p @ sK7 ) ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f341]) ).
thf(f350,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( ( p @ sK7 )
= $true )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f349]) ).
thf(f351,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
| ( $true = sF0 )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) )
@ sK7 ) ) ),
inference(not_proxy_clausification,[],[f328]) ).
thf(f352,plain,
( ( $true = sF0 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) )
@ sK7 ) ) ),
inference(not_proxy_clausification,[],[f351]) ).
thf(f353,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK11 ) )
| ( $true = sF0 )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) )
@ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f352]) ).
thf(f354,plain,
( ( $false
= ( ~ ( rel_s5 @ sK1 @ sK7 )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ sK7 ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK11 )
| ~ ( p @ sK11 ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f353]) ).
thf(f355,plain,
( ( $false
= ( ~ ( rel_s5 @ sK1 @ sK11 )
| ~ ( p @ sK11 ) ) )
| ( $true = sF0 )
| ( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ sK7 ) ) ) ) ),
inference(or_proxy_clausification,[],[f354]) ).
thf(f356,plain,
( ( $false
= ( ~ ( rel_s5 @ sK1 @ sK11 )
| ~ ( p @ sK11 ) ) )
| ( $true = sF0 )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK7 ) ) ) ),
inference(or_proxy_clausification,[],[f354]) ).
thf(f357,plain,
( ( $false
= ( ~ ( rel_s5 @ sK1 @ sK7 ) ) )
| ( $true = sF0 )
| ( $false
= ( ~ ( p @ sK11 ) ) ) ),
inference(or_proxy_clausification,[],[f356]) ).
thf(f358,plain,
( ( $false
= ( ~ ( rel_s5 @ sK1 @ sK11 ) ) )
| ( $true = sF0 )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK7 ) ) ) ),
inference(or_proxy_clausification,[],[f356]) ).
thf(f359,plain,
( ( $false
= ( ~ ( rel_s5 @ sK1 @ sK7 ) ) )
| ( $true = sF0 )
| ( $true
= ( rel_s5 @ sK1 @ sK11 ) ) ),
inference(not_proxy_clausification,[],[f358]) ).
thf(f360,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK11 ) )
| ( $true = sF0 )
| ( ( rel_s5 @ sK1 @ sK7 )
= $true ) ),
inference(not_proxy_clausification,[],[f359]) ).
thf(f361,plain,
( ( $false
= ( ~ ( p @ sK11 ) ) )
| ( $true = sF0 )
| ( ( rel_s5 @ sK1 @ sK7 )
= $true ) ),
inference(not_proxy_clausification,[],[f357]) ).
thf(f362,plain,
( ( ( p @ sK11 )
= $true )
| ( ( rel_s5 @ sK1 @ sK7 )
= $true )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f361]) ).
thf(f363,plain,
( ( $true = sF0 )
| ( $false
= ( ~ ( p @ sK11 ) ) )
| ( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ sK7 ) ) ) ) ),
inference(or_proxy_clausification,[],[f355]) ).
thf(f364,plain,
( ( $true = sF0 )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK11 ) ) )
| ( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ sK7 ) ) ) ) ),
inference(or_proxy_clausification,[],[f355]) ).
thf(f365,plain,
( ( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ sK7 ) ) ) )
| ( $true
= ( rel_s5 @ sK1 @ sK11 ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f364]) ).
thf(f366,plain,
( ( $true = sF0 )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ sK7 ) ) ) )
| ( $true
= ( rel_s5 @ sK1 @ sK11 ) ) ),
inference(not_proxy_clausification,[],[f365]) ).
thf(f367,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ sK7 ) ) )
| ( $true
= ( rel_s5 @ sK1 @ sK11 ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f366]) ).
thf(f368,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK11 ) )
| ( $true = sF0 )
| ( $false
= ( ~ ( p @ sK7 ) ) ) ),
inference(or_proxy_clausification,[],[f367]) ).
thf(f369,plain,
( ( $true = sF0 )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( rel_s5 @ sK1 @ sK11 ) ) ),
inference(or_proxy_clausification,[],[f367]) ).
thf(f370,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( rel_s5 @ sK1 @ sK11 ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f369]) ).
thf(f371,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK11 ) ) ),
inference(pi_proxy_clausification,[],[f370]) ).
thf(f372,plain,
! [X1: $i] :
( ( ( ~ ( rel_s5 @ sK7 @ X1 )
| ( q @ X1 ) )
= $true )
| ( $true
= ( rel_s5 @ sK1 @ sK11 ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f371]) ).
thf(f373,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( ( ~ ( rel_s5 @ sK7 @ X1 ) )
= $true )
| ( $true = sF0 )
| ( $true
= ( rel_s5 @ sK1 @ sK11 ) ) ),
inference(or_proxy_clausification,[],[f372]) ).
thf(f374,plain,
! [X1: $i] :
( ( $false
= ( rel_s5 @ sK7 @ X1 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK11 ) )
| ( $true = sF0 )
| ( $true
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f373]) ).
thf(f375,plain,
( ( $true = sF0 )
| ( $true
= ( rel_s5 @ sK1 @ sK11 ) )
| ( ( p @ sK7 )
= $true ) ),
inference(not_proxy_clausification,[],[f368]) ).
thf(f376,plain,
( ( ( p @ sK11 )
= $true )
| ( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ sK7 ) ) ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f363]) ).
thf(f377,plain,
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ sK7 ) ) ) )
| ( ( p @ sK11 )
= $true )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f376]) ).
thf(f378,plain,
( ( $true = sF0 )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ sK7 ) ) )
| ( ( p @ sK11 )
= $true ) ),
inference(not_proxy_clausification,[],[f377]) ).
thf(f379,plain,
( ( $true = sF0 )
| ( ( p @ sK11 )
= $true )
| ( $false
= ( ~ ( p @ sK7 ) ) ) ),
inference(or_proxy_clausification,[],[f378]) ).
thf(f380,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true = sF0 )
| ( ( p @ sK11 )
= $true ) ),
inference(or_proxy_clausification,[],[f378]) ).
thf(f381,plain,
( ( $true = sF0 )
| ( ( p @ sK11 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f380]) ).
thf(f382,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( ( p @ sK11 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK7 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f381]) ).
thf(f383,plain,
! [X1: $i] :
( ( ( ~ ( rel_s5 @ sK7 @ X1 )
| ( q @ X1 ) )
= $true )
| ( ( p @ sK11 )
= $true )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f382]) ).
thf(f384,plain,
! [X1: $i] :
( ( ( p @ sK11 )
= $true )
| ( $true
= ( q @ X1 ) )
| ( ( ~ ( rel_s5 @ sK7 @ X1 ) )
= $true )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f383]) ).
thf(f385,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_s5 @ sK7 @ X1 ) )
| ( ( p @ sK11 )
= $true ) ),
inference(not_proxy_clausification,[],[f384]) ).
thf(f386,plain,
( ( ( p @ sK7 )
= $true )
| ( ( p @ sK11 )
= $true )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f379]) ).
thf(f502,definition,
( spl18_1
<=> ( $true
= ( rel_s5 @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_1])],[avatar_definition]) ).
thf(f504,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK2 ) )
| ~ spl18_1 ),
inference(avatar_component_clause,[],[f502]) ).
thf(f506,definition,
( spl18_2
<=> ! [X2: $i] :
( ( ( rel_s5 @ X2 @ ( sK3 @ X2 ) )
= $true )
| ( $false
= ( p @ X2 ) )
| ( ( rel_s5 @ sK1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl18_2])],[avatar_definition]) ).
thf(f507,plain,
( ! [X2: $i] :
( ( ( rel_s5 @ X2 @ ( sK3 @ X2 ) )
= $true )
| ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $false
= ( p @ X2 ) ) )
| ~ spl18_2 ),
inference(avatar_component_clause,[],[f506]) ).
thf(f509,definition,
( spl18_3
<=> ! [X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl18_3])],[avatar_definition]) ).
thf(f510,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) ) )
| ~ spl18_3 ),
inference(avatar_component_clause,[],[f509]) ).
thf(f512,definition,
( spl18_4
<=> ( $true = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl18_4])],[avatar_definition]) ).
thf(f515,plain,
( spl18_1
| spl18_2
| spl18_3
| spl18_4 ),
inference(avatar_split_clause,[],[f213,f512,f509,f506,f502]) ).
thf(f517,definition,
( spl18_5
<=> ! [X2: $i] :
( ( $false
= ( q @ ( sK3 @ X2 ) ) )
| ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $false
= ( p @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl18_5])],[avatar_definition]) ).
thf(f518,plain,
( ! [X2: $i] :
( ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $false
= ( q @ ( sK3 @ X2 ) ) )
| ( $false
= ( p @ X2 ) ) )
| ~ spl18_5 ),
inference(avatar_component_clause,[],[f517]) ).
thf(f519,plain,
( spl18_4
| spl18_1
| spl18_3
| spl18_5 ),
inference(avatar_split_clause,[],[f211,f517,f509,f502,f512]) ).
thf(f521,definition,
( spl18_6
<=> ( $false
= ( q @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_6])],[avatar_definition]) ).
thf(f523,plain,
( ( $false
= ( q @ sK2 ) )
| ~ spl18_6 ),
inference(avatar_component_clause,[],[f521]) ).
thf(f525,definition,
( spl18_7
<=> ! [X2: $i] :
( ( $false
= ( p @ X2 ) )
| ( $true
= ( rel_s5 @ X2 @ ( sK4 @ X2 ) ) )
| ( ( rel_s5 @ sK1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl18_7])],[avatar_definition]) ).
thf(f526,plain,
( ! [X2: $i] :
( ( $true
= ( rel_s5 @ X2 @ ( sK4 @ X2 ) ) )
| ( $false
= ( p @ X2 ) )
| ( ( rel_s5 @ sK1 @ X2 )
= $false ) )
| ~ spl18_7 ),
inference(avatar_component_clause,[],[f525]) ).
thf(f527,plain,
( spl18_3
| spl18_4
| spl18_6
| spl18_7 ),
inference(avatar_split_clause,[],[f222,f525,f521,f512,f509]) ).
thf(f529,definition,
( spl18_8
<=> ! [X2: $i] :
( ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( q @ ( sK4 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl18_8])],[avatar_definition]) ).
thf(f530,plain,
( ! [X2: $i] :
( ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( q @ ( sK4 @ X2 ) ) ) )
| ~ spl18_8 ),
inference(avatar_component_clause,[],[f529]) ).
thf(f531,plain,
( spl18_6
| spl18_8
| spl18_4
| spl18_3 ),
inference(avatar_split_clause,[],[f220,f509,f512,f529,f521]) ).
thf(f533,definition,
( spl18_9
<=> ! [X2: $i] :
( ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $true
= ( q @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl18_9])],[avatar_definition]) ).
thf(f534,plain,
( ! [X2: $i] :
( ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $true
= ( q @ X2 ) ) )
| ~ spl18_9 ),
inference(avatar_component_clause,[],[f533]) ).
thf(f536,definition,
( spl18_10
<=> ( $true
= ( rel_s5 @ sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_10])],[avatar_definition]) ).
thf(f538,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK5 ) )
| ~ spl18_10 ),
inference(avatar_component_clause,[],[f536]) ).
thf(f539,plain,
( spl18_3
| spl18_4
| spl18_9
| spl18_10 ),
inference(avatar_split_clause,[],[f244,f536,f533,f512,f509]) ).
thf(f541,definition,
( spl18_11
<=> ( $false
= ( q @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_11])],[avatar_definition]) ).
thf(f543,plain,
( ( $false
= ( q @ sK5 ) )
| ~ spl18_11 ),
inference(avatar_component_clause,[],[f541]) ).
thf(f544,plain,
( spl18_4
| spl18_11
| spl18_9
| spl18_3 ),
inference(avatar_split_clause,[],[f249,f509,f533,f541,f512]) ).
thf(f558,definition,
( spl18_14
<=> ( ( rel_s5 @ sK1 @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl18_14])],[avatar_definition]) ).
thf(f560,plain,
( ( ( rel_s5 @ sK1 @ sK7 )
= $true )
| ~ spl18_14 ),
inference(avatar_component_clause,[],[f558]) ).
thf(f570,definition,
( spl18_17
<=> ! [X2: $i] :
( ( $false
= ( rel_s5 @ sK7 @ X2 ) )
| ( $true
= ( q @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl18_17])],[avatar_definition]) ).
thf(f571,plain,
( ! [X2: $i] :
( ( $false
= ( rel_s5 @ sK7 @ X2 ) )
| ( $true
= ( q @ X2 ) ) )
| ~ spl18_17 ),
inference(avatar_component_clause,[],[f570]) ).
thf(f584,definition,
( spl18_21
<=> ( ( p @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl18_21])],[avatar_definition]) ).
thf(f586,plain,
( ( ( p @ sK7 )
= $true )
| ~ spl18_21 ),
inference(avatar_component_clause,[],[f584]) ).
thf(f592,plain,
( spl18_4
| spl18_14
| spl18_9 ),
inference(avatar_split_clause,[],[f337,f533,f558,f512]) ).
thf(f593,plain,
( spl18_9
| spl18_17
| spl18_4 ),
inference(avatar_split_clause,[],[f348,f512,f570,f533]) ).
thf(f594,plain,
( spl18_4
| spl18_9
| spl18_21 ),
inference(avatar_split_clause,[],[f350,f584,f533,f512]) ).
thf(f596,definition,
( spl18_23
<=> ( $true
= ( rel_s5 @ sK1 @ sK11 ) ) ),
introduced(definition,[new_symbols(definition,[spl18_23])],[avatar_definition]) ).
thf(f598,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK11 ) )
| ~ spl18_23 ),
inference(avatar_component_clause,[],[f596]) ).
thf(f599,plain,
( spl18_4
| spl18_14
| spl18_23 ),
inference(avatar_split_clause,[],[f360,f596,f558,f512]) ).
thf(f601,definition,
( spl18_24
<=> ( ( p @ sK11 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl18_24])],[avatar_definition]) ).
thf(f603,plain,
( ( ( p @ sK11 )
= $true )
| ~ spl18_24 ),
inference(avatar_component_clause,[],[f601]) ).
thf(f604,plain,
( spl18_14
| spl18_4
| spl18_24 ),
inference(avatar_split_clause,[],[f362,f601,f512,f558]) ).
thf(f605,plain,
( spl18_4
| spl18_17
| spl18_23 ),
inference(avatar_split_clause,[],[f374,f596,f570,f512]) ).
thf(f606,plain,
( spl18_23
| spl18_21
| spl18_4 ),
inference(avatar_split_clause,[],[f375,f512,f584,f596]) ).
thf(f607,plain,
( spl18_4
| spl18_17
| spl18_24 ),
inference(avatar_split_clause,[],[f385,f601,f570,f512]) ).
thf(f608,plain,
( spl18_24
| spl18_21
| spl18_4 ),
inference(avatar_split_clause,[],[f386,f512,f584,f601]) ).
thf(f661,plain,
~ spl18_4,
inference(avatar_split_clause,[],[f157,f512]) ).
thf(f676,plain,
( ( $false = $true )
| ( ( p @ sK7 )
= $false )
| ~ spl18_3
| ~ spl18_14 ),
inference(constrained_superposition,[],[f560,f510]) ).
thf(f679,plain,
( ( ( p @ sK7 )
= $false )
| ~ spl18_3
| ~ spl18_14 ),
inference(trivial_inequality_removal,[],[f676]) ).
thf(f685,plain,
( ( $false = $true )
| ~ spl18_3
| ~ spl18_14
| ~ spl18_21 ),
inference(forward_demodulation,[],[f679,f586]) ).
thf(f686,plain,
( $false
| ~ spl18_3
| ~ spl18_14
| ~ spl18_21 ),
inference(trivial_inequality_removal,[],[f685]) ).
thf(f687,plain,
( ~ spl18_3
| ~ spl18_14
| ~ spl18_21 ),
inference(avatar_contradiction_clause,[],[f686]) ).
thf(f700,plain,
( ( $false = $true )
| ( $false
= ( p @ sK11 ) )
| ~ spl18_3
| ~ spl18_23 ),
inference(constrained_superposition,[],[f598,f510]) ).
thf(f703,plain,
( ( $false
= ( p @ sK11 ) )
| ~ spl18_3
| ~ spl18_23 ),
inference(trivial_inequality_removal,[],[f700]) ).
thf(f707,plain,
( ( $false = $true )
| ~ spl18_3
| ~ spl18_23
| ~ spl18_24 ),
inference(forward_demodulation,[],[f703,f603]) ).
thf(f708,plain,
( $false
| ~ spl18_3
| ~ spl18_23
| ~ spl18_24 ),
inference(trivial_inequality_removal,[],[f707]) ).
thf(f709,plain,
( ~ spl18_3
| ~ spl18_23
| ~ spl18_24 ),
inference(avatar_contradiction_clause,[],[f708]) ).
thf(f713,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false = $true )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( ( rel_s5 @ X0 @ X2 )
= $true ) ),
inference(constrained_superposition,[],[f172,f163]) ).
thf(f715,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ sK11 @ X0 )
= $false )
| ( $true
= ( rel_s5 @ sK1 @ X0 ) )
| ( $false = $true ) )
| ~ spl18_23 ),
inference(constrained_superposition,[],[f172,f598]) ).
thf(f725,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( ( rel_s5 @ X0 @ X2 )
= $true ) ),
inference(trivial_inequality_removal,[],[f713]) ).
thf(f728,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ sK1 @ X0 ) )
| ( ( rel_s5 @ sK11 @ X0 )
= $false ) )
| ~ spl18_23 ),
inference(trivial_inequality_removal,[],[f715]) ).
thf(f748,plain,
( ( $true
= ( q @ sK2 ) )
| ( $false = $true )
| ~ spl18_1
| ~ spl18_9 ),
inference(constrained_superposition,[],[f534,f504]) ).
thf(f769,plain,
( ( $true
= ( q @ sK2 ) )
| ~ spl18_1
| ~ spl18_9 ),
inference(trivial_inequality_removal,[],[f748]) ).
thf(f781,plain,
( ( $false = $true )
| ~ spl18_1
| ~ spl18_6
| ~ spl18_9 ),
inference(forward_demodulation,[],[f769,f523]) ).
thf(f782,plain,
( $false
| ~ spl18_1
| ~ spl18_6
| ~ spl18_9 ),
inference(trivial_inequality_removal,[],[f781]) ).
thf(f783,plain,
( ~ spl18_1
| ~ spl18_6
| ~ spl18_9 ),
inference(avatar_contradiction_clause,[],[f782]) ).
thf(f788,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( rel_s5 @ sK1 @ X0 ) )
| ( ( rel_s5 @ sK5 @ X0 )
= $true ) )
| ~ spl18_10 ),
inference(constrained_superposition,[],[f725,f538]) ).
thf(f800,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X0 ) )
| ( ( rel_s5 @ sK5 @ X0 )
= $true ) )
| ~ spl18_10 ),
inference(trivial_inequality_removal,[],[f788]) ).
thf(f847,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK7 ) )
| ( ( q @ X0 )
= $true )
| ( $false = $true ) )
| ~ spl18_17 ),
inference(constrained_superposition,[],[f163,f571]) ).
thf(f849,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK7 ) )
| ( ( q @ X0 )
= $true ) )
| ~ spl18_17 ),
inference(trivial_inequality_removal,[],[f847]) ).
thf(f865,plain,
( ( ( p @ sK7 )
= $false )
| ( $false
= ( q @ ( sK3 @ sK7 ) ) )
| ( $false = $true )
| ~ spl18_5
| ~ spl18_14 ),
inference(constrained_superposition,[],[f560,f518]) ).
thf(f866,plain,
( ( $false
= ( p @ sK11 ) )
| ( $false = $true )
| ( $false
= ( q @ ( sK3 @ sK11 ) ) )
| ~ spl18_5
| ~ spl18_23 ),
inference(constrained_superposition,[],[f598,f518]) ).
thf(f869,plain,
( ( $false
= ( q @ ( sK3 @ sK11 ) ) )
| ( $false
= ( p @ sK11 ) )
| ~ spl18_5
| ~ spl18_23 ),
inference(trivial_inequality_removal,[],[f866]) ).
thf(f878,plain,
( ( $false
= ( q @ ( sK3 @ sK7 ) ) )
| ( ( p @ sK7 )
= $false )
| ~ spl18_5
| ~ spl18_14 ),
inference(trivial_inequality_removal,[],[f865]) ).
thf(f889,plain,
( ( $false
= ( q @ ( sK3 @ sK11 ) ) )
| ( $false = $true )
| ~ spl18_5
| ~ spl18_23
| ~ spl18_24 ),
inference(forward_demodulation,[],[f869,f603]) ).
thf(f890,plain,
( ( $false
= ( q @ ( sK3 @ sK11 ) ) )
| ~ spl18_5
| ~ spl18_23
| ~ spl18_24 ),
inference(trivial_inequality_removal,[],[f889]) ).
thf(f1087,plain,
( ( ( rel_s5 @ sK5 @ sK7 )
= $true )
| ( $false = $true )
| ~ spl18_10
| ~ spl18_14 ),
inference(constrained_superposition,[],[f800,f560]) ).
thf(f1104,plain,
( ( ( rel_s5 @ sK5 @ sK7 )
= $true )
| ~ spl18_10
| ~ spl18_14 ),
inference(trivial_inequality_removal,[],[f1087]) ).
thf(f1135,plain,
( ( $false = $true )
| ( $true
= ( q @ sK5 ) )
| ~ spl18_10
| ~ spl18_14
| ~ spl18_17 ),
inference(constrained_superposition,[],[f849,f1104]) ).
thf(f1143,plain,
( ( $true
= ( q @ sK5 ) )
| ~ spl18_10
| ~ spl18_14
| ~ spl18_17 ),
inference(trivial_inequality_removal,[],[f1135]) ).
thf(f1271,plain,
( ! [X0: $i] :
( ( ( q @ X0 )
= $true )
| ( ( rel_s5 @ sK11 @ X0 )
= $false )
| ( $false = $true ) )
| ~ spl18_9
| ~ spl18_23 ),
inference(constrained_superposition,[],[f728,f534]) ).
thf(f1303,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ sK11 @ X0 )
= $false )
| ( ( q @ X0 )
= $true ) )
| ~ spl18_9
| ~ spl18_23 ),
inference(trivial_inequality_removal,[],[f1271]) ).
thf(f1385,plain,
( ( $false
= ( rel_s5 @ sK1 @ sK11 ) )
| ( ( q @ ( sK3 @ sK11 ) )
= $true )
| ( $false = $true )
| ( $false
= ( p @ sK11 ) )
| ~ spl18_2
| ~ spl18_9
| ~ spl18_23 ),
inference(constrained_superposition,[],[f507,f1303]) ).
thf(f1392,plain,
( ( $false
= ( rel_s5 @ sK1 @ sK11 ) )
| ( $false
= ( p @ sK11 ) )
| ( ( q @ ( sK3 @ sK11 ) )
= $true )
| ~ spl18_2
| ~ spl18_9
| ~ spl18_23 ),
inference(trivial_inequality_removal,[],[f1385]) ).
thf(f1395,plain,
( ( $false = $true )
| ( $false
= ( p @ sK11 ) )
| ( ( q @ ( sK3 @ sK11 ) )
= $true )
| ~ spl18_2
| ~ spl18_9
| ~ spl18_23 ),
inference(forward_demodulation,[],[f1392,f598]) ).
thf(f1396,plain,
( ( ( q @ ( sK3 @ sK11 ) )
= $true )
| ( $false
= ( p @ sK11 ) )
| ~ spl18_2
| ~ spl18_9
| ~ spl18_23 ),
inference(trivial_inequality_removal,[],[f1395]) ).
thf(f1399,plain,
( ( $false
= ( p @ sK11 ) )
| ( $false = $true )
| ~ spl18_2
| ~ spl18_5
| ~ spl18_9
| ~ spl18_23
| ~ spl18_24 ),
inference(forward_demodulation,[],[f1396,f890]) ).
thf(f1400,plain,
( ( $false
= ( p @ sK11 ) )
| ~ spl18_2
| ~ spl18_5
| ~ spl18_9
| ~ spl18_23
| ~ spl18_24 ),
inference(trivial_inequality_removal,[],[f1399]) ).
thf(f1404,plain,
( ( $false = $true )
| ~ spl18_2
| ~ spl18_5
| ~ spl18_9
| ~ spl18_23
| ~ spl18_24 ),
inference(forward_demodulation,[],[f1400,f603]) ).
thf(f1405,plain,
( $false
| ~ spl18_2
| ~ spl18_5
| ~ spl18_9
| ~ spl18_23
| ~ spl18_24 ),
inference(trivial_inequality_removal,[],[f1404]) ).
thf(f1406,plain,
( ~ spl18_2
| ~ spl18_5
| ~ spl18_9
| ~ spl18_23
| ~ spl18_24 ),
inference(avatar_contradiction_clause,[],[f1405]) ).
thf(f1500,plain,
( ( ( p @ sK7 )
= $false )
| ( $false
= ( q @ ( sK4 @ sK7 ) ) )
| ( $false = $true )
| ~ spl18_8
| ~ spl18_14 ),
inference(constrained_superposition,[],[f560,f530]) ).
thf(f1501,plain,
( ( $false = $true )
| ( $false
= ( p @ sK11 ) )
| ( $false
= ( q @ ( sK4 @ sK11 ) ) )
| ~ spl18_8
| ~ spl18_23 ),
inference(constrained_superposition,[],[f598,f530]) ).
thf(f1504,plain,
( ( $false
= ( p @ sK11 ) )
| ( $false
= ( q @ ( sK4 @ sK11 ) ) )
| ~ spl18_8
| ~ spl18_23 ),
inference(trivial_inequality_removal,[],[f1501]) ).
thf(f1521,plain,
( ( ( p @ sK7 )
= $false )
| ( $false
= ( q @ ( sK4 @ sK7 ) ) )
| ~ spl18_8
| ~ spl18_14 ),
inference(trivial_inequality_removal,[],[f1500]) ).
thf(f1525,plain,
( ( $false
= ( q @ ( sK4 @ sK11 ) ) )
| ( $false = $true )
| ~ spl18_8
| ~ spl18_23
| ~ spl18_24 ),
inference(forward_demodulation,[],[f1504,f603]) ).
thf(f1526,plain,
( ( $false
= ( q @ ( sK4 @ sK11 ) ) )
| ~ spl18_8
| ~ spl18_23
| ~ spl18_24 ),
inference(trivial_inequality_removal,[],[f1525]) ).
thf(f1584,plain,
( ( $false = $true )
| ( ( p @ sK7 )
= $false )
| ( $true
= ( q @ ( sK4 @ sK7 ) ) )
| ( $false
= ( rel_s5 @ sK1 @ sK7 ) )
| ~ spl18_7
| ~ spl18_17 ),
inference(constrained_superposition,[],[f526,f571]) ).
thf(f1585,plain,
( ( $false
= ( p @ sK11 ) )
| ( $false
= ( rel_s5 @ sK1 @ sK11 ) )
| ( $false = $true )
| ( $true
= ( q @ ( sK4 @ sK11 ) ) )
| ~ spl18_7
| ~ spl18_9
| ~ spl18_23 ),
inference(constrained_superposition,[],[f526,f1303]) ).
thf(f1606,plain,
( ( $false
= ( p @ sK11 ) )
| ( $true
= ( q @ ( sK4 @ sK11 ) ) )
| ( $false
= ( rel_s5 @ sK1 @ sK11 ) )
| ~ spl18_7
| ~ spl18_9
| ~ spl18_23 ),
inference(trivial_inequality_removal,[],[f1585]) ).
thf(f1616,plain,
( ( ( p @ sK7 )
= $false )
| ( $false
= ( rel_s5 @ sK1 @ sK7 ) )
| ( $true
= ( q @ ( sK4 @ sK7 ) ) )
| ~ spl18_7
| ~ spl18_17 ),
inference(trivial_inequality_removal,[],[f1584]) ).
thf(f1623,plain,
( ( $true
= ( q @ ( sK4 @ sK11 ) ) )
| ( $false = $true )
| ( $false
= ( rel_s5 @ sK1 @ sK11 ) )
| ~ spl18_7
| ~ spl18_9
| ~ spl18_23
| ~ spl18_24 ),
inference(forward_demodulation,[],[f1606,f603]) ).
thf(f1624,plain,
( ( $true
= ( q @ ( sK4 @ sK11 ) ) )
| ( $false
= ( rel_s5 @ sK1 @ sK11 ) )
| ~ spl18_7
| ~ spl18_9
| ~ spl18_23
| ~ spl18_24 ),
inference(trivial_inequality_removal,[],[f1623]) ).
thf(f1627,plain,
( ( $false = $true )
| ( $false
= ( rel_s5 @ sK1 @ sK11 ) )
| ~ spl18_7
| ~ spl18_8
| ~ spl18_9
| ~ spl18_23
| ~ spl18_24 ),
inference(forward_demodulation,[],[f1624,f1526]) ).
thf(f1628,plain,
( ( $false
= ( rel_s5 @ sK1 @ sK11 ) )
| ~ spl18_7
| ~ spl18_8
| ~ spl18_9
| ~ spl18_23
| ~ spl18_24 ),
inference(trivial_inequality_removal,[],[f1627]) ).
thf(f1632,plain,
( ( $false = $true )
| ~ spl18_7
| ~ spl18_8
| ~ spl18_9
| ~ spl18_23
| ~ spl18_24 ),
inference(forward_demodulation,[],[f1628,f598]) ).
thf(f1633,plain,
( $false
| ~ spl18_7
| ~ spl18_8
| ~ spl18_9
| ~ spl18_23
| ~ spl18_24 ),
inference(trivial_inequality_removal,[],[f1632]) ).
thf(f1634,plain,
( ~ spl18_7
| ~ spl18_8
| ~ spl18_9
| ~ spl18_23
| ~ spl18_24 ),
inference(avatar_contradiction_clause,[],[f1633]) ).
thf(f1636,definition,
( spl18_46
<=> ( $false
= ( q @ ( sK3 @ sK7 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl18_46])],[avatar_definition]) ).
thf(f1638,plain,
( ( $false
= ( q @ ( sK3 @ sK7 ) ) )
| ~ spl18_46 ),
inference(avatar_component_clause,[],[f1636]) ).
thf(f1640,definition,
( spl18_47
<=> ( ( p @ sK7 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl18_47])],[avatar_definition]) ).
thf(f1642,plain,
( ( ( p @ sK7 )
= $false )
| ~ spl18_47 ),
inference(avatar_component_clause,[],[f1640]) ).
thf(f1645,definition,
( spl18_48
<=> ( $false
= ( q @ ( sK4 @ sK7 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl18_48])],[avatar_definition]) ).
thf(f1647,plain,
( ( $false
= ( q @ ( sK4 @ sK7 ) ) )
| ~ spl18_48 ),
inference(avatar_component_clause,[],[f1645]) ).
thf(f1655,plain,
( spl18_47
| spl18_46
| ~ spl18_5
| ~ spl18_14 ),
inference(avatar_split_clause,[],[f878,f558,f517,f1636,f1640]) ).
thf(f1658,plain,
( ( $false = $true )
| ( ( p @ sK7 )
= $false )
| ( $true
= ( q @ ( sK4 @ sK7 ) ) )
| ~ spl18_7
| ~ spl18_14
| ~ spl18_17 ),
inference(forward_demodulation,[],[f1616,f560]) ).
thf(f1659,plain,
( ( ( p @ sK7 )
= $false )
| ( $true
= ( q @ ( sK4 @ sK7 ) ) )
| ~ spl18_7
| ~ spl18_14
| ~ spl18_17 ),
inference(trivial_inequality_removal,[],[f1658]) ).
thf(f1660,plain,
( spl18_48
| spl18_47
| ~ spl18_8
| ~ spl18_14 ),
inference(avatar_split_clause,[],[f1521,f558,f529,f1640,f1645]) ).
thf(f1662,definition,
( spl18_50
<=> ( $true
= ( q @ ( sK4 @ sK7 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl18_50])],[avatar_definition]) ).
thf(f1664,plain,
( ( $true
= ( q @ ( sK4 @ sK7 ) ) )
| ~ spl18_50 ),
inference(avatar_component_clause,[],[f1662]) ).
thf(f1666,plain,
( spl18_47
| spl18_50
| ~ spl18_7
| ~ spl18_14
| ~ spl18_17 ),
inference(avatar_split_clause,[],[f1659,f570,f558,f525,f1662,f1640]) ).
thf(f1667,plain,
( ( $false = $true )
| ~ spl18_21
| ~ spl18_47 ),
inference(forward_demodulation,[],[f1642,f586]) ).
thf(f1668,plain,
( $false
| ~ spl18_21
| ~ spl18_47 ),
inference(trivial_inequality_removal,[],[f1667]) ).
thf(f1669,plain,
( ~ spl18_21
| ~ spl18_47 ),
inference(avatar_contradiction_clause,[],[f1668]) ).
thf(f1675,plain,
( ( $false = $true )
| ~ spl18_48
| ~ spl18_50 ),
inference(forward_demodulation,[],[f1664,f1647]) ).
thf(f1676,plain,
( $false
| ~ spl18_48
| ~ spl18_50 ),
inference(trivial_inequality_removal,[],[f1675]) ).
thf(f1677,plain,
( ~ spl18_48
| ~ spl18_50 ),
inference(avatar_contradiction_clause,[],[f1676]) ).
thf(f1775,plain,
( ( ( p @ sK7 )
= $false )
| ( $false
= ( rel_s5 @ sK1 @ sK7 ) )
| ( ( q @ ( sK3 @ sK7 ) )
= $true )
| ( $false = $true )
| ~ spl18_2
| ~ spl18_17 ),
inference(constrained_superposition,[],[f507,f571]) ).
thf(f1800,plain,
( ( $false
= ( rel_s5 @ sK1 @ sK7 ) )
| ( ( p @ sK7 )
= $false )
| ( ( q @ ( sK3 @ sK7 ) )
= $true )
| ~ spl18_2
| ~ spl18_17 ),
inference(trivial_inequality_removal,[],[f1775]) ).
thf(f1804,plain,
( ( $false = $true )
| ( ( p @ sK7 )
= $false )
| ( ( q @ ( sK3 @ sK7 ) )
= $true )
| ~ spl18_2
| ~ spl18_14
| ~ spl18_17 ),
inference(forward_demodulation,[],[f1800,f560]) ).
thf(f1805,plain,
( ( ( q @ ( sK3 @ sK7 ) )
= $true )
| ( ( p @ sK7 )
= $false )
| ~ spl18_2
| ~ spl18_14
| ~ spl18_17 ),
inference(trivial_inequality_removal,[],[f1804]) ).
thf(f1808,plain,
( ( $false = $true )
| ( ( p @ sK7 )
= $false )
| ~ spl18_2
| ~ spl18_14
| ~ spl18_17
| ~ spl18_46 ),
inference(forward_demodulation,[],[f1805,f1638]) ).
thf(f1809,plain,
( ( ( p @ sK7 )
= $false )
| ~ spl18_2
| ~ spl18_14
| ~ spl18_17
| ~ spl18_46 ),
inference(trivial_inequality_removal,[],[f1808]) ).
thf(f1813,plain,
( ( $false = $true )
| ~ spl18_2
| ~ spl18_14
| ~ spl18_17
| ~ spl18_21
| ~ spl18_46 ),
inference(forward_demodulation,[],[f1809,f586]) ).
thf(f1814,plain,
( $false
| ~ spl18_2
| ~ spl18_14
| ~ spl18_17
| ~ spl18_21
| ~ spl18_46 ),
inference(trivial_inequality_removal,[],[f1813]) ).
thf(f1815,plain,
( ~ spl18_2
| ~ spl18_14
| ~ spl18_17
| ~ spl18_21
| ~ spl18_46 ),
inference(avatar_contradiction_clause,[],[f1814]) ).
thf(f1826,plain,
( ( $false = $true )
| ~ spl18_10
| ~ spl18_11
| ~ spl18_14
| ~ spl18_17 ),
inference(forward_demodulation,[],[f1143,f543]) ).
thf(f1827,plain,
( $false
| ~ spl18_10
| ~ spl18_11
| ~ spl18_14
| ~ spl18_17 ),
inference(trivial_inequality_removal,[],[f1826]) ).
thf(f1828,plain,
( ~ spl18_10
| ~ spl18_11
| ~ spl18_14
| ~ spl18_17 ),
inference(avatar_contradiction_clause,[],[f1827]) ).
cnf(s1,plain,
( spl18_1
| spl18_2
| spl18_3
| spl18_4 ),
inference(sat_conversion,[],[f515]) ).
cnf(s2,plain,
( spl18_1
| spl18_3
| spl18_4
| spl18_5 ),
inference(sat_conversion,[],[f519]) ).
cnf(s3,plain,
( spl18_3
| spl18_4
| spl18_6
| spl18_7 ),
inference(sat_conversion,[],[f527]) ).
cnf(s4,plain,
( spl18_3
| spl18_4
| spl18_6
| spl18_8 ),
inference(sat_conversion,[],[f531]) ).
cnf(s5,plain,
( spl18_3
| spl18_4
| spl18_9
| spl18_10 ),
inference(sat_conversion,[],[f539]) ).
cnf(s6,plain,
( spl18_3
| spl18_4
| spl18_9
| spl18_11 ),
inference(sat_conversion,[],[f544]) ).
cnf(s17,plain,
( spl18_4
| spl18_9
| spl18_14 ),
inference(sat_conversion,[],[f592]) ).
cnf(s18,plain,
( spl18_4
| spl18_9
| spl18_17 ),
inference(sat_conversion,[],[f593]) ).
cnf(s19,plain,
( spl18_4
| spl18_9
| spl18_21 ),
inference(sat_conversion,[],[f594]) ).
cnf(s20,plain,
( spl18_4
| spl18_14
| spl18_23 ),
inference(sat_conversion,[],[f599]) ).
cnf(s21,plain,
( spl18_4
| spl18_14
| spl18_24 ),
inference(sat_conversion,[],[f604]) ).
cnf(s22,plain,
( spl18_4
| spl18_17
| spl18_23 ),
inference(sat_conversion,[],[f605]) ).
cnf(s23,plain,
( spl18_4
| spl18_21
| spl18_23 ),
inference(sat_conversion,[],[f606]) ).
cnf(s24,plain,
( spl18_4
| spl18_17
| spl18_24 ),
inference(sat_conversion,[],[f607]) ).
cnf(s25,plain,
( spl18_4
| spl18_21
| spl18_24 ),
inference(sat_conversion,[],[f608]) ).
cnf(s38,plain,
~ spl18_4,
inference(sat_conversion,[],[f661]) ).
cnf(s40,plain,
( ~ spl18_3
| ~ spl18_14
| ~ spl18_21 ),
inference(sat_conversion,[],[f687]) ).
cnf(s42,plain,
( ~ spl18_3
| ~ spl18_23
| ~ spl18_24 ),
inference(sat_conversion,[],[f709]) ).
cnf(s46,plain,
( ~ spl18_1
| ~ spl18_6
| ~ spl18_9 ),
inference(sat_conversion,[],[f783]) ).
cnf(s52,plain,
( ~ spl18_2
| ~ spl18_5
| ~ spl18_9
| ~ spl18_23
| ~ spl18_24 ),
inference(sat_conversion,[],[f1406]) ).
cnf(s60,plain,
( ~ spl18_7
| ~ spl18_8
| ~ spl18_9
| ~ spl18_23
| ~ spl18_24 ),
inference(sat_conversion,[],[f1634]) ).
cnf(s65,plain,
( ~ spl18_5
| ~ spl18_14
| spl18_46
| spl18_47 ),
inference(sat_conversion,[],[f1655]) ).
cnf(s66,plain,
( ~ spl18_8
| ~ spl18_14
| spl18_47
| spl18_48 ),
inference(sat_conversion,[],[f1660]) ).
cnf(s68,plain,
( ~ spl18_7
| ~ spl18_14
| ~ spl18_17
| spl18_47
| spl18_50 ),
inference(sat_conversion,[],[f1666]) ).
cnf(s69,plain,
( ~ spl18_21
| ~ spl18_47 ),
inference(sat_conversion,[],[f1669]) ).
cnf(s70,plain,
( ~ spl18_48
| ~ spl18_50 ),
inference(sat_conversion,[],[f1677]) ).
cnf(s72,plain,
( ~ spl18_2
| ~ spl18_14
| ~ spl18_17
| ~ spl18_21
| ~ spl18_46 ),
inference(sat_conversion,[],[f1815]) ).
cnf(s73,plain,
( ~ spl18_10
| ~ spl18_11
| ~ spl18_14
| ~ spl18_17 ),
inference(sat_conversion,[],[f1828]) ).
cnf(s74,plain,
( spl18_21
| spl18_24 ),
inference(rat,[],[s25,s38]) ).
cnf(s75,plain,
( spl18_17
| spl18_24 ),
inference(rat,[],[s24,s38]) ).
cnf(s76,plain,
( spl18_21
| spl18_23 ),
inference(rat,[],[s23,s38]) ).
cnf(s77,plain,
( spl18_17
| spl18_23 ),
inference(rat,[],[s22,s38]) ).
cnf(s78,plain,
( spl18_14
| spl18_24 ),
inference(rat,[],[s21,s38]) ).
cnf(s79,plain,
( spl18_14
| spl18_23 ),
inference(rat,[],[s20,s38]) ).
cnf(s80,plain,
( spl18_9
| spl18_21 ),
inference(rat,[],[s19,s38]) ).
cnf(s81,plain,
( spl18_9
| spl18_17 ),
inference(rat,[],[s18,s38]) ).
cnf(s82,plain,
( spl18_9
| spl18_14 ),
inference(rat,[],[s17,s38]) ).
cnf(s93,plain,
( spl18_3
| spl18_9
| spl18_11 ),
inference(rat,[],[s6,s38]) ).
cnf(s94,plain,
( spl18_3
| spl18_9
| spl18_10 ),
inference(rat,[],[s5,s38]) ).
cnf(s95,plain,
( spl18_3
| spl18_6
| spl18_8 ),
inference(rat,[],[s4,s38]) ).
cnf(s96,plain,
( spl18_3
| spl18_6
| spl18_7 ),
inference(rat,[],[s3,s38]) ).
cnf(s97,plain,
( spl18_1
| spl18_3
| spl18_5 ),
inference(rat,[],[s2,s38]) ).
cnf(s98,plain,
( spl18_1
| spl18_2
| spl18_3 ),
inference(rat,[],[s1,s38]) ).
cnf(s100,plain,
( spl18_21
| ~ spl18_3 ),
inference(rat,[],[s42,s76,s74]) ).
cnf(s101,plain,
( ~ spl18_21
| ~ spl18_3 ),
inference(rat,[],[s42,s79,s78,s40]) ).
cnf(s102,plain,
~ spl18_3,
inference(rat,[],[s101,s100]) ).
cnf(s103,plain,
( spl18_21
| spl18_1 ),
inference(rat,[],[s52,s80,s76,s74,s97,s98,s102]) ).
cnf(s104,plain,
( spl18_17
| spl18_1 ),
inference(rat,[],[s52,s81,s77,s75,s97,s98,s102]) ).
cnf(s105,plain,
( ~ spl18_14
| spl18_1 ),
inference(rat,[],[s72,s65,s97,s98,s69,s103,s104,s102]) ).
cnf(s106,plain,
spl18_1,
inference(rat,[],[s79,s52,s82,s78,s105,s98,s97,s102]) ).
cnf(s107,plain,
spl18_21,
inference(rat,[],[s60,s96,s95,s46,s80,s76,s74,s102,s106]) ).
cnf(s108,plain,
~ spl18_47,
inference(rat,[],[s69,s107]) ).
cnf(s110,plain,
spl18_9,
inference(rat,[],[s82,s73,s94,s93,s81,s102]) ).
cnf(s111,plain,
~ spl18_6,
inference(rat,[],[s46,s106,s110]) ).
cnf(s112,plain,
spl18_8,
inference(rat,[],[s95,s102,s111]) ).
cnf(s113,plain,
spl18_7,
inference(rat,[],[s96,s102,s111]) ).
cnf(s114,plain,
spl18_24,
inference(rat,[],[s70,s68,s66,s78,s75,s113,s108,s112]) ).
cnf(s115,plain,
~ spl18_23,
inference(rat,[],[s60,s114,s112,s110,s113]) ).
cnf(s116,plain,
spl18_17,
inference(rat,[],[s77,s115]) ).
cnf(s117,plain,
spl18_14,
inference(rat,[],[s79,s115]) ).
cnf(s118,plain,
spl18_50,
inference(rat,[],[s68,s108,s117,s113,s116]) ).
cnf(s119,plain,
spl18_48,
inference(rat,[],[s66,s108,s112,s117]) ).
cnf(s120,plain,
$false,
inference(rat,[],[s70,s118,s119]) ).
thf(f1829,plain,
$false,
inference(avatar_sat_refutation,[],[s120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO447^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.19 % Computer : n019.cluster.edu
% 0.13/0.19 % Model : x86_64 x86_64
% 0.13/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.19 % Memory : 8046.5625MB
% 0.13/0.19 % OS : Linux 6.8.0-71-generic
% 0.13/0.19 % CPULimit : 300
% 0.13/0.19 % WCLimit : 300
% 0.13/0.19 % DateTime : Tue Sep 29 16:52:03 UTC 2026
% 0.13/0.19 % CPUTime :
% 0.13/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.23 Running higher-order theorem proving
% 0.13/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.26/0.33 % (1057443)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.26/0.33 % (1057452)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3174593416:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.26/0.33 % (1057454)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.26/0.33 % (1057454)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
% 0.26/0.33 % (1057450)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2288211705:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.26/0.33 % (1057448)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3755912185:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.26/0.33 % (1057449)lrs+10_16_si=on:nwc=1.5:random_seed=1752750526:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.26/0.33 % (1057451)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=1918291790: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)
% 0.26/0.33 % (1057453)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1100226811:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.26/0.33 % (1057454)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=2703552125:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.26/0.33 % (1057452)Instruction limit reached!
% 0.26/0.33 % (1057452)------------------------------
% 0.26/0.33 % (1057452)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.33 % (1057452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.33 % (1057452)CaDiCaL version: 2.1.3
% 0.26/0.33 % (1057452)Termination reason: Instruction limit
% 0.26/0.33 % (1057452)Termination phase: Saturation
% 0.26/0.33 % (1057452)Time elapsed: 0.008 s
% 0.26/0.33 % (1057452)Peak memory usage: 11 MB
% 0.26/0.33 % (1057452)Instructions burned: 25 (million)
% 0.26/0.33 % (1057450)Instruction limit reached!
% 0.26/0.33 % (1057450)------------------------------
% 0.26/0.33 % (1057450)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.33 % (1057450)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.33 % (1057450)CaDiCaL version: 2.1.3
% 0.26/0.33 % (1057450)Termination reason: Instruction limit
% 0.26/0.33 % (1057450)Termination phase: Property scanning
% 0.26/0.33 % (1057450)Time elapsed: 0.002 s
% 0.26/0.33 % (1057450)Peak memory usage: 10 MB
% 0.26/0.33 % (1057450)Instructions burned: 3 (million)
% 0.26/0.33 % (1057449)Instruction limit reached!
% 0.26/0.33 % (1057449)------------------------------
% 0.26/0.33 % (1057449)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.33 % (1057449)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.33 % (1057449)CaDiCaL version: 2.1.3
% 0.26/0.33 % (1057449)Termination reason: Instruction limit
% 0.26/0.33 % (1057449)Termination phase: Saturation
% 0.26/0.33 % (1057449)Time elapsed: 0.009 s
% 0.26/0.33 % (1057449)Peak memory usage: 12 MB
% 0.26/0.33 % (1057449)Instructions burned: 18 (million)
% 0.26/0.33 % (1057463)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3972605762:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.26/0.33 % (1057463)Instruction limit reached!
% 0.26/0.33 % (1057463)------------------------------
% 0.26/0.33 % (1057463)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.33 % (1057463)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.33 % (1057463)CaDiCaL version: 2.1.3
% 0.26/0.33 % (1057463)Termination reason: Instruction limit
% 0.26/0.33 % (1057463)Termination phase: Saturation
% 0.26/0.33 % (1057463)Time elapsed: 0.002 s
% 0.26/0.33 % (1057463)Peak memory usage: 10 MB
% 0.26/0.33 % (1057463)Instructions burned: 8 (million)
% 0.26/0.33 % (1057464)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.26/0.33 % (1057464)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2955398718:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.26/0.33 % (1057462)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=996947580:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.26/0.33 % (1057462)Instruction limit reached!
% 0.26/0.33 % (1057462)------------------------------
% 0.26/0.33 % (1057462)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.33 % (1057462)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.33 % (1057462)CaDiCaL version: 2.1.3
% 0.26/0.33 % (1057462)Termination reason: Instruction limit
% 0.26/0.33 % (1057462)Termination phase: Preprocessing 1
% 0.26/0.33 % (1057462)Time elapsed: 0.002 s
% 0.26/0.33 % (1057462)Peak memory usage: 10 MB
% 0.26/0.33 % (1057462)Instructions burned: 4 (million)
% 0.26/0.33 % (1057464)Instruction limit reached!
% 0.26/0.33 % (1057464)------------------------------
% 0.26/0.33 % (1057464)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.33 % (1057464)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.33 % (1057464)CaDiCaL version: 2.1.3
% 0.26/0.33 % (1057464)Termination reason: Instruction limit
% 0.26/0.33 % (1057464)Termination phase: Saturation
% 0.26/0.33 % (1057464)Time elapsed: 0.004 s
% 0.26/0.33 % (1057464)Peak memory usage: 11 MB
% 0.26/0.33 % (1057464)Instructions burned: 8 (million)
% 0.26/0.33 % (1057454) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1057443-1057454"...
% 0.26/0.33 % (1057453)Instruction limit reached!
% 0.26/0.33 % (1057453)------------------------------
% 0.26/0.33 % (1057453)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.33 % (1057453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.33 % (1057453)CaDiCaL version: 2.1.3
% 0.26/0.33 % (1057453)Termination reason: Instruction limit
% 0.26/0.33 % (1057453)Termination phase: Saturation
% 0.26/0.33 % (1057453)Time elapsed: 0.035 s
% 0.26/0.33 % (1057453)Peak memory usage: 12 MB
% 0.26/0.33 % (1057453)Instructions burned: 76 (million)
% 0.26/0.33 % (1057466)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1614943174:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.26/0.33 % (1057466)Instruction limit reached!
% 0.26/0.33 % (1057466)------------------------------
% 0.26/0.33 % (1057466)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.33 % (1057466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.33 % (1057466)CaDiCaL version: 2.1.3
% 0.26/0.33 % (1057466)Termination reason: Instruction limit
% 0.26/0.33 % (1057466)Termination phase: Saturation
% 0.26/0.33 % (1057466)Time elapsed: 0.006 s
% 0.26/0.33 % (1057466)Peak memory usage: 12 MB
% 0.26/0.33 % (1057466)Instructions burned: 13 (million)
% 0.26/0.33 % (1057454)...printing done.
% 0.26/0.33 % (1057454)Refutation found. Thanks to Tanya!
% 0.26/0.33 % SZS status Theorem for theBenchmark
% 0.26/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.26/0.34 % (1057454)------------------------------
% 0.26/0.34 % (1057454)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.26/0.34 % (1057454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.26/0.34 % (1057454)CaDiCaL version: 2.1.3
% 0.26/0.34 % (1057454)Termination reason: Refutation
% 0.26/0.34 % (1057454)Time elapsed: 0.042 s
% 0.26/0.34 % (1057454)Peak memory usage: 13 MB
% 0.26/0.34 % (1057454)Instructions burned: 106 (million)
% 0.26/0.34 % (1057443)Success in time 0.079 s
% 0.26/0.34 % Vampire exiting
%------------------------------------------------------------------------------