%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO462^5 : 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 : n018.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 08:47:54 AM UTC 2026
% Result : Theorem 0.18s 0.27s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 16
% Syntax : Number of formulae : 176 ( 47 unt; 0 typ; 8 def)
% Number of atoms : 1367 ( 240 equ; 0 cnn)
% Maximal formula atoms : 11 ( 7 avg)
% Number of connectives : 1672 ( 331 ~; 365 |; 0 &; 903 @)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 116 ( 116 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 62 usr; 15 con; 0-4 aty)
% ( 65 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 303 ( 0 sgn 55 !; 0 ?; 303 :)
% 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_s4: $i > $i > $o ).
thf(func_def_33,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s4: ( $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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_42,type,
vOR: $o > $o > $o ).
thf(func_def_45,type,
vNOT: $o > $o ).
thf(func_def_46,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
vIMP: $o > $o > $o ).
thf(func_def_48,type,
vAND: $o > $o > $o ).
thf(func_def_49,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) )
= mand ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
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(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f36,conjecture,
mvalid @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f37,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f40,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f41,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f47,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f48,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f58,plain,
~ ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f59,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) )
!= $true ),
inference(fool_elimination,[],[f58]) ).
thf(f68,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f69,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f70,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f71,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f72,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f96,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f97,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f96]) ).
thf(f98,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) )
!= $true ),
inference(flattening,[],[f59]) ).
thf(f100,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f71]) ).
thf(f101,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f117,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f118,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f120,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f122,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f127,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f97]) ).
thf(f132,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f137,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,[],[f100,f101,f117,f101,f101]) ).
thf(f138,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,[],[f132,f117,f101]) ).
thf(f140,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,[],[f122,f137,f138,f138]) ).
thf(f148,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ p
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ q ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f118,f120,f138,f127,f140,f140,f127,f127]) ).
thf(f150,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( ~ ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f151,plain,
( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( ~ ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
( ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f155,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X1: $i] :
( ( ~ ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) )
| ~ ( rel_s4 @ sK0 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
! [X1: $i] :
( ( ( ~ ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) )
= $true )
| ( ( ~ ( rel_s4 @ sK0 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( ( ( ~ ( rel_s4 @ sK0 @ X1 ) )
= $true )
| ( $false
= ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) ) ),
inference(not_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $false
= ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) ) ),
inference(not_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X1: $i] :
( ( ( ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) )
= $false )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f163,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( ( ~ ( p @ X1 )
| ( q @ X1 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X1: $i] :
( ( ( ~ ( p @ X1 ) )
= $true )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( ( q @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $false
= ( p @ X1 ) )
| ( ( q @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( $true
= ( ~ ( q @ X1 )
| ( p @ X1 ) ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f167,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( ( ~ ( q @ X1 ) )
= $true )
| ( $true
= ( p @ X1 ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( ( q @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f169,plain,
( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f153]) ).
thf(f170,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) )
= $true )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) )
= $false )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
= $false )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) )
= $false )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f174,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
= $true )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X1: $i] :
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ X1 ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ X1 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f179,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X2: $i,X1: $i] :
( ( ( ( q @ X2 )
| ~ ( rel_s4 @ sK0 @ X2 ) )
= $true )
| ( $true
= ( ( p @ X1 )
| ~ ( rel_s4 @ sK0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f182,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK0 @ X2 ) )
= $true )
| ( $true
= ( ( p @ X1 )
| ~ ( rel_s4 @ sK0 @ X1 ) ) )
| ( ( q @ X2 )
= $true ) ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X2: $i,X1: $i] :
( ( ( q @ X2 )
= $true )
| ( $true
= ( ( p @ X1 )
| ~ ( rel_s4 @ sK0 @ X1 ) ) )
| ( ( rel_s4 @ sK0 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ sK0 @ X1 ) )
= $true )
| ( $true
= ( p @ X1 ) )
| ( ( rel_s4 @ sK0 @ X2 )
= $false )
| ( ( q @ X2 )
= $true ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( ( rel_s4 @ sK0 @ X2 )
= $false )
| ( $true
= ( p @ X1 ) )
| ( ( q @ X2 )
= $true ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f177]) ).
thf(f187,plain,
! [X1: $i] :
( ( ( ( p @ sK1 )
| ~ ( rel_s4 @ sK0 @ sK1 ) )
= $false )
| ( $true
= ( ( p @ X1 )
| ~ ( rel_s4 @ sK0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f186]) ).
thf(f188,plain,
! [X1: $i] :
( ( $true
= ( ( p @ X1 )
| ~ ( rel_s4 @ sK0 @ X1 ) ) )
| ( ( ~ ( rel_s4 @ sK0 @ sK1 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X1: $i] :
( ( ( p @ sK1 )
= $false )
| ( $true
= ( ( p @ X1 )
| ~ ( rel_s4 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f187]) ).
thf(f190,plain,
! [X1: $i] :
( ( ( ~ ( rel_s4 @ sK0 @ X1 ) )
= $true )
| ( $true
= ( p @ X1 ) )
| ( ( p @ sK1 )
= $false ) ),
inference(or_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( ( p @ sK1 )
= $false )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X1: $i] :
( ( ( ~ ( rel_s4 @ sK0 @ sK1 ) )
= $false )
| ( $true
= ( p @ X1 ) )
| ( ( ~ ( rel_s4 @ sK0 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f188]) ).
thf(f193,plain,
! [X1: $i] :
( ( ( ~ ( rel_s4 @ sK0 @ X1 ) )
= $true )
| ( $true
= ( p @ X1 ) )
| ( ( rel_s4 @ sK0 @ sK1 )
= $true ) ),
inference(not_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X1: $i] :
( ( ( rel_s4 @ sK0 @ sK1 )
= $true )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f193]) ).
thf(f195,plain,
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f172]) ).
thf(f196,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ sK2 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f195]) ).
thf(f197,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ sK2 ) ) ),
inference(or_proxy_clausification,[],[f196]) ).
thf(f198,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ sK2 ) )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f196]) ).
thf(f199,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ sK2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ sK2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X1: $i] :
( ( $true
= ( ( q @ X1 )
| ~ ( rel_s4 @ sK0 @ X1 ) ) )
| ( ( ( q @ sK2 )
| ~ ( rel_s4 @ sK0 @ sK2 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f200]) ).
thf(f202,plain,
! [X1: $i] :
( ( ( ( q @ sK2 )
| ~ ( rel_s4 @ sK0 @ sK2 ) )
= $false )
| ( ( ~ ( rel_s4 @ sK0 @ X1 ) )
= $true )
| ( ( q @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f201]) ).
thf(f203,plain,
! [X1: $i] :
( ( ( ~ ( rel_s4 @ sK0 @ X1 ) )
= $true )
| ( $false
= ( ~ ( rel_s4 @ sK0 @ sK2 ) ) )
| ( ( q @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X1: $i] :
( ( ( ~ ( rel_s4 @ sK0 @ X1 ) )
= $true )
| ( ( q @ sK2 )
= $false )
| ( ( q @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f202]) ).
thf(f205,plain,
! [X1: $i] :
( ( ( q @ X1 )
= $true )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( ( q @ sK2 )
= $false ) ),
inference(not_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $false
= ( ~ ( rel_s4 @ sK0 @ sK2 ) ) )
| ( ( q @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f203]) ).
thf(f207,plain,
! [X1: $i] :
( ( ( q @ X1 )
= $true )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( ( rel_s4 @ sK0 @ sK2 )
= $true ) ),
inference(not_proxy_clausification,[],[f206]) ).
thf(f208,plain,
( ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ sK3 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f197]) ).
thf(f209,plain,
( ( ( ( q @ sK2 )
| ~ ( rel_s4 @ sK0 @ sK2 ) )
= $false )
| ( $false
= ( ( p @ sK3 )
| ~ ( rel_s4 @ sK0 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f208]) ).
thf(f210,plain,
( ( $false
= ( ( p @ sK3 )
| ~ ( rel_s4 @ sK0 @ sK3 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK0 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f209]) ).
thf(f211,plain,
( ( $false
= ( ( p @ sK3 )
| ~ ( rel_s4 @ sK0 @ sK3 ) ) )
| ( ( q @ sK2 )
= $false ) ),
inference(or_proxy_clausification,[],[f209]) ).
thf(f212,plain,
( ( ( q @ sK2 )
= $false )
| ( ( ~ ( rel_s4 @ sK0 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f211]) ).
thf(f213,plain,
( ( ( q @ sK2 )
= $false )
| ( $false
= ( p @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f211]) ).
thf(f214,plain,
( ( ( rel_s4 @ sK0 @ sK3 )
= $true )
| ( ( q @ sK2 )
= $false ) ),
inference(not_proxy_clausification,[],[f212]) ).
thf(f215,plain,
( ( $false
= ( ~ ( rel_s4 @ sK0 @ sK2 ) ) )
| ( ( ~ ( rel_s4 @ sK0 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f210]) ).
thf(f216,plain,
( ( $false
= ( ~ ( rel_s4 @ sK0 @ sK2 ) ) )
| ( $false
= ( p @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f210]) ).
thf(f217,plain,
( ( $false
= ( p @ sK3 ) )
| ( ( rel_s4 @ sK0 @ sK2 )
= $true ) ),
inference(not_proxy_clausification,[],[f216]) ).
thf(f218,plain,
( ( ( rel_s4 @ sK0 @ sK2 )
= $true )
| ( ( ~ ( rel_s4 @ sK0 @ sK3 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f215]) ).
thf(f219,plain,
( ( ( rel_s4 @ sK0 @ sK2 )
= $true )
| ( ( rel_s4 @ sK0 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f218]) ).
thf(f233,definition,
( spl4_1
<=> ! [X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f234,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f233]) ).
thf(f236,definition,
( spl4_2
<=> ! [X2: $i] :
( ( ( rel_s4 @ sK0 @ X2 )
= $false )
| ( ( q @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f237,plain,
( ! [X2: $i] :
( ( ( rel_s4 @ sK0 @ X2 )
= $false )
| ( ( q @ X2 )
= $true ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f236]) ).
thf(f238,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f185,f236,f233]) ).
thf(f240,definition,
( spl4_3
<=> ( ( p @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f242,plain,
( ( ( p @ sK1 )
= $false )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f240]) ).
thf(f243,plain,
( spl4_3
| spl4_1 ),
inference(avatar_split_clause,[],[f191,f233,f240]) ).
thf(f245,definition,
( spl4_4
<=> ( ( rel_s4 @ sK0 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f247,plain,
( ( ( rel_s4 @ sK0 @ sK1 )
= $true )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f245]) ).
thf(f248,plain,
( spl4_1
| spl4_4 ),
inference(avatar_split_clause,[],[f194,f245,f233]) ).
thf(f250,definition,
( spl4_5
<=> ( ( q @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f252,plain,
( ( ( q @ sK2 )
= $false )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f250]) ).
thf(f253,plain,
( spl4_5
| spl4_2 ),
inference(avatar_split_clause,[],[f205,f236,f250]) ).
thf(f255,definition,
( spl4_6
<=> ( ( rel_s4 @ sK0 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f257,plain,
( ( ( rel_s4 @ sK0 @ sK2 )
= $true )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f255]) ).
thf(f258,plain,
( spl4_2
| spl4_6 ),
inference(avatar_split_clause,[],[f207,f255,f236]) ).
thf(f260,definition,
( spl4_7
<=> ( $false
= ( p @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
thf(f262,plain,
( ( $false
= ( p @ sK3 ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f260]) ).
thf(f263,plain,
( spl4_7
| spl4_5 ),
inference(avatar_split_clause,[],[f213,f250,f260]) ).
thf(f265,definition,
( spl4_8
<=> ( ( rel_s4 @ sK0 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
thf(f267,plain,
( ( ( rel_s4 @ sK0 @ sK3 )
= $true )
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f265]) ).
thf(f268,plain,
( spl4_5
| spl4_8 ),
inference(avatar_split_clause,[],[f214,f265,f250]) ).
thf(f269,plain,
( spl4_7
| spl4_6 ),
inference(avatar_split_clause,[],[f217,f255,f260]) ).
thf(f270,plain,
( spl4_8
| spl4_6 ),
inference(avatar_split_clause,[],[f219,f255,f265]) ).
thf(f276,plain,
( ( ( q @ sK2 )
= $true )
| ( $true = $false )
| ( $false
= ( p @ sK2 ) )
| ~ spl4_6 ),
inference(constrained_superposition,[],[f165,f257]) ).
thf(f277,plain,
( ( ( q @ sK2 )
= $true )
| ( $false
= ( p @ sK2 ) )
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f276]) ).
thf(f279,plain,
( ( $true = $false )
| ( $false
= ( p @ sK2 ) )
| ~ spl4_5
| ~ spl4_6 ),
inference(forward_demodulation,[],[f277,f252]) ).
thf(f280,plain,
( ( $false
= ( p @ sK2 ) )
| ~ spl4_5
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f279]) ).
thf(f285,plain,
( ( $true = $false )
| ( ( q @ sK1 )
= $true )
| ~ spl4_2
| ~ spl4_4 ),
inference(constrained_superposition,[],[f247,f237]) ).
thf(f300,plain,
( ( $true = $false )
| ( $true
= ( p @ sK2 ) )
| ~ spl4_1
| ~ spl4_6 ),
inference(constrained_superposition,[],[f257,f234]) ).
thf(f304,plain,
( ( $true
= ( p @ sK2 ) )
| ~ spl4_1
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f300]) ).
thf(f314,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_5
| ~ spl4_6 ),
inference(forward_demodulation,[],[f304,f280]) ).
thf(f315,plain,
( $false
| ~ spl4_1
| ~ spl4_5
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f314]) ).
thf(f316,plain,
( ~ spl4_1
| ~ spl4_5
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f315]) ).
thf(f317,plain,
( ( ( q @ sK1 )
= $true )
| ~ spl4_2
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f285]) ).
thf(f328,plain,
( ( $true = $false )
| ( ( q @ sK3 )
= $true )
| ~ spl4_2
| ~ spl4_8 ),
inference(constrained_superposition,[],[f267,f237]) ).
thf(f329,plain,
( ( ( q @ sK3 )
= $true )
| ~ spl4_2
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f328]) ).
thf(f333,plain,
( ( ( q @ sK1 )
= $false )
| ( $true = $false )
| ( ( p @ sK1 )
= $true )
| ~ spl4_4 ),
inference(constrained_superposition,[],[f168,f247]) ).
thf(f337,plain,
( ( ( q @ sK3 )
= $false )
| ( $true
= ( p @ sK3 ) )
| ( $true = $false )
| ~ spl4_8 ),
inference(constrained_superposition,[],[f267,f168]) ).
thf(f339,plain,
( ( ( q @ sK1 )
= $false )
| ( ( p @ sK1 )
= $true )
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f333]) ).
thf(f341,plain,
( ( $true
= ( p @ sK3 ) )
| ( ( q @ sK3 )
= $false )
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f337]) ).
thf(f344,plain,
( ( ( p @ sK1 )
= $true )
| ( $true = $false )
| ~ spl4_2
| ~ spl4_4 ),
inference(forward_demodulation,[],[f339,f317]) ).
thf(f345,plain,
( ( ( p @ sK1 )
= $true )
| ~ spl4_2
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f344]) ).
thf(f348,plain,
( ( $true = $false )
| ( ( q @ sK3 )
= $false )
| ~ spl4_7
| ~ spl4_8 ),
inference(forward_demodulation,[],[f341,f262]) ).
thf(f349,plain,
( ( ( q @ sK3 )
= $false )
| ~ spl4_7
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f348]) ).
thf(f353,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_4 ),
inference(forward_demodulation,[],[f345,f242]) ).
thf(f354,plain,
( $false
| ~ spl4_2
| ~ spl4_3
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f353]) ).
thf(f355,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f354]) ).
thf(f359,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_7
| ~ spl4_8 ),
inference(forward_demodulation,[],[f349,f329]) ).
thf(f360,plain,
( $false
| ~ spl4_2
| ~ spl4_7
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f359]) ).
thf(f361,plain,
( ~ spl4_2
| ~ spl4_7
| ~ spl4_8 ),
inference(avatar_contradiction_clause,[],[f360]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f238]) ).
cnf(s2,plain,
( spl4_1
| spl4_3 ),
inference(sat_conversion,[],[f243]) ).
cnf(s3,plain,
( spl4_1
| spl4_4 ),
inference(sat_conversion,[],[f248]) ).
cnf(s4,plain,
( spl4_2
| spl4_5 ),
inference(sat_conversion,[],[f253]) ).
cnf(s5,plain,
( spl4_2
| spl4_6 ),
inference(sat_conversion,[],[f258]) ).
cnf(s6,plain,
( spl4_5
| spl4_7 ),
inference(sat_conversion,[],[f263]) ).
cnf(s7,plain,
( spl4_5
| spl4_8 ),
inference(sat_conversion,[],[f268]) ).
cnf(s8,plain,
( spl4_6
| spl4_7 ),
inference(sat_conversion,[],[f269]) ).
cnf(s9,plain,
( spl4_6
| spl4_8 ),
inference(sat_conversion,[],[f270]) ).
cnf(s15,plain,
( ~ spl4_1
| ~ spl4_5
| ~ spl4_6 ),
inference(sat_conversion,[],[f316]) ).
cnf(s17,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f355]) ).
cnf(s19,plain,
( ~ spl4_2
| ~ spl4_7
| ~ spl4_8 ),
inference(sat_conversion,[],[f361]) ).
cnf(s20,plain,
spl4_1,
inference(rat,[],[s17,s1,s2,s3]) ).
cnf(s21,plain,
( spl4_5
| ~ spl4_2 ),
inference(rat,[],[s19,s6,s7]) ).
cnf(s22,plain,
~ spl4_2,
inference(rat,[],[s19,s8,s9,s15,s21,s20]) ).
cnf(s23,plain,
spl4_6,
inference(rat,[],[s5,s22]) ).
cnf(s24,plain,
spl4_5,
inference(rat,[],[s4,s22]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s15,s20,s23,s24]) ).
thf(f362,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO462^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n018.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 17:01:11 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.23 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
% 0.18/0.27 % (353315)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.18/0.27 % (353320)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2731926694:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.18/0.27 % (353320) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-353315-353320"...
% 0.18/0.27 % (353322)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=654557437:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.18/0.27 % (353324)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3658112198:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.18/0.27 % (353321)lrs+10_16_si=on:nwc=1.5:random_seed=2835168966:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.18/0.27 % (353323)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=2457976627: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)
% 0.18/0.27 % (353320)...printing done.
% 0.18/0.27 % (353322)Instruction limit reached!
% 0.18/0.27 % (353322)------------------------------
% 0.18/0.27 % (353322)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.27 % (353322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.27 % (353322)CaDiCaL version: 2.1.3
% 0.18/0.27 % (353322)Termination reason: Instruction limit
% 0.18/0.27 % (353322)Termination phase: Property scanning
% 0.18/0.27 % (353322)Time elapsed: 0.002 s
% 0.18/0.27 % (353322)Peak memory usage: 10 MB
% 0.18/0.27 % (353322)Instructions burned: 4 (million)
% 0.18/0.27 % (353320)Refutation found. Thanks to Tanya!
% 0.18/0.27 % SZS status Theorem for theBenchmark
% 0.18/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.27 % (353320)------------------------------
% 0.18/0.27 % (353320)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.27 % (353320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.27 % (353320)CaDiCaL version: 2.1.3
% 0.18/0.27 % (353320)Termination reason: Refutation
% 0.18/0.27 % (353320)Time elapsed: 0.008 s
% 0.18/0.27 % (353320)Peak memory usage: 13 MB
% 0.18/0.27 % (353320)Instructions burned: 26 (million)
% 0.18/0.27 % (353315)Success in time 0.035 s
% 0.18/0.27 % Vampire exiting
%------------------------------------------------------------------------------