%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO463^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 08:50:10 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 23
% Syntax : Number of formulae : 224 ( 71 unt; 0 typ; 13 def)
% Number of atoms : 1638 ( 279 equ; 0 cnn)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 2102 ( 388 ~; 422 |; 13 &;1154 @)
% ( 13 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 127 ( 127 >; 0 *; 0 +; 0 <<)
% Number of symbols : 72 ( 68 usr; 21 con; 0-4 aty)
% ( 100 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 378 ( 0 sgn 84 !; 0 ?; 378 :)
% 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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_40,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_41,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vNOT: $o > $o ).
thf(func_def_43,type,
vOR: $o > $o > $o ).
thf(func_def_44,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vIMP: $o > $o > $o ).
thf(func_def_49,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_50,type,
vAND: $o > $o > $o ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
thf(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,
( 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,
( 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(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( 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,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f35,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',a2) ).
thf(f36,conjecture,
mvalid @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mbox_s4 @ ( 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 ) ) @ ( mbox_s4 @ ( mequiv @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f40,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f41,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f42,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f43,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f44,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f45,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f47,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f67,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f68,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f67]) ).
thf(f81,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f82,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f89,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f90,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f89]) ).
thf(f94,plain,
mtransitive @ rel_s4,
inference(rectify,[],[f35]) ).
thf(f95,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f94]) ).
thf(f96,plain,
~ ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mbox_s4 @ ( mequiv @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f97,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mbox_s4 @ ( mequiv @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f96]) ).
thf(f98,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mbox_s4 @ ( mequiv @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ) )
!= $true ),
inference(flattening,[],[f97]) ).
thf(f101,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f102,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f103,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f104,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f106,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f119,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f126,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f130,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f133,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f95]) ).
thf(f134,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mequiv @ p @ q ) ) @ ( mbox_s4 @ ( mequiv @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f98]) ).
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,[],[f103,f101,f102,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,[],[f104,f102,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,[],[f106,f137,f138,f138]) ).
thf(f148,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f133,f119]) ).
thf(f149,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ 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] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) ) ) ) ) ),
inference(definition_unfolding,[],[f134,f126,f138,f130,f140,f130,f140,f130,f130]) ).
thf(f150,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( ~ ( ~ ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( q @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( ~ ( ~ ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( q @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f155,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X1: $i] :
( $true
= ( ~ ( rel_s4 @ sK0 @ X1 )
| ~ ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
! [X1: $i] :
( ( $true
= ( ~ ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( ( $false
= ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X1: $i] :
( ( $false
= ( ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X1: $i] :
( ( $false
= ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f162,plain,
! [X1: $i] :
( ( $true
= ( ~ ( p @ X1 )
| ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( $true
= ( ~ ( q @ X1 )
| ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f160]) ).
thf(f167,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f153]) ).
thf(f171,plain,
( $false
= ( ~ ( rel_s4 @ sK0 @ sK1 )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f172,plain,
( $false
= ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( $false
= ( ~ ( rel_s4 @ sK0 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f174,plain,
( $true
= ( rel_s4 @ sK0 @ sK1 ) ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f176,plain,
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f176]) ).
thf(f178,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f179,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f180,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f185,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 )
| ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X2 )
| ( p @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f186]) ).
thf(f188,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK1 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK1 @ X1 ) )
| ( $false
= ( rel_s4 @ sK1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f183]) ).
thf(f193,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 )
| ( q @ X1 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK2 )
| ( q @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f192]) ).
thf(f194,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK2 )
| ( q @ sK2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( q @ sK2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f194]) ).
thf(f197,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK1 @ sK2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_s4 @ sK1 @ sK2 ) )
| ( $false
= ( rel_s4 @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( q @ sK2 ) )
| ( $false
= ( rel_s4 @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f195]) ).
thf(f200,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ sK3 ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f178]) ).
thf(f201,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ sK3 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f200]) ).
thf(f202,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ sK3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f201]) ).
thf(f203,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ sK3 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f201]) ).
thf(f204,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ sK3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ sK3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 )
| ( p @ sK3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 )
| ( p @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f205]) ).
thf(f207,plain,
! [X1: $i] :
( ( $false
= ( p @ sK3 ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 )
| ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 )
| ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f206]) ).
thf(f209,plain,
! [X1: $i] :
( ( $true
= ( rel_s4 @ sK1 @ sK3 ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 )
| ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f208]) ).
thf(f210,plain,
! [X1: $i] :
( ( $true
= ( rel_s4 @ sK1 @ sK3 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f209]) ).
thf(f211,plain,
! [X1: $i] :
( ( $true
= ( rel_s4 @ sK1 @ sK3 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s4 @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f210]) ).
thf(f212,plain,
! [X1: $i] :
( ( $false
= ( p @ sK3 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f207]) ).
thf(f213,plain,
! [X1: $i] :
( ( $false
= ( p @ sK3 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s4 @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f212]) ).
thf(f214,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f202]) ).
thf(f215,plain,
( ( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 )
| ( p @ sK3 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK4 )
| ( q @ sK4 ) ) ) ),
inference(beta-eta_normalization,[],[f214]) ).
thf(f216,plain,
( ( $false
= ( p @ sK3 ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK4 )
| ( q @ sK4 ) ) ) ),
inference(or_proxy_clausification,[],[f215]) ).
thf(f217,plain,
( ( $false
= ( ~ ( rel_s4 @ sK1 @ sK3 ) ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK4 )
| ( q @ sK4 ) ) ) ),
inference(or_proxy_clausification,[],[f215]) ).
thf(f218,plain,
( ( $true
= ( rel_s4 @ sK1 @ sK3 ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK4 )
| ( q @ sK4 ) ) ) ),
inference(not_proxy_clausification,[],[f217]) ).
thf(f219,plain,
( ( $true
= ( rel_s4 @ sK1 @ sK3 ) )
| ( $false
= ( q @ sK4 ) ) ),
inference(or_proxy_clausification,[],[f218]) ).
thf(f220,plain,
( ( $true
= ( rel_s4 @ sK1 @ sK3 ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK4 ) ) ) ),
inference(or_proxy_clausification,[],[f218]) ).
thf(f221,plain,
( ( $true
= ( rel_s4 @ sK1 @ sK3 ) )
| ( $true
= ( rel_s4 @ sK1 @ sK4 ) ) ),
inference(not_proxy_clausification,[],[f220]) ).
thf(f222,plain,
( ( $false
= ( p @ sK3 ) )
| ( $false
= ( q @ sK4 ) ) ),
inference(or_proxy_clausification,[],[f216]) ).
thf(f223,plain,
( ( $false
= ( p @ sK3 ) )
| ( $false
= ( ~ ( rel_s4 @ sK1 @ sK4 ) ) ) ),
inference(or_proxy_clausification,[],[f216]) ).
thf(f224,plain,
( ( $false
= ( p @ sK3 ) )
| ( $true
= ( rel_s4 @ sK1 @ sK4 ) ) ),
inference(not_proxy_clausification,[],[f223]) ).
thf(f225,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y2 @ Y1 )
& ( rel_s4 @ Y1 @ Y0 ) )
=> ( rel_s4 @ Y2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f226,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y2 @ Y1 )
& ( rel_s4 @ Y1 @ Y0 ) )
=> ( rel_s4 @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y1 @ Y0 )
& ( rel_s4 @ Y0 @ X1 ) )
=> ( rel_s4 @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f226]) ).
thf(f228,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y1 @ Y0 )
& ( rel_s4 @ Y0 @ X1 ) )
=> ( rel_s4 @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s4 @ Y0 @ X2 )
& ( rel_s4 @ X2 @ X1 ) )
=> ( rel_s4 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f228]) ).
thf(f230,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s4 @ Y0 @ X2 )
& ( rel_s4 @ X2 @ X1 ) )
=> ( rel_s4 @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f229]) ).
thf(f231,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s4 @ X3 @ X2 )
& ( rel_s4 @ X2 @ X1 ) )
=> ( rel_s4 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f230]) ).
thf(f232,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( rel_s4 @ X3 @ X2 )
& ( rel_s4 @ X2 @ X1 ) ) )
| ( $true
= ( rel_s4 @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f231]) ).
thf(f233,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X2 @ X1 ) )
| ( $true
= ( rel_s4 @ X3 @ X1 ) )
| ( $false
= ( rel_s4 @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f232]) ).
thf(f238,definition,
( spl5_1
<=> ! [X2: $i] :
( ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_s4 @ sK1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f239,plain,
( ! [X2: $i] :
( ( $false
= ( rel_s4 @ sK1 @ X2 ) )
| ( $true
= ( p @ X2 ) ) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f238]) ).
thf(f241,definition,
( spl5_2
<=> ! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_s4 @ sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f242,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s4 @ sK1 @ X1 ) )
| ( $true
= ( q @ X1 ) ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f241]) ).
thf(f243,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f191,f241,f238]) ).
thf(f245,definition,
( spl5_3
<=> ( $true
= ( rel_s4 @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
thf(f247,plain,
( ( $true
= ( rel_s4 @ sK1 @ sK2 ) )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f245]) ).
thf(f248,plain,
( spl5_3
| spl5_2 ),
inference(avatar_split_clause,[],[f198,f241,f245]) ).
thf(f250,definition,
( spl5_4
<=> ( $false
= ( q @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
thf(f252,plain,
( ( $false
= ( q @ sK2 ) )
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f250]) ).
thf(f253,plain,
( spl5_4
| spl5_2 ),
inference(avatar_split_clause,[],[f199,f241,f250]) ).
thf(f255,definition,
( spl5_5
<=> ( $true
= ( rel_s4 @ sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
thf(f257,plain,
( ( $true
= ( rel_s4 @ sK1 @ sK3 ) )
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f255]) ).
thf(f258,plain,
( spl5_1
| spl5_5 ),
inference(avatar_split_clause,[],[f211,f255,f238]) ).
thf(f260,definition,
( spl5_6
<=> ( $false
= ( p @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
thf(f262,plain,
( ( $false
= ( p @ sK3 ) )
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f260]) ).
thf(f263,plain,
( spl5_1
| spl5_6 ),
inference(avatar_split_clause,[],[f213,f260,f238]) ).
thf(f265,definition,
( spl5_7
<=> ( $true
= ( rel_s4 @ sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
thf(f267,plain,
( ( $true
= ( rel_s4 @ sK1 @ sK4 ) )
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f265]) ).
thf(f268,plain,
( spl5_7
| spl5_5 ),
inference(avatar_split_clause,[],[f221,f255,f265]) ).
thf(f270,definition,
( spl5_8
<=> ( $false
= ( q @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
thf(f272,plain,
( ( $false
= ( q @ sK4 ) )
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f270]) ).
thf(f273,plain,
( spl5_8
| spl5_5 ),
inference(avatar_split_clause,[],[f219,f255,f270]) ).
thf(f274,plain,
( spl5_7
| spl5_6 ),
inference(avatar_split_clause,[],[f224,f260,f265]) ).
thf(f275,plain,
( spl5_8
| spl5_6 ),
inference(avatar_split_clause,[],[f222,f260,f270]) ).
thf(f276,plain,
( ( $true = $false )
| ( $true
= ( q @ sK3 ) )
| ~ spl5_2
| ~ spl5_5 ),
inference(constrained_superposition,[],[f242,f257]) ).
thf(f424,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s4 @ X0 @ sK3 ) )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) ) )
| ~ spl5_5 ),
inference(constrained_superposition,[],[f257,f233]) ).
thf(f444,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s4 @ X0 @ sK3 ) )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) ) )
| ~ spl5_5 ),
inference(trivial_inequality_removal,[],[f424]) ).
thf(f500,plain,
( ( $true = $false )
| ( $false
= ( rel_s4 @ sK0 @ sK1 ) )
| ( $true
= ( p @ sK3 ) )
| ( $false
= ( q @ sK3 ) )
| ~ spl5_5 ),
inference(constrained_superposition,[],[f444,f169]) ).
thf(f517,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK1 ) )
| ( $true
= ( p @ sK3 ) )
| ( $false
= ( q @ sK3 ) )
| ~ spl5_5 ),
inference(trivial_inequality_removal,[],[f500]) ).
thf(f520,definition,
( spl5_17
<=> ( $false
= ( rel_s4 @ sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_17])],[avatar_definition]) ).
thf(f522,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK1 ) )
| ~ spl5_17 ),
inference(avatar_component_clause,[],[f520]) ).
thf(f524,definition,
( spl5_18
<=> ( $false
= ( q @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_18])],[avatar_definition]) ).
thf(f526,plain,
( ( $false
= ( q @ sK3 ) )
| ~ spl5_18 ),
inference(avatar_component_clause,[],[f524]) ).
thf(f528,definition,
( spl5_19
<=> ( $true
= ( p @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_19])],[avatar_definition]) ).
thf(f530,plain,
( ( $true
= ( p @ sK3 ) )
| ~ spl5_19 ),
inference(avatar_component_clause,[],[f528]) ).
thf(f532,plain,
( spl5_18
| spl5_19
| spl5_17
| ~ spl5_5 ),
inference(avatar_split_clause,[],[f517,f255,f520,f528,f524]) ).
thf(f655,plain,
( ( $true = $false )
| ( $true
= ( q @ sK4 ) )
| ~ spl5_2
| ~ spl5_7 ),
inference(constrained_superposition,[],[f242,f267]) ).
thf(f660,plain,
( ( $true
= ( q @ sK4 ) )
| ~ spl5_2
| ~ spl5_7 ),
inference(trivial_inequality_removal,[],[f655]) ).
thf(f664,plain,
( ( $true = $false )
| ~ spl5_2
| ~ spl5_7
| ~ spl5_8 ),
inference(constrained_superposition,[],[f660,f272]) ).
thf(f668,plain,
( $false
| ~ spl5_2
| ~ spl5_7
| ~ spl5_8 ),
inference(trivial_inequality_removal,[],[f664]) ).
thf(f669,plain,
( ~ spl5_2
| ~ spl5_7
| ~ spl5_8 ),
inference(avatar_contradiction_clause,[],[f668]) ).
thf(f670,plain,
( ( $true
= ( q @ sK3 ) )
| ~ spl5_2
| ~ spl5_5 ),
inference(trivial_inequality_removal,[],[f276]) ).
thf(f672,plain,
( ( $true = $false )
| ~ spl5_6
| ~ spl5_19 ),
inference(constrained_superposition,[],[f530,f262]) ).
thf(f676,plain,
( $false
| ~ spl5_6
| ~ spl5_19 ),
inference(trivial_inequality_removal,[],[f672]) ).
thf(f677,plain,
( ~ spl5_6
| ~ spl5_19 ),
inference(avatar_contradiction_clause,[],[f676]) ).
thf(f683,plain,
( ( $true = $false )
| ~ spl5_2
| ~ spl5_5
| ~ spl5_18 ),
inference(constrained_superposition,[],[f670,f526]) ).
thf(f687,plain,
( $false
| ~ spl5_2
| ~ spl5_5
| ~ spl5_18 ),
inference(trivial_inequality_removal,[],[f683]) ).
thf(f688,plain,
( ~ spl5_2
| ~ spl5_5
| ~ spl5_18 ),
inference(avatar_contradiction_clause,[],[f687]) ).
thf(f725,plain,
( ( $true = $false )
| ~ spl5_17 ),
inference(constrained_superposition,[],[f522,f174]) ).
thf(f739,plain,
( $false
| ~ spl5_17 ),
inference(trivial_inequality_removal,[],[f725]) ).
thf(f740,plain,
~ spl5_17,
inference(avatar_contradiction_clause,[],[f739]) ).
thf(f749,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s4 @ X0 @ sK2 ) )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) ) )
| ~ spl5_3 ),
inference(constrained_superposition,[],[f233,f247]) ).
thf(f752,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s4 @ X0 @ sK2 ) )
| ( $false
= ( rel_s4 @ X0 @ sK1 ) ) )
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f749]) ).
thf(f949,plain,
( ( $true = $false )
| ( $true
= ( p @ sK2 ) )
| ~ spl5_1
| ~ spl5_3 ),
inference(constrained_superposition,[],[f247,f239]) ).
thf(f954,plain,
( ( $true
= ( p @ sK2 ) )
| ~ spl5_1
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f949]) ).
thf(f1025,plain,
( ( $true = $false )
| ( $false
= ( rel_s4 @ sK0 @ sK1 ) )
| ( $true
= ( q @ sK2 ) )
| ( $false
= ( p @ sK2 ) )
| ~ spl5_3 ),
inference(constrained_superposition,[],[f752,f165]) ).
thf(f1070,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK1 ) )
| ( $true
= ( q @ sK2 ) )
| ( $false
= ( p @ sK2 ) )
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f1025]) ).
thf(f1073,definition,
( spl5_21
<=> ( $false
= ( p @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_21])],[avatar_definition]) ).
thf(f1075,plain,
( ( $false
= ( p @ sK2 ) )
| ~ spl5_21 ),
inference(avatar_component_clause,[],[f1073]) ).
thf(f1077,definition,
( spl5_22
<=> ( $true
= ( q @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_22])],[avatar_definition]) ).
thf(f1079,plain,
( ( $true
= ( q @ sK2 ) )
| ~ spl5_22 ),
inference(avatar_component_clause,[],[f1077]) ).
thf(f1081,plain,
( spl5_21
| spl5_22
| spl5_17
| ~ spl5_3 ),
inference(avatar_split_clause,[],[f1070,f245,f520,f1077,f1073]) ).
thf(f1084,plain,
( ( $true = $false )
| ~ spl5_4
| ~ spl5_22 ),
inference(constrained_superposition,[],[f1079,f252]) ).
thf(f1088,plain,
( $false
| ~ spl5_4
| ~ spl5_22 ),
inference(trivial_inequality_removal,[],[f1084]) ).
thf(f1089,plain,
( ~ spl5_4
| ~ spl5_22 ),
inference(avatar_contradiction_clause,[],[f1088]) ).
thf(f1090,plain,
( ( $true = $false )
| ~ spl5_1
| ~ spl5_3
| ~ spl5_21 ),
inference(constrained_superposition,[],[f1075,f954]) ).
thf(f1096,plain,
( $false
| ~ spl5_1
| ~ spl5_3
| ~ spl5_21 ),
inference(trivial_inequality_removal,[],[f1090]) ).
thf(f1097,plain,
( ~ spl5_1
| ~ spl5_3
| ~ spl5_21 ),
inference(avatar_contradiction_clause,[],[f1096]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f243]) ).
cnf(s2,plain,
( spl5_2
| spl5_3 ),
inference(sat_conversion,[],[f248]) ).
cnf(s3,plain,
( spl5_2
| spl5_4 ),
inference(sat_conversion,[],[f253]) ).
cnf(s4,plain,
( spl5_1
| spl5_5 ),
inference(sat_conversion,[],[f258]) ).
cnf(s5,plain,
( spl5_1
| spl5_6 ),
inference(sat_conversion,[],[f263]) ).
cnf(s6,plain,
( spl5_5
| spl5_7 ),
inference(sat_conversion,[],[f268]) ).
cnf(s7,plain,
( spl5_5
| spl5_8 ),
inference(sat_conversion,[],[f273]) ).
cnf(s8,plain,
( spl5_6
| spl5_7 ),
inference(sat_conversion,[],[f274]) ).
cnf(s9,plain,
( spl5_6
| spl5_8 ),
inference(sat_conversion,[],[f275]) ).
cnf(s25,plain,
( ~ spl5_5
| spl5_17
| spl5_18
| spl5_19 ),
inference(sat_conversion,[],[f532]) ).
cnf(s27,plain,
( ~ spl5_2
| ~ spl5_7
| ~ spl5_8 ),
inference(sat_conversion,[],[f669]) ).
cnf(s29,plain,
( ~ spl5_6
| ~ spl5_19 ),
inference(sat_conversion,[],[f677]) ).
cnf(s31,plain,
( ~ spl5_2
| ~ spl5_5
| ~ spl5_18 ),
inference(sat_conversion,[],[f688]) ).
cnf(s33,plain,
~ spl5_17,
inference(sat_conversion,[],[f740]) ).
cnf(s37,plain,
( ~ spl5_3
| spl5_17
| spl5_21
| spl5_22 ),
inference(sat_conversion,[],[f1081]) ).
cnf(s39,plain,
( ~ spl5_4
| ~ spl5_22 ),
inference(sat_conversion,[],[f1089]) ).
cnf(s41,plain,
( ~ spl5_1
| ~ spl5_3
| ~ spl5_21 ),
inference(sat_conversion,[],[f1097]) ).
cnf(s42,plain,
( ~ spl5_5
| spl5_18
| spl5_19 ),
inference(rat,[],[s25,s33]) ).
cnf(s44,plain,
spl5_1,
inference(rat,[],[s42,s31,s29,s1,s4,s5]) ).
cnf(s45,plain,
spl5_2,
inference(rat,[],[s37,s41,s39,s2,s3,s33,s44]) ).
cnf(s50,plain,
spl5_6,
inference(rat,[],[s27,s8,s9,s45]) ).
cnf(s51,plain,
~ spl5_19,
inference(rat,[],[s29,s50]) ).
cnf(s52,plain,
~ spl5_5,
inference(rat,[],[s42,s31,s51,s45]) ).
cnf(s53,plain,
spl5_8,
inference(rat,[],[s7,s52]) ).
cnf(s54,plain,
spl5_7,
inference(rat,[],[s6,s52]) ).
cnf(s55,plain,
$false,
inference(rat,[],[s27,s45,s53,s54]) ).
thf(f1098,plain,
$false,
inference(avatar_sat_refutation,[],[s55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO463^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n007.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 16:57:27 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.29 % (3649422)Will run a generic schedule for satisfiability detection.
% 0.20/0.29 % (3649432)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1156038336:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.29 % (3649428)% WARNING: option uhcvi not known.
% 0.20/0.29 % (3649427)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3691772218_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.29 % (3649428)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3095429520:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.29 % (3649429)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3069420923:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.29 % (3649430)dis+10_1_sil=32000:sp=arity:random_seed=1515949706:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.29 % (3649431)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=479292625:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.29 % (3649433)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2064952552:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.29 % (3649428)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.29 % (3649431)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.29 % Exception at run slice level
% 0.20/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.29 % (3649428)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.29 % (3649441)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=654080795:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.29 % (3649432)Instruction limit reached!
% 0.20/0.29 % (3649432)------------------------------
% 0.20/0.29 % (3649432)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (3649432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (3649432)CaDiCaL version: 2.1.3
% 0.20/0.29 % (3649432)Termination reason: Instruction limit
% 0.20/0.29 % (3649432)Termination phase: Saturation
% 0.20/0.29 % (3649432)Time elapsed: 0.031 s
% 0.20/0.29 % (3649432)Peak memory usage: 12 MB
% 0.20/0.29 % (3649432)Instructions burned: 132 (million)
% 0.20/0.29 % Exception at run slice level
% 0.20/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.29 % (3649443)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2426294384:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.29 % (3649433) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3649422-3649433"...
% 0.20/0.29 % (3649433)...printing done.
% 0.20/0.29 % (3649433)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.30 % (3649433)------------------------------
% 0.20/0.30 % (3649433)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3649433)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3649433)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3649433)Termination reason: Refutation
% 0.20/0.30 % (3649433)Time elapsed: 0.041 s
% 0.20/0.30 % (3649433)Peak memory usage: 13 MB
% 0.20/0.30 % (3649433)Instructions burned: 83 (million)
% 0.20/0.30 % (3649422)Success in time 0.077 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------