%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN367^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 08:41:41 AM UTC 2026
% Result : Theorem 2.66s 0.76s
% Output : Refutation 2.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 16
% Syntax : Number of formulae : 207 ( 171 unt; 0 typ; 2 def)
% Number of atoms : 1994 ( 190 equ; 0 cnn)
% Maximal formula atoms : 27 ( 9 avg)
% Number of connectives : 4209 ( 703 ~; 511 |; 25 &;2476 @)
% ( 2 <=>; 94 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 114 ( 114 >; 0 *; 0 +; 0 <<)
% Number of symbols : 68 ( 63 usr; 14 con; 0-4 aty)
% ( 394 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 661 ( 0 sgn 73 !; 2 ?; 661 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
qmltpeq: 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,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_7,type,
mtrue: $i > $o ).
thf(func_def_8,type,
mfalse: $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
exists_in_world: mu > $i > $o ).
thf(func_def_16,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_17,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_18,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_19,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
mvalid: ( $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,
minvalid: ( $i > $o ) > $o ).
thf(func_def_33,type,
rel_s4: $i > $i > $o ).
thf(func_def_34,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(func_def_36,type,
p: $i > $o ).
thf(func_def_37,type,
big_r: mu > $i > $o ).
thf(func_def_38,type,
big_q: mu > $i > $o ).
thf(func_def_39,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_40,type,
vOR: $o > $o > $o ).
thf(func_def_41,type,
vNOT: $o > $o ).
thf(func_def_42,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_48,type,
vIMP: $o > $o > $o ).
thf(func_def_49,type,
vAND: $o > $o > $o ).
thf(func_def_50,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_52,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_53,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_56,type,
sK2: $i > mu ).
thf(func_def_59,type,
sK5: mu ).
thf(func_def_60,type,
sK6: mu ).
thf(f2,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mnot) ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mor) ).
thf(f8,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) )
= mand ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mand) ).
thf(f9,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mimplies) ).
thf(f14,axiom,
! [X0: $i] :
? [X1: mu] : ( exists_in_world @ X1 @ X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',nonempty_ax) ).
thf(f15,axiom,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_ind ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mforall_ind) ).
thf(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mreflexive) ).
thf(f21,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) )
= mtransitive ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mtransitive) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) )
= mbox_s4 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f34,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',a1) ).
thf(f35,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',a2) ).
thf(f36,axiom,
! [X1: $i,X2: $i,X0: mu] :
( ( ( rel_s4 @ X1 @ X2 )
& ( exists_in_world @ X0 @ X1 ) )
=> ( exists_in_world @ X0 @ X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^1.ax',cumulative_ax) ).
thf(f37,conjecture,
( mvalid
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] : ( mor @ ( mand @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( big_q @ X0 ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ p ) ) ) @ ( mbox_s4 @ ( big_r @ X0 ) ) ) ) ) )
@ ( mor
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] : ( mbox_s4 @ ( big_q @ X0 ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] : ( mbox_s4 @ ( big_r @ X0 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x2118) ).
thf(f38,negated_conjecture,
~ ( mvalid
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] : ( mor @ ( mand @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( big_q @ X0 ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ p ) ) ) @ ( mbox_s4 @ ( big_r @ X0 ) ) ) ) ) )
@ ( mor
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] : ( mbox_s4 @ ( big_q @ X0 ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] : ( mbox_s4 @ ( big_r @ X0 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f39,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) )
= mbox_s4 ),
inference(rectify,[],[f32]) ).
thf(f40,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f42,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f50,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f51,plain,
~ ( mvalid
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] : ( mor @ ( mand @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( big_q @ X0 ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ p ) ) ) @ ( mbox_s4 @ ( big_r @ X0 ) ) ) ) ) )
@ ( mor
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( big_q @ X1 ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X2: mu] : ( mbox_s4 @ ( big_r @ X2 ) ) ) ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f52,plain,
( $true
= ( ~ ( mvalid
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] : ( mor @ ( mand @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( big_q @ Y0 ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ p ) ) ) @ ( mbox_s4 @ ( big_r @ Y0 ) ) ) ) ) )
@ ( mor
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] : ( mbox_s4 @ ( big_q @ Y0 ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] : ( mbox_s4 @ ( big_r @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f51]) ).
thf(f53,plain,
mreflexive @ rel_s4,
inference(rectify,[],[f34]) ).
thf(f54,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f53]) ).
thf(f59,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X2 @ X1 ) )
=> ( X0 @ X2 @ X3 ) ) )
= mtransitive ),
inference(rectify,[],[f21]) ).
thf(f60,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f59]) ).
thf(f61,plain,
mtransitive @ rel_s4,
inference(rectify,[],[f35]) ).
thf(f62,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f61]) ).
thf(f65,plain,
! [X0: $i,X1: $i,X2: mu] :
( ( ( rel_s4 @ X0 @ X1 )
& ( exists_in_world @ X2 @ X0 ) )
=> ( exists_in_world @ X2 @ X1 ) ),
inference(rectify,[],[f36]) ).
thf(f66,plain,
( ( !! @ mu
@ ^ [Y0: mu] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( exists_in_world @ Y0 @ Y2 )
& ( rel_s4 @ Y2 @ Y1 ) )
=> ( exists_in_world @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f65]) ).
thf(f69,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f70,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f79,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f3]) ).
thf(f80,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f79]) ).
thf(f86,plain,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_ind ),
inference(rectify,[],[f15]) ).
thf(f87,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f86]) ).
thf(f88,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f89,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f88]) ).
thf(f93,plain,
! [X0: $i] :
? [X1: mu] : ( exists_in_world @ X1 @ X0 ),
inference(rectify,[],[f14]) ).
thf(f94,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] : ( exists_in_world @ Y1 @ Y0 ) ) )
= $true ),
inference(fool_elimination,[],[f93]) ).
thf(f101,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f105,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] : ( exists_in_world @ Y1 @ Y0 ) ) )
= $true ),
inference(cnf_transformation,[],[f94]) ).
thf(f110,plain,
( ( !! @ mu
@ ^ [Y0: mu] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( exists_in_world @ Y0 @ Y2 )
& ( rel_s4 @ Y2 @ Y1 ) )
=> ( exists_in_world @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f66]) ).
thf(f115,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f118,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f62]) ).
thf(f119,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f89]) ).
thf(f120,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f125,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f80]) ).
thf(f127,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f54]) ).
thf(f128,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f101]) ).
thf(f129,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f132,plain,
( $true
= ( ~ ( mvalid
@ ( mbox_s4
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] : ( mor @ ( mand @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( big_q @ Y0 ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ p ) ) ) @ ( mbox_s4 @ ( big_r @ Y0 ) ) ) ) ) )
@ ( mor
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] : ( mbox_s4 @ ( big_q @ Y0 ) ) ) )
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] : ( mbox_s4 @ ( big_r @ Y0 ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f134,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f135,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f136,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f87]) ).
thf(f143,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,[],[f128,f134,f125,f134,f134]) ).
thf(f144,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,[],[f115,f125,f134]) ).
thf(f152,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ rel_s4 )
= $true ),
inference(definition_unfolding,[],[f118,f129]) ).
thf(f153,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s4 )
= $true ),
inference(definition_unfolding,[],[f127,f119]) ).
thf(f154,plain,
( ( ~ ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ 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] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i > $o,Y3: $i] :
( ( Y2 @ Y3 )
| ( Y1 @ Y3 ) )
@ ( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y4 @ Y5 )
| ( Y3 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y2 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ p )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( big_q @ Y0 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y4 @ Y5 )
| ( Y3 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y2 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ p ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( big_r @ Y0 ) ) ) ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( big_q @ Y0 ) ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( big_r @ Y0 ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f132,f135,f120,f144,f120,f136,f125,f143,f120,f120,f143,f120,f134,f120,f120,f125,f120,f136,f120,f120,f136,f120]) ).
thf(f155,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y1 @ Y2 )
& ( rel_s4 @ Y2 @ Y0 ) )
=> ( rel_s4 @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f156,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y2 @ Y4 )
| ( big_r @ Y3 @ Y4 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y2 @ Y4 )
| ( big_q @ Y3 @ Y4 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y2 @ Y4 )
| ( big_r @ Y3 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( rel_s4 @ Y4 @ Y5 )
| ( p @ Y5 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y2 @ Y4 )
| ( big_q @ Y3 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y2 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f157,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f158,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( ( rel_s4 @ X1 @ X1 )
= $true ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y2 @ Y4 )
| ( big_r @ Y3 @ Y4 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y2 @ Y4 )
| ( big_q @ Y3 @ Y4 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y2 @ Y4 )
| ( big_r @ Y3 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( rel_s4 @ Y4 @ Y5 )
| ( p @ Y5 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y2 @ Y4 )
| ( big_q @ Y3 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y2 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f156]) ).
thf(f161,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y2 @ Y4 )
| ( big_r @ Y3 @ Y4 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y2 @ Y4 )
| ( big_q @ Y3 @ Y4 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y2 @ Y4 )
| ( big_r @ Y3 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y2 @ Y4 )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( rel_s4 @ Y4 @ Y5 )
| ( p @ Y5 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y2 @ Y4 )
| ( big_q @ Y3 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y2 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y1 @ Y3 )
| ( big_r @ Y2 @ Y3 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y1 @ Y3 )
| ( big_q @ Y2 @ Y3 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y1 @ Y3 )
| ( big_r @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y1 @ Y3 )
| ( big_q @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y1 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y1 @ Y3 )
| ( big_r @ Y2 @ Y3 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y1 @ Y3 )
| ( big_q @ Y2 @ Y3 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y1 @ Y3 )
| ( big_r @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y1 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y1 @ Y3 )
| ( big_q @ Y2 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y1 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( ~ ( rel_s4 @ sK0 @ sK1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( big_r @ Y1 @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( big_q @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( big_r @ Y1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( big_q @ Y1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( big_r @ Y1 @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( big_q @ Y1 @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( big_r @ Y1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( big_q @ Y1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( $false
= ( ~ ( rel_s4 @ sK0 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f167,plain,
( $true
= ( rel_s4 @ sK0 @ sK1 ) ),
inference(not_proxy_clausification,[],[f166]) ).
thf(f170,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ?? @ mu
@ ^ [Y1: mu] : ( exists_in_world @ Y1 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f105]) ).
thf(f171,plain,
! [X1: $i] :
( ( ?? @ mu
@ ^ [Y0: mu] : ( exists_in_world @ Y0 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f177,plain,
! [X1: $i] :
( ( ^ [Y0: mu] : ( exists_in_world @ Y0 @ X1 )
@ ( sK2 @ X1 ) )
= $true ),
inference(sigma_proxy_clausification,[],[f171]) ).
thf(f178,plain,
! [X1: $i] :
( ( exists_in_world @ ( sK2 @ X1 ) @ X1 )
= $true ),
inference(beta-eta_normalization,[],[f177]) ).
thf(f179,plain,
! [X1: mu] :
( ( ^ [Y0: mu] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( exists_in_world @ Y0 @ Y2 )
& ( rel_s4 @ Y2 @ Y1 ) )
=> ( exists_in_world @ Y0 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f110]) ).
thf(f180,plain,
! [X1: mu] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( exists_in_world @ X1 @ Y1 )
& ( rel_s4 @ Y1 @ Y0 ) )
=> ( exists_in_world @ X1 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f181,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( big_r @ Y1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( big_q @ Y1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f182,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( big_r @ Y1 @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( big_q @ Y1 @ Y2 ) ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f185,plain,
! [X2: $i,X1: mu] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( exists_in_world @ X1 @ Y1 )
& ( rel_s4 @ Y1 @ Y0 ) )
=> ( exists_in_world @ X1 @ Y0 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f180]) ).
thf(f186,plain,
! [X2: $i,X1: mu] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( exists_in_world @ X1 @ Y0 )
& ( rel_s4 @ Y0 @ X2 ) )
=> ( exists_in_world @ X1 @ X2 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f187,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( big_q @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f188,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( big_r @ Y1 @ Y2 ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f189,plain,
! [X2: $i,X3: $i,X1: mu] :
( ( ^ [Y0: $i] :
( ( ( exists_in_world @ X1 @ Y0 )
& ( rel_s4 @ Y0 @ X2 ) )
=> ( exists_in_world @ X1 @ X2 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f186]) ).
thf(f190,plain,
! [X2: $i,X3: $i,X1: mu] :
( ( ( ( exists_in_world @ X1 @ X3 )
& ( rel_s4 @ X3 @ X2 ) )
=> ( exists_in_world @ X1 @ X2 ) )
= $true ),
inference(beta-eta_normalization,[],[f189]) ).
thf(f191,plain,
( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( big_q @ Y1 @ Y2 ) ) ) ) ) )
@ sK3 )
= $false ),
inference(sigma_proxy_clausification,[],[f187]) ).
thf(f192,plain,
( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 )
| ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK3 @ Y1 )
| ( big_q @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f196,plain,
! [X0: mu] :
( ( ( ( exists_in_world @ X0 @ sK0 )
& $true )
=> ( exists_in_world @ X0 @ sK1 ) )
= $true ),
inference(superposition,[],[f190,f167]) ).
thf(f202,plain,
! [X0: mu] :
( ( ( exists_in_world @ X0 @ sK0 )
=> ( exists_in_world @ X0 @ sK1 ) )
= $true ),
inference(boolean_simplification,[],[f196]) ).
thf(f205,plain,
( ( $true
=> ( exists_in_world @ ( sK2 @ sK0 ) @ sK1 ) )
= $true ),
inference(superposition,[],[f202,f178]) ).
thf(f207,plain,
( ( exists_in_world @ ( sK2 @ sK0 ) @ sK1 )
= $true ),
inference(boolean_simplification,[],[f205]) ).
thf(f208,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y1 @ Y2 )
& ( rel_s4 @ Y2 @ Y0 ) )
=> ( rel_s4 @ Y1 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f155]) ).
thf(f209,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y0 @ Y1 )
& ( rel_s4 @ Y1 @ X1 ) )
=> ( rel_s4 @ Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f208]) ).
thf(f216,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y0 @ Y1 )
& ( rel_s4 @ Y1 @ X1 ) )
=> ( rel_s4 @ Y0 @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f209]) ).
thf(f217,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s4 @ X2 @ Y0 )
& ( rel_s4 @ Y0 @ X1 ) )
=> ( rel_s4 @ X2 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f216]) ).
thf(f225,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( rel_s4 @ X2 @ Y0 )
& ( rel_s4 @ Y0 @ X1 ) )
=> ( rel_s4 @ X2 @ X1 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f217]) ).
thf(f226,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( rel_s4 @ X2 @ X3 )
& ( rel_s4 @ X3 @ X1 ) )
=> ( rel_s4 @ X2 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f225]) ).
thf(f227,plain,
( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK3 @ Y1 )
| ( big_q @ Y0 @ Y1 ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f228,plain,
( ( ~ ( rel_s4 @ sK1 @ sK3 ) )
= $false ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f244,plain,
( ( rel_s4 @ sK1 @ sK3 )
= $true ),
inference(not_proxy_clausification,[],[f228]) ).
thf(f260,plain,
! [X0: $i] :
( $true
= ( ( $true
& ( rel_s4 @ sK3 @ X0 ) )
=> ( rel_s4 @ sK1 @ X0 ) ) ),
inference(superposition,[],[f226,f244]) ).
thf(f272,plain,
! [X0: $i] :
( $true
= ( ( rel_s4 @ sK3 @ X0 )
=> ( rel_s4 @ sK1 @ X0 ) ) ),
inference(boolean_simplification,[],[f260]) ).
thf(f307,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( big_r @ Y1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( big_q @ Y1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f316,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( big_r @ Y1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( big_q @ Y1 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f307]) ).
thf(f317,plain,
! [X1: $i] :
( ( ~ ( rel_s4 @ sK1 @ X1 )
| ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ X1 @ Y1 )
| ( big_r @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ X1 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ X1 @ Y1 )
| ( big_q @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ X1 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f316]) ).
thf(f330,plain,
( ( ~ $true
| ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK1 @ Y1 )
| ( big_r @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK1 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK1 @ Y1 )
| ( big_q @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK1 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) )
= $true ),
inference(superposition,[],[f317,f159]) ).
thf(f331,plain,
( ( ~ $true
| ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK3 )
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK3 @ Y1 )
| ( big_r @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK3 @ Y1 )
| ( big_q @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK3 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) )
= $true ),
inference(superposition,[],[f317,f244]) ).
thf(f333,plain,
( $true
= ( $false
| ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK3 )
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK3 @ Y1 )
| ( big_r @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK3 @ Y1 )
| ( big_q @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK3 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f331]) ).
thf(f334,plain,
( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK3 )
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK3 @ Y1 )
| ( big_r @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK3 @ Y1 )
| ( big_q @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK3 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f333]) ).
thf(f336,plain,
( ( $false
| ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK1 @ Y1 )
| ( big_r @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK1 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK1 @ Y1 )
| ( big_q @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK1 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f330]) ).
thf(f337,plain,
( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK1 @ Y1 )
| ( big_r @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK1 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK1 @ Y1 )
| ( big_q @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK1 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f336]) ).
thf(f349,plain,
( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y0 @ Y2 )
| ( big_r @ Y1 @ Y2 ) ) ) ) ) )
@ sK4 )
= $false ),
inference(sigma_proxy_clausification,[],[f188]) ).
thf(f350,plain,
( ( ~ ( rel_s4 @ sK1 @ sK4 )
| ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK4 @ Y1 )
| ( big_r @ Y0 @ Y1 ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f349]) ).
thf(f358,plain,
( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK4 @ Y1 )
| ( big_r @ Y0 @ Y1 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f350]) ).
thf(f359,plain,
( $false
= ( ~ ( rel_s4 @ sK1 @ sK4 ) ) ),
inference(or_proxy_clausification,[],[f350]) ).
thf(f362,plain,
( $true
= ( $false
| ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK4 @ Y1 )
| ( big_r @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK4 @ Y1 )
| ( big_q @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK4 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ) ),
inference(superposition,[],[f317,f359]) ).
thf(f363,plain,
( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK4 @ Y1 )
| ( big_r @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK4 @ Y1 )
| ( big_q @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK4 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f362]) ).
thf(f365,plain,
! [X1: mu] :
( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK1 @ Y1 )
| ( big_r @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK1 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK1 @ Y1 )
| ( big_q @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK1 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f337]) ).
thf(f366,plain,
! [X1: mu] :
( $true
= ( ( exists_in_world @ X1 @ sK1 )
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( big_r @ X1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( big_q @ X1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f365]) ).
thf(f392,plain,
( $true
= ( $true
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( big_r @ ( sK2 @ sK0 ) @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( big_q @ ( sK2 @ sK0 ) @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(superposition,[],[f366,f207]) ).
thf(f394,plain,
( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( big_r @ ( sK2 @ sK0 ) @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( big_q @ ( sK2 @ sK0 ) @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(boolean_simplification,[],[f392]) ).
thf(f408,plain,
( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK3 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK3 @ Y1 )
| ( big_q @ Y0 @ Y1 ) ) ) )
@ sK5 ) ),
inference(sigma_proxy_clausification,[],[f227]) ).
thf(f409,plain,
( $false
= ( ( exists_in_world @ sK5 @ sK3 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( big_q @ sK5 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f408]) ).
thf(f418,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( big_q @ sK5 @ Y0 ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f409]) ).
thf(f419,plain,
( ( exists_in_world @ sK5 @ sK3 )
= $true ),
inference(imp_proxy_clausification,[],[f409]) ).
thf(f428,plain,
( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK4 @ Y1 )
| ( big_r @ Y0 @ Y1 ) ) ) )
@ sK6 )
= $false ),
inference(sigma_proxy_clausification,[],[f358]) ).
thf(f429,plain,
( $false
= ( ( exists_in_world @ sK6 @ sK4 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( big_r @ sK6 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f428]) ).
thf(f436,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( big_r @ sK6 @ Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f429]) ).
thf(f437,plain,
( ( exists_in_world @ sK6 @ sK4 )
= $true ),
inference(imp_proxy_clausification,[],[f429]) ).
thf(f444,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( big_q @ ( sK2 @ sK0 ) @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( big_r @ ( sK2 @ sK0 ) @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f394]) ).
thf(f446,definition,
( spl7_1
<=> ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( big_r @ ( sK2 @ sK0 ) @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
thf(f448,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( big_r @ ( sK2 @ sK0 ) @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
= $true )
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f446]) ).
thf(f450,definition,
( spl7_2
<=> ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( big_q @ ( sK2 @ sK0 ) @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
thf(f452,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( big_q @ ( sK2 @ sK0 ) @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true )
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f450]) ).
thf(f453,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f444,f450,f446]) ).
thf(f463,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( big_q @ ( sK2 @ sK0 ) @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false )
| ~ spl7_2 ),
inference(not_proxy_clausification,[],[f452]) ).
thf(f477,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false )
| ~ spl7_2 ),
inference(or_proxy_clausification,[],[f463]) ).
thf(f545,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
= $true )
| ~ spl7_2 ),
inference(not_proxy_clausification,[],[f477]) ).
thf(f557,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ~ spl7_2 ),
inference(pi_proxy_clausification,[],[f545]) ).
thf(f558,plain,
( ! [X1: $i] :
( ( ~ ( rel_s4 @ sK1 @ X1 )
| ( p @ X1 ) )
= $true )
| ~ spl7_2 ),
inference(beta-eta_normalization,[],[f557]) ).
thf(f559,plain,
( ! [X1: $i] :
( ( ( ~ ( rel_s4 @ sK1 @ X1 ) )
= $true )
| ( ( p @ X1 )
= $true ) )
| ~ spl7_2 ),
inference(or_proxy_clausification,[],[f558]) ).
thf(f573,plain,
( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( big_q @ sK5 @ Y0 ) )
@ sK8 )
= $false ),
inference(sigma_proxy_clausification,[],[f418]) ).
thf(f574,plain,
( ( ~ ( rel_s4 @ sK3 @ sK8 )
| ( big_q @ sK5 @ sK8 ) )
= $false ),
inference(beta-eta_normalization,[],[f573]) ).
thf(f578,plain,
( ( ~ ( rel_s4 @ sK3 @ sK8 ) )
= $false ),
inference(or_proxy_clausification,[],[f574]) ).
thf(f594,plain,
( $true
= ( rel_s4 @ sK3 @ sK8 ) ),
inference(not_proxy_clausification,[],[f578]) ).
thf(f614,plain,
( ( $true
=> ( rel_s4 @ sK1 @ sK8 ) )
= $true ),
inference(superposition,[],[f272,f594]) ).
thf(f625,plain,
( ( rel_s4 @ sK1 @ sK8 )
= $true ),
inference(boolean_simplification,[],[f614]) ).
thf(f630,plain,
! [X1: mu] :
( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK3 )
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK3 @ Y1 )
| ( big_r @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK3 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK3 @ Y1 )
| ( big_q @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK3 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f334]) ).
thf(f631,plain,
! [X1: mu] :
( ( ( exists_in_world @ X1 @ sK3 )
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( big_r @ X1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( big_q @ X1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f630]) ).
thf(f650,plain,
( ( $true
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( big_r @ sK5 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( big_q @ sK5 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ) )
= $true ),
inference(superposition,[],[f631,f419]) ).
thf(f654,plain,
( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( big_r @ sK5 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( big_q @ sK5 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(boolean_simplification,[],[f650]) ).
thf(f655,plain,
( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( big_r @ sK5 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ~ ( ~ $false
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true ),
inference(forward_demodulation,[],[f654,f418]) ).
thf(f656,plain,
( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( big_r @ sK5 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ~ ( $true
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f655]) ).
thf(f657,plain,
( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( big_r @ sK5 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ~ $true )
= $true ),
inference(boolean_simplification,[],[f656]) ).
thf(f658,plain,
( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( big_r @ sK5 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| $false )
= $true ),
inference(boolean_simplification,[],[f657]) ).
thf(f659,plain,
( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( big_r @ sK5 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f658]) ).
thf(f669,plain,
! [X0: $i] :
( ( ( $true
& ( rel_s4 @ sK8 @ X0 ) )
=> ( rel_s4 @ sK1 @ X0 ) )
= $true ),
inference(superposition,[],[f226,f625]) ).
thf(f680,plain,
! [X0: $i] :
( ( ( rel_s4 @ sK8 @ X0 )
=> ( rel_s4 @ sK1 @ X0 ) )
= $true ),
inference(boolean_simplification,[],[f669]) ).
thf(f690,plain,
! [X1: mu] :
( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK4 @ Y1 )
| ( big_r @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK4 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK4 @ Y1 )
| ( big_q @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ sK4 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f363]) ).
thf(f691,plain,
! [X1: mu] :
( ( ( exists_in_world @ X1 @ sK4 )
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( big_r @ X1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( big_q @ X1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( p @ Y0 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f690]) ).
thf(f698,plain,
( ( $true
=> ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( big_r @ sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( big_q @ sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( p @ Y0 ) ) ) ) ) )
= $true ),
inference(superposition,[],[f691,f437]) ).
thf(f700,plain,
( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( big_r @ sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( big_q @ sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f698]) ).
thf(f703,plain,
( ( ~ ( ~ $false
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( big_q @ sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true ),
inference(forward_demodulation,[],[f700,f436]) ).
thf(f704,plain,
( ( ~ ( $true
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( big_q @ sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f703]) ).
thf(f705,plain,
( $true
= ( ~ $true
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( big_q @ sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(boolean_simplification,[],[f704]) ).
thf(f706,plain,
( ( $false
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( big_q @ sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f705]) ).
thf(f707,plain,
( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( big_q @ sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f706]) ).
thf(f943,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( big_q @ sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f707]) ).
thf(f954,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f943]) ).
thf(f958,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ( big_r @ sK5 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f659]) ).
thf(f974,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f958]) ).
thf(f1544,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f974]) ).
thf(f1549,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK3 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f1544]) ).
thf(f1550,plain,
! [X1: $i] :
( ( ~ ( rel_s4 @ sK3 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( p @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f1549]) ).
thf(f1561,plain,
( ( $false
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK8 @ Y0 )
| ( p @ Y0 ) ) ) )
= $true ),
inference(superposition,[],[f1550,f578]) ).
thf(f1562,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK8 @ Y0 )
| ( p @ Y0 ) ) ) )
= $true ),
inference(boolean_simplification,[],[f1561]) ).
thf(f1642,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK8 @ Y0 )
| ( p @ Y0 ) ) )
= $false ),
inference(not_proxy_clausification,[],[f1562]) ).
thf(f1645,plain,
( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK8 @ Y0 )
| ( p @ Y0 ) )
@ sK11 )
= $false ),
inference(sigma_proxy_clausification,[],[f1642]) ).
thf(f1646,plain,
( $false
= ( ~ ( rel_s4 @ sK8 @ sK11 )
| ( p @ sK11 ) ) ),
inference(beta-eta_normalization,[],[f1645]) ).
thf(f1845,plain,
( ( p @ sK11 )
= $false ),
inference(or_proxy_clausification,[],[f1646]) ).
thf(f1846,plain,
( ( ~ ( rel_s4 @ sK8 @ sK11 ) )
= $false ),
inference(or_proxy_clausification,[],[f1646]) ).
thf(f1864,plain,
( ( rel_s4 @ sK8 @ sK11 )
= $true ),
inference(not_proxy_clausification,[],[f1846]) ).
thf(f1886,plain,
( ( $true
=> ( rel_s4 @ sK1 @ sK11 ) )
= $true ),
inference(superposition,[],[f680,f1864]) ).
thf(f1900,plain,
( ( rel_s4 @ sK1 @ sK11 )
= $true ),
inference(boolean_simplification,[],[f1886]) ).
thf(f1946,plain,
( ( ( ~ $true ) = $true )
| ( ( p @ sK11 )
= $true )
| ~ spl7_2 ),
inference(superposition,[],[f559,f1900]) ).
thf(f1969,plain,
( ( ( p @ sK11 )
= $true )
| ( $false = $true )
| ~ spl7_2 ),
inference(boolean_simplification,[],[f1946]) ).
thf(f1970,plain,
( ( ( p @ sK11 )
= $true )
| ~ spl7_2 ),
inference(trivial_inequality_removal,[],[f1969]) ).
thf(f1979,plain,
( ( $false = $true )
| ~ spl7_2 ),
inference(forward_demodulation,[],[f1970,f1845]) ).
thf(f1980,plain,
( $false
| ~ spl7_2 ),
inference(trivial_inequality_removal,[],[f1979]) ).
thf(f1981,plain,
~ spl7_2,
inference(avatar_contradiction_clause,[],[f1980]) ).
thf(f2092,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( big_r @ ( sK2 @ sK0 ) @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
= $false )
| ~ spl7_1 ),
inference(not_proxy_clausification,[],[f448]) ).
thf(f2123,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
= $false )
| ~ spl7_1 ),
inference(or_proxy_clausification,[],[f2092]) ).
thf(f2442,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
= $true )
| ~ spl7_1 ),
inference(not_proxy_clausification,[],[f2123]) ).
thf(f2461,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X1 )
= $true )
| ~ spl7_1 ),
inference(pi_proxy_clausification,[],[f2442]) ).
thf(f2462,plain,
( ! [X1: $i] :
( ( ~ ( rel_s4 @ sK1 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( p @ Y0 ) ) ) )
= $true )
| ~ spl7_1 ),
inference(beta-eta_normalization,[],[f2461]) ).
thf(f2478,plain,
( ( ( $false
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( p @ Y0 ) ) ) )
= $true )
| ~ spl7_1 ),
inference(superposition,[],[f2462,f359]) ).
thf(f2491,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( p @ Y0 ) ) ) )
= $true )
| ~ spl7_1 ),
inference(boolean_simplification,[],[f2478]) ).
thf(f2506,plain,
( ( $false = $true )
| ~ spl7_1 ),
inference(forward_demodulation,[],[f2491,f954]) ).
thf(f2507,plain,
( $false
| ~ spl7_1 ),
inference(trivial_inequality_removal,[],[f2506]) ).
thf(f2508,plain,
~ spl7_1,
inference(avatar_contradiction_clause,[],[f2507]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f453]) ).
cnf(s14,plain,
~ spl7_2,
inference(sat_conversion,[],[f1981]) ).
cnf(s19,plain,
~ spl7_1,
inference(sat_conversion,[],[f2508]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s1,s14,s19]) ).
thf(f2513,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN367^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n006.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 16:15:10 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.76/0.39 % (925603)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.76/0.39 % (925612)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2786151936:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.76/0.39 % (925608)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=840178787:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.76/0.39 % (925610)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3677414776:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.76/0.39 % (925611)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=3653992800: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)
% 0.76/0.39 % (925613)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1111093975:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.76/0.39 % (925612)Instruction limit reached!
% 0.76/0.39 % (925612)------------------------------
% 0.76/0.39 % (925612)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.39 % (925612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.39 % (925612)CaDiCaL version: 2.1.3
% 0.76/0.39 % (925612)Termination reason: Instruction limit
% 0.76/0.39 % (925612)Termination phase: Saturation
% 0.76/0.39 % (925612)Time elapsed: 0.008 s
% 0.76/0.39 % (925612)Peak memory usage: 12 MB
% 0.76/0.39 % (925612)Instructions burned: 26 (million)
% 0.76/0.39 % (925609)lrs+10_16_si=on:nwc=1.5:random_seed=2295964195:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.76/0.39 % (925610)Instruction limit reached!
% 0.76/0.39 % (925610)------------------------------
% 0.76/0.39 % (925610)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.39 % (925610)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.39 % (925610)CaDiCaL version: 2.1.3
% 0.76/0.39 % (925610)Termination reason: Instruction limit
% 0.76/0.39 % (925610)Termination phase: Property scanning
% 0.76/0.39 % (925610)Time elapsed: 0.002 s
% 0.76/0.39 % (925610)Peak memory usage: 10 MB
% 0.76/0.39 % (925610)Instructions burned: 4 (million)
% 0.76/0.39 % (925614)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.76/0.39 % (925614)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
% 0.76/0.39 % (925614)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=2483410527:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.76/0.39 % (925609)Instruction limit reached!
% 0.76/0.39 % (925609)------------------------------
% 0.76/0.39 % (925609)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.39 % (925609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.39 % (925609)CaDiCaL version: 2.1.3
% 0.76/0.39 % (925609)Termination reason: Instruction limit
% 0.76/0.39 % (925609)Termination phase: Saturation
% 0.76/0.39 % (925609)Time elapsed: 0.010 s
% 0.76/0.39 % (925609)Peak memory usage: 12 MB
% 0.76/0.39 % (925609)Instructions burned: 18 (million)
% 0.76/0.39 % (925622)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3401064928:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.76/0.39 % (925621)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=623327969:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.76/0.39 % (925621)Instruction limit reached!
% 0.76/0.39 % (925621)------------------------------
% 0.76/0.39 % (925621)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.39 % (925621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.39 % (925621)CaDiCaL version: 2.1.3
% 0.76/0.39 % (925621)Termination reason: Instruction limit
% 0.76/0.39 % (925621)Termination phase: Clausification
% 0.76/0.39 % (925621)Time elapsed: 0.002 s
% 0.76/0.39 % (925621)Peak memory usage: 10 MB
% 0.76/0.39 % (925621)Instructions burned: 5 (million)
% 0.76/0.39 % (925622)Instruction limit reached!
% 0.76/0.44 % (925622)------------------------------
% 0.76/0.44 % (925622)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.44 % (925622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.44 % (925622)CaDiCaL version: 2.1.3
% 0.76/0.44 % (925622)Termination reason: Instruction limit
% 0.76/0.44 % (925622)Termination phase: Function definition elimination
% 0.76/0.44 % (925622)Time elapsed: 0.003 s
% 0.76/0.44 % (925622)Peak memory usage: 10 MB
% 0.76/0.44 % (925622)Instructions burned: 7 (million)
% 0.76/0.44 % (925624)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.76/0.44 % (925613)Instruction limit reached!
% 0.76/0.44 % (925613)------------------------------
% 0.76/0.44 % (925613)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.44 % (925613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.44 % (925613)CaDiCaL version: 2.1.3
% 0.76/0.44 % (925613)Termination reason: Instruction limit
% 0.76/0.44 % (925613)Termination phase: Saturation
% 0.76/0.44 % (925613)Time elapsed: 0.036 s
% 0.76/0.44 % (925613)Peak memory usage: 12 MB
% 0.76/0.44 % (925613)Instructions burned: 75 (million)
% 0.76/0.44 % (925624)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2849828358:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.76/0.44 % (925628)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
% 0.76/0.44 % (925628)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.76/0.44 % (925624)Instruction limit reached!
% 0.76/0.44 % (925624)------------------------------
% 0.76/0.44 % (925624)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.44 % (925624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.44 % (925624)CaDiCaL version: 2.1.3
% 0.76/0.44 % (925624)Termination reason: Instruction limit
% 0.76/0.44 % (925624)Termination phase: Function definition elimination
% 0.76/0.44 % (925624)Time elapsed: 0.003 s
% 0.76/0.44 % (925624)Peak memory usage: 10 MB
% 0.76/0.44 % (925624)Instructions burned: 7 (million)
% 0.76/0.44 % (925608)Instruction limit reached!
% 0.76/0.44 % (925608)------------------------------
% 0.76/0.44 % (925608)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.44 % (925608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.44 % (925608)CaDiCaL version: 2.1.3
% 0.76/0.44 % (925608)Termination reason: Instruction limit
% 0.76/0.44 % (925608)Termination phase: Saturation
% 0.76/0.44 % (925608)Time elapsed: 0.045 s
% 0.76/0.44 % (925608)Peak memory usage: 12 MB
% 0.76/0.44 % (925608)Instructions burned: 88 (million)
% 0.76/0.44 % (925628)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1509247495:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.76/0.44 % (925614)Instruction limit reached!
% 0.76/0.44 % (925614)------------------------------
% 0.76/0.44 % (925614)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.44 % (925614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.44 % (925614)CaDiCaL version: 2.1.3
% 0.76/0.44 % (925614)Termination reason: Instruction limit
% 0.76/0.44 % (925614)Termination phase: Saturation
% 0.76/0.44 % (925614)Time elapsed: 0.042 s
% 0.76/0.44 % (925614)Peak memory usage: 13 MB
% 0.76/0.44 % (925614)Instructions burned: 159 (million)
% 0.76/0.44 % (925628)Instruction limit reached!
% 0.76/0.44 % (925628)------------------------------
% 0.76/0.44 % (925628)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.44 % (925628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.44 % (925628)CaDiCaL version: 2.1.3
% 0.76/0.44 % (925628)Termination reason: Instruction limit
% 0.76/0.44 % (925628)Termination phase: Saturation
% 0.76/0.44 % (925628)Time elapsed: 0.014 s
% 0.76/0.44 % (925628)Peak memory usage: 11 MB
% 0.76/0.44 % (925628)Instructions burned: 30 (million)
% 0.76/0.44 % (925634)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2068275619:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.76/0.47 % (925633)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.76/0.47 % (925627)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1349394985:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.76/0.47 % (925633)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=4086154837:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.76/0.47 % (925629)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=3315137071:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.76/0.47 % (925633)Instruction limit reached!
% 0.76/0.47 % (925633)------------------------------
% 0.76/0.47 % (925633)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.47 % (925633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.47 % (925633)CaDiCaL version: 2.1.3
% 0.76/0.47 % (925633)Termination reason: Instruction limit
% 0.76/0.47 % (925633)Termination phase: Property scanning
% 0.76/0.47 % (925633)Time elapsed: 0.002 s
% 0.76/0.47 % (925633)Peak memory usage: 9 MB
% 0.76/0.47 % (925633)Instructions burned: 4 (million)
% 0.76/0.47 % (925634)Refutation not found, incomplete strategy
% 0.76/0.47 % (925634)------------------------------
% 0.76/0.47 % (925634)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.47 % (925634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.47 % (925634)CaDiCaL version: 2.1.3
% 0.76/0.47 % (925634)Termination reason: Refutation not found, incomplete strategy
% 0.76/0.47 % (925634)Time elapsed: 0.006 s
% 0.76/0.47 % (925634)Peak memory usage: 12 MB
% 0.76/0.47 % (925634)Instructions burned: 22 (million)
% 0.76/0.47 % (925634)------------------------------
% 0.76/0.47 % (925634)------------------------------
% 0.76/0.47 % (925627)Instruction limit reached!
% 0.76/0.47 % (925627)------------------------------
% 0.76/0.47 % (925627)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.47 % (925627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.47 % (925627)CaDiCaL version: 2.1.3
% 0.76/0.47 % (925627)Termination reason: Instruction limit
% 0.76/0.47 % (925627)Termination phase: Saturation
% 0.76/0.47 % (925627)Time elapsed: 0.007 s
% 0.76/0.47 % (925627)Peak memory usage: 11 MB
% 0.76/0.47 % (925627)Instructions burned: 14 (million)
% 0.76/0.47 % (925641)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=756467631:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.76/0.47 % (925641)Instruction limit reached!
% 0.76/0.47 % (925641)------------------------------
% 0.76/0.47 % (925641)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.47 % (925641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.47 % (925641)CaDiCaL version: 2.1.3
% 0.76/0.47 % (925641)Termination reason: Instruction limit
% 0.76/0.47 % (925641)Termination phase: Saturation
% 0.76/0.47 % (925641)Time elapsed: 0.003 s
% 0.76/0.47 % (925641)Peak memory usage: 11 MB
% 0.76/0.47 % (925641)Instructions burned: 15 (million)
% 0.76/0.47 % (925636)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=439780737:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.76/0.47 % (925631)lrs+10_1_si=on:cs=on:random_seed=671992121:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.76/0.47 % (925640)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2222379161:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.76/0.47 % (925642)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=1787575287:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.76/0.47 % (925631)Instruction limit reached!
% 0.76/0.47 % (925631)------------------------------
% 0.76/0.47 % (925631)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.76/0.47 % (925631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.76/0.47 % (925631)CaDiCaL version: 2.1.3
% 1.53/0.55 % (925631)Termination reason: Instruction limit
% 1.53/0.55 % (925631)Termination phase: Saturation
% 1.53/0.55 % (925631)Time elapsed: 0.005 s
% 1.53/0.55 % (925631)Peak memory usage: 11 MB
% 1.53/0.55 % (925631)Instructions burned: 10 (million)
% 1.53/0.55 % (925636)Refutation not found, incomplete strategy
% 1.53/0.55 % (925636)------------------------------
% 1.53/0.55 % (925636)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.53/0.55 % (925636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.53/0.55 % (925636)CaDiCaL version: 2.1.3
% 1.53/0.55 % (925636)Termination reason: Refutation not found, incomplete strategy
% 1.53/0.55 % (925636)Time elapsed: 0.009 s
% 1.53/0.55 % (925636)Peak memory usage: 12 MB
% 1.53/0.55 % (925636)Instructions burned: 14 (million)
% 1.53/0.55 % (925645)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=3322170298:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.53/0.55 % (925636)------------------------------
% 1.53/0.55 % (925636)------------------------------
% 1.53/0.55 % (925645)Instruction limit reached!
% 1.53/0.55 % (925645)------------------------------
% 1.53/0.55 % (925645)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.53/0.55 % (925645)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.53/0.55 % (925645)CaDiCaL version: 2.1.3
% 1.53/0.55 % (925645)Termination reason: Instruction limit
% 1.53/0.55 % (925645)Termination phase: Saturation
% 1.53/0.55 % (925645)Time elapsed: 0.004 s
% 1.53/0.55 % (925645)Peak memory usage: 12 MB
% 1.53/0.55 % (925645)Instructions burned: 17 (million)
% 1.53/0.55 % (925640)Instruction limit reached!
% 1.53/0.55 % (925640)------------------------------
% 1.53/0.55 % (925640)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.53/0.55 % (925640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.53/0.55 % (925640)CaDiCaL version: 2.1.3
% 1.53/0.55 % (925640)Termination reason: Instruction limit
% 1.53/0.55 % (925640)Termination phase: Saturation
% 1.53/0.55 % (925640)Time elapsed: 0.015 s
% 1.53/0.55 % (925640)Peak memory usage: 12 MB
% 1.53/0.55 % (925640)Instructions burned: 26 (million)
% 1.53/0.55 % (925653)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2618119554:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.53/0.55 % (925651)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=3987886355:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.53/0.55 % (925649)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1346202937: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)
% 1.53/0.55 % (925649)Instruction limit reached!
% 1.53/0.55 % (925649)------------------------------
% 1.53/0.55 % (925649)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.53/0.55 % (925649)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.53/0.55 % (925649)CaDiCaL version: 2.1.3
% 1.53/0.55 % (925649)Termination reason: Instruction limit
% 1.53/0.55 % (925649)Termination phase: shuffling
% 1.53/0.55 % (925649)Time elapsed: 0.002 s
% 1.53/0.55 % (925649)Peak memory usage: 9 MB
% 1.53/0.55 % (925649)Instructions burned: 2 (million)
% 1.53/0.55 % (925652)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1369550628:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.53/0.55 % (925653)Instruction limit reached!
% 1.53/0.55 % (925653)------------------------------
% 1.53/0.55 % (925653)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.53/0.55 % (925653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.53/0.55 % (925653)CaDiCaL version: 2.1.3
% 1.53/0.55 % (925653)Termination reason: Instruction limit
% 1.53/0.55 % (925653)Termination phase: Saturation
% 1.53/0.55 % (925653)Time elapsed: 0.018 s
% 1.53/0.55 % (925653)Peak memory usage: 12 MB
% 1.53/0.55 % (925653)Instructions burned: 61 (million)
% 1.53/0.55 % (925651)Instruction limit reached!
% 1.53/0.55 % (925651)------------------------------
% 1.53/0.55 % (925651)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.53/0.55 % (925651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.53/0.55 % (925651)CaDiCaL version: 2.1.3
% 1.53/0.55 % (925651)Termination reason: Instruction limit
% 1.53/0.61 % (925651)Termination phase: Saturation
% 1.53/0.61 % (925651)Time elapsed: 0.016 s
% 1.53/0.61 % (925651)Peak memory usage: 12 MB
% 1.53/0.61 % (925651)Instructions burned: 26 (million)
% 1.53/0.61 % (925659)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.53/0.61 % (925659)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=477508366:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.53/0.61 % (925657)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
% 1.53/0.61 % (925657)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.53/0.61 % (925652)Instruction limit reached!
% 1.53/0.61 % (925652)------------------------------
% 1.53/0.61 % (925652)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.53/0.61 % (925652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.53/0.61 % (925652)CaDiCaL version: 2.1.3
% 1.53/0.61 % (925652)Termination reason: Instruction limit
% 1.53/0.61 % (925652)Termination phase: Saturation
% 1.53/0.61 % (925652)Time elapsed: 0.011 s
% 1.53/0.61 % (925652)Peak memory usage: 11 MB
% 1.53/0.61 % (925652)Instructions burned: 24 (million)
% 1.53/0.61 % (925659)Instruction limit reached!
% 1.53/0.61 % (925659)------------------------------
% 1.53/0.61 % (925659)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.53/0.61 % (925659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.53/0.61 % (925659)CaDiCaL version: 2.1.3
% 1.53/0.61 % (925659)Termination reason: Instruction limit
% 1.53/0.61 % (925659)Termination phase: Function definition elimination
% 1.53/0.61 % (925659)Time elapsed: 0.002 s
% 1.53/0.61 % (925659)Peak memory usage: 10 MB
% 1.53/0.61 % (925659)Instructions burned: 8 (million)
% 1.53/0.61 % (925657)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=3616834603:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.53/0.61 % (925629)Instruction limit reached!
% 1.53/0.61 % (925629)------------------------------
% 1.53/0.61 % (925629)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.53/0.61 % (925629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.53/0.61 % (925629)CaDiCaL version: 2.1.3
% 1.53/0.61 % (925629)Termination reason: Instruction limit
% 1.53/0.61 % (925629)Termination phase: Saturation
% 1.53/0.61 % (925629)Time elapsed: 0.087 s
% 1.53/0.61 % (925629)Peak memory usage: 12 MB
% 1.53/0.61 % (925629)Instructions burned: 86 (million)
% 1.53/0.61 % (925657)Instruction limit reached!
% 1.53/0.61 % (925657)------------------------------
% 1.53/0.61 % (925657)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.53/0.61 % (925657)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.53/0.61 % (925657)CaDiCaL version: 2.1.3
% 1.53/0.61 % (925657)Termination reason: Instruction limit
% 1.53/0.61 % (925657)Termination phase: Saturation
% 1.53/0.61 % (925657)Time elapsed: 0.007 s
% 1.53/0.61 % (925657)Peak memory usage: 12 MB
% 1.53/0.61 % (925657)Instructions burned: 15 (million)
% 1.53/0.61 % (925660)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=2647976402:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.53/0.61 % (925662)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3212729675:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.53/0.61 % (925663)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=306643103:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.53/0.61 % (925666)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=2193853046:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.53/0.61 % (925662)Instruction limit reached!
% 1.53/0.61 % (925662)------------------------------
% 1.53/0.61 % (925662)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.53/0.61 % (925662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.67 % (925662)CaDiCaL version: 2.1.3
% 2.52/0.67 % (925662)Termination reason: Instruction limit
% 2.52/0.67 % (925662)Termination phase: Function definition elimination
% 2.52/0.67 % (925662)Time elapsed: 0.003 s
% 2.52/0.67 % (925662)Peak memory usage: 10 MB
% 2.52/0.67 % (925662)Instructions burned: 7 (million)
% 2.52/0.67 % (925665)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=3339698464:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.52/0.67 % (925663)Instruction limit reached!
% 2.52/0.67 % (925663)------------------------------
% 2.52/0.67 % (925663)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.67 % (925663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.67 % (925663)CaDiCaL version: 2.1.3
% 2.52/0.67 % (925663)Termination reason: Instruction limit
% 2.52/0.67 % (925663)Termination phase: Saturation
% 2.52/0.67 % (925663)Time elapsed: 0.011 s
% 2.52/0.67 % (925663)Peak memory usage: 12 MB
% 2.52/0.67 % (925663)Instructions burned: 24 (million)
% 2.52/0.67 % (925665)Instruction limit reached!
% 2.52/0.67 % (925665)------------------------------
% 2.52/0.67 % (925665)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.67 % (925665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.67 % (925665)CaDiCaL version: 2.1.3
% 2.52/0.67 % (925665)Termination reason: Instruction limit
% 2.52/0.67 % (925665)Termination phase: Saturation
% 2.52/0.67 % (925665)Time elapsed: 0.011 s
% 2.52/0.67 % (925665)Peak memory usage: 12 MB
% 2.52/0.67 % (925665)Instructions burned: 20 (million)
% 2.52/0.67 % (925671)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=4025388963:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2997 on theBenchmark for (2997ds/143Mi)
% 2.52/0.67 % (925660)Instruction limit reached!
% 2.52/0.67 % (925660)------------------------------
% 2.52/0.67 % (925660)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.67 % (925660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.67 % (925660)CaDiCaL version: 2.1.3
% 2.52/0.67 % (925660)Termination reason: Instruction limit
% 2.52/0.67 % (925660)Termination phase: Saturation
% 2.52/0.67 % (925660)Time elapsed: 0.030 s
% 2.52/0.67 % (925660)Peak memory usage: 12 MB
% 2.52/0.67 % (925660)Instructions burned: 32 (million)
% 2.52/0.67 % (925673)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=1995621261:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/193Mi)
% 2.52/0.67 % (925675)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2118797382:i=42:hud=10:rtra=on_2997 on theBenchmark for (2997ds/42Mi)
% 2.52/0.67 % (925676)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.52/0.67 % (925676)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2169776975:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2997 on theBenchmark for (2997ds/7Mi)
% 2.52/0.67 % (925675)Instruction limit reached!
% 2.52/0.67 % (925675)------------------------------
% 2.52/0.67 % (925675)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.67 % (925675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.67 % (925675)CaDiCaL version: 2.1.3
% 2.52/0.67 % (925675)Termination reason: Instruction limit
% 2.52/0.67 % (925675)Termination phase: Saturation
% 2.52/0.67 % (925675)Time elapsed: 0.027 s
% 2.52/0.67 % (925675)Peak memory usage: 12 MB
% 2.52/0.67 % (925675)Instructions burned: 43 (million)
% 2.52/0.67 % (925676)Instruction limit reached!
% 2.52/0.67 % (925676)------------------------------
% 2.52/0.67 % (925676)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.52/0.67 % (925676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/0.67 % (925676)CaDiCaL version: 2.1.3
% 2.52/0.67 % (925676)Termination reason: Instruction limit
% 2.52/0.67 % (925676)Termination phase: Function definition elimination
% 2.52/0.67 % (925676)Time elapsed: 0.003 s
% 2.52/0.67 % (925676)Peak memory usage: 10 MB
% 2.52/0.67 % (925676)Instructions burned: 7 (million)
% 2.52/0.67 % (925673)Refutation not found, incomplete strategy
% 2.52/0.67 % (925673)------------------------------
% 2.52/0.67 % (925673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.75 % (925673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.75 % (925673)CaDiCaL version: 2.1.3
% 2.66/0.75 % (925673)Termination reason: Refutation not found, incomplete strategy
% 2.66/0.75 % (925673)Time elapsed: 0.050 s
% 2.66/0.75 % (925673)Peak memory usage: 12 MB
% 2.66/0.75 % (925673)Instructions burned: 75 (million)
% 2.66/0.75 % (925673)------------------------------
% 2.66/0.75 % (925673)------------------------------
% 2.66/0.75 % (925680)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=1480793771:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.66/0.75 % (925681)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=2532418779:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.66/0.75 % (925642)Instruction limit reached!
% 2.66/0.75 % (925642)------------------------------
% 2.66/0.75 % (925642)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.75 % (925642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.75 % (925642)CaDiCaL version: 2.1.3
% 2.66/0.75 % (925642)Termination reason: Instruction limit
% 2.66/0.75 % (925642)Termination phase: Saturation
% 2.66/0.75 % (925642)Time elapsed: 0.173 s
% 2.66/0.75 % (925642)Peak memory usage: 13 MB
% 2.66/0.75 % (925642)Instructions burned: 328 (million)
% 2.66/0.75 % (925682)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.66/0.75 % (925682)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=3466361017:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.66/0.75 % (925682)Instruction limit reached!
% 2.66/0.75 % (925682)------------------------------
% 2.66/0.75 % (925682)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.75 % (925682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.75 % (925682)CaDiCaL version: 2.1.3
% 2.66/0.75 % (925682)Termination reason: Instruction limit
% 2.66/0.75 % (925682)Termination phase: Property scanning
% 2.66/0.75 % (925682)Time elapsed: 0.003 s
% 2.66/0.75 % (925682)Peak memory usage: 10 MB
% 2.66/0.75 % (925682)Instructions burned: 7 (million)
% 2.66/0.75 % (925671)Instruction limit reached!
% 2.66/0.75 % (925671)------------------------------
% 2.66/0.75 % (925671)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.75 % (925671)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.75 % (925671)CaDiCaL version: 2.1.3
% 2.66/0.75 % (925671)Termination reason: Instruction limit
% 2.66/0.75 % (925671)Termination phase: Saturation
% 2.66/0.75 % (925671)Time elapsed: 0.091 s
% 2.66/0.75 % (925671)Peak memory usage: 13 MB
% 2.66/0.75 % (925671)Instructions burned: 144 (million)
% 2.66/0.75 % (925685)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2243221971:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2996 on theBenchmark for (2996ds/22Mi)
% 2.66/0.75 % (925685)Instruction limit reached!
% 2.66/0.75 % (925685)------------------------------
% 2.66/0.75 % (925685)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.75 % (925685)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.75 % (925685)CaDiCaL version: 2.1.3
% 2.66/0.75 % (925685)Termination reason: Instruction limit
% 2.66/0.75 % (925685)Termination phase: Saturation
% 2.66/0.75 % (925685)Time elapsed: 0.012 s
% 2.66/0.75 % (925685)Peak memory usage: 12 MB
% 2.66/0.75 % (925685)Instructions burned: 24 (million)
% 2.66/0.75 % (925687)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3549211880:i=19:add=on:rtra=on_2996 on theBenchmark for (2996ds/19Mi)
% 2.66/0.75 % (925611)Instruction limit reached!
% 2.66/0.75 % (925611)------------------------------
% 2.66/0.75 % (925611)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.75 % (925611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.75 % (925611)CaDiCaL version: 2.1.3
% 2.66/0.75 % (925611)Termination reason: Instruction limit
% 2.66/0.75 % (925611)Termination phase: Saturation
% 2.66/0.75 % (925611)Time elapsed: 0.303 s
% 2.66/0.75 % (925611)Peak memory usage: 15 MB
% 2.66/0.75 % (925611)Instructions burned: 635 (million)
% 2.66/0.76 % (925687)Instruction limit reached!
% 2.66/0.76 % (925687)------------------------------
% 2.66/0.76 % (925687)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.76 % (925687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.76 % (925687)CaDiCaL version: 2.1.3
% 2.66/0.76 % (925687)Termination reason: Instruction limit
% 2.66/0.76 % (925687)Termination phase: Saturation
% 2.66/0.76 % (925687)Time elapsed: 0.010 s
% 2.66/0.76 % (925687)Peak memory usage: 12 MB
% 2.66/0.76 % (925687)Instructions burned: 20 (million)
% 2.66/0.76 % (925690)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=3942434174:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2996 on theBenchmark for (2996ds/853Mi)
% 2.66/0.76 % (925688)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=2935901331:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/316Mi)
% 2.66/0.76 % (925692)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=3537063073:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2996 on theBenchmark for (2996ds/45Mi)
% 2.66/0.76 % (925693)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=291208417:i=480:rtra=on_2996 on theBenchmark for (2996ds/480Mi)
% 2.66/0.76 % (925693)Refutation not found, incomplete strategy
% 2.66/0.76 % (925693)------------------------------
% 2.66/0.76 % (925693)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.76 % (925693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.76 % (925693)CaDiCaL version: 2.1.3
% 2.66/0.76 % (925693)Termination reason: Refutation not found, incomplete strategy
% 2.66/0.76 % (925693)Time elapsed: 0.005 s
% 2.66/0.76 % (925693)Peak memory usage: 12 MB
% 2.66/0.76 % (925693)Instructions burned: 9 (million)
% 2.66/0.76 % (925693)------------------------------
% 2.66/0.76 % (925693)------------------------------
% 2.66/0.76 % (925680)Instruction limit reached!
% 2.66/0.76 % (925680)------------------------------
% 2.66/0.76 % (925680)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.76 % (925680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.76 % (925680)CaDiCaL version: 2.1.3
% 2.66/0.76 % (925680)Termination reason: Instruction limit
% 2.66/0.76 % (925680)Termination phase: Saturation
% 2.66/0.76 % (925680)Time elapsed: 0.087 s
% 2.66/0.76 % (925680)Peak memory usage: 13 MB
% 2.66/0.76 % (925680)Instructions burned: 181 (million)
% 2.66/0.76 % (925692)Instruction limit reached!
% 2.66/0.76 % (925692)------------------------------
% 2.66/0.76 % (925692)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.76 % (925692)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.76 % (925692)CaDiCaL version: 2.1.3
% 2.66/0.76 % (925692)Termination reason: Instruction limit
% 2.66/0.76 % (925692)Termination phase: Saturation
% 2.66/0.76 % (925692)Time elapsed: 0.026 s
% 2.66/0.76 % (925692)Peak memory usage: 12 MB
% 2.66/0.76 % (925692)Instructions burned: 46 (million)
% 2.66/0.76 % (925699)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 2.66/0.76 % (925698)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=1053364808:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 2.66/0.76 % (925699)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=3953107360:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 2.66/0.76 % (925698)Instruction limit reached!
% 2.66/0.76 % (925698)------------------------------
% 2.66/0.76 % (925698)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.76 % (925698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.76 % (925698)CaDiCaL version: 2.1.3
% 2.66/0.76 % (925698)Termination reason: Instruction limit
% 2.66/0.76 % (925698)Termination phase: Saturation
% 2.66/0.76 % (925698)Time elapsed: 0.011 s
% 2.66/0.76 % (925698)Peak memory usage: 12 MB
% 2.66/0.76 % (925698)Instructions burned: 21 (million)
% 2.66/0.76 % (925700)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=4126248484:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 2.66/0.76 % (925700)Instruction limit reached!
% 2.66/0.76 % (925700)------------------------------
% 2.66/0.76 % (925700)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.76 % (925700)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.76 % (925700)CaDiCaL version: 2.1.3
% 2.66/0.76 % (925700)Termination reason: Instruction limit
% 2.66/0.76 % (925700)Termination phase: Saturation
% 2.66/0.76 % (925700)Time elapsed: 0.008 s
% 2.66/0.76 % (925700)Peak memory usage: 12 MB
% 2.66/0.76 % (925700)Instructions burned: 14 (million)
% 2.66/0.76 % (925681)Instruction limit reached!
% 2.66/0.76 % (925681)------------------------------
% 2.66/0.76 % (925681)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.76 % (925681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.76 % (925681)CaDiCaL version: 2.1.3
% 2.66/0.76 % (925681)Termination reason: Instruction limit
% 2.66/0.76 % (925681)Termination phase: Saturation
% 2.66/0.76 % (925681)Time elapsed: 0.133 s
% 2.66/0.76 % (925681)Peak memory usage: 13 MB
% 2.66/0.76 % (925681)Instructions burned: 169 (million)
% 2.66/0.76 % (925703)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=823971282:i=66:s2at=3:nm=2:rtra=on:rawr=on_2995 on theBenchmark for (2995ds/66Mi)
% 2.66/0.76 % (925705)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=2293157764:i=51:fsr=off:rtra=on_2995 on theBenchmark for (2995ds/51Mi)
% 2.66/0.76 % (925707)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=1057580820:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2995 on theBenchmark for (2995ds/31Mi)
% 2.66/0.76 % (925703)Instruction limit reached!
% 2.66/0.76 % (925703)------------------------------
% 2.66/0.76 % (925703)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.76 % (925703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.76 % (925703)CaDiCaL version: 2.1.3
% 2.66/0.76 % (925703)Termination reason: Instruction limit
% 2.66/0.76 % (925703)Termination phase: Saturation
% 2.66/0.76 % (925703)Time elapsed: 0.036 s
% 2.66/0.76 % (925703)Peak memory usage: 12 MB
% 2.66/0.76 % (925703)Instructions burned: 66 (million)
% 2.66/0.76 % (925705)Instruction limit reached!
% 2.66/0.76 % (925705)------------------------------
% 2.66/0.76 % (925705)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.76 % (925705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.76 % (925705)CaDiCaL version: 2.1.3
% 2.66/0.76 % (925705)Termination reason: Instruction limit
% 2.66/0.76 % (925705)Termination phase: Saturation
% 2.66/0.76 % (925705)Time elapsed: 0.026 s
% 2.66/0.76 % (925705)Peak memory usage: 12 MB
% 2.66/0.76 % (925705)Instructions burned: 51 (million)
% 2.66/0.76 % (925707)Instruction limit reached!
% 2.66/0.76 % (925707)------------------------------
% 2.66/0.76 % (925707)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.76 % (925707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.76 % (925707)CaDiCaL version: 2.1.3
% 2.66/0.76 % (925707)Termination reason: Instruction limit
% 2.66/0.76 % (925707)Termination phase: Saturation
% 2.66/0.76 % (925707)Time elapsed: 0.016 s
% 2.66/0.76 % (925707)Peak memory usage: 12 MB
% 2.66/0.76 % (925707)Instructions burned: 32 (million)
% 2.66/0.76 % (925688) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-925603-925688"...
% 2.66/0.76 % (925699)Instruction limit reached!
% 2.66/0.76 % (925699)------------------------------
% 2.66/0.76 % (925699)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.76 % (925710)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=1800624856:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2995 on theBenchmark for (2995ds/137Mi)
% 2.66/0.76 % (925699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.76 % (925699)CaDiCaL version: 2.1.3
% 2.66/0.76 % (925699)Termination reason: Instruction limit
% 2.66/0.76 % (925699)Termination phase: Saturation
% 2.66/0.76 % (925699)Time elapsed: 0.085 s
% 2.66/0.76 % (925699)Peak memory usage: 12 MB
% 2.66/0.76 % (925699)Instructions burned: 203 (million)
% 2.66/0.76 % (925711)dis+10_2_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_pi_sigma_gen:si=on:sp=occurrence:plsqr=5,1:bsr=on:plsql=on:random_seed=3531952174:cond=on:i=34:hud=10:nm=10:rtra=on_2995 on theBenchmark for (2995ds/34Mi)
% 2.66/0.76 % (925712)lrs+1010_1_sil=128000:hsqc=4:si=on:sos=on:random_seed=3381784959:hsq=on:i=67:hsqaw=5:rtra=on:fe=abstraction:ntd=on_2995 on theBenchmark for (2995ds/67Mi)
% 2.66/0.76 % (925688)...printing done.
% 2.66/0.76 % (925688)Refutation found. Thanks to Tanya!
% 2.66/0.76 % SZS status Theorem for theBenchmark
% 2.66/0.76 % SZS output start Proof for theBenchmark
% See solution above
% 2.66/0.76 % (925688)------------------------------
% 2.66/0.76 % (925688)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.66/0.76 % (925688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.66/0.76 % (925688)CaDiCaL version: 2.1.3
% 2.66/0.76 % (925688)Termination reason: Refutation
% 2.66/0.76 % (925688)Time elapsed: 0.135 s
% 2.66/0.76 % (925688)Peak memory usage: 15 MB
% 2.66/0.76 % (925688)Instructions burned: 239 (million)
% 2.66/0.76 % (925603)Success in time 0.497 s
% 2.66/0.76 % Vampire exiting
%------------------------------------------------------------------------------