%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO449^1 : 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 : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:47:44 AM UTC 2026
% Result : Theorem 0.80s 0.45s
% Output : Refutation 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 17
% Syntax : Number of formulae : 205 ( 76 unt; 0 typ; 4 def)
% Number of atoms : 1831 ( 278 equ; 0 cnn)
% Maximal formula atoms : 13 ( 8 avg)
% Number of connectives : 3055 ( 533 ~; 598 |; 13 &;1660 @)
% ( 4 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 134 ( 134 >; 0 *; 0 +; 0 <<)
% Number of symbols : 64 ( 60 usr; 13 con; 0-4 aty)
% ( 225 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 514 ( 0 sgn 101 !; 0 ?; 514 :)
% 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,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_40,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_43,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vNOT: $o > $o ).
thf(func_def_46,type,
vOR: $o > $o > $o ).
thf(func_def_47,type,
vIMP: $o > $o > $o ).
thf(func_def_48,type,
vAND: $o > $o > $o ).
thf(func_def_49,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
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] :
( ( X0 @ X2 )
| ( X1 @ 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,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) )
= mequiv ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $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 @ 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,
( ( ^ [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(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 @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ ( mimplies @ ( mdia_s5 @ p ) @ q ) ) @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ q ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ ( mimplies @ ( mdia_s5 @ p ) @ q ) ) @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ q ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f39,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f49,plain,
~ ( mvalid @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ ( mimplies @ ( mdia_s5 @ p ) @ q ) ) @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ q ) ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f50,plain,
( ( ~ ( mvalid @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ ( mimplies @ ( mdia_s5 @ p ) @ q ) ) @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ q ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f49]) ).
thf(f51,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) )
= mbox_s5 ),
inference(rectify,[],[f32]) ).
thf(f52,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f51]) ).
thf(f53,plain,
msymmetric @ rel_s5,
inference(rectify,[],[f36]) ).
thf(f54,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f53]) ).
thf(f59,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f60,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f59]) ).
thf(f61,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
=> ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f62,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f61]) ).
thf(f63,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X2 )
& ( X0 @ X1 @ X3 ) )
=> ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f64,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f68,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f69,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f82,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f85,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f86,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f85]) ).
thf(f89,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f90,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f93,plain,
mtransitive @ rel_s5,
inference(rectify,[],[f35]) ).
thf(f94,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f93]) ).
thf(f103,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f94]) ).
thf(f105,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f89]) ).
thf(f108,plain,
( ( ~ ( mvalid @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ ( mimplies @ ( mdia_s5 @ p ) @ q ) ) @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ q ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f50]) ).
thf(f109,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f54]) ).
thf(f115,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f86]) ).
thf(f116,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f120,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f122,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f123,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f130,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f131,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f134,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f135,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
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] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f134,f120,f115,f120,f120]) ).
thf(f142,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f130,f115,f120]) ).
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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f122,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,[],[f105,f120,f116,f120]) ).
thf(f151,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f103,f135]) ).
thf(f152,plain,
( $true
= ( ~ ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ 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 )
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ p
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f108,f131,f116,f144,f116,f142,f150,f116,f142,f116]) ).
thf(f153,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f109,f123]) ).
thf(f155,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y0 @ Y1 )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f157,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y2 @ Y0 )
& ( rel_s5 @ Y0 @ Y1 ) )
=> ( rel_s5 @ Y2 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f158,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 )
| ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( p @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( q @ Y3 ) ) )
| ~ ( p @ Y2 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( q @ Y3 ) ) )
| ~ ( p @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 )
| ~ ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f159,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( p @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( q @ Y3 ) ) )
| ~ ( p @ Y2 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( q @ Y3 ) ) )
| ~ ( p @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( p @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f158]) ).
thf(f160,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( p @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( q @ Y3 ) ) )
| ~ ( p @ Y2 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( q @ Y3 ) ) )
| ~ ( p @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( p @ Y3 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( q @ Y3 ) ) )
| ~ ( p @ Y2 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( q @ Y3 ) ) )
| ~ ( p @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ~ ( p @ Y3 ) ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) )
| ~ ( p @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) )
| ~ ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) )
| ~ ( p @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) )
| ~ ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) ) ) ) ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
( $false
= ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f168,plain,
( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f165]) ).
thf(f169,plain,
( ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) ) )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) ) )
= $true )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f174,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f176,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f178,definition,
( spl2_1
<=> ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f180,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f178]) ).
thf(f182,definition,
( spl2_2
<=> ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f183,plain,
( ( $false
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) )
| spl2_2 ),
inference(avatar_component_clause,[],[f182]) ).
thf(f184,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f182]) ).
thf(f185,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f175,f182,f178]) ).
thf(f186,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f187,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f190,definition,
( spl2_3
<=> ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
thf(f192,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f190]) ).
thf(f193,plain,
( spl2_3
| spl2_1 ),
inference(avatar_split_clause,[],[f186,f178,f190]) ).
thf(f194,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f196,definition,
( spl2_4
<=> ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
thf(f198,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f196]) ).
thf(f200,plain,
( spl2_4
| spl2_3 ),
inference(avatar_split_clause,[],[f194,f190,f196]) ).
thf(f201,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) )
@ sK3 ) )
| ~ spl2_2 ),
inference(sigma_proxy_clausification,[],[f184]) ).
thf(f202,plain,
( ( ( ~ ( rel_s5 @ sK1 @ sK3 )
| ( q @ sK3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ~ ( p @ Y0 ) ) ) )
= $false )
| ~ spl2_2 ),
inference(beta-eta_normalization,[],[f201]) ).
thf(f203,plain,
( ( $false
= ( ( q @ sK3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
| ~ spl2_2 ),
inference(or_proxy_clausification,[],[f202]) ).
thf(f204,plain,
( ( $false
= ( ~ ( rel_s5 @ sK1 @ sK3 ) ) )
| ~ spl2_2 ),
inference(or_proxy_clausification,[],[f202]) ).
thf(f205,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ~ ( p @ Y0 ) ) )
= $false )
| ~ spl2_2 ),
inference(or_proxy_clausification,[],[f203]) ).
thf(f206,plain,
( ( $false
= ( q @ sK3 ) )
| ~ spl2_2 ),
inference(or_proxy_clausification,[],[f203]) ).
thf(f207,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK3 ) )
| ~ spl2_2 ),
inference(not_proxy_clausification,[],[f204]) ).
thf(f221,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) )
@ X1 ) )
| ~ spl2_3 ),
inference(pi_proxy_clausification,[],[f192]) ).
thf(f222,plain,
( ! [X1: $i] :
( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ X1 ) ) )
| ~ spl2_3 ),
inference(beta-eta_normalization,[],[f221]) ).
thf(f223,plain,
( ! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ X1 ) )
= $true ) )
| ~ spl2_3 ),
inference(or_proxy_clausification,[],[f222]) ).
thf(f224,plain,
( ! [X1: $i] :
( ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ X1 ) )
= $true ) )
| ~ spl2_3 ),
inference(not_proxy_clausification,[],[f223]) ).
thf(f225,plain,
( ! [X1: $i] :
( ( $true
= ( ~ ( p @ X1 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( ( rel_s5 @ sK1 @ X1 )
= $false ) )
| ~ spl2_3 ),
inference(or_proxy_clausification,[],[f224]) ).
thf(f226,plain,
( ! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( p @ X1 )
= $false ) )
| ~ spl2_3 ),
inference(not_proxy_clausification,[],[f225]) ).
thf(f231,plain,
( ! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( p @ X1 )
= $false ) )
| ~ spl2_3 ),
inference(pi_proxy_clausification,[],[f226]) ).
thf(f232,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ X1 @ X2 )
| ( q @ X2 ) ) )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( p @ X1 )
= $false ) )
| ~ spl2_3 ),
inference(beta-eta_normalization,[],[f231]) ).
thf(f233,plain,
( ! [X2: $i,X1: $i] :
( ( ( q @ X2 )
= $true )
| ( ( p @ X1 )
= $false )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) )
| ( ( rel_s5 @ sK1 @ X1 )
= $false ) )
| ~ spl2_3 ),
inference(or_proxy_clausification,[],[f232]) ).
thf(f234,plain,
( ! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( ( q @ X2 )
= $true )
| ( ( p @ X1 )
= $false ) )
| ~ spl2_3 ),
inference(not_proxy_clausification,[],[f233]) ).
thf(f272,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y0 @ Y1 )
=> ( rel_s5 @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f155]) ).
thf(f273,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ X1 @ Y0 )
=> ( rel_s5 @ Y0 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f272]) ).
thf(f290,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel_s5 @ X1 @ Y0 )
=> ( rel_s5 @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f273]) ).
thf(f291,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ X1 @ X2 )
=> ( rel_s5 @ X2 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f290]) ).
thf(f292,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X2 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f291]) ).
thf(f293,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK4 ) )
| ~ spl2_2 ),
inference(sigma_proxy_clausification,[],[f205]) ).
thf(f295,plain,
( ( $false
= ( ~ ( rel_s5 @ sK3 @ sK4 )
| ~ ( p @ sK4 ) ) )
| ~ spl2_2 ),
inference(beta-eta_normalization,[],[f293]) ).
thf(f297,plain,
( ( $false
= ( ~ ( p @ sK4 ) ) )
| ~ spl2_2 ),
inference(or_proxy_clausification,[],[f295]) ).
thf(f298,plain,
( ( $false
= ( ~ ( rel_s5 @ sK3 @ sK4 ) ) )
| ~ spl2_2 ),
inference(or_proxy_clausification,[],[f295]) ).
thf(f299,plain,
( ( $true
= ( rel_s5 @ sK3 @ sK4 ) )
| ~ spl2_2 ),
inference(not_proxy_clausification,[],[f298]) ).
thf(f300,plain,
( ( ( p @ sK4 )
= $true )
| ~ spl2_2 ),
inference(not_proxy_clausification,[],[f297]) ).
thf(f335,plain,
( ( $false = $true )
| ~ spl2_2
| ~ spl2_4 ),
inference(forward_demodulation,[],[f198,f184]) ).
thf(f336,plain,
( $false
| ~ spl2_2
| ~ spl2_4 ),
inference(trivial_inequality_removal,[],[f335]) ).
thf(f337,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f336]) ).
thf(f338,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y2 @ Y0 )
& ( rel_s5 @ Y0 @ Y1 ) )
=> ( rel_s5 @ Y2 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f157]) ).
thf(f339,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y1 @ X1 )
& ( rel_s5 @ X1 @ Y0 ) )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f338]) ).
thf(f340,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) )
@ sK5 ) )
| ~ spl2_1 ),
inference(sigma_proxy_clausification,[],[f180]) ).
thf(f343,plain,
( ( $false
= ( ~ ( rel_s5 @ sK1 @ sK5 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ sK5 ) ) )
| ~ spl2_1 ),
inference(beta-eta_normalization,[],[f340]) ).
thf(f344,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ sK5 ) ) )
| ~ spl2_1 ),
inference(or_proxy_clausification,[],[f343]) ).
thf(f345,plain,
( ( $false
= ( ~ ( rel_s5 @ sK1 @ sK5 ) ) )
| ~ spl2_1 ),
inference(or_proxy_clausification,[],[f343]) ).
thf(f346,plain,
( ( ( ~ ( p @ sK5 ) )
= $false )
| ~ spl2_1 ),
inference(or_proxy_clausification,[],[f344]) ).
thf(f348,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK5 ) )
| ~ spl2_1 ),
inference(not_proxy_clausification,[],[f345]) ).
thf(f349,plain,
( ( $true
= ( p @ sK5 ) )
| ~ spl2_1 ),
inference(not_proxy_clausification,[],[f346]) ).
thf(f350,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y1 @ X1 )
& ( rel_s5 @ X1 @ Y0 ) )
=> ( rel_s5 @ Y1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f339]) ).
thf(f351,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s5 @ Y0 @ X1 )
& ( rel_s5 @ X1 @ X2 ) )
=> ( rel_s5 @ Y0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f350]) ).
thf(f352,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) ) )
@ X1 )
= $true )
| spl2_2 ),
inference(pi_proxy_clausification,[],[f183]) ).
thf(f354,plain,
( ! [X1: $i] :
( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ( q @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
| spl2_2 ),
inference(beta-eta_normalization,[],[f352]) ).
thf(f355,plain,
( ! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true
= ( ( q @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) )
| spl2_2 ),
inference(or_proxy_clausification,[],[f354]) ).
thf(f356,plain,
( ! [X1: $i] :
( ( $true
= ( ( q @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
| ( ( rel_s5 @ sK1 @ X1 )
= $false ) )
| spl2_2 ),
inference(not_proxy_clausification,[],[f355]) ).
thf(f357,plain,
( ! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( p @ Y0 ) ) ) )
| ( ( q @ X1 )
= $true )
| ( ( rel_s5 @ sK1 @ X1 )
= $false ) )
| spl2_2 ),
inference(or_proxy_clausification,[],[f356]) ).
thf(f358,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s5 @ Y0 @ X1 )
& ( rel_s5 @ X1 @ X2 ) )
=> ( rel_s5 @ Y0 @ X2 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f351]) ).
thf(f359,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s5 @ X3 @ X1 )
& ( rel_s5 @ X1 @ X2 ) )
=> ( rel_s5 @ X3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f358]) ).
thf(f360,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X3 @ X2 ) )
| ( $false
= ( ( rel_s5 @ X3 @ X1 )
& ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f359]) ).
thf(f361,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X3 @ X2 ) )
| ( ( rel_s5 @ X3 @ X1 )
= $false )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f360]) ).
thf(f362,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( p @ Y0 ) )
@ X2 ) )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( q @ X1 )
= $true ) )
| spl2_2 ),
inference(pi_proxy_clausification,[],[f357]) ).
thf(f363,plain,
( ! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( q @ X1 )
= $true )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 )
| ~ ( p @ X2 ) ) ) )
| spl2_2 ),
inference(beta-eta_normalization,[],[f362]) ).
thf(f364,plain,
( ! [X2: $i,X1: $i] :
( ( ( q @ X1 )
= $true )
| ( $true
= ( ~ ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) )
| ( ( rel_s5 @ sK1 @ X1 )
= $false ) )
| spl2_2 ),
inference(or_proxy_clausification,[],[f363]) ).
thf(f365,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( p @ X2 ) ) )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( q @ X1 )
= $true )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) )
| spl2_2 ),
inference(not_proxy_clausification,[],[f364]) ).
thf(f366,plain,
( ! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( p @ X2 )
= $false )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( ( q @ X1 )
= $true ) )
| spl2_2 ),
inference(not_proxy_clausification,[],[f365]) ).
thf(f370,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false = $true )
| ( $true
= ( q @ X0 ) )
| ( $false
= ( rel_s5 @ X2 @ X0 ) )
| ( $false
= ( rel_s5 @ sK1 @ X2 ) )
| ( ( p @ X1 )
= $false )
| ( $false
= ( rel_s5 @ X0 @ X1 ) ) )
| spl2_2 ),
inference(superposition,[],[f366,f361]) ).
thf(f382,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X2 ) )
| ( $false
= ( rel_s5 @ X2 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ X1 ) )
| ( ( p @ X1 )
= $false )
| ( $true
= ( q @ X0 ) ) )
| spl2_2 ),
inference(trivial_inequality_removal,[],[f370]) ).
thf(f433,plain,
( ( $false = $true )
| ~ spl2_1
| ~ spl2_3 ),
inference(forward_demodulation,[],[f192,f180]) ).
thf(f434,plain,
( $false
| ~ spl2_1
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f433]) ).
thf(f435,plain,
( ~ spl2_1
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f434]) ).
thf(f661,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK5 @ X0 ) )
| ( $true
= ( q @ X0 ) )
| ( ( p @ X1 )
= $false )
| ( $false
= ( rel_s5 @ X0 @ X1 ) )
| ( $false = $true ) )
| ~ spl2_1
| spl2_2 ),
inference(superposition,[],[f348,f382]) ).
thf(f667,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK5 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ X1 ) )
| ( ( p @ X1 )
= $false )
| ( $true
= ( q @ X0 ) ) )
| ~ spl2_1
| spl2_2 ),
inference(trivial_inequality_removal,[],[f661]) ).
thf(f820,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X2 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ X1 ) )
| ( $false
= ( p @ X0 ) )
| ( ( q @ X1 )
= $true )
| ( $false = $true )
| ( $false
= ( rel_s5 @ sK1 @ X2 ) ) )
| ~ spl2_3 ),
inference(superposition,[],[f234,f361]) ).
thf(f830,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X2 ) )
| ( $false
= ( rel_s5 @ X2 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ X1 ) )
| ( $false
= ( p @ X0 ) )
| ( ( q @ X1 )
= $true ) )
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f820]) ).
thf(f907,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X0 @ X1 ) )
| ( $false
= ( rel_s5 @ sK3 @ X0 ) )
| ( $false = $true )
| ( ( q @ X1 )
= $true )
| ( $false
= ( p @ X0 ) ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(superposition,[],[f207,f830]) ).
thf(f911,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK3 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ X1 ) )
| ( ( q @ X1 )
= $true )
| ( $false
= ( p @ X0 ) ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f907]) ).
thf(f924,plain,
( ! [X0: $i] :
( ( $true
= ( q @ X0 ) )
| ( $false
= ( rel_s5 @ sK4 @ X0 ) )
| ( $false = $true )
| ( $false
= ( p @ sK4 ) ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(superposition,[],[f911,f299]) ).
thf(f935,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK4 @ X0 ) )
| ( $true
= ( q @ X0 ) )
| ( $false
= ( p @ sK4 ) ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f924]) ).
thf(f941,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK4 @ X0 ) )
| ( $true
= ( q @ X0 ) )
| ( $false = $true ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(forward_demodulation,[],[f935,f300]) ).
thf(f942,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK4 @ X0 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f941]) ).
thf(f947,plain,
( ! [X0: $i] :
( ( $true
= ( q @ X0 ) )
| ( $false = $true )
| ( $false
= ( rel_s5 @ X0 @ sK4 ) ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(superposition,[],[f942,f292]) ).
thf(f955,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK4 ) )
| ( $true
= ( q @ X0 ) ) )
| ~ spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f947]) ).
thf(f959,plain,
( ( ( q @ sK3 )
= $true )
| ( $false = $true )
| ~ spl2_2
| ~ spl2_3 ),
inference(superposition,[],[f955,f299]) ).
thf(f971,plain,
( ( ( q @ sK3 )
= $true )
| ~ spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f959]) ).
thf(f977,plain,
( ( $false = $true )
| ~ spl2_2
| ~ spl2_3 ),
inference(forward_demodulation,[],[f971,f206]) ).
thf(f978,plain,
( $false
| ~ spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f977]) ).
thf(f979,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f978]) ).
thf(f1214,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( p @ Y0 ) )
@ sK5 ) )
| ~ spl2_1 ),
inference(sigma_proxy_clausification,[],[f180]) ).
thf(f1216,plain,
( ( $false
= ( ~ ( rel_s5 @ sK1 @ sK5 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ sK5 ) ) )
| ~ spl2_1 ),
inference(beta-eta_normalization,[],[f1214]) ).
thf(f1218,plain,
( ( $false
= ( ~ $true
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ sK5 ) ) )
| ~ spl2_1 ),
inference(forward_demodulation,[],[f1216,f348]) ).
thf(f1219,plain,
( ( $false
= ( $false
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ sK5 ) ) )
| ~ spl2_1 ),
inference(boolean_simplification,[],[f1218]) ).
thf(f1220,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( p @ sK5 ) ) )
| ~ spl2_1 ),
inference(boolean_simplification,[],[f1219]) ).
thf(f1221,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) )
| ~ $true ) )
| ~ spl2_1 ),
inference(forward_demodulation,[],[f1220,f349]) ).
thf(f1222,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) )
| $false ) )
| ~ spl2_1 ),
inference(boolean_simplification,[],[f1221]) ).
thf(f1223,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ spl2_1 ),
inference(boolean_simplification,[],[f1222]) ).
thf(f1224,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) )
@ sK6 ) )
| ~ spl2_1 ),
inference(sigma_proxy_clausification,[],[f1223]) ).
thf(f1227,plain,
( ( $false
= ( ~ ( rel_s5 @ sK5 @ sK6 )
| ( q @ sK6 ) ) )
| ~ spl2_1 ),
inference(beta-eta_normalization,[],[f1224]) ).
thf(f1228,plain,
( ( $false
= ( q @ sK6 ) )
| ~ spl2_1 ),
inference(or_proxy_clausification,[],[f1227]) ).
thf(f1229,plain,
( ( $false
= ( ~ ( rel_s5 @ sK5 @ sK6 ) ) )
| ~ spl2_1 ),
inference(or_proxy_clausification,[],[f1227]) ).
thf(f1230,plain,
( ( $true
= ( rel_s5 @ sK5 @ sK6 ) )
| ~ spl2_1 ),
inference(not_proxy_clausification,[],[f1229]) ).
thf(f1248,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK6 @ X0 ) )
| ( $false = $true )
| ( $false
= ( p @ X0 ) )
| ( $true
= ( q @ sK6 ) ) )
| ~ spl2_1
| spl2_2 ),
inference(superposition,[],[f667,f1230]) ).
thf(f1255,plain,
( ! [X0: $i] :
( ( $false
= ( p @ X0 ) )
| ( $true
= ( q @ sK6 ) )
| ( $false
= ( rel_s5 @ sK6 @ X0 ) ) )
| ~ spl2_1
| spl2_2 ),
inference(trivial_inequality_removal,[],[f1248]) ).
thf(f1265,plain,
( ! [X0: $i] :
( ( $false
= ( p @ X0 ) )
| ( $false = $true )
| ( $false
= ( rel_s5 @ sK6 @ X0 ) ) )
| ~ spl2_1
| spl2_2 ),
inference(forward_demodulation,[],[f1255,f1228]) ).
thf(f1266,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK6 @ X0 ) )
| ( $false
= ( p @ X0 ) ) )
| ~ spl2_1
| spl2_2 ),
inference(trivial_inequality_removal,[],[f1265]) ).
thf(f1297,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ X0 @ sK6 )
= $false )
| ( $false
= ( p @ X0 ) )
| ( $false = $true ) )
| ~ spl2_1
| spl2_2 ),
inference(superposition,[],[f292,f1266]) ).
thf(f1299,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ X0 @ sK6 )
= $false )
| ( $false
= ( p @ X0 ) ) )
| ~ spl2_1
| spl2_2 ),
inference(trivial_inequality_removal,[],[f1297]) ).
thf(f1312,plain,
( ( $false
= ( p @ sK5 ) )
| ( $false = $true )
| ~ spl2_1
| spl2_2 ),
inference(superposition,[],[f1230,f1299]) ).
thf(f1317,plain,
( ( $false
= ( p @ sK5 ) )
| ~ spl2_1
| spl2_2 ),
inference(trivial_inequality_removal,[],[f1312]) ).
thf(f1327,plain,
( ( $false = $true )
| ~ spl2_1
| spl2_2 ),
inference(superposition,[],[f349,f1317]) ).
thf(f1330,plain,
( $false
| ~ spl2_1
| spl2_2 ),
inference(trivial_inequality_removal,[],[f1327]) ).
thf(f1331,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_contradiction_clause,[],[f1330]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f185]) ).
cnf(s2,plain,
( spl2_1
| spl2_3 ),
inference(sat_conversion,[],[f193]) ).
cnf(s4,plain,
( spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f200]) ).
cnf(s15,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(sat_conversion,[],[f337]) ).
cnf(s20,plain,
( ~ spl2_1
| ~ spl2_3 ),
inference(sat_conversion,[],[f435]) ).
cnf(s55,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f979]) ).
cnf(s64,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f1331]) ).
cnf(s65,plain,
spl2_1,
inference(rat,[],[s55,s1,s2]) ).
cnf(s66,plain,
spl2_2,
inference(rat,[],[s64,s65]) ).
cnf(s68,plain,
~ spl2_3,
inference(rat,[],[s20,s65]) ).
cnf(s69,plain,
~ spl2_4,
inference(rat,[],[s15,s66]) ).
cnf(s73,plain,
$false,
inference(rat,[],[s4,s69,s68]) ).
thf(f1333,plain,
$false,
inference(avatar_sat_refutation,[],[s73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO449^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n009.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:52:16 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.24 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
% 0.21/0.36 % (66411)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.36 % (66416)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2623299215:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.36 % (66422)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.36 % (66422)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
% 0.21/0.36 % (66417)lrs+10_16_si=on:nwc=1.5:random_seed=1322509690:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.36 % (66418)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2923213898:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.36 % (66421)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1352808776:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.36 % (66419)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=2546038743: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)
% 0.21/0.36 % (66420)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=741826278:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.36 % (66422)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=1698129664:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.36 % (66418)Instruction limit reached!
% 0.21/0.36 % (66418)------------------------------
% 0.21/0.36 % (66418)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (66418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (66418)CaDiCaL version: 2.1.3
% 0.21/0.36 % (66418)Termination reason: Instruction limit
% 0.21/0.36 % (66418)Termination phase: Property scanning
% 0.21/0.36 % (66418)Time elapsed: 0.002 s
% 0.21/0.36 % (66418)Peak memory usage: 10 MB
% 0.21/0.36 % (66418)Instructions burned: 4 (million)
% 0.21/0.36 % (66417)Instruction limit reached!
% 0.21/0.36 % (66417)------------------------------
% 0.21/0.36 % (66417)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (66417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (66417)CaDiCaL version: 2.1.3
% 0.21/0.36 % (66417)Termination reason: Instruction limit
% 0.21/0.36 % (66417)Termination phase: Saturation
% 0.21/0.36 % (66417)Time elapsed: 0.009 s
% 0.21/0.36 % (66417)Peak memory usage: 12 MB
% 0.21/0.36 % (66417)Instructions burned: 19 (million)
% 0.21/0.36 % (66420)Instruction limit reached!
% 0.21/0.36 % (66420)------------------------------
% 0.21/0.36 % (66420)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (66420)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (66420)CaDiCaL version: 2.1.3
% 0.21/0.36 % (66420)Termination reason: Instruction limit
% 0.21/0.36 % (66420)Termination phase: Saturation
% 0.21/0.36 % (66420)Time elapsed: 0.014 s
% 0.21/0.36 % (66420)Peak memory usage: 11 MB
% 0.21/0.36 % (66420)Instructions burned: 25 (million)
% 0.21/0.36 % (66416)Instruction limit reached!
% 0.21/0.36 % (66416)------------------------------
% 0.21/0.36 % (66416)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (66416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (66416)CaDiCaL version: 2.1.3
% 0.21/0.36 % (66416)Termination reason: Instruction limit
% 0.21/0.36 % (66416)Termination phase: Saturation
% 0.21/0.36 % (66416)Time elapsed: 0.025 s
% 0.21/0.36 % (66416)Peak memory usage: 12 MB
% 0.21/0.36 % (66416)Instructions burned: 87 (million)
% 0.21/0.36 % (66433)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=968230803:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.36 % (66433)Instruction limit reached!
% 0.21/0.36 % (66433)------------------------------
% 0.21/0.36 % (66433)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (66433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.38 % (66433)CaDiCaL version: 2.1.3
% 0.80/0.38 % (66433)Termination reason: Instruction limit
% 0.80/0.38 % (66433)Termination phase: Property scanning
% 0.80/0.38 % (66433)Time elapsed: 0.002 s
% 0.80/0.38 % (66433)Peak memory usage: 10 MB
% 0.80/0.38 % (66433)Instructions burned: 4 (million)
% 0.80/0.38 % (66438)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1731908604:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.80/0.38 % (66436)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=915973242:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.80/0.38 % (66437)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.80/0.38 % (66438)Instruction limit reached!
% 0.80/0.38 % (66438)------------------------------
% 0.80/0.38 % (66438)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.38 % (66438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.38 % (66438)CaDiCaL version: 2.1.3
% 0.80/0.38 % (66438)Termination reason: Instruction limit
% 0.80/0.38 % (66438)Termination phase: Saturation
% 0.80/0.38 % (66438)Time elapsed: 0.003 s
% 0.80/0.38 % (66438)Peak memory usage: 11 MB
% 0.80/0.38 % (66438)Instructions burned: 12 (million)
% 0.80/0.38 % (66436)Instruction limit reached!
% 0.80/0.38 % (66436)------------------------------
% 0.80/0.38 % (66436)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.38 % (66436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.38 % (66436)CaDiCaL version: 2.1.3
% 0.80/0.38 % (66436)Termination reason: Instruction limit
% 0.80/0.38 % (66436)Termination phase: Function definition elimination
% 0.80/0.38 % (66436)Time elapsed: 0.003 s
% 0.80/0.38 % (66436)Peak memory usage: 10 MB
% 0.80/0.38 % (66436)Instructions burned: 6 (million)
% 0.80/0.38 % (66437)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2730056311:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.80/0.38 % (66421)Instruction limit reached!
% 0.80/0.38 % (66421)------------------------------
% 0.80/0.38 % (66421)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.38 % (66421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.38 % (66421)CaDiCaL version: 2.1.3
% 0.80/0.38 % (66421)Termination reason: Instruction limit
% 0.80/0.38 % (66421)Termination phase: Saturation
% 0.80/0.38 % (66421)Time elapsed: 0.036 s
% 0.80/0.38 % (66421)Peak memory usage: 12 MB
% 0.80/0.38 % (66421)Instructions burned: 76 (million)
% 0.80/0.38 % (66443)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
% 0.80/0.38 % (66443)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.80/0.38 % (66437)Instruction limit reached!
% 0.80/0.38 % (66437)------------------------------
% 0.80/0.38 % (66437)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.38 % (66437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.38 % (66437)CaDiCaL version: 2.1.3
% 0.80/0.38 % (66437)Termination reason: Instruction limit
% 0.80/0.38 % (66437)Termination phase: Saturation
% 0.80/0.38 % (66437)Time elapsed: 0.004 s
% 0.80/0.38 % (66437)Peak memory usage: 11 MB
% 0.80/0.38 % (66437)Instructions burned: 9 (million)
% 0.80/0.38 % (66447)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=2954472533:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.80/0.38 % (66443)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3739755256:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.80/0.38 % (66448)lrs+10_1_si=on:cs=on:random_seed=2133561366:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.80/0.38 % (66453)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.80/0.38 % (66453)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=1228487614:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.80/0.41 % (66448)Instruction limit reached!
% 0.80/0.41 % (66448)------------------------------
% 0.80/0.41 % (66448)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.41 % (66448)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.41 % (66448)CaDiCaL version: 2.1.3
% 0.80/0.41 % (66448)Termination reason: Instruction limit
% 0.80/0.41 % (66448)Termination phase: Saturation
% 0.80/0.41 % (66448)Time elapsed: 0.007 s
% 0.80/0.41 % (66448)Peak memory usage: 11 MB
% 0.80/0.41 % (66448)Instructions burned: 15 (million)
% 0.80/0.41 % (66443)Instruction limit reached!
% 0.80/0.41 % (66443)------------------------------
% 0.80/0.41 % (66443)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.41 % (66443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.41 % (66443)CaDiCaL version: 2.1.3
% 0.80/0.41 % (66443)Termination reason: Instruction limit
% 0.80/0.41 % (66443)Termination phase: Saturation
% 0.80/0.41 % (66443)Time elapsed: 0.015 s
% 0.80/0.41 % (66443)Peak memory usage: 11 MB
% 0.80/0.41 % (66443)Instructions burned: 34 (million)
% 0.80/0.41 % (66456)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1219050308:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.80/0.41 % (66453)Instruction limit reached!
% 0.80/0.41 % (66453)------------------------------
% 0.80/0.41 % (66453)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.41 % (66453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.41 % (66453)CaDiCaL version: 2.1.3
% 0.80/0.41 % (66453)Termination reason: Instruction limit
% 0.80/0.41 % (66453)Termination phase: Function definition elimination
% 0.80/0.41 % (66453)Time elapsed: 0.003 s
% 0.80/0.41 % (66453)Peak memory usage: 10 MB
% 0.80/0.41 % (66453)Instructions burned: 6 (million)
% 0.80/0.41 % (66456)Refutation not found, incomplete strategy
% 0.80/0.41 % (66456)------------------------------
% 0.80/0.41 % (66456)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.41 % (66456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.41 % (66456)CaDiCaL version: 2.1.3
% 0.80/0.41 % (66456)Termination reason: Refutation not found, incomplete strategy
% 0.80/0.41 % (66456)Time elapsed: 0.005 s
% 0.80/0.41 % (66456)Peak memory usage: 12 MB
% 0.80/0.41 % (66456)Instructions burned: 8 (million)
% 0.80/0.41 % (66456)------------------------------
% 0.80/0.41 % (66456)------------------------------
% 0.80/0.41 % (66447)Instruction limit reached!
% 0.80/0.41 % (66447)------------------------------
% 0.80/0.41 % (66447)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.41 % (66447)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.41 % (66447)CaDiCaL version: 2.1.3
% 0.80/0.41 % (66447)Termination reason: Instruction limit
% 0.80/0.41 % (66447)Termination phase: Saturation
% 0.80/0.41 % (66447)Time elapsed: 0.024 s
% 0.80/0.41 % (66447)Peak memory usage: 12 MB
% 0.80/0.41 % (66447)Instructions burned: 87 (million)
% 0.80/0.41 % (66477)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1631791268:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.80/0.41 % (66422)Instruction limit reached!
% 0.80/0.41 % (66422)------------------------------
% 0.80/0.41 % (66422)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.41 % (66422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.41 % (66422)CaDiCaL version: 2.1.3
% 0.80/0.41 % (66422)Termination reason: Instruction limit
% 0.80/0.41 % (66422)Termination phase: Saturation
% 0.80/0.41 % (66422)Time elapsed: 0.079 s
% 0.80/0.41 % (66422)Peak memory usage: 13 MB
% 0.80/0.41 % (66422)Instructions burned: 158 (million)
% 0.80/0.41 % (66473)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=3430504904:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.80/0.41 % (66475)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1986936142:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.80/0.41 % (66486)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=438776427:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/14Mi)
% 0.80/0.45 % (66477)Instruction limit reached!
% 0.80/0.45 % (66477)------------------------------
% 0.80/0.45 % (66477)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.45 % (66477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.45 % (66477)CaDiCaL version: 2.1.3
% 0.80/0.45 % (66477)Termination reason: Instruction limit
% 0.80/0.45 % (66477)Termination phase: Saturation
% 0.80/0.45 % (66477)Time elapsed: 0.007 s
% 0.80/0.45 % (66477)Peak memory usage: 12 MB
% 0.80/0.45 % (66477)Instructions burned: 14 (million)
% 0.80/0.45 % (66473)Refutation not found, incomplete strategy
% 0.80/0.45 % (66473)------------------------------
% 0.80/0.45 % (66473)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.45 % (66473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.45 % (66473)CaDiCaL version: 2.1.3
% 0.80/0.45 % (66473)Termination reason: Refutation not found, incomplete strategy
% 0.80/0.45 % (66473)Time elapsed: 0.005 s
% 0.80/0.45 % (66473)Peak memory usage: 12 MB
% 0.80/0.45 % (66473)Instructions burned: 9 (million)
% 0.80/0.45 % (66473)------------------------------
% 0.80/0.45 % (66473)------------------------------
% 0.80/0.45 % (66486)Instruction limit reached!
% 0.80/0.45 % (66486)------------------------------
% 0.80/0.45 % (66486)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.45 % (66486)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.45 % (66486)CaDiCaL version: 2.1.3
% 0.80/0.45 % (66486)Termination reason: Instruction limit
% 0.80/0.45 % (66486)Termination phase: Saturation
% 0.80/0.45 % (66486)Time elapsed: 0.004 s
% 0.80/0.45 % (66486)Peak memory usage: 12 MB
% 0.80/0.45 % (66486)Instructions burned: 16 (million)
% 0.80/0.45 % (66482)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=4022446674:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 0.80/0.45 % (66475)Instruction limit reached!
% 0.80/0.45 % (66475)------------------------------
% 0.80/0.45 % (66475)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.45 % (66475)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.45 % (66475)CaDiCaL version: 2.1.3
% 0.80/0.45 % (66475)Termination reason: Instruction limit
% 0.80/0.45 % (66475)Termination phase: Saturation
% 0.80/0.45 % (66475)Time elapsed: 0.014 s
% 0.80/0.45 % (66475)Peak memory usage: 12 MB
% 0.80/0.45 % (66475)Instructions burned: 25 (million)
% 0.80/0.45 % (66496)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=2691174021:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.80/0.45 % (66503)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2176048521:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.80/0.45 % (66496)Instruction limit reached!
% 0.80/0.45 % (66496)------------------------------
% 0.80/0.45 % (66496)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.45 % (66496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.45 % (66496)CaDiCaL version: 2.1.3
% 0.80/0.45 % (66496)Termination reason: Instruction limit
% 0.80/0.45 % (66496)Termination phase: SInE selection
% 0.80/0.45 % (66496)Time elapsed: 0.002 s
% 0.80/0.45 % (66496)Peak memory usage: 10 MB
% 0.80/0.45 % (66496)Instructions burned: 4 (million)
% 0.80/0.45 % (66501)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3980477164:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.80/0.45 % (66503)Instruction limit reached!
% 0.80/0.45 % (66503)------------------------------
% 0.80/0.45 % (66503)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.45 % (66503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.45 % (66503)CaDiCaL version: 2.1.3
% 0.80/0.45 % (66503)Termination reason: Instruction limit
% 0.80/0.45 % (66503)Termination phase: Saturation
% 0.80/0.45 % (66503)Time elapsed: 0.006 s
% 0.80/0.45 % (66503)Peak memory usage: 11 MB
% 0.80/0.45 % (66503)Instructions burned: 25 (million)
% 0.80/0.45 % (66504)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=868470602:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 0.80/0.45 % (66506)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) 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
% 0.80/0.45 % (66506)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 0.80/0.45 % (66506)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=1804260122:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.80/0.45 % (66512)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 0.80/0.45 % (66514)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=3095064081:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 0.80/0.45 % (66501)Instruction limit reached!
% 0.80/0.45 % (66501)------------------------------
% 0.80/0.45 % (66501)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.45 % (66501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.45 % (66501)CaDiCaL version: 2.1.3
% 0.80/0.45 % (66501)Termination reason: Instruction limit
% 0.80/0.45 % (66501)Termination phase: Saturation
% 0.80/0.45 % (66501)Time elapsed: 0.014 s
% 0.80/0.45 % (66501)Peak memory usage: 12 MB
% 0.80/0.45 % (66501)Instructions burned: 27 (million)
% 0.80/0.45 % (66512)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=836996255:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 0.80/0.45 % (66506)Instruction limit reached!
% 0.80/0.45 % (66506)------------------------------
% 0.80/0.45 % (66506)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.45 % (66506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.45 % (66506)CaDiCaL version: 2.1.3
% 0.80/0.45 % (66506)Termination reason: Instruction limit
% 0.80/0.45 % (66506)Termination phase: Saturation
% 0.80/0.45 % (66506)Time elapsed: 0.007 s
% 0.80/0.45 % (66506)Peak memory usage: 12 MB
% 0.80/0.45 % (66506)Instructions burned: 15 (million)
% 0.80/0.45 % (66512)Instruction limit reached!
% 0.80/0.45 % (66512)------------------------------
% 0.80/0.45 % (66512)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.45 % (66512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.45 % (66512)CaDiCaL version: 2.1.3
% 0.80/0.45 % (66512)Termination reason: Instruction limit
% 0.80/0.45 % (66512)Termination phase: Property scanning
% 0.80/0.45 % (66512)Time elapsed: 0.004 s
% 0.80/0.45 % (66512)Peak memory usage: 10 MB
% 0.80/0.45 % (66512)Instructions burned: 9 (million)
% 0.80/0.45 % (66514)Instruction limit reached!
% 0.80/0.45 % (66514)------------------------------
% 0.80/0.45 % (66514)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.45 % (66514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.45 % (66514)CaDiCaL version: 2.1.3
% 0.80/0.45 % (66514)Termination reason: Instruction limit
% 0.80/0.45 % (66514)Termination phase: Saturation
% 0.80/0.45 % (66514)Time elapsed: 0.008 s
% 0.80/0.45 % (66514)Peak memory usage: 12 MB
% 0.80/0.45 % (66514)Instructions burned: 31 (million)
% 0.80/0.45 % (66522)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=531627770:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 0.80/0.45 % (66518)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=2609590581:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 0.80/0.45 % (66518)Instruction limit reached!
% 0.80/0.45 % (66518)------------------------------
% 0.80/0.45 % (66518)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.45 % (66518)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.45 % (66518)CaDiCaL version: 2.1.3
% 0.80/0.45 % (66518)Termination reason: Instruction limit
% 0.80/0.45 % (66518)Termination phase: Function definition elimination
% 0.80/0.45 % (66518)Time elapsed: 0.003 s
% 0.80/0.45 % (66518)Peak memory usage: 10 MB
% 0.80/0.45 % (66518)Instructions burned: 7 (million)
% 0.80/0.45 % (66520)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=3742354188:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.80/0.45 % (66504)Instruction limit reached!
% 0.80/0.45 % (66504)------------------------------
% 0.80/0.45 % (66504)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.45 % (66504)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.45 % (66504)CaDiCaL version: 2.1.3
% 0.80/0.45 % (66504)Termination reason: Instruction limit
% 0.80/0.45 % (66504)Termination phase: Saturation
% 0.80/0.45 % (66504)Time elapsed: 0.034 s
% 0.80/0.45 % (66504)Peak memory usage: 12 MB
% 0.80/0.45 % (66504)Instructions burned: 61 (million)
% 0.80/0.45 % (66521)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=145071065:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 0.80/0.45 % (66520)Instruction limit reached!
% 0.80/0.45 % (66520)------------------------------
% 0.80/0.45 % (66520)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.45 % (66520)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.45 % (66520)CaDiCaL version: 2.1.3
% 0.80/0.45 % (66520)Termination reason: Instruction limit
% 0.80/0.45 % (66520)Termination phase: Saturation
% 0.80/0.45 % (66520)Time elapsed: 0.010 s
% 0.80/0.45 % (66520)Peak memory usage: 11 MB
% 0.80/0.45 % (66520)Instructions burned: 23 (million)
% 0.80/0.45 % (66521)Instruction limit reached!
% 0.80/0.45 % (66521)------------------------------
% 0.80/0.45 % (66521)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.45 % (66521)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.45 % (66521)CaDiCaL version: 2.1.3
% 0.80/0.45 % (66521)Termination reason: Instruction limit
% 0.80/0.45 % (66521)Termination phase: Saturation
% 0.80/0.45 % (66521)Time elapsed: 0.015 s
% 0.80/0.45 % (66521)Peak memory usage: 13 MB
% 0.80/0.45 % (66521)Instructions burned: 27 (million)
% 0.80/0.45 % (66525)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=737310481:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 0.80/0.45 % (66527)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1715649809:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 0.80/0.45 % (66522) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-66411-66522"...
% 0.80/0.45 % (66482) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-66411-66482"...
% 0.80/0.45 % (66527)Refutation not found, incomplete strategy
% 0.80/0.45 % (66527)------------------------------
% 0.80/0.45 % (66527)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.45 % (66527)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.45 % (66527)CaDiCaL version: 2.1.3
% 0.80/0.45 % (66527)Termination reason: Refutation not found, incomplete strategy
% 0.80/0.45 % (66527)Time elapsed: 0.006 s
% 0.80/0.45 % (66527)Peak memory usage: 12 MB
% 0.80/0.45 % (66527)Instructions burned: 11 (million)
% 0.80/0.45 % (66527)------------------------------
% 0.80/0.45 % (66527)------------------------------
% 0.80/0.45 % (66522)...printing done.
% 0.80/0.45 % (66529)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3486990153:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 0.80/0.45 % (66522)Refutation found. Thanks to Tanya!
% 0.80/0.45 % SZS status Theorem for theBenchmark
% 0.80/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.80/0.45 % (66522)------------------------------
% 0.80/0.45 % (66522)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.80/0.45 % (66522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.80/0.45 % (66522)CaDiCaL version: 2.1.3
% 0.80/0.45 % (66522)Termination reason: Refutation
% 0.80/0.45 % (66522)Time elapsed: 0.033 s
% 0.80/0.45 % (66522)Peak memory usage: 13 MB
% 0.80/0.45 % (66522)Instructions burned: 124 (million)
% 0.80/0.45 % (66411)Success in time 0.195 s
% 0.80/0.45 % Vampire exiting
%------------------------------------------------------------------------------