%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO441^1 : 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 : n026.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 08:49:58 AM UTC 2026
% Result : Theorem 14.51s 2.35s
% Output : Refutation 14.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 29
% Syntax : Number of formulae : 307 ( 87 unt; 0 typ; 14 def)
% Number of atoms : 2927 ( 541 equ; 0 cnn)
% Maximal formula atoms : 9 ( 9 avg)
% Number of connectives : 4220 ( 840 ~; 801 |; 13 &;2266 @)
% ( 14 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 140 ( 140 >; 0 *; 0 +; 0 <<)
% Number of symbols : 78 ( 74 usr; 23 con; 0-4 aty)
% ( 264 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 706 ( 0 sgn 229 !; 0 ?; 706 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
rel_s5: $i > $i > $o ).
thf(func_def_33,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
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_57,type,
sK6: $i > $i ).
thf(func_def_59,type,
sK8: $i > $i ).
thf(func_def_61,type,
sK10: $i > $i ).
thf(func_def_63,type,
sK12: $i > $i ).
thf(func_def_64,type,
sK13: $i > $i ).
thf(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(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_s5
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(f33,axiom,
( mdia_s5
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',mdia_s5) ).
thf(f34,axiom,
mreflexive @ rel_s5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a1) ).
thf(f35,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a2) ).
thf(f36,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a3) ).
thf(f37,conjecture,
mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) ) @ ( mbox_s5 @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) ) @ ( mbox_s5 @ p ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f41,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f42,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f43,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f44,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f43]) ).
thf(f45,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f46,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f48,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f62,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f63,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f64,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f65,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f64]) ).
thf(f68,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f69,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f82,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f83,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f82]) ).
thf(f90,plain,
( mbox_s5
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f91,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f90]) ).
thf(f92,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f93,plain,
mreflexive @ rel_s5,
inference(rectify,[],[f34]) ).
thf(f94,plain,
( ( mreflexive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f93]) ).
thf(f95,plain,
mtransitive @ rel_s5,
inference(rectify,[],[f35]) ).
thf(f96,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f95]) ).
thf(f97,plain,
msymmetric @ rel_s5,
inference(rectify,[],[f36]) ).
thf(f98,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f97]) ).
thf(f99,plain,
~ ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) ) @ ( mbox_s5 @ p ) ) ),
inference(rectify,[],[f38]) ).
thf(f100,plain,
( ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) ) @ ( mbox_s5 @ p ) ) )
!= $true ),
inference(fool_elimination,[],[f99]) ).
thf(f101,plain,
( ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) ) @ ( mbox_s5 @ p ) ) )
!= $true ),
inference(flattening,[],[f100]) ).
thf(f104,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f105,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f106,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f107,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f109,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f119,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f120,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f65]) ).
thf(f122,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f129,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f83]) ).
thf(f133,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f91]) ).
thf(f134,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f135,plain,
( ( mreflexive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f94]) ).
thf(f136,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f96]) ).
thf(f137,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f138,plain,
( ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) ) @ ( mbox_s5 @ p ) ) )
!= $true ),
inference(cnf_transformation,[],[f101]) ).
thf(f141,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f106,f104,f105,f104,f104]) ).
thf(f142,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,[],[f107,f105,f104]) ).
thf(f144,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( 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,[],[f109,f141,f142,f142]) ).
thf(f150,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f134,f104,f133,f104]) ).
thf(f151,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f135,f119]) ).
thf(f152,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f136,f122]) ).
thf(f153,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f137,f120]) ).
thf(f154,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p ) ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p ) ) ) ),
inference(definition_unfolding,[],[f138,f129,f144,f150,f150,f150,f133,f133]) ).
thf(f155,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s5 @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s5 @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,plain,
( $false
= ( ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s5 @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s5 @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( $false
= ( ~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f163,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f168,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( p @ X1 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f172,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f175,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f178,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ sK2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ sK2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK2 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f182,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f184,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f186,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ sK3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK2 @ sK3 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f189,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK2 @ sK3 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f188]) ).
thf(f191,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( rel_s5 @ sK2 @ sK3 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f193,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK3 @ X2 )
| ( p @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f193]) ).
thf(f195,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK3 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( rel_s5 @ sK3 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f166]) ).
thf(f198,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( p @ X1 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK4 )
| ( p @ sK4 ) ) ) ),
inference(beta-eta_normalization,[],[f197]) ).
thf(f199,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK4 )
| ( p @ sK4 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( p @ sK4 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK4 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f199]) ).
thf(f202,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK4 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f201]) ).
thf(f203,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK4 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( p @ sK4 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f200]) ).
thf(f205,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f206,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) )
@ X1 ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) )
@ X1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f207]) ).
thf(f286,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK11 ) ) ),
inference(sigma_proxy_clausification,[],[f208]) ).
thf(f287,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK11 )
| ( p @ sK11 ) ) ) ),
inference(beta-eta_normalization,[],[f286]) ).
thf(f288,plain,
! [X1: $i] :
( ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK11 )
| ( p @ sK11 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f287]) ).
thf(f289,plain,
! [X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK11 )
| ( p @ sK11 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f288]) ).
thf(f290,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK11 )
| ( p @ sK11 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f289]) ).
thf(f291,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X2 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK11 )
| ( p @ sK11 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f290]) ).
thf(f292,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X2 ) )
| ( $false
= ( p @ sK11 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f291]) ).
thf(f293,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X2 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK11 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f291]) ).
thf(f294,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X2 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK11 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f293]) ).
thf(f295,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X2 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f294]) ).
thf(f296,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ X1 @ X2 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f295]) ).
thf(f297,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f296]) ).
thf(f298,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f297]) ).
thf(f299,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f298]) ).
thf(f300,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X3 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f299]) ).
thf(f301,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X3 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f300]) ).
thf(f302,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ X2 @ X3 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f301]) ).
thf(f303,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( rel_s5 @ X2 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f302]) ).
thf(f304,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X3 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( rel_s5 @ X2 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f303]) ).
thf(f305,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X3 @ Y0 )
| ( p @ Y0 ) )
@ ( sK12 @ X3 ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( rel_s5 @ X2 @ X3 ) ) ) ),
inference(sigma_proxy_clausification,[],[f304]) ).
thf(f306,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X3 @ Y0 )
| ( p @ Y0 ) )
@ ( sK12 @ X3 ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s5 @ X2 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f305]) ).
thf(f307,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ X3 @ ( sK12 @ X3 ) )
| ( p @ ( sK12 @ X3 ) ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s5 @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f306]) ).
thf(f308,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p @ ( sK12 @ X3 ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s5 @ X2 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f307]) ).
thf(f309,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ X3 @ ( sK12 @ X3 ) ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s5 @ X2 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f307]) ).
thf(f310,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X3 @ ( sK12 @ X3 ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s5 @ X2 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f309]) ).
thf(f311,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X2 ) )
| ( $false
= ( p @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f292]) ).
thf(f312,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ X1 @ X2 )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $false
= ( p @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f311]) ).
thf(f313,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $false
= ( p @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f312]) ).
thf(f314,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $false
= ( p @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f313]) ).
thf(f315,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ( $false
= ( p @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f314]) ).
thf(f316,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X3 ) )
| ( $false
= ( p @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(pi_proxy_clausification,[],[f315]) ).
thf(f317,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X3 ) )
| ( $false
= ( p @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f316]) ).
thf(f318,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ X2 @ X3 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $false
= ( p @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f317]) ).
thf(f319,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $false
= ( p @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( rel_s5 @ X2 @ X3 ) ) ) ),
inference(or_proxy_clausification,[],[f318]) ).
thf(f320,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X3 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $false
= ( p @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( rel_s5 @ X2 @ X3 ) ) ) ),
inference(not_proxy_clausification,[],[f319]) ).
thf(f321,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X3 @ Y0 )
| ( p @ Y0 ) )
@ ( sK13 @ X3 ) ) )
| ( $false
= ( p @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( rel_s5 @ X2 @ X3 ) ) ) ),
inference(sigma_proxy_clausification,[],[f320]) ).
thf(f322,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X3 @ Y0 )
| ( p @ Y0 ) )
@ ( sK13 @ X3 ) ) )
| ( $false
= ( p @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s5 @ X2 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f321]) ).
thf(f323,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ X3 @ ( sK13 @ X3 ) )
| ( p @ ( sK13 @ X3 ) ) ) )
| ( $false
= ( p @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s5 @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f322]) ).
thf(f324,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p @ ( sK13 @ X3 ) ) )
| ( $false
= ( p @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s5 @ X2 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f323]) ).
thf(f325,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ X3 @ ( sK13 @ X3 ) ) ) )
| ( $false
= ( p @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s5 @ X2 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f323]) ).
thf(f326,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X3 @ ( sK13 @ X3 ) ) )
| ( $false
= ( p @ sK11 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s5 @ X2 @ X3 ) ) ),
inference(not_proxy_clausification,[],[f325]) ).
thf(f327,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f328,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f327]) ).
thf(f329,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f328]) ).
thf(f330,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f329]) ).
thf(f331,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel_s5 @ X2 @ X1 )
=> ( rel_s5 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f330]) ).
thf(f332,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X2 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f331]) ).
thf(f333,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y2 @ Y1 )
& ( rel_s5 @ Y1 @ Y0 ) )
=> ( rel_s5 @ Y2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f334,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y2 @ Y1 )
& ( rel_s5 @ Y1 @ Y0 ) )
=> ( rel_s5 @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f333]) ).
thf(f335,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y1 @ Y0 )
& ( rel_s5 @ Y0 @ X1 ) )
=> ( rel_s5 @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f334]) ).
thf(f336,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y1 @ Y0 )
& ( rel_s5 @ Y0 @ X1 ) )
=> ( rel_s5 @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f335]) ).
thf(f337,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s5 @ Y0 @ X2 )
& ( rel_s5 @ X2 @ X1 ) )
=> ( rel_s5 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f336]) ).
thf(f338,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s5 @ Y0 @ X2 )
& ( rel_s5 @ X2 @ X1 ) )
=> ( rel_s5 @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f337]) ).
thf(f339,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s5 @ X3 @ X2 )
& ( rel_s5 @ X2 @ X1 ) )
=> ( rel_s5 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f338]) ).
thf(f340,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( rel_s5 @ X3 @ X2 )
& ( rel_s5 @ X2 @ X1 ) ) )
| ( $true
= ( rel_s5 @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f339]) ).
thf(f341,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X2 @ X1 ) )
| ( $true
= ( rel_s5 @ X3 @ X1 ) )
| ( $false
= ( rel_s5 @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f340]) ).
thf(f342,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f343,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f342]) ).
thf(f344,plain,
! [X1: $i] :
( $true
= ( rel_s5 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f343]) ).
thf(f346,definition,
( spl14_1
<=> ( $false
= ( p @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
thf(f348,plain,
( ( $false
= ( p @ sK4 ) )
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f346]) ).
thf(f350,definition,
( spl14_2
<=> ! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
thf(f351,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) ) )
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f350]) ).
thf(f352,plain,
( spl14_1
| spl14_2 ),
inference(avatar_split_clause,[],[f204,f350,f346]) ).
thf(f354,definition,
( spl14_3
<=> ( $false
= ( p @ sK11 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
thf(f355,plain,
( ( $false
!= ( p @ sK11 ) )
| spl14_3 ),
inference(avatar_component_clause,[],[f354]) ).
thf(f356,plain,
( ( $false
= ( p @ sK11 ) )
| ~ spl14_3 ),
inference(avatar_component_clause,[],[f354]) ).
thf(f358,definition,
( spl14_4
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $false
= ( p @ ( sK13 @ X3 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( rel_s5 @ X2 @ X3 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition]) ).
thf(f359,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p @ ( sK13 @ X3 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( rel_s5 @ X2 @ X3 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) )
| ~ spl14_4 ),
inference(avatar_component_clause,[],[f358]) ).
thf(f360,plain,
( spl14_3
| spl14_4 ),
inference(avatar_split_clause,[],[f324,f358,f354]) ).
thf(f387,definition,
( spl14_7
<=> ( $true
= ( rel_s5 @ sK0 @ sK11 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_7])],[avatar_definition]) ).
thf(f388,plain,
( ( $true
!= ( rel_s5 @ sK0 @ sK11 ) )
| spl14_7 ),
inference(avatar_component_clause,[],[f387]) ).
thf(f389,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK11 ) )
| ~ spl14_7 ),
inference(avatar_component_clause,[],[f387]) ).
thf(f391,definition,
( spl14_8
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $false
= ( p @ ( sK12 @ X3 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( rel_s5 @ X2 @ X3 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl14_8])],[avatar_definition]) ).
thf(f392,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( p @ ( sK12 @ X3 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( rel_s5 @ X2 @ X3 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) )
| ~ spl14_8 ),
inference(avatar_component_clause,[],[f391]) ).
thf(f393,plain,
( spl14_7
| spl14_8 ),
inference(avatar_split_clause,[],[f308,f391,f387]) ).
thf(f394,plain,
( ( $true = $false )
| ( $true
= ( p @ sK11 ) )
| ~ spl14_2
| ~ spl14_7 ),
inference(constrained_superposition,[],[f389,f351]) ).
thf(f397,plain,
( ( $true
= ( p @ sK11 ) )
| ~ spl14_2
| ~ spl14_7 ),
inference(trivial_inequality_removal,[],[f394]) ).
thf(f401,plain,
( ( $true = $false )
| ~ spl14_2
| ~ spl14_3
| ~ spl14_7 ),
inference(forward_demodulation,[],[f397,f356]) ).
thf(f402,plain,
( $false
| ~ spl14_2
| ~ spl14_3
| ~ spl14_7 ),
inference(trivial_inequality_removal,[],[f401]) ).
thf(f403,plain,
( ~ spl14_2
| ~ spl14_3
| ~ spl14_7 ),
inference(avatar_contradiction_clause,[],[f402]) ).
thf(f407,definition,
( spl14_9
<=> ( $true
= ( rel_s5 @ sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_9])],[avatar_definition]) ).
thf(f409,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ~ spl14_9 ),
inference(avatar_component_clause,[],[f407]) ).
thf(f410,plain,
( spl14_9
| spl14_2 ),
inference(avatar_split_clause,[],[f176,f350,f407]) ).
thf(f433,plain,
( ! [X0: $i] :
( ( $false != $false )
| ( $false
= ( p @ ( sK12 @ X0 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ X0 ) ) )
| ~ spl14_8 ),
inference(equality_factoring,[],[f392]) ).
thf(f434,plain,
( ! [X0: $i] :
( ( $false
= ( p @ ( sK12 @ X0 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ X0 ) ) )
| ~ spl14_8 ),
inference(trivial_inequality_removal,[],[f433]) ).
thf(f470,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X3 @ ( sK12 @ X3 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s5 @ X2 @ X3 ) ) )
| spl14_7 ),
inference(forward_subsumption_resolution,[],[f310,f388]) ).
thf(f479,plain,
( ! [X0: $i] :
( ( $false != $false )
| ( $true
= ( rel_s5 @ X0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| spl14_7 ),
inference(equality_factoring,[],[f470]) ).
thf(f480,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ X0 @ ( sK12 @ X0 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| spl14_7 ),
inference(trivial_inequality_removal,[],[f479]) ).
thf(f493,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK12 @ sK0 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl14_2
| spl14_7 ),
inference(constrained_superposition,[],[f351,f480]) ).
thf(f494,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK12 @ sK0 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl14_2
| spl14_7 ),
inference(duplicate_literal_removal,[],[f493]) ).
thf(f495,plain,
( ( $true
= ( p @ ( sK12 @ sK0 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl14_2
| spl14_7 ),
inference(trivial_inequality_removal,[],[f494]) ).
thf(f502,definition,
( spl14_14
<=> ( $false
= ( rel_s5 @ sK0 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_14])],[avatar_definition]) ).
thf(f504,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl14_14 ),
inference(avatar_component_clause,[],[f502]) ).
thf(f506,definition,
( spl14_15
<=> ( $true
= ( p @ ( sK12 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_15])],[avatar_definition]) ).
thf(f508,plain,
( ( $true
= ( p @ ( sK12 @ sK0 ) ) )
| ~ spl14_15 ),
inference(avatar_component_clause,[],[f506]) ).
thf(f509,plain,
( spl14_14
| spl14_15
| ~ spl14_2
| spl14_7 ),
inference(avatar_split_clause,[],[f495,f387,f350,f506,f502]) ).
thf(f526,plain,
( ! [X0: $i] :
( ( $false != $false )
| ( $false
= ( p @ ( sK13 @ X0 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ X0 ) ) )
| ~ spl14_4 ),
inference(equality_factoring,[],[f359]) ).
thf(f527,plain,
( ! [X0: $i] :
( ( $false
= ( p @ ( sK13 @ X0 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ X0 ) ) )
| ~ spl14_4 ),
inference(trivial_inequality_removal,[],[f526]) ).
thf(f547,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X3 @ ( sK13 @ X3 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $false
= ( rel_s5 @ X2 @ X3 ) ) )
| spl14_3 ),
inference(forward_subsumption_resolution,[],[f326,f355]) ).
thf(f558,plain,
( ! [X0: $i] :
( ( $false != $false )
| ( $true
= ( rel_s5 @ X0 @ ( sK13 @ X0 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| spl14_3 ),
inference(equality_factoring,[],[f547]) ).
thf(f559,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ X0 @ ( sK13 @ X0 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| spl14_3 ),
inference(trivial_inequality_removal,[],[f558]) ).
thf(f576,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK13 @ sK0 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl14_2
| spl14_3 ),
inference(constrained_superposition,[],[f351,f559]) ).
thf(f577,plain,
( ( $true = $false )
| ( $true
= ( p @ ( sK13 @ sK0 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl14_2
| spl14_3 ),
inference(duplicate_literal_removal,[],[f576]) ).
thf(f578,plain,
( ( $true
= ( p @ ( sK13 @ sK0 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl14_2
| spl14_3 ),
inference(trivial_inequality_removal,[],[f577]) ).
thf(f587,definition,
( spl14_16
<=> ( $true
= ( p @ ( sK13 @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_16])],[avatar_definition]) ).
thf(f589,plain,
( ( $true
= ( p @ ( sK13 @ sK0 ) ) )
| ~ spl14_16 ),
inference(avatar_component_clause,[],[f587]) ).
thf(f590,plain,
( spl14_14
| spl14_16
| ~ spl14_2
| spl14_3 ),
inference(avatar_split_clause,[],[f578,f354,f350,f587,f502]) ).
thf(f592,definition,
( spl14_17
<=> ( $true
= ( rel_s5 @ sK0 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_17])],[avatar_definition]) ).
thf(f594,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK4 ) )
| ~ spl14_17 ),
inference(avatar_component_clause,[],[f592]) ).
thf(f595,plain,
( spl14_17
| spl14_2 ),
inference(avatar_split_clause,[],[f203,f350,f592]) ).
thf(f597,definition,
( spl14_18
<=> ( $true
= ( rel_s5 @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_18])],[avatar_definition]) ).
thf(f599,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK2 ) )
| ~ spl14_18 ),
inference(avatar_component_clause,[],[f597]) ).
thf(f600,plain,
( spl14_18
| spl14_2 ),
inference(avatar_split_clause,[],[f184,f350,f597]) ).
thf(f634,definition,
( spl14_19
<=> ( $true
= ( rel_s5 @ sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_19])],[avatar_definition]) ).
thf(f636,plain,
( ( $true
= ( rel_s5 @ sK2 @ sK3 ) )
| ~ spl14_19 ),
inference(avatar_component_clause,[],[f634]) ).
thf(f637,plain,
( spl14_19
| spl14_2 ),
inference(avatar_split_clause,[],[f191,f350,f634]) ).
thf(f659,definition,
( spl14_20
<=> ! [X2: $i] :
( ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_20])],[avatar_definition]) ).
thf(f660,plain,
( ! [X2: $i] :
( ( $false
= ( rel_s5 @ sK3 @ X2 ) )
| ( $true
= ( p @ X2 ) ) )
| ~ spl14_20 ),
inference(avatar_component_clause,[],[f659]) ).
thf(f661,plain,
( spl14_20
| spl14_2 ),
inference(avatar_split_clause,[],[f196,f350,f659]) ).
thf(f981,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s5 @ X0 @ sK1 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl14_9 ),
inference(constrained_superposition,[],[f409,f341]) ).
thf(f982,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s5 @ X0 @ sK4 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl14_17 ),
inference(constrained_superposition,[],[f594,f341]) ).
thf(f985,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s5 @ X0 @ sK2 ) )
| ( $false
= ( rel_s5 @ X0 @ sK1 ) ) )
| ~ spl14_18 ),
inference(constrained_superposition,[],[f599,f341]) ).
thf(f986,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s5 @ X0 @ sK3 ) )
| ( $false
= ( rel_s5 @ X0 @ sK2 ) ) )
| ~ spl14_19 ),
inference(constrained_superposition,[],[f636,f341]) ).
thf(f1065,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ X0 @ sK3 ) )
| ( $false
= ( rel_s5 @ X0 @ sK2 ) ) )
| ~ spl14_19 ),
inference(trivial_inequality_removal,[],[f986]) ).
thf(f1066,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ X0 @ sK2 ) )
| ( $false
= ( rel_s5 @ X0 @ sK1 ) ) )
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f985]) ).
thf(f1069,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ X0 @ sK4 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl14_17 ),
inference(trivial_inequality_removal,[],[f982]) ).
thf(f1070,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ X0 @ sK1 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl14_9 ),
inference(trivial_inequality_removal,[],[f981]) ).
thf(f1151,plain,
( ( $true = $false )
| ( $true
= ( p @ sK4 ) )
| ( $false
= ( rel_s5 @ sK3 @ sK0 ) )
| ~ spl14_17
| ~ spl14_20 ),
inference(constrained_superposition,[],[f660,f1069]) ).
thf(f1154,plain,
( ( $true
= ( p @ sK4 ) )
| ( $false
= ( rel_s5 @ sK3 @ sK0 ) )
| ~ spl14_17
| ~ spl14_20 ),
inference(trivial_inequality_removal,[],[f1151]) ).
thf(f1183,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK3 @ sK0 ) )
| ~ spl14_1
| ~ spl14_17
| ~ spl14_20 ),
inference(forward_demodulation,[],[f1154,f348]) ).
thf(f1184,plain,
( ( $false
= ( rel_s5 @ sK3 @ sK0 ) )
| ~ spl14_1
| ~ spl14_17
| ~ spl14_20 ),
inference(trivial_inequality_removal,[],[f1183]) ).
thf(f1192,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK3 ) )
| ~ spl14_1
| ~ spl14_17
| ~ spl14_20 ),
inference(constrained_superposition,[],[f332,f1184]) ).
thf(f1195,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK3 ) )
| ~ spl14_1
| ~ spl14_17
| ~ spl14_20 ),
inference(trivial_inequality_removal,[],[f1192]) ).
thf(f1690,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK2 ) )
| ~ spl14_1
| ~ spl14_17
| ~ spl14_19
| ~ spl14_20 ),
inference(constrained_superposition,[],[f1195,f1065]) ).
thf(f1695,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK2 ) )
| ~ spl14_1
| ~ spl14_17
| ~ spl14_19
| ~ spl14_20 ),
inference(trivial_inequality_removal,[],[f1690]) ).
thf(f1729,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK1 ) )
| ~ spl14_1
| ~ spl14_17
| ~ spl14_18
| ~ spl14_19
| ~ spl14_20 ),
inference(constrained_superposition,[],[f1066,f1695]) ).
thf(f1730,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK1 ) )
| ~ spl14_1
| ~ spl14_17
| ~ spl14_18
| ~ spl14_19
| ~ spl14_20 ),
inference(trivial_inequality_removal,[],[f1729]) ).
thf(f1736,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl14_1
| ~ spl14_9
| ~ spl14_17
| ~ spl14_18
| ~ spl14_19
| ~ spl14_20 ),
inference(constrained_superposition,[],[f1730,f1070]) ).
thf(f1749,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl14_1
| ~ spl14_9
| ~ spl14_17
| ~ spl14_18
| ~ spl14_19
| ~ spl14_20 ),
inference(trivial_inequality_removal,[],[f1736]) ).
thf(f1754,plain,
( ( $true = $false )
| ~ spl14_1
| ~ spl14_9
| ~ spl14_17
| ~ spl14_18
| ~ spl14_19
| ~ spl14_20 ),
inference(forward_demodulation,[],[f1749,f344]) ).
thf(f1755,plain,
( $false
| ~ spl14_1
| ~ spl14_9
| ~ spl14_17
| ~ spl14_18
| ~ spl14_19
| ~ spl14_20 ),
inference(trivial_inequality_removal,[],[f1754]) ).
thf(f1756,plain,
( ~ spl14_1
| ~ spl14_9
| ~ spl14_17
| ~ spl14_18
| ~ spl14_19
| ~ spl14_20 ),
inference(avatar_contradiction_clause,[],[f1755]) ).
thf(f1771,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl14_8
| ~ spl14_15 ),
inference(constrained_superposition,[],[f434,f508]) ).
thf(f1774,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl14_8
| ~ spl14_15 ),
inference(duplicate_literal_removal,[],[f1771]) ).
thf(f1775,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl14_8
| ~ spl14_15 ),
inference(trivial_inequality_removal,[],[f1774]) ).
thf(f1789,plain,
( ( $true = $false )
| ~ spl14_8
| ~ spl14_15 ),
inference(forward_demodulation,[],[f1775,f344]) ).
thf(f1790,plain,
( $false
| ~ spl14_8
| ~ spl14_15 ),
inference(trivial_inequality_removal,[],[f1789]) ).
thf(f1791,plain,
( ~ spl14_8
| ~ spl14_15 ),
inference(avatar_contradiction_clause,[],[f1790]) ).
thf(f1851,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl14_4
| ~ spl14_16 ),
inference(constrained_superposition,[],[f527,f589]) ).
thf(f1854,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl14_4
| ~ spl14_16 ),
inference(duplicate_literal_removal,[],[f1851]) ).
thf(f1855,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl14_4
| ~ spl14_16 ),
inference(trivial_inequality_removal,[],[f1854]) ).
thf(f1869,plain,
( ( $true = $false )
| ~ spl14_4
| ~ spl14_16 ),
inference(forward_demodulation,[],[f1855,f344]) ).
thf(f1870,plain,
( $false
| ~ spl14_4
| ~ spl14_16 ),
inference(trivial_inequality_removal,[],[f1869]) ).
thf(f1871,plain,
( ~ spl14_4
| ~ spl14_16 ),
inference(avatar_contradiction_clause,[],[f1870]) ).
thf(f1893,plain,
( ( $true = $false )
| ~ spl14_14 ),
inference(forward_demodulation,[],[f504,f344]) ).
thf(f1894,plain,
( $false
| ~ spl14_14 ),
inference(trivial_inequality_removal,[],[f1893]) ).
thf(f1895,plain,
~ spl14_14,
inference(avatar_contradiction_clause,[],[f1894]) ).
cnf(s1,plain,
( spl14_1
| spl14_2 ),
inference(sat_conversion,[],[f352]) ).
cnf(s2,plain,
( spl14_3
| spl14_4 ),
inference(sat_conversion,[],[f360]) ).
cnf(s4,plain,
( spl14_7
| spl14_8 ),
inference(sat_conversion,[],[f393]) ).
cnf(s6,plain,
( ~ spl14_2
| ~ spl14_3
| ~ spl14_7 ),
inference(sat_conversion,[],[f403]) ).
cnf(s7,plain,
( spl14_2
| spl14_9 ),
inference(sat_conversion,[],[f410]) ).
cnf(s10,plain,
( ~ spl14_2
| spl14_7
| spl14_14
| spl14_15 ),
inference(sat_conversion,[],[f509]) ).
cnf(s11,plain,
( ~ spl14_2
| spl14_3
| spl14_14
| spl14_16 ),
inference(sat_conversion,[],[f590]) ).
cnf(s12,plain,
( spl14_2
| spl14_17 ),
inference(sat_conversion,[],[f595]) ).
cnf(s13,plain,
( spl14_2
| spl14_18 ),
inference(sat_conversion,[],[f600]) ).
cnf(s14,plain,
( spl14_2
| spl14_19 ),
inference(sat_conversion,[],[f637]) ).
cnf(s15,plain,
( spl14_2
| spl14_20 ),
inference(sat_conversion,[],[f661]) ).
cnf(s22,plain,
( ~ spl14_1
| ~ spl14_9
| ~ spl14_17
| ~ spl14_18
| ~ spl14_19
| ~ spl14_20 ),
inference(sat_conversion,[],[f1756]) ).
cnf(s23,plain,
( ~ spl14_8
| ~ spl14_15 ),
inference(sat_conversion,[],[f1791]) ).
cnf(s31,plain,
( ~ spl14_4
| ~ spl14_16 ),
inference(sat_conversion,[],[f1871]) ).
cnf(s39,plain,
~ spl14_14,
inference(sat_conversion,[],[f1895]) ).
cnf(s40,plain,
( ~ spl14_2
| spl14_3
| spl14_16 ),
inference(rat,[],[s11,s39]) ).
cnf(s41,plain,
( ~ spl14_2
| spl14_7
| spl14_15 ),
inference(rat,[],[s10,s39]) ).
cnf(s42,plain,
( spl14_3
| ~ spl14_2 ),
inference(rat,[],[s31,s2,s40]) ).
cnf(s43,plain,
( spl14_7
| ~ spl14_2 ),
inference(rat,[],[s23,s4,s41]) ).
cnf(s44,plain,
( ~ spl14_3
| ~ spl14_2 ),
inference(rat,[],[s43,s6]) ).
cnf(s45,plain,
~ spl14_2,
inference(rat,[],[s44,s42]) ).
cnf(s46,plain,
spl14_20,
inference(rat,[],[s15,s45]) ).
cnf(s47,plain,
spl14_19,
inference(rat,[],[s14,s45]) ).
cnf(s48,plain,
spl14_18,
inference(rat,[],[s13,s45]) ).
cnf(s49,plain,
spl14_17,
inference(rat,[],[s12,s45]) ).
cnf(s50,plain,
spl14_9,
inference(rat,[],[s7,s45]) ).
cnf(s51,plain,
spl14_1,
inference(rat,[],[s1,s45]) ).
cnf(s52,plain,
$false,
inference(rat,[],[s22,s46,s47,s48,s49,s51,s50]) ).
thf(f1896,plain,
$false,
inference(avatar_sat_refutation,[],[s52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO441^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n026.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:54:42 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 3.86/0.91 % (859516)Will run a generic schedule for satisfiability detection.
% 3.86/0.91 % (859542)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3751437734:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.86/0.91 % (859538)% WARNING: option uhcvi not known.
% 3.86/0.91 % (859539)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4241033771:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.86/0.91 % (859537)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3932635175_2999 on theBenchmark for (2999ds/0Mi)
% 3.86/0.91 % (859538)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3161545703:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.86/0.91 % (859541)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=628783961:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.86/0.91 % (859540)dis+10_1_sil=32000:sp=arity:random_seed=3857478142:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.86/0.91 % (859543)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=205600455:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.86/0.91 % (859538)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.86/0.91 % (859541)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.86/0.91 % Exception at run slice level
% 3.86/0.91 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.86/0.91 % (859538)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.86/0.91 % (859557)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2265971503:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.86/0.91 % Exception at run slice level
% 3.86/0.91 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.86/0.91 % (859542)Instruction limit reached!
% 3.86/0.91 % (859542)------------------------------
% 3.86/0.91 % (859542)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.86/0.91 % (859542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/0.91 % (859542)CaDiCaL version: 2.1.3
% 3.86/0.91 % (859542)Termination reason: Instruction limit
% 3.86/0.91 % (859542)Termination phase: Saturation
% 3.86/0.91 % (859542)Time elapsed: 0.039 s
% 3.86/0.91 % (859542)Peak memory usage: 12 MB
% 3.86/0.91 % (859542)Instructions burned: 136 (million)
% 3.86/0.91 % (859565)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=4021888667:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.86/0.91 % (859566)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2406061948:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.86/0.91 % (859541)Instruction limit reached!
% 3.86/0.91 % (859541)------------------------------
% 3.86/0.91 % (859541)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.86/0.91 % (859541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/0.91 % (859541)CaDiCaL version: 2.1.3
% 3.86/0.91 % (859541)Termination reason: Instruction limit
% 3.86/0.91 % (859541)Termination phase: Saturation
% 3.86/0.91 % (859541)Time elapsed: 0.052 s
% 3.86/0.91 % (859541)Peak memory usage: 12 MB
% 3.86/0.91 % (859541)Instructions burned: 118 (million)
% 3.86/0.91 % (859566)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.86/0.91 % (859566)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.86/0.91 % (859540)Instruction limit reached!
% 3.86/0.91 % (859540)------------------------------
% 3.86/0.91 % (859540)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.86/0.91 % (859540)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.86/0.91 % (859540)CaDiCaL version: 2.1.3
% 3.86/0.91 % (859540)Termination reason: Instruction limit
% 3.86/0.91 % (859540)Termination phase: Saturation
% 3.86/0.91 % (859540)Time elapsed: 0.055 s
% 3.86/0.91 % (859540)Peak memory usage: 11 MB
% 3.86/0.91 % (859540)Instructions burned: 104 (million)
% 3.86/0.91 % (859565)Instruction limit reached!
% 3.86/0.91 % (859565)------------------------------
% 3.86/0.91 % (859565)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.86/0.91 % (859565)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.51/2.35 % (859565)CaDiCaL version: 2.1.3
% 14.51/2.35 % (859565)Termination reason: Instruction limit
% 14.51/2.35 % (859565)Termination phase: Saturation
% 14.51/2.35 % (859565)Time elapsed: 0.032 s
% 14.51/2.35 % (859565)Peak memory usage: 12 MB
% 14.51/2.35 % (859565)Instructions burned: 132 (million)
% 14.51/2.35 % (859543)Instruction limit reached!
% 14.51/2.35 % (859543)------------------------------
% 14.51/2.35 % (859543)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.51/2.35 % (859543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.51/2.35 % (859543)CaDiCaL version: 2.1.3
% 14.51/2.35 % (859543)Termination reason: Instruction limit
% 14.51/2.35 % (859543)Termination phase: Saturation
% 14.51/2.35 % (859543)Time elapsed: 0.075 s
% 14.51/2.35 % (859543)Peak memory usage: 12 MB
% 14.51/2.35 % (859543)Instructions burned: 161 (million)
% 14.51/2.35 % (859578)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1273419014:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 14.51/2.35 % (859582)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=353897327:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 14.51/2.35 % (859577)ott-21_1_sil=16000:fs=off:random_seed=2115251165:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 14.51/2.35 % Exception at run slice level
% 14.51/2.35 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 14.51/2.35 % (859583)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2934260242:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 14.51/2.35 % (859587)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=4212529636:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 14.51/2.35 % Exception at run slice level
% 14.51/2.35 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 14.51/2.35 % (859590)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=840224967:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 14.51/2.35 % (859590)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 14.51/2.35 % (859577)Instruction limit reached!
% 14.51/2.35 % (859577)------------------------------
% 14.51/2.35 % (859577)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.51/2.35 % (859577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.51/2.35 % (859577)CaDiCaL version: 2.1.3
% 14.51/2.35 % (859577)Termination reason: Instruction limit
% 14.51/2.35 % (859577)Termination phase: Saturation
% 14.51/2.35 % (859577)Time elapsed: 0.091 s
% 14.51/2.35 % (859577)Peak memory usage: 12 MB
% 14.51/2.35 % (859577)Instructions burned: 180 (million)
% 14.51/2.35 % (859612)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=2306372529:i=879:kws=inv_precedence:fsr=off_2997 on theBenchmark for (2997ds/879Mi)
% 14.51/2.35 % (859612)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 14.51/2.35 % (859590)Instruction limit reached!
% 14.51/2.35 % (859590)------------------------------
% 14.51/2.35 % (859590)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.51/2.35 % (859590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.51/2.35 % (859590)CaDiCaL version: 2.1.3
% 14.51/2.35 % (859590)Termination reason: Instruction limit
% 14.51/2.35 % (859590)Termination phase: Saturation
% 14.51/2.35 % (859590)Time elapsed: 0.164 s
% 14.51/2.35 % (859590)Peak memory usage: 14 MB
% 14.51/2.35 % (859590)Instructions burned: 695 (million)
% 14.51/2.35 % (859632)fmb+10_1_sil=64000:random_seed=505740126:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 14.51/2.35 % (859632)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 14.51/2.35 % Exception at run slice level
% 14.51/2.35 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 14.51/2.35 % (859634)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=153660429:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 14.51/2.35 % Exception at run slice level
% 14.51/2.35 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 14.51/2.35 % (859639)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2823608384:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 14.51/2.35 % Exception at run slice level
% 14.51/2.35 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 14.51/2.35 % (859578)Instruction limit reached!
% 14.51/2.35 % (859578)------------------------------
% 14.51/2.35 % (859578)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.51/2.35 % (859578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.51/2.35 % (859578)CaDiCaL version: 2.1.3
% 14.51/2.35 % (859578)Termination reason: Instruction limit
% 14.51/2.35 % (859578)Termination phase: Saturation
% 14.51/2.35 % (859578)Time elapsed: 0.244 s
% 14.51/2.35 % (859578)Peak memory usage: 13 MB
% 14.51/2.35 % (859578)Instructions burned: 479 (million)
% 14.51/2.35 % (859644)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=1323712661:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 14.51/2.35 % (859644)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 14.51/2.35 % (859645)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=4065958882:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 14.51/2.35 % (859645)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 14.51/2.35 % (859645)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 14.51/2.35 % (859566)Instruction limit reached!
% 14.51/2.35 % (859566)------------------------------
% 14.51/2.35 % (859566)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.51/2.35 % (859566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.51/2.35 % (859566)CaDiCaL version: 2.1.3
% 14.51/2.35 % (859566)Termination reason: Instruction limit
% 14.51/2.35 % (859566)Termination phase: Saturation
% 14.51/2.35 % (859566)Time elapsed: 0.307 s
% 14.51/2.35 % (859566)Peak memory usage: 15 MB
% 14.51/2.35 % (859566)Instructions burned: 684 (million)
% 14.51/2.35 % (859661)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=3018089655:i=6324_2995 on theBenchmark for (2995ds/6324Mi)
% 14.51/2.35 % Exception at run slice level
% 14.51/2.35 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 14.51/2.35 % (859671)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2978314426:fmbsr=2.30978:i=2174_2995 on theBenchmark for (2995ds/2174Mi)
% 14.51/2.35 % Exception at run slice level
% 14.51/2.35 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 14.51/2.35 % (859674)ott-2_1_sil=16000:newcnf=on:random_seed=4199188191:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2995 on theBenchmark for (2995ds/869Mi)
% 14.51/2.35 % (859674)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 14.51/2.35 % (859583)Instruction limit reached!
% 14.51/2.35 % (859583)------------------------------
% 14.51/2.35 % (859583)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.51/2.35 % (859583)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.51/2.35 % (859583)CaDiCaL version: 2.1.3
% 14.51/2.35 % (859583)Termination reason: Instruction limit
% 14.51/2.35 % (859583)Termination phase: Saturation
% 14.51/2.35 % (859583)Time elapsed: 0.486 s
% 14.51/2.35 % (859583)Peak memory usage: 12 MB
% 14.51/2.35 % (859583)Instructions burned: 1181 (million)
% 14.51/2.35 % (859612)Instruction limit reached!
% 14.51/2.35 % (859612)------------------------------
% 14.51/2.35 % (859612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.51/2.35 % (859612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.51/2.35 % (859612)CaDiCaL version: 2.1.3
% 14.51/2.35 % (859612)Termination reason: Instruction limit
% 14.51/2.35 % (859612)Termination phase: Saturation
% 14.51/2.35 % (859612)Time elapsed: 0.394 s
% 14.51/2.35 % (859612)Peak memory usage: 13 MB
% 14.51/2.35 % (859612)Instructions burned: 881 (million)
% 14.51/2.35 % (859698)ott+10_1_sil=32000:tgt=ground:random_seed=1999914975:i=5114:av=off_2993 on theBenchmark for (2993ds/5114Mi)
% 14.51/2.35 % (859703)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=3541992447:i=54282_2993 on theBenchmark for (2993ds/54282Mi)
% 14.51/2.35 % Exception at run slice level
% 14.51/2.35 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 14.51/2.35 % (859719)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=2034157413:i=3512:aac=none_2993 on theBenchmark for (2993ds/3512Mi)
% 14.51/2.35 % (859719)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 14.51/2.35 % (859674)Instruction limit reached!
% 14.51/2.35 % (859674)------------------------------
% 14.51/2.35 % (859674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.51/2.35 % (859674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.51/2.35 % (859674)CaDiCaL version: 2.1.3
% 14.51/2.35 % (859674)Termination reason: Instruction limit
% 14.51/2.35 % (859674)Termination phase: Saturation
% 14.51/2.35 % (859674)Time elapsed: 0.418 s
% 14.51/2.35 % (859674)Peak memory usage: 14 MB
% 14.51/2.35 % (859674)Instructions burned: 870 (million)
% 14.51/2.35 % (859787)dis+21_1_sil=32000:sas=cadical:random_seed=1563450701:i=3773:amm=off_2990 on theBenchmark for (2990ds/3773Mi)
% 14.51/2.35 % (859645)Instruction limit reached!
% 14.51/2.35 % (859645)------------------------------
% 14.51/2.35 % (859645)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.51/2.35 % (859645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.51/2.35 % (859645)CaDiCaL version: 2.1.3
% 14.51/2.35 % (859645)Termination reason: Instruction limit
% 14.51/2.35 % (859645)Termination phase: Saturation
% 14.51/2.35 % (859645)Time elapsed: 0.747 s
% 14.51/2.35 % (859645)Peak memory usage: 20 MB
% 14.51/2.35 % (859645)Instructions burned: 1472 (million)
% 14.51/2.35 % (859836)ott+11_1_sil=16000:gs=on:random_seed=1079211988:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2988 on theBenchmark for (2988ds/2251Mi)
% 14.51/2.35 % (859836)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 14.51/2.35 % (859644)Instruction limit reached!
% 14.51/2.35 % (859644)------------------------------
% 14.51/2.35 % (859644)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.51/2.35 % (859644)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.51/2.35 % (859644)CaDiCaL version: 2.1.3
% 14.51/2.35 % (859644)Termination reason: Instruction limit
% 14.51/2.35 % (859644)Termination phase: Saturation
% 14.51/2.35 % (859644)Time elapsed: 1.063 s
% 14.51/2.35 % (859644)Peak memory usage: 17 MB
% 14.51/2.35 % (859644)Instructions burned: 5136 (million)
% 14.51/2.35 % (859838)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=3722050233:fmbsr=1.6:i=67534_2985 on theBenchmark for (2985ds/67534Mi)
% 14.51/2.35 % Exception at run slice level
% 14.51/2.35 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 14.51/2.35 % (859840)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=527689044:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2985 on theBenchmark for (2985ds/4591Mi)
% 14.51/2.35 % (859836)Instruction limit reached!
% 14.51/2.35 % (859836)------------------------------
% 14.51/2.35 % (859836)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.51/2.35 % (859836)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.51/2.35 % (859836)CaDiCaL version: 2.1.3
% 14.51/2.35 % (859836)Termination reason: Instruction limit
% 14.51/2.35 % (859836)Termination phase: Saturation
% 14.51/2.35 % (859836)Time elapsed: 0.845 s
% 14.51/2.35 % (859836)Peak memory usage: 13 MB
% 14.51/2.35 % (859836)Instructions burned: 2251 (million)
% 14.51/2.35 % (859842)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=1337971460:i=29340_2980 on theBenchmark for (2980ds/29340Mi)
% 14.51/2.35 % (859719)Instruction limit reached!
% 14.51/2.35 % (859719)------------------------------
% 14.51/2.35 % (859719)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.51/2.35 % (859719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.51/2.35 % (859719)CaDiCaL version: 2.1.3
% 14.51/2.35 % (859719)Termination reason: Instruction limit
% 14.51/2.35 % (859719)Termination phase: Saturation
% 14.51/2.35 % (859719)Time elapsed: 1.359 s
% 14.51/2.35 % (859719)Peak memory usage: 16 MB
% 14.51/2.35 % (859719)Instructions burned: 3513 (million)
% 14.51/2.35 % (859844)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=4291639317:i=5211_2979 on theBenchmark for (2979ds/5211Mi)
% 14.51/2.35 % (859842) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-859516-859842"...
% 14.51/2.35 % (859842)...printing done.
% 14.51/2.35 % (859842)Refutation found. Thanks to Tanya!
% 14.51/2.35 % SZS status Theorem for theBenchmark
% 14.51/2.35 % SZS output start Proof for theBenchmark
% See solution above
% 14.51/2.35 % (859842)------------------------------
% 14.51/2.35 % (859842)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 14.51/2.35 % (859842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 14.51/2.35 % (859842)CaDiCaL version: 2.1.3
% 14.51/2.35 % (859842)Termination reason: Refutation
% 14.51/2.35 % (859842)Time elapsed: 0.086 s
% 14.51/2.35 % (859842)Peak memory usage: 13 MB
% 14.51/2.35 % (859842)Instructions burned: 182 (million)
% 14.51/2.35 % (859516)Success in time 2.11 s
% 14.51/2.35 % Vampire exiting
%------------------------------------------------------------------------------