%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO474^6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 08:48:04 AM UTC 2026
% Result : Theorem 0.22s 0.34s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 18
% Syntax : Number of formulae : 132 ( 65 unt; 0 typ; 7 def)
% Number of atoms : 872 ( 151 equ; 0 cnn)
% Maximal formula atoms : 17 ( 6 avg)
% Number of connectives : 1351 ( 167 ~; 182 |; 13 &; 868 @)
% ( 6 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 151 ( 151 >; 0 *; 0 +; 0 <<)
% Number of symbols : 70 ( 66 usr; 13 con; 0-4 aty)
% ( 93 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 371 ( 0 sgn 60 !; 0 ?; 371 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
rel_s5: $i > $i > $o ).
thf(func_def_33,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
vNOT: $o > $o ).
thf(func_def_37,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_40,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
vIMP: $o > $o > $o ).
thf(func_def_42,type,
vAND: $o > $o > $o ).
thf(func_def_43,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vOR: $o > $o > $o ).
thf(func_def_46,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_47,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_48,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
sF0: $o ).
thf(func_def_52,type,
sK1: $i > $i ).
thf(func_def_53,type,
sK2: $i > $i ).
thf(func_def_54,type,
sK3: $i > $i ).
thf(func_def_55,type,
sK4: $i > $i ).
thf(func_def_56,type,
sK5: $i > $i ).
thf(func_def_58,type,
sK7: $i > $i ).
thf(func_def_59,type,
sK8: $i > $i ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i,X3: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s5 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s5 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(f33,axiom,
( ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ X0 ) ) ) )
= mdia_s5 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',mdia_s5) ).
thf(f35,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a2) ).
thf(f36,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a3) ).
thf(f37,conjecture,
mvalid @ ( mimplies @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ) ) @ ( mimplies @ ( mdia_s5 @ ( mbox_s5 @ p ) ) @ ( mbox_s5 @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ) ) @ ( mimplies @ ( mdia_s5 @ ( mbox_s5 @ p ) ) @ ( mbox_s5 @ p ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f39,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f40,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f43,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f48,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f49,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f57,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f60,plain,
msymmetric @ rel_s5,
inference(rectify,[],[f36]) ).
thf(f61,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f60]) ).
thf(f66,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
=> ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f67,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f66]) ).
thf(f69,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X1 )
& ( X0 @ X1 @ X3 ) )
=> ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f70,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f76,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f77,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f76]) ).
thf(f83,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s5 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s5 ),
inference(rectify,[],[f32]) ).
thf(f84,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f97,plain,
mtransitive @ rel_s5,
inference(rectify,[],[f35]) ).
thf(f98,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f97]) ).
thf(f99,plain,
~ ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ) ) @ ( mimplies @ ( mdia_s5 @ ( mbox_s5 @ p ) ) @ ( mbox_s5 @ p ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f100,plain,
( ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ) ) @ ( mimplies @ ( mdia_s5 @ ( mbox_s5 @ p ) ) @ ( mbox_s5 @ p ) ) ) )
!= $true ),
inference(fool_elimination,[],[f99]) ).
thf(f101,plain,
( ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ) ) @ ( mimplies @ ( mdia_s5 @ ( mbox_s5 @ p ) ) @ ( mbox_s5 @ p ) ) ) )
!= $true ),
inference(flattening,[],[f100]) ).
thf(f102,plain,
( ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ p ) ) ) @ ( mbox_s5 @ p ) ) ) @ ( mimplies @ ( mdia_s5 @ ( mbox_s5 @ p ) ) @ ( mbox_s5 @ p ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f101]) ).
thf(f106,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f107,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f112,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f61]) ).
thf(f120,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f121,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f57]) ).
thf(f124,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f77]) ).
thf(f131,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f135,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f137,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f138,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f142,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f107,f135,f137]) ).
thf(f150,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f121,f137,f106,f137]) ).
thf(f151,plain,
( ( ^ [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: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ ( ^ [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: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ ( ^ [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 )
@ p
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ p ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ p ) ) )
@ ( ^ [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: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ p ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ p ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f102,f124,f142,f106,f142,f106,f142,f106,f106,f142,f150,f106,f106]) ).
thf(f152,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
@ rel_s5 )
= $true ),
inference(definition_unfolding,[],[f112,f120]) ).
thf(f154,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ rel_s5 )
= $true ),
inference(definition_unfolding,[],[f131,f138]) ).
thf(f155,definition,
( sF0
= ( ^ [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: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ ( ^ [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: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ ( ^ [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 )
@ p
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ p ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ p ) ) )
@ ( ^ [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: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ p ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ p ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f156,plain,
sF0 != $true,
inference(definition_folding,[],[f151,f155]) ).
thf(f157,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y0 @ Y1 )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f158,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y0 @ Y1 )
=> ( rel_s5 @ Y1 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ X1 @ Y0 )
=> ( rel_s5 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( rel_s5 @ X1 @ Y0 )
=> ( rel_s5 @ Y0 @ X1 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel_s5 @ X1 @ X2 )
=> ( rel_s5 @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f162,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ X2 @ X1 )
= $true )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y2 @ Y0 )
& ( rel_s5 @ Y1 @ Y2 ) )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f164,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y2 @ Y0 )
& ( rel_s5 @ Y1 @ Y2 ) )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y1 @ X1 )
& ( rel_s5 @ Y0 @ Y1 ) )
=> ( rel_s5 @ Y0 @ X1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f164]) ).
thf(f166,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y1 @ X1 )
& ( rel_s5 @ Y0 @ Y1 ) )
=> ( rel_s5 @ Y0 @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s5 @ Y0 @ X1 )
& ( rel_s5 @ X2 @ Y0 ) )
=> ( rel_s5 @ X2 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f166]) ).
thf(f168,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s5 @ Y0 @ X1 )
& ( rel_s5 @ X2 @ Y0 ) )
=> ( rel_s5 @ X2 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( rel_s5 @ X3 @ X1 )
& ( rel_s5 @ X2 @ X3 ) )
=> ( rel_s5 @ X2 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f168]) ).
thf(f170,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s5 @ X2 @ X1 )
= $true )
| ( $false
= ( ( rel_s5 @ X3 @ X1 )
& ( rel_s5 @ X2 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X2 @ X3 ) )
| ( ( rel_s5 @ X3 @ X1 )
= $false )
| ( ( rel_s5 @ X2 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( $false
= ( ^ [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: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ ( ^ [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: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ ( ^ [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 )
@ p
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ p ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ p ) ) )
@ ( ^ [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: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ p ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
@ p ) ) ) ) )
| ( sF0 = $true ) ),
inference(iff_proxy_clausification,[],[f155]) ).
thf(f245,plain,
( ( sF0 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( p @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f246,plain,
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( p @ Y2 )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( p @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) )
@ sK6 ) ) ),
inference(sigma_proxy_clausification,[],[f245]) ).
thf(f247,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK6 @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK6 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK6 @ Y0 ) ) ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f246]) ).
thf(f248,plain,
( ( sF0 = $true )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK6 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK6 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f247]) ).
thf(f274,plain,
( ( sF0 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK6 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f248]) ).
thf(f275,plain,
( ( sF0 = $true )
| ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK6 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f248]) ).
thf(f276,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK6 @ Y0 ) ) ) ) )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f275]) ).
thf(f277,plain,
( ( sF0 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK6 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f276]) ).
thf(f278,plain,
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK6 @ Y0 ) )
@ sK9 ) ) ),
inference(sigma_proxy_clausification,[],[f277]) ).
thf(f279,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK9 @ Y0 ) ) )
| ~ ( rel_s5 @ sK6 @ sK9 ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f278]) ).
thf(f280,plain,
( ( $false
= ( ~ ( rel_s5 @ sK6 @ sK9 ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f279]) ).
thf(f281,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK9 @ Y0 ) ) ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f279]) ).
thf(f282,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK9 @ Y0 ) ) )
= $true )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f281]) ).
thf(f283,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK9 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f282]) ).
thf(f284,plain,
! [X1: $i] :
( ( ( ( p @ X1 )
| ~ ( rel_s5 @ sK9 @ X1 ) )
= $true )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f283]) ).
thf(f285,plain,
! [X1: $i] :
( ( ( ~ ( rel_s5 @ sK9 @ X1 ) )
= $true )
| ( ( p @ X1 )
= $true )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f284]) ).
thf(f286,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( $false
= ( rel_s5 @ sK9 @ X1 ) )
| ( ( p @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f285]) ).
thf(f287,plain,
( ( sF0 = $true )
| ( ( rel_s5 @ sK6 @ sK9 )
= $true ) ),
inference(not_proxy_clausification,[],[f280]) ).
thf(f288,plain,
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s5 @ sK6 @ Y0 ) )
@ sK10 ) ) ),
inference(sigma_proxy_clausification,[],[f274]) ).
thf(f289,plain,
( ( $false
= ( ( p @ sK10 )
| ~ ( rel_s5 @ sK6 @ sK10 ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f288]) ).
thf(f290,plain,
( ( $false
= ( ~ ( rel_s5 @ sK6 @ sK10 ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f289]) ).
thf(f291,plain,
( ( sF0 = $true )
| ( $false
= ( p @ sK10 ) ) ),
inference(or_proxy_clausification,[],[f289]) ).
thf(f292,plain,
( ( sF0 = $true )
| ( ( rel_s5 @ sK6 @ sK10 )
= $true ) ),
inference(not_proxy_clausification,[],[f290]) ).
thf(f333,definition,
( spl11_10
<=> ( sF0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl11_10])],[avatar_definition]) ).
thf(f353,definition,
( spl11_15
<=> ! [X1: $i] :
( ( $false
= ( rel_s5 @ sK9 @ X1 ) )
| ( ( p @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl11_15])],[avatar_definition]) ).
thf(f354,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s5 @ sK9 @ X1 ) )
| ( ( p @ X1 )
= $true ) )
| ~ spl11_15 ),
inference(avatar_component_clause,[],[f353]) ).
thf(f355,plain,
( spl11_15
| spl11_10 ),
inference(avatar_split_clause,[],[f286,f333,f353]) ).
thf(f357,definition,
( spl11_16
<=> ( ( rel_s5 @ sK6 @ sK9 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl11_16])],[avatar_definition]) ).
thf(f359,plain,
( ( ( rel_s5 @ sK6 @ sK9 )
= $true )
| ~ spl11_16 ),
inference(avatar_component_clause,[],[f357]) ).
thf(f360,plain,
( spl11_10
| spl11_16 ),
inference(avatar_split_clause,[],[f287,f357,f333]) ).
thf(f362,definition,
( spl11_17
<=> ( $false
= ( p @ sK10 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_17])],[avatar_definition]) ).
thf(f364,plain,
( ( $false
= ( p @ sK10 ) )
| ~ spl11_17 ),
inference(avatar_component_clause,[],[f362]) ).
thf(f365,plain,
( spl11_10
| spl11_17 ),
inference(avatar_split_clause,[],[f291,f362,f333]) ).
thf(f367,definition,
( spl11_18
<=> ( ( rel_s5 @ sK6 @ sK10 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl11_18])],[avatar_definition]) ).
thf(f369,plain,
( ( ( rel_s5 @ sK6 @ sK10 )
= $true )
| ~ spl11_18 ),
inference(avatar_component_clause,[],[f367]) ).
thf(f370,plain,
( spl11_18
| spl11_10 ),
inference(avatar_split_clause,[],[f292,f333,f367]) ).
thf(f371,plain,
~ spl11_10,
inference(avatar_split_clause,[],[f156,f333]) ).
thf(f410,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false = $true )
| ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $true
= ( rel_s5 @ X0 @ X2 ) ) ),
inference(constrained_superposition,[],[f171,f162]) ).
thf(f425,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X0 @ X2 ) )
| ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f410]) ).
thf(f441,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X1 @ sK9 ) )
| ( $false = $true )
| ( $false
= ( rel_s5 @ X1 @ X0 ) )
| ( ( p @ X0 )
= $true ) )
| ~ spl11_15 ),
inference(constrained_superposition,[],[f354,f425]) ).
thf(f448,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X1 @ sK9 ) )
| ( ( p @ X0 )
= $true )
| ( $false
= ( rel_s5 @ X1 @ X0 ) ) )
| ~ spl11_15 ),
inference(trivial_inequality_removal,[],[f441]) ).
thf(f461,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK6 @ X0 ) )
| ( ( p @ X0 )
= $true )
| ( $false = $true ) )
| ~ spl11_15
| ~ spl11_16 ),
inference(constrained_superposition,[],[f448,f359]) ).
thf(f483,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK6 @ X0 ) )
| ( ( p @ X0 )
= $true ) )
| ~ spl11_15
| ~ spl11_16 ),
inference(trivial_inequality_removal,[],[f461]) ).
thf(f492,definition,
( spl11_19
<=> ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK6 @ X0 ) )
| ( ( p @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl11_19])],[avatar_definition]) ).
thf(f493,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK6 @ X0 ) )
| ( ( p @ X0 )
= $true ) )
| ~ spl11_19 ),
inference(avatar_component_clause,[],[f492]) ).
thf(f502,plain,
( spl11_19
| ~ spl11_15
| ~ spl11_16 ),
inference(avatar_split_clause,[],[f483,f357,f353,f492]) ).
thf(f517,plain,
( ( $false = $true )
| ( ( p @ sK10 )
= $true )
| ~ spl11_18
| ~ spl11_19 ),
inference(constrained_superposition,[],[f369,f493]) ).
thf(f532,plain,
( ( ( p @ sK10 )
= $true )
| ~ spl11_18
| ~ spl11_19 ),
inference(trivial_inequality_removal,[],[f517]) ).
thf(f536,plain,
( ( $false = $true )
| ~ spl11_17
| ~ spl11_18
| ~ spl11_19 ),
inference(forward_demodulation,[],[f532,f364]) ).
thf(f537,plain,
( $false
| ~ spl11_17
| ~ spl11_18
| ~ spl11_19 ),
inference(trivial_inequality_removal,[],[f536]) ).
thf(f538,plain,
( ~ spl11_17
| ~ spl11_18
| ~ spl11_19 ),
inference(avatar_contradiction_clause,[],[f537]) ).
cnf(s13,plain,
( spl11_10
| spl11_15 ),
inference(sat_conversion,[],[f355]) ).
cnf(s14,plain,
( spl11_10
| spl11_16 ),
inference(sat_conversion,[],[f360]) ).
cnf(s15,plain,
( spl11_10
| spl11_17 ),
inference(sat_conversion,[],[f365]) ).
cnf(s16,plain,
( spl11_10
| spl11_18 ),
inference(sat_conversion,[],[f370]) ).
cnf(s17,plain,
~ spl11_10,
inference(sat_conversion,[],[f371]) ).
cnf(s20,plain,
( ~ spl11_15
| ~ spl11_16
| spl11_19 ),
inference(sat_conversion,[],[f502]) ).
cnf(s25,plain,
( ~ spl11_17
| ~ spl11_18
| ~ spl11_19 ),
inference(sat_conversion,[],[f538]) ).
cnf(s26,plain,
spl11_18,
inference(rat,[],[s16,s17]) ).
cnf(s27,plain,
spl11_17,
inference(rat,[],[s15,s17]) ).
cnf(s28,plain,
~ spl11_19,
inference(rat,[],[s25,s26,s27]) ).
cnf(s29,plain,
spl11_16,
inference(rat,[],[s14,s17]) ).
cnf(s30,plain,
~ spl11_15,
inference(rat,[],[s20,s28,s29]) ).
cnf(s31,plain,
$false,
inference(rat,[],[s13,s30,s17]) ).
thf(f539,plain,
$false,
inference(avatar_sat_refutation,[],[s31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO474^6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n011.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 17:08:16 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running higher-order theorem proving
% 0.08/0.26 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
% 0.22/0.34 % (371795)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.34 % (371801)lrs+10_16_si=on:nwc=1.5:random_seed=801655641:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.34 % (371800)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2681489974:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.34 % (371801)Instruction limit reached!
% 0.22/0.34 % (371801)------------------------------
% 0.22/0.34 % (371801)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (371801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (371801)CaDiCaL version: 2.1.3
% 0.22/0.34 % (371801)Termination reason: Instruction limit
% 0.22/0.34 % (371801)Termination phase: Saturation
% 0.22/0.34 % (371801)Time elapsed: 0.009 s
% 0.22/0.34 % (371801)Peak memory usage: 12 MB
% 0.22/0.34 % (371801)Instructions burned: 20 (million)
% 0.22/0.34 % (371806)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.34 % (371806)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
% 0.22/0.34 % (371806)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=2592153555:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.34 % (371802)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2276409735:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.34 % (371803)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=3669564529: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)
% 0.22/0.34 % (371804)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3638762541:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.34 % (371805)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1170785223:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.34 % (371802)Instruction limit reached!
% 0.22/0.34 % (371802)------------------------------
% 0.22/0.34 % (371802)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (371802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (371802)CaDiCaL version: 2.1.3
% 0.22/0.34 % (371802)Termination reason: Instruction limit
% 0.22/0.34 % (371802)Termination phase: Property scanning
% 0.22/0.34 % (371802)Time elapsed: 0.003 s
% 0.22/0.34 % (371802)Peak memory usage: 10 MB
% 0.22/0.34 % (371802)Instructions burned: 3 (million)
% 0.22/0.34 % (371806) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-371795-371806"...
% 0.22/0.34 % (371806)...printing done.
% 0.22/0.34 % (371806)Refutation found. Thanks to Tanya!
% 0.22/0.34 % SZS status Theorem for theBenchmark
% 0.22/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.35 % (371806)------------------------------
% 0.22/0.35 % (371806)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.35 % (371806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.35 % (371806)CaDiCaL version: 2.1.3
% 0.22/0.35 % (371806)Termination reason: Refutation
% 0.22/0.35 % (371806)Time elapsed: 0.021 s
% 0.22/0.35 % (371806)Peak memory usage: 13 MB
% 0.22/0.35 % (371806)Instructions burned: 33 (million)
% 0.22/0.35 % (371795)Success in time 0.075 s
% 0.22/0.35 % Vampire exiting
%------------------------------------------------------------------------------