%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO392^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 08:49:51 AM UTC 2026
% Result : Theorem 0.19s 0.32s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 33
% Syntax : Number of formulae : 408 ( 48 unt; 0 typ; 24 def)
% Number of atoms : 4647 ( 874 equ; 0 cnn)
% Maximal formula atoms : 12 ( 11 avg)
% Number of connectives : 7013 (1564 ~;1422 |; 0 &;3658 @)
% ( 24 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 113 ( 113 >; 0 *; 0 +; 0 <<)
% Number of symbols : 92 ( 88 usr; 30 con; 0-4 aty)
% ( 345 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 946 ( 0 sgn 361 !; 0 ?; 946 :)
% 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_k: $i > $i > $o ).
thf(func_def_33,type,
mbox_k: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_k: ( $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_62,type,
sK11: $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(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_k
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_k @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^1.ax',mbox_k) ).
thf(f33,axiom,
( mdia_k
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_k @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^1.ax',mdia_k) ).
thf(f34,conjecture,
mvalid @ ( mequiv @ ( mnot @ ( mbox_k @ ( mdia_k @ ( mbox_k @ p ) ) ) ) @ ( mdia_k @ ( mbox_k @ ( mdia_k @ ( mnot @ p ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f35,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mnot @ ( mbox_k @ ( mdia_k @ ( mbox_k @ p ) ) ) ) @ ( mdia_k @ ( mbox_k @ ( mdia_k @ ( mnot @ p ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
thf(f38,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f39,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f40,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f41,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f42,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f43,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f45,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f79,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f80,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f79]) ).
thf(f87,plain,
( mbox_k
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_k @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f88,plain,
( mbox_k
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f87]) ).
thf(f89,plain,
( mdia_k
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_k @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f90,plain,
~ ( mvalid @ ( mequiv @ ( mnot @ ( mbox_k @ ( mdia_k @ ( mbox_k @ p ) ) ) ) @ ( mdia_k @ ( mbox_k @ ( mdia_k @ ( mnot @ p ) ) ) ) ) ),
inference(rectify,[],[f35]) ).
thf(f91,plain,
( ( mvalid @ ( mequiv @ ( mnot @ ( mbox_k @ ( mdia_k @ ( mbox_k @ p ) ) ) ) @ ( mdia_k @ ( mbox_k @ ( mdia_k @ ( mnot @ p ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f90]) ).
thf(f92,plain,
( ( mvalid @ ( mequiv @ ( mnot @ ( mbox_k @ ( mdia_k @ ( mbox_k @ p ) ) ) ) @ ( mdia_k @ ( mbox_k @ ( mdia_k @ ( mnot @ p ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f91]) ).
thf(f95,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f96,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f97,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f98,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f100,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f120,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f80]) ).
thf(f124,plain,
( mbox_k
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f125,plain,
( mdia_k
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_k @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f89]) ).
thf(f126,plain,
( ( mvalid @ ( mequiv @ ( mnot @ ( mbox_k @ ( mdia_k @ ( mbox_k @ p ) ) ) ) @ ( mdia_k @ ( mbox_k @ ( mdia_k @ ( mnot @ p ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f92]) ).
thf(f129,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,[],[f97,f95,f96,f95,f95]) ).
thf(f130,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,[],[f98,f96,f95]) ).
thf(f132,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,[],[f100,f129,f130,f130]) ).
thf(f138,plain,
( mdia_k
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_k @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f125,f95,f124,f95]) ).
thf(f139,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] :
~ ( Y0 @ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_k @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p ) ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_k @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_k @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ p ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f126,f120,f132,f95,f124,f138,f124,f138,f124,f138,f95]) ).
thf(f140,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_k @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_k @ Y2 @ Y3 )
| ~ ~ ( p @ Y3 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_k @ Y2 @ Y3 )
| ~ ~ ( p @ Y3 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_k @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f141,plain,
( $false
= ( ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_k @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_k @ Y2 @ Y3 )
| ~ ~ ( p @ Y3 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_k @ Y2 @ Y3 )
| ~ ~ ( p @ Y3 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_k @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f140]) ).
thf(f142,plain,
( $false
= ( ~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f143,plain,
( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f142]) ).
thf(f144,plain,
( ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f143]) ).
thf(f145,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f145]) ).
thf(f148,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f147]) ).
thf(f149,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f148]) ).
thf(f150,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) )
@ sK1 ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f149]) ).
thf(f151,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) )
@ sK1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) )
@ sK1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) )
@ sK1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f151]) ).
thf(f154,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) )
@ sK1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f153]) ).
thf(f155,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) )
@ sK1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( ( $false
= ( ~ ( rel_k @ sK0 @ sK1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( $false
= ( ~ ( rel_k @ sK0 @ sK1 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f160,plain,
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f163,plain,
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( rel_k @ sK0 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f165,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( ~ ( rel_k @ sK2 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK2 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ( p @ Y0 ) )
@ ( sK3 @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK2 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ( p @ Y0 ) )
@ ( sK3 @ X1 ) ) )
| ( $false
= ( rel_k @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( ~ ( rel_k @ X1 @ ( sK3 @ X1 ) )
| ( p @ ( sK3 @ X1 ) ) ) )
| ( $false
= ( rel_k @ sK2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f172,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( p @ ( sK3 @ X1 ) ) )
| ( $false
= ( rel_k @ sK2 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( ~ ( rel_k @ X1 @ ( sK3 @ X1 ) ) ) )
| ( $false
= ( rel_k @ sK2 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f174,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( rel_k @ X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( rel_k @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f158]) ).
thf(f176,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) )
@ X1 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f179,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( rel_k @ sK0 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_k @ sK1 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) ) )
| ( $true
= ( rel_k @ sK0 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f181,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) ) )
| ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( ~ ( rel_k @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) )
| ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( ~ ( rel_k @ sK1 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ~ ( p @ Y0 ) )
@ ( sK4 @ X1 ) ) )
| ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( ~ ( rel_k @ sK1 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ~ ( p @ Y0 ) )
@ ( sK4 @ X1 ) ) )
| ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_k @ X1 @ ( sK4 @ X1 ) )
| ~ ~ ( p @ ( sK4 @ X1 ) ) ) )
| ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f184]) ).
thf(f186,plain,
! [X1: $i] :
( ( $false
= ( ~ ~ ( p @ ( sK4 @ X1 ) ) ) )
| ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_k @ X1 @ ( sK4 @ X1 ) ) ) )
| ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f185]) ).
thf(f188,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK4 @ X1 ) ) )
| ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X1: $i] :
( ( $true
= ( ~ ( p @ ( sK4 @ X1 ) ) ) )
| ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f186]) ).
thf(f190,plain,
! [X1: $i] :
( ( $false
= ( p @ ( sK4 @ X1 ) ) )
| ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f192,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f191]) ).
thf(f193,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_k @ sK1 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK2 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f192]) ).
thf(f194,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK2 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK2 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK1 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ~ ( p @ Y0 ) )
@ ( sK5 @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK2 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK1 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ~ ( p @ Y0 ) )
@ ( sK5 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK2 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ~ ( p @ Y0 ) )
@ ( sK5 @ X1 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ~ ( p @ Y0 ) )
@ ( sK5 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ( p @ Y0 ) )
@ ( sK6 @ X2 ) ) )
| ( $true
= ( ~ ( rel_k @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK2 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ~ ( p @ Y0 ) )
@ ( sK5 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ( p @ Y0 ) )
@ ( sK6 @ X2 ) ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) )
| ( $true
= ( ~ ( rel_k @ sK2 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ~ ( p @ Y0 ) )
@ ( sK5 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ( p @ Y0 ) )
@ ( sK6 @ X2 ) ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) )
| ( $false
= ( rel_k @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_k @ X1 @ ( sK5 @ X1 ) )
| ~ ~ ( p @ ( sK5 @ X1 ) ) ) )
| ( $false
= ( ~ ( rel_k @ X2 @ ( sK6 @ X2 ) )
| ( p @ ( sK6 @ X2 ) ) ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) )
| ( $false
= ( rel_k @ sK2 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f201]) ).
thf(f203,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ~ ( p @ ( sK5 @ X1 ) ) ) )
| ( $false
= ( ~ ( rel_k @ X2 @ ( sK6 @ X2 ) )
| ( p @ ( sK6 @ X2 ) ) ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) )
| ( $false
= ( rel_k @ sK2 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_k @ X1 @ ( sK5 @ X1 ) ) ) )
| ( $false
= ( ~ ( rel_k @ X2 @ ( sK6 @ X2 ) )
| ( p @ ( sK6 @ X2 ) ) ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) )
| ( $false
= ( rel_k @ sK2 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f202]) ).
thf(f205,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( ~ ( rel_k @ X2 @ ( sK6 @ X2 ) )
| ( p @ ( sK6 @ X2 ) ) ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) )
| ( $false
= ( rel_k @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( p @ ( sK6 @ X2 ) ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) )
| ( $false
= ( rel_k @ sK2 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( ~ ( rel_k @ X2 @ ( sK6 @ X2 ) ) ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) )
| ( $false
= ( rel_k @ sK2 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f205]) ).
thf(f208,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK5 @ X1 ) ) )
| ( $true
= ( rel_k @ X2 @ ( sK6 @ X2 ) ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) )
| ( $false
= ( rel_k @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( p @ ( sK5 @ X1 ) ) ) )
| ( $false
= ( ~ ( rel_k @ X2 @ ( sK6 @ X2 ) )
| ( p @ ( sK6 @ X2 ) ) ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) )
| ( $false
= ( rel_k @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f203]) ).
thf(f210,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ ( sK5 @ X1 ) ) )
| ( $false
= ( ~ ( rel_k @ X2 @ ( sK6 @ X2 ) )
| ( p @ ( sK6 @ X2 ) ) ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) )
| ( $false
= ( rel_k @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f209]) ).
thf(f211,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ ( sK5 @ X1 ) ) )
| ( $false
= ( p @ ( sK6 @ X2 ) ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) )
| ( $false
= ( rel_k @ sK2 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f210]) ).
thf(f212,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ ( sK5 @ X1 ) ) )
| ( $false
= ( ~ ( rel_k @ X2 @ ( sK6 @ X2 ) ) ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) )
| ( $false
= ( rel_k @ sK2 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f210]) ).
thf(f213,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ ( sK5 @ X1 ) ) )
| ( $true
= ( rel_k @ X2 @ ( sK6 @ X2 ) ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) )
| ( $false
= ( rel_k @ sK2 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f212]) ).
thf(f214,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) )
@ sK1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f152]) ).
thf(f215,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) )
@ sK1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f214]) ).
thf(f216,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_k @ sK0 @ sK1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f215]) ).
thf(f217,plain,
! [X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f216]) ).
thf(f218,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_k @ sK0 @ sK1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f216]) ).
thf(f219,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f218]) ).
thf(f220,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f219]) ).
thf(f221,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f220]) ).
thf(f222,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) )
@ ( sK7 @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f221]) ).
thf(f223,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) )
@ ( sK7 @ X1 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f222]) ).
thf(f224,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( ~ ( rel_k @ X1 @ ( sK7 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ ( sK7 @ X1 ) @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f223]) ).
thf(f225,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ ( sK7 @ X1 ) @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f224]) ).
thf(f226,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( ~ ( rel_k @ X1 @ ( sK7 @ X1 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f224]) ).
thf(f227,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( rel_k @ X1 @ ( sK7 @ X1 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f226]) ).
thf(f228,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ ( sK7 @ X1 ) @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f225]) ).
thf(f229,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ ( sK7 @ X1 ) @ Y0 )
| ~ ~ ( p @ Y0 ) )
@ X2 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( ~ ( rel_k @ ( sK7 @ X1 ) @ X2 )
| ~ ~ ( p @ X2 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f229]) ).
thf(f231,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( ~ ~ ( p @ X2 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_k @ ( sK7 @ X1 ) @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f230]) ).
thf(f232,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( ~ ( p @ X2 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_k @ ( sK7 @ X1 ) @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f231]) ).
thf(f233,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_k @ ( sK7 @ X1 ) @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ ( sK7 @ X1 ) @ X2 ) ) ),
inference(not_proxy_clausification,[],[f233]) ).
thf(f235,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f217]) ).
thf(f236,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f235]) ).
thf(f237,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f236]) ).
thf(f238,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) )
@ X2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f237]) ).
thf(f239,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) )
@ ( sK8 @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f238]) ).
thf(f240,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) )
@ X2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) )
@ ( sK8 @ X1 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f239]) ).
thf(f241,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_k @ sK1 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_k @ X1 @ ( sK8 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ ( sK8 @ X1 ) @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f240]) ).
thf(f242,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_k @ X1 @ ( sK8 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ ( sK8 @ X1 ) @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_k @ sK1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f241]) ).
thf(f243,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) )
| ( $false
= ( ~ ( rel_k @ X1 @ ( sK8 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ ( sK8 @ X1 ) @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_k @ sK1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f242]) ).
thf(f244,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ~ ~ ( p @ Y0 ) )
@ ( sK9 @ X2 ) ) )
| ( $false
= ( ~ ( rel_k @ X1 @ ( sK8 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ ( sK8 @ X1 ) @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_k @ sK1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f243]) ).
thf(f245,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ~ ~ ( p @ Y0 ) )
@ ( sK9 @ X2 ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ ( sK8 @ X1 ) @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_k @ sK1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f244]) ).
thf(f246,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ~ ~ ( p @ Y0 ) )
@ ( sK9 @ X2 ) ) )
| ( $false
= ( ~ ( rel_k @ X1 @ ( sK8 @ X1 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_k @ sK1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f244]) ).
thf(f247,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ~ ~ ( p @ Y0 ) )
@ ( sK9 @ X2 ) ) )
| ( $true
= ( rel_k @ X1 @ ( sK8 @ X1 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_k @ sK1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f246]) ).
thf(f248,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ~ ~ ( p @ Y0 ) )
@ ( sK9 @ X2 ) ) )
| ( $true
= ( rel_k @ X1 @ ( sK8 @ X1 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f247]) ).
thf(f249,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_k @ X2 @ ( sK9 @ X2 ) )
| ~ ~ ( p @ ( sK9 @ X2 ) ) ) )
| ( $true
= ( rel_k @ X1 @ ( sK8 @ X1 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f248]) ).
thf(f250,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ~ ( p @ ( sK9 @ X2 ) ) ) )
| ( $true
= ( rel_k @ X1 @ ( sK8 @ X1 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK1 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f249]) ).
thf(f251,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_k @ X2 @ ( sK9 @ X2 ) ) ) )
| ( $true
= ( rel_k @ X1 @ ( sK8 @ X1 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK1 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f249]) ).
thf(f252,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_k @ X2 @ ( sK9 @ X2 ) ) )
| ( $true
= ( rel_k @ X1 @ ( sK8 @ X1 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f251]) ).
thf(f253,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( p @ ( sK9 @ X2 ) ) ) )
| ( $true
= ( rel_k @ X1 @ ( sK8 @ X1 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f250]) ).
thf(f254,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ ( sK9 @ X2 ) ) )
| ( $true
= ( rel_k @ X1 @ ( sK8 @ X1 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f253]) ).
thf(f255,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ~ ~ ( p @ Y0 ) )
@ ( sK9 @ X2 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ ( sK8 @ X1 ) @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_k @ sK1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f245]) ).
thf(f256,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ~ ~ ( p @ Y0 ) )
@ ( sK9 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ ( sK8 @ X1 ) @ Y0 )
| ~ ~ ( p @ Y0 ) )
@ X3 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_k @ sK1 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f255]) ).
thf(f257,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ~ ~ ( p @ Y0 ) )
@ ( sK9 @ X2 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ ( sK8 @ X1 ) @ Y0 )
| ~ ~ ( p @ Y0 ) )
@ X3 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f256]) ).
thf(f258,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ~ ( rel_k @ X2 @ ( sK9 @ X2 ) )
| ~ ~ ( p @ ( sK9 @ X2 ) ) ) )
| ( $true
= ( ~ ( rel_k @ ( sK8 @ X1 ) @ X3 )
| ~ ~ ( p @ X3 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f257]) ).
thf(f259,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ~ ~ ( p @ ( sK9 @ X2 ) ) ) )
| ( $true
= ( ~ ( rel_k @ ( sK8 @ X1 ) @ X3 )
| ~ ~ ( p @ X3 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK1 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f258]) ).
thf(f260,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ~ ( rel_k @ X2 @ ( sK9 @ X2 ) ) ) )
| ( $true
= ( ~ ( rel_k @ ( sK8 @ X1 ) @ X3 )
| ~ ~ ( p @ X3 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK1 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f258]) ).
thf(f261,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_k @ X2 @ ( sK9 @ X2 ) ) )
| ( $true
= ( ~ ( rel_k @ ( sK8 @ X1 ) @ X3 )
| ~ ~ ( p @ X3 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f260]) ).
thf(f262,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_k @ X2 @ ( sK9 @ X2 ) ) )
| ( $true
= ( ~ ~ ( p @ X3 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK1 @ X2 ) )
| ( $true
= ( ~ ( rel_k @ ( sK8 @ X1 ) @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f261]) ).
thf(f263,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_k @ X2 @ ( sK9 @ X2 ) ) )
| ( $false
= ( ~ ( p @ X3 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK1 @ X2 ) )
| ( $true
= ( ~ ( rel_k @ ( sK8 @ X1 ) @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f262]) ).
thf(f264,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_k @ X2 @ ( sK9 @ X2 ) ) )
| ( $true
= ( p @ X3 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK1 @ X2 ) )
| ( $true
= ( ~ ( rel_k @ ( sK8 @ X1 ) @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f263]) ).
thf(f265,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_k @ X2 @ ( sK9 @ X2 ) ) )
| ( $true
= ( p @ X3 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK1 @ X2 ) )
| ( $false
= ( rel_k @ ( sK8 @ X1 ) @ X3 ) ) ),
inference(not_proxy_clausification,[],[f264]) ).
thf(f266,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( p @ ( sK9 @ X2 ) ) ) )
| ( $true
= ( ~ ( rel_k @ ( sK8 @ X1 ) @ X3 )
| ~ ~ ( p @ X3 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f259]) ).
thf(f267,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p @ ( sK9 @ X2 ) ) )
| ( $true
= ( ~ ( rel_k @ ( sK8 @ X1 ) @ X3 )
| ~ ~ ( p @ X3 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f266]) ).
thf(f268,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p @ ( sK9 @ X2 ) ) )
| ( $true
= ( ~ ~ ( p @ X3 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK1 @ X2 ) )
| ( $true
= ( ~ ( rel_k @ ( sK8 @ X1 ) @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f267]) ).
thf(f269,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p @ ( sK9 @ X2 ) ) )
| ( $false
= ( ~ ( p @ X3 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK1 @ X2 ) )
| ( $true
= ( ~ ( rel_k @ ( sK8 @ X1 ) @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f268]) ).
thf(f270,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p @ ( sK9 @ X2 ) ) )
| ( $true
= ( p @ X3 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK1 @ X2 ) )
| ( $true
= ( ~ ( rel_k @ ( sK8 @ X1 ) @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f269]) ).
thf(f271,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p @ ( sK9 @ X2 ) ) )
| ( $true
= ( p @ X3 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK1 @ X2 ) )
| ( $false
= ( rel_k @ ( sK8 @ X1 ) @ X3 ) ) ),
inference(not_proxy_clausification,[],[f270]) ).
thf(f272,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f146]) ).
thf(f273,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X1 ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f272]) ).
thf(f274,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f273]) ).
thf(f275,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f274]) ).
thf(f325,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f275]) ).
thf(f326,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ~ ~ ( p @ Y2 ) ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f325]) ).
thf(f327,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_k @ sK0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f326]) ).
thf(f328,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f327]) ).
thf(f329,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f328]) ).
thf(f330,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ ( sK14 @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f329]) ).
thf(f331,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ ( sK14 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f330]) ).
thf(f332,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ ( sK14 @ X1 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f331]) ).
thf(f333,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ ( sK14 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) )
@ ( sK15 @ X2 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f332]) ).
thf(f334,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ ( sK14 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) )
@ ( sK15 @ X2 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f333]) ).
thf(f335,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ ( sK14 @ X1 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( p @ Y1 ) ) ) )
@ ( sK15 @ X2 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f334]) ).
thf(f336,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_k @ X1 @ ( sK14 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ ( sK14 @ X1 ) @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_k @ X2 @ ( sK15 @ X2 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ ( sK15 @ X2 ) @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f335]) ).
thf(f337,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ ( sK14 @ X1 ) @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_k @ X2 @ ( sK15 @ X2 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ ( sK15 @ X2 ) @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f336]) ).
thf(f338,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_k @ X1 @ ( sK14 @ X1 ) ) ) )
| ( $false
= ( ~ ( rel_k @ X2 @ ( sK15 @ X2 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ ( sK15 @ X2 ) @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f336]) ).
thf(f339,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK14 @ X1 ) ) )
| ( $false
= ( ~ ( rel_k @ X2 @ ( sK15 @ X2 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ ( sK15 @ X2 ) @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f338]) ).
thf(f340,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK14 @ X1 ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ ( sK15 @ X2 ) @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f339]) ).
thf(f341,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK14 @ X1 ) ) )
| ( $false
= ( ~ ( rel_k @ X2 @ ( sK15 @ X2 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f339]) ).
thf(f342,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK14 @ X1 ) ) )
| ( $true
= ( rel_k @ X2 @ ( sK15 @ X2 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f341]) ).
thf(f343,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK14 @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ ( sK15 @ X2 ) @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f340]) ).
thf(f344,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK14 @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ ( sK15 @ X2 ) @ Y0 )
| ~ ~ ( p @ Y0 ) )
@ X3 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f343]) ).
thf(f345,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK14 @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ ( sK15 @ X2 ) @ X3 )
| ~ ~ ( p @ X3 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f344]) ).
thf(f346,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK14 @ X1 ) ) )
| ( $true
= ( ~ ~ ( p @ X3 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $true
= ( ~ ( rel_k @ ( sK15 @ X2 ) @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f345]) ).
thf(f347,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK14 @ X1 ) ) )
| ( $false
= ( ~ ( p @ X3 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $true
= ( ~ ( rel_k @ ( sK15 @ X2 ) @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f346]) ).
thf(f348,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK14 @ X1 ) ) )
| ( $true
= ( p @ X3 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $true
= ( ~ ( rel_k @ ( sK15 @ X2 ) @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f347]) ).
thf(f349,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK14 @ X1 ) ) )
| ( $true
= ( p @ X3 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $false
= ( rel_k @ ( sK15 @ X2 ) @ X3 ) ) ),
inference(not_proxy_clausification,[],[f348]) ).
thf(f350,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ ( sK14 @ X1 ) @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $false
= ( ~ ( rel_k @ X2 @ ( sK15 @ X2 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ ( sK15 @ X2 ) @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f337]) ).
thf(f351,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ ( sK14 @ X1 ) @ Y0 )
| ( p @ Y0 ) )
@ X3 ) )
| ( $false
= ( ~ ( rel_k @ X2 @ ( sK15 @ X2 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ ( sK15 @ X2 ) @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f350]) ).
thf(f352,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ ( sK14 @ X1 ) @ Y0 )
| ( p @ Y0 ) )
@ X3 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ ( sK15 @ X2 ) @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f351]) ).
thf(f353,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ ( sK14 @ X1 ) @ Y0 )
| ( p @ Y0 ) )
@ X3 ) )
| ( $false
= ( ~ ( rel_k @ X2 @ ( sK15 @ X2 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f351]) ).
thf(f354,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ ( sK14 @ X1 ) @ Y0 )
| ( p @ Y0 ) )
@ X3 ) )
| ( $true
= ( rel_k @ X2 @ ( sK15 @ X2 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f353]) ).
thf(f355,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( rel_k @ ( sK14 @ X1 ) @ X3 )
| ( p @ X3 ) ) )
| ( $true
= ( rel_k @ X2 @ ( sK15 @ X2 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f354]) ).
thf(f356,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p @ X3 ) )
| ( $true
= ( rel_k @ X2 @ ( sK15 @ X2 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $true
= ( ~ ( rel_k @ ( sK14 @ X1 ) @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f355]) ).
thf(f357,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( p @ X3 ) )
| ( $true
= ( rel_k @ X2 @ ( sK15 @ X2 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $false
= ( rel_k @ ( sK14 @ X1 ) @ X3 ) ) ),
inference(not_proxy_clausification,[],[f356]) ).
thf(f358,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ ( sK14 @ X1 ) @ Y0 )
| ( p @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ ( sK15 @ X2 ) @ Y0 )
| ~ ~ ( p @ Y0 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f352]) ).
thf(f359,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ ( sK14 @ X1 ) @ Y0 )
| ( p @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ ( sK15 @ X2 ) @ Y0 )
| ~ ~ ( p @ Y0 ) )
@ X4 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f358]) ).
thf(f360,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_k @ ( sK14 @ X1 ) @ X3 )
| ( p @ X3 ) ) )
| ( $true
= ( ~ ( rel_k @ ( sK15 @ X2 ) @ X4 )
| ~ ~ ( p @ X4 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f359]) ).
thf(f361,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( p @ X3 ) )
| ( $true
= ( ~ ( rel_k @ ( sK15 @ X2 ) @ X4 )
| ~ ~ ( p @ X4 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $true
= ( ~ ( rel_k @ ( sK14 @ X1 ) @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f360]) ).
thf(f362,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( p @ X3 ) )
| ( $true
= ( ~ ~ ( p @ X4 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $true
= ( ~ ( rel_k @ ( sK14 @ X1 ) @ X3 ) ) )
| ( $true
= ( ~ ( rel_k @ ( sK15 @ X2 ) @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f361]) ).
thf(f363,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( p @ X3 ) )
| ( $false
= ( ~ ( p @ X4 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $true
= ( ~ ( rel_k @ ( sK14 @ X1 ) @ X3 ) ) )
| ( $true
= ( ~ ( rel_k @ ( sK15 @ X2 ) @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f362]) ).
thf(f364,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X4 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $true
= ( ~ ( rel_k @ ( sK14 @ X1 ) @ X3 ) ) )
| ( $true
= ( ~ ( rel_k @ ( sK15 @ X2 ) @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f363]) ).
thf(f365,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X4 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $false
= ( rel_k @ ( sK14 @ X1 ) @ X3 ) )
| ( $true
= ( ~ ( rel_k @ ( sK15 @ X2 ) @ X4 ) ) ) ),
inference(not_proxy_clausification,[],[f364]) ).
thf(f366,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( p @ X3 ) )
| ( $true
= ( p @ X4 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $false
= ( rel_k @ ( sK14 @ X1 ) @ X3 ) )
| ( $false
= ( rel_k @ ( sK15 @ X2 ) @ X4 ) ) ),
inference(not_proxy_clausification,[],[f365]) ).
thf(f368,definition,
( spl16_1
<=> ( $true
= ( rel_k @ sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_1])],[avatar_definition]) ).
thf(f370,plain,
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ~ spl16_1 ),
inference(avatar_component_clause,[],[f368]) ).
thf(f372,definition,
( spl16_2
<=> ( $true
= ( rel_k @ sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_2])],[avatar_definition]) ).
thf(f374,plain,
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ~ spl16_2 ),
inference(avatar_component_clause,[],[f372]) ).
thf(f375,plain,
( spl16_1
| spl16_2 ),
inference(avatar_split_clause,[],[f163,f372,f368]) ).
thf(f377,definition,
( spl16_3
<=> ! [X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( rel_k @ sK2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_3])],[avatar_definition]) ).
thf(f378,plain,
( ! [X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( rel_k @ sK2 @ X1 ) ) )
| ~ spl16_3 ),
inference(avatar_component_clause,[],[f377]) ).
thf(f379,plain,
( spl16_3
| spl16_2 ),
inference(avatar_split_clause,[],[f174,f372,f377]) ).
thf(f381,definition,
( spl16_4
<=> ! [X1: $i] :
( ( $false
= ( p @ ( sK3 @ X1 ) ) )
| ( $false
= ( rel_k @ sK2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_4])],[avatar_definition]) ).
thf(f382,plain,
( ! [X1: $i] :
( ( $false
= ( rel_k @ sK2 @ X1 ) )
| ( $false
= ( p @ ( sK3 @ X1 ) ) ) )
| ~ spl16_4 ),
inference(avatar_component_clause,[],[f381]) ).
thf(f383,plain,
( spl16_4
| spl16_2 ),
inference(avatar_split_clause,[],[f172,f372,f381]) ).
thf(f385,definition,
( spl16_5
<=> ! [X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK4 @ X1 ) ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_5])],[avatar_definition]) ).
thf(f386,plain,
( ! [X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK4 @ X1 ) ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) ) )
| ~ spl16_5 ),
inference(avatar_component_clause,[],[f385]) ).
thf(f387,plain,
( spl16_1
| spl16_5 ),
inference(avatar_split_clause,[],[f188,f385,f368]) ).
thf(f389,definition,
( spl16_6
<=> ! [X1: $i] :
( ( $false
= ( p @ ( sK4 @ X1 ) ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_6])],[avatar_definition]) ).
thf(f390,plain,
( ! [X1: $i] :
( ( $false
= ( rel_k @ sK1 @ X1 ) )
| ( $false
= ( p @ ( sK4 @ X1 ) ) ) )
| ~ spl16_6 ),
inference(avatar_component_clause,[],[f389]) ).
thf(f391,plain,
( spl16_1
| spl16_6 ),
inference(avatar_split_clause,[],[f190,f389,f368]) ).
thf(f393,definition,
( spl16_7
<=> ! [X2: $i] :
( ( $true
= ( rel_k @ X2 @ ( sK6 @ X2 ) ) )
| ( $false
= ( rel_k @ sK2 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_7])],[avatar_definition]) ).
thf(f394,plain,
( ! [X2: $i] :
( ( $true
= ( rel_k @ X2 @ ( sK6 @ X2 ) ) )
| ( $false
= ( rel_k @ sK2 @ X2 ) ) )
| ~ spl16_7 ),
inference(avatar_component_clause,[],[f393]) ).
thf(f396,definition,
( spl16_8
<=> ! [X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_8])],[avatar_definition]) ).
thf(f397,plain,
( ! [X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK5 @ X1 ) ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) ) )
| ~ spl16_8 ),
inference(avatar_component_clause,[],[f396]) ).
thf(f398,plain,
( spl16_7
| spl16_8 ),
inference(avatar_split_clause,[],[f208,f396,f393]) ).
thf(f400,definition,
( spl16_9
<=> ! [X2: $i] :
( ( $false
= ( p @ ( sK6 @ X2 ) ) )
| ( $false
= ( rel_k @ sK2 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_9])],[avatar_definition]) ).
thf(f401,plain,
( ! [X2: $i] :
( ( $false
= ( rel_k @ sK2 @ X2 ) )
| ( $false
= ( p @ ( sK6 @ X2 ) ) ) )
| ~ spl16_9 ),
inference(avatar_component_clause,[],[f400]) ).
thf(f402,plain,
( spl16_9
| spl16_8 ),
inference(avatar_split_clause,[],[f206,f396,f400]) ).
thf(f404,definition,
( spl16_10
<=> ! [X1: $i] :
( ( $false
= ( p @ ( sK5 @ X1 ) ) )
| ( $false
= ( rel_k @ sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_10])],[avatar_definition]) ).
thf(f405,plain,
( ! [X1: $i] :
( ( $false
= ( rel_k @ sK1 @ X1 ) )
| ( $false
= ( p @ ( sK5 @ X1 ) ) ) )
| ~ spl16_10 ),
inference(avatar_component_clause,[],[f404]) ).
thf(f406,plain,
( spl16_7
| spl16_10 ),
inference(avatar_split_clause,[],[f213,f404,f393]) ).
thf(f407,plain,
( spl16_9
| spl16_10 ),
inference(avatar_split_clause,[],[f211,f404,f400]) ).
thf(f409,definition,
( spl16_11
<=> ! [X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK7 @ X1 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_11])],[avatar_definition]) ).
thf(f410,plain,
( ! [X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK7 @ X1 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) )
| ~ spl16_11 ),
inference(avatar_component_clause,[],[f409]) ).
thf(f411,plain,
( spl16_11
| spl16_2 ),
inference(avatar_split_clause,[],[f227,f372,f409]) ).
thf(f413,definition,
( spl16_12
<=> ! [X2: $i,X1: $i] :
( ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ ( sK7 @ X1 ) @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_12])],[avatar_definition]) ).
thf(f414,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( rel_k @ ( sK7 @ X1 ) @ X2 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( p @ X2 ) ) )
| ~ spl16_12 ),
inference(avatar_component_clause,[],[f413]) ).
thf(f415,plain,
( spl16_12
| spl16_2 ),
inference(avatar_split_clause,[],[f234,f372,f413]) ).
thf(f417,definition,
( spl16_13
<=> ! [X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK8 @ X1 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_13])],[avatar_definition]) ).
thf(f418,plain,
( ! [X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK8 @ X1 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) )
| ~ spl16_13 ),
inference(avatar_component_clause,[],[f417]) ).
thf(f420,definition,
( spl16_14
<=> ! [X2: $i] :
( ( $true
= ( rel_k @ X2 @ ( sK9 @ X2 ) ) )
| ( $false
= ( rel_k @ sK1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_14])],[avatar_definition]) ).
thf(f421,plain,
( ! [X2: $i] :
( ( $true
= ( rel_k @ X2 @ ( sK9 @ X2 ) ) )
| ( $false
= ( rel_k @ sK1 @ X2 ) ) )
| ~ spl16_14 ),
inference(avatar_component_clause,[],[f420]) ).
thf(f422,plain,
( spl16_13
| spl16_14 ),
inference(avatar_split_clause,[],[f252,f420,f417]) ).
thf(f424,definition,
( spl16_15
<=> ! [X2: $i] :
( ( $false
= ( p @ ( sK9 @ X2 ) ) )
| ( $false
= ( rel_k @ sK1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_15])],[avatar_definition]) ).
thf(f425,plain,
( ! [X2: $i] :
( ( $false
= ( rel_k @ sK1 @ X2 ) )
| ( $false
= ( p @ ( sK9 @ X2 ) ) ) )
| ~ spl16_15 ),
inference(avatar_component_clause,[],[f424]) ).
thf(f426,plain,
( spl16_13
| spl16_15 ),
inference(avatar_split_clause,[],[f254,f424,f417]) ).
thf(f428,definition,
( spl16_16
<=> ! [X1: $i,X3: $i] :
( ( $true
= ( p @ X3 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ ( sK8 @ X1 ) @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_16])],[avatar_definition]) ).
thf(f429,plain,
( ! [X3: $i,X1: $i] :
( ( $false
= ( rel_k @ ( sK8 @ X1 ) @ X3 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( p @ X3 ) ) )
| ~ spl16_16 ),
inference(avatar_component_clause,[],[f428]) ).
thf(f430,plain,
( spl16_16
| spl16_14 ),
inference(avatar_split_clause,[],[f265,f420,f428]) ).
thf(f431,plain,
( spl16_16
| spl16_15 ),
inference(avatar_split_clause,[],[f271,f424,f428]) ).
thf(f461,definition,
( spl16_24
<=> ! [X2: $i] :
( ( $true
= ( rel_k @ X2 @ ( sK15 @ X2 ) ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_24])],[avatar_definition]) ).
thf(f462,plain,
( ! [X2: $i] :
( ( $true
= ( rel_k @ X2 @ ( sK15 @ X2 ) ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) )
| ~ spl16_24 ),
inference(avatar_component_clause,[],[f461]) ).
thf(f464,definition,
( spl16_25
<=> ! [X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK14 @ X1 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_25])],[avatar_definition]) ).
thf(f465,plain,
( ! [X1: $i] :
( ( $true
= ( rel_k @ X1 @ ( sK14 @ X1 ) ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) )
| ~ spl16_25 ),
inference(avatar_component_clause,[],[f464]) ).
thf(f466,plain,
( spl16_24
| spl16_25 ),
inference(avatar_split_clause,[],[f342,f464,f461]) ).
thf(f468,definition,
( spl16_26
<=> ! [X2: $i,X3: $i] :
( ( $true
= ( p @ X3 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $false
= ( rel_k @ ( sK15 @ X2 ) @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_26])],[avatar_definition]) ).
thf(f469,plain,
( ! [X2: $i,X3: $i] :
( ( $false
= ( rel_k @ ( sK15 @ X2 ) @ X3 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $true
= ( p @ X3 ) ) )
| ~ spl16_26 ),
inference(avatar_component_clause,[],[f468]) ).
thf(f470,plain,
( spl16_26
| spl16_25 ),
inference(avatar_split_clause,[],[f349,f464,f468]) ).
thf(f472,definition,
( spl16_27
<=> ! [X1: $i,X3: $i] :
( ( $true
= ( p @ X3 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ ( sK14 @ X1 ) @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_27])],[avatar_definition]) ).
thf(f473,plain,
( ! [X3: $i,X1: $i] :
( ( $false
= ( rel_k @ ( sK14 @ X1 ) @ X3 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( p @ X3 ) ) )
| ~ spl16_27 ),
inference(avatar_component_clause,[],[f472]) ).
thf(f474,plain,
( spl16_24
| spl16_27 ),
inference(avatar_split_clause,[],[f357,f472,f461]) ).
thf(f475,plain,
( spl16_26
| spl16_27 ),
inference(avatar_split_clause,[],[f366,f472,f468]) ).
thf(f527,plain,
( ( $true = $false )
| ( $false
= ( p @ ( sK9 @ ( sK15 @ sK1 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ sK1 ) )
| ~ spl16_15
| ~ spl16_24 ),
inference(constrained_superposition,[],[f425,f462]) ).
thf(f532,plain,
( ( $false
= ( p @ ( sK9 @ ( sK15 @ sK1 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ sK1 ) )
| ~ spl16_15
| ~ spl16_24 ),
inference(trivial_inequality_removal,[],[f527]) ).
thf(f580,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_k @ sK0 @ X0 ) )
| ( $true
= ( p @ ( sK9 @ ( sK15 @ X0 ) ) ) )
| ( $false
= ( rel_k @ sK1 @ ( sK15 @ X0 ) ) ) )
| ~ spl16_14
| ~ spl16_26 ),
inference(constrained_superposition,[],[f469,f421]) ).
thf(f585,plain,
( ! [X0: $i] :
( ( $false
= ( rel_k @ sK1 @ ( sK15 @ X0 ) ) )
| ( $true
= ( p @ ( sK9 @ ( sK15 @ X0 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X0 ) ) )
| ~ spl16_14
| ~ spl16_26 ),
inference(trivial_inequality_removal,[],[f580]) ).
thf(f606,plain,
( ( $true = $false )
| ( $false
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( p @ ( sK4 @ ( sK8 @ sK1 ) ) ) )
| ~ spl16_6
| ~ spl16_13 ),
inference(constrained_superposition,[],[f418,f390]) ).
thf(f615,plain,
( ( $false
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( p @ ( sK4 @ ( sK8 @ sK1 ) ) ) )
| ~ spl16_6
| ~ spl16_13 ),
inference(trivial_inequality_removal,[],[f606]) ).
thf(f717,plain,
( ( $true = $false )
| ( $false
= ( rel_k @ sK0 @ sK2 ) )
| ( $false
= ( p @ ( sK6 @ ( sK8 @ sK2 ) ) ) )
| ~ spl16_9
| ~ spl16_13 ),
inference(constrained_superposition,[],[f418,f401]) ).
thf(f718,plain,
( ( $false
= ( rel_k @ sK0 @ sK2 ) )
| ( $false
= ( p @ ( sK6 @ ( sK8 @ sK2 ) ) ) )
| ~ spl16_9
| ~ spl16_13 ),
inference(trivial_inequality_removal,[],[f717]) ).
thf(f725,plain,
( ( $true = $false )
| ( $false
= ( p @ ( sK6 @ ( sK8 @ sK2 ) ) ) )
| ~ spl16_1
| ~ spl16_9
| ~ spl16_13 ),
inference(forward_demodulation,[],[f718,f370]) ).
thf(f726,plain,
( ( $false
= ( p @ ( sK6 @ ( sK8 @ sK2 ) ) ) )
| ~ spl16_1
| ~ spl16_9
| ~ spl16_13 ),
inference(trivial_inequality_removal,[],[f725]) ).
thf(f747,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_k @ sK0 @ X0 ) )
| ( $true
= ( p @ ( sK6 @ ( sK8 @ X0 ) ) ) )
| ( $false
= ( rel_k @ sK2 @ ( sK8 @ X0 ) ) ) )
| ~ spl16_7
| ~ spl16_16 ),
inference(constrained_superposition,[],[f429,f394]) ).
thf(f754,plain,
( ! [X0: $i] :
( ( $false
= ( rel_k @ sK2 @ ( sK8 @ X0 ) ) )
| ( $true
= ( p @ ( sK6 @ ( sK8 @ X0 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X0 ) ) )
| ~ spl16_7
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f747]) ).
thf(f839,plain,
( ( $true = $false )
| ( $false
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( p @ ( sK6 @ ( sK8 @ sK2 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ sK2 ) )
| ~ spl16_7
| ~ spl16_13
| ~ spl16_16 ),
inference(constrained_superposition,[],[f418,f754]) ).
thf(f840,plain,
( ( $true = $false )
| ( $false
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( p @ ( sK6 @ ( sK8 @ sK2 ) ) ) )
| ~ spl16_7
| ~ spl16_13
| ~ spl16_16 ),
inference(duplicate_literal_removal,[],[f839]) ).
thf(f841,plain,
( ( $false
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( p @ ( sK6 @ ( sK8 @ sK2 ) ) ) )
| ~ spl16_7
| ~ spl16_13
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f840]) ).
thf(f845,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK6 @ ( sK8 @ sK2 ) ) ) )
| ~ spl16_1
| ~ spl16_7
| ~ spl16_13
| ~ spl16_16 ),
inference(forward_demodulation,[],[f841,f370]) ).
thf(f846,plain,
( ( $true
= ( p @ ( sK6 @ ( sK8 @ sK2 ) ) ) )
| ~ spl16_1
| ~ spl16_7
| ~ spl16_13
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f845]) ).
thf(f849,plain,
( ( $true = $false )
| ~ spl16_1
| ~ spl16_7
| ~ spl16_9
| ~ spl16_13
| ~ spl16_16 ),
inference(forward_demodulation,[],[f846,f726]) ).
thf(f850,plain,
( $false
| ~ spl16_1
| ~ spl16_7
| ~ spl16_9
| ~ spl16_13
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f849]) ).
thf(f851,plain,
( ~ spl16_1
| ~ spl16_7
| ~ spl16_9
| ~ spl16_13
| ~ spl16_16 ),
inference(avatar_contradiction_clause,[],[f850]) ).
thf(f860,plain,
( ( $true = $false )
| ( $false
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( p @ ( sK5 @ ( sK8 @ sK1 ) ) ) )
| ~ spl16_10
| ~ spl16_13 ),
inference(constrained_superposition,[],[f418,f405]) ).
thf(f865,plain,
( ( $false
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( p @ ( sK5 @ ( sK8 @ sK1 ) ) ) )
| ~ spl16_10
| ~ spl16_13 ),
inference(trivial_inequality_removal,[],[f860]) ).
thf(f876,plain,
( ( $true = $false )
| ( $false
= ( p @ ( sK5 @ ( sK8 @ sK1 ) ) ) )
| ~ spl16_2
| ~ spl16_10
| ~ spl16_13 ),
inference(forward_demodulation,[],[f865,f374]) ).
thf(f877,plain,
( ( $false
= ( p @ ( sK5 @ ( sK8 @ sK1 ) ) ) )
| ~ spl16_2
| ~ spl16_10
| ~ spl16_13 ),
inference(trivial_inequality_removal,[],[f876]) ).
thf(f892,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_k @ sK0 @ X0 ) )
| ( $true
= ( p @ ( sK5 @ ( sK8 @ X0 ) ) ) )
| ( $false
= ( rel_k @ sK1 @ ( sK8 @ X0 ) ) ) )
| ~ spl16_8
| ~ spl16_16 ),
inference(constrained_superposition,[],[f429,f397]) ).
thf(f899,plain,
( ! [X0: $i] :
( ( $false
= ( rel_k @ sK1 @ ( sK8 @ X0 ) ) )
| ( $true
= ( p @ ( sK5 @ ( sK8 @ X0 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X0 ) ) )
| ~ spl16_8
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f892]) ).
thf(f964,plain,
( ( $true = $false )
| ( $false
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( p @ ( sK5 @ ( sK8 @ sK1 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ sK1 ) )
| ~ spl16_8
| ~ spl16_13
| ~ spl16_16 ),
inference(constrained_superposition,[],[f418,f899]) ).
thf(f965,plain,
( ( $true = $false )
| ( $false
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( p @ ( sK5 @ ( sK8 @ sK1 ) ) ) )
| ~ spl16_8
| ~ spl16_13
| ~ spl16_16 ),
inference(duplicate_literal_removal,[],[f964]) ).
thf(f966,plain,
( ( $false
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( p @ ( sK5 @ ( sK8 @ sK1 ) ) ) )
| ~ spl16_8
| ~ spl16_13
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f965]) ).
thf(f970,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK5 @ ( sK8 @ sK1 ) ) ) )
| ~ spl16_2
| ~ spl16_8
| ~ spl16_13
| ~ spl16_16 ),
inference(forward_demodulation,[],[f966,f374]) ).
thf(f971,plain,
( ( $true
= ( p @ ( sK5 @ ( sK8 @ sK1 ) ) ) )
| ~ spl16_2
| ~ spl16_8
| ~ spl16_13
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f970]) ).
thf(f974,plain,
( ( $true = $false )
| ~ spl16_2
| ~ spl16_8
| ~ spl16_10
| ~ spl16_13
| ~ spl16_16 ),
inference(forward_demodulation,[],[f971,f877]) ).
thf(f975,plain,
( $false
| ~ spl16_2
| ~ spl16_8
| ~ spl16_10
| ~ spl16_13
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f974]) ).
thf(f976,plain,
( ~ spl16_2
| ~ spl16_8
| ~ spl16_10
| ~ spl16_13
| ~ spl16_16 ),
inference(avatar_contradiction_clause,[],[f975]) ).
thf(f978,definition,
( spl16_46
<=> ( $false
= ( rel_k @ sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl16_46])],[avatar_definition]) ).
thf(f979,plain,
( ( $false
!= ( rel_k @ sK0 @ sK1 ) )
| spl16_46 ),
inference(avatar_component_clause,[],[f978]) ).
thf(f980,plain,
( ( $false
= ( rel_k @ sK0 @ sK1 ) )
| ~ spl16_46 ),
inference(avatar_component_clause,[],[f978]) ).
thf(f994,definition,
( spl16_49
<=> ( $false
= ( p @ ( sK9 @ ( sK15 @ sK1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_49])],[avatar_definition]) ).
thf(f996,plain,
( ( $false
= ( p @ ( sK9 @ ( sK15 @ sK1 ) ) ) )
| ~ spl16_49 ),
inference(avatar_component_clause,[],[f994]) ).
thf(f1003,plain,
( spl16_46
| spl16_49
| ~ spl16_15
| ~ spl16_24 ),
inference(avatar_split_clause,[],[f532,f461,f424,f994,f978]) ).
thf(f1006,definition,
( spl16_51
<=> ( $false
= ( p @ ( sK4 @ ( sK8 @ sK1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_51])],[avatar_definition]) ).
thf(f1008,plain,
( ( $false
= ( p @ ( sK4 @ ( sK8 @ sK1 ) ) ) )
| ~ spl16_51 ),
inference(avatar_component_clause,[],[f1006]) ).
thf(f1015,plain,
( spl16_51
| spl16_46
| ~ spl16_6
| ~ spl16_13 ),
inference(avatar_split_clause,[],[f615,f417,f389,f978,f1006]) ).
thf(f1100,plain,
( ( $true = $false )
| ( $false
= ( p @ ( sK3 @ ( sK7 @ sK2 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ sK2 ) )
| ~ spl16_4
| ~ spl16_11 ),
inference(constrained_superposition,[],[f382,f410]) ).
thf(f1101,plain,
( ( $false
= ( p @ ( sK3 @ ( sK7 @ sK2 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ sK2 ) )
| ~ spl16_4
| ~ spl16_11 ),
inference(trivial_inequality_removal,[],[f1100]) ).
thf(f1115,plain,
( ( $true = $false )
| ( $false
= ( p @ ( sK3 @ ( sK7 @ sK2 ) ) ) )
| ~ spl16_1
| ~ spl16_4
| ~ spl16_11 ),
inference(forward_demodulation,[],[f1101,f370]) ).
thf(f1116,plain,
( ( $false
= ( p @ ( sK3 @ ( sK7 @ sK2 ) ) ) )
| ~ spl16_1
| ~ spl16_4
| ~ spl16_11 ),
inference(trivial_inequality_removal,[],[f1115]) ).
thf(f1153,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_k @ sK0 @ X0 ) )
| ( $true
= ( p @ ( sK3 @ ( sK7 @ X0 ) ) ) )
| ( $false
= ( rel_k @ sK2 @ ( sK7 @ X0 ) ) ) )
| ~ spl16_3
| ~ spl16_12 ),
inference(constrained_superposition,[],[f414,f378]) ).
thf(f1168,plain,
( ! [X0: $i] :
( ( $false
= ( rel_k @ sK2 @ ( sK7 @ X0 ) ) )
| ( $true
= ( p @ ( sK3 @ ( sK7 @ X0 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X0 ) ) )
| ~ spl16_3
| ~ spl16_12 ),
inference(trivial_inequality_removal,[],[f1153]) ).
thf(f1258,plain,
( ( $true = $false )
| ( $false
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( p @ ( sK9 @ ( sK14 @ sK1 ) ) ) )
| ~ spl16_15
| ~ spl16_25 ),
inference(constrained_superposition,[],[f465,f425]) ).
thf(f1277,plain,
( ( $false
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( p @ ( sK9 @ ( sK14 @ sK1 ) ) ) )
| ~ spl16_15
| ~ spl16_25 ),
inference(trivial_inequality_removal,[],[f1258]) ).
thf(f1578,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_k @ sK0 @ X0 ) )
| ( $true
= ( p @ ( sK9 @ ( sK14 @ X0 ) ) ) )
| ( $false
= ( rel_k @ sK1 @ ( sK14 @ X0 ) ) ) )
| ~ spl16_14
| ~ spl16_27 ),
inference(constrained_superposition,[],[f473,f421]) ).
thf(f1589,plain,
( ! [X0: $i] :
( ( $false
= ( rel_k @ sK1 @ ( sK14 @ X0 ) ) )
| ( $true
= ( p @ ( sK9 @ ( sK14 @ X0 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ X0 ) ) )
| ~ spl16_14
| ~ spl16_27 ),
inference(trivial_inequality_removal,[],[f1578]) ).
thf(f1620,plain,
( ( $true = $false )
| ( $false
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( p @ ( sK3 @ ( sK7 @ sK2 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ sK2 ) )
| ~ spl16_3
| ~ spl16_11
| ~ spl16_12 ),
inference(constrained_superposition,[],[f410,f1168]) ).
thf(f1621,plain,
( ( $true = $false )
| ( $false
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( p @ ( sK3 @ ( sK7 @ sK2 ) ) ) )
| ~ spl16_3
| ~ spl16_11
| ~ spl16_12 ),
inference(duplicate_literal_removal,[],[f1620]) ).
thf(f1622,plain,
( ( $false
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( p @ ( sK3 @ ( sK7 @ sK2 ) ) ) )
| ~ spl16_3
| ~ spl16_11
| ~ spl16_12 ),
inference(trivial_inequality_removal,[],[f1621]) ).
thf(f1626,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK3 @ ( sK7 @ sK2 ) ) ) )
| ~ spl16_1
| ~ spl16_3
| ~ spl16_11
| ~ spl16_12 ),
inference(forward_demodulation,[],[f1622,f370]) ).
thf(f1627,plain,
( ( $true
= ( p @ ( sK3 @ ( sK7 @ sK2 ) ) ) )
| ~ spl16_1
| ~ spl16_3
| ~ spl16_11
| ~ spl16_12 ),
inference(trivial_inequality_removal,[],[f1626]) ).
thf(f1630,plain,
( ( $true = $false )
| ~ spl16_1
| ~ spl16_3
| ~ spl16_4
| ~ spl16_11
| ~ spl16_12 ),
inference(forward_demodulation,[],[f1627,f1116]) ).
thf(f1631,plain,
( $false
| ~ spl16_1
| ~ spl16_3
| ~ spl16_4
| ~ spl16_11
| ~ spl16_12 ),
inference(trivial_inequality_removal,[],[f1630]) ).
thf(f1632,plain,
( ~ spl16_1
| ~ spl16_3
| ~ spl16_4
| ~ spl16_11
| ~ spl16_12 ),
inference(avatar_contradiction_clause,[],[f1631]) ).
thf(f1651,plain,
( ( $true = $false )
| ~ spl16_2
| ~ spl16_46 ),
inference(forward_demodulation,[],[f374,f980]) ).
thf(f1652,plain,
( $false
| ~ spl16_2
| ~ spl16_46 ),
inference(trivial_inequality_removal,[],[f1651]) ).
thf(f1653,plain,
( ~ spl16_2
| ~ spl16_46 ),
inference(avatar_contradiction_clause,[],[f1652]) ).
thf(f1666,definition,
( spl16_73
<=> ( $false
= ( p @ ( sK9 @ ( sK14 @ sK1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl16_73])],[avatar_definition]) ).
thf(f1668,plain,
( ( $false
= ( p @ ( sK9 @ ( sK14 @ sK1 ) ) ) )
| ~ spl16_73 ),
inference(avatar_component_clause,[],[f1666]) ).
thf(f1676,plain,
( spl16_73
| spl16_46
| ~ spl16_15
| ~ spl16_25 ),
inference(avatar_split_clause,[],[f1277,f464,f424,f978,f1666]) ).
thf(f1790,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK9 @ ( sK15 @ sK1 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( rel_k @ sK0 @ sK1 ) )
| ~ spl16_14
| ~ spl16_24
| ~ spl16_26 ),
inference(constrained_superposition,[],[f585,f462]) ).
thf(f1794,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK9 @ ( sK15 @ sK1 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ sK1 ) )
| ~ spl16_14
| ~ spl16_24
| ~ spl16_26 ),
inference(duplicate_literal_removal,[],[f1790]) ).
thf(f1795,plain,
( ( $true
= ( p @ ( sK9 @ ( sK15 @ sK1 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ sK1 ) )
| ~ spl16_14
| ~ spl16_24
| ~ spl16_26 ),
inference(trivial_inequality_removal,[],[f1794]) ).
thf(f1798,plain,
( ( $true
= ( p @ ( sK9 @ ( sK15 @ sK1 ) ) ) )
| ~ spl16_14
| ~ spl16_24
| ~ spl16_26
| spl16_46 ),
inference(forward_subsumption_resolution,[],[f1795,f979]) ).
thf(f1802,plain,
( ( $true = $false )
| ~ spl16_14
| ~ spl16_24
| ~ spl16_26
| spl16_46
| ~ spl16_49 ),
inference(forward_demodulation,[],[f1798,f996]) ).
thf(f1803,plain,
( $false
| ~ spl16_14
| ~ spl16_24
| ~ spl16_26
| spl16_46
| ~ spl16_49 ),
inference(trivial_inequality_removal,[],[f1802]) ).
thf(f1804,plain,
( ~ spl16_14
| ~ spl16_24
| ~ spl16_26
| spl16_46
| ~ spl16_49 ),
inference(avatar_contradiction_clause,[],[f1803]) ).
thf(f2096,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK9 @ ( sK14 @ sK1 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( rel_k @ sK0 @ sK1 ) )
| ~ spl16_14
| ~ spl16_25
| ~ spl16_27 ),
inference(constrained_superposition,[],[f1589,f465]) ).
thf(f2100,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK9 @ ( sK14 @ sK1 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ sK1 ) )
| ~ spl16_14
| ~ spl16_25
| ~ spl16_27 ),
inference(duplicate_literal_removal,[],[f2096]) ).
thf(f2101,plain,
( ( $true
= ( p @ ( sK9 @ ( sK14 @ sK1 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ sK1 ) )
| ~ spl16_14
| ~ spl16_25
| ~ spl16_27 ),
inference(trivial_inequality_removal,[],[f2100]) ).
thf(f2104,plain,
( ( $true
= ( p @ ( sK9 @ ( sK14 @ sK1 ) ) ) )
| ~ spl16_14
| ~ spl16_25
| ~ spl16_27
| spl16_46 ),
inference(forward_subsumption_resolution,[],[f2101,f979]) ).
thf(f2108,plain,
( ( $true = $false )
| ~ spl16_14
| ~ spl16_25
| ~ spl16_27
| spl16_46
| ~ spl16_73 ),
inference(forward_demodulation,[],[f2104,f1668]) ).
thf(f2109,plain,
( $false
| ~ spl16_14
| ~ spl16_25
| ~ spl16_27
| spl16_46
| ~ spl16_73 ),
inference(trivial_inequality_removal,[],[f2108]) ).
thf(f2110,plain,
( ~ spl16_14
| ~ spl16_25
| ~ spl16_27
| spl16_46
| ~ spl16_73 ),
inference(avatar_contradiction_clause,[],[f2109]) ).
thf(f2443,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_k @ sK1 @ ( sK8 @ X0 ) ) )
| ( $false
= ( rel_k @ sK0 @ X0 ) )
| ( $true
= ( p @ ( sK4 @ ( sK8 @ X0 ) ) ) ) )
| ~ spl16_5
| ~ spl16_16 ),
inference(constrained_superposition,[],[f386,f429]) ).
thf(f2456,plain,
( ! [X0: $i] :
( ( $false
= ( rel_k @ sK1 @ ( sK8 @ X0 ) ) )
| ( $false
= ( rel_k @ sK0 @ X0 ) )
| ( $true
= ( p @ ( sK4 @ ( sK8 @ X0 ) ) ) ) )
| ~ spl16_5
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f2443]) ).
thf(f2990,plain,
( ( $true = $false )
| ( $false
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( p @ ( sK4 @ ( sK8 @ sK1 ) ) ) )
| ( $false
= ( rel_k @ sK0 @ sK1 ) )
| ~ spl16_5
| ~ spl16_13
| ~ spl16_16 ),
inference(constrained_superposition,[],[f2456,f418]) ).
thf(f2994,plain,
( ( $true = $false )
| ( $false
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( p @ ( sK4 @ ( sK8 @ sK1 ) ) ) )
| ~ spl16_5
| ~ spl16_13
| ~ spl16_16 ),
inference(duplicate_literal_removal,[],[f2990]) ).
thf(f2995,plain,
( ( $false
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( p @ ( sK4 @ ( sK8 @ sK1 ) ) ) )
| ~ spl16_5
| ~ spl16_13
| ~ spl16_16 ),
inference(trivial_inequality_removal,[],[f2994]) ).
thf(f2998,plain,
( ( $true
= ( p @ ( sK4 @ ( sK8 @ sK1 ) ) ) )
| ~ spl16_5
| ~ spl16_13
| ~ spl16_16
| spl16_46 ),
inference(forward_subsumption_resolution,[],[f2995,f979]) ).
thf(f3002,plain,
( ( $true = $false )
| ~ spl16_5
| ~ spl16_13
| ~ spl16_16
| spl16_46
| ~ spl16_51 ),
inference(forward_demodulation,[],[f2998,f1008]) ).
thf(f3003,plain,
( $false
| ~ spl16_5
| ~ spl16_13
| ~ spl16_16
| spl16_46
| ~ spl16_51 ),
inference(trivial_inequality_removal,[],[f3002]) ).
thf(f3004,plain,
( ~ spl16_5
| ~ spl16_13
| ~ spl16_16
| spl16_46
| ~ spl16_51 ),
inference(avatar_contradiction_clause,[],[f3003]) ).
cnf(s1,plain,
( spl16_1
| spl16_2 ),
inference(sat_conversion,[],[f375]) ).
cnf(s2,plain,
( spl16_2
| spl16_3 ),
inference(sat_conversion,[],[f379]) ).
cnf(s3,plain,
( spl16_2
| spl16_4 ),
inference(sat_conversion,[],[f383]) ).
cnf(s4,plain,
( spl16_1
| spl16_5 ),
inference(sat_conversion,[],[f387]) ).
cnf(s5,plain,
( spl16_1
| spl16_6 ),
inference(sat_conversion,[],[f391]) ).
cnf(s6,plain,
( spl16_7
| spl16_8 ),
inference(sat_conversion,[],[f398]) ).
cnf(s7,plain,
( spl16_8
| spl16_9 ),
inference(sat_conversion,[],[f402]) ).
cnf(s8,plain,
( spl16_7
| spl16_10 ),
inference(sat_conversion,[],[f406]) ).
cnf(s9,plain,
( spl16_9
| spl16_10 ),
inference(sat_conversion,[],[f407]) ).
cnf(s10,plain,
( spl16_2
| spl16_11 ),
inference(sat_conversion,[],[f411]) ).
cnf(s11,plain,
( spl16_2
| spl16_12 ),
inference(sat_conversion,[],[f415]) ).
cnf(s12,plain,
( spl16_13
| spl16_14 ),
inference(sat_conversion,[],[f422]) ).
cnf(s13,plain,
( spl16_13
| spl16_15 ),
inference(sat_conversion,[],[f426]) ).
cnf(s14,plain,
( spl16_14
| spl16_16 ),
inference(sat_conversion,[],[f430]) ).
cnf(s15,plain,
( spl16_15
| spl16_16 ),
inference(sat_conversion,[],[f431]) ).
cnf(s22,plain,
( spl16_24
| spl16_25 ),
inference(sat_conversion,[],[f466]) ).
cnf(s23,plain,
( spl16_25
| spl16_26 ),
inference(sat_conversion,[],[f470]) ).
cnf(s24,plain,
( spl16_24
| spl16_27 ),
inference(sat_conversion,[],[f474]) ).
cnf(s25,plain,
( spl16_26
| spl16_27 ),
inference(sat_conversion,[],[f475]) ).
cnf(s48,plain,
( ~ spl16_1
| ~ spl16_7
| ~ spl16_9
| ~ spl16_13
| ~ spl16_16 ),
inference(sat_conversion,[],[f851]) ).
cnf(s55,plain,
( ~ spl16_2
| ~ spl16_8
| ~ spl16_10
| ~ spl16_13
| ~ spl16_16 ),
inference(sat_conversion,[],[f976]) ).
cnf(s62,plain,
( ~ spl16_15
| ~ spl16_24
| spl16_46
| spl16_49 ),
inference(sat_conversion,[],[f1003]) ).
cnf(s66,plain,
( ~ spl16_6
| ~ spl16_13
| spl16_46
| spl16_51 ),
inference(sat_conversion,[],[f1015]) ).
cnf(s110,plain,
( ~ spl16_1
| ~ spl16_3
| ~ spl16_4
| ~ spl16_11
| ~ spl16_12 ),
inference(sat_conversion,[],[f1632]) ).
cnf(s111,plain,
( ~ spl16_2
| ~ spl16_46 ),
inference(sat_conversion,[],[f1653]) ).
cnf(s140,plain,
( ~ spl16_15
| ~ spl16_25
| spl16_46
| spl16_73 ),
inference(sat_conversion,[],[f1676]) ).
cnf(s145,plain,
( ~ spl16_14
| ~ spl16_24
| ~ spl16_26
| spl16_46
| ~ spl16_49 ),
inference(sat_conversion,[],[f1804]) ).
cnf(s178,plain,
( ~ spl16_14
| ~ spl16_25
| ~ spl16_27
| spl16_46
| ~ spl16_73 ),
inference(sat_conversion,[],[f2110]) ).
cnf(s253,plain,
( ~ spl16_5
| ~ spl16_13
| ~ spl16_16
| spl16_46
| ~ spl16_51 ),
inference(sat_conversion,[],[f3004]) ).
cnf(s255,plain,
( spl16_24
| spl16_13
| spl16_46 ),
inference(rat,[],[s140,s178,s22,s24,s13,s12]) ).
cnf(s256,plain,
( spl16_13
| spl16_46 ),
inference(rat,[],[s140,s178,s23,s25,s145,s62,s255,s12,s13]) ).
cnf(s257,plain,
( spl16_24
| spl16_16
| spl16_46 ),
inference(rat,[],[s140,s178,s22,s24,s15,s14]) ).
cnf(s258,plain,
( spl16_16
| spl16_46 ),
inference(rat,[],[s140,s178,s23,s25,s145,s62,s257,s14,s15]) ).
cnf(s259,plain,
spl16_1,
inference(rat,[],[s253,s258,s66,s256,s111,s1,s4,s5]) ).
cnf(s260,plain,
( spl16_7
| ~ spl16_2 ),
inference(rat,[],[s55,s6,s8,s256,s258,s111]) ).
cnf(s261,plain,
~ spl16_2,
inference(rat,[],[s55,s7,s9,s48,s260,s258,s256,s111,s259]) ).
cnf(s263,plain,
spl16_12,
inference(rat,[],[s11,s261]) ).
cnf(s264,plain,
spl16_11,
inference(rat,[],[s10,s261]) ).
cnf(s265,plain,
spl16_4,
inference(rat,[],[s3,s261]) ).
cnf(s266,plain,
spl16_3,
inference(rat,[],[s2,s261]) ).
cnf(s267,plain,
$false,
inference(rat,[],[s110,s265,s266,s259,s263,s264]) ).
thf(f3005,plain,
$false,
inference(avatar_sat_refutation,[],[s267]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO392^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n009.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 16:50:31 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.32 % (60387)Will run a generic schedule for satisfiability detection.
% 0.19/0.32 % (60393)% WARNING: option uhcvi not known.
% 0.19/0.32 % (60393)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2765010432:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.32 % (60393)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.32 % (60393)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.32 % (60394)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2927408644:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.32 % (60392)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2091614929_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.32 % (60397)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2911616189:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.32 % (60395)dis+10_1_sil=32000:sp=arity:random_seed=4029007314:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.32 % (60396)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3794940977:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.32 % (60398)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2886848799:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.32 % (60396)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.32 % Exception at run slice level
% 0.19/0.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.32 % (60406)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3038183624:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.32 % Exception at run slice level
% 0.19/0.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.32 % (60408)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1233843535:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.32 % (60395)Instruction limit reached!
% 0.19/0.32 % (60395)------------------------------
% 0.19/0.32 % (60395)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.32 % (60395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.32 % (60395)CaDiCaL version: 2.1.3
% 0.19/0.32 % (60395)Termination reason: Instruction limit
% 0.19/0.32 % (60395)Termination phase: Saturation
% 0.19/0.32 % (60395)Time elapsed: 0.053 s
% 0.19/0.32 % (60395)Peak memory usage: 12 MB
% 0.19/0.32 % (60395)Instructions burned: 104 (million)
% 0.19/0.32 % (60393) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-60387-60393"...
% 0.19/0.32 % (60396)Instruction limit reached!
% 0.19/0.32 % (60396)------------------------------
% 0.19/0.32 % (60396)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.32 % (60396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.32 % (60396)CaDiCaL version: 2.1.3
% 0.19/0.32 % (60396)Termination reason: Instruction limit
% 0.19/0.32 % (60396)Termination phase: Saturation
% 0.19/0.32 % (60396)Time elapsed: 0.058 s
% 0.19/0.32 % (60396)Peak memory usage: 12 MB
% 0.19/0.32 % (60396)Instructions burned: 116 (million)
% 0.19/0.32 % (60393)...printing done.
% 0.19/0.32 % (60393)Refutation found. Thanks to Tanya!
% 0.19/0.32 % SZS status Theorem for theBenchmark
% 0.19/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.33 % (60393)------------------------------
% 0.19/0.33 % (60393)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.33 % (60393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.33 % (60393)CaDiCaL version: 2.1.3
% 0.19/0.33 % (60393)Termination reason: Refutation
% 0.19/0.33 % (60393)Time elapsed: 0.069 s
% 0.19/0.33 % (60393)Peak memory usage: 14 MB
% 0.19/0.33 % (60393)Instructions burned: 258 (million)
% 0.19/0.33 % (60387)Success in time 0.099 s
% 0.19/0.33 % Vampire exiting
%------------------------------------------------------------------------------