%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO568^7 : 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 : n020.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 08:48:26 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 21
% Syntax : Number of formulae : 191 ( 86 unt; 0 typ; 7 def)
% Number of atoms : 1383 ( 245 equ; 0 cnn)
% Maximal formula atoms : 14 ( 7 avg)
% Number of connectives : 1930 ( 269 ~; 306 |; 13 &;1217 @)
% ( 7 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 131 ( 131 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 62 usr; 14 con; 0-4 aty)
% ( 94 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 372 ( 0 sgn 90 !; 0 ?; 372 :)
% 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,
f: mu > $i > $o ).
thf(func_def_37,type,
a: mu ).
thf(func_def_40,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_44,type,
vNOT: $o > $o ).
thf(func_def_45,type,
vIMP: $o > $o > $o ).
thf(func_def_46,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_48,type,
vAND: $o > $o > $o ).
thf(func_def_49,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vOR: $o > $o > $o ).
thf(func_def_51,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_52,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
sK0: $i > mu ).
thf(f2,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mnot) ).
thf(f3,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mor) ).
thf(f8,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
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(f11,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) )
= mequiv ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mequiv) ).
thf(f15,axiom,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mforall_ind) ).
thf(f18,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mreflexive) ).
thf(f21,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X3: $i,X2: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) )
= mtransitive ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mtransitive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
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(f37,axiom,
! [X0: $i] : ( exists_in_world @ a @ X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_a_ax) ).
thf(f38,conjecture,
( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [X0: mu] : ( mor @ ( mbox_s4 @ ( f @ X0 ) ) @ ( mbox_s4 @ ( mnot @ ( f @ X0 ) ) ) ) )
@ ( mbox_s4 @ ( mequiv @ ( mbox_s4 @ ( f @ a ) ) @ ( f @ a ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f39,negated_conjecture,
~ ( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [X0: mu] : ( mor @ ( mbox_s4 @ ( f @ X0 ) ) @ ( mbox_s4 @ ( mnot @ ( f @ X0 ) ) ) ) )
@ ( mbox_s4 @ ( mequiv @ ( mbox_s4 @ ( f @ a ) ) @ ( f @ a ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
thf(f40,plain,
! [X0: $i] : ( exists_in_world @ a @ X0 ),
inference(rectify,[],[f37]) ).
thf(f41,plain,
! [X0: $i] :
( ( exists_in_world @ a @ X0 )
= $true ),
inference(fool_elimination,[],[f40]) ).
thf(f42,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f43,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f49,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f53,plain,
~ ( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [X0: mu] : ( mor @ ( mbox_s4 @ ( f @ X0 ) ) @ ( mbox_s4 @ ( mnot @ ( f @ X0 ) ) ) ) )
@ ( mbox_s4 @ ( mequiv @ ( mbox_s4 @ ( f @ a ) ) @ ( f @ a ) ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f54,plain,
( $true
!= ( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [Y0: mu] : ( mor @ ( mbox_s4 @ ( f @ Y0 ) ) @ ( mbox_s4 @ ( mnot @ ( f @ Y0 ) ) ) ) )
@ ( mbox_s4 @ ( mequiv @ ( mbox_s4 @ ( f @ a ) ) @ ( f @ a ) ) ) ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f57,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
inference(rectify,[],[f18]) ).
thf(f58,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f68,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f69,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f70,plain,
mtransitive @ rel_s4,
inference(rectify,[],[f35]) ).
thf(f71,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f70]) ).
thf(f74,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f76,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f77,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f78,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f77]) ).
thf(f83,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f84,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f94,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X3 @ X2 ) )
=> ( X0 @ X1 @ X2 ) ) )
= mtransitive ),
inference(rectify,[],[f21]) ).
thf(f95,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f94]) ).
thf(f98,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f2]) ).
thf(f99,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f98]) ).
thf(f103,plain,
mreflexive @ rel_s4,
inference(rectify,[],[f34]) ).
thf(f104,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f103]) ).
thf(f105,plain,
( $true
!= ( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [Y0: mu] : ( mor @ ( mbox_s4 @ ( f @ Y0 ) ) @ ( mbox_s4 @ ( mnot @ ( f @ Y0 ) ) ) ) )
@ ( mbox_s4 @ ( mequiv @ ( mbox_s4 @ ( f @ a ) ) @ ( f @ a ) ) ) ) ) ),
inference(flattening,[],[f54]) ).
thf(f112,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f99]) ).
thf(f120,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f122,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f127,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f95]) ).
thf(f131,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f76]) ).
thf(f132,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f104]) ).
thf(f133,plain,
! [X0: $i] :
( ( exists_in_world @ a @ X0 )
= $true ),
inference(cnf_transformation,[],[f41]) ).
thf(f134,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f135,plain,
( $true
!= ( mvalid
@ ( mimplies
@ ( mforall_ind
@ ^ [Y0: mu] : ( mor @ ( mbox_s4 @ ( f @ Y0 ) ) @ ( mbox_s4 @ ( mnot @ ( f @ Y0 ) ) ) ) )
@ ( mbox_s4 @ ( mequiv @ ( mbox_s4 @ ( f @ a ) ) @ ( f @ a ) ) ) ) ) ),
inference(cnf_transformation,[],[f105]) ).
thf(f140,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f143,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f78]) ).
thf(f144,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f145,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f71]) ).
thf(f147,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f151,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f147,f112,f134,f112,f112]) ).
thf(f152,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f120,f134,f112]) ).
thf(f154,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f131,f151,f152,f152]) ).
thf(f160,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f132,f122]) ).
thf(f161,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [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] :
( ( Y1 @ Y3 )
| ( Y2 @ Y3 ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( f @ Y0 ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( f @ Y0 ) ) ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( f @ a ) )
@ ( f @ a ) ) ) ) ) ),
inference(definition_unfolding,[],[f135,f144,f152,f143,f134,f140,f140,f112,f140,f154,f140]) ).
thf(f162,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f145,f127]) ).
thf(f163,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ Y1 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( f @ Y1 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ a @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( f @ a @ Y1 ) )
| ~ ( ~ ( f @ a @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ a @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f164,plain,
( ( ^ [Y0: $i] :
( ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ Y1 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( f @ Y1 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ a @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( f @ a @ Y1 ) )
| ~ ( ~ ( f @ a @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( f @ a @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ Y0 @ Y1 )
| ~ ( rel_s4 @ sK1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( f @ Y0 @ Y1 )
| ~ ( rel_s4 @ sK1 @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ a @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( f @ a @ Y0 ) )
| ~ ( ~ ( f @ a @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ a @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f164]) ).
thf(f166,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ a @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( f @ a @ Y0 ) )
| ~ ( ~ ( f @ a @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ a @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
= $false ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f167,plain,
( ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ Y0 @ Y1 )
| ~ ( rel_s4 @ sK1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( f @ Y0 @ Y1 )
| ~ ( rel_s4 @ sK1 @ Y1 ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f168,plain,
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ Y0 @ Y1 )
| ~ ( rel_s4 @ sK1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( f @ Y0 @ Y1 )
| ~ ( rel_s4 @ sK1 @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X1: mu] :
( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ Y0 @ Y1 )
| ~ ( rel_s4 @ sK1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( f @ Y0 @ Y1 )
| ~ ( rel_s4 @ sK1 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X1: mu] :
( ( ( exists_in_world @ X1 @ sK1 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ X1 @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( f @ X1 @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f171,plain,
! [X1: mu] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ X1 @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( f @ X1 @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) )
= $true )
| ( ( exists_in_world @ X1 @ sK1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X1: mu] :
( ( ( exists_in_world @ X1 @ sK1 )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( f @ X1 @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ X1 @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X2: $i,X1: mu] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ X1 @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
= $true )
| ( ( exists_in_world @ X1 @ sK1 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( f @ X1 @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X2: $i,X3: $i,X1: mu] :
( ( $true
= ( ^ [Y0: $i] :
( ( f @ X1 @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ X3 ) )
| ( ( ^ [Y0: $i] :
( ~ ( f @ X1 @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ X2 )
= $true )
| ( ( exists_in_world @ X1 @ sK1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X2: $i,X3: $i,X1: mu] :
( ( ( exists_in_world @ X1 @ sK1 )
= $false )
| ( $true
= ( ( f @ X1 @ X3 )
| ~ ( rel_s4 @ sK1 @ X3 ) ) )
| ( ( ~ ( f @ X1 @ X2 )
| ~ ( rel_s4 @ sK1 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
! [X2: $i,X3: $i,X1: mu] :
( ( ( ~ ( f @ X1 @ X2 )
| ~ ( rel_s4 @ sK1 @ X2 ) )
= $true )
| ( ( exists_in_world @ X1 @ sK1 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X3 ) ) )
| ( $true
= ( f @ X1 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X2: $i,X3: $i,X1: mu] :
( ( $true
= ( ~ ( rel_s4 @ sK1 @ X3 ) ) )
| ( ( ~ ( rel_s4 @ sK1 @ X2 ) )
= $true )
| ( ( ~ ( f @ X1 @ X2 ) )
= $true )
| ( ( exists_in_world @ X1 @ sK1 )
= $false )
| ( $true
= ( f @ X1 @ X3 ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X2: $i,X3: $i,X1: mu] :
( ( $true
= ( f @ X1 @ X3 ) )
| ( ( ~ ( f @ X1 @ X2 ) )
= $true )
| ( ( ~ ( rel_s4 @ sK1 @ X2 ) )
= $true )
| ( ( rel_s4 @ sK1 @ X3 )
= $false )
| ( ( exists_in_world @ X1 @ sK1 )
= $false ) ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X2: $i,X3: $i,X1: mu] :
( ( ( f @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ X1 @ sK1 )
= $false )
| ( ( rel_s4 @ sK1 @ X3 )
= $false )
| ( $true
= ( f @ X1 @ X3 ) )
| ( ( ~ ( rel_s4 @ sK1 @ X2 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X2: $i,X3: $i,X1: mu] :
( ( $true
= ( f @ X1 @ X3 ) )
| ( ( f @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ X1 @ sK1 )
= $false )
| ( ( rel_s4 @ sK1 @ X2 )
= $false )
| ( ( rel_s4 @ sK1 @ X3 )
= $false ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ a @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( f @ a @ Y0 ) )
| ~ ( ~ ( f @ a @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( f @ a @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f166]) ).
thf(f182,plain,
( ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ( f @ a @ sK2 ) )
| ~ ( ~ ( f @ a @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) ) )
| ~ ( rel_s4 @ sK1 @ sK2 ) )
= $false ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f183,plain,
( ( ~ ( rel_s4 @ sK1 @ sK2 ) )
= $false ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f184,plain,
( ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ( f @ a @ sK2 ) )
| ~ ( ~ ( f @ a @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f185,plain,
( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ( f @ a @ sK2 ) )
| ~ ( ~ ( f @ a @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f186,plain,
( ( $true
= ( ~ ( ~ ( f @ a @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) ) ) )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ( f @ a @ sK2 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f185]) ).
thf(f187,plain,
( ( ( ~ ( f @ a @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ( f @ a @ sK2 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f186]) ).
thf(f188,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
= $false )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ( f @ a @ sK2 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f187]) ).
thf(f189,plain,
( ( ( ~ ( f @ a @ sK2 ) )
= $false )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ( f @ a @ sK2 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f187]) ).
thf(f190,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ( f @ a @ sK2 ) ) )
= $true )
| ( $true
= ( f @ a @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f191,plain,
( ( $true
= ( f @ a @ sK2 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ( f @ a @ sK2 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f193,plain,
( ( $true
= ( f @ a @ sK2 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f191]) ).
thf(f194,plain,
( ( $true
= ( f @ a @ sK2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X1: $i] :
( ( $true
= ( f @ a @ sK2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X1: $i] :
( ( $true
= ( f @ a @ sK2 ) )
| ( $true
= ( ( f @ a @ X1 )
| ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f195]) ).
thf(f197,plain,
! [X1: $i] :
( ( ( f @ a @ X1 )
= $true )
| ( ( ~ ( rel_s4 @ sK2 @ X1 ) )
= $true )
| ( $true
= ( f @ a @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X1: $i] :
( ( ( f @ a @ X1 )
= $true )
| ( $true
= ( f @ a @ sK2 ) )
| ( ( rel_s4 @ sK2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f197]) ).
thf(f199,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ( f @ a @ sK2 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) )
@ sK3 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f188]) ).
thf(f200,plain,
( ( ( ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) )
@ sK3 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ( f @ a @ sK2 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f199]) ).
thf(f201,plain,
( ( ( ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) )
@ sK3 )
= $false )
| ( ( f @ a @ sK2 )
= $false ) ),
inference(or_proxy_clausification,[],[f200]) ).
thf(f202,plain,
( ( ( ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) )
@ sK3 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f200]) ).
thf(f203,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) )
@ sK3 )
= $false ) ),
inference(not_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) )
@ sK3 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( f @ a @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X1: $i] :
( ( $false
= ( ( f @ a @ sK3 )
| ~ ( rel_s4 @ sK2 @ sK3 ) ) )
| ( $true
= ( ( f @ a @ X1 )
| ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f204]) ).
thf(f206,plain,
! [X1: $i] :
( ( $true
= ( ( f @ a @ X1 )
| ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( ( ~ ( rel_s4 @ sK2 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X1: $i] :
( ( ( f @ a @ sK3 )
= $false )
| ( $true
= ( ( f @ a @ X1 )
| ~ ( rel_s4 @ sK2 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f205]) ).
thf(f208,plain,
! [X1: $i] :
( ( ( f @ a @ X1 )
= $true )
| ( ( f @ a @ sK3 )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X1: $i] :
( ( ( f @ a @ X1 )
= $true )
| ( ( f @ a @ sK3 )
= $false )
| ( ( rel_s4 @ sK2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f208]) ).
thf(f210,plain,
! [X1: $i] :
( ( ( ~ ( rel_s4 @ sK2 @ sK3 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK2 @ X1 ) )
= $true )
| ( ( f @ a @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f206]) ).
thf(f211,plain,
! [X1: $i] :
( ( ( ~ ( rel_s4 @ sK2 @ X1 ) )
= $true )
| ( $true
= ( rel_s4 @ sK2 @ sK3 ) )
| ( ( f @ a @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f210]) ).
thf(f212,plain,
! [X1: $i] :
( ( ( rel_s4 @ sK2 @ X1 )
= $false )
| ( $true
= ( rel_s4 @ sK2 @ sK3 ) )
| ( ( f @ a @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f211]) ).
thf(f213,plain,
( ( ( f @ a @ sK2 )
= $false )
| ( $false
= ( ( f @ a @ sK3 )
| ~ ( rel_s4 @ sK2 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f201]) ).
thf(f214,plain,
( ( ( ~ ( rel_s4 @ sK2 @ sK3 ) )
= $false )
| ( ( f @ a @ sK2 )
= $false ) ),
inference(or_proxy_clausification,[],[f213]) ).
thf(f215,plain,
( ( ( f @ a @ sK2 )
= $false )
| ( ( f @ a @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f213]) ).
thf(f216,plain,
( ( ( f @ a @ sK2 )
= $false )
| ( $true
= ( rel_s4 @ sK2 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f214]) ).
thf(f217,plain,
( ( rel_s4 @ sK1 @ sK2 )
= $true ),
inference(not_proxy_clausification,[],[f183]) ).
thf(f218,plain,
( ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) )
= $true ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f219,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f218]) ).
thf(f220,plain,
! [X1: $i] :
( ( rel_s4 @ X1 @ X1 )
= $true ),
inference(beta-eta_normalization,[],[f219]) ).
thf(f221,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y0 @ Y1 )
& ( rel_s4 @ Y2 @ Y0 ) )
=> ( rel_s4 @ Y2 @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f222,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y0 @ Y1 )
& ( rel_s4 @ Y2 @ Y0 ) )
=> ( rel_s4 @ Y2 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f221]) ).
thf(f223,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ X1 @ Y0 )
& ( rel_s4 @ Y1 @ X1 ) )
=> ( rel_s4 @ Y1 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f222]) ).
thf(f224,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ X1 @ Y0 )
& ( rel_s4 @ Y1 @ X1 ) )
=> ( rel_s4 @ Y1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f223]) ).
thf(f225,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s4 @ X1 @ X2 )
& ( rel_s4 @ Y0 @ X1 ) )
=> ( rel_s4 @ Y0 @ X2 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f224]) ).
thf(f226,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( rel_s4 @ X1 @ X2 )
& ( rel_s4 @ Y0 @ X1 ) )
=> ( rel_s4 @ Y0 @ X2 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s4 @ X1 @ X2 )
& ( rel_s4 @ X3 @ X1 ) )
=> ( rel_s4 @ X3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f226]) ).
thf(f228,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_s4 @ X3 @ X2 ) )
| ( ( ( rel_s4 @ X1 @ X2 )
& ( rel_s4 @ X3 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s4 @ X3 @ X1 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( rel_s4 @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f228]) ).
thf(f231,definition,
( spl4_1
<=> ( $true
= ( f @ a @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f233,plain,
( ( $true
= ( f @ a @ sK2 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f231]) ).
thf(f235,definition,
( spl4_2
<=> ! [X1: $i] :
( ( ( f @ a @ X1 )
= $true )
| ( ( rel_s4 @ sK2 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f236,plain,
( ! [X1: $i] :
( ( ( f @ a @ X1 )
= $true )
| ( ( rel_s4 @ sK2 @ X1 )
= $false ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f235]) ).
thf(f237,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f198,f235,f231]) ).
thf(f239,definition,
( spl4_3
<=> ( ( f @ a @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f241,plain,
( ( ( f @ a @ sK3 )
= $false )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f239]) ).
thf(f242,plain,
( spl4_2
| spl4_3 ),
inference(avatar_split_clause,[],[f209,f239,f235]) ).
thf(f244,definition,
( spl4_4
<=> ( $true
= ( rel_s4 @ sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f246,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK3 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f244]) ).
thf(f247,plain,
( spl4_2
| spl4_4 ),
inference(avatar_split_clause,[],[f212,f244,f235]) ).
thf(f249,definition,
( spl4_5
<=> ( ( f @ a @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f251,plain,
( ( ( f @ a @ sK2 )
= $false )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f249]) ).
thf(f252,plain,
( spl4_3
| spl4_5 ),
inference(avatar_split_clause,[],[f215,f249,f239]) ).
thf(f253,plain,
( spl4_5
| spl4_4 ),
inference(avatar_split_clause,[],[f216,f244,f249]) ).
thf(f274,definition,
( spl4_7
<=> ( ( rel_s4 @ sK1 @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
thf(f276,plain,
( ( ( rel_s4 @ sK1 @ sK3 )
= $false )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f274]) ).
thf(f280,plain,
( ( $true = $false )
| ( ( rel_s4 @ sK2 @ sK3 )
= $false )
| ~ spl4_2
| ~ spl4_3 ),
inference(constrained_superposition,[],[f236,f241]) ).
thf(f286,plain,
( ( ( rel_s4 @ sK2 @ sK3 )
= $false )
| ~ spl4_2
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f280]) ).
thf(f294,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_4 ),
inference(forward_demodulation,[],[f286,f246]) ).
thf(f295,plain,
( $false
| ~ spl4_2
| ~ spl4_3
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f294]) ).
thf(f296,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f295]) ).
thf(f298,definition,
( spl4_8
<=> ! [X1: $i] :
( ( ( rel_s4 @ sK1 @ X1 )
= $false )
| ( ( f @ a @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
thf(f299,plain,
( ! [X1: $i] :
( ( ( f @ a @ X1 )
= $true )
| ( ( rel_s4 @ sK1 @ X1 )
= $false ) )
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f298]) ).
thf(f306,plain,
( ! [X0: $i] :
( ( ( exists_in_world @ a @ sK1 )
= $false )
| ( $true = $false )
| ( ( rel_s4 @ sK1 @ X0 )
= $false )
| ( ( rel_s4 @ sK1 @ sK2 )
= $false )
| ( ( f @ a @ X0 )
= $true ) )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f180,f233]) ).
thf(f307,plain,
( ! [X0: $i] :
( ( ( rel_s4 @ sK1 @ sK2 )
= $false )
| ( ( f @ a @ X0 )
= $true )
| ( ( exists_in_world @ a @ sK1 )
= $false )
| ( ( rel_s4 @ sK1 @ X0 )
= $false ) )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f306]) ).
thf(f309,plain,
( ! [X0: $i] :
( ( ( f @ a @ X0 )
= $true )
| ( $true = $false )
| ( ( exists_in_world @ a @ sK1 )
= $false )
| ( ( rel_s4 @ sK1 @ X0 )
= $false ) )
| ~ spl4_1 ),
inference(forward_demodulation,[],[f307,f217]) ).
thf(f310,plain,
( ! [X0: $i] :
( ( ( rel_s4 @ sK1 @ X0 )
= $false )
| ( ( f @ a @ X0 )
= $true )
| ( ( exists_in_world @ a @ sK1 )
= $false ) )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f309]) ).
thf(f313,plain,
( ! [X0: $i] :
( ( ( f @ a @ X0 )
= $true )
| ( $true = $false )
| ( ( rel_s4 @ sK1 @ X0 )
= $false ) )
| ~ spl4_1 ),
inference(forward_demodulation,[],[f310,f133]) ).
thf(f314,plain,
( ! [X0: $i] :
( ( ( rel_s4 @ sK1 @ X0 )
= $false )
| ( ( f @ a @ X0 )
= $true ) )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f313]) ).
thf(f317,plain,
( spl4_8
| ~ spl4_1 ),
inference(avatar_split_clause,[],[f314,f231,f298]) ).
thf(f321,plain,
( ( $true = $false )
| ( ( rel_s4 @ sK1 @ sK3 )
= $false )
| ~ spl4_3
| ~ spl4_8 ),
inference(constrained_superposition,[],[f241,f299]) ).
thf(f322,plain,
( ( ( rel_s4 @ sK1 @ sK3 )
= $false )
| ~ spl4_3
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f321]) ).
thf(f328,plain,
( spl4_7
| ~ spl4_3
| ~ spl4_8 ),
inference(avatar_split_clause,[],[f322,f298,f239,f274]) ).
thf(f369,plain,
( ( ( rel_s4 @ sK2 @ sK2 )
= $false )
| ( $true = $false )
| ~ spl4_2
| ~ spl4_5 ),
inference(constrained_superposition,[],[f236,f251]) ).
thf(f380,plain,
( ( ( rel_s4 @ sK2 @ sK2 )
= $false )
| ~ spl4_2
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f369]) ).
thf(f385,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_5 ),
inference(forward_demodulation,[],[f380,f220]) ).
thf(f386,plain,
( $false
| ~ spl4_2
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f385]) ).
thf(f387,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f386]) ).
thf(f477,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( rel_s4 @ X0 @ sK2 )
= $false )
| ( $true
= ( rel_s4 @ X0 @ sK3 ) ) )
| ~ spl4_4 ),
inference(constrained_superposition,[],[f229,f246]) ).
thf(f504,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s4 @ X0 @ sK3 ) )
| ( ( rel_s4 @ X0 @ sK2 )
= $false ) )
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f477]) ).
thf(f538,plain,
( ( $true = $false )
| ( ( rel_s4 @ sK1 @ sK2 )
= $false )
| ~ spl4_4
| ~ spl4_7 ),
inference(constrained_superposition,[],[f276,f504]) ).
thf(f549,plain,
( ( ( rel_s4 @ sK1 @ sK2 )
= $false )
| ~ spl4_4
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f538]) ).
thf(f555,plain,
( ( $true = $false )
| ~ spl4_4
| ~ spl4_7 ),
inference(forward_demodulation,[],[f549,f217]) ).
thf(f556,plain,
( $false
| ~ spl4_4
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f555]) ).
thf(f557,plain,
( ~ spl4_4
| ~ spl4_7 ),
inference(avatar_contradiction_clause,[],[f556]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f237]) ).
cnf(s2,plain,
( spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f242]) ).
cnf(s3,plain,
( spl4_2
| spl4_4 ),
inference(sat_conversion,[],[f247]) ).
cnf(s4,plain,
( spl4_3
| spl4_5 ),
inference(sat_conversion,[],[f252]) ).
cnf(s5,plain,
( spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f253]) ).
cnf(s9,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f296]) ).
cnf(s12,plain,
( ~ spl4_1
| spl4_8 ),
inference(sat_conversion,[],[f317]) ).
cnf(s14,plain,
( ~ spl4_3
| spl4_7
| ~ spl4_8 ),
inference(sat_conversion,[],[f328]) ).
cnf(s20,plain,
( ~ spl4_2
| ~ spl4_5 ),
inference(sat_conversion,[],[f387]) ).
cnf(s31,plain,
( ~ spl4_4
| ~ spl4_7 ),
inference(sat_conversion,[],[f557]) ).
cnf(s34,plain,
~ spl4_2,
inference(rat,[],[s9,s4,s5,s20]) ).
cnf(s35,plain,
spl4_4,
inference(rat,[],[s3,s34]) ).
cnf(s36,plain,
spl4_3,
inference(rat,[],[s2,s34]) ).
cnf(s37,plain,
spl4_1,
inference(rat,[],[s1,s34]) ).
cnf(s38,plain,
~ spl4_7,
inference(rat,[],[s31,s35]) ).
cnf(s41,plain,
spl4_8,
inference(rat,[],[s12,s37]) ).
cnf(s42,plain,
$false,
inference(rat,[],[s14,s36,s41,s38]) ).
thf(f558,plain,
$false,
inference(avatar_sat_refutation,[],[s42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO568^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n020.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 17:16:05 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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
% 0.21/0.29 % (1343926)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (1343944)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2119709371:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (1343951)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.29 % (1343951)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.29 % (1343945)lrs+10_16_si=on:nwc=1.5:random_seed=432887954:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (1343944) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1343926-1343944"...
% 0.21/0.29 % (1343946)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1735243203:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (1343950)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2610009387:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (1343947)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=813354008:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.29 % (1343948)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1307537202:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (1343951)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=611769258:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (1343946)Instruction limit reached!
% 0.21/0.29 % (1343946)------------------------------
% 0.21/0.29 % (1343946)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (1343946)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (1343946)CaDiCaL version: 2.1.3
% 0.21/0.29 % (1343946)Termination reason: Instruction limit
% 0.21/0.29 % (1343946)Termination phase: Property scanning
% 0.21/0.29 % (1343946)Time elapsed: 0.002 s
% 0.21/0.29 % (1343946)Peak memory usage: 10 MB
% 0.21/0.29 % (1343946)Instructions burned: 4 (million)
% 0.21/0.29 % (1343944)...printing done.
% 0.21/0.29 % (1343944)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.30 % (1343944)------------------------------
% 0.21/0.30 % (1343944)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (1343944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (1343944)CaDiCaL version: 2.1.3
% 0.21/0.30 % (1343944)Termination reason: Refutation
% 0.21/0.30 % (1343944)Time elapsed: 0.011 s
% 0.21/0.30 % (1343944)Peak memory usage: 13 MB
% 0.21/0.30 % (1343944)Instructions burned: 39 (million)
% 0.21/0.30 % (1343926)Success in time 0.047 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------