%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO441^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:47:42 AM UTC 2026
% Result : Theorem 0.21s 0.38s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 19
% Syntax : Number of formulae : 194 ( 86 unt; 0 typ; 4 def)
% Number of atoms : 1427 ( 167 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 2848 ( 540 ~; 418 |; 15 &;1571 @)
% ( 4 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 140 ( 140 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 58 usr; 12 con; 0-4 aty)
% ( 268 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 506 ( 0 sgn 50 !; 0 ?; 506 :)
% 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,
vOR: $o > $o > $o ).
thf(func_def_37,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_41,type,
vNOT: $o > $o ).
thf(func_def_44,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_45,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
vAND: $o > $o > $o ).
thf(func_def_47,type,
vIMP: $o > $o > $o ).
thf(func_def_48,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_50,type,
db4:
!>[X0: $tType] : X0 ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) )
= mand ),
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,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
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,X3: $i,X2: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) )
= mbox_s5 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(f33,axiom,
( ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ X0 ) ) ) )
= mdia_s5 ),
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 @ ( mdia_s5 @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) ) @ ( mbox_s5 @ p ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) ) @ ( mbox_s5 @ p ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f39,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f40,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
~ ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) ) @ ( mbox_s5 @ p ) ) ),
inference(rectify,[],[f38]) ).
thf(f42,plain,
( ( ~ ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) ) @ ( mbox_s5 @ p ) ) ) )
= $true ),
inference(fool_elimination,[],[f41]) ).
thf(f50,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f51,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f52,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f51]) ).
thf(f55,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
inference(rectify,[],[f18]) ).
thf(f56,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f64,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f65,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f64]) ).
thf(f66,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X3 @ X2 ) )
=> ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f67,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f66]) ).
thf(f68,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f69,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f72,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) )
= mbox_s5 ),
inference(rectify,[],[f32]) ).
thf(f73,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f72]) ).
thf(f74,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f75,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f84,plain,
mtransitive @ rel_s5,
inference(rectify,[],[f35]) ).
thf(f85,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f84]) ).
thf(f95,plain,
mreflexive @ rel_s5,
inference(rectify,[],[f34]) ).
thf(f96,plain,
( ( mreflexive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f95]) ).
thf(f97,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f100,plain,
msymmetric @ rel_s5,
inference(rectify,[],[f36]) ).
thf(f101,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f100]) ).
thf(f103,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f101]) ).
thf(f105,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f85]) ).
thf(f107,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f108,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f65]) ).
thf(f109,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f110,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f111,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f118,plain,
( ( mreflexive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f96]) ).
thf(f119,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f120,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f97]) ).
thf(f123,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f125,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f129,plain,
( ( ~ ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mdia_s5 @ ( mdia_s5 @ ( mbox_s5 @ p ) ) ) ) @ ( mbox_s5 @ p ) ) ) )
= $true ),
inference(cnf_transformation,[],[f42]) ).
thf(f132,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f135,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f73]) ).
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,[],[f111,f109,f125,f109,f109]) ).
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,[],[f120,f125,f109]) ).
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,[],[f107,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,[],[f132,f109,f135,f109]) ).
thf(f151,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f103,f119]) ).
thf(f152,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f105,f110]) ).
thf(f153,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s5 )
= $true ),
inference(definition_unfolding,[],[f118,f123]) ).
thf(f154,plain,
( ( ~ ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p ) ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p ) ) ) )
= $true ),
inference(definition_unfolding,[],[f129,f108,f144,f150,f150,f150,f135,f135]) ).
thf(f155,plain,
( ( !! @ $i
@ ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 ) )
= $true ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f156,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f157,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s5 @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s5 @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f158,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s5 @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s5 @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f157]) ).
thf(f159,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s5 @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s5 @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f158]) ).
thf(f160,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s5 @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s5 @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f159]) ).
thf(f161,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y0 @ Y1 )
& ( rel_s5 @ Y2 @ Y0 ) )
=> ( rel_s5 @ Y2 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f162,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f155]) ).
thf(f163,plain,
! [X1: $i] :
( $true
= ( rel_s5 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s5 @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s5 @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f160]) ).
thf(f165,plain,
( ( ^ [Y0: $i] :
~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s5 @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s5 @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f167]) ).
thf(f172,definition,
( spl1_1
<=> ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f174,plain,
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f172]) ).
thf(f176,definition,
( spl1_2
<=> ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f177,plain,
( ( $true
!= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) )
| spl1_2 ),
inference(avatar_component_clause,[],[f176]) ).
thf(f178,plain,
( ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f176]) ).
thf(f179,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f168,f176,f172]) ).
thf(f180,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f186,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
= $false )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f187,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
= $false )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f180]) ).
thf(f188,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f186]) ).
thf(f189,plain,
( ( ( ~ ( rel_s5 @ sK0 @ sK2 )
| ( p @ sK2 ) )
= $false )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f188]) ).
thf(f190,plain,
( ( ( p @ sK2 )
= $false )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f189]) ).
thf(f191,plain,
( ( ( ~ ( rel_s5 @ sK0 @ sK2 ) )
= $false )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f189]) ).
thf(f194,plain,
( ( ( rel_s5 @ sK0 @ sK2 )
= $true )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f191]) ).
thf(f202,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) )
@ sK3 )
= $false )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f187]) ).
thf(f203,plain,
( ( ( ~ ( rel_s5 @ sK0 @ sK3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) )
= $false )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f202]) ).
thf(f204,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f203]) ).
thf(f205,plain,
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK3 ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f203]) ).
thf(f206,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK3 ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f205]) ).
thf(f214,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ sK4 )
= $false )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f204]) ).
thf(f215,plain,
( ( $false
= ( ~ ( rel_s5 @ sK3 @ sK4 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f214]) ).
thf(f216,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
= $false )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f215]) ).
thf(f217,plain,
( ( ( ~ ( rel_s5 @ sK3 @ sK4 ) )
= $false )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f215]) ).
thf(f218,plain,
( ( ( rel_s5 @ sK3 @ sK4 )
= $true )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f217]) ).
thf(f226,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ sK5 )
= $false )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f216]) ).
thf(f227,plain,
( ( ( ~ ( rel_s5 @ sK4 @ sK5 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f226]) ).
thf(f228,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f227]) ).
thf(f229,plain,
( ( ( ~ ( rel_s5 @ sK4 @ sK5 ) )
= $false )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f227]) ).
thf(f230,plain,
( ( ( rel_s5 @ sK4 @ sK5 )
= $true )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f229]) ).
thf(f238,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( p @ Y0 ) ) )
= $true )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f228]) ).
thf(f239,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ~ spl1_2 ),
inference(pi_proxy_clausification,[],[f238]) ).
thf(f240,plain,
( ! [X1: $i] :
( ( ~ ( rel_s5 @ sK5 @ X1 )
| ( p @ X1 ) )
= $true )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f239]) ).
thf(f242,plain,
( ( $true
= ( ~ ( rel_s5 @ sK5 @ sK2 )
| $false ) )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f240,f190]) ).
thf(f244,plain,
( ( $true
= ( ~ ( rel_s5 @ sK5 @ sK2 ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f242]) ).
thf(f249,plain,
( ( ( rel_s5 @ sK5 @ sK2 )
= $false )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f244]) ).
thf(f257,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f156]) ).
thf(f258,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f257]) ).
thf(f259,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f258]) ).
thf(f260,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel_s5 @ X2 @ X1 )
=> ( rel_s5 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f259]) ).
thf(f325,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y0 @ Y1 )
& ( rel_s5 @ Y2 @ Y0 ) )
=> ( rel_s5 @ Y2 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f161]) ).
thf(f326,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ X1 @ Y0 )
& ( rel_s5 @ Y1 @ X1 ) )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f325]) ).
thf(f327,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ X1 @ Y0 )
& ( rel_s5 @ Y1 @ X1 ) )
=> ( rel_s5 @ Y1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f326]) ).
thf(f328,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s5 @ X1 @ X2 )
& ( rel_s5 @ Y0 @ X1 ) )
=> ( rel_s5 @ Y0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f327]) ).
thf(f329,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( rel_s5 @ X1 @ X2 )
& ( rel_s5 @ Y0 @ X1 ) )
=> ( rel_s5 @ Y0 @ X2 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f328]) ).
thf(f330,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s5 @ X1 @ X2 )
& ( rel_s5 @ X3 @ X1 ) )
=> ( rel_s5 @ X3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f329]) ).
thf(f348,plain,
( ! [X0: $i] :
( $true
= ( ( ( rel_s5 @ sK3 @ X0 )
& $true )
=> ( rel_s5 @ sK0 @ X0 ) ) )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f330,f206]) ).
thf(f350,plain,
( ! [X0: $i] :
( ( ( ( rel_s5 @ sK4 @ X0 )
& $true )
=> ( rel_s5 @ sK3 @ X0 ) )
= $true )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f330,f218]) ).
thf(f357,plain,
( ! [X0: $i] :
( $true
= ( ( $true
& ( rel_s5 @ X0 @ sK0 ) )
=> ( rel_s5 @ X0 @ sK2 ) ) )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f330,f194]) ).
thf(f373,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ sK3 @ X0 )
=> ( rel_s5 @ sK0 @ X0 ) )
= $true )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f348]) ).
thf(f391,plain,
( ! [X0: $i] :
( $true
= ( ( rel_s5 @ sK4 @ X0 )
=> ( rel_s5 @ sK3 @ X0 ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f350]) ).
thf(f394,plain,
( ! [X0: $i] :
( $true
= ( ( rel_s5 @ X0 @ sK0 )
=> ( rel_s5 @ X0 @ sK2 ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f357]) ).
thf(f497,plain,
( ( $true
= ( ( rel_s5 @ sK5 @ sK0 )
=> $false ) )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f394,f249]) ).
thf(f510,plain,
( ( $true
= ( ~ ( rel_s5 @ sK5 @ sK0 ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f497]) ).
thf(f536,plain,
( ( ( rel_s5 @ sK5 @ sK0 )
= $false )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f510]) ).
thf(f548,plain,
( ( ( ( rel_s5 @ sK0 @ sK5 )
=> $false )
= $true )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f260,f536]) ).
thf(f557,plain,
( ( ( ~ ( rel_s5 @ sK0 @ sK5 ) )
= $true )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f548]) ).
thf(f562,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK5 ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f557]) ).
thf(f565,plain,
( ( $true
= ( ( rel_s5 @ sK3 @ sK5 )
=> $false ) )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f373,f562]) ).
thf(f571,plain,
( ( ( ~ ( rel_s5 @ sK3 @ sK5 ) )
= $true )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f565]) ).
thf(f581,plain,
( ( $false
= ( rel_s5 @ sK3 @ sK5 ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f571]) ).
thf(f653,plain,
( ( ( $true
=> ( rel_s5 @ sK3 @ sK5 ) )
= $true )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f391,f230]) ).
thf(f663,plain,
( ( $true
= ( rel_s5 @ sK3 @ sK5 ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f653]) ).
thf(f667,plain,
( ( $true = $false )
| ~ spl1_2 ),
inference(forward_demodulation,[],[f663,f581]) ).
thf(f668,plain,
( $false
| ~ spl1_2 ),
inference(trivial_inequality_removal,[],[f667]) ).
thf(f669,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[],[f668]) ).
thf(f670,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
= $true )
| spl1_2 ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f686,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
| spl1_2 ),
inference(or_proxy_clausification,[],[f670]) ).
thf(f688,definition,
( spl1_3
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
thf(f690,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
= $true )
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f688]) ).
thf(f692,definition,
( spl1_4
<=> ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
thf(f693,plain,
( ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
| spl1_4 ),
inference(avatar_component_clause,[],[f692]) ).
thf(f694,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f692]) ).
thf(f695,plain,
( spl1_3
| spl1_4
| spl1_2 ),
inference(avatar_split_clause,[],[f686,f176,f692,f688]) ).
thf(f707,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f713,plain,
( ( ( ~ $true
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) )
= $false )
| ~ spl1_1
| ~ spl1_4 ),
inference(forward_demodulation,[],[f707,f694]) ).
thf(f714,plain,
( ( ( $false
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) )
= $false )
| ~ spl1_1
| ~ spl1_4 ),
inference(boolean_simplification,[],[f713]) ).
thf(f715,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) )
= $false )
| ~ spl1_1
| ~ spl1_4 ),
inference(boolean_simplification,[],[f714]) ).
thf(f716,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
= $true )
| ~ spl1_1
| ~ spl1_4 ),
inference(not_proxy_clausification,[],[f715]) ).
thf(f717,plain,
( spl1_3
| ~ spl1_1
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f716,f692,f172,f688]) ).
thf(f718,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) )
@ X1 )
= $true )
| ~ spl1_3 ),
inference(pi_proxy_clausification,[],[f690]) ).
thf(f719,plain,
( ! [X1: $i] :
( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) )
| ~ spl1_3 ),
inference(beta-eta_normalization,[],[f718]) ).
thf(f721,plain,
( ( $true
= ( ~ $true
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) )
| ~ spl1_3 ),
inference(constrained_superposition,[],[f719,f163]) ).
thf(f725,plain,
( ( ( $false
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) )
= $true )
| ~ spl1_3 ),
inference(boolean_simplification,[],[f721]) ).
thf(f726,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl1_3 ),
inference(boolean_simplification,[],[f725]) ).
thf(f727,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X1 )
= $true )
| ~ spl1_3 ),
inference(pi_proxy_clausification,[],[f726]) ).
thf(f728,plain,
( ! [X1: $i] :
( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ~ spl1_3 ),
inference(beta-eta_normalization,[],[f727]) ).
thf(f730,plain,
( ( $true
= ( ~ $true
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ~ spl1_3 ),
inference(constrained_superposition,[],[f728,f163]) ).
thf(f734,plain,
( ( $true
= ( $false
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ~ spl1_3 ),
inference(boolean_simplification,[],[f730]) ).
thf(f735,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ~ spl1_3 ),
inference(boolean_simplification,[],[f734]) ).
thf(f736,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X1 ) )
| ~ spl1_3 ),
inference(pi_proxy_clausification,[],[f735]) ).
thf(f737,plain,
( ! [X1: $i] :
( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ~ spl1_3 ),
inference(beta-eta_normalization,[],[f736]) ).
thf(f739,plain,
( ( $true
= ( ~ $true
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ~ spl1_3 ),
inference(constrained_superposition,[],[f737,f163]) ).
thf(f743,plain,
( ( $true
= ( $false
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ~ spl1_3 ),
inference(boolean_simplification,[],[f739]) ).
thf(f744,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
= $true )
| ~ spl1_3 ),
inference(boolean_simplification,[],[f743]) ).
thf(f745,plain,
( ( $true = ( ~ $true ) )
| ~ spl1_3
| ~ spl1_4 ),
inference(forward_demodulation,[],[f744,f694]) ).
thf(f746,plain,
( ( $true = $false )
| ~ spl1_3
| ~ spl1_4 ),
inference(boolean_simplification,[],[f745]) ).
thf(f747,plain,
( $false
| ~ spl1_3
| ~ spl1_4 ),
inference(trivial_inequality_removal,[],[f746]) ).
thf(f748,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f747]) ).
thf(f749,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ $true )
= $false )
| ~ spl1_1
| ~ spl1_3 ),
inference(forward_demodulation,[],[f707,f690]) ).
thf(f750,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| $false )
= $false )
| ~ spl1_1
| ~ spl1_3 ),
inference(boolean_simplification,[],[f749]) ).
thf(f751,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false )
| ~ spl1_1
| ~ spl1_3 ),
inference(boolean_simplification,[],[f750]) ).
thf(f868,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(not_proxy_clausification,[],[f751]) ).
thf(f869,plain,
( $false
| ~ spl1_1
| ~ spl1_3
| spl1_4 ),
inference(forward_subsumption_resolution,[],[f868,f693]) ).
thf(f870,plain,
( ~ spl1_1
| ~ spl1_3
| spl1_4 ),
inference(avatar_contradiction_clause,[],[f869]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f179]) ).
cnf(s3,plain,
~ spl1_2,
inference(sat_conversion,[],[f669]) ).
cnf(s4,plain,
( spl1_2
| spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f695]) ).
cnf(s5,plain,
( ~ spl1_1
| spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f717]) ).
cnf(s6,plain,
( ~ spl1_3
| ~ spl1_4 ),
inference(sat_conversion,[],[f748]) ).
cnf(s7,plain,
( ~ spl1_1
| ~ spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f870]) ).
cnf(s8,plain,
spl1_1,
inference(rat,[],[s1,s3]) ).
cnf(s9,plain,
spl1_3,
inference(rat,[],[s4,s5,s3,s8]) ).
cnf(s10,plain,
spl1_4,
inference(rat,[],[s7,s8,s9]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s6,s10,s9]) ).
thf(f871,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO441^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n006.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:51:40 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.37 % (1009305)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.37 % (1009310)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3427313594:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.37 % (1009313)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1937947064:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.37 % (1009311)lrs+10_16_si=on:nwc=1.5:random_seed=572369534:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.37 % (1009312)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3234288147:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.37 % (1009314)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1037703886:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.37 % (1009315)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=953567401:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.37 % (1009316)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.37 % (1009316)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.37 % (1009312)Instruction limit reached!
% 0.21/0.37 % (1009312)------------------------------
% 0.21/0.37 % (1009312)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (1009312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (1009312)CaDiCaL version: 2.1.3
% 0.21/0.37 % (1009312)Termination reason: Instruction limit
% 0.21/0.37 % (1009312)Termination phase: Property scanning
% 0.21/0.37 % (1009312)Time elapsed: 0.003 s
% 0.21/0.37 % (1009312)Peak memory usage: 10 MB
% 0.21/0.37 % (1009312)Instructions burned: 7 (million)
% 0.21/0.37 % (1009316)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2002337546:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.37 % (1009311)Instruction limit reached!
% 0.21/0.37 % (1009311)------------------------------
% 0.21/0.37 % (1009311)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (1009311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (1009311)CaDiCaL version: 2.1.3
% 0.21/0.37 % (1009311)Termination reason: Instruction limit
% 0.21/0.37 % (1009311)Termination phase: Saturation
% 0.21/0.37 % (1009311)Time elapsed: 0.009 s
% 0.21/0.37 % (1009311)Peak memory usage: 12 MB
% 0.21/0.37 % (1009311)Instructions burned: 19 (million)
% 0.21/0.37 % (1009314)Instruction limit reached!
% 0.21/0.37 % (1009314)------------------------------
% 0.21/0.37 % (1009314)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (1009314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (1009314)CaDiCaL version: 2.1.3
% 0.21/0.37 % (1009314)Termination reason: Instruction limit
% 0.21/0.37 % (1009314)Termination phase: Saturation
% 0.21/0.37 % (1009314)Time elapsed: 0.014 s
% 0.21/0.37 % (1009314)Peak memory usage: 11 MB
% 0.21/0.37 % (1009314)Instructions burned: 24 (million)
% 0.21/0.37 % (1009310)Instruction limit reached!
% 0.21/0.37 % (1009310)------------------------------
% 0.21/0.37 % (1009310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (1009310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (1009310)CaDiCaL version: 2.1.3
% 0.21/0.37 % (1009310)Termination reason: Instruction limit
% 0.21/0.37 % (1009310)Termination phase: Saturation
% 0.21/0.37 % (1009310)Time elapsed: 0.027 s
% 0.21/0.37 % (1009310)Peak memory usage: 12 MB
% 0.21/0.37 % (1009310)Instructions burned: 90 (million)
% 0.21/0.37 % (1009324)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1618515749:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.37 % (1009324)Instruction limit reached!
% 0.21/0.37 % (1009324)------------------------------
% 0.21/0.37 % (1009324)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (1009324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (1009324)CaDiCaL version: 2.1.3
% 0.21/0.38 % (1009324)Termination reason: Instruction limit
% 0.21/0.38 % (1009324)Termination phase: Function definition elimination
% 0.21/0.38 % (1009324)Time elapsed: 0.003 s
% 0.21/0.38 % (1009324)Peak memory usage: 10 MB
% 0.21/0.38 % (1009324)Instructions burned: 6 (million)
% 0.21/0.38 % (1009325)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=742812236:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.38 % (1009326)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.38 % (1009327)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4153973486:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.21/0.38 % (1009325)Instruction limit reached!
% 0.21/0.38 % (1009325)------------------------------
% 0.21/0.38 % (1009325)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (1009325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (1009325)CaDiCaL version: 2.1.3
% 0.21/0.38 % (1009325)Termination reason: Instruction limit
% 0.21/0.38 % (1009325)Termination phase: Property scanning
% 0.21/0.38 % (1009325)Time elapsed: 0.002 s
% 0.21/0.38 % (1009325)Peak memory usage: 10 MB
% 0.21/0.38 % (1009325)Instructions burned: 5 (million)
% 0.21/0.38 % (1009326)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3824275620:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.38 % (1009327)Instruction limit reached!
% 0.21/0.38 % (1009327)------------------------------
% 0.21/0.38 % (1009327)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (1009327)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (1009327)CaDiCaL version: 2.1.3
% 0.21/0.38 % (1009327)Termination reason: Instruction limit
% 0.21/0.38 % (1009327)Termination phase: Saturation
% 0.21/0.38 % (1009327)Time elapsed: 0.003 s
% 0.21/0.38 % (1009327)Peak memory usage: 11 MB
% 0.21/0.38 % (1009327)Instructions burned: 14 (million)
% 0.21/0.38 % (1009315)Instruction limit reached!
% 0.21/0.38 % (1009315)------------------------------
% 0.21/0.38 % (1009315)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (1009315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (1009315)CaDiCaL version: 2.1.3
% 0.21/0.38 % (1009315)Termination reason: Instruction limit
% 0.21/0.38 % (1009315)Termination phase: Saturation
% 0.21/0.38 % (1009315)Time elapsed: 0.035 s
% 0.21/0.38 % (1009315)Peak memory usage: 12 MB
% 0.21/0.38 % (1009315)Instructions burned: 76 (million)
% 0.21/0.38 % (1009326)Instruction limit reached!
% 0.21/0.38 % (1009326)------------------------------
% 0.21/0.38 % (1009326)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (1009326)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (1009326)CaDiCaL version: 2.1.3
% 0.21/0.38 % (1009326)Termination reason: Instruction limit
% 0.21/0.38 % (1009326)Termination phase: Property scanning
% 0.21/0.38 % (1009326)Time elapsed: 0.003 s
% 0.21/0.38 % (1009326)Peak memory usage: 10 MB
% 0.21/0.38 % (1009326)Instructions burned: 7 (million)
% 0.21/0.38 % (1009329)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.38 % (1009329)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.38 % (1009329)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2436188256:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.21/0.38 % (1009334)lrs+10_1_si=on:cs=on:random_seed=2489836514:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.21/0.38 % (1009332)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=3933389698:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.21/0.38 % (1009335)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.21/0.38 % (1009334)Instruction limit reached!
% 0.21/0.38 % (1009334)------------------------------
% 0.21/0.38 % (1009334)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (1009334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (1009334)CaDiCaL version: 2.1.3
% 0.21/0.38 % (1009334)Termination reason: Instruction limit
% 0.21/0.38 % (1009334)Termination phase: Saturation
% 0.21/0.38 % (1009334)Time elapsed: 0.004 s
% 0.21/0.38 % (1009334)Peak memory usage: 11 MB
% 0.21/0.38 % (1009334)Instructions burned: 10 (million)
% 0.21/0.38 % (1009336)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=769758348:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.21/0.38 % (1009329)Instruction limit reached!
% 0.21/0.38 % (1009329)------------------------------
% 0.21/0.38 % (1009329)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (1009329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (1009329)CaDiCaL version: 2.1.3
% 0.21/0.38 % (1009329)Termination reason: Instruction limit
% 0.21/0.38 % (1009329)Termination phase: Saturation
% 0.21/0.38 % (1009329)Time elapsed: 0.013 s
% 0.21/0.38 % (1009329)Peak memory usage: 11 MB
% 0.21/0.38 % (1009329)Instructions burned: 29 (million)
% 0.21/0.38 % (1009335)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=1928071369:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.38 % (1009336)Refutation not found, incomplete strategy
% 0.21/0.38 % (1009336)------------------------------
% 0.21/0.38 % (1009336)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (1009336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (1009336)CaDiCaL version: 2.1.3
% 0.21/0.38 % (1009336)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.38 % (1009336)Time elapsed: 0.004 s
% 0.21/0.38 % (1009336)Peak memory usage: 12 MB
% 0.21/0.38 % (1009336)Instructions burned: 7 (million)
% 0.21/0.38 % (1009336)------------------------------
% 0.21/0.38 % (1009336)------------------------------
% 0.21/0.38 % (1009335)Instruction limit reached!
% 0.21/0.38 % (1009335)------------------------------
% 0.21/0.38 % (1009335)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (1009335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (1009335)CaDiCaL version: 2.1.3
% 0.21/0.38 % (1009335)Termination reason: Instruction limit
% 0.21/0.38 % (1009335)Termination phase: Property scanning
% 0.21/0.38 % (1009335)Time elapsed: 0.002 s
% 0.21/0.38 % (1009335)Peak memory usage: 10 MB
% 0.21/0.38 % (1009335)Instructions burned: 4 (million)
% 0.21/0.38 % (1009344)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=745866574:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.21/0.38 % (1009344)Instruction limit reached!
% 0.21/0.38 % (1009344)------------------------------
% 0.21/0.38 % (1009344)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (1009344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (1009344)CaDiCaL version: 2.1.3
% 0.21/0.38 % (1009344)Termination reason: Instruction limit
% 0.21/0.38 % (1009344)Termination phase: Saturation
% 0.21/0.38 % (1009344)Time elapsed: 0.004 s
% 0.21/0.38 % (1009344)Peak memory usage: 12 MB
% 0.21/0.38 % (1009344)Instructions burned: 15 (million)
% 0.21/0.38 % (1009340)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=659564721:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.21/0.38 % (1009343)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3745266142:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.21/0.38 % (1009345)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=2853848681:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 0.21/0.38 % (1009340)Refutation not found, incomplete strategy
% 0.21/0.38 % (1009340)------------------------------
% 0.21/0.38 % (1009340)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (1009340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (1009340)CaDiCaL version: 2.1.3
% 0.21/0.38 % (1009340)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.38 % (1009340)Time elapsed: 0.004 s
% 0.21/0.38 % (1009340)Peak memory usage: 12 MB
% 0.21/0.38 % (1009340)Instructions burned: 8 (million)
% 0.21/0.38 % (1009340)------------------------------
% 0.21/0.38 % (1009340)------------------------------
% 0.21/0.38 % (1009332) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1009305-1009332"...
% 0.21/0.38 % (1009348)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2460116276:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 0.21/0.38 % (1009348)Instruction limit reached!
% 0.21/0.38 % (1009348)------------------------------
% 0.21/0.38 % (1009348)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (1009348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (1009348)CaDiCaL version: 2.1.3
% 0.21/0.38 % (1009348)Termination reason: Instruction limit
% 0.21/0.38 % (1009348)Termination phase: Saturation
% 0.21/0.38 % (1009348)Time elapsed: 0.003 s
% 0.21/0.38 % (1009348)Peak memory usage: 11 MB
% 0.21/0.38 % (1009348)Instructions burned: 15 (million)
% 0.21/0.38 % (1009332)...printing done.
% 0.21/0.38 % (1009332)Refutation found. Thanks to Tanya!
% 0.21/0.38 % SZS status Theorem for theBenchmark
% 0.21/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.38 % (1009332)------------------------------
% 0.21/0.38 % (1009332)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.38 % (1009332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.38 % (1009332)CaDiCaL version: 2.1.3
% 0.21/0.38 % (1009332)Termination reason: Refutation
% 0.21/0.38 % (1009332)Time elapsed: 0.039 s
% 0.21/0.38 % (1009332)Peak memory usage: 13 MB
% 0.21/0.38 % (1009332)Instructions burned: 75 (million)
% 0.21/0.38 % (1009305)Success in time 0.127 s
% 0.21/0.38 % Vampire exiting
%------------------------------------------------------------------------------