%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO430^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 08:49:56 AM UTC 2026
% Result : Theorem 0.87s 0.39s
% Output : Refutation 0.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 29
% Syntax : Number of formulae : 358 ( 60 unt; 0 typ; 18 def)
% Number of atoms : 3836 ( 705 equ; 0 cnn)
% Maximal formula atoms : 10 ( 10 avg)
% Number of connectives : 5732 (1122 ~;1179 |; 0 &;3071 @)
% ( 18 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 121 ( 121 >; 0 *; 0 +; 0 <<)
% Number of symbols : 88 ( 84 usr; 25 con; 0-4 aty)
% ( 332 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 851 ( 0 sgn 292 !; 0 ?; 851 :)
% 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_b: $i > $i > $o ).
thf(func_def_33,type,
mbox_b: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_b: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_39,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vNOT: $o > $o ).
thf(func_def_42,type,
vOR: $o > $o > $o ).
thf(func_def_43,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vIMP: $o > $o > $o ).
thf(func_def_48,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
vAND: $o > $o > $o ).
thf(func_def_50,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_54,type,
sK3: $i > $i ).
thf(func_def_55,type,
sK4: $i > $i ).
thf(func_def_56,type,
sK5: $i > $i ).
thf(func_def_57,type,
sK6: $i > $i ).
thf(func_def_58,type,
sK7: $i > $i ).
thf(func_def_59,type,
sK8: $i > $i ).
thf(func_def_60,type,
sK9: $i > $i ).
thf(func_def_61,type,
sK10: $i > $i ).
thf(func_def_63,type,
sK12: $i > $i ).
thf(func_def_64,type,
sK13: $i > $i ).
thf(func_def_65,type,
sK14: $i > $i ).
thf(func_def_66,type,
sK15: $i > $i ).
thf(func_def_67,type,
sK16: $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_b
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_b @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^4.ax',mbox_b) ).
thf(f33,axiom,
( mdia_b
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_b @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^4.ax',mdia_b) ).
thf(f35,axiom,
msymmetric @ rel_b,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^4.ax',a2) ).
thf(f36,conjecture,
mvalid @ ( mequiv @ ( mdia_b @ ( mbox_b @ p ) ) @ ( mdia_b @ ( mbox_b @ ( mdia_b @ ( mbox_b @ p ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f37,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mdia_b @ ( mbox_b @ p ) ) @ ( mdia_b @ ( mbox_b @ ( mdia_b @ ( mbox_b @ p ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f40,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f41,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f42,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f43,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f44,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f45,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f47,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f63,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f64,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f81,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f82,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f89,plain,
( mbox_b
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_b @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f90,plain,
( mbox_b
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f89]) ).
thf(f91,plain,
( mdia_b
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_b @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f94,plain,
msymmetric @ rel_b,
inference(rectify,[],[f35]) ).
thf(f95,plain,
( ( msymmetric @ rel_b )
= $true ),
inference(fool_elimination,[],[f94]) ).
thf(f96,plain,
~ ( mvalid @ ( mequiv @ ( mdia_b @ ( mbox_b @ p ) ) @ ( mdia_b @ ( mbox_b @ ( mdia_b @ ( mbox_b @ p ) ) ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f97,plain,
( ( mvalid @ ( mequiv @ ( mdia_b @ ( mbox_b @ p ) ) @ ( mdia_b @ ( mbox_b @ ( mdia_b @ ( mbox_b @ p ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f96]) ).
thf(f98,plain,
( ( mvalid @ ( mequiv @ ( mdia_b @ ( mbox_b @ p ) ) @ ( mdia_b @ ( mbox_b @ ( mdia_b @ ( mbox_b @ p ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f97]) ).
thf(f101,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f102,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f103,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f104,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f106,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f117,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f126,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f130,plain,
( mbox_b
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f131,plain,
( mdia_b
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_b @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f91]) ).
thf(f133,plain,
( ( msymmetric @ rel_b )
= $true ),
inference(cnf_transformation,[],[f95]) ).
thf(f134,plain,
( ( mvalid @ ( mequiv @ ( mdia_b @ ( mbox_b @ p ) ) @ ( mdia_b @ ( mbox_b @ ( mdia_b @ ( mbox_b @ p ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f137,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f103,f101,f102,f101,f101]) ).
thf(f138,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f104,f102,f101]) ).
thf(f140,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] :
( ( Y4 @ Y6 )
| ( Y5 @ 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] :
( ( Y4 @ Y6 )
| ( Y5 @ 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] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f106,f137,f138,f138]) ).
thf(f146,plain,
( mdia_b
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f131,f101,f130,f101]) ).
thf(f148,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ rel_b ) ),
inference(definition_unfolding,[],[f133,f117]) ).
thf(f149,plain,
( $true
!= ( ^ [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] :
( ( Y4 @ Y6 )
| ( Y5 @ 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] :
( ( Y4 @ Y6 )
| ( Y5 @ 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] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f134,f126,f140,f146,f130,f146,f130,f146,f130]) ).
thf(f150,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_b @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_b @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
( $false
= ( ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_b @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_b @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( $false
= ( ~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f153]) ).
thf(f155,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f155]) ).
thf(f158,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) )
@ sK1 ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) )
@ sK1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f160]) ).
thf(f163,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) )
@ sK1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f164,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) )
@ sK1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) )
@ sK1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f165]) ).
thf(f167,plain,
( ( $false
= ( ~ ( rel_b @ sK0 @ sK1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) )
| ( $false
= ( ~ ( rel_b @ sK0 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f166]) ).
thf(f168,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) )
| ( $false
= ( ~ ( rel_b @ sK0 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f167]) ).
thf(f169,plain,
( ( $false
= ( ~ ( rel_b @ sK0 @ sK1 ) ) )
| ( $false
= ( ~ ( rel_b @ sK0 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f167]) ).
thf(f170,plain,
( ( $true
= ( rel_b @ sK0 @ sK1 ) )
| ( $false
= ( ~ ( rel_b @ sK0 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ( $true
= ( rel_b @ sK0 @ sK1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( $true
= ( rel_b @ sK0 @ sK1 ) )
| ( $false
= ( ~ ( rel_b @ sK0 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f173,plain,
( ( $true
= ( rel_b @ sK0 @ sK1 ) )
| ( $true
= ( rel_b @ sK0 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( $true
= ( rel_b @ sK0 @ sK1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f175,plain,
! [X1: $i] :
( ( $true
= ( rel_b @ sK0 @ sK1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X1: $i] :
( ( $true
= ( rel_b @ sK0 @ sK1 ) )
| ( $true
= ( ~ ( rel_b @ sK2 @ X1 )
| ( p @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( ( $true
= ( rel_b @ sK0 @ sK1 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_b @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X1: $i] :
( ( $true
= ( rel_b @ sK0 @ sK1 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_b @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f179,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) )
| ( $false
= ( ~ ( rel_b @ sK0 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f180,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X1 ) )
| ( $false
= ( ~ ( rel_b @ sK0 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X1 ) )
| ( $false
= ( ~ ( rel_b @ sK0 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f183,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X1 ) )
| ( $true
= ( rel_b @ sK0 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_b @ sK1 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( rel_b @ sK0 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f183]) ).
thf(f185,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( rel_b @ sK0 @ sK2 ) )
| ( $true
= ( ~ ( rel_b @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ( $true
= ( rel_b @ sK0 @ sK2 ) )
| ( $true
= ( ~ ( rel_b @ sK1 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ ( sK3 @ X1 ) ) )
| ( $true
= ( rel_b @ sK0 @ sK2 ) )
| ( $true
= ( ~ ( rel_b @ sK1 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ ( sK3 @ X1 ) ) )
| ( $true
= ( rel_b @ sK0 @ sK2 ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_b @ X1 @ ( sK3 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ ( sK3 @ X1 ) @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( rel_b @ sK0 @ sK2 ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f188]) ).
thf(f190,plain,
! [X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ ( sK3 @ X1 ) @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( rel_b @ sK0 @ sK2 ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_b @ X1 @ ( sK3 @ X1 ) ) ) )
| ( $true
= ( rel_b @ sK0 @ sK2 ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f189]) ).
thf(f192,plain,
! [X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK3 @ X1 ) ) )
| ( $true
= ( rel_b @ sK0 @ sK2 ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f191]) ).
thf(f193,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ ( sK3 @ X1 ) @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( rel_b @ sK0 @ sK2 ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f194,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ ( sK3 @ X1 ) @ Y0 )
| ( p @ Y0 ) )
@ X2 ) )
| ( $true
= ( rel_b @ sK0 @ sK2 ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_b @ ( sK3 @ X1 ) @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( rel_b @ sK0 @ sK2 ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f194]) ).
thf(f196,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X2 ) )
| ( $true
= ( rel_b @ sK0 @ sK2 ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) )
| ( $true
= ( ~ ( rel_b @ ( sK3 @ X1 ) @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X2 ) )
| ( $true
= ( rel_b @ sK0 @ sK2 ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) )
| ( $false
= ( rel_b @ ( sK3 @ X1 ) @ X2 ) ) ),
inference(not_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK2 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f199,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK2 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_b @ sK1 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( rel_b @ sK2 @ X2 )
| ( p @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f199]) ).
thf(f201,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( rel_b @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_b @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( rel_b @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_b @ sK1 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f201]) ).
thf(f203,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ ( sK4 @ X1 ) ) )
| ( $true
= ( ~ ( rel_b @ sK2 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_b @ sK1 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ ( sK4 @ X1 ) ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_b @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( rel_b @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ ( sK4 @ X1 ) ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) )
| ( $true
= ( ~ ( rel_b @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ ( sK4 @ X1 ) ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) )
| ( $false
= ( rel_b @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_b @ X1 @ ( sK4 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ ( sK4 @ X1 ) @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) )
| ( $false
= ( rel_b @ sK2 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f206]) ).
thf(f208,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ ( sK4 @ X1 ) @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) )
| ( $false
= ( rel_b @ sK2 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_b @ X1 @ ( sK4 @ X1 ) ) ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) )
| ( $false
= ( rel_b @ sK2 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f207]) ).
thf(f210,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK4 @ X1 ) ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) )
| ( $false
= ( rel_b @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f209]) ).
thf(f211,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ ( sK4 @ X1 ) @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) )
| ( $false
= ( rel_b @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f208]) ).
thf(f212,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ ( sK4 @ X1 ) @ Y0 )
| ( p @ Y0 ) )
@ X3 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) )
| ( $false
= ( rel_b @ sK2 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f211]) ).
thf(f213,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( rel_b @ ( sK4 @ X1 ) @ X3 )
| ( p @ X3 ) ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) )
| ( $false
= ( rel_b @ sK2 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f212]) ).
thf(f214,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) )
| ( $false
= ( rel_b @ sK2 @ X2 ) )
| ( $true
= ( ~ ( rel_b @ ( sK4 @ X1 ) @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f213]) ).
thf(f215,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) )
| ( $false
= ( rel_b @ sK2 @ X2 ) )
| ( $false
= ( rel_b @ ( sK4 @ X1 ) @ X3 ) ) ),
inference(not_proxy_clausification,[],[f214]) ).
thf(f292,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f156]) ).
thf(f293,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f292]) ).
thf(f294,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f293]) ).
thf(f295,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f294]) ).
thf(f296,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f294]) ).
thf(f297,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f296]) ).
thf(f298,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f297]) ).
thf(f299,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ sK11 ) ) ),
inference(sigma_proxy_clausification,[],[f298]) ).
thf(f300,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_b @ sK0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_b @ sK0 @ sK11 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK11 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f299]) ).
thf(f301,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_b @ sK0 @ sK11 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK11 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f300]) ).
thf(f302,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $false
= ( ~ ( rel_b @ sK0 @ sK11 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK11 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f301]) ).
thf(f303,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ( p @ Y0 ) )
@ ( sK12 @ X1 ) ) )
| ( $false
= ( ~ ( rel_b @ sK0 @ sK11 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK11 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f302]) ).
thf(f304,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ( p @ Y0 ) )
@ ( sK12 @ X1 ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK11 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f303]) ).
thf(f305,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ( p @ Y0 ) )
@ ( sK12 @ X1 ) ) )
| ( $false
= ( ~ ( rel_b @ sK0 @ sK11 ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f303]) ).
thf(f306,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ( p @ Y0 ) )
@ ( sK12 @ X1 ) ) )
| ( $true
= ( rel_b @ sK0 @ sK11 ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f305]) ).
thf(f307,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ( p @ Y0 ) )
@ ( sK12 @ X1 ) ) )
| ( $true
= ( rel_b @ sK0 @ sK11 ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f306]) ).
thf(f308,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_b @ X1 @ ( sK12 @ X1 ) )
| ( p @ ( sK12 @ X1 ) ) ) )
| ( $true
= ( rel_b @ sK0 @ sK11 ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f307]) ).
thf(f309,plain,
! [X1: $i] :
( ( $false
= ( p @ ( sK12 @ X1 ) ) )
| ( $true
= ( rel_b @ sK0 @ sK11 ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f308]) ).
thf(f310,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_b @ X1 @ ( sK12 @ X1 ) ) ) )
| ( $true
= ( rel_b @ sK0 @ sK11 ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f308]) ).
thf(f311,plain,
! [X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK12 @ X1 ) ) )
| ( $true
= ( rel_b @ sK0 @ sK11 ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f310]) ).
thf(f312,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ( p @ Y0 ) )
@ ( sK12 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK11 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f304]) ).
thf(f313,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ( p @ Y0 ) )
@ ( sK12 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK11 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f312]) ).
thf(f314,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ( p @ Y0 ) )
@ ( sK12 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK11 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f313]) ).
thf(f315,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_b @ X1 @ ( sK12 @ X1 ) )
| ( p @ ( sK12 @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_b @ sK11 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f314]) ).
thf(f316,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ ( sK12 @ X1 ) ) )
| ( $true
= ( ~ ( rel_b @ sK11 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f315]) ).
thf(f317,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_b @ X1 @ ( sK12 @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_b @ sK11 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f315]) ).
thf(f318,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK12 @ X1 ) ) )
| ( $true
= ( ~ ( rel_b @ sK11 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f317]) ).
thf(f319,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK12 @ X1 ) ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_b @ sK11 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f318]) ).
thf(f320,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK12 @ X1 ) ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK11 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f319]) ).
thf(f321,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ ( sK12 @ X1 ) ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_b @ sK11 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f316]) ).
thf(f322,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ ( sK12 @ X1 ) ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK11 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f321]) ).
thf(f323,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f295]) ).
thf(f324,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f323]) ).
thf(f325,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_b @ sK0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f324]) ).
thf(f326,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f325]) ).
thf(f327,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f326]) ).
thf(f328,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ( p @ Y0 ) )
@ ( sK13 @ X1 ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f327]) ).
thf(f329,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ( p @ Y0 ) )
@ ( sK13 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f328]) ).
thf(f330,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ( p @ Y0 ) )
@ ( sK13 @ X1 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f329]) ).
thf(f331,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ( p @ Y0 ) )
@ ( sK13 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ ( sK14 @ X2 ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f330]) ).
thf(f332,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ( p @ Y0 ) )
@ ( sK13 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ ( sK14 @ X2 ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_b @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f331]) ).
thf(f333,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ( p @ Y0 ) )
@ ( sK13 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ ( sK14 @ X2 ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f332]) ).
thf(f334,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_b @ X1 @ ( sK13 @ X1 ) )
| ( p @ ( sK13 @ X1 ) ) ) )
| ( $false
= ( ~ ( rel_b @ X2 @ ( sK14 @ X2 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ ( sK14 @ X2 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f333]) ).
thf(f335,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ ( sK13 @ X1 ) ) )
| ( $false
= ( ~ ( rel_b @ X2 @ ( sK14 @ X2 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ ( sK14 @ X2 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f334]) ).
thf(f336,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_b @ X1 @ ( sK13 @ X1 ) ) ) )
| ( $false
= ( ~ ( rel_b @ X2 @ ( sK14 @ X2 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ ( sK14 @ X2 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f334]) ).
thf(f337,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK13 @ X1 ) ) )
| ( $false
= ( ~ ( rel_b @ X2 @ ( sK14 @ X2 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ ( sK14 @ X2 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f336]) ).
thf(f338,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK13 @ X1 ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ ( sK14 @ X2 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f337]) ).
thf(f339,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK13 @ X1 ) ) )
| ( $false
= ( ~ ( rel_b @ X2 @ ( sK14 @ X2 ) ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f337]) ).
thf(f340,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK13 @ X1 ) ) )
| ( $true
= ( rel_b @ X2 @ ( sK14 @ X2 ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f339]) ).
thf(f341,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK13 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ ( sK14 @ X2 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f338]) ).
thf(f342,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK13 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ ( sK14 @ X2 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X3 ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f341]) ).
thf(f343,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK13 @ X1 ) ) )
| ( $true
= ( ~ ( rel_b @ ( sK14 @ X2 ) @ X3 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f342]) ).
thf(f344,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK13 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) )
| ( $true
= ( ~ ( rel_b @ ( sK14 @ X2 ) @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f343]) ).
thf(f345,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK13 @ X1 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X3 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) )
| ( $true
= ( ~ ( rel_b @ ( sK14 @ X2 ) @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f344]) ).
thf(f346,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK13 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X3 @ Y0 )
| ( p @ Y0 ) )
@ ( sK15 @ X3 ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) )
| ( $true
= ( ~ ( rel_b @ ( sK14 @ X2 ) @ X3 ) ) ) ),
inference(sigma_proxy_clausification,[],[f345]) ).
thf(f347,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK13 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X3 @ Y0 )
| ( p @ Y0 ) )
@ ( sK15 @ X3 ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) )
| ( $false
= ( rel_b @ ( sK14 @ X2 ) @ X3 ) ) ),
inference(not_proxy_clausification,[],[f346]) ).
thf(f348,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK13 @ X1 ) ) )
| ( $false
= ( ~ ( rel_b @ X3 @ ( sK15 @ X3 ) )
| ( p @ ( sK15 @ X3 ) ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) )
| ( $false
= ( rel_b @ ( sK14 @ X2 ) @ X3 ) ) ),
inference(beta-eta_normalization,[],[f347]) ).
thf(f349,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK13 @ X1 ) ) )
| ( $false
= ( p @ ( sK15 @ X3 ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) )
| ( $false
= ( rel_b @ ( sK14 @ X2 ) @ X3 ) ) ),
inference(or_proxy_clausification,[],[f348]) ).
thf(f350,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK13 @ X1 ) ) )
| ( $false
= ( ~ ( rel_b @ X3 @ ( sK15 @ X3 ) ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) )
| ( $false
= ( rel_b @ ( sK14 @ X2 ) @ X3 ) ) ),
inference(or_proxy_clausification,[],[f348]) ).
thf(f351,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK13 @ X1 ) ) )
| ( $true
= ( rel_b @ X3 @ ( sK15 @ X3 ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) )
| ( $false
= ( rel_b @ ( sK14 @ X2 ) @ X3 ) ) ),
inference(not_proxy_clausification,[],[f350]) ).
thf(f352,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ ( sK13 @ X1 ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ ( sK14 @ X2 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f335]) ).
thf(f353,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ ( sK13 @ X1 ) ) )
| ( $false
= ( ~ ( rel_b @ X2 @ ( sK14 @ X2 ) ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f335]) ).
thf(f354,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ ( sK13 @ X1 ) ) )
| ( $true
= ( rel_b @ X2 @ ( sK14 @ X2 ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f353]) ).
thf(f355,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ ( sK13 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ ( sK14 @ X2 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f352]) ).
thf(f356,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p @ ( sK13 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ ( sK14 @ X2 ) @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X3 ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f355]) ).
thf(f357,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p @ ( sK13 @ X1 ) ) )
| ( $true
= ( ~ ( rel_b @ ( sK14 @ X2 ) @ X3 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f356]) ).
thf(f358,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p @ ( sK13 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) )
| ( $true
= ( ~ ( rel_b @ ( sK14 @ X2 ) @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f357]) ).
thf(f359,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p @ ( sK13 @ X1 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X3 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) )
| ( $true
= ( ~ ( rel_b @ ( sK14 @ X2 ) @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f358]) ).
thf(f360,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p @ ( sK13 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X3 @ Y0 )
| ( p @ Y0 ) )
@ ( sK16 @ X3 ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) )
| ( $true
= ( ~ ( rel_b @ ( sK14 @ X2 ) @ X3 ) ) ) ),
inference(sigma_proxy_clausification,[],[f359]) ).
thf(f361,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p @ ( sK13 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ X3 @ Y0 )
| ( p @ Y0 ) )
@ ( sK16 @ X3 ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) )
| ( $false
= ( rel_b @ ( sK14 @ X2 ) @ X3 ) ) ),
inference(not_proxy_clausification,[],[f360]) ).
thf(f362,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p @ ( sK13 @ X1 ) ) )
| ( $false
= ( ~ ( rel_b @ X3 @ ( sK16 @ X3 ) )
| ( p @ ( sK16 @ X3 ) ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) )
| ( $false
= ( rel_b @ ( sK14 @ X2 ) @ X3 ) ) ),
inference(beta-eta_normalization,[],[f361]) ).
thf(f363,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p @ ( sK13 @ X1 ) ) )
| ( $false
= ( p @ ( sK16 @ X3 ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) )
| ( $false
= ( rel_b @ ( sK14 @ X2 ) @ X3 ) ) ),
inference(or_proxy_clausification,[],[f362]) ).
thf(f364,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p @ ( sK13 @ X1 ) ) )
| ( $false
= ( ~ ( rel_b @ X3 @ ( sK16 @ X3 ) ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) )
| ( $false
= ( rel_b @ ( sK14 @ X2 ) @ X3 ) ) ),
inference(or_proxy_clausification,[],[f362]) ).
thf(f365,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p @ ( sK13 @ X1 ) ) )
| ( $true
= ( rel_b @ X3 @ ( sK16 @ X3 ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) )
| ( $false
= ( rel_b @ ( sK14 @ X2 ) @ X3 ) ) ),
inference(not_proxy_clausification,[],[f364]) ).
thf(f366,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_b @ Y1 @ Y0 )
=> ( rel_b @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f367,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_b @ Y1 @ Y0 )
=> ( rel_b @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f366]) ).
thf(f368,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_b @ Y0 @ X1 )
=> ( rel_b @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f367]) ).
thf(f369,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel_b @ Y0 @ X1 )
=> ( rel_b @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f368]) ).
thf(f370,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel_b @ X2 @ X1 )
=> ( rel_b @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f369]) ).
thf(f371,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_b @ X2 @ X1 ) )
| ( ( rel_b @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f370]) ).
thf(f376,definition,
( spl17_1
<=> ( $true
= ( rel_b @ sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl17_1])],[avatar_definition]) ).
thf(f378,plain,
( ( $true
= ( rel_b @ sK0 @ sK2 ) )
| ~ spl17_1 ),
inference(avatar_component_clause,[],[f376]) ).
thf(f380,definition,
( spl17_2
<=> ( $true
= ( rel_b @ sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl17_2])],[avatar_definition]) ).
thf(f382,plain,
( ( $true
= ( rel_b @ sK0 @ sK1 ) )
| ~ spl17_2 ),
inference(avatar_component_clause,[],[f380]) ).
thf(f383,plain,
( spl17_1
| spl17_2 ),
inference(avatar_split_clause,[],[f173,f380,f376]) ).
thf(f385,definition,
( spl17_3
<=> ! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_b @ sK2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl17_3])],[avatar_definition]) ).
thf(f386,plain,
( ! [X1: $i] :
( ( $false
= ( rel_b @ sK2 @ X1 ) )
| ( $true
= ( p @ X1 ) ) )
| ~ spl17_3 ),
inference(avatar_component_clause,[],[f385]) ).
thf(f387,plain,
( spl17_3
| spl17_2 ),
inference(avatar_split_clause,[],[f178,f380,f385]) ).
thf(f389,definition,
( spl17_4
<=> ! [X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl17_4])],[avatar_definition]) ).
thf(f390,plain,
( ! [X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) ) )
| ~ spl17_4 ),
inference(avatar_component_clause,[],[f389]) ).
thf(f391,plain,
( spl17_1
| spl17_4 ),
inference(avatar_split_clause,[],[f192,f389,f376]) ).
thf(f393,definition,
( spl17_5
<=> ! [X2: $i,X1: $i] :
( ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) )
| ( $false
= ( rel_b @ ( sK3 @ X1 ) @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl17_5])],[avatar_definition]) ).
thf(f394,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( rel_b @ ( sK3 @ X1 ) @ X2 ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) )
| ( $true
= ( p @ X2 ) ) )
| ~ spl17_5 ),
inference(avatar_component_clause,[],[f393]) ).
thf(f395,plain,
( spl17_1
| spl17_5 ),
inference(avatar_split_clause,[],[f197,f393,f376]) ).
thf(f397,definition,
( spl17_6
<=> ! [X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK4 @ X1 ) ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl17_6])],[avatar_definition]) ).
thf(f398,plain,
( ! [X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK4 @ X1 ) ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) ) )
| ~ spl17_6 ),
inference(avatar_component_clause,[],[f397]) ).
thf(f399,plain,
( spl17_3
| spl17_6 ),
inference(avatar_split_clause,[],[f210,f397,f385]) ).
thf(f401,definition,
( spl17_7
<=> ! [X1: $i,X3: $i] :
( ( $true
= ( p @ X3 ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) )
| ( $false
= ( rel_b @ ( sK4 @ X1 ) @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl17_7])],[avatar_definition]) ).
thf(f402,plain,
( ! [X3: $i,X1: $i] :
( ( $false
= ( rel_b @ ( sK4 @ X1 ) @ X3 ) )
| ( $false
= ( rel_b @ sK1 @ X1 ) )
| ( $true
= ( p @ X3 ) ) )
| ~ spl17_7 ),
inference(avatar_component_clause,[],[f401]) ).
thf(f403,plain,
( spl17_3
| spl17_7 ),
inference(avatar_split_clause,[],[f215,f401,f385]) ).
thf(f444,definition,
( spl17_18
<=> ( $true
= ( rel_b @ sK0 @ sK11 ) ) ),
introduced(definition,[new_symbols(definition,[spl17_18])],[avatar_definition]) ).
thf(f446,plain,
( ( $true
= ( rel_b @ sK0 @ sK11 ) )
| ~ spl17_18 ),
inference(avatar_component_clause,[],[f444]) ).
thf(f448,definition,
( spl17_19
<=> ! [X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK12 @ X1 ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl17_19])],[avatar_definition]) ).
thf(f449,plain,
( ! [X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK12 @ X1 ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) ) )
| ~ spl17_19 ),
inference(avatar_component_clause,[],[f448]) ).
thf(f450,plain,
( spl17_18
| spl17_19 ),
inference(avatar_split_clause,[],[f311,f448,f444]) ).
thf(f452,definition,
( spl17_20
<=> ! [X1: $i] :
( ( $false
= ( p @ ( sK12 @ X1 ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl17_20])],[avatar_definition]) ).
thf(f453,plain,
( ! [X1: $i] :
( ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( p @ ( sK12 @ X1 ) ) ) )
| ~ spl17_20 ),
inference(avatar_component_clause,[],[f452]) ).
thf(f454,plain,
( spl17_18
| spl17_20 ),
inference(avatar_split_clause,[],[f309,f452,f444]) ).
thf(f456,definition,
( spl17_21
<=> ! [X2: $i] :
( ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_b @ sK11 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl17_21])],[avatar_definition]) ).
thf(f457,plain,
( ! [X2: $i] :
( ( $false
= ( rel_b @ sK11 @ X2 ) )
| ( $true
= ( p @ X2 ) ) )
| ~ spl17_21 ),
inference(avatar_component_clause,[],[f456]) ).
thf(f458,plain,
( spl17_21
| spl17_19 ),
inference(avatar_split_clause,[],[f320,f448,f456]) ).
thf(f459,plain,
( spl17_21
| spl17_20 ),
inference(avatar_split_clause,[],[f322,f452,f456]) ).
thf(f461,definition,
( spl17_22
<=> ! [X2: $i] :
( ( $true
= ( rel_b @ X2 @ ( sK14 @ X2 ) ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl17_22])],[avatar_definition]) ).
thf(f462,plain,
( ! [X2: $i] :
( ( $true
= ( rel_b @ X2 @ ( sK14 @ X2 ) ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) ) )
| ~ spl17_22 ),
inference(avatar_component_clause,[],[f461]) ).
thf(f464,definition,
( spl17_23
<=> ! [X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK13 @ X1 ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl17_23])],[avatar_definition]) ).
thf(f465,plain,
( ! [X1: $i] :
( ( $true
= ( rel_b @ X1 @ ( sK13 @ X1 ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) ) )
| ~ spl17_23 ),
inference(avatar_component_clause,[],[f464]) ).
thf(f466,plain,
( spl17_22
| spl17_23 ),
inference(avatar_split_clause,[],[f340,f464,f461]) ).
thf(f468,definition,
( spl17_24
<=> ! [X2: $i,X3: $i] :
( ( $true
= ( rel_b @ X3 @ ( sK15 @ X3 ) ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) )
| ( $false
= ( rel_b @ ( sK14 @ X2 ) @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl17_24])],[avatar_definition]) ).
thf(f469,plain,
( ! [X2: $i,X3: $i] :
( ( $true
= ( rel_b @ X3 @ ( sK15 @ X3 ) ) )
| ( $false
= ( rel_b @ ( sK14 @ X2 ) @ X3 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) ) )
| ~ spl17_24 ),
inference(avatar_component_clause,[],[f468]) ).
thf(f470,plain,
( spl17_24
| spl17_23 ),
inference(avatar_split_clause,[],[f351,f464,f468]) ).
thf(f472,definition,
( spl17_25
<=> ! [X2: $i,X3: $i] :
( ( $false
= ( p @ ( sK15 @ X3 ) ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) )
| ( $false
= ( rel_b @ ( sK14 @ X2 ) @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl17_25])],[avatar_definition]) ).
thf(f473,plain,
( ! [X2: $i,X3: $i] :
( ( $false
= ( rel_b @ ( sK14 @ X2 ) @ X3 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) )
| ( $false
= ( p @ ( sK15 @ X3 ) ) ) )
| ~ spl17_25 ),
inference(avatar_component_clause,[],[f472]) ).
thf(f474,plain,
( spl17_25
| spl17_23 ),
inference(avatar_split_clause,[],[f349,f464,f472]) ).
thf(f476,definition,
( spl17_26
<=> ! [X1: $i] :
( ( $false
= ( p @ ( sK13 @ X1 ) ) )
| ( $false
= ( rel_b @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl17_26])],[avatar_definition]) ).
thf(f477,plain,
( ! [X1: $i] :
( ( $false
= ( rel_b @ sK0 @ X1 ) )
| ( $false
= ( p @ ( sK13 @ X1 ) ) ) )
| ~ spl17_26 ),
inference(avatar_component_clause,[],[f476]) ).
thf(f478,plain,
( spl17_22
| spl17_26 ),
inference(avatar_split_clause,[],[f354,f476,f461]) ).
thf(f480,definition,
( spl17_27
<=> ! [X2: $i,X3: $i] :
( ( $true
= ( rel_b @ X3 @ ( sK16 @ X3 ) ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) )
| ( $false
= ( rel_b @ ( sK14 @ X2 ) @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl17_27])],[avatar_definition]) ).
thf(f481,plain,
( ! [X2: $i,X3: $i] :
( ( $true
= ( rel_b @ X3 @ ( sK16 @ X3 ) ) )
| ( $false
= ( rel_b @ ( sK14 @ X2 ) @ X3 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) ) )
| ~ spl17_27 ),
inference(avatar_component_clause,[],[f480]) ).
thf(f482,plain,
( spl17_27
| spl17_26 ),
inference(avatar_split_clause,[],[f365,f476,f480]) ).
thf(f484,definition,
( spl17_28
<=> ! [X2: $i,X3: $i] :
( ( $false
= ( p @ ( sK16 @ X3 ) ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) )
| ( $false
= ( rel_b @ ( sK14 @ X2 ) @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl17_28])],[avatar_definition]) ).
thf(f485,plain,
( ! [X2: $i,X3: $i] :
( ( $false
= ( rel_b @ ( sK14 @ X2 ) @ X3 ) )
| ( $false
= ( rel_b @ sK0 @ X2 ) )
| ( $false
= ( p @ ( sK16 @ X3 ) ) ) )
| ~ spl17_28 ),
inference(avatar_component_clause,[],[f484]) ).
thf(f486,plain,
( spl17_28
| spl17_26 ),
inference(avatar_split_clause,[],[f363,f476,f484]) ).
thf(f504,plain,
( ( $true = $false )
| ( $false
= ( p @ ( sK13 @ sK11 ) ) )
| ~ spl17_18
| ~ spl17_26 ),
inference(constrained_superposition,[],[f446,f477]) ).
thf(f505,plain,
( ( $false
= ( p @ ( sK13 @ sK11 ) ) )
| ~ spl17_18
| ~ spl17_26 ),
inference(trivial_inequality_removal,[],[f504]) ).
thf(f520,plain,
( ( $true = $false )
| ( $false
= ( rel_b @ sK0 @ sK11 ) )
| ( $true
= ( p @ ( sK13 @ sK11 ) ) )
| ~ spl17_21
| ~ spl17_23 ),
inference(constrained_superposition,[],[f465,f457]) ).
thf(f527,plain,
( ( $false
= ( rel_b @ sK0 @ sK11 ) )
| ( $true
= ( p @ ( sK13 @ sK11 ) ) )
| ~ spl17_21
| ~ spl17_23 ),
inference(trivial_inequality_removal,[],[f520]) ).
thf(f543,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK13 @ sK11 ) ) )
| ~ spl17_18
| ~ spl17_21
| ~ spl17_23 ),
inference(forward_demodulation,[],[f527,f446]) ).
thf(f544,plain,
( ( $true
= ( p @ ( sK13 @ sK11 ) ) )
| ~ spl17_18
| ~ spl17_21
| ~ spl17_23 ),
inference(trivial_inequality_removal,[],[f543]) ).
thf(f548,plain,
( ( $true = $false )
| ~ spl17_18
| ~ spl17_21
| ~ spl17_23
| ~ spl17_26 ),
inference(forward_demodulation,[],[f544,f505]) ).
thf(f549,plain,
( $false
| ~ spl17_18
| ~ spl17_21
| ~ spl17_23
| ~ spl17_26 ),
inference(trivial_inequality_removal,[],[f548]) ).
thf(f550,plain,
( ~ spl17_18
| ~ spl17_21
| ~ spl17_23
| ~ spl17_26 ),
inference(avatar_contradiction_clause,[],[f549]) ).
thf(f675,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_b @ sK0 @ X0 ) )
| ( $true
= ( rel_b @ ( sK14 @ X0 ) @ X0 ) ) )
| ~ spl17_22 ),
inference(constrained_superposition,[],[f462,f371]) ).
thf(f698,plain,
( ! [X0: $i] :
( ( $true
= ( rel_b @ ( sK14 @ X0 ) @ X0 ) )
| ( $false
= ( rel_b @ sK0 @ X0 ) ) )
| ~ spl17_22 ),
inference(trivial_inequality_removal,[],[f675]) ).
thf(f940,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_b @ sK0 @ X0 ) )
| ( $false
= ( rel_b @ sK0 @ X0 ) )
| ( $false
= ( p @ ( sK16 @ X0 ) ) ) )
| ~ spl17_22
| ~ spl17_28 ),
inference(constrained_superposition,[],[f698,f485]) ).
thf(f941,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_b @ sK0 @ X0 ) )
| ( $false
= ( p @ ( sK16 @ X0 ) ) ) )
| ~ spl17_22
| ~ spl17_28 ),
inference(duplicate_literal_removal,[],[f940]) ).
thf(f942,plain,
( ! [X0: $i] :
( ( $false
= ( rel_b @ sK0 @ X0 ) )
| ( $false
= ( p @ ( sK16 @ X0 ) ) ) )
| ~ spl17_22
| ~ spl17_28 ),
inference(trivial_inequality_removal,[],[f941]) ).
thf(f972,plain,
( ( $true = $false )
| ( $false
= ( p @ ( sK16 @ sK11 ) ) )
| ~ spl17_18
| ~ spl17_22
| ~ spl17_28 ),
inference(constrained_superposition,[],[f446,f942]) ).
thf(f973,plain,
( ( $false
= ( p @ ( sK16 @ sK11 ) ) )
| ~ spl17_18
| ~ spl17_22
| ~ spl17_28 ),
inference(trivial_inequality_removal,[],[f972]) ).
thf(f1082,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_b @ sK0 @ X0 ) )
| ( $true
= ( rel_b @ X0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( rel_b @ sK0 @ X0 ) ) )
| ~ spl17_22
| ~ spl17_27 ),
inference(constrained_superposition,[],[f698,f481]) ).
thf(f1084,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_b @ sK0 @ X0 ) )
| ( $true
= ( rel_b @ X0 @ ( sK16 @ X0 ) ) ) )
| ~ spl17_22
| ~ spl17_27 ),
inference(duplicate_literal_removal,[],[f1082]) ).
thf(f1085,plain,
( ! [X0: $i] :
( ( $true
= ( rel_b @ X0 @ ( sK16 @ X0 ) ) )
| ( $false
= ( rel_b @ sK0 @ X0 ) ) )
| ~ spl17_22
| ~ spl17_27 ),
inference(trivial_inequality_removal,[],[f1084]) ).
thf(f1181,plain,
( ( $true = $false )
| ( $false
= ( rel_b @ sK0 @ sK11 ) )
| ( $true
= ( p @ ( sK16 @ sK11 ) ) )
| ~ spl17_21
| ~ spl17_22
| ~ spl17_27 ),
inference(constrained_superposition,[],[f1085,f457]) ).
thf(f1200,plain,
( ( $false
= ( rel_b @ sK0 @ sK11 ) )
| ( $true
= ( p @ ( sK16 @ sK11 ) ) )
| ~ spl17_21
| ~ spl17_22
| ~ spl17_27 ),
inference(trivial_inequality_removal,[],[f1181]) ).
thf(f1215,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK16 @ sK11 ) ) )
| ~ spl17_18
| ~ spl17_21
| ~ spl17_22
| ~ spl17_27 ),
inference(forward_demodulation,[],[f1200,f446]) ).
thf(f1216,plain,
( ( $true
= ( p @ ( sK16 @ sK11 ) ) )
| ~ spl17_18
| ~ spl17_21
| ~ spl17_22
| ~ spl17_27 ),
inference(trivial_inequality_removal,[],[f1215]) ).
thf(f1221,plain,
( ( $true = $false )
| ~ spl17_18
| ~ spl17_21
| ~ spl17_22
| ~ spl17_27
| ~ spl17_28 ),
inference(forward_demodulation,[],[f1216,f973]) ).
thf(f1222,plain,
( $false
| ~ spl17_18
| ~ spl17_21
| ~ spl17_22
| ~ spl17_27
| ~ spl17_28 ),
inference(trivial_inequality_removal,[],[f1221]) ).
thf(f1223,plain,
( ~ spl17_18
| ~ spl17_21
| ~ spl17_22
| ~ spl17_27
| ~ spl17_28 ),
inference(avatar_contradiction_clause,[],[f1222]) ).
thf(f1311,plain,
( ( $true = $false )
| ( $false
= ( p @ ( sK12 @ sK1 ) ) )
| ~ spl17_2
| ~ spl17_20 ),
inference(constrained_superposition,[],[f382,f453]) ).
thf(f1312,plain,
( ( $true = $false )
| ( $false
= ( p @ ( sK12 @ sK2 ) ) )
| ~ spl17_1
| ~ spl17_20 ),
inference(constrained_superposition,[],[f378,f453]) ).
thf(f1313,plain,
( ( $false
= ( p @ ( sK12 @ sK2 ) ) )
| ~ spl17_1
| ~ spl17_20 ),
inference(trivial_inequality_removal,[],[f1312]) ).
thf(f1314,plain,
( ( $false
= ( p @ ( sK12 @ sK1 ) ) )
| ~ spl17_2
| ~ spl17_20 ),
inference(trivial_inequality_removal,[],[f1311]) ).
thf(f1569,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_b @ ( sK3 @ X0 ) @ X0 ) )
| ( $false
= ( rel_b @ sK1 @ X0 ) ) )
| ~ spl17_4 ),
inference(constrained_superposition,[],[f371,f390]) ).
thf(f1580,plain,
( ! [X0: $i] :
( ( $true
= ( rel_b @ ( sK3 @ X0 ) @ X0 ) )
| ( $false
= ( rel_b @ sK1 @ X0 ) ) )
| ~ spl17_4 ),
inference(trivial_inequality_removal,[],[f1569]) ).
thf(f1611,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_b @ ( sK4 @ X0 ) @ X0 ) )
| ( $false
= ( rel_b @ sK1 @ X0 ) ) )
| ~ spl17_6 ),
inference(constrained_superposition,[],[f371,f398]) ).
thf(f1622,plain,
( ! [X0: $i] :
( ( $true
= ( rel_b @ ( sK4 @ X0 ) @ X0 ) )
| ( $false
= ( rel_b @ sK1 @ X0 ) ) )
| ~ spl17_6 ),
inference(trivial_inequality_removal,[],[f1611]) ).
thf(f1737,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_b @ sK1 @ X0 ) )
| ( $false
= ( rel_b @ sK1 @ X0 ) )
| ( $true
= ( p @ X0 ) ) )
| ~ spl17_4
| ~ spl17_5 ),
inference(constrained_superposition,[],[f1580,f394]) ).
thf(f1738,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_b @ sK1 @ X0 ) )
| ( $true
= ( p @ X0 ) ) )
| ~ spl17_4
| ~ spl17_5 ),
inference(duplicate_literal_removal,[],[f1737]) ).
thf(f1739,plain,
( ! [X0: $i] :
( ( $false
= ( rel_b @ sK1 @ X0 ) )
| ( $true
= ( p @ X0 ) ) )
| ~ spl17_4
| ~ spl17_5 ),
inference(trivial_inequality_removal,[],[f1738]) ).
thf(f1815,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_b @ sK1 @ X0 ) )
| ( $false
= ( rel_b @ sK1 @ X0 ) )
| ( $true
= ( p @ X0 ) ) )
| ~ spl17_6
| ~ spl17_7 ),
inference(constrained_superposition,[],[f1622,f402]) ).
thf(f1816,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_b @ sK1 @ X0 ) )
| ( $true
= ( p @ X0 ) ) )
| ~ spl17_6
| ~ spl17_7 ),
inference(duplicate_literal_removal,[],[f1815]) ).
thf(f1817,plain,
( ! [X0: $i] :
( ( $false
= ( rel_b @ sK1 @ X0 ) )
| ( $true
= ( p @ X0 ) ) )
| ~ spl17_6
| ~ spl17_7 ),
inference(trivial_inequality_removal,[],[f1816]) ).
thf(f1893,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_b @ sK0 @ X0 ) )
| ( $false
= ( rel_b @ sK0 @ X0 ) )
| ( $false
= ( p @ ( sK15 @ X0 ) ) ) )
| ~ spl17_22
| ~ spl17_25 ),
inference(constrained_superposition,[],[f698,f473]) ).
thf(f1894,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_b @ sK0 @ X0 ) )
| ( $false
= ( p @ ( sK15 @ X0 ) ) ) )
| ~ spl17_22
| ~ spl17_25 ),
inference(duplicate_literal_removal,[],[f1893]) ).
thf(f1895,plain,
( ! [X0: $i] :
( ( $false
= ( rel_b @ sK0 @ X0 ) )
| ( $false
= ( p @ ( sK15 @ X0 ) ) ) )
| ~ spl17_22
| ~ spl17_25 ),
inference(trivial_inequality_removal,[],[f1894]) ).
thf(f1987,plain,
( ( $true = $false )
| ( $false
= ( p @ ( sK15 @ sK11 ) ) )
| ~ spl17_18
| ~ spl17_22
| ~ spl17_25 ),
inference(constrained_superposition,[],[f446,f1895]) ).
thf(f1988,plain,
( ( $false
= ( p @ ( sK15 @ sK11 ) ) )
| ~ spl17_18
| ~ spl17_22
| ~ spl17_25 ),
inference(trivial_inequality_removal,[],[f1987]) ).
thf(f2075,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_b @ sK0 @ X0 ) )
| ( $true
= ( rel_b @ X0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( rel_b @ sK0 @ X0 ) ) )
| ~ spl17_22
| ~ spl17_24 ),
inference(constrained_superposition,[],[f698,f469]) ).
thf(f2077,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_b @ sK0 @ X0 ) )
| ( $true
= ( rel_b @ X0 @ ( sK15 @ X0 ) ) ) )
| ~ spl17_22
| ~ spl17_24 ),
inference(duplicate_literal_removal,[],[f2075]) ).
thf(f2078,plain,
( ! [X0: $i] :
( ( $true
= ( rel_b @ X0 @ ( sK15 @ X0 ) ) )
| ( $false
= ( rel_b @ sK0 @ X0 ) ) )
| ~ spl17_22
| ~ spl17_24 ),
inference(trivial_inequality_removal,[],[f2077]) ).
thf(f2210,plain,
( ( $true = $false )
| ( $false
= ( rel_b @ sK0 @ sK11 ) )
| ( $true
= ( p @ ( sK15 @ sK11 ) ) )
| ~ spl17_21
| ~ spl17_22
| ~ spl17_24 ),
inference(constrained_superposition,[],[f2078,f457]) ).
thf(f2237,plain,
( ( $false
= ( rel_b @ sK0 @ sK11 ) )
| ( $true
= ( p @ ( sK15 @ sK11 ) ) )
| ~ spl17_21
| ~ spl17_22
| ~ spl17_24 ),
inference(trivial_inequality_removal,[],[f2210]) ).
thf(f2254,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK15 @ sK11 ) ) )
| ~ spl17_18
| ~ spl17_21
| ~ spl17_22
| ~ spl17_24 ),
inference(forward_demodulation,[],[f2237,f446]) ).
thf(f2255,plain,
( ( $true
= ( p @ ( sK15 @ sK11 ) ) )
| ~ spl17_18
| ~ spl17_21
| ~ spl17_22
| ~ spl17_24 ),
inference(trivial_inequality_removal,[],[f2254]) ).
thf(f2258,plain,
( ( $true = $false )
| ~ spl17_18
| ~ spl17_21
| ~ spl17_22
| ~ spl17_24
| ~ spl17_25 ),
inference(forward_demodulation,[],[f2255,f1988]) ).
thf(f2259,plain,
( $false
| ~ spl17_18
| ~ spl17_21
| ~ spl17_22
| ~ spl17_24
| ~ spl17_25 ),
inference(trivial_inequality_removal,[],[f2258]) ).
thf(f2260,plain,
( ~ spl17_18
| ~ spl17_21
| ~ spl17_22
| ~ spl17_24
| ~ spl17_25 ),
inference(avatar_contradiction_clause,[],[f2259]) ).
thf(f2445,plain,
( ( $true = $false )
| ( $false
= ( rel_b @ sK0 @ sK1 ) )
| ( $true
= ( p @ ( sK12 @ sK1 ) ) )
| ~ spl17_4
| ~ spl17_5
| ~ spl17_19 ),
inference(constrained_superposition,[],[f449,f1739]) ).
thf(f2448,plain,
( ( $false
= ( rel_b @ sK0 @ sK1 ) )
| ( $true
= ( p @ ( sK12 @ sK1 ) ) )
| ~ spl17_4
| ~ spl17_5
| ~ spl17_19 ),
inference(trivial_inequality_removal,[],[f2445]) ).
thf(f2460,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK12 @ sK1 ) ) )
| ~ spl17_2
| ~ spl17_4
| ~ spl17_5
| ~ spl17_19 ),
inference(forward_demodulation,[],[f2448,f382]) ).
thf(f2461,plain,
( ( $true
= ( p @ ( sK12 @ sK1 ) ) )
| ~ spl17_2
| ~ spl17_4
| ~ spl17_5
| ~ spl17_19 ),
inference(trivial_inequality_removal,[],[f2460]) ).
thf(f2464,plain,
( ( $true = $false )
| ~ spl17_2
| ~ spl17_4
| ~ spl17_5
| ~ spl17_19
| ~ spl17_20 ),
inference(forward_demodulation,[],[f2461,f1314]) ).
thf(f2465,plain,
( $false
| ~ spl17_2
| ~ spl17_4
| ~ spl17_5
| ~ spl17_19
| ~ spl17_20 ),
inference(trivial_inequality_removal,[],[f2464]) ).
thf(f2466,plain,
( ~ spl17_2
| ~ spl17_4
| ~ spl17_5
| ~ spl17_19
| ~ spl17_20 ),
inference(avatar_contradiction_clause,[],[f2465]) ).
thf(f2787,plain,
( ( $true = $false )
| ( $false
= ( rel_b @ sK0 @ sK1 ) )
| ( $true
= ( p @ ( sK12 @ sK1 ) ) )
| ~ spl17_6
| ~ spl17_7
| ~ spl17_19 ),
inference(constrained_superposition,[],[f449,f1817]) ).
thf(f2790,plain,
( ( $false
= ( rel_b @ sK0 @ sK1 ) )
| ( $true
= ( p @ ( sK12 @ sK1 ) ) )
| ~ spl17_6
| ~ spl17_7
| ~ spl17_19 ),
inference(trivial_inequality_removal,[],[f2787]) ).
thf(f2800,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK12 @ sK1 ) ) )
| ~ spl17_2
| ~ spl17_6
| ~ spl17_7
| ~ spl17_19 ),
inference(forward_demodulation,[],[f2790,f382]) ).
thf(f2801,plain,
( ( $true
= ( p @ ( sK12 @ sK1 ) ) )
| ~ spl17_2
| ~ spl17_6
| ~ spl17_7
| ~ spl17_19 ),
inference(trivial_inequality_removal,[],[f2800]) ).
thf(f2804,plain,
( ( $true = $false )
| ~ spl17_2
| ~ spl17_6
| ~ spl17_7
| ~ spl17_19
| ~ spl17_20 ),
inference(forward_demodulation,[],[f2801,f1314]) ).
thf(f2805,plain,
( $false
| ~ spl17_2
| ~ spl17_6
| ~ spl17_7
| ~ spl17_19
| ~ spl17_20 ),
inference(trivial_inequality_removal,[],[f2804]) ).
thf(f2806,plain,
( ~ spl17_2
| ~ spl17_6
| ~ spl17_7
| ~ spl17_19
| ~ spl17_20 ),
inference(avatar_contradiction_clause,[],[f2805]) ).
thf(f3062,plain,
( ( $true = $false )
| ( $false
= ( rel_b @ sK0 @ sK2 ) )
| ( $true
= ( p @ ( sK12 @ sK2 ) ) )
| ~ spl17_3
| ~ spl17_19 ),
inference(constrained_superposition,[],[f449,f386]) ).
thf(f3065,plain,
( ( $false
= ( rel_b @ sK0 @ sK2 ) )
| ( $true
= ( p @ ( sK12 @ sK2 ) ) )
| ~ spl17_3
| ~ spl17_19 ),
inference(trivial_inequality_removal,[],[f3062]) ).
thf(f3075,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK12 @ sK2 ) ) )
| ~ spl17_1
| ~ spl17_3
| ~ spl17_19 ),
inference(forward_demodulation,[],[f3065,f378]) ).
thf(f3076,plain,
( ( $true
= ( p @ ( sK12 @ sK2 ) ) )
| ~ spl17_1
| ~ spl17_3
| ~ spl17_19 ),
inference(trivial_inequality_removal,[],[f3075]) ).
thf(f3085,plain,
( ( $true = $false )
| ~ spl17_1
| ~ spl17_3
| ~ spl17_19
| ~ spl17_20 ),
inference(forward_demodulation,[],[f3076,f1313]) ).
thf(f3086,plain,
( $false
| ~ spl17_1
| ~ spl17_3
| ~ spl17_19
| ~ spl17_20 ),
inference(trivial_inequality_removal,[],[f3085]) ).
thf(f3087,plain,
( ~ spl17_1
| ~ spl17_3
| ~ spl17_19
| ~ spl17_20 ),
inference(avatar_contradiction_clause,[],[f3086]) ).
cnf(s1,plain,
( spl17_1
| spl17_2 ),
inference(sat_conversion,[],[f383]) ).
cnf(s2,plain,
( spl17_2
| spl17_3 ),
inference(sat_conversion,[],[f387]) ).
cnf(s3,plain,
( spl17_1
| spl17_4 ),
inference(sat_conversion,[],[f391]) ).
cnf(s4,plain,
( spl17_1
| spl17_5 ),
inference(sat_conversion,[],[f395]) ).
cnf(s5,plain,
( spl17_3
| spl17_6 ),
inference(sat_conversion,[],[f399]) ).
cnf(s6,plain,
( spl17_3
| spl17_7 ),
inference(sat_conversion,[],[f403]) ).
cnf(s16,plain,
( spl17_18
| spl17_19 ),
inference(sat_conversion,[],[f450]) ).
cnf(s17,plain,
( spl17_18
| spl17_20 ),
inference(sat_conversion,[],[f454]) ).
cnf(s18,plain,
( spl17_19
| spl17_21 ),
inference(sat_conversion,[],[f458]) ).
cnf(s19,plain,
( spl17_20
| spl17_21 ),
inference(sat_conversion,[],[f459]) ).
cnf(s20,plain,
( spl17_22
| spl17_23 ),
inference(sat_conversion,[],[f466]) ).
cnf(s21,plain,
( spl17_23
| spl17_24 ),
inference(sat_conversion,[],[f470]) ).
cnf(s22,plain,
( spl17_23
| spl17_25 ),
inference(sat_conversion,[],[f474]) ).
cnf(s23,plain,
( spl17_22
| spl17_26 ),
inference(sat_conversion,[],[f478]) ).
cnf(s24,plain,
( spl17_26
| spl17_27 ),
inference(sat_conversion,[],[f482]) ).
cnf(s25,plain,
( spl17_26
| spl17_28 ),
inference(sat_conversion,[],[f486]) ).
cnf(s28,plain,
( ~ spl17_18
| ~ spl17_21
| ~ spl17_23
| ~ spl17_26 ),
inference(sat_conversion,[],[f550]) ).
cnf(s40,plain,
( ~ spl17_18
| ~ spl17_21
| ~ spl17_22
| ~ spl17_27
| ~ spl17_28 ),
inference(sat_conversion,[],[f1223]) ).
cnf(s70,plain,
( ~ spl17_18
| ~ spl17_21
| ~ spl17_22
| ~ spl17_24
| ~ spl17_25 ),
inference(sat_conversion,[],[f2260]) ).
cnf(s74,plain,
( ~ spl17_2
| ~ spl17_4
| ~ spl17_5
| ~ spl17_19
| ~ spl17_20 ),
inference(sat_conversion,[],[f2466]) ).
cnf(s84,plain,
( ~ spl17_2
| ~ spl17_6
| ~ spl17_7
| ~ spl17_19
| ~ spl17_20 ),
inference(sat_conversion,[],[f2806]) ).
cnf(s95,plain,
( ~ spl17_1
| ~ spl17_3
| ~ spl17_19
| ~ spl17_20 ),
inference(sat_conversion,[],[f3087]) ).
cnf(s98,plain,
( spl17_18
| spl17_3
| ~ spl17_2 ),
inference(rat,[],[s84,s16,s17,s6,s5]) ).
cnf(s99,plain,
( spl17_22
| ~ spl17_21
| ~ spl17_18 ),
inference(rat,[],[s28,s20,s23]) ).
cnf(s102,plain,
( spl17_21
| spl17_3
| ~ spl17_2 ),
inference(rat,[],[s84,s18,s19,s6,s5]) ).
cnf(s103,plain,
( spl17_26
| ~ spl17_21
| ~ spl17_18 ),
inference(rat,[],[s40,s24,s25,s99]) ).
cnf(s104,plain,
( ~ spl17_21
| ~ spl17_18 ),
inference(rat,[],[s70,s21,s22,s28,s103,s99]) ).
cnf(s105,plain,
( spl17_3
| ~ spl17_2 ),
inference(rat,[],[s104,s102,s98]) ).
cnf(s106,plain,
( spl17_21
| spl17_1 ),
inference(rat,[],[s74,s18,s19,s4,s3,s1]) ).
cnf(s107,plain,
spl17_1,
inference(rat,[],[s74,s16,s17,s104,s106,s1,s3,s4]) ).
cnf(s108,plain,
spl17_3,
inference(rat,[],[s105,s2]) ).
cnf(s109,plain,
spl17_21,
inference(rat,[],[s95,s18,s19,s107,s108]) ).
cnf(s110,plain,
~ spl17_18,
inference(rat,[],[s104,s109]) ).
cnf(s111,plain,
spl17_20,
inference(rat,[],[s17,s110]) ).
cnf(s112,plain,
spl17_19,
inference(rat,[],[s16,s110]) ).
cnf(s113,plain,
$false,
inference(rat,[],[s95,s108,s107,s111,s112]) ).
thf(f3088,plain,
$false,
inference(avatar_sat_refutation,[],[s113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO430^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 % Computer : n003.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 16:53:29 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.87/0.39 % (2753043)Will run a generic schedule for satisfiability detection.
% 0.87/0.39 % (2753054)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2358228507:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.87/0.39 % (2753049)% WARNING: option uhcvi not known.
% 0.87/0.39 % (2753048)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3810283857_2999 on theBenchmark for (2999ds/0Mi)
% 0.87/0.39 % (2753050)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3276725426:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.87/0.39 % (2753049)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3274424196:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.87/0.39 % (2753049)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.87/0.39 % Exception at run slice level
% 0.87/0.39 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.87/0.39 % (2753049)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.87/0.39 % (2753051)dis+10_1_sil=32000:sp=arity:random_seed=2307665561:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.87/0.39 % (2753052)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1119470340:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.87/0.39 % (2753052)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.87/0.39 % (2753053)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=539722863:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.87/0.39 % (2753060)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=227134511:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.87/0.39 % Exception at run slice level
% 0.87/0.39 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.87/0.39 % (2753054)Instruction limit reached!
% 0.87/0.39 % (2753054)------------------------------
% 0.87/0.39 % (2753054)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.39 % (2753054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.39 % (2753054)CaDiCaL version: 2.1.3
% 0.87/0.39 % (2753054)Termination reason: Instruction limit
% 0.87/0.39 % (2753054)Termination phase: Saturation
% 0.87/0.39 % (2753054)Time elapsed: 0.043 s
% 0.87/0.39 % (2753054)Peak memory usage: 13 MB
% 0.87/0.39 % (2753054)Instructions burned: 163 (million)
% 0.87/0.39 % (2753064)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3619849520:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.87/0.39 % (2753065)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3683995325:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.87/0.39 % (2753065)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.87/0.39 % (2753065)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.87/0.39 % (2753051)Instruction limit reached!
% 0.87/0.39 % (2753051)------------------------------
% 0.87/0.39 % (2753051)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.39 % (2753051)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.39 % (2753051)CaDiCaL version: 2.1.3
% 0.87/0.39 % (2753051)Termination reason: Instruction limit
% 0.87/0.39 % (2753051)Termination phase: Saturation
% 0.87/0.39 % (2753051)Time elapsed: 0.054 s
% 0.87/0.39 % (2753051)Peak memory usage: 12 MB
% 0.87/0.39 % (2753051)Instructions burned: 103 (million)
% 0.87/0.39 % (2753053)Instruction limit reached!
% 0.87/0.39 % (2753053)------------------------------
% 0.87/0.39 % (2753053)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.39 % (2753053)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.39 % (2753053)CaDiCaL version: 2.1.3
% 0.87/0.39 % (2753053)Termination reason: Instruction limit
% 0.87/0.39 % (2753053)Termination phase: Saturation
% 0.87/0.39 % (2753053)Time elapsed: 0.066 s
% 0.87/0.39 % (2753053)Peak memory usage: 12 MB
% 0.87/0.39 % (2753053)Instructions burned: 132 (million)
% 0.87/0.39 % (2753068)ott-21_1_sil=16000:fs=off:random_seed=4145591929:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.87/0.39 % (2753069)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=183865506:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.87/0.39 % (2753065) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2753043-2753065"...
% 0.87/0.39 % (2753052)Instruction limit reached!
% 0.87/0.39 % (2753052)------------------------------
% 0.87/0.39 % (2753052)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.39 % (2753052)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.39 % (2753052)CaDiCaL version: 2.1.3
% 0.87/0.39 % (2753052)Termination reason: Instruction limit
% 0.87/0.39 % (2753052)Termination phase: Saturation
% 0.87/0.39 % (2753052)Time elapsed: 0.105 s
% 0.87/0.39 % (2753052)Peak memory usage: 12 MB
% 0.87/0.39 % (2753052)Instructions burned: 117 (million)
% 0.87/0.39 % (2753064)Instruction limit reached!
% 0.87/0.39 % (2753064)------------------------------
% 0.87/0.39 % (2753064)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.39 % (2753064)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.39 % (2753064)CaDiCaL version: 2.1.3
% 0.87/0.39 % (2753064)Termination reason: Instruction limit
% 0.87/0.39 % (2753064)Termination phase: Saturation
% 0.87/0.39 % (2753064)Time elapsed: 0.065 s
% 0.87/0.39 % (2753064)Peak memory usage: 12 MB
% 0.87/0.39 % (2753064)Instructions burned: 131 (million)
% 0.87/0.39 % (2753065)...printing done.
% 0.87/0.39 % (2753065)Refutation found. Thanks to Tanya!
% 0.87/0.39 % SZS status Theorem for theBenchmark
% 0.87/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.87/0.40 % (2753065)------------------------------
% 0.87/0.40 % (2753065)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.87/0.40 % (2753065)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.87/0.40 % (2753065)CaDiCaL version: 2.1.3
% 0.87/0.40 % (2753065)Termination reason: Refutation
% 0.87/0.40 % (2753065)Time elapsed: 0.061 s
% 0.87/0.40 % (2753065)Peak memory usage: 14 MB
% 0.87/0.40 % (2753065)Instructions burned: 235 (million)
% 0.87/0.40 % (2753043)Success in time 0.145 s
% 0.87/0.40 % Vampire exiting
%------------------------------------------------------------------------------