%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO447^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 08:49:59 AM UTC 2026
% Result : Theorem 59.61s 8.69s
% Output : Refutation 59.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 58
% Number of leaves : 29
% Syntax : Number of formulae : 424 ( 88 unt; 0 typ; 14 def)
% Number of atoms : 4298 ( 781 equ; 0 cnn)
% Maximal formula atoms : 12 ( 10 avg)
% Number of connectives : 5563 (1345 ~;1300 |; 13 &;2640 @)
% ( 14 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 150 ( 150 >; 0 *; 0 +; 0 <<)
% Number of symbols : 77 ( 73 usr; 21 con; 0-4 aty)
% ( 229 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 717 ( 0 sgn 234 !; 0 ?; 717 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
rel_s5: $i > $i > $o ).
thf(func_def_33,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
q: $i > $o ).
thf(func_def_37,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_40,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_41,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vNOT: $o > $o ).
thf(func_def_43,type,
vOR: $o > $o > $o ).
thf(func_def_44,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vIMP: $o > $o > $o ).
thf(func_def_49,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_50,type,
vAND: $o > $o > $o ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_55,type,
sK3: $i > $i ).
thf(func_def_56,type,
sK4: $i > $i ).
thf(func_def_57,type,
sK5: $i > $i ).
thf(func_def_60,type,
sK8: $i > $i ).
thf(func_def_61,type,
sK9: $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_s5
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(f33,axiom,
( mdia_s5
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mdia_s5) ).
thf(f34,axiom,
mreflexive @ rel_s5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',a1) ).
thf(f35,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',a2) ).
thf(f36,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',a3) ).
thf(f37,conjecture,
mvalid @ ( mequiv @ ( mand @ ( mdia_s5 @ p ) @ ( mbox_s5 @ q ) ) @ ( mdia_s5 @ ( mand @ p @ ( mbox_s5 @ q ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mand @ ( mdia_s5 @ p ) @ ( mbox_s5 @ q ) ) @ ( mdia_s5 @ ( mand @ p @ ( mbox_s5 @ q ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(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 @ ( mand @ ( mdia_s5 @ p ) @ ( mbox_s5 @ q ) ) @ ( mdia_s5 @ ( mand @ p @ ( mbox_s5 @ q ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f100,plain,
( ( mvalid @ ( mequiv @ ( mand @ ( mdia_s5 @ p ) @ ( mbox_s5 @ q ) ) @ ( mdia_s5 @ ( mand @ p @ ( mbox_s5 @ q ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f99]) ).
thf(f101,plain,
( ( mvalid @ ( mequiv @ ( mand @ ( mdia_s5 @ p ) @ ( mbox_s5 @ q ) ) @ ( mdia_s5 @ ( mand @ p @ ( mbox_s5 @ q ) ) ) ) )
!= $true ),
inference(flattening,[],[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 @ ( mand @ ( mdia_s5 @ p ) @ ( mbox_s5 @ q ) ) @ ( mdia_s5 @ ( mand @ p @ ( mbox_s5 @ q ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f101]) ).
thf(f141,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( 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 > $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 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ p
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) ) ) ) ) ),
inference(definition_unfolding,[],[f138,f129,f144,f141,f150,f133,f150,f141,f133]) ).
thf(f155,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( ~ ( p @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( ~ ( p @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f156,plain,
( $false
= ( ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( ~ ( p @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( ~ ( p @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( $false
= ( ~ ( ~ ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
( $true
= ( ~ ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( $false
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f163,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
@ sK1 ) )
| ( $true
= ( ~ ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
@ sK1 ) )
| ( $false
= ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f165]) ).
thf(f168,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
@ sK1 ) )
| ( $false
= ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f169,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
@ sK1 ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
@ sK1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
@ sK1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
@ sK1 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f173,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
@ sK1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
@ sK1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f174]) ).
thf(f176,plain,
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 )
| ~ ~ ( ~ ( p @ sK1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 )
| ~ ( p @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f177,plain,
( ( $false
= ( ~ ~ ( ~ ( p @ sK1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 )
| ~ ( p @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f178,plain,
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 )
| ~ ( p @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f179,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 )
| ~ ( p @ sK2 ) ) ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f180,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $false
= ( ~ ( p @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f182,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f183,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( p @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f180]) ).
thf(f184,plain,
( ( $true
= ( ~ ( ~ ( p @ sK1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 )
| ~ ( p @ sK2 ) ) ) ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f185,plain,
( ( $false
= ( ~ ( p @ sK1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 )
| ~ ( p @ sK2 ) ) ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f186,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 )
| ~ ( p @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f185]) ).
thf(f187,plain,
( ( $false
= ( ~ ( p @ sK1 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 )
| ~ ( p @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f185]) ).
thf(f188,plain,
( ( $true
= ( p @ sK1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 )
| ~ ( p @ sK2 ) ) ) ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f189,plain,
( ( $true
= ( p @ sK1 ) )
| ( $false
= ( ~ ( p @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f188]) ).
thf(f190,plain,
( ( $true
= ( p @ sK1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f188]) ).
thf(f191,plain,
( ( $true
= ( p @ sK1 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f192,plain,
( ( $true
= ( p @ sK1 ) )
| ( $true
= ( p @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f193,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 )
| ~ ( p @ sK2 ) ) ) ),
inference(not_proxy_clausification,[],[f186]) ).
thf(f194,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 )
| ~ ( p @ sK2 ) ) ) ),
inference(pi_proxy_clausification,[],[f193]) ).
thf(f196,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f194]) ).
thf(f197,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ( q @ X1 ) ) )
| ( $true
= ( rel_s5 @ sK0 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f197]) ).
thf(f199,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s5 @ sK0 @ sK2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f199]) ).
thf(f205,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
@ sK1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f206,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
@ sK1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 )
| ~ ~ ( ~ ( p @ sK1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( q @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f206]) ).
thf(f208,plain,
! [X1: $i] :
( ( $false
= ( ~ ~ ( ~ ( p @ sK1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( q @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( q @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f207]) ).
thf(f210,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( q @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f209]) ).
thf(f211,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f210]) ).
thf(f212,plain,
! [X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f211]) ).
thf(f213,plain,
! [X1: $i] :
( ( $true
= ( ~ ( ~ ( p @ sK1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( q @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f208]) ).
thf(f214,plain,
! [X1: $i] :
( ( $false
= ( ~ ( p @ sK1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( q @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f213]) ).
thf(f215,plain,
! [X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( q @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f214]) ).
thf(f220,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( q @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f215]) ).
thf(f221,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( q @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f220]) ).
thf(f222,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f221]) ).
thf(f223,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f222]) ).
thf(f224,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 )
| ( q @ X2 ) ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f223]) ).
thf(f225,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X2 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f224]) ).
thf(f226,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X2 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( rel_s5 @ sK1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f225]) ).
thf(f279,plain,
( ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f280,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f279]) ).
thf(f281,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f280]) ).
thf(f282,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK6 ) )
| ( $true
= ( ~ ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f281]) ).
thf(f283,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK6 ) )
| ( $false
= ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f282]) ).
thf(f284,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK6 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f283]) ).
thf(f285,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK6 ) )
| ( $false
= ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f283]) ).
thf(f286,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK6 ) )
| ( $true
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f285]) ).
thf(f287,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK6 ) )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f286]) ).
thf(f288,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK6 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f287]) ).
thf(f320,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK6 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f288]) ).
thf(f321,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK6 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f320]) ).
thf(f322,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK6 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f321]) ).
thf(f323,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK6 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f322]) ).
thf(f324,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK6 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f323]) ).
thf(f325,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK6 )
| ( q @ sK6 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f324]) ).
thf(f326,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK6 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f325]) ).
thf(f334,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK6 ) )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f326]) ).
thf(f335,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK6 ) )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f334]) ).
thf(f336,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK6 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f335]) ).
thf(f337,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK6 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f336]) ).
thf(f338,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK6 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f337]) ).
thf(f339,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK6 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f284]) ).
thf(f340,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK6 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
@ X1 ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f339]) ).
thf(f341,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK6 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f340]) ).
thf(f342,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK6 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f341]) ).
thf(f343,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK6 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ~ ( ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f342]) ).
thf(f344,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK6 )
| ( q @ sK6 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ~ ( ~ ( p @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f343]) ).
thf(f345,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK6 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ~ ( ~ ( p @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f344]) ).
thf(f346,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK6 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ~ ( ~ ( p @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f344]) ).
thf(f347,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ~ ( ~ ( p @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f346]) ).
thf(f348,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $true
= ( ~ ~ ( ~ ( p @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f347]) ).
thf(f349,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( ~ ( ~ ( p @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f348]) ).
thf(f350,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $true
= ( ~ ( p @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f349]) ).
thf(f351,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f350]) ).
thf(f352,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f351]) ).
thf(f353,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ ( sK8 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f352]) ).
thf(f354,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ ( sK8 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f353]) ).
thf(f355,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ ( sK8 @ X1 ) ) )
| ( $false
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f354]) ).
thf(f356,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ ( sK8 @ X1 ) ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f355]) ).
thf(f357,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ ( sK8 @ X1 ) ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f356]) ).
thf(f358,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ ( sK8 @ X1 ) ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f357]) ).
thf(f359,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( ~ ( rel_s5 @ X1 @ ( sK8 @ X1 ) )
| ( q @ ( sK8 @ X1 ) ) ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f358]) ).
thf(f360,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( q @ ( sK8 @ X1 ) ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f359]) ).
thf(f361,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $false
= ( ~ ( rel_s5 @ X1 @ ( sK8 @ X1 ) ) ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f359]) ).
thf(f362,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ( $true
= ( rel_s5 @ X1 @ ( sK8 @ X1 ) ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f361]) ).
thf(f363,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK6 ) )
| ( $true
= ( ~ ~ ( ~ ( p @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f345]) ).
thf(f364,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK6 ) )
| ( $false
= ( ~ ( ~ ( p @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f363]) ).
thf(f365,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK6 ) )
| ( $true
= ( ~ ( p @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f364]) ).
thf(f366,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK6 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f365]) ).
thf(f367,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK6 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f366]) ).
thf(f368,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ ( sK9 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 )
| ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f367]) ).
thf(f369,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ ( sK9 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f368]) ).
thf(f370,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ ( sK9 @ X1 ) ) )
| ( $false
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f369]) ).
thf(f371,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ ( sK9 @ X1 ) ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f370]) ).
thf(f372,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ ( sK9 @ X1 ) ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f371]) ).
thf(f373,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ ( sK9 @ X1 ) ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f372]) ).
thf(f374,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK6 ) )
| ( $false
= ( ~ ( rel_s5 @ X1 @ ( sK9 @ X1 ) )
| ( q @ ( sK9 @ X1 ) ) ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f373]) ).
thf(f375,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK6 ) )
| ( $false
= ( q @ ( sK9 @ X1 ) ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f374]) ).
thf(f376,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK6 ) )
| ( $false
= ( ~ ( rel_s5 @ X1 @ ( sK9 @ X1 ) ) ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(or_proxy_clausification,[],[f374]) ).
thf(f377,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( q @ sK6 ) )
| ( $true
= ( rel_s5 @ X1 @ ( sK9 @ X1 ) ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f376]) ).
thf(f378,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f379,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f378]) ).
thf(f380,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f379]) ).
thf(f381,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f380]) ).
thf(f382,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel_s5 @ X2 @ X1 )
=> ( rel_s5 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f381]) ).
thf(f383,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X2 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f382]) ).
thf(f384,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(f385,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,[],[f384]) ).
thf(f386,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,[],[f385]) ).
thf(f387,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,[],[f386]) ).
thf(f388,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,[],[f387]) ).
thf(f389,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,[],[f388]) ).
thf(f390,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s5 @ X3 @ X2 )
& ( rel_s5 @ X2 @ X1 ) )
=> ( rel_s5 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f389]) ).
thf(f391,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,[],[f390]) ).
thf(f392,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,[],[f391]) ).
thf(f393,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f394,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f393]) ).
thf(f395,plain,
! [X1: $i] :
( $true
= ( rel_s5 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f394]) ).
thf(f397,definition,
( spl10_1
<=> ( $true
= ( p @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
thf(f398,plain,
( ( $true
!= ( p @ sK2 ) )
| spl10_1 ),
inference(avatar_component_clause,[],[f397]) ).
thf(f399,plain,
( ( $true
= ( p @ sK2 ) )
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f397]) ).
thf(f401,definition,
( spl10_2
<=> ( $true
= ( p @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
thf(f403,plain,
( ( $true
= ( p @ sK1 ) )
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f401]) ).
thf(f404,plain,
( spl10_1
| spl10_2 ),
inference(avatar_split_clause,[],[f192,f401,f397]) ).
thf(f406,definition,
( spl10_3
<=> ( $true
= ( rel_s5 @ sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
thf(f407,plain,
( ( $true
!= ( rel_s5 @ sK0 @ sK2 ) )
| spl10_3 ),
inference(avatar_component_clause,[],[f406]) ).
thf(f408,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK2 ) )
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f406]) ).
thf(f409,plain,
( spl10_3
| spl10_2 ),
inference(avatar_split_clause,[],[f191,f401,f406]) ).
thf(f411,definition,
( spl10_4
<=> ( $true
= ( rel_s5 @ sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
thf(f412,plain,
( ( $true
!= ( rel_s5 @ sK0 @ sK1 ) )
| spl10_4 ),
inference(avatar_component_clause,[],[f411]) ).
thf(f413,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK1 ) )
| ~ spl10_4 ),
inference(avatar_component_clause,[],[f411]) ).
thf(f414,plain,
( spl10_3
| spl10_4 ),
inference(avatar_split_clause,[],[f182,f411,f406]) ).
thf(f422,definition,
( spl10_7
<=> ! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_7])],[avatar_definition]) ).
thf(f423,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $true
= ( q @ X1 ) ) )
| ~ spl10_7 ),
inference(avatar_component_clause,[],[f422]) ).
thf(f424,plain,
( spl10_7
| spl10_4 ),
inference(avatar_split_clause,[],[f212,f411,f422]) ).
thf(f437,definition,
( spl10_9
<=> ! [X1: $i] :
( ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_9])],[avatar_definition]) ).
thf(f438,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) ) )
| ~ spl10_9 ),
inference(avatar_component_clause,[],[f437]) ).
thf(f458,plain,
( ( $true = $false )
| ( $false
= ( p @ sK2 ) )
| ~ spl10_3
| ~ spl10_9 ),
inference(constrained_superposition,[],[f408,f438]) ).
thf(f459,plain,
( ( $true = $false )
| ( $false
= ( p @ sK1 ) )
| ~ spl10_4
| ~ spl10_9 ),
inference(constrained_superposition,[],[f413,f438]) ).
thf(f460,plain,
( ( $false
= ( p @ sK1 ) )
| ~ spl10_4
| ~ spl10_9 ),
inference(trivial_inequality_removal,[],[f459]) ).
thf(f461,plain,
( ( $false
= ( p @ sK2 ) )
| ~ spl10_3
| ~ spl10_9 ),
inference(trivial_inequality_removal,[],[f458]) ).
thf(f464,plain,
( ( $true = $false )
| ~ spl10_2
| ~ spl10_4
| ~ spl10_9 ),
inference(constrained_superposition,[],[f460,f403]) ).
thf(f468,plain,
( $false
| ~ spl10_2
| ~ spl10_4
| ~ spl10_9 ),
inference(trivial_inequality_removal,[],[f464]) ).
thf(f469,plain,
( ~ spl10_2
| ~ spl10_4
| ~ spl10_9 ),
inference(avatar_contradiction_clause,[],[f468]) ).
thf(f471,plain,
( ( $true = $false )
| ~ spl10_1
| ~ spl10_3
| ~ spl10_9 ),
inference(constrained_superposition,[],[f461,f399]) ).
thf(f475,plain,
( $false
| ~ spl10_1
| ~ spl10_3
| ~ spl10_9 ),
inference(trivial_inequality_removal,[],[f471]) ).
thf(f476,plain,
( ~ spl10_1
| ~ spl10_3
| ~ spl10_9 ),
inference(avatar_contradiction_clause,[],[f475]) ).
thf(f496,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( q @ X1 ) ) )
| spl10_3 ),
inference(forward_subsumption_resolution,[],[f200,f407]) ).
thf(f501,definition,
( spl10_13
<=> ( $false
= ( q @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_13])],[avatar_definition]) ).
thf(f502,plain,
( ( $false
!= ( q @ sK6 ) )
| spl10_13 ),
inference(avatar_component_clause,[],[f501]) ).
thf(f503,plain,
( ( $false
= ( q @ sK6 ) )
| ~ spl10_13 ),
inference(avatar_component_clause,[],[f501]) ).
thf(f504,plain,
( spl10_9
| spl10_7
| spl10_13 ),
inference(avatar_split_clause,[],[f338,f501,f422,f437]) ).
thf(f518,definition,
( spl10_15
<=> ! [X1: $i] :
( ( $false
= ( q @ ( sK9 @ X1 ) ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_15])],[avatar_definition]) ).
thf(f519,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( q @ ( sK9 @ X1 ) ) ) )
| ~ spl10_15 ),
inference(avatar_component_clause,[],[f518]) ).
thf(f520,plain,
( spl10_9
| spl10_15
| spl10_13 ),
inference(avatar_split_clause,[],[f375,f501,f518,f437]) ).
thf(f614,definition,
( spl10_19
<=> ! [X1: $i] :
( ( $false
= ( q @ ( sK8 @ X1 ) ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_19])],[avatar_definition]) ).
thf(f615,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( q @ ( sK8 @ X1 ) ) ) )
| ~ spl10_19 ),
inference(avatar_component_clause,[],[f614]) ).
thf(f617,definition,
( spl10_20
<=> ( $true
= ( rel_s5 @ sK0 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_20])],[avatar_definition]) ).
thf(f619,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK6 ) )
| ~ spl10_20 ),
inference(avatar_component_clause,[],[f617]) ).
thf(f620,plain,
( spl10_9
| spl10_19
| spl10_20 ),
inference(avatar_split_clause,[],[f360,f617,f614,f437]) ).
thf(f627,definition,
( spl10_22
<=> ! [X1: $i] :
( ( $true
= ( rel_s5 @ X1 @ ( sK8 @ X1 ) ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_22])],[avatar_definition]) ).
thf(f628,plain,
( ! [X1: $i] :
( ( $true
= ( rel_s5 @ X1 @ ( sK8 @ X1 ) ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) )
| ~ spl10_22 ),
inference(avatar_component_clause,[],[f627]) ).
thf(f629,plain,
( spl10_9
| spl10_22
| spl10_20 ),
inference(avatar_split_clause,[],[f362,f617,f627,f437]) ).
thf(f630,plain,
( ( $true = $false )
| ( $true
= ( q @ sK6 ) )
| ~ spl10_7
| ~ spl10_20 ),
inference(constrained_superposition,[],[f619,f423]) ).
thf(f633,plain,
( ( $true
= ( q @ sK6 ) )
| ~ spl10_7
| ~ spl10_20 ),
inference(trivial_inequality_removal,[],[f630]) ).
thf(f637,plain,
( ( $true = $false )
| ~ spl10_7
| ~ spl10_13
| ~ spl10_20 ),
inference(forward_demodulation,[],[f633,f503]) ).
thf(f638,plain,
( $false
| ~ spl10_7
| ~ spl10_13
| ~ spl10_20 ),
inference(trivial_inequality_removal,[],[f637]) ).
thf(f639,plain,
( ~ spl10_7
| ~ spl10_13
| ~ spl10_20 ),
inference(avatar_contradiction_clause,[],[f638]) ).
thf(f735,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( q @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK1 ) ) )
| spl10_3 ),
inference(constrained_superposition,[],[f496,f383]) ).
thf(f737,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK1 ) )
| ( $true
= ( q @ X0 ) ) )
| spl10_3 ),
inference(trivial_inequality_removal,[],[f735]) ).
thf(f885,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s5 @ X0 @ sK1 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl10_4 ),
inference(constrained_superposition,[],[f413,f392]) ).
thf(f890,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( $true
= ( rel_s5 @ X2 @ X1 ) )
| ( $false
= ( rel_s5 @ X2 @ X0 ) ) ),
inference(constrained_superposition,[],[f383,f392]) ).
thf(f895,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $true
= ( rel_s5 @ X1 @ X0 ) )
| ( $false
= ( rel_s5 @ X2 @ X1 ) )
| ( $false
= ( rel_s5 @ X0 @ X2 ) ) ),
inference(constrained_superposition,[],[f383,f392]) ).
thf(f899,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $true
= ( rel_s5 @ X0 @ X2 ) ) ),
inference(constrained_superposition,[],[f383,f392]) ).
thf(f902,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $true
= ( rel_s5 @ X0 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f899]) ).
thf(f906,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X1 @ X0 ) )
| ( $false
= ( rel_s5 @ X2 @ X1 ) )
| ( $false
= ( rel_s5 @ X0 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f895]) ).
thf(f911,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( $true
= ( rel_s5 @ X2 @ X1 ) )
| ( $false
= ( rel_s5 @ X2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f890]) ).
thf(f915,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ X0 @ sK1 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl10_4 ),
inference(trivial_inequality_removal,[],[f885]) ).
thf(f1146,definition,
( spl10_34
<=> ( $false
= ( rel_s5 @ sK1 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_34])],[avatar_definition]) ).
thf(f1147,plain,
( ( $false
!= ( rel_s5 @ sK1 @ sK0 ) )
| spl10_34 ),
inference(avatar_component_clause,[],[f1146]) ).
thf(f1148,plain,
( ( $false
= ( rel_s5 @ sK1 @ sK0 ) )
| ~ spl10_34 ),
inference(avatar_component_clause,[],[f1146]) ).
thf(f1158,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK1 ) )
| ~ spl10_34 ),
inference(constrained_superposition,[],[f383,f1148]) ).
thf(f1159,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK1 ) )
| ~ spl10_34 ),
inference(trivial_inequality_removal,[],[f1158]) ).
thf(f1166,plain,
( ( $true = $false )
| ~ spl10_4
| ~ spl10_34 ),
inference(constrained_superposition,[],[f1159,f413]) ).
thf(f1172,plain,
( $false
| ~ spl10_4
| ~ spl10_34 ),
inference(trivial_inequality_removal,[],[f1166]) ).
thf(f1173,plain,
( ~ spl10_4
| ~ spl10_34 ),
inference(avatar_contradiction_clause,[],[f1172]) ).
thf(f1201,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( q @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| spl10_3
| ~ spl10_4 ),
inference(constrained_superposition,[],[f737,f915]) ).
thf(f1206,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK0 ) )
| ( $true
= ( q @ X0 ) ) )
| spl10_3
| ~ spl10_4 ),
inference(trivial_inequality_removal,[],[f1201]) ).
thf(f1247,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( q @ X0 ) ) )
| spl10_3
| ~ spl10_4 ),
inference(constrained_superposition,[],[f383,f1206]) ).
thf(f1250,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( q @ X0 ) ) )
| spl10_3
| ~ spl10_4 ),
inference(trivial_inequality_removal,[],[f1247]) ).
thf(f1257,plain,
( spl10_7
| spl10_3
| ~ spl10_4 ),
inference(avatar_split_clause,[],[f1250,f411,f406,f422]) ).
thf(f1875,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s5 @ X0 @ sK6 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl10_20 ),
inference(constrained_superposition,[],[f392,f619]) ).
thf(f1880,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ X0 @ sK6 ) )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl10_20 ),
inference(trivial_inequality_removal,[],[f1875]) ).
thf(f2610,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( rel_s5 @ X0 @ sK1 ) ) )
| ~ spl10_4 ),
inference(constrained_superposition,[],[f413,f902]) ).
thf(f2702,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( rel_s5 @ X0 @ sK1 ) ) )
| ~ spl10_4 ),
inference(trivial_inequality_removal,[],[f2610]) ).
thf(f13045,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X1 @ ( sK9 @ X1 ) ) )
| ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X2 ) ) )
| spl10_13 ),
inference(forward_subsumption_resolution,[],[f377,f502]) ).
thf(f28494,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) )
| ( $true
= ( rel_s5 @ X1 @ X0 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) ) )
| ~ spl10_4 ),
inference(constrained_superposition,[],[f915,f906]) ).
thf(f28607,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK0 ) )
| ( $true
= ( rel_s5 @ X1 @ X0 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) ) )
| ~ spl10_4 ),
inference(trivial_inequality_removal,[],[f28494]) ).
thf(f46213,definition,
( spl10_48
<=> ! [X1: $i] :
( ( $true
= ( rel_s5 @ X1 @ ( sK9 @ X1 ) ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_48])],[avatar_definition]) ).
thf(f46214,plain,
( ! [X1: $i] :
( ( $true
= ( rel_s5 @ X1 @ ( sK9 @ X1 ) ) )
| ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK0 @ X1 ) ) )
| ~ spl10_48 ),
inference(avatar_component_clause,[],[f46213]) ).
thf(f46215,plain,
( spl10_9
| spl10_48
| spl10_13 ),
inference(avatar_split_clause,[],[f13045,f501,f46213,f437]) ).
thf(f53661,plain,
( ( $true = $false )
| ( $false
= ( p @ sK1 ) )
| ( $false
= ( q @ ( sK9 @ sK1 ) ) )
| ~ spl10_4
| ~ spl10_15 ),
inference(constrained_superposition,[],[f413,f519]) ).
thf(f53667,plain,
( ( $false
= ( p @ sK1 ) )
| ( $false
= ( q @ ( sK9 @ sK1 ) ) )
| ~ spl10_4
| ~ spl10_15 ),
inference(trivial_inequality_removal,[],[f53661]) ).
thf(f53763,plain,
( ( $true = $false )
| ( $false
= ( q @ ( sK9 @ sK1 ) ) )
| ~ spl10_2
| ~ spl10_4
| ~ spl10_15 ),
inference(forward_demodulation,[],[f53667,f403]) ).
thf(f53764,plain,
( ( $false
= ( q @ ( sK9 @ sK1 ) ) )
| ~ spl10_2
| ~ spl10_4
| ~ spl10_15 ),
inference(trivial_inequality_removal,[],[f53763]) ).
thf(f58619,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( rel_s5 @ X0 @ sK2 ) ) )
| ~ spl10_3 ),
inference(constrained_superposition,[],[f902,f408]) ).
thf(f58620,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s5 @ X0 @ sK0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK2 ) ) )
| ~ spl10_3 ),
inference(constrained_superposition,[],[f911,f408]) ).
thf(f58647,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK2 ) )
| ( $true
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl10_3 ),
inference(trivial_inequality_removal,[],[f58620]) ).
thf(f58648,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( rel_s5 @ X0 @ sK2 ) ) )
| ~ spl10_3 ),
inference(trivial_inequality_removal,[],[f58619]) ).
thf(f59331,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK2 @ X0 ) )
| ( $true
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl10_3 ),
inference(constrained_superposition,[],[f383,f58647]) ).
thf(f59412,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK2 @ X0 ) )
| ( $true
= ( rel_s5 @ X0 @ sK0 ) ) )
| ~ spl10_3 ),
inference(trivial_inequality_removal,[],[f59331]) ).
thf(f77826,definition,
( spl10_60
<=> ! [X2: $i] :
( ( $true
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_60])],[avatar_definition]) ).
thf(f77827,plain,
( ! [X2: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X2 ) )
| ( $true
= ( q @ X2 ) ) )
| ~ spl10_60 ),
inference(avatar_component_clause,[],[f77826]) ).
thf(f77828,plain,
( spl10_7
| spl10_60 ),
inference(avatar_split_clause,[],[f226,f77826,f422]) ).
thf(f78569,plain,
( ( $true = $false )
| ( $true
= ( q @ sK6 ) )
| ( $false
= ( rel_s5 @ sK1 @ sK0 ) )
| ~ spl10_20
| ~ spl10_60 ),
inference(constrained_superposition,[],[f77827,f1880]) ).
thf(f78603,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ X0 @ sK1 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl10_60 ),
inference(constrained_superposition,[],[f383,f77827]) ).
thf(f78619,plain,
( ( $true = $false )
| ( $false
= ( p @ sK1 ) )
| ( $false
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( q @ ( sK9 @ sK1 ) ) )
| ~ spl10_48
| ~ spl10_60 ),
inference(constrained_superposition,[],[f46214,f77827]) ).
thf(f78708,plain,
( ( $false
= ( p @ sK1 ) )
| ( $false
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( q @ ( sK9 @ sK1 ) ) )
| ~ spl10_48
| ~ spl10_60 ),
inference(trivial_inequality_removal,[],[f78619]) ).
thf(f78724,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK1 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl10_60 ),
inference(trivial_inequality_removal,[],[f78603]) ).
thf(f78758,plain,
( ( $true
= ( q @ sK6 ) )
| ( $false
= ( rel_s5 @ sK1 @ sK0 ) )
| ~ spl10_20
| ~ spl10_60 ),
inference(trivial_inequality_removal,[],[f78569]) ).
thf(f78823,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( q @ ( sK9 @ sK1 ) ) )
| ~ spl10_2
| ~ spl10_48
| ~ spl10_60 ),
inference(forward_demodulation,[],[f78708,f403]) ).
thf(f78824,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( q @ ( sK9 @ sK1 ) ) )
| ~ spl10_2
| ~ spl10_48
| ~ spl10_60 ),
inference(trivial_inequality_removal,[],[f78823]) ).
thf(f78865,plain,
( ( $true
= ( q @ sK6 ) )
| ~ spl10_20
| spl10_34
| ~ spl10_60 ),
inference(forward_subsumption_resolution,[],[f78758,f1147]) ).
thf(f78915,plain,
( ( $true = $false )
| ( $true
= ( q @ ( sK9 @ sK1 ) ) )
| ~ spl10_2
| ~ spl10_4
| ~ spl10_48
| ~ spl10_60 ),
inference(forward_demodulation,[],[f78824,f413]) ).
thf(f78916,plain,
( ( $true
= ( q @ ( sK9 @ sK1 ) ) )
| ~ spl10_2
| ~ spl10_4
| ~ spl10_48
| ~ spl10_60 ),
inference(trivial_inequality_removal,[],[f78915]) ).
thf(f78923,plain,
( ( $true = $false )
| ~ spl10_13
| ~ spl10_20
| spl10_34
| ~ spl10_60 ),
inference(forward_demodulation,[],[f78865,f503]) ).
thf(f78924,plain,
( $false
| ~ spl10_13
| ~ spl10_20
| spl10_34
| ~ spl10_60 ),
inference(trivial_inequality_removal,[],[f78923]) ).
thf(f78925,plain,
( ~ spl10_13
| ~ spl10_20
| spl10_34
| ~ spl10_60 ),
inference(avatar_contradiction_clause,[],[f78924]) ).
thf(f78928,plain,
( ( $true = $false )
| ~ spl10_2
| ~ spl10_4
| ~ spl10_15
| ~ spl10_48
| ~ spl10_60 ),
inference(forward_demodulation,[],[f78916,f53764]) ).
thf(f78929,plain,
( $false
| ~ spl10_2
| ~ spl10_4
| ~ spl10_15
| ~ spl10_48
| ~ spl10_60 ),
inference(trivial_inequality_removal,[],[f78928]) ).
thf(f78930,plain,
( ~ spl10_2
| ~ spl10_4
| ~ spl10_15
| ~ spl10_48
| ~ spl10_60 ),
inference(avatar_contradiction_clause,[],[f78929]) ).
thf(f79957,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl10_4
| ~ spl10_60 ),
inference(constrained_superposition,[],[f2702,f78724]) ).
thf(f80012,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK0 @ X0 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl10_4
| ~ spl10_60 ),
inference(trivial_inequality_removal,[],[f79957]) ).
thf(f80099,plain,
( spl10_7
| ~ spl10_4
| ~ spl10_60 ),
inference(avatar_split_clause,[],[f80012,f77826,f411,f422]) ).
thf(f80140,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ X0 @ sK0 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl10_7 ),
inference(constrained_superposition,[],[f383,f423]) ).
thf(f80214,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK0 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl10_7 ),
inference(trivial_inequality_removal,[],[f80140]) ).
thf(f80324,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ( $false
= ( rel_s5 @ sK1 @ X0 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl10_4
| ~ spl10_7 ),
inference(constrained_superposition,[],[f28607,f80214]) ).
thf(f80327,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK2 @ X0 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl10_3
| ~ spl10_7 ),
inference(constrained_superposition,[],[f59412,f80214]) ).
thf(f80382,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK2 @ X0 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl10_3
| ~ spl10_7 ),
inference(trivial_inequality_removal,[],[f80327]) ).
thf(f80385,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ( $false
= ( rel_s5 @ sK1 @ X0 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl10_4
| ~ spl10_7 ),
inference(trivial_inequality_removal,[],[f80324]) ).
thf(f80870,plain,
( ( $true = $false )
| ( $false
= ( p @ sK2 ) )
| ( $false
= ( rel_s5 @ sK0 @ sK2 ) )
| ( $true
= ( q @ ( sK9 @ sK2 ) ) )
| ~ spl10_3
| ~ spl10_7
| ~ spl10_48 ),
inference(constrained_superposition,[],[f46214,f80382]) ).
thf(f80925,plain,
( ( $false
= ( p @ sK2 ) )
| ( $false
= ( rel_s5 @ sK0 @ sK2 ) )
| ( $true
= ( q @ ( sK9 @ sK2 ) ) )
| ~ spl10_3
| ~ spl10_7
| ~ spl10_48 ),
inference(trivial_inequality_removal,[],[f80870]) ).
thf(f82604,plain,
( ( $true = $false )
| ( $false
= ( p @ sK1 ) )
| ( $false
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( q @ ( sK8 @ sK1 ) ) )
| ~ spl10_22
| ~ spl10_60 ),
inference(constrained_superposition,[],[f628,f77827]) ).
thf(f82607,plain,
( ( $true = $false )
| ( $false
= ( p @ sK2 ) )
| ( $false
= ( rel_s5 @ sK0 @ sK2 ) )
| ( $true
= ( q @ ( sK8 @ sK2 ) ) )
| ~ spl10_3
| ~ spl10_7
| ~ spl10_22 ),
inference(constrained_superposition,[],[f628,f80382]) ).
thf(f82722,plain,
( ( $false
= ( p @ sK2 ) )
| ( $false
= ( rel_s5 @ sK0 @ sK2 ) )
| ( $true
= ( q @ ( sK8 @ sK2 ) ) )
| ~ spl10_3
| ~ spl10_7
| ~ spl10_22 ),
inference(trivial_inequality_removal,[],[f82607]) ).
thf(f82725,plain,
( ( $false
= ( p @ sK1 ) )
| ( $false
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( q @ ( sK8 @ sK1 ) ) )
| ~ spl10_22
| ~ spl10_60 ),
inference(trivial_inequality_removal,[],[f82604]) ).
thf(f82783,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK2 ) )
| ( $true
= ( q @ ( sK8 @ sK2 ) ) )
| ~ spl10_1
| ~ spl10_3
| ~ spl10_7
| ~ spl10_22 ),
inference(forward_demodulation,[],[f82722,f399]) ).
thf(f82784,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK2 ) )
| ( $true
= ( q @ ( sK8 @ sK2 ) ) )
| ~ spl10_1
| ~ spl10_3
| ~ spl10_7
| ~ spl10_22 ),
inference(trivial_inequality_removal,[],[f82783]) ).
thf(f82789,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( q @ ( sK8 @ sK1 ) ) )
| ~ spl10_2
| ~ spl10_22
| ~ spl10_60 ),
inference(forward_demodulation,[],[f82725,f403]) ).
thf(f82790,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK1 ) )
| ( $true
= ( q @ ( sK8 @ sK1 ) ) )
| ~ spl10_2
| ~ spl10_22
| ~ spl10_60 ),
inference(trivial_inequality_removal,[],[f82789]) ).
thf(f82811,plain,
( ( $true = $false )
| ( $true
= ( q @ ( sK8 @ sK2 ) ) )
| ~ spl10_1
| ~ spl10_3
| ~ spl10_7
| ~ spl10_22 ),
inference(forward_demodulation,[],[f82784,f408]) ).
thf(f82812,plain,
( ( $true
= ( q @ ( sK8 @ sK2 ) ) )
| ~ spl10_1
| ~ spl10_3
| ~ spl10_7
| ~ spl10_22 ),
inference(trivial_inequality_removal,[],[f82811]) ).
thf(f82817,plain,
( ( $true = $false )
| ( $true
= ( q @ ( sK8 @ sK1 ) ) )
| ~ spl10_2
| ~ spl10_4
| ~ spl10_22
| ~ spl10_60 ),
inference(forward_demodulation,[],[f82790,f413]) ).
thf(f82818,plain,
( ( $true
= ( q @ ( sK8 @ sK1 ) ) )
| ~ spl10_2
| ~ spl10_4
| ~ spl10_22
| ~ spl10_60 ),
inference(trivial_inequality_removal,[],[f82817]) ).
thf(f83612,plain,
( ( $true = $false )
| ( $false
= ( p @ sK1 ) )
| ( $false
= ( q @ ( sK8 @ sK1 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl10_4
| ~ spl10_19 ),
inference(constrained_superposition,[],[f615,f915]) ).
thf(f83618,plain,
( ( $true = $false )
| ( $false
= ( p @ sK2 ) )
| ( $false
= ( q @ ( sK8 @ sK2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl10_3
| ~ spl10_19 ),
inference(constrained_superposition,[],[f615,f58648]) ).
thf(f83744,plain,
( ( $false
= ( p @ sK2 ) )
| ( $false
= ( q @ ( sK8 @ sK2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl10_3
| ~ spl10_19 ),
inference(trivial_inequality_removal,[],[f83618]) ).
thf(f83752,plain,
( ( $false
= ( p @ sK1 ) )
| ( $false
= ( q @ ( sK8 @ sK1 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl10_4
| ~ spl10_19 ),
inference(trivial_inequality_removal,[],[f83612]) ).
thf(f83803,plain,
( ( $true = $false )
| ( $false
= ( q @ ( sK8 @ sK2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl10_1
| ~ spl10_3
| ~ spl10_19 ),
inference(forward_demodulation,[],[f83744,f399]) ).
thf(f83804,plain,
( ( $false
= ( q @ ( sK8 @ sK2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl10_1
| ~ spl10_3
| ~ spl10_19 ),
inference(trivial_inequality_removal,[],[f83803]) ).
thf(f83815,plain,
( ( $true = $false )
| ( $false
= ( q @ ( sK8 @ sK1 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl10_2
| ~ spl10_4
| ~ spl10_19 ),
inference(forward_demodulation,[],[f83752,f403]) ).
thf(f83816,plain,
( ( $false
= ( q @ ( sK8 @ sK1 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl10_2
| ~ spl10_4
| ~ spl10_19 ),
inference(trivial_inequality_removal,[],[f83815]) ).
thf(f83844,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl10_1
| ~ spl10_3
| ~ spl10_7
| ~ spl10_19
| ~ spl10_22 ),
inference(forward_demodulation,[],[f83804,f82812]) ).
thf(f83845,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl10_1
| ~ spl10_3
| ~ spl10_7
| ~ spl10_19
| ~ spl10_22 ),
inference(trivial_inequality_removal,[],[f83844]) ).
thf(f83856,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl10_2
| ~ spl10_4
| ~ spl10_19
| ~ spl10_22
| ~ spl10_60 ),
inference(forward_demodulation,[],[f83816,f82818]) ).
thf(f83857,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl10_2
| ~ spl10_4
| ~ spl10_19
| ~ spl10_22
| ~ spl10_60 ),
inference(trivial_inequality_removal,[],[f83856]) ).
thf(f83863,plain,
( ( $true = $false )
| ~ spl10_1
| ~ spl10_3
| ~ spl10_7
| ~ spl10_19
| ~ spl10_22 ),
inference(forward_demodulation,[],[f83845,f395]) ).
thf(f83864,plain,
( $false
| ~ spl10_1
| ~ spl10_3
| ~ spl10_7
| ~ spl10_19
| ~ spl10_22 ),
inference(trivial_inequality_removal,[],[f83863]) ).
thf(f83865,plain,
( ~ spl10_1
| ~ spl10_3
| ~ spl10_7
| ~ spl10_19
| ~ spl10_22 ),
inference(avatar_contradiction_clause,[],[f83864]) ).
thf(f83871,plain,
( ( $true = $false )
| ~ spl10_2
| ~ spl10_4
| ~ spl10_19
| ~ spl10_22
| ~ spl10_60 ),
inference(forward_demodulation,[],[f83857,f395]) ).
thf(f83872,plain,
( $false
| ~ spl10_2
| ~ spl10_4
| ~ spl10_19
| ~ spl10_22
| ~ spl10_60 ),
inference(trivial_inequality_removal,[],[f83871]) ).
thf(f83873,plain,
( ~ spl10_2
| ~ spl10_4
| ~ spl10_19
| ~ spl10_22
| ~ spl10_60 ),
inference(avatar_contradiction_clause,[],[f83872]) ).
thf(f83921,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK1 @ X0 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl10_4
| ~ spl10_7 ),
inference(forward_demodulation,[],[f80385,f395]) ).
thf(f83922,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X0 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl10_4
| ~ spl10_7 ),
inference(trivial_inequality_removal,[],[f83921]) ).
thf(f84036,plain,
( ( $true = $false )
| ( $false
= ( p @ sK2 ) )
| ( $true
= ( q @ ( sK9 @ sK2 ) ) )
| ~ spl10_3
| ~ spl10_7
| ~ spl10_48 ),
inference(forward_demodulation,[],[f80925,f408]) ).
thf(f84037,plain,
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( q @ ( sK9 @ sK2 ) ) )
| ~ spl10_3
| ~ spl10_7
| ~ spl10_48 ),
inference(trivial_inequality_removal,[],[f84036]) ).
thf(f84819,plain,
( ( $true = $false )
| ( $true
= ( q @ ( sK9 @ sK2 ) ) )
| ~ spl10_1
| ~ spl10_3
| ~ spl10_7
| ~ spl10_48 ),
inference(forward_demodulation,[],[f84037,f399]) ).
thf(f84820,plain,
( ( $true
= ( q @ ( sK9 @ sK2 ) ) )
| ~ spl10_1
| ~ spl10_3
| ~ spl10_7
| ~ spl10_48 ),
inference(trivial_inequality_removal,[],[f84819]) ).
thf(f85037,plain,
( spl10_60
| ~ spl10_4
| ~ spl10_7 ),
inference(avatar_split_clause,[],[f83922,f422,f411,f77826]) ).
thf(f96217,plain,
( ( $true = $false )
| ( $false
= ( p @ sK2 ) )
| ( $false
= ( q @ ( sK9 @ sK2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl10_3
| ~ spl10_15 ),
inference(constrained_superposition,[],[f519,f58648]) ).
thf(f96356,plain,
( ( $false
= ( p @ sK2 ) )
| ( $false
= ( q @ ( sK9 @ sK2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl10_3
| ~ spl10_15 ),
inference(trivial_inequality_removal,[],[f96217]) ).
thf(f96398,plain,
( ( $true = $false )
| ( $false
= ( q @ ( sK9 @ sK2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl10_1
| ~ spl10_3
| ~ spl10_15 ),
inference(forward_demodulation,[],[f96356,f399]) ).
thf(f96399,plain,
( ( $false
= ( q @ ( sK9 @ sK2 ) ) )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl10_1
| ~ spl10_3
| ~ spl10_15 ),
inference(trivial_inequality_removal,[],[f96398]) ).
thf(f96415,plain,
( ( $true = $false )
| ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl10_1
| ~ spl10_3
| ~ spl10_7
| ~ spl10_15
| ~ spl10_48 ),
inference(forward_demodulation,[],[f96399,f84820]) ).
thf(f96416,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK0 ) )
| ~ spl10_1
| ~ spl10_3
| ~ spl10_7
| ~ spl10_15
| ~ spl10_48 ),
inference(trivial_inequality_removal,[],[f96415]) ).
thf(f96420,plain,
( ( $true = $false )
| ~ spl10_1
| ~ spl10_3
| ~ spl10_7
| ~ spl10_15
| ~ spl10_48 ),
inference(forward_demodulation,[],[f96416,f395]) ).
thf(f96421,plain,
( $false
| ~ spl10_1
| ~ spl10_3
| ~ spl10_7
| ~ spl10_15
| ~ spl10_48 ),
inference(trivial_inequality_removal,[],[f96420]) ).
thf(f96422,plain,
( ~ spl10_1
| ~ spl10_3
| ~ spl10_7
| ~ spl10_15
| ~ spl10_48 ),
inference(avatar_contradiction_clause,[],[f96421]) ).
thf(f98019,plain,
( ( $true
= ( p @ sK2 ) )
| spl10_4 ),
inference(forward_subsumption_resolution,[],[f183,f412]) ).
thf(f98020,plain,
( $false
| spl10_1
| spl10_4 ),
inference(forward_subsumption_resolution,[],[f98019,f398]) ).
thf(f98021,plain,
( spl10_1
| spl10_4 ),
inference(avatar_contradiction_clause,[],[f98020]) ).
cnf(s33,plain,
( spl10_1
| spl10_2 ),
inference(sat_conversion,[],[f404]) ).
cnf(s37,plain,
( spl10_2
| spl10_3 ),
inference(sat_conversion,[],[f409]) ).
cnf(s41,plain,
( spl10_3
| spl10_4 ),
inference(sat_conversion,[],[f414]) ).
cnf(s45,plain,
( spl10_4
| spl10_7 ),
inference(sat_conversion,[],[f424]) ).
cnf(s71,plain,
( ~ spl10_2
| ~ spl10_4
| ~ spl10_9 ),
inference(sat_conversion,[],[f469]) ).
cnf(s74,plain,
( ~ spl10_1
| ~ spl10_3
| ~ spl10_9 ),
inference(sat_conversion,[],[f476]) ).
cnf(s105,plain,
( spl10_7
| spl10_9
| spl10_13 ),
inference(sat_conversion,[],[f504]) ).
cnf(s115,plain,
( spl10_9
| spl10_13
| spl10_15 ),
inference(sat_conversion,[],[f520]) ).
cnf(s142,plain,
( spl10_9
| spl10_19
| spl10_20 ),
inference(sat_conversion,[],[f620]) ).
cnf(s147,plain,
( spl10_9
| spl10_20
| spl10_22 ),
inference(sat_conversion,[],[f629]) ).
cnf(s152,plain,
( ~ spl10_7
| ~ spl10_13
| ~ spl10_20 ),
inference(sat_conversion,[],[f639]) ).
cnf(s342,plain,
( ~ spl10_4
| ~ spl10_34 ),
inference(sat_conversion,[],[f1173]) ).
cnf(s376,plain,
( spl10_3
| ~ spl10_4
| spl10_7 ),
inference(sat_conversion,[],[f1257]) ).
cnf(s4822,plain,
( spl10_9
| spl10_13
| spl10_48 ),
inference(sat_conversion,[],[f46215]) ).
cnf(s12684,plain,
( spl10_7
| spl10_60 ),
inference(sat_conversion,[],[f77828]) ).
cnf(s12887,plain,
( ~ spl10_13
| ~ spl10_20
| spl10_34
| ~ spl10_60 ),
inference(sat_conversion,[],[f78925]) ).
cnf(s12908,plain,
( ~ spl10_2
| ~ spl10_4
| ~ spl10_15
| ~ spl10_48
| ~ spl10_60 ),
inference(sat_conversion,[],[f78930]) ).
cnf(s13934,plain,
( ~ spl10_4
| spl10_7
| ~ spl10_60 ),
inference(sat_conversion,[],[f80099]) ).
cnf(s14575,plain,
( ~ spl10_1
| ~ spl10_3
| ~ spl10_7
| ~ spl10_19
| ~ spl10_22 ),
inference(sat_conversion,[],[f83865]) ).
cnf(s14581,plain,
( ~ spl10_2
| ~ spl10_4
| ~ spl10_19
| ~ spl10_22
| ~ spl10_60 ),
inference(sat_conversion,[],[f83873]) ).
cnf(s15127,plain,
( ~ spl10_4
| ~ spl10_7
| spl10_60 ),
inference(sat_conversion,[],[f85037]) ).
cnf(s16598,plain,
( ~ spl10_1
| ~ spl10_3
| ~ spl10_7
| ~ spl10_15
| ~ spl10_48 ),
inference(sat_conversion,[],[f96422]) ).
cnf(s17543,plain,
( spl10_1
| spl10_4 ),
inference(sat_conversion,[],[f98021]) ).
cnf(s17544,plain,
( spl10_20
| ~ spl10_60
| spl10_1 ),
inference(rat,[],[s14581,s142,s147,s71,s33,s17543]) ).
cnf(s17545,plain,
( ~ spl10_60
| spl10_1 ),
inference(rat,[],[s12908,s115,s4822,s12887,s17544,s342,s71,s33,s17543]) ).
cnf(s17546,plain,
spl10_1,
inference(rat,[],[s15127,s12684,s17545,s17543]) ).
cnf(s17548,plain,
( spl10_20
| spl10_3
| ~ spl10_2 ),
inference(rat,[],[s14581,s142,s147,s71,s15127,s376,s41]) ).
cnf(s17549,plain,
( spl10_3
| ~ spl10_2 ),
inference(rat,[],[s12908,s115,s4822,s12887,s17548,s15127,s376,s71,s342,s41]) ).
cnf(s17550,plain,
( spl10_20
| ~ spl10_4
| ~ spl10_2 ),
inference(rat,[],[s12684,s14575,s14581,s142,s147,s74,s17549,s17546]) ).
cnf(s17551,plain,
( ~ spl10_20
| ~ spl10_13
| spl10_34 ),
inference(rat,[],[s12684,s152,s12887]) ).
cnf(s17552,plain,
( spl10_13
| ~ spl10_3 ),
inference(rat,[],[s16598,s105,s115,s4822,s74,s17546]) ).
cnf(s17553,plain,
( ~ spl10_4
| ~ spl10_2 ),
inference(rat,[],[s17551,s17550,s342,s17552,s17549]) ).
cnf(s17554,plain,
~ spl10_2,
inference(rat,[],[s14575,s142,s147,s152,s45,s17553,s17552,s74,s17549,s17546]) ).
cnf(s17555,plain,
spl10_3,
inference(rat,[],[s37,s17554]) ).
cnf(s17557,plain,
~ spl10_9,
inference(rat,[],[s74,s17546,s17555]) ).
cnf(s17558,plain,
spl10_13,
inference(rat,[],[s17552,s17555]) ).
cnf(s17568,plain,
( spl10_7
| ~ spl10_4 ),
inference(rat,[],[s12684,s13934]) ).
cnf(s17569,plain,
~ spl10_4,
inference(rat,[],[s17568,s14575,s142,s147,s17551,s342,s17546,s17555,s17557,s17558]) ).
cnf(s17571,plain,
spl10_7,
inference(rat,[],[s45,s17569]) ).
cnf(s17572,plain,
~ spl10_20,
inference(rat,[],[s152,s17558,s17571]) ).
cnf(s17574,plain,
spl10_22,
inference(rat,[],[s147,s17557,s17572]) ).
cnf(s17575,plain,
spl10_19,
inference(rat,[],[s142,s17557,s17572]) ).
cnf(s17576,plain,
$false,
inference(rat,[],[s14575,s17571,s17555,s17546,s17574,s17575]) ).
thf(f98022,plain,
$false,
inference(avatar_sat_refutation,[],[s17576]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO447^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.16 % Computer : n001.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 16:57:51 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 Running first-order model finding
% 0.09/0.18 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.73/0.83 % (1510064)Will run a generic schedule for satisfiability detection.
% 3.73/0.83 % (1510071)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3763561572:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.73/0.83 % (1510070)% WARNING: option uhcvi not known.
% 3.73/0.83 % (1510072)dis+10_1_sil=32000:sp=arity:random_seed=940477905:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.73/0.83 % (1510070)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2947843403:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.73/0.83 % (1510069)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=180809262_2999 on theBenchmark for (2999ds/0Mi)
% 3.73/0.83 % (1510075)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=830620267:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.73/0.83 % (1510073)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1580774972:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.73/0.83 % (1510074)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1430752106:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.73/0.83 % (1510070)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.73/0.83 % (1510073)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.73/0.83 % Exception at run slice level
% 3.73/0.83 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.73/0.83 % (1510070)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.73/0.83 % (1510083)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=702575532:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.73/0.83 % Exception at run slice level
% 3.73/0.83 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.73/0.83 % (1510072)Instruction limit reached!
% 3.73/0.83 % (1510072)------------------------------
% 3.73/0.83 % (1510072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.73/0.83 % (1510072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.73/0.83 % (1510072)CaDiCaL version: 2.1.3
% 3.73/0.83 % (1510072)Termination reason: Instruction limit
% 3.73/0.83 % (1510072)Termination phase: Saturation
% 3.73/0.83 % (1510072)Time elapsed: 0.046 s
% 3.73/0.83 % (1510072)Peak memory usage: 12 MB
% 3.73/0.83 % (1510072)Instructions burned: 103 (million)
% 3.73/0.83 % (1510085)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1241129936:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.73/0.83 % (1510073)Instruction limit reached!
% 3.73/0.83 % (1510073)------------------------------
% 3.73/0.83 % (1510073)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.73/0.83 % (1510073)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.73/0.83 % (1510073)CaDiCaL version: 2.1.3
% 3.73/0.83 % (1510073)Termination reason: Instruction limit
% 3.73/0.83 % (1510073)Termination phase: Saturation
% 3.73/0.83 % (1510073)Time elapsed: 0.052 s
% 3.73/0.83 % (1510073)Peak memory usage: 12 MB
% 3.73/0.83 % (1510073)Instructions burned: 118 (million)
% 3.73/0.83 % (1510074)Instruction limit reached!
% 3.73/0.83 % (1510074)------------------------------
% 3.73/0.83 % (1510074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.73/0.83 % (1510074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.73/0.83 % (1510074)CaDiCaL version: 2.1.3
% 3.73/0.83 % (1510074)Termination reason: Instruction limit
% 3.73/0.83 % (1510074)Termination phase: Saturation
% 3.73/0.83 % (1510074)Time elapsed: 0.058 s
% 3.73/0.83 % (1510074)Peak memory usage: 12 MB
% 3.73/0.83 % (1510074)Instructions burned: 133 (million)
% 3.73/0.83 % (1510086)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=2613326771:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 3.73/0.83 % (1510086)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.73/0.83 % (1510086)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.73/0.83 % (1510088)ott-21_1_sil=16000:fs=off:random_seed=440778202:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 3.73/0.83 % (1510075)Instruction limit reached!
% 16.24/2.60 % (1510075)------------------------------
% 16.24/2.60 % (1510075)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.24/2.60 % (1510075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.24/2.60 % (1510075)CaDiCaL version: 2.1.3
% 16.24/2.60 % (1510075)Termination reason: Instruction limit
% 16.24/2.60 % (1510075)Termination phase: Saturation
% 16.24/2.60 % (1510075)Time elapsed: 0.077 s
% 16.24/2.60 % (1510075)Peak memory usage: 12 MB
% 16.24/2.60 % (1510075)Instructions burned: 159 (million)
% 16.24/2.60 % (1510089)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=497190744:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 16.24/2.60 % (1510093)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=2689023841:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 16.24/2.60 % Exception at run slice level
% 16.24/2.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.24/2.60 % (1510085)Instruction limit reached!
% 16.24/2.60 % (1510085)------------------------------
% 16.24/2.60 % (1510085)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.24/2.60 % (1510085)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.24/2.60 % (1510085)CaDiCaL version: 2.1.3
% 16.24/2.60 % (1510085)Termination reason: Instruction limit
% 16.24/2.60 % (1510085)Termination phase: Saturation
% 16.24/2.60 % (1510085)Time elapsed: 0.059 s
% 16.24/2.60 % (1510085)Peak memory usage: 12 MB
% 16.24/2.60 % (1510085)Instructions burned: 135 (million)
% 16.24/2.60 % (1510095)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3051350836:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 16.24/2.60 % (1510096)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2514496318:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 16.24/2.60 % Exception at run slice level
% 16.24/2.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.24/2.60 % (1510088)Instruction limit reached!
% 16.24/2.60 % (1510088)------------------------------
% 16.24/2.60 % (1510088)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.24/2.60 % (1510088)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.24/2.60 % (1510088)CaDiCaL version: 2.1.3
% 16.24/2.60 % (1510088)Termination reason: Instruction limit
% 16.24/2.60 % (1510088)Termination phase: Saturation
% 16.24/2.60 % (1510088)Time elapsed: 0.077 s
% 16.24/2.60 % (1510088)Peak memory usage: 12 MB
% 16.24/2.60 % (1510088)Instructions burned: 181 (million)
% 16.24/2.60 % (1510099)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=4010650586: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)
% 16.24/2.60 % (1510099)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 16.24/2.60 % (1510100)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3414527541:i=879:kws=inv_precedence:fsr=off_2998 on theBenchmark for (2998ds/879Mi)
% 16.24/2.60 % (1510100)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 16.24/2.60 % (1510089)Instruction limit reached!
% 16.24/2.60 % (1510089)------------------------------
% 16.24/2.60 % (1510089)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 16.24/2.60 % (1510089)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 16.24/2.60 % (1510089)CaDiCaL version: 2.1.3
% 16.24/2.60 % (1510089)Termination reason: Instruction limit
% 16.24/2.60 % (1510089)Termination phase: Saturation
% 16.24/2.60 % (1510089)Time elapsed: 0.216 s
% 16.24/2.60 % (1510089)Peak memory usage: 13 MB
% 16.24/2.60 % (1510089)Instructions burned: 479 (million)
% 16.24/2.60 % (1510103)fmb+10_1_sil=64000:random_seed=1806622431:i=22061:nm=2:gsp=on_2996 on theBenchmark for (2996ds/22061Mi)
% 16.24/2.60 % (1510103)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 16.24/2.60 % Exception at run slice level
% 16.24/2.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 16.24/2.60 % (1510105)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=3876476962:i=9515:nm=5_2996 on theBenchmark for (2996ds/9515Mi)
% 16.24/2.60 % Exception at run slice level
% 16.24/2.60 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 39.74/5.80 % (1510107)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=2635482944:fmbsr=1.7:i=920_2996 on theBenchmark for (2996ds/920Mi)
% 39.74/5.80 % (1510086)Instruction limit reached!
% 39.74/5.80 % (1510086)------------------------------
% 39.74/5.80 % (1510086)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 39.74/5.80 % (1510086)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 39.74/5.80 % (1510086)CaDiCaL version: 2.1.3
% 39.74/5.80 % (1510086)Termination reason: Instruction limit
% 39.74/5.80 % (1510086)Termination phase: Saturation
% 39.74/5.80 % (1510086)Time elapsed: 0.293 s
% 39.74/5.80 % (1510086)Peak memory usage: 15 MB
% 39.74/5.80 % (1510086)Instructions burned: 686 (million)
% 39.74/5.80 % Exception at run slice level
% 39.74/5.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 39.74/5.80 % (1510109)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=1815731799:i=5131_2996 on theBenchmark for (2996ds/5131Mi)
% 39.74/5.80 % (1510109)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 39.74/5.80 % (1510110)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=1311521458:i=1472:ins=7:fdi=8:gsp=on_2996 on theBenchmark for (2996ds/1472Mi)
% 39.74/5.80 % (1510110)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 39.74/5.80 % (1510110)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 39.74/5.80 % (1510099)Instruction limit reached!
% 39.74/5.80 % (1510099)------------------------------
% 39.74/5.80 % (1510099)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 39.74/5.80 % (1510099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 39.74/5.80 % (1510099)CaDiCaL version: 2.1.3
% 39.74/5.80 % (1510099)Termination reason: Instruction limit
% 39.74/5.80 % (1510099)Termination phase: Saturation
% 39.74/5.80 % (1510099)Time elapsed: 0.299 s
% 39.74/5.80 % (1510099)Peak memory usage: 14 MB
% 39.74/5.80 % (1510099)Instructions burned: 694 (million)
% 39.74/5.80 % (1510113)fmb+10_1_sil=16000:sas=cadical:bce=on:fmbss=77:random_seed=2452391505:i=6324_2995 on theBenchmark for (2995ds/6324Mi)
% 39.74/5.80 % Exception at run slice level
% 39.74/5.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 39.74/5.80 % (1510115)fmb+10_1_fmbas=function:sil=32000:sas=cadical:fmbss=16:random_seed=2988734725:fmbsr=2.30978:i=2174_2994 on theBenchmark for (2994ds/2174Mi)
% 39.74/5.80 % Exception at run slice level
% 39.74/5.80 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 39.74/5.80 % (1510117)ott-2_1_sil=16000:newcnf=on:random_seed=2422667012:avsq=on:i=869:avsqr=1,16:kws=inv_arity_squared_2994 on theBenchmark for (2994ds/869Mi)
% 39.74/5.80 % (1510117)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 39.74/5.80 % (1510100)Instruction limit reached!
% 39.74/5.80 % (1510100)------------------------------
% 39.74/5.80 % (1510100)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 39.74/5.80 % (1510100)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 39.74/5.80 % (1510100)CaDiCaL version: 2.1.3
% 39.74/5.80 % (1510100)Termination reason: Instruction limit
% 39.74/5.80 % (1510100)Termination phase: Saturation
% 39.74/5.80 % (1510100)Time elapsed: 0.362 s
% 39.74/5.80 % (1510100)Peak memory usage: 13 MB
% 39.74/5.80 % (1510100)Instructions burned: 881 (million)
% 39.74/5.80 % (1510119)ott+10_1_sil=32000:tgt=ground:random_seed=3135138543:i=5114:av=off_2994 on theBenchmark for (2994ds/5114Mi)
% 39.74/5.80 % (1510095)Instruction limit reached!
% 39.74/5.80 % (1510095)------------------------------
% 39.74/5.80 % (1510095)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 39.74/5.80 % (1510095)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 39.74/5.80 % (1510095)CaDiCaL version: 2.1.3
% 39.74/5.80 % (1510095)Termination reason: Instruction limit
% 39.74/5.80 % (1510095)Termination phase: Saturation
% 39.74/5.80 % (1510095)Time elapsed: 0.460 s
% 39.74/5.80 % (1510095)Peak memory usage: 12 MB
% 39.74/5.80 % (1510095)Instructions burned: 1179 (million)
% 39.74/5.80 % (1510121)fmb+10_1_sil=64000:sas=cadical:bce=on:rp=on:random_seed=1991883799:i=54282_2993 on theBenchmark for (2993ds/54282Mi)
% 39.74/5.80 % Exception at run slice level
% 59.61/8.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 59.61/8.69 % (1510123)dis-11_1_sil=16000:sp=reverse_frequency:alpa=true:random_seed=389832695:i=3512:aac=none_2993 on theBenchmark for (2993ds/3512Mi)
% 59.61/8.69 % (1510123)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 59.61/8.69 % (1510117)Instruction limit reached!
% 59.61/8.69 % (1510117)------------------------------
% 59.61/8.69 % (1510117)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 59.61/8.69 % (1510117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 59.61/8.69 % (1510117)CaDiCaL version: 2.1.3
% 59.61/8.69 % (1510117)Termination reason: Instruction limit
% 59.61/8.69 % (1510117)Termination phase: Saturation
% 59.61/8.69 % (1510117)Time elapsed: 0.380 s
% 59.61/8.69 % (1510117)Peak memory usage: 14 MB
% 59.61/8.69 % (1510117)Instructions burned: 871 (million)
% 59.61/8.69 % (1510125)dis+21_1_sil=32000:sas=cadical:random_seed=1376026360:i=3773:amm=off_2990 on theBenchmark for (2990ds/3773Mi)
% 59.61/8.69 % (1510110)Instruction limit reached!
% 59.61/8.69 % (1510110)------------------------------
% 59.61/8.69 % (1510110)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 59.61/8.69 % (1510110)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 59.61/8.69 % (1510110)CaDiCaL version: 2.1.3
% 59.61/8.69 % (1510110)Termination reason: Instruction limit
% 59.61/8.69 % (1510110)Termination phase: Saturation
% 59.61/8.69 % (1510110)Time elapsed: 0.719 s
% 59.61/8.69 % (1510110)Peak memory usage: 18 MB
% 59.61/8.69 % (1510110)Instructions burned: 1472 (million)
% 59.61/8.69 % (1510127)ott+11_1_sil=16000:gs=on:random_seed=1389897413:s2a=on:i=2251:s2at=3:kws=inv_arity_squared:nm=2:fsr=off:fsd=on_2988 on theBenchmark for (2988ds/2251Mi)
% 59.61/8.69 % (1510127)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 59.61/8.69 % (1510127)Instruction limit reached!
% 59.61/8.69 % (1510127)------------------------------
% 59.61/8.69 % (1510127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 59.61/8.69 % (1510127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 59.61/8.69 % (1510127)CaDiCaL version: 2.1.3
% 59.61/8.69 % (1510127)Termination reason: Instruction limit
% 59.61/8.69 % (1510127)Termination phase: Saturation
% 59.61/8.69 % (1510127)Time elapsed: 0.838 s
% 59.61/8.69 % (1510127)Peak memory usage: 12 MB
% 59.61/8.69 % (1510127)Instructions burned: 2252 (million)
% 59.61/8.69 % (1510129)fmb+10_1_fmbas=predicate:sil=64000:tgt=ground:fmbss=7:random_seed=486082120:fmbsr=1.6:i=67534_2980 on theBenchmark for (2980ds/67534Mi)
% 59.61/8.69 % Exception at run slice level
% 59.61/8.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 59.61/8.69 % (1510123)Instruction limit reached!
% 59.61/8.69 % (1510123)------------------------------
% 59.61/8.69 % (1510123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 59.61/8.69 % (1510123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 59.61/8.69 % (1510123)CaDiCaL version: 2.1.3
% 59.61/8.69 % (1510123)Termination reason: Instruction limit
% 59.61/8.69 % (1510123)Termination phase: Saturation
% 59.61/8.69 % (1510123)Time elapsed: 1.368 s
% 59.61/8.69 % (1510123)Peak memory usage: 16 MB
% 59.61/8.69 % (1510123)Instructions burned: 3514 (million)
% 59.61/8.69 % (1510131)ott-22_32_sil=16000:tgt=full:fdtod=off:sp=weighted_frequency:rnwc=on:alpa=false:random_seed=3786623823:avsq=on:i=4591:add=off:avsqr=1,16:kws=inv_arity:nm=10:ins=9:fdi=4_2979 on theBenchmark for (2979ds/4591Mi)
% 59.61/8.69 % (1510132)dis+10_64_to=lpo:sil=32000:spb=intro:urr=on:sac=on:random_seed=605147388:i=29340_2979 on theBenchmark for (2979ds/29340Mi)
% 59.61/8.69 % (1510109)Instruction limit reached!
% 59.61/8.69 % (1510109)------------------------------
% 59.61/8.69 % (1510109)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 59.61/8.69 % (1510109)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 59.61/8.69 % (1510109)CaDiCaL version: 2.1.3
% 59.61/8.69 % (1510109)Termination reason: Instruction limit
% 59.61/8.69 % (1510109)Termination phase: Saturation
% 59.61/8.69 % (1510109)Time elapsed: 1.974 s
% 59.61/8.69 % (1510109)Peak memory usage: 18 MB
% 59.61/8.69 % (1510109)Instructions burned: 5131 (million)
% 59.61/8.69 % (1510135)dis-10_1_sil=64000:sas=cadical:cn=on:random_seed=1859079741:i=5211_2976 on theBenchmark for (2976ds/5211Mi)
% 59.61/8.69 % (1510125)Instruction limit reached!
% 59.61/8.69 % (1510125)------------------------------
% 59.61/8.69 % (1510125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 59.61/8.69 % (1510125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 59.61/8.69 % (1510125)CaDiCaL version: 2.1.3
% 59.61/8.69 % (1510125)Termination reason: Instruction limit
% 59.61/8.69 % (1510125)Termination phase: Saturation
% 59.61/8.69 % (1510125)Time elapsed: 1.466 s
% 59.61/8.69 % (1510125)Peak memory usage: 17 MB
% 59.61/8.69 % (1510125)Instructions burned: 3774 (million)
% 59.61/8.69 % (1510137)fmb+10_1_sil=32000:sas=cadical:bce=on:fmbss=17:random_seed=2214166747:i=5497:nm=2_2975 on theBenchmark for (2975ds/5497Mi)
% 59.61/8.69 % Exception at run slice level
% 59.61/8.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 59.61/8.69 % (1510139)fmb+10_1_fmbas=predicate:sil=64000:tgt=full:sas=cadical:fmbss=15:random_seed=3842838532:fmbsr=2:i=46332_2975 on theBenchmark for (2975ds/46332Mi)
% 59.61/8.69 % Exception at run slice level
% 59.61/8.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 59.61/8.69 % (1510141)fmb+10_1_sil=128000:tgt=full:sas=cadical:fmbss=12:random_seed=4129000825:i=14071_2975 on theBenchmark for (2975ds/14071Mi)
% 59.61/8.69 % Exception at run slice level
% 59.61/8.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 59.61/8.69 % (1510143)dis+10_161_sil=128000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=229614112:i=22565:add=on:rawr=on_2975 on theBenchmark for (2975ds/22565Mi)
% 59.61/8.69 % (1510119)Instruction limit reached!
% 59.61/8.69 % (1510119)------------------------------
% 59.61/8.69 % (1510119)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 59.61/8.69 % (1510119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 59.61/8.69 % (1510119)CaDiCaL version: 2.1.3
% 59.61/8.69 % (1510119)Termination reason: Instruction limit
% 59.61/8.69 % (1510119)Termination phase: Saturation
% 59.61/8.69 % (1510119)Time elapsed: 1.921 s
% 59.61/8.69 % (1510119)Peak memory usage: 14 MB
% 59.61/8.69 % (1510119)Instructions burned: 5114 (million)
% 59.61/8.69 % (1510145)ott+4_1_sil=16000:sp=arity:gs=on:random_seed=4271434398:i=8173:av=off_2974 on theBenchmark for (2974ds/8173Mi)
% 59.61/8.69 % (1510131)Instruction limit reached!
% 59.61/8.69 % (1510131)------------------------------
% 59.61/8.69 % (1510131)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 59.61/8.69 % (1510131)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 59.61/8.69 % (1510131)CaDiCaL version: 2.1.3
% 59.61/8.69 % (1510131)Termination reason: Instruction limit
% 59.61/8.69 % (1510131)Termination phase: Saturation
% 59.61/8.69 % (1510131)Time elapsed: 1.775 s
% 59.61/8.69 % (1510131)Peak memory usage: 16 MB
% 59.61/8.69 % (1510131)Instructions burned: 4591 (million)
% 59.61/8.69 % (1510147)dis+10_16:1_sil=16000:random_seed=3965235274:i=9155:fsr=off_2961 on theBenchmark for (2961ds/9155Mi)
% 59.61/8.69 % (1510135)Instruction limit reached!
% 59.61/8.69 % (1510135)------------------------------
% 59.61/8.69 % (1510135)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 59.61/8.69 % (1510135)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 59.61/8.69 % (1510135)CaDiCaL version: 2.1.3
% 59.61/8.69 % (1510135)Termination reason: Instruction limit
% 59.61/8.69 % (1510135)Termination phase: Saturation
% 59.61/8.69 % (1510135)Time elapsed: 2.052 s
% 59.61/8.69 % (1510135)Peak memory usage: 18 MB
% 59.61/8.69 % (1510135)Instructions burned: 5212 (million)
% 59.61/8.69 % (1510149)ott-3_8_sil=64000:random_seed=758678991:i=20139:bs=on_2955 on theBenchmark for (2955ds/20139Mi)
% 59.61/8.69 % (1510145)Instruction limit reached!
% 59.61/8.69 % (1510145)------------------------------
% 59.61/8.69 % (1510145)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 59.61/8.69 % (1510145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 59.61/8.69 % (1510145)CaDiCaL version: 2.1.3
% 59.61/8.69 % (1510145)Termination reason: Instruction limit
% 59.61/8.69 % (1510145)Termination phase: Saturation
% 59.61/8.69 % (1510145)Time elapsed: 3.067 s
% 59.61/8.69 % (1510145)Peak memory usage: 15 MB
% 59.61/8.69 % (1510145)Instructions burned: 8174 (million)
% 59.61/8.69 % (1510151)fmb+10_1_sil=64000:tgt=ground:sas=cadical:bce=on:fmbss=9:random_seed=3161269939:fmbsr=2:i=32576_2944 on theBenchmark for (2944ds/32576Mi)
% 59.61/8.69 % Exception at run slice level
% 59.61/8.69 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 59.61/8.69 % (1510153)ott+10_8:1_sil=16000:sp=arity:gs=on:random_seed=1347584818:i=11404_2943 on theBenchmark for (2943ds/11404Mi)
% 59.61/8.69 % (1510147)Instruction limit reached!
% 59.61/8.69 % (1510147)------------------------------
% 59.61/8.69 % (1510147)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 59.61/8.69 % (1510147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 59.61/8.69 % (1510147)CaDiCaL version: 2.1.3
% 59.61/8.69 % (1510147)Termination reason: Instruction limit
% 59.61/8.69 % (1510147)Termination phase: Saturation
% 59.61/8.69 % (1510147)Time elapsed: 3.339 s
% 59.61/8.69 % (1510147)Peak memory usage: 18 MB
% 59.61/8.69 % (1510147)Instructions burned: 9156 (million)
% 59.61/8.69 % (1510155)ott-11_1_sil=16000:alpa=false:sac=on:random_seed=820508188:i=14134_2928 on theBenchmark for (2928ds/14134Mi)
% 59.61/8.69 % (1510155)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 59.61/8.69 % (1510143) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1510064-1510143"...
% 59.61/8.69 % (1510143)...printing done.
% 59.61/8.69 % (1510143)Refutation found. Thanks to Tanya!
% 59.61/8.69 % SZS status Theorem for theBenchmark
% 59.61/8.69 % SZS output start Proof for theBenchmark
% See solution above
% 59.61/8.69 % (1510143)------------------------------
% 59.61/8.69 % (1510143)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 59.61/8.69 % (1510143)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 59.61/8.69 % (1510143)CaDiCaL version: 2.1.3
% 59.61/8.69 % (1510143)Termination reason: Refutation
% 59.61/8.69 % (1510143)Time elapsed: 5.975 s
% 59.61/8.69 % (1510143)Peak memory usage: 52 MB
% 59.61/8.69 % (1510143)Instructions burned: 11431 (million)
% 59.61/8.69 % (1510064)Success in time 8.495 s
% 59.61/8.69 % Vampire exiting
%------------------------------------------------------------------------------