%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO443^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:47:43 AM UTC 2026
% Result : Theorem 0.31s 0.40s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 27
% Syntax : Number of formulae : 286 ( 71 unt; 0 typ; 15 def)
% Number of atoms : 2906 ( 539 equ; 0 cnn)
% Maximal formula atoms : 14 ( 10 avg)
% Number of connectives : 3553 ( 573 ~; 860 |; 13 &;1890 @)
% ( 14 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 179 ( 179 >; 0 *; 0 +; 0 <<)
% Number of symbols : 79 ( 75 usr; 24 con; 0-4 aty)
% ( 181 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 620 ( 0 sgn 160 !; 0 ?; 620 :)
% 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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
vIMP: $o > $o > $o ).
thf(func_def_39,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_43,type,
vAND: $o > $o > $o ).
thf(func_def_44,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_46,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
vNOT: $o > $o ).
thf(func_def_48,type,
vOR: $o > $o > $o ).
thf(func_def_49,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
sF0: $o ).
thf(func_def_53,type,
sK1: $i > $i ).
thf(func_def_54,type,
sK2: $i > $i ).
thf(func_def_55,type,
sK3: $i > $i ).
thf(func_def_56,type,
sK4: $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
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(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X3: $i,X1: $i,X2: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) )
= mbox_s5 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(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 @ ( mequiv @ ( mbox_s5 @ ( mor @ ( mnot @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mor @ ( mbox_s5 @ ( mnot @ p ) ) @ ( mbox_s5 @ q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mbox_s5 @ ( mor @ ( mnot @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mor @ ( mbox_s5 @ ( mnot @ p ) ) @ ( mbox_s5 @ q ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f39,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
=> ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f40,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f48,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f50,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f51,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f50]) ).
thf(f65,plain,
mtransitive @ rel_s5,
inference(rectify,[],[f35]) ).
thf(f66,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f65]) ).
thf(f69,plain,
~ ( mvalid @ ( mequiv @ ( mbox_s5 @ ( mor @ ( mnot @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mor @ ( mbox_s5 @ ( mnot @ p ) ) @ ( mbox_s5 @ q ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f70,plain,
( ( mvalid @ ( mequiv @ ( mbox_s5 @ ( mor @ ( mnot @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mor @ ( mbox_s5 @ ( mnot @ p ) ) @ ( mbox_s5 @ q ) ) ) )
!= $true ),
inference(fool_elimination,[],[f69]) ).
thf(f73,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) )
= mbox_s5 ),
inference(rectify,[],[f32]) ).
thf(f74,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f73]) ).
thf(f77,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X3 @ X1 ) )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f78,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f77]) ).
thf(f81,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f82,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f87,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f88,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f87]) ).
thf(f92,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f95,plain,
msymmetric @ rel_s5,
inference(rectify,[],[f36]) ).
thf(f96,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f95]) ).
thf(f98,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f101,plain,
( ( mvalid @ ( mequiv @ ( mbox_s5 @ ( mor @ ( mnot @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mor @ ( mbox_s5 @ ( mnot @ p ) ) @ ( mbox_s5 @ q ) ) ) )
!= $true ),
inference(flattening,[],[f70]) ).
thf(f108,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f109,plain,
( ( mvalid @ ( mequiv @ ( mbox_s5 @ ( mor @ ( mnot @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mor @ ( mbox_s5 @ ( mnot @ p ) ) @ ( mbox_s5 @ q ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f101]) ).
thf(f114,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f118,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f123,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f124,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f78]) ).
thf(f129,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f131,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f133,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f98]) ).
thf(f135,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f96]) ).
thf(f137,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f66]) ).
thf(f138,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f141,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f129,f131,f123,f131,f131]) ).
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,[],[f108,f123,f131]) ).
thf(f144,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( 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,[],[f133,f141,f142,f142]) ).
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 > $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] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ 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 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ p ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f109,f114,f144,f118,f123,f131,f118,f123,f118,f131,f118]) ).
thf(f153,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
@ rel_s5 )
= $true ),
inference(definition_unfolding,[],[f135,f138]) ).
thf(f154,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
@ rel_s5 )
= $true ),
inference(definition_unfolding,[],[f137,f124]) ).
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 > $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] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ 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 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ p ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f156,plain,
sF0 != $true,
inference(definition_folding,[],[f152,f155]) ).
thf(f160,plain,
( ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ 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 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ p ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) ) ) )
= $false )
| ( sF0 = $true ) ),
inference(iff_proxy_clausification,[],[f155]) ).
thf(f241,plain,
( ( ( !! @ $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 ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) ) ) ) ) )
= $false )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f242,plain,
( ( sF0 = $true )
| ( ( ^ [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 ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) ) ) ) )
@ sK5 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f241]) ).
thf(f243,plain,
( ( ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) ) )
= $false )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f242]) ).
thf(f244,plain,
( ( sF0 = $true )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f243]) ).
thf(f245,plain,
( ( sF0 = $true )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f244]) ).
thf(f246,plain,
( ( sF0 = $true )
| ( ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f245]) ).
thf(f247,plain,
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) )
= $false )
| ( sF0 = $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f246]) ).
thf(f248,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
= $false )
| ( sF0 = $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f247]) ).
thf(f249,plain,
( ( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) ) ) ) )
| ( sF0 = $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f247]) ).
thf(f250,plain,
( ( sF0 = $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f249]) ).
thf(f251,plain,
( ( sF0 = $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f250]) ).
thf(f252,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) ) )
= $true )
| ( sF0 = $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f250]) ).
thf(f253,plain,
( ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f252]) ).
thf(f254,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) )
= $false )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f253]) ).
thf(f255,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) )
= $false )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f254]) ).
thf(f256,plain,
! [X2: $i,X1: $i] :
( ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) )
@ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f255]) ).
thf(f257,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) )
@ X1 )
= $true )
| ( sF0 = $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f256]) ).
thf(f258,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( rel_s5 @ sK5 @ X1 )
| ~ ( p @ X1 ) )
= $true )
| ( ( ~ ( rel_s5 @ sK5 @ X2 )
| ( q @ X2 ) )
= $true )
| ( ( ~ ( rel_s5 @ sK5 @ X3 )
| ~ ( p @ X3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X3 @ Y0 )
| ( q @ Y0 ) ) ) )
= $true )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f257]) ).
thf(f259,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( p @ X1 ) )
= $true )
| ( ( ~ ( rel_s5 @ sK5 @ X3 )
| ~ ( p @ X3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X3 @ Y0 )
| ( q @ Y0 ) ) ) )
= $true )
| ( sF0 = $true )
| ( ( ~ ( rel_s5 @ sK5 @ X2 )
| ( q @ X2 ) )
= $true )
| ( ( ~ ( rel_s5 @ sK5 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f258]) ).
thf(f260,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( rel_s5 @ sK5 @ X1 ) )
= $true )
| ( ( ~ ( rel_s5 @ sK5 @ X2 )
| ( q @ X2 ) )
= $true )
| ( ( p @ X1 )
= $false )
| ( sF0 = $true )
| ( ( ~ ( rel_s5 @ sK5 @ X3 )
| ~ ( p @ X3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X3 @ Y0 )
| ( q @ Y0 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f259]) ).
thf(f261,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s5 @ sK5 @ X1 )
= $false )
| ( ( ~ ( rel_s5 @ sK5 @ X3 )
| ~ ( p @ X3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X3 @ Y0 )
| ( q @ Y0 ) ) ) )
= $true )
| ( ( ~ ( rel_s5 @ sK5 @ X2 )
| ( q @ X2 ) )
= $true )
| ( ( p @ X1 )
= $false )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f260]) ).
thf(f262,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ~ ( rel_s5 @ sK5 @ X3 ) )
= $true )
| ( sF0 = $true )
| ( ( rel_s5 @ sK5 @ X1 )
= $false )
| ( ( ~ ( p @ X3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X3 @ Y0 )
| ( q @ Y0 ) ) ) )
= $true )
| ( ( ~ ( rel_s5 @ sK5 @ X2 )
| ( q @ X2 ) )
= $true )
| ( ( p @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f261]) ).
thf(f263,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF0 = $true )
| ( ( p @ X1 )
= $false )
| ( ( rel_s5 @ sK5 @ X3 )
= $false )
| ( ( ~ ( p @ X3 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X3 @ Y0 )
| ( q @ Y0 ) ) ) )
= $true )
| ( ( ~ ( rel_s5 @ sK5 @ X2 )
| ( q @ X2 ) )
= $true )
| ( ( rel_s5 @ sK5 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f262]) ).
thf(f264,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X3 @ Y0 )
| ( q @ Y0 ) ) )
= $true )
| ( ( p @ X1 )
= $false )
| ( ( ~ ( rel_s5 @ sK5 @ X2 )
| ( q @ X2 ) )
= $true )
| ( ( rel_s5 @ sK5 @ X3 )
= $false )
| ( ( ~ ( p @ X3 ) )
= $true )
| ( ( rel_s5 @ sK5 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f263]) ).
thf(f265,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( rel_s5 @ sK5 @ X3 )
= $false )
| ( ( rel_s5 @ sK5 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X3 @ Y0 )
| ( q @ Y0 ) )
@ X4 )
= $true )
| ( ( p @ X1 )
= $false )
| ( sF0 = $true )
| ( ( ~ ( rel_s5 @ sK5 @ X2 )
| ( q @ X2 ) )
= $true )
| ( ( ~ ( p @ X3 ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f264]) ).
thf(f266,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( q @ X2 )
= $true )
| ( ( p @ X1 )
= $false )
| ( sF0 = $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X3 @ Y0 )
| ( q @ Y0 ) )
@ X4 )
= $true )
| ( ( ~ ( p @ X3 ) )
= $true )
| ( ( ~ ( rel_s5 @ sK5 @ X2 ) )
= $true )
| ( ( rel_s5 @ sK5 @ X3 )
= $false )
| ( ( rel_s5 @ sK5 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f265]) ).
thf(f267,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X3 @ Y0 )
| ( q @ Y0 ) )
@ X4 )
= $true )
| ( ( rel_s5 @ sK5 @ X1 )
= $false )
| ( sF0 = $true )
| ( ( ~ ( rel_s5 @ sK5 @ X2 ) )
= $true )
| ( ( p @ X1 )
= $false )
| ( ( rel_s5 @ sK5 @ X3 )
= $false )
| ( ( p @ X3 )
= $false )
| ( ( q @ X2 )
= $true ) ),
inference(not_proxy_clausification,[],[f266]) ).
thf(f268,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( p @ X3 )
= $false )
| ( sF0 = $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X3 @ Y0 )
| ( q @ Y0 ) )
@ X4 )
= $true )
| ( ( rel_s5 @ sK5 @ X2 )
= $false )
| ( ( p @ X1 )
= $false )
| ( ( rel_s5 @ sK5 @ X3 )
= $false )
| ( ( rel_s5 @ sK5 @ X1 )
= $false )
| ( ( q @ X2 )
= $true ) ),
inference(not_proxy_clausification,[],[f267]) ).
thf(f269,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( p @ X3 )
= $false )
| ( ( rel_s5 @ sK5 @ X2 )
= $false )
| ( ( q @ X2 )
= $true )
| ( ( p @ X1 )
= $false )
| ( ( ~ ( rel_s5 @ X3 @ X4 )
| ( q @ X4 ) )
= $true )
| ( ( rel_s5 @ sK5 @ X1 )
= $false )
| ( ( rel_s5 @ sK5 @ X3 )
= $false )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f268]) ).
thf(f270,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( rel_s5 @ sK5 @ X2 )
= $false )
| ( sF0 = $true )
| ( ( p @ X1 )
= $false )
| ( ( p @ X3 )
= $false )
| ( ( rel_s5 @ sK5 @ X3 )
= $false )
| ( ( rel_s5 @ sK5 @ X1 )
= $false )
| ( ( q @ X2 )
= $true )
| ( ( q @ X4 )
= $true )
| ( ( ~ ( rel_s5 @ X3 @ X4 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f269]) ).
thf(f271,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( rel_s5 @ sK5 @ X1 )
= $false )
| ( ( rel_s5 @ sK5 @ X3 )
= $false )
| ( sF0 = $true )
| ( ( rel_s5 @ sK5 @ X2 )
= $false )
| ( ( p @ X3 )
= $false )
| ( ( p @ X1 )
= $false )
| ( ( q @ X4 )
= $true )
| ( ( q @ X2 )
= $true )
| ( ( rel_s5 @ X3 @ X4 )
= $false ) ),
inference(not_proxy_clausification,[],[f270]) ).
thf(f273,plain,
( ( sF0 = $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f251]) ).
thf(f274,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) )
= $true )
| ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f273]) ).
thf(f275,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) )
@ X1 )
= $true )
| ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f274]) ).
thf(f276,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) )
@ X2 )
= $true )
| ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f275]) ).
thf(f277,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK6 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) )
@ X2 )
= $true )
| ( sF0 = $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) )
@ X1 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f276]) ).
thf(f278,plain,
! [X2: $i,X1: $i] :
( ( sF0 = $true )
| ( ( ~ ( rel_s5 @ sK5 @ sK6 )
| ~ ( p @ sK6 ) )
= $false )
| ( ( ~ ( rel_s5 @ sK5 @ X2 )
| ~ ( p @ X2 ) )
= $true )
| ( ( ~ ( rel_s5 @ sK5 @ X1 )
| ( q @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f277]) ).
thf(f279,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( p @ sK6 ) ) )
| ( ( ~ ( rel_s5 @ sK5 @ X2 )
| ~ ( p @ X2 ) )
= $true )
| ( sF0 = $true )
| ( ( ~ ( rel_s5 @ sK5 @ X1 )
| ( q @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f278]) ).
thf(f280,plain,
! [X2: $i,X1: $i] :
( ( sF0 = $true )
| ( ( ~ ( rel_s5 @ sK5 @ X2 )
| ~ ( p @ X2 ) )
= $true )
| ( ( ~ ( rel_s5 @ sK5 @ X1 )
| ( q @ X1 ) )
= $true )
| ( ( ~ ( rel_s5 @ sK5 @ sK6 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f278]) ).
thf(f281,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s5 @ sK5 @ X1 )
| ( q @ X1 ) )
= $true )
| ( ( ~ ( rel_s5 @ sK5 @ X2 ) )
= $true )
| ( ( ~ ( rel_s5 @ sK5 @ sK6 ) )
= $false )
| ( sF0 = $true )
| ( ( ~ ( p @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f280]) ).
thf(f282,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s5 @ sK5 @ X1 ) )
= $true )
| ( ( ~ ( rel_s5 @ sK5 @ sK6 ) )
= $false )
| ( ( ~ ( p @ X2 ) )
= $true )
| ( ( q @ X1 )
= $true )
| ( sF0 = $true )
| ( ( ~ ( rel_s5 @ sK5 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f281]) ).
thf(f283,plain,
! [X2: $i,X1: $i] :
( ( sF0 = $true )
| ( ( ~ ( rel_s5 @ sK5 @ X2 ) )
= $true )
| ( ( ~ ( p @ X2 ) )
= $true )
| ( ( ~ ( rel_s5 @ sK5 @ sK6 ) )
= $false )
| ( ( q @ X1 )
= $true )
| ( ( rel_s5 @ sK5 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f282]) ).
thf(f284,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK5 @ X1 )
= $false )
| ( ( rel_s5 @ sK5 @ X2 )
= $false )
| ( ( ~ ( rel_s5 @ sK5 @ sK6 ) )
= $false )
| ( sF0 = $true )
| ( ( q @ X1 )
= $true )
| ( ( ~ ( p @ X2 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f283]) ).
thf(f285,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( p @ X2 ) )
= $true )
| ( sF0 = $true )
| ( ( rel_s5 @ sK5 @ sK6 )
= $true )
| ( ( q @ X1 )
= $true )
| ( ( rel_s5 @ sK5 @ X2 )
= $false )
| ( ( rel_s5 @ sK5 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f284]) ).
thf(f286,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK5 @ X1 )
= $false )
| ( ( q @ X1 )
= $true )
| ( sF0 = $true )
| ( ( rel_s5 @ sK5 @ X2 )
= $false )
| ( ( rel_s5 @ sK5 @ sK6 )
= $true )
| ( $false
= ( p @ X2 ) ) ),
inference(not_proxy_clausification,[],[f285]) ).
thf(f287,plain,
! [X2: $i,X1: $i] :
( ( ( p @ sK6 )
= $true )
| ( sF0 = $true )
| ( ( ~ ( rel_s5 @ sK5 @ X2 )
| ~ ( p @ X2 ) )
= $true )
| ( ( ~ ( rel_s5 @ sK5 @ X1 )
| ( q @ X1 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f279]) ).
thf(f288,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( p @ X2 ) )
= $true )
| ( ( ~ ( rel_s5 @ sK5 @ X1 )
| ( q @ X1 ) )
= $true )
| ( ( p @ sK6 )
= $true )
| ( sF0 = $true )
| ( ( ~ ( rel_s5 @ sK5 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f287]) ).
thf(f289,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ X2 ) )
| ( ( p @ sK6 )
= $true )
| ( ( ~ ( rel_s5 @ sK5 @ X1 )
| ( q @ X1 ) )
= $true )
| ( ( ~ ( rel_s5 @ sK5 @ X2 ) )
= $true )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f288]) ).
thf(f290,plain,
! [X2: $i,X1: $i] :
( ( sF0 = $true )
| ( ( p @ sK6 )
= $true )
| ( ( q @ X1 )
= $true )
| ( $false
= ( p @ X2 ) )
| ( ( ~ ( rel_s5 @ sK5 @ X2 ) )
= $true )
| ( ( ~ ( rel_s5 @ sK5 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f289]) ).
thf(f291,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ X2 ) )
| ( ( ~ ( rel_s5 @ sK5 @ X1 ) )
= $true )
| ( ( rel_s5 @ sK5 @ X2 )
= $false )
| ( ( q @ X1 )
= $true )
| ( ( p @ sK6 )
= $true )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f290]) ).
thf(f292,plain,
! [X2: $i,X1: $i] :
( ( sF0 = $true )
| ( $false
= ( p @ X2 ) )
| ( ( rel_s5 @ sK5 @ X1 )
= $false )
| ( ( q @ X1 )
= $true )
| ( ( rel_s5 @ sK5 @ X2 )
= $false )
| ( ( p @ sK6 )
= $true ) ),
inference(not_proxy_clausification,[],[f291]) ).
thf(f306,plain,
( ( sF0 = $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ sK8 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f248]) ).
thf(f307,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ sK8 )
= $false )
| ( sF0 = $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f306]) ).
thf(f337,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ sK8 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) ) )
= $false )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f307]) ).
thf(f338,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ sK8 )
= $false )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f307]) ).
thf(f339,plain,
( ( sF0 = $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK10 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ sK8 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f338]) ).
thf(f340,plain,
( ( ( ~ ( rel_s5 @ sK5 @ sK10 )
| ~ ( p @ sK10 ) )
= $false )
| ( ( ~ ( rel_s5 @ sK5 @ sK8 )
| ~ ( p @ sK8 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK8 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f339]) ).
thf(f341,plain,
( ( ( ~ ( rel_s5 @ sK5 @ sK8 )
| ~ ( p @ sK8 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK8 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false )
| ( sF0 = $true )
| ( ( ~ ( p @ sK10 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f340]) ).
thf(f342,plain,
( ( sF0 = $true )
| ( ( ~ ( rel_s5 @ sK5 @ sK10 ) )
= $false )
| ( ( ~ ( rel_s5 @ sK5 @ sK8 )
| ~ ( p @ sK8 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK8 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f340]) ).
thf(f343,plain,
( ( ( ~ ( rel_s5 @ sK5 @ sK8 )
| ~ ( p @ sK8 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK8 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false )
| ( sF0 = $true )
| ( ( rel_s5 @ sK5 @ sK10 )
= $true ) ),
inference(not_proxy_clausification,[],[f342]) ).
thf(f344,plain,
( ( ( ~ ( p @ sK8 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK8 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false )
| ( ( rel_s5 @ sK5 @ sK10 )
= $true )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f343]) ).
thf(f345,plain,
( ( ( ~ ( rel_s5 @ sK5 @ sK8 ) )
= $false )
| ( sF0 = $true )
| ( ( rel_s5 @ sK5 @ sK10 )
= $true ) ),
inference(or_proxy_clausification,[],[f343]) ).
thf(f346,plain,
( ( ( rel_s5 @ sK5 @ sK10 )
= $true )
| ( sF0 = $true )
| ( ( rel_s5 @ sK5 @ sK8 )
= $true ) ),
inference(not_proxy_clausification,[],[f345]) ).
thf(f348,plain,
( ( ( rel_s5 @ sK5 @ sK10 )
= $true )
| ( ( ~ ( p @ sK8 ) )
= $false )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f344]) ).
thf(f349,plain,
( ( ( rel_s5 @ sK5 @ sK10 )
= $true )
| ( sF0 = $true )
| ( ( p @ sK8 )
= $true ) ),
inference(not_proxy_clausification,[],[f348]) ).
thf(f355,plain,
( ( sF0 = $true )
| ( ( ~ ( p @ sK8 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK8 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false )
| ( ( ~ ( p @ sK10 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f341]) ).
thf(f356,plain,
( ( sF0 = $true )
| ( ( ~ ( rel_s5 @ sK5 @ sK8 ) )
= $false )
| ( ( ~ ( p @ sK10 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f341]) ).
thf(f357,plain,
( ( ( rel_s5 @ sK5 @ sK8 )
= $true )
| ( sF0 = $true )
| ( ( ~ ( p @ sK10 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f356]) ).
thf(f358,plain,
( ( ( rel_s5 @ sK5 @ sK8 )
= $true )
| ( sF0 = $true )
| ( ( p @ sK10 )
= $true ) ),
inference(not_proxy_clausification,[],[f357]) ).
thf(f360,plain,
( ( sF0 = $true )
| ( ( ~ ( p @ sK10 ) )
= $false )
| ( ( ~ ( p @ sK8 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f355]) ).
thf(f361,plain,
( ( ( p @ sK10 )
= $true )
| ( ( ~ ( p @ sK8 ) )
= $false )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f360]) ).
thf(f362,plain,
( ( sF0 = $true )
| ( ( p @ sK10 )
= $true )
| ( ( p @ sK8 )
= $true ) ),
inference(not_proxy_clausification,[],[f361]) ).
thf(f369,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ sK8 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK5 @ Y0 )
| ( q @ Y0 ) )
@ sK13 )
= $false )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f337]) ).
thf(f370,plain,
( ( ( ~ ( rel_s5 @ sK5 @ sK8 )
| ~ ( p @ sK8 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK8 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false )
| ( sF0 = $true )
| ( ( ~ ( rel_s5 @ sK5 @ sK13 )
| ( q @ sK13 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f369]) ).
thf(f371,plain,
( ( ( ~ ( p @ sK8 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK8 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false )
| ( ( ~ ( rel_s5 @ sK5 @ sK13 )
| ( q @ sK13 ) )
= $false )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f370]) ).
thf(f372,plain,
( ( ( ~ ( rel_s5 @ sK5 @ sK8 ) )
= $false )
| ( sF0 = $true )
| ( ( ~ ( rel_s5 @ sK5 @ sK13 )
| ( q @ sK13 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f370]) ).
thf(f373,plain,
( ( ( ~ ( rel_s5 @ sK5 @ sK13 )
| ( q @ sK13 ) )
= $false )
| ( sF0 = $true )
| ( ( rel_s5 @ sK5 @ sK8 )
= $true ) ),
inference(not_proxy_clausification,[],[f372]) ).
thf(f374,plain,
( ( ( rel_s5 @ sK5 @ sK8 )
= $true )
| ( ( q @ sK13 )
= $false )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f373]) ).
thf(f375,plain,
( ( ( ~ ( rel_s5 @ sK5 @ sK13 ) )
= $false )
| ( ( rel_s5 @ sK5 @ sK8 )
= $true )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f373]) ).
thf(f376,plain,
( ( ( rel_s5 @ sK5 @ sK13 )
= $true )
| ( ( rel_s5 @ sK5 @ sK8 )
= $true )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f375]) ).
thf(f377,plain,
( ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK8 @ Y0 )
| ( q @ Y0 ) ) )
= $false )
| ( ( ~ ( rel_s5 @ sK5 @ sK13 )
| ( q @ sK13 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f371]) ).
thf(f384,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK8 @ Y0 )
| ( q @ Y0 ) )
@ sK14 )
= $false )
| ( ( ~ ( rel_s5 @ sK5 @ sK13 )
| ( q @ sK13 ) )
= $false )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f377]) ).
thf(f385,plain,
( ( ( q @ sK13 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK8 @ Y0 )
| ( q @ Y0 ) )
@ sK14 )
= $false )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f384]) ).
thf(f386,plain,
( ( sF0 = $true )
| ( ( ~ ( rel_s5 @ sK5 @ sK13 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK8 @ Y0 )
| ( q @ Y0 ) )
@ sK14 )
= $false ) ),
inference(or_proxy_clausification,[],[f384]) ).
thf(f387,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK8 @ Y0 )
| ( q @ Y0 ) )
@ sK14 )
= $false )
| ( ( rel_s5 @ sK5 @ sK13 )
= $true )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f386]) ).
thf(f388,plain,
( ( sF0 = $true )
| ( ( rel_s5 @ sK5 @ sK13 )
= $true )
| ( ( ~ ( rel_s5 @ sK8 @ sK14 )
| ( q @ sK14 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f387]) ).
thf(f389,plain,
( ( ( q @ sK14 )
= $false )
| ( sF0 = $true )
| ( ( rel_s5 @ sK5 @ sK13 )
= $true ) ),
inference(or_proxy_clausification,[],[f388]) ).
thf(f390,plain,
( ( sF0 = $true )
| ( ( ~ ( rel_s5 @ sK8 @ sK14 ) )
= $false )
| ( ( rel_s5 @ sK5 @ sK13 )
= $true ) ),
inference(or_proxy_clausification,[],[f388]) ).
thf(f391,plain,
( ( ( rel_s5 @ sK8 @ sK14 )
= $true )
| ( ( rel_s5 @ sK5 @ sK13 )
= $true )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f390]) ).
thf(f392,plain,
( ( sF0 = $true )
| ( ( ~ ( rel_s5 @ sK8 @ sK14 )
| ( q @ sK14 ) )
= $false )
| ( ( q @ sK13 )
= $false ) ),
inference(beta-eta_normalization,[],[f385]) ).
thf(f393,plain,
( ( ( q @ sK14 )
= $false )
| ( sF0 = $true )
| ( ( q @ sK13 )
= $false ) ),
inference(or_proxy_clausification,[],[f392]) ).
thf(f394,plain,
( ( ( q @ sK13 )
= $false )
| ( sF0 = $true )
| ( ( ~ ( rel_s5 @ sK8 @ sK14 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f392]) ).
thf(f395,plain,
( ( sF0 = $true )
| ( ( q @ sK13 )
= $false )
| ( ( rel_s5 @ sK8 @ sK14 )
= $true ) ),
inference(not_proxy_clausification,[],[f394]) ).
thf(f396,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y0 @ Y1 )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f397,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y0 @ Y1 )
=> ( rel_s5 @ Y1 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f396]) ).
thf(f398,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ X1 @ Y0 )
=> ( rel_s5 @ Y0 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f397]) ).
thf(f399,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( rel_s5 @ X1 @ Y0 )
=> ( rel_s5 @ Y0 @ X1 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f398]) ).
thf(f400,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ X1 @ X2 )
=> ( rel_s5 @ X2 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f399]) ).
thf(f401,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ X2 @ X1 )
= $true )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f400]) ).
thf(f402,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y0 @ Y2 )
& ( rel_s5 @ Y1 @ Y0 ) )
=> ( rel_s5 @ Y1 @ Y2 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f403,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y0 @ Y2 )
& ( rel_s5 @ Y1 @ Y0 ) )
=> ( rel_s5 @ Y1 @ Y2 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f402]) ).
thf(f404,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ X1 @ Y1 )
& ( rel_s5 @ Y0 @ X1 ) )
=> ( rel_s5 @ Y0 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f403]) ).
thf(f405,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ X1 @ Y1 )
& ( rel_s5 @ Y0 @ X1 ) )
=> ( rel_s5 @ Y0 @ Y1 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f404]) ).
thf(f406,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s5 @ X1 @ Y0 )
& ( rel_s5 @ X2 @ X1 ) )
=> ( rel_s5 @ X2 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f405]) ).
thf(f407,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( rel_s5 @ X1 @ Y0 )
& ( rel_s5 @ X2 @ X1 ) )
=> ( rel_s5 @ X2 @ Y0 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f406]) ).
thf(f408,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( rel_s5 @ X1 @ X3 )
& ( rel_s5 @ X2 @ X1 ) )
=> ( rel_s5 @ X2 @ X3 ) )
= $true ),
inference(beta-eta_normalization,[],[f407]) ).
thf(f409,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s5 @ X2 @ X3 )
= $true )
| ( ( ( rel_s5 @ X1 @ X3 )
& ( rel_s5 @ X2 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f408]) ).
thf(f410,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s5 @ X2 @ X3 )
= $true )
| ( ( rel_s5 @ X1 @ X3 )
= $false )
| ( ( rel_s5 @ X2 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f409]) ).
thf(f448,definition,
( spl15_10
<=> ! [X2: $i] :
( ( ( rel_s5 @ sK5 @ X2 )
= $false )
| ( ( q @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl15_10])],[avatar_definition]) ).
thf(f449,plain,
( ! [X2: $i] :
( ( ( rel_s5 @ sK5 @ X2 )
= $false )
| ( ( q @ X2 )
= $true ) )
| ~ spl15_10 ),
inference(avatar_component_clause,[],[f448]) ).
thf(f451,definition,
( spl15_11
<=> ! [X1: $i] :
( ( ( rel_s5 @ sK5 @ X1 )
= $false )
| ( ( p @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl15_11])],[avatar_definition]) ).
thf(f452,plain,
( ! [X1: $i] :
( ( ( rel_s5 @ sK5 @ X1 )
= $false )
| ( ( p @ X1 )
= $false ) )
| ~ spl15_11 ),
inference(avatar_component_clause,[],[f451]) ).
thf(f454,definition,
( spl15_12
<=> ( sF0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl15_12])],[avatar_definition]) ).
thf(f458,definition,
( spl15_13
<=> ! [X4: $i,X3: $i] :
( ( ( rel_s5 @ sK5 @ X3 )
= $false )
| ( ( rel_s5 @ X3 @ X4 )
= $false )
| ( ( q @ X4 )
= $true )
| ( ( p @ X3 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl15_13])],[avatar_definition]) ).
thf(f459,plain,
( ! [X3: $i,X4: $i] :
( ( ( rel_s5 @ sK5 @ X3 )
= $false )
| ( ( rel_s5 @ X3 @ X4 )
= $false )
| ( ( p @ X3 )
= $false )
| ( ( q @ X4 )
= $true ) )
| ~ spl15_13 ),
inference(avatar_component_clause,[],[f458]) ).
thf(f460,plain,
( spl15_10
| spl15_11
| spl15_12
| spl15_13 ),
inference(avatar_split_clause,[],[f271,f458,f454,f451,f448]) ).
thf(f462,definition,
( spl15_14
<=> ( ( rel_s5 @ sK5 @ sK6 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl15_14])],[avatar_definition]) ).
thf(f464,plain,
( ( ( rel_s5 @ sK5 @ sK6 )
= $true )
| ~ spl15_14 ),
inference(avatar_component_clause,[],[f462]) ).
thf(f465,plain,
( spl15_11
| spl15_14
| spl15_12
| spl15_10 ),
inference(avatar_split_clause,[],[f286,f448,f454,f462,f451]) ).
thf(f467,definition,
( spl15_15
<=> ( ( p @ sK6 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl15_15])],[avatar_definition]) ).
thf(f469,plain,
( ( ( p @ sK6 )
= $true )
| ~ spl15_15 ),
inference(avatar_component_clause,[],[f467]) ).
thf(f470,plain,
( spl15_10
| spl15_15
| spl15_12
| spl15_11 ),
inference(avatar_split_clause,[],[f292,f451,f454,f467,f448]) ).
thf(f482,definition,
( spl15_18
<=> ( ( rel_s5 @ sK5 @ sK8 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl15_18])],[avatar_definition]) ).
thf(f484,plain,
( ( ( rel_s5 @ sK5 @ sK8 )
= $true )
| ~ spl15_18 ),
inference(avatar_component_clause,[],[f482]) ).
thf(f487,definition,
( spl15_19
<=> ( ( p @ sK8 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl15_19])],[avatar_definition]) ).
thf(f489,plain,
( ( ( p @ sK8 )
= $true )
| ~ spl15_19 ),
inference(avatar_component_clause,[],[f487]) ).
thf(f502,definition,
( spl15_22
<=> ( ( rel_s5 @ sK5 @ sK10 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl15_22])],[avatar_definition]) ).
thf(f504,plain,
( ( ( rel_s5 @ sK5 @ sK10 )
= $true )
| ~ spl15_22 ),
inference(avatar_component_clause,[],[f502]) ).
thf(f505,plain,
( spl15_22
| spl15_12
| spl15_18 ),
inference(avatar_split_clause,[],[f346,f482,f454,f502]) ).
thf(f506,plain,
( spl15_19
| spl15_22
| spl15_12 ),
inference(avatar_split_clause,[],[f349,f454,f502,f487]) ).
thf(f518,definition,
( spl15_25
<=> ( ( p @ sK10 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl15_25])],[avatar_definition]) ).
thf(f520,plain,
( ( ( p @ sK10 )
= $true )
| ~ spl15_25 ),
inference(avatar_component_clause,[],[f518]) ).
thf(f521,plain,
( spl15_25
| spl15_12
| spl15_18 ),
inference(avatar_split_clause,[],[f358,f482,f454,f518]) ).
thf(f522,plain,
( spl15_25
| spl15_19
| spl15_12 ),
inference(avatar_split_clause,[],[f362,f454,f487,f518]) ).
thf(f534,definition,
( spl15_28
<=> ( ( rel_s5 @ sK5 @ sK13 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl15_28])],[avatar_definition]) ).
thf(f536,plain,
( ( ( rel_s5 @ sK5 @ sK13 )
= $true )
| ~ spl15_28 ),
inference(avatar_component_clause,[],[f534]) ).
thf(f537,plain,
( spl15_28
| spl15_12
| spl15_18 ),
inference(avatar_split_clause,[],[f376,f482,f454,f534]) ).
thf(f539,definition,
( spl15_29
<=> ( ( q @ sK13 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl15_29])],[avatar_definition]) ).
thf(f541,plain,
( ( ( q @ sK13 )
= $false )
| ~ spl15_29 ),
inference(avatar_component_clause,[],[f539]) ).
thf(f542,plain,
( spl15_18
| spl15_12
| spl15_29 ),
inference(avatar_split_clause,[],[f374,f539,f454,f482]) ).
thf(f546,definition,
( spl15_30
<=> ( ( rel_s5 @ sK8 @ sK14 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl15_30])],[avatar_definition]) ).
thf(f548,plain,
( ( ( rel_s5 @ sK8 @ sK14 )
= $true )
| ~ spl15_30 ),
inference(avatar_component_clause,[],[f546]) ).
thf(f549,plain,
( spl15_30
| spl15_12
| spl15_28 ),
inference(avatar_split_clause,[],[f391,f534,f454,f546]) ).
thf(f551,definition,
( spl15_31
<=> ( ( q @ sK14 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl15_31])],[avatar_definition]) ).
thf(f553,plain,
( ( ( q @ sK14 )
= $false )
| ~ spl15_31 ),
inference(avatar_component_clause,[],[f551]) ).
thf(f554,plain,
( spl15_31
| spl15_12
| spl15_28 ),
inference(avatar_split_clause,[],[f389,f534,f454,f551]) ).
thf(f555,plain,
( spl15_29
| spl15_30
| spl15_12 ),
inference(avatar_split_clause,[],[f395,f454,f546,f539]) ).
thf(f556,plain,
( spl15_29
| spl15_31
| spl15_12 ),
inference(avatar_split_clause,[],[f393,f454,f551,f539]) ).
thf(f557,plain,
~ spl15_12,
inference(avatar_split_clause,[],[f156,f454]) ).
thf(f576,plain,
( ( ( q @ sK13 )
= $true )
| ( $false = $true )
| ~ spl15_10
| ~ spl15_28 ),
inference(constrained_superposition,[],[f536,f449]) ).
thf(f581,plain,
( ( ( q @ sK13 )
= $true )
| ~ spl15_10
| ~ spl15_28 ),
inference(trivial_inequality_removal,[],[f576]) ).
thf(f587,plain,
( ( $false = $true )
| ~ spl15_10
| ~ spl15_28
| ~ spl15_29 ),
inference(forward_demodulation,[],[f581,f541]) ).
thf(f588,plain,
( $false
| ~ spl15_10
| ~ spl15_28
| ~ spl15_29 ),
inference(trivial_inequality_removal,[],[f587]) ).
thf(f589,plain,
( ~ spl15_10
| ~ spl15_28
| ~ spl15_29 ),
inference(avatar_contradiction_clause,[],[f588]) ).
thf(f593,plain,
( ( $false = $true )
| ( ( p @ sK10 )
= $false )
| ~ spl15_11
| ~ spl15_22 ),
inference(constrained_superposition,[],[f452,f504]) ).
thf(f607,plain,
( ( ( p @ sK10 )
= $false )
| ~ spl15_11
| ~ spl15_22 ),
inference(trivial_inequality_removal,[],[f593]) ).
thf(f612,plain,
( ( $false = $true )
| ~ spl15_11
| ~ spl15_22
| ~ spl15_25 ),
inference(forward_demodulation,[],[f607,f520]) ).
thf(f613,plain,
( $false
| ~ spl15_11
| ~ spl15_22
| ~ spl15_25 ),
inference(trivial_inequality_removal,[],[f612]) ).
thf(f614,plain,
( ~ spl15_11
| ~ spl15_22
| ~ spl15_25 ),
inference(avatar_contradiction_clause,[],[f613]) ).
thf(f757,plain,
( ! [X0: $i,X1: $i] :
( ( ( rel_s5 @ sK5 @ X1 )
= $false )
| ( ( q @ X0 )
= $true )
| ( ( rel_s5 @ X1 @ X0 )
= $false )
| ( $false = $true ) )
| ~ spl15_10 ),
inference(constrained_superposition,[],[f410,f449]) ).
thf(f767,plain,
( ! [X0: $i,X1: $i] :
( ( ( rel_s5 @ sK5 @ X1 )
= $false )
| ( ( q @ X0 )
= $true )
| ( ( rel_s5 @ X1 @ X0 )
= $false ) )
| ~ spl15_10 ),
inference(trivial_inequality_removal,[],[f757]) ).
thf(f902,plain,
( ! [X0: $i] :
( ( ( q @ X0 )
= $true )
| ( $false = $true )
| ( ( rel_s5 @ sK8 @ X0 )
= $false ) )
| ~ spl15_10
| ~ spl15_18 ),
inference(constrained_superposition,[],[f767,f484]) ).
thf(f915,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ sK8 @ X0 )
= $false )
| ( ( q @ X0 )
= $true ) )
| ~ spl15_10
| ~ spl15_18 ),
inference(trivial_inequality_removal,[],[f902]) ).
thf(f964,plain,
( ( $false = $true )
| ( ( q @ sK14 )
= $true )
| ~ spl15_10
| ~ spl15_18
| ~ spl15_30 ),
inference(constrained_superposition,[],[f915,f548]) ).
thf(f984,plain,
( ( ( q @ sK14 )
= $true )
| ~ spl15_10
| ~ spl15_18
| ~ spl15_30 ),
inference(trivial_inequality_removal,[],[f964]) ).
thf(f1000,plain,
( ( $false = $true )
| ~ spl15_10
| ~ spl15_18
| ~ spl15_30
| ~ spl15_31 ),
inference(forward_demodulation,[],[f984,f553]) ).
thf(f1001,plain,
( $false
| ~ spl15_10
| ~ spl15_18
| ~ spl15_30
| ~ spl15_31 ),
inference(trivial_inequality_removal,[],[f1000]) ).
thf(f1002,plain,
( ~ spl15_10
| ~ spl15_18
| ~ spl15_30
| ~ spl15_31 ),
inference(avatar_contradiction_clause,[],[f1001]) ).
thf(f1008,plain,
( ( ( p @ sK8 )
= $false )
| ( $false = $true )
| ~ spl15_11
| ~ spl15_18 ),
inference(constrained_superposition,[],[f452,f484]) ).
thf(f1026,plain,
( ( ( p @ sK8 )
= $false )
| ~ spl15_11
| ~ spl15_18 ),
inference(trivial_inequality_removal,[],[f1008]) ).
thf(f1032,plain,
( ( $false = $true )
| ~ spl15_11
| ~ spl15_18
| ~ spl15_19 ),
inference(forward_demodulation,[],[f1026,f489]) ).
thf(f1033,plain,
( $false
| ~ spl15_11
| ~ spl15_18
| ~ spl15_19 ),
inference(trivial_inequality_removal,[],[f1032]) ).
thf(f1034,plain,
( ~ spl15_11
| ~ spl15_18
| ~ spl15_19 ),
inference(avatar_contradiction_clause,[],[f1033]) ).
thf(f1064,plain,
( ! [X0: $i] :
( ( ( p @ sK6 )
= $false )
| ( ( q @ X0 )
= $true )
| ( $false = $true )
| ( ( rel_s5 @ sK6 @ X0 )
= $false ) )
| ~ spl15_13
| ~ spl15_14 ),
inference(constrained_superposition,[],[f459,f464]) ).
thf(f1079,plain,
( ! [X0: $i] :
( ( ( q @ X0 )
= $true )
| ( ( p @ sK6 )
= $false )
| ( ( rel_s5 @ sK6 @ X0 )
= $false ) )
| ~ spl15_13
| ~ spl15_14 ),
inference(trivial_inequality_removal,[],[f1064]) ).
thf(f1093,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ sK6 @ X0 )
= $false )
| ( ( q @ X0 )
= $true )
| ( $false = $true ) )
| ~ spl15_13
| ~ spl15_14
| ~ spl15_15 ),
inference(forward_demodulation,[],[f1079,f469]) ).
thf(f1094,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ sK6 @ X0 )
= $false )
| ( ( q @ X0 )
= $true ) )
| ~ spl15_13
| ~ spl15_14
| ~ spl15_15 ),
inference(trivial_inequality_removal,[],[f1093]) ).
thf(f1119,plain,
( ! [X0: $i] :
( ( ( q @ X0 )
= $true )
| ( $false = $true )
| ( ( rel_s5 @ X0 @ sK6 )
= $false ) )
| ~ spl15_13
| ~ spl15_14
| ~ spl15_15 ),
inference(constrained_superposition,[],[f1094,f401]) ).
thf(f1125,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ X0 @ sK6 )
= $false )
| ( ( q @ X0 )
= $true ) )
| ~ spl15_13
| ~ spl15_14
| ~ spl15_15 ),
inference(trivial_inequality_removal,[],[f1119]) ).
thf(f1147,plain,
( ! [X0: $i,X1: $i] :
( ( ( q @ X0 )
= $true )
| ( ( rel_s5 @ X1 @ sK6 )
= $false )
| ( $false = $true )
| ( ( rel_s5 @ X0 @ X1 )
= $false ) )
| ~ spl15_13
| ~ spl15_14
| ~ spl15_15 ),
inference(constrained_superposition,[],[f1125,f410]) ).
thf(f1154,plain,
( ! [X0: $i,X1: $i] :
( ( ( rel_s5 @ X1 @ sK6 )
= $false )
| ( ( q @ X0 )
= $true )
| ( ( rel_s5 @ X0 @ X1 )
= $false ) )
| ~ spl15_13
| ~ spl15_14
| ~ spl15_15 ),
inference(trivial_inequality_removal,[],[f1147]) ).
thf(f1252,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ X0 @ sK5 )
= $false )
| ( $false = $true )
| ( ( q @ X0 )
= $true ) )
| ~ spl15_13
| ~ spl15_14
| ~ spl15_15 ),
inference(constrained_superposition,[],[f464,f1154]) ).
thf(f1258,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ X0 @ sK5 )
= $false )
| ( ( q @ X0 )
= $true ) )
| ~ spl15_13
| ~ spl15_14
| ~ spl15_15 ),
inference(trivial_inequality_removal,[],[f1252]) ).
thf(f1273,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( ( rel_s5 @ sK5 @ X0 )
= $false )
| ( ( q @ X0 )
= $true ) )
| ~ spl15_13
| ~ spl15_14
| ~ spl15_15 ),
inference(constrained_superposition,[],[f401,f1258]) ).
thf(f1279,plain,
( ! [X0: $i] :
( ( ( q @ X0 )
= $true )
| ( ( rel_s5 @ sK5 @ X0 )
= $false ) )
| ~ spl15_13
| ~ spl15_14
| ~ spl15_15 ),
inference(trivial_inequality_removal,[],[f1273]) ).
thf(f1281,plain,
( spl15_10
| ~ spl15_13
| ~ spl15_14
| ~ spl15_15 ),
inference(avatar_split_clause,[],[f1279,f467,f462,f458,f448]) ).
cnf(s9,plain,
( spl15_10
| spl15_11
| spl15_12
| spl15_13 ),
inference(sat_conversion,[],[f460]) ).
cnf(s10,plain,
( spl15_10
| spl15_11
| spl15_12
| spl15_14 ),
inference(sat_conversion,[],[f465]) ).
cnf(s11,plain,
( spl15_10
| spl15_11
| spl15_12
| spl15_15 ),
inference(sat_conversion,[],[f470]) ).
cnf(s18,plain,
( spl15_12
| spl15_18
| spl15_22 ),
inference(sat_conversion,[],[f505]) ).
cnf(s19,plain,
( spl15_12
| spl15_19
| spl15_22 ),
inference(sat_conversion,[],[f506]) ).
cnf(s22,plain,
( spl15_12
| spl15_18
| spl15_25 ),
inference(sat_conversion,[],[f521]) ).
cnf(s23,plain,
( spl15_12
| spl15_19
| spl15_25 ),
inference(sat_conversion,[],[f522]) ).
cnf(s26,plain,
( spl15_12
| spl15_18
| spl15_28 ),
inference(sat_conversion,[],[f537]) ).
cnf(s27,plain,
( spl15_12
| spl15_18
| spl15_29 ),
inference(sat_conversion,[],[f542]) ).
cnf(s30,plain,
( spl15_12
| spl15_28
| spl15_30 ),
inference(sat_conversion,[],[f549]) ).
cnf(s31,plain,
( spl15_12
| spl15_28
| spl15_31 ),
inference(sat_conversion,[],[f554]) ).
cnf(s32,plain,
( spl15_12
| spl15_29
| spl15_30 ),
inference(sat_conversion,[],[f555]) ).
cnf(s33,plain,
( spl15_12
| spl15_29
| spl15_31 ),
inference(sat_conversion,[],[f556]) ).
cnf(s34,plain,
~ spl15_12,
inference(sat_conversion,[],[f557]) ).
cnf(s36,plain,
( ~ spl15_10
| ~ spl15_28
| ~ spl15_29 ),
inference(sat_conversion,[],[f589]) ).
cnf(s38,plain,
( ~ spl15_11
| ~ spl15_22
| ~ spl15_25 ),
inference(sat_conversion,[],[f614]) ).
cnf(s65,plain,
( ~ spl15_10
| ~ spl15_18
| ~ spl15_30
| ~ spl15_31 ),
inference(sat_conversion,[],[f1002]) ).
cnf(s69,plain,
( ~ spl15_11
| ~ spl15_18
| ~ spl15_19 ),
inference(sat_conversion,[],[f1034]) ).
cnf(s72,plain,
( spl15_10
| ~ spl15_13
| ~ spl15_14
| ~ spl15_15 ),
inference(sat_conversion,[],[f1281]) ).
cnf(s74,plain,
( spl15_29
| spl15_31 ),
inference(rat,[],[s33,s34]) ).
cnf(s75,plain,
( spl15_29
| spl15_30 ),
inference(rat,[],[s32,s34]) ).
cnf(s76,plain,
( spl15_28
| spl15_31 ),
inference(rat,[],[s31,s34]) ).
cnf(s77,plain,
( spl15_28
| spl15_30 ),
inference(rat,[],[s30,s34]) ).
cnf(s80,plain,
( spl15_18
| spl15_29 ),
inference(rat,[],[s27,s34]) ).
cnf(s81,plain,
( spl15_18
| spl15_28 ),
inference(rat,[],[s26,s34]) ).
cnf(s84,plain,
( spl15_19
| spl15_25 ),
inference(rat,[],[s23,s34]) ).
cnf(s85,plain,
( spl15_18
| spl15_25 ),
inference(rat,[],[s22,s34]) ).
cnf(s88,plain,
( spl15_19
| spl15_22 ),
inference(rat,[],[s19,s34]) ).
cnf(s89,plain,
( spl15_18
| spl15_22 ),
inference(rat,[],[s18,s34]) ).
cnf(s96,plain,
( spl15_10
| spl15_11
| spl15_15 ),
inference(rat,[],[s11,s34]) ).
cnf(s97,plain,
( spl15_10
| spl15_11
| spl15_14 ),
inference(rat,[],[s10,s34]) ).
cnf(s98,plain,
( spl15_10
| spl15_11
| spl15_13 ),
inference(rat,[],[s9,s34]) ).
cnf(s99,plain,
( spl15_11
| spl15_10 ),
inference(rat,[],[s72,s98,s97,s96]) ).
cnf(s100,plain,
( spl15_18
| ~ spl15_11 ),
inference(rat,[],[s38,s89,s85]) ).
cnf(s101,plain,
( ~ spl15_18
| ~ spl15_11 ),
inference(rat,[],[s38,s88,s84,s69]) ).
cnf(s102,plain,
~ spl15_11,
inference(rat,[],[s101,s100]) ).
cnf(s103,plain,
spl15_10,
inference(rat,[],[s99,s102]) ).
cnf(s105,plain,
spl15_18,
inference(rat,[],[s36,s81,s80,s103]) ).
cnf(s107,plain,
spl15_29,
inference(rat,[],[s65,s75,s74,s103,s105]) ).
cnf(s109,plain,
~ spl15_28,
inference(rat,[],[s36,s103,s107]) ).
cnf(s110,plain,
spl15_31,
inference(rat,[],[s76,s109]) ).
cnf(s111,plain,
spl15_30,
inference(rat,[],[s77,s109]) ).
cnf(s112,plain,
$false,
inference(rat,[],[s65,s105,s103,s110,s111]) ).
thf(f1282,plain,
$false,
inference(avatar_sat_refutation,[],[s112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO443^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.26 % Computer : n026.cluster.edu
% 0.08/0.26 % Model : x86_64 x86_64
% 0.08/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.26 % Memory : 8046.5625MB
% 0.08/0.26 % OS : Linux 6.8.0-71-generic
% 0.08/0.26 % CPULimit : 300
% 0.08/0.26 % WCLimit : 300
% 0.08/0.26 % DateTime : Tue Sep 29 16:54:43 UTC 2026
% 0.08/0.26 % CPUTime :
% 0.08/0.26 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.31 Running higher-order theorem proving
% 0.25/0.33 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
% 0.31/0.40 % (859647)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.31/0.40 % (859658)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.31/0.40 % (859658)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
% 0.31/0.40 % (859658)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=84291295:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.31/0.40 % (859653)lrs+10_16_si=on:nwc=1.5:random_seed=1616705846:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.31/0.40 % (859656)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2668915943:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.31/0.40 % (859654)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2332063628:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.31/0.40 % (859655)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=3367210913: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)
% 0.31/0.40 % (859657)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3718531009:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.31/0.40 % (859654)Instruction limit reached!
% 0.31/0.40 % (859654)------------------------------
% 0.31/0.40 % (859654)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.40 % (859654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.40 % (859654)CaDiCaL version: 2.1.3
% 0.31/0.40 % (859654)Termination reason: Instruction limit
% 0.31/0.40 % (859654)Termination phase: Property scanning
% 0.31/0.40 % (859654)Time elapsed: 0.003 s
% 0.31/0.40 % (859654)Peak memory usage: 10 MB
% 0.31/0.40 % (859654)Instructions burned: 3 (million)
% 0.31/0.40 % (859652)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1204766440:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.31/0.40 % (859658) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-859647-859658"...
% 0.31/0.40 % (859653)Instruction limit reached!
% 0.31/0.40 % (859653)------------------------------
% 0.31/0.40 % (859653)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.40 % (859653)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.40 % (859653)CaDiCaL version: 2.1.3
% 0.31/0.40 % (859653)Termination reason: Instruction limit
% 0.31/0.40 % (859653)Termination phase: Saturation
% 0.31/0.40 % (859653)Time elapsed: 0.016 s
% 0.31/0.40 % (859653)Peak memory usage: 12 MB
% 0.31/0.40 % (859653)Instructions burned: 18 (million)
% 0.31/0.40 % (859658)...printing done.
% 0.31/0.40 % (859658)Refutation found. Thanks to Tanya!
% 0.31/0.40 % SZS status Theorem for theBenchmark
% 0.31/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.31/0.41 % (859658)------------------------------
% 0.31/0.41 % (859658)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.31/0.41 % (859658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.31/0.41 % (859658)CaDiCaL version: 2.1.3
% 0.31/0.41 % (859658)Termination reason: Refutation
% 0.31/0.41 % (859658)Time elapsed: 0.035 s
% 0.31/0.41 % (859658)Peak memory usage: 13 MB
% 0.31/0.41 % (859658)Instructions burned: 73 (million)
% 0.31/0.41 % (859647)Success in time 0.06 s
% 0.31/0.41 % Vampire exiting
%------------------------------------------------------------------------------