%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO463^6 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 08:47:55 AM UTC 2026
% Result : Theorem 0.22s 0.31s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 20
% Syntax : Number of formulae : 210 ( 68 unt; 0 typ; 10 def)
% Number of atoms : 1622 ( 279 equ; 0 cnn)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 2080 ( 371 ~; 421 |; 13 &;1150 @)
% ( 10 <=>; 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 : 70 ( 66 usr; 19 con; 0-4 aty)
% ( 103 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 373 ( 0 sgn 80 !; 0 ?; 373 :)
% 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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_41,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
vOR: $o > $o > $o ).
thf(func_def_43,type,
vNOT: $o > $o ).
thf(func_def_44,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vIMP: $o > $o > $o ).
thf(func_def_46,type,
vAND: $o > $o > $o ).
thf(func_def_47,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_48,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/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) )
= mequiv ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f21,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X3: $i,X2: $i,X1: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) )
= mtransitive ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_s5
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(f35,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a2) ).
thf(f37,conjecture,
mvalid @ ( mimplies @ ( mbox_s5 @ ( mequiv @ p @ q ) ) @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mequiv @ p @ q ) ) @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f41,plain,
( mbox_s5
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f42,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f55,plain,
mtransitive @ rel_s5,
inference(rectify,[],[f35]) ).
thf(f56,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f55]) ).
thf(f57,plain,
~ ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mequiv @ p @ q ) ) @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f58,plain,
( ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mequiv @ p @ q ) ) @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f57]) ).
thf(f62,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f63,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f64,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f65,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X2 )
& ( X0 @ X2 @ X1 ) )
=> ( X0 @ X3 @ X1 ) ) )
= mtransitive ),
inference(rectify,[],[f21]) ).
thf(f66,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f65]) ).
thf(f73,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f81,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f82,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f83,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f82]) ).
thf(f87,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f88,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f87]) ).
thf(f101,plain,
( ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mequiv @ p @ q ) ) @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) ) ) )
!= $true ),
inference(flattening,[],[f58]) ).
thf(f104,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f107,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f109,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f114,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f115,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f122,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f73]) ).
thf(f126,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f56]) ).
thf(f129,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f131,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f83]) ).
thf(f133,plain,
( ( mvalid @ ( mimplies @ ( mbox_s5 @ ( mequiv @ p @ q ) ) @ ( mbox_s5 @ ( mequiv @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f101]) ).
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] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f107,f109,f104,f109,f109]) ).
thf(f142,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f129,f104,f109]) ).
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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f122,f141,f142,f142]) ).
thf(f153,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f126,f115]) ).
thf(f154,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ p
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f133,f131,f142,f114,f144,f114,f144,f114,f114]) ).
thf(f161,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y1 @ Y2 )
& ( rel_s5 @ Y0 @ Y1 ) )
=> ( rel_s5 @ Y0 @ Y2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f162,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y1 @ Y2 )
& ( rel_s5 @ Y0 @ Y1 ) )
=> ( rel_s5 @ Y0 @ Y2 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y0 @ Y1 )
& ( rel_s5 @ X1 @ Y0 ) )
=> ( rel_s5 @ X1 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y0 @ Y1 )
& ( rel_s5 @ X1 @ Y0 ) )
=> ( rel_s5 @ X1 @ Y1 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s5 @ X2 @ Y0 )
& ( rel_s5 @ X1 @ X2 ) )
=> ( rel_s5 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f164]) ).
thf(f166,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s5 @ X2 @ Y0 )
& ( rel_s5 @ X1 @ X2 ) )
=> ( rel_s5 @ X1 @ Y0 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( rel_s5 @ X2 @ X3 )
& ( rel_s5 @ X1 @ X2 ) )
=> ( rel_s5 @ X1 @ X3 ) )
= $true ),
inference(beta-eta_normalization,[],[f166]) ).
thf(f168,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X1 @ X3 ) )
| ( $false
= ( ( rel_s5 @ X2 @ X3 )
& ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $true
= ( rel_s5 @ X1 @ X3 ) )
| ( ( rel_s5 @ X2 @ X3 )
= $false ) ),
inference(and_proxy_clausification,[],[f168]) ).
thf(f173,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( ~ ( ( p @ Y1 )
| ~ ( q @ Y1 ) )
| ~ ( ( q @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f174,plain,
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( ~ ( ( p @ Y1 )
| ~ ( q @ Y1 ) )
| ~ ( ( q @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( ~ ( ( !! @ $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 )
| ( q @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( ~ ( ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( ( q @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( ~ ( ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( ( q @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( ~ ( ( !! @ $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 )
| ( q @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f178,plain,
( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( ~ ( ( !! @ $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 )
| ( q @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f177]) ).
thf(f179,plain,
( ( ~ ( rel_s5 @ sK0 @ sK1 )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f178]) ).
thf(f180,plain,
( $false
= ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( ~ ( rel_s5 @ sK0 @ sK1 ) )
= $false ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f182,plain,
( $true
= ( rel_s5 @ sK0 @ sK1 ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f183,plain,
( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f180]) ).
thf(f184,plain,
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) )
= $true )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f185,plain,
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f186,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f185]) ).
thf(f187,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f186]) ).
thf(f188,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f186]) ).
thf(f189,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f188]) ).
thf(f190,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f188]) ).
thf(f191,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ sK2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f190]) ).
thf(f192,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ sK2 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ sK3 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f191]) ).
thf(f193,plain,
( ( $false
= ( ~ ( rel_s5 @ sK1 @ sK3 )
| ( p @ sK3 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK2 )
| ( q @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f192]) ).
thf(f194,plain,
( ( $false
= ( ~ ( rel_s5 @ sK1 @ sK2 )
| ( q @ sK2 ) ) )
| ( $false
= ( p @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f195,plain,
( ( ( ~ ( rel_s5 @ sK1 @ sK3 ) )
= $false )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK2 )
| ( q @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f196,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK3 ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK2 )
| ( q @ sK2 ) ) ) ),
inference(not_proxy_clausification,[],[f195]) ).
thf(f197,plain,
( ( $false
= ( q @ sK2 ) )
| ( $true
= ( rel_s5 @ sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f196]) ).
thf(f198,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK3 ) )
| ( ( ~ ( rel_s5 @ sK1 @ sK2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f196]) ).
thf(f199,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK3 ) )
| ( ( rel_s5 @ sK1 @ sK2 )
= $true ) ),
inference(not_proxy_clausification,[],[f198]) ).
thf(f200,plain,
( ( $false
= ( q @ sK2 ) )
| ( $false
= ( p @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f194]) ).
thf(f201,plain,
( ( ( ~ ( rel_s5 @ sK1 @ sK2 ) )
= $false )
| ( $false
= ( p @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f194]) ).
thf(f202,plain,
( ( $false
= ( p @ sK3 ) )
| ( ( rel_s5 @ sK1 @ sK2 )
= $true ) ),
inference(not_proxy_clausification,[],[f201]) ).
thf(f203,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f204,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
= $false ) ),
inference(pi_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X1: $i] :
( ( ( ~ ( rel_s5 @ sK1 @ X1 )
| ( q @ X1 ) )
= $true )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK4 )
| ( q @ sK4 ) ) ) ),
inference(beta-eta_normalization,[],[f205]) ).
thf(f207,plain,
! [X1: $i] :
( ( ( q @ X1 )
= $true )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK4 )
| ( q @ sK4 ) ) ) ),
inference(or_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X1: $i] :
( ( ( q @ X1 )
= $true )
| ( $false
= ( ~ ( rel_s5 @ sK1 @ sK4 )
| ( q @ sK4 ) ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $false
= ( q @ sK4 ) )
| ( ( q @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f208]) ).
thf(f210,plain,
! [X1: $i] :
( ( ( ~ ( rel_s5 @ sK1 @ sK4 ) )
= $false )
| ( ( q @ X1 )
= $true )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f208]) ).
thf(f211,plain,
! [X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( ( q @ X1 )
= $true )
| ( ( rel_s5 @ sK1 @ sK4 )
= $true ) ),
inference(not_proxy_clausification,[],[f210]) ).
thf(f212,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f213,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f212]) ).
thf(f214,plain,
! [X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f213]) ).
thf(f215,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f213]) ).
thf(f216,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ sK5 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f215]) ).
thf(f217,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ( p @ X1 ) ) )
| ( ( ~ ( rel_s5 @ sK1 @ sK5 )
| ( p @ sK5 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f216]) ).
thf(f218,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true
= ( p @ X1 ) )
| ( ( ~ ( rel_s5 @ sK1 @ sK5 )
| ( p @ sK5 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f217]) ).
thf(f219,plain,
! [X1: $i] :
( ( ( ~ ( rel_s5 @ sK1 @ sK5 )
| ( p @ sK5 ) )
= $false )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f218]) ).
thf(f220,plain,
! [X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( ( p @ sK5 )
= $false )
| ( $true
= ( p @ X1 ) ) ),
inference(or_proxy_clausification,[],[f219]) ).
thf(f221,plain,
! [X1: $i] :
( ( ( ~ ( rel_s5 @ sK1 @ sK5 ) )
= $false )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f219]) ).
thf(f222,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( ( rel_s5 @ sK1 @ sK5 )
= $true ) ),
inference(not_proxy_clausification,[],[f221]) ).
thf(f223,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f214]) ).
thf(f224,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ X2 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f223]) ).
thf(f225,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 )
| ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 )
| ( q @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f224]) ).
thf(f226,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK1 @ X1 ) ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 )
| ( q @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 )
| ( q @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f226]) ).
thf(f228,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK1 @ X2 ) ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( q @ X2 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ sK1 @ X2 )
= $false )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( q @ X2 ) ) ),
inference(not_proxy_clausification,[],[f228]) ).
thf(f230,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( ~ ( ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( ( q @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f176]) ).
thf(f231,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( ~ ( ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( ( q @ Y0 )
| ~ ( p @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f230]) ).
thf(f232,plain,
! [X1: $i] :
( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( ~ ( ( p @ X1 )
| ~ ( q @ X1 ) )
| ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f231]) ).
thf(f233,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( ~ ( ( p @ X1 )
| ~ ( q @ X1 ) )
| ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $true
= ( ~ ( ~ ( ( p @ X1 )
| ~ ( q @ X1 ) )
| ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f233]) ).
thf(f235,plain,
! [X1: $i] :
( ( $false
= ( ~ ( ( p @ X1 )
| ~ ( q @ X1 ) )
| ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) ) )
| ( ( rel_s5 @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f234]) ).
thf(f236,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( ( ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f235]) ).
thf(f237,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $false
= ( ~ ( ( p @ X1 )
| ~ ( q @ X1 ) ) ) ) ),
inference(or_proxy_clausification,[],[f235]) ).
thf(f238,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $true
= ( ( p @ X1 )
| ~ ( q @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f237]) ).
thf(f239,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f238]) ).
thf(f240,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( ( q @ X1 )
= $false )
| ( $true
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f239]) ).
thf(f241,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( ( ( q @ X1 )
| ~ ( p @ X1 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f236]) ).
thf(f242,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( ( ~ ( p @ X1 ) )
= $true )
| ( ( q @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f241]) ).
thf(f243,plain,
! [X1: $i] :
( ( ( rel_s5 @ sK0 @ X1 )
= $false )
| ( ( p @ X1 )
= $false )
| ( ( q @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f242]) ).
thf(f245,definition,
( spl6_1
<=> ( ( rel_s5 @ sK1 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
thf(f247,plain,
( ( ( rel_s5 @ sK1 @ sK2 )
= $true )
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f245]) ).
thf(f249,definition,
( spl6_2
<=> ( $true
= ( rel_s5 @ sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f251,plain,
( ( $true
= ( rel_s5 @ sK1 @ sK3 ) )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f249]) ).
thf(f252,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f199,f249,f245]) ).
thf(f254,definition,
( spl6_3
<=> ( $false
= ( q @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_3])],[avatar_definition]) ).
thf(f256,plain,
( ( $false
= ( q @ sK2 ) )
| ~ spl6_3 ),
inference(avatar_component_clause,[],[f254]) ).
thf(f257,plain,
( spl6_3
| spl6_2 ),
inference(avatar_split_clause,[],[f197,f249,f254]) ).
thf(f259,definition,
( spl6_4
<=> ( $false
= ( p @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
thf(f261,plain,
( ( $false
= ( p @ sK3 ) )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f259]) ).
thf(f262,plain,
( spl6_4
| spl6_1 ),
inference(avatar_split_clause,[],[f202,f245,f259]) ).
thf(f263,plain,
( spl6_4
| spl6_3 ),
inference(avatar_split_clause,[],[f200,f254,f259]) ).
thf(f265,definition,
( spl6_5
<=> ( ( rel_s5 @ sK1 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
thf(f267,plain,
( ( ( rel_s5 @ sK1 @ sK4 )
= $true )
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f265]) ).
thf(f269,definition,
( spl6_6
<=> ! [X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( ( q @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
thf(f270,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( ( q @ X1 )
= $true ) )
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f269]) ).
thf(f271,plain,
( spl6_5
| spl6_6 ),
inference(avatar_split_clause,[],[f211,f269,f265]) ).
thf(f273,definition,
( spl6_7
<=> ( $false
= ( q @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
thf(f275,plain,
( ( $false
= ( q @ sK4 ) )
| ~ spl6_7 ),
inference(avatar_component_clause,[],[f273]) ).
thf(f276,plain,
( spl6_6
| spl6_7 ),
inference(avatar_split_clause,[],[f209,f273,f269]) ).
thf(f278,definition,
( spl6_8
<=> ! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_s5 @ sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
thf(f279,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s5 @ sK1 @ X1 ) )
| ( $true
= ( p @ X1 ) ) )
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f278]) ).
thf(f281,definition,
( spl6_9
<=> ( ( rel_s5 @ sK1 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition]) ).
thf(f283,plain,
( ( ( rel_s5 @ sK1 @ sK5 )
= $true )
| ~ spl6_9 ),
inference(avatar_component_clause,[],[f281]) ).
thf(f284,plain,
( spl6_8
| spl6_9 ),
inference(avatar_split_clause,[],[f222,f281,f278]) ).
thf(f286,definition,
( spl6_10
<=> ( ( p @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition]) ).
thf(f288,plain,
( ( ( p @ sK5 )
= $false )
| ~ spl6_10 ),
inference(avatar_component_clause,[],[f286]) ).
thf(f289,plain,
( spl6_10
| spl6_8 ),
inference(avatar_split_clause,[],[f220,f278,f286]) ).
thf(f290,plain,
( spl6_8
| spl6_6 ),
inference(avatar_split_clause,[],[f229,f269,f278]) ).
thf(f295,plain,
( ( $true = $false )
| ( $true
= ( p @ sK3 ) )
| ~ spl6_2
| ~ spl6_8 ),
inference(constrained_superposition,[],[f279,f251]) ).
thf(f298,plain,
( ( $true
= ( p @ sK3 ) )
| ~ spl6_2
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f295]) ).
thf(f302,plain,
( ( $true = $false )
| ~ spl6_2
| ~ spl6_4
| ~ spl6_8 ),
inference(forward_demodulation,[],[f298,f261]) ).
thf(f303,plain,
( $false
| ~ spl6_2
| ~ spl6_4
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f302]) ).
thf(f304,plain,
( ~ spl6_2
| ~ spl6_4
| ~ spl6_8 ),
inference(avatar_contradiction_clause,[],[f303]) ).
thf(f305,plain,
( ( $true = $false )
| ( $true
= ( q @ sK5 ) )
| ~ spl6_6
| ~ spl6_9 ),
inference(constrained_superposition,[],[f283,f270]) ).
thf(f307,plain,
( ( $true
= ( q @ sK5 ) )
| ~ spl6_6
| ~ spl6_9 ),
inference(trivial_inequality_removal,[],[f305]) ).
thf(f423,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( rel_s5 @ X0 @ sK1 )
= $false )
| ( ( rel_s5 @ X0 @ sK5 )
= $true ) )
| ~ spl6_9 ),
inference(constrained_superposition,[],[f169,f283]) ).
thf(f457,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ X0 @ sK5 )
= $true )
| ( ( rel_s5 @ X0 @ sK1 )
= $false ) )
| ~ spl6_9 ),
inference(trivial_inequality_removal,[],[f423]) ).
thf(f531,plain,
( ( $false
= ( q @ sK5 ) )
| ( $true = $false )
| ( ( rel_s5 @ sK0 @ sK1 )
= $false )
| ( ( p @ sK5 )
= $true )
| ~ spl6_9 ),
inference(constrained_superposition,[],[f457,f240]) ).
thf(f553,plain,
( ( ( rel_s5 @ sK0 @ sK1 )
= $false )
| ( ( p @ sK5 )
= $true )
| ( $false
= ( q @ sK5 ) )
| ~ spl6_9 ),
inference(trivial_inequality_removal,[],[f531]) ).
thf(f558,plain,
( ( $true = $false )
| ( $false
= ( q @ sK5 ) )
| ( ( p @ sK5 )
= $true )
| ~ spl6_9 ),
inference(forward_demodulation,[],[f553,f182]) ).
thf(f559,plain,
( ( ( p @ sK5 )
= $true )
| ( $false
= ( q @ sK5 ) )
| ~ spl6_9 ),
inference(trivial_inequality_removal,[],[f558]) ).
thf(f562,plain,
( ( $false
= ( q @ sK5 ) )
| ( $true = $false )
| ~ spl6_9
| ~ spl6_10 ),
inference(forward_demodulation,[],[f559,f288]) ).
thf(f563,plain,
( ( $false
= ( q @ sK5 ) )
| ~ spl6_9
| ~ spl6_10 ),
inference(trivial_inequality_removal,[],[f562]) ).
thf(f567,plain,
( ( $true = $false )
| ~ spl6_6
| ~ spl6_9
| ~ spl6_10 ),
inference(forward_demodulation,[],[f563,f307]) ).
thf(f568,plain,
( $false
| ~ spl6_6
| ~ spl6_9
| ~ spl6_10 ),
inference(trivial_inequality_removal,[],[f567]) ).
thf(f569,plain,
( ~ spl6_6
| ~ spl6_9
| ~ spl6_10 ),
inference(avatar_contradiction_clause,[],[f568]) ).
thf(f575,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s5 @ X0 @ sK4 ) )
| ( ( rel_s5 @ X0 @ sK1 )
= $false ) )
| ~ spl6_5 ),
inference(constrained_superposition,[],[f267,f169]) ).
thf(f577,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ X0 @ sK4 ) )
| ( ( rel_s5 @ X0 @ sK1 )
= $false ) )
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f575]) ).
thf(f598,plain,
( ( $true = $false )
| ( $true
= ( p @ sK4 ) )
| ~ spl6_5
| ~ spl6_8 ),
inference(constrained_superposition,[],[f267,f279]) ).
thf(f601,plain,
( ( $true
= ( p @ sK4 ) )
| ~ spl6_5
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f598]) ).
thf(f726,plain,
( ( $true
= ( q @ sK4 ) )
| ( ( rel_s5 @ sK0 @ sK1 )
= $false )
| ( $false
= ( p @ sK4 ) )
| ( $true = $false )
| ~ spl6_5 ),
inference(constrained_superposition,[],[f577,f243]) ).
thf(f751,plain,
( ( ( rel_s5 @ sK0 @ sK1 )
= $false )
| ( $false
= ( p @ sK4 ) )
| ( $true
= ( q @ sK4 ) )
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f726]) ).
thf(f755,plain,
( ( $true = $false )
| ( $true
= ( q @ sK4 ) )
| ( $false
= ( p @ sK4 ) )
| ~ spl6_5 ),
inference(forward_demodulation,[],[f751,f182]) ).
thf(f756,plain,
( ( $true
= ( q @ sK4 ) )
| ( $false
= ( p @ sK4 ) )
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f755]) ).
thf(f759,plain,
( ( $true = $false )
| ( $false
= ( p @ sK4 ) )
| ~ spl6_5
| ~ spl6_7 ),
inference(forward_demodulation,[],[f756,f275]) ).
thf(f760,plain,
( ( $false
= ( p @ sK4 ) )
| ~ spl6_5
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f759]) ).
thf(f764,plain,
( ( $true = $false )
| ~ spl6_5
| ~ spl6_7
| ~ spl6_8 ),
inference(forward_demodulation,[],[f760,f601]) ).
thf(f765,plain,
( $false
| ~ spl6_5
| ~ spl6_7
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f764]) ).
thf(f766,plain,
( ~ spl6_5
| ~ spl6_7
| ~ spl6_8 ),
inference(avatar_contradiction_clause,[],[f765]) ).
thf(f796,plain,
( ( $true
= ( q @ sK2 ) )
| ( $true = $false )
| ~ spl6_1
| ~ spl6_6 ),
inference(constrained_superposition,[],[f247,f270]) ).
thf(f812,plain,
( ( $true
= ( q @ sK2 ) )
| ~ spl6_1
| ~ spl6_6 ),
inference(trivial_inequality_removal,[],[f796]) ).
thf(f818,plain,
( ( $true = $false )
| ~ spl6_1
| ~ spl6_3
| ~ spl6_6 ),
inference(forward_demodulation,[],[f812,f256]) ).
thf(f819,plain,
( $false
| ~ spl6_1
| ~ spl6_3
| ~ spl6_6 ),
inference(trivial_inequality_removal,[],[f818]) ).
thf(f820,plain,
( ~ spl6_1
| ~ spl6_3
| ~ spl6_6 ),
inference(avatar_contradiction_clause,[],[f819]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f252]) ).
cnf(s2,plain,
( spl6_2
| spl6_3 ),
inference(sat_conversion,[],[f257]) ).
cnf(s3,plain,
( spl6_1
| spl6_4 ),
inference(sat_conversion,[],[f262]) ).
cnf(s4,plain,
( spl6_3
| spl6_4 ),
inference(sat_conversion,[],[f263]) ).
cnf(s5,plain,
( spl6_5
| spl6_6 ),
inference(sat_conversion,[],[f271]) ).
cnf(s6,plain,
( spl6_6
| spl6_7 ),
inference(sat_conversion,[],[f276]) ).
cnf(s7,plain,
( spl6_8
| spl6_9 ),
inference(sat_conversion,[],[f284]) ).
cnf(s8,plain,
( spl6_8
| spl6_10 ),
inference(sat_conversion,[],[f289]) ).
cnf(s9,plain,
( spl6_6
| spl6_8 ),
inference(sat_conversion,[],[f290]) ).
cnf(s11,plain,
( ~ spl6_2
| ~ spl6_4
| ~ spl6_8 ),
inference(sat_conversion,[],[f304]) ).
cnf(s19,plain,
( ~ spl6_6
| ~ spl6_9
| ~ spl6_10 ),
inference(sat_conversion,[],[f569]) ).
cnf(s25,plain,
( ~ spl6_5
| ~ spl6_7
| ~ spl6_8 ),
inference(sat_conversion,[],[f766]) ).
cnf(s27,plain,
( ~ spl6_1
| ~ spl6_3
| ~ spl6_6 ),
inference(sat_conversion,[],[f820]) ).
cnf(s28,plain,
spl6_8,
inference(rat,[],[s19,s7,s8,s9]) ).
cnf(s29,plain,
spl6_1,
inference(rat,[],[s11,s1,s3,s28]) ).
cnf(s30,plain,
spl6_6,
inference(rat,[],[s25,s5,s6,s28]) ).
cnf(s31,plain,
~ spl6_3,
inference(rat,[],[s27,s29,s30]) ).
cnf(s32,plain,
spl6_4,
inference(rat,[],[s4,s31]) ).
cnf(s33,plain,
spl6_2,
inference(rat,[],[s2,s31]) ).
cnf(s34,plain,
$false,
inference(rat,[],[s11,s28,s32,s33]) ).
thf(f821,plain,
$false,
inference(avatar_sat_refutation,[],[s34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO463^6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n003.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 17:01:14 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.31 % (2764014)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.31 % (2764019)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3629319403:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.31 % (2764025)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.31 % (2764025)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.31 % (2764020)lrs+10_16_si=on:nwc=1.5:random_seed=172806777:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.31 % (2764021)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3998032501:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.31 % (2764023)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2898175686:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.31 % (2764022)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=4284930337:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.31 % (2764024)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=93661042:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.31 % (2764025)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=2555574916:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.31 % (2764021)Instruction limit reached!
% 0.22/0.31 % (2764021)------------------------------
% 0.22/0.31 % (2764021)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (2764021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (2764021)CaDiCaL version: 2.1.3
% 0.22/0.31 % (2764021)Termination reason: Instruction limit
% 0.22/0.31 % (2764021)Termination phase: Property scanning
% 0.22/0.31 % (2764021)Time elapsed: 0.002 s
% 0.22/0.31 % (2764021)Peak memory usage: 10 MB
% 0.22/0.31 % (2764021)Instructions burned: 4 (million)
% 0.22/0.31 % (2764019) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2764014-2764019"...
% 0.22/0.31 % (2764019)...printing done.
% 0.22/0.31 % (2764019)Refutation found. Thanks to Tanya!
% 0.22/0.31 % SZS status Theorem for theBenchmark
% 0.22/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.31 % (2764019)------------------------------
% 0.22/0.31 % (2764019)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (2764019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (2764019)CaDiCaL version: 2.1.3
% 0.22/0.31 % (2764019)Termination reason: Refutation
% 0.22/0.31 % (2764019)Time elapsed: 0.015 s
% 0.22/0.31 % (2764019)Peak memory usage: 13 MB
% 0.22/0.31 % (2764019)Instructions burned: 52 (million)
% 0.22/0.31 % (2764014)Success in time 0.052 s
% 0.22/0.31 % Vampire exiting
%------------------------------------------------------------------------------