%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO451^6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:47:46 AM UTC 2026
% Result : Theorem 0.27s 0.35s
% Output : Refutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 18
% Syntax : Number of formulae : 153 ( 66 unt; 0 typ; 7 def)
% Number of atoms : 1093 ( 216 equ; 0 cnn)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 1467 ( 210 ~; 257 |; 13 &; 878 @)
% ( 6 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 138 ( 138 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 62 usr; 12 con; 0-4 aty)
% ( 81 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 351 ( 0 sgn 67 !; 0 ?; 351 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
rel_s5: $i > $i > $o ).
thf(func_def_33,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
q: $i > $o ).
thf(func_def_37,type,
vNOT: $o > $o ).
thf(func_def_38,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_41,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vIMP: $o > $o > $o ).
thf(func_def_46,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_47,type,
vOR: $o > $o > $o ).
thf(func_def_48,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_50,type,
vAND: $o > $o > $o ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
sF0: $o ).
thf(func_def_54,type,
sK2: $i > $i ).
thf(func_def_56,type,
sK4: $i > $i ).
thf(func_def_57,type,
sK5: $i > $i ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i,X3: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_s5
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(f33,axiom,
( mdia_s5
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mdia_s5) ).
thf(f35,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',a2) ).
thf(f36,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',a3) ).
thf(f37,conjecture,
mvalid @ ( mimplies @ ( mbox_s5 @ ( mor @ p @ ( mdia_s5 @ q ) ) ) @ ( mor @ ( mbox_s5 @ p ) @ ( mdia_s5 @ q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mor @ p @ ( mdia_s5 @ q ) ) ) @ ( mor @ ( mbox_s5 @ p ) @ ( mdia_s5 @ q ) ) ) ),
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(f44,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f45,plain,
msymmetric @ rel_s5,
inference(rectify,[],[f36]) ).
thf(f46,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f45]) ).
thf(f48,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f49,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f53,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f59,plain,
~ ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mor @ p @ ( mdia_s5 @ q ) ) ) @ ( mor @ ( mbox_s5 @ p ) @ ( mdia_s5 @ q ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f60,plain,
( ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mor @ p @ ( mdia_s5 @ q ) ) ) @ ( mor @ ( mbox_s5 @ p ) @ ( mdia_s5 @ q ) ) ) )
!= $true ),
inference(fool_elimination,[],[f59]) ).
thf(f62,plain,
( mbox_s5
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f63,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f74,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f75,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f74]) ).
thf(f80,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f81,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f80]) ).
thf(f84,plain,
mtransitive @ rel_s5,
inference(rectify,[],[f35]) ).
thf(f85,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f84]) ).
thf(f91,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(f92,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,[],[f91]) ).
thf(f101,plain,
( ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mor @ p @ ( mdia_s5 @ q ) ) ) @ ( mor @ ( mbox_s5 @ p ) @ ( mdia_s5 @ q ) ) ) )
!= $true ),
inference(flattening,[],[f60]) ).
thf(f105,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f46]) ).
thf(f108,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f109,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f110,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,[],[f92]) ).
thf(f111,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f114,plain,
( ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mor @ p @ ( mdia_s5 @ q ) ) ) @ ( mor @ ( mbox_s5 @ p ) @ ( mdia_s5 @ q ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f101]) ).
thf(f121,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f122,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f123,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f129,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f85]) ).
thf(f132,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f81]) ).
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,[],[f111,f108,f122]) ).
thf(f150,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f121,f122,f109,f122]) ).
thf(f151,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f105,f123]) ).
thf(f152,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] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ p
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ q ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ q ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f114,f132,f142,f109,f108,f150,f108,f109,f150]) ).
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,[],[f129,f110]) ).
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] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ p
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ q ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ q ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f156,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] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ p
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ q ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ q ) ) ) )
= sF0 ),
inference(reorient_equations,[],[f155]) ).
thf(f157,plain,
sF0 != $true,
inference(definition_folding,[],[f152,f156]) ).
thf(f159,plain,
( ( sF0 = $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: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ p
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ q ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ q ) ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f156]) ).
thf(f160,plain,
( ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( q @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( q @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( sF0 = $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
= $false )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f165,plain,
( ( sF0 = $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( ~ ( rel_s5 @ sK1 @ X1 )
| ( p @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( ( p @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
= $true )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
= $true )
| ( sF0 = $true )
| ( ( p @ X1 )
= $true )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( sF0 = $true )
| ( ( p @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( p @ X1 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( ( rel_s5 @ sK1 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( p @ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) )
@ ( sK2 @ X1 ) )
= $false )
| ( ( rel_s5 @ sK1 @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X1: $i] :
( ( ( ~ ( rel_s5 @ X1 @ ( sK2 @ X1 ) )
| ~ ( q @ ( sK2 @ X1 ) ) )
= $false )
| ( sF0 = $true )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( p @ X1 )
= $true ) ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f174,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( ~ ( q @ ( sK2 @ X1 ) ) )
= $false )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( p @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X1: $i] :
( ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_s5 @ X1 @ ( sK2 @ X1 ) ) )
= $false )
| ( sF0 = $true )
| ( ( rel_s5 @ sK1 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f176,plain,
! [X1: $i] :
( ( ( p @ X1 )
= $true )
| ( ( rel_s5 @ X1 @ ( sK2 @ X1 ) )
= $true )
| ( sF0 = $true )
| ( ( rel_s5 @ sK1 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( ( ( p @ X1 )
= $true )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( sF0 = $true )
| ( ( q @ ( sK2 @ X1 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f178,plain,
( ( sF0 = $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f179,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f180,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ sK3 )
= $false )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( $false
= ( ~ ( rel_s5 @ sK1 @ sK3 )
| ( p @ sK3 ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f182,plain,
( ( $false
= ( p @ sK3 ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f183,plain,
( ( $false
= ( ~ ( rel_s5 @ sK1 @ sK3 ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f184,plain,
( ( sF0 = $true )
| ( ( rel_s5 @ sK1 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f183]) ).
thf(f185,plain,
( ( sF0 = $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f186,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ~ ( q @ Y0 ) )
@ X1 ) )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ~ ( q @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f186]) ).
thf(f188,plain,
! [X1: $i] :
( ( $true
= ( ~ ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( ( q @ X1 )
= $false )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( q @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f241,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f242,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f241]) ).
thf(f243,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f242]) ).
thf(f244,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f243]) ).
thf(f245,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ X2 @ X1 )
=> ( rel_s5 @ X1 @ X2 ) )
= $true ),
inference(beta-eta_normalization,[],[f244]) ).
thf(f246,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ X2 @ X1 )
= $false )
| ( ( rel_s5 @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f245]) ).
thf(f250,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(f251,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,[],[f250]) ).
thf(f252,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y1 @ X1 )
& ( rel_s5 @ Y0 @ Y1 ) )
=> ( rel_s5 @ Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f251]) ).
thf(f253,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y1 @ X1 )
& ( rel_s5 @ Y0 @ Y1 ) )
=> ( rel_s5 @ Y0 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f252]) ).
thf(f254,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,[],[f253]) ).
thf(f255,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,[],[f254]) ).
thf(f256,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( rel_s5 @ X3 @ X1 )
& ( rel_s5 @ X2 @ X3 ) )
=> ( rel_s5 @ X2 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f255]) ).
thf(f257,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( rel_s5 @ X3 @ X1 )
& ( rel_s5 @ X2 @ X3 ) ) )
| ( ( rel_s5 @ X2 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f256]) ).
thf(f258,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s5 @ X3 @ X1 )
= $false )
| ( ( rel_s5 @ X2 @ X1 )
= $true )
| ( ( rel_s5 @ X2 @ X3 )
= $false ) ),
inference(and_proxy_clausification,[],[f257]) ).
thf(f260,definition,
( spl6_1
<=> ! [X1: $i] :
( ( ( p @ X1 )
= $true )
| ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( rel_s5 @ X1 @ ( sK2 @ X1 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f261,plain,
( ! [X1: $i] :
( ( ( rel_s5 @ X1 @ ( sK2 @ X1 ) )
= $true )
| ( ( p @ X1 )
= $true )
| ( ( rel_s5 @ sK1 @ X1 )
= $false ) )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f260]) ).
thf(f263,definition,
( spl6_2
<=> ( sF0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f266,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f176,f263,f260]) ).
thf(f268,definition,
( spl6_3
<=> ! [X1: $i] :
( ( ( p @ X1 )
= $true )
| ( ( q @ ( sK2 @ X1 ) )
= $true )
| ( ( rel_s5 @ sK1 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
thf(f269,plain,
( ! [X1: $i] :
( ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( q @ ( sK2 @ X1 ) )
= $true ) )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f268]) ).
thf(f270,plain,
( spl6_2
| spl6_3 ),
inference(avatar_split_clause,[],[f177,f268,f263]) ).
thf(f272,definition,
( spl6_4
<=> ( ( rel_s5 @ sK1 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
thf(f274,plain,
( ( ( rel_s5 @ sK1 @ sK3 )
= $true )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f272]) ).
thf(f275,plain,
( spl6_2
| spl6_4 ),
inference(avatar_split_clause,[],[f184,f272,f263]) ).
thf(f277,definition,
( spl6_5
<=> ( $false
= ( p @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
thf(f279,plain,
( ( $false
= ( p @ sK3 ) )
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f277]) ).
thf(f280,plain,
( spl6_2
| spl6_5 ),
inference(avatar_split_clause,[],[f182,f277,f263]) ).
thf(f282,definition,
( spl6_6
<=> ! [X1: $i] :
( ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( q @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
thf(f283,plain,
( ! [X1: $i] :
( ( ( rel_s5 @ sK1 @ X1 )
= $false )
| ( ( q @ X1 )
= $false ) )
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f282]) ).
thf(f284,plain,
( spl6_2
| spl6_6 ),
inference(avatar_split_clause,[],[f190,f282,f263]) ).
thf(f313,plain,
~ spl6_2,
inference(avatar_split_clause,[],[f157,f263]) ).
thf(f341,plain,
( ( ( rel_s5 @ sK3 @ sK1 )
= $true )
| ( $false = $true )
| ~ spl6_4 ),
inference(constrained_superposition,[],[f246,f274]) ).
thf(f347,plain,
( ( ( rel_s5 @ sK3 @ sK1 )
= $true )
| ~ spl6_4 ),
inference(trivial_inequality_removal,[],[f341]) ).
thf(f357,plain,
( ( $true
= ( p @ sK3 ) )
| ( $false = $true )
| ( $true
= ( q @ ( sK2 @ sK3 ) ) )
| ~ spl6_3
| ~ spl6_4 ),
inference(constrained_superposition,[],[f269,f274]) ).
thf(f361,plain,
( ( $true
= ( q @ ( sK2 @ sK3 ) ) )
| ( $true
= ( p @ sK3 ) )
| ~ spl6_3
| ~ spl6_4 ),
inference(trivial_inequality_removal,[],[f357]) ).
thf(f366,plain,
( ( $false = $true )
| ( $true
= ( q @ ( sK2 @ sK3 ) ) )
| ~ spl6_3
| ~ spl6_4
| ~ spl6_5 ),
inference(forward_demodulation,[],[f361,f279]) ).
thf(f367,plain,
( ( $true
= ( q @ ( sK2 @ sK3 ) ) )
| ~ spl6_3
| ~ spl6_4
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f366]) ).
thf(f385,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ X0 @ sK3 )
= $false )
| ( ( rel_s5 @ X0 @ sK1 )
= $true )
| ( $false = $true ) )
| ~ spl6_4 ),
inference(constrained_superposition,[],[f347,f258]) ).
thf(f392,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ X0 @ sK3 )
= $false )
| ( ( rel_s5 @ X0 @ sK1 )
= $true ) )
| ~ spl6_4 ),
inference(trivial_inequality_removal,[],[f385]) ).
thf(f442,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X0 ) )
| ( ( rel_s5 @ ( sK2 @ X0 ) @ X0 )
= $true )
| ( $false = $true )
| ( $true
= ( p @ X0 ) ) )
| ~ spl6_1 ),
inference(constrained_superposition,[],[f261,f246]) ).
thf(f449,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ ( sK2 @ X0 ) @ X0 )
= $true )
| ( $false
= ( rel_s5 @ sK1 @ X0 ) )
| ( $true
= ( p @ X0 ) ) )
| ~ spl6_1 ),
inference(trivial_inequality_removal,[],[f442]) ).
thf(f460,plain,
( ( $false = $true )
| ( $true
= ( rel_s5 @ ( sK2 @ sK3 ) @ sK1 ) )
| ( $true
= ( p @ sK3 ) )
| ( ( rel_s5 @ sK1 @ sK3 )
= $false )
| ~ spl6_1
| ~ spl6_4 ),
inference(constrained_superposition,[],[f392,f449]) ).
thf(f463,plain,
( ( $true
= ( rel_s5 @ ( sK2 @ sK3 ) @ sK1 ) )
| ( ( rel_s5 @ sK1 @ sK3 )
= $false )
| ( $true
= ( p @ sK3 ) )
| ~ spl6_1
| ~ spl6_4 ),
inference(trivial_inequality_removal,[],[f460]) ).
thf(f467,plain,
( ( $true
= ( rel_s5 @ ( sK2 @ sK3 ) @ sK1 ) )
| ( $false = $true )
| ( $true
= ( p @ sK3 ) )
| ~ spl6_1
| ~ spl6_4 ),
inference(forward_demodulation,[],[f463,f274]) ).
thf(f468,plain,
( ( $true
= ( rel_s5 @ ( sK2 @ sK3 ) @ sK1 ) )
| ( $true
= ( p @ sK3 ) )
| ~ spl6_1
| ~ spl6_4 ),
inference(trivial_inequality_removal,[],[f467]) ).
thf(f471,plain,
( ( $false = $true )
| ( $true
= ( rel_s5 @ ( sK2 @ sK3 ) @ sK1 ) )
| ~ spl6_1
| ~ spl6_4
| ~ spl6_5 ),
inference(forward_demodulation,[],[f468,f279]) ).
thf(f472,plain,
( ( $true
= ( rel_s5 @ ( sK2 @ sK3 ) @ sK1 ) )
| ~ spl6_1
| ~ spl6_4
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f471]) ).
thf(f516,plain,
( ( ( rel_s5 @ sK1 @ ( sK2 @ sK3 ) )
= $true )
| ( $false = $true )
| ~ spl6_1
| ~ spl6_4
| ~ spl6_5 ),
inference(constrained_superposition,[],[f472,f246]) ).
thf(f519,plain,
( ( ( rel_s5 @ sK1 @ ( sK2 @ sK3 ) )
= $true )
| ~ spl6_1
| ~ spl6_4
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f516]) ).
thf(f524,plain,
( ( $false = $true )
| ( $false
= ( q @ ( sK2 @ sK3 ) ) )
| ~ spl6_1
| ~ spl6_4
| ~ spl6_5
| ~ spl6_6 ),
inference(constrained_superposition,[],[f519,f283]) ).
thf(f535,plain,
( ( $false
= ( q @ ( sK2 @ sK3 ) ) )
| ~ spl6_1
| ~ spl6_4
| ~ spl6_5
| ~ spl6_6 ),
inference(trivial_inequality_removal,[],[f524]) ).
thf(f552,plain,
( ( $false = $true )
| ~ spl6_1
| ~ spl6_3
| ~ spl6_4
| ~ spl6_5
| ~ spl6_6 ),
inference(forward_demodulation,[],[f535,f367]) ).
thf(f553,plain,
( $false
| ~ spl6_1
| ~ spl6_3
| ~ spl6_4
| ~ spl6_5
| ~ spl6_6 ),
inference(trivial_inequality_removal,[],[f552]) ).
thf(f554,plain,
( ~ spl6_1
| ~ spl6_3
| ~ spl6_4
| ~ spl6_5
| ~ spl6_6 ),
inference(avatar_contradiction_clause,[],[f553]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f266]) ).
cnf(s2,plain,
( spl6_2
| spl6_3 ),
inference(sat_conversion,[],[f270]) ).
cnf(s3,plain,
( spl6_2
| spl6_4 ),
inference(sat_conversion,[],[f275]) ).
cnf(s4,plain,
( spl6_2
| spl6_5 ),
inference(sat_conversion,[],[f280]) ).
cnf(s5,plain,
( spl6_2
| spl6_6 ),
inference(sat_conversion,[],[f284]) ).
cnf(s12,plain,
~ spl6_2,
inference(sat_conversion,[],[f313]) ).
cnf(s23,plain,
( ~ spl6_1
| ~ spl6_3
| ~ spl6_4
| ~ spl6_5
| ~ spl6_6 ),
inference(sat_conversion,[],[f554]) ).
cnf(s25,plain,
spl6_6,
inference(rat,[],[s5,s12]) ).
cnf(s26,plain,
spl6_5,
inference(rat,[],[s4,s12]) ).
cnf(s27,plain,
spl6_4,
inference(rat,[],[s3,s12]) ).
cnf(s28,plain,
spl6_3,
inference(rat,[],[s2,s12]) ).
cnf(s29,plain,
~ spl6_1,
inference(rat,[],[s23,s25,s26,s27,s28]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s1,s12,s29]) ).
thf(f555,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO451^6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 % Computer : n010.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 16:52:49 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.27 Running higher-order theorem proving
% 0.10/0.28 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.27/0.35 % (3133306)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.27/0.35 % (3133315)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=895387608:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.27/0.35 % (3133319)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.27/0.35 % (3133319)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
% 0.27/0.35 % (3133315)Instruction limit reached!
% 0.27/0.35 % (3133315)------------------------------
% 0.27/0.35 % (3133315)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.35 % (3133315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.35 % (3133315)CaDiCaL version: 2.1.3
% 0.27/0.35 % (3133315)Termination reason: Instruction limit
% 0.27/0.35 % (3133315)Termination phase: Property scanning
% 0.27/0.35 % (3133315)Time elapsed: 0.002 s
% 0.27/0.35 % (3133315)Peak memory usage: 10 MB
% 0.27/0.35 % (3133315)Instructions burned: 5 (million)
% 0.27/0.35 % (3133319)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=2864714108:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.27/0.35 % (3133313)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2811940158:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.27/0.35 % (3133314)lrs+10_16_si=on:nwc=1.5:random_seed=2399106023:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.27/0.35 % (3133317)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=404681649:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.27/0.35 % (3133316)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=4002825559: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)
% 0.27/0.35 % (3133318)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1058237719:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.27/0.35 % (3133323)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3310642094:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.27/0.35 % (3133319) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3133306-3133319"...
% 0.27/0.35 % (3133323)Instruction limit reached!
% 0.27/0.35 % (3133323)------------------------------
% 0.27/0.35 % (3133323)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.35 % (3133323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.35 % (3133323)CaDiCaL version: 2.1.3
% 0.27/0.35 % (3133323)Termination reason: Instruction limit
% 0.27/0.35 % (3133323)Termination phase: Property scanning
% 0.27/0.35 % (3133323)Time elapsed: 0.001 s
% 0.27/0.35 % (3133323)Peak memory usage: 10 MB
% 0.27/0.35 % (3133323)Instructions burned: 3 (million)
% 0.27/0.35 % (3133319)...printing done.
% 0.27/0.35 % (3133319)Refutation found. Thanks to Tanya!
% 0.27/0.35 % SZS status Theorem for theBenchmark
% 0.27/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.27/0.35 % (3133319)------------------------------
% 0.27/0.35 % (3133319)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.27/0.35 % (3133319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.27/0.35 % (3133319)CaDiCaL version: 2.1.3
% 0.27/0.35 % (3133319)Termination reason: Refutation
% 0.27/0.35 % (3133319)Time elapsed: 0.020 s
% 0.27/0.35 % (3133319)Peak memory usage: 13 MB
% 0.27/0.35 % (3133319)Instructions burned: 33 (million)
% 0.27/0.35 % (3133306)Success in time 0.054 s
% 0.27/0.35 % Vampire exiting
%------------------------------------------------------------------------------