%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO404^1 : 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 : n014.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 08:47:37 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 20
% Syntax : Number of formulae : 230 ( 45 unt; 0 typ; 12 def)
% Number of atoms : 2220 ( 364 equ; 0 cnn)
% Maximal formula atoms : 14 ( 9 avg)
% Number of connectives : 2699 ( 610 ~; 659 |; 0 &;1317 @)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 110 ( 110 >; 0 *; 0 +; 0 <<)
% Number of symbols : 71 ( 67 usr; 20 con; 0-4 aty)
% ( 101 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 339 ( 0 sgn 60 !; 0 ?; 339 :)
% 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_k: $i > $i > $o ).
thf(func_def_33,type,
mbox_k: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_k: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
q: $i > $o ).
thf(func_def_37,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_39,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_43,type,
vIMP: $o > $o > $o ).
thf(func_def_44,type,
vAND: $o > $o > $o ).
thf(func_def_45,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_49,type,
vNOT: $o > $o ).
thf(func_def_50,type,
vOR: $o > $o > $o ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
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(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_k
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_k @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^1.ax',mbox_k) ).
thf(f34,conjecture,
mvalid @ ( mequiv @ ( mand @ ( mbox_k @ ( mimplies @ q @ p ) ) @ ( mbox_k @ ( mimplies @ ( mnot @ q ) @ p ) ) ) @ ( mbox_k @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f35,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mand @ ( mbox_k @ ( mimplies @ q @ p ) ) @ ( mbox_k @ ( mimplies @ ( mnot @ q ) @ p ) ) ) @ ( mbox_k @ p ) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
thf(f51,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f52,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f51]) ).
thf(f53,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f54,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f57,plain,
( mbox_k
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_k @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f58,plain,
( mbox_k
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_k @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f59,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f72,plain,
~ ( mvalid @ ( mequiv @ ( mand @ ( mbox_k @ ( mimplies @ q @ p ) ) @ ( mbox_k @ ( mimplies @ ( mnot @ q ) @ p ) ) ) @ ( mbox_k @ p ) ) ),
inference(rectify,[],[f35]) ).
thf(f73,plain,
( ( mvalid @ ( mequiv @ ( mand @ ( mbox_k @ ( mimplies @ q @ p ) ) @ ( mbox_k @ ( mimplies @ ( mnot @ q ) @ p ) ) ) @ ( mbox_k @ p ) ) )
!= $true ),
inference(fool_elimination,[],[f72]) ).
thf(f81,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f82,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f88,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f89,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f88]) ).
thf(f92,plain,
( ( mvalid @ ( mequiv @ ( mand @ ( mbox_k @ ( mimplies @ q @ p ) ) @ ( mbox_k @ ( mimplies @ ( mnot @ q ) @ p ) ) ) @ ( mbox_k @ p ) ) )
!= $true ),
inference(flattening,[],[f73]) ).
thf(f100,plain,
( ( mvalid @ ( mequiv @ ( mand @ ( mbox_k @ ( mimplies @ q @ p ) ) @ ( mbox_k @ ( mimplies @ ( mnot @ q ) @ p ) ) ) @ ( mbox_k @ p ) ) )
!= $true ),
inference(cnf_transformation,[],[f92]) ).
thf(f103,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f89]) ).
thf(f104,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f109,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f110,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f113,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f115,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f122,plain,
( mbox_k
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_k @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f129,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,[],[f115,f103,f110,f103,f103]) ).
thf(f130,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,[],[f113,f110,f103]) ).
thf(f132,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,[],[f104,f129,f130,f130]) ).
thf(f139,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( 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 > $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 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_k @ Y1 @ Y2 ) ) )
@ ( ^ [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 )
@ q
@ p ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_k @ Y1 @ Y2 ) ) )
@ ( ^ [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] :
~ ( Y0 @ Y1 )
@ q )
@ p ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_k @ Y1 @ Y2 ) ) )
@ p ) ) )
!= $true ),
inference(definition_unfolding,[],[f100,f109,f132,f129,f122,f130,f122,f130,f103,f122]) ).
thf(f140,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ~ ( q @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( q @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ~ ( q @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( q @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f141,plain,
( $false
= ( ^ [Y0: $i] :
~ ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ~ ( q @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( q @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ~ ( q @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( q @ Y1 )
| ~ ( rel_k @ Y0 @ Y1 ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f140]) ).
thf(f142,plain,
( $false
= ( ~ ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f143,plain,
( ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f142]) ).
thf(f144,plain,
( ( ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) )
= $true )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f143]) ).
thf(f145,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) )
= $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f145]) ).
thf(f148,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f147]) ).
thf(f150,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f148]) ).
thf(f151,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f153]) ).
thf(f155,plain,
( ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ sK1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ sK2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ sK1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ sK3 ) )
| ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ sK1 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f156]) ).
thf(f158,plain,
( ( $false
= ( ( p @ sK1 )
| ~ ( q @ sK1 )
| ~ ( rel_k @ sK0 @ sK1 ) ) )
| ( $false
= ( ( p @ sK2 )
| ~ ~ ( q @ sK2 )
| ~ ( rel_k @ sK0 @ sK2 ) ) )
| ( ( ( p @ sK3 )
| ~ ( rel_k @ sK0 @ sK3 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f159,plain,
( ( $false
= ( ( p @ sK2 )
| ~ ~ ( q @ sK2 )
| ~ ( rel_k @ sK0 @ sK2 ) ) )
| ( ( ~ ( rel_k @ sK0 @ sK1 ) )
= $false )
| ( ( ( p @ sK3 )
| ~ ( rel_k @ sK0 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( ( $false
= ( ( p @ sK2 )
| ~ ~ ( q @ sK2 )
| ~ ( rel_k @ sK0 @ sK2 ) ) )
| ( ( ( p @ sK3 )
| ~ ( rel_k @ sK0 @ sK3 ) )
= $false )
| ( $false
= ( ( p @ sK1 )
| ~ ( q @ sK1 ) ) ) ),
inference(or_proxy_clausification,[],[f158]) ).
thf(f161,plain,
( ( ( ( p @ sK3 )
| ~ ( rel_k @ sK0 @ sK3 ) )
= $false )
| ( ( ~ ( rel_k @ sK0 @ sK2 ) )
= $false )
| ( $false
= ( ( p @ sK1 )
| ~ ( q @ sK1 ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( ( ( p @ sK3 )
| ~ ( rel_k @ sK0 @ sK3 ) )
= $false )
| ( $false
= ( ( p @ sK2 )
| ~ ~ ( q @ sK2 ) ) )
| ( $false
= ( ( p @ sK1 )
| ~ ( q @ sK1 ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f163,plain,
( ( ( ~ ( rel_k @ sK0 @ sK3 ) )
= $false )
| ( $false
= ( ( p @ sK1 )
| ~ ( q @ sK1 ) ) )
| ( $false
= ( ( p @ sK2 )
| ~ ~ ( q @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $false
= ( ( p @ sK2 )
| ~ ~ ( q @ sK2 ) ) )
| ( ( p @ sK3 )
= $false )
| ( $false
= ( ( p @ sK1 )
| ~ ( q @ sK1 ) ) ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f166,plain,
( ( $false
= ( ( p @ sK1 )
| ~ ( q @ sK1 ) ) )
| ( ( p @ sK3 )
= $false )
| ( $false
= ( p @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f167,plain,
( ( ( p @ sK3 )
= $false )
| ( $false
= ( p @ sK2 ) )
| ( ( ~ ( q @ sK1 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( $false
= ( p @ sK1 ) )
| ( $false
= ( p @ sK2 ) )
| ( ( p @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f169,plain,
( ( ( p @ sK3 )
= $false )
| ( ( q @ sK1 )
= $true )
| ( $false
= ( p @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f176,plain,
( ( ( rel_k @ sK0 @ sK3 )
= $true )
| ( $false
= ( ( p @ sK2 )
| ~ ~ ( q @ sK2 ) ) )
| ( $false
= ( ( p @ sK1 )
| ~ ( q @ sK1 ) ) ) ),
inference(not_proxy_clausification,[],[f163]) ).
thf(f178,plain,
( ( ( rel_k @ sK0 @ sK3 )
= $true )
| ( $false
= ( p @ sK2 ) )
| ( $false
= ( ( p @ sK1 )
| ~ ( q @ sK1 ) ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f179,plain,
( ( ( rel_k @ sK0 @ sK3 )
= $true )
| ( ( ~ ( q @ sK1 ) )
= $false )
| ( $false
= ( p @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f178]) ).
thf(f180,plain,
( ( $false
= ( p @ sK1 ) )
| ( $false
= ( p @ sK2 ) )
| ( ( rel_k @ sK0 @ sK3 )
= $true ) ),
inference(or_proxy_clausification,[],[f178]) ).
thf(f181,plain,
( ( ( q @ sK1 )
= $true )
| ( $false
= ( p @ sK2 ) )
| ( ( rel_k @ sK0 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f187,plain,
( ( ( ~ ( rel_k @ sK0 @ sK2 ) )
= $false )
| ( ( ~ ( rel_k @ sK0 @ sK3 ) )
= $false )
| ( $false
= ( ( p @ sK1 )
| ~ ( q @ sK1 ) ) ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f188,plain,
( ( ( p @ sK3 )
= $false )
| ( $false
= ( ( p @ sK1 )
| ~ ( q @ sK1 ) ) )
| ( ( ~ ( rel_k @ sK0 @ sK2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f190,plain,
( ( ( p @ sK3 )
= $false )
| ( $false
= ( p @ sK1 ) )
| ( ( ~ ( rel_k @ sK0 @ sK2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f188]) ).
thf(f191,plain,
( ( ( rel_k @ sK0 @ sK2 )
= $true )
| ( ( p @ sK3 )
= $false )
| ( $false
= ( p @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f194,plain,
( ( $false
= ( ( p @ sK1 )
| ~ ( q @ sK1 ) ) )
| ( ( rel_k @ sK0 @ sK2 )
= $true )
| ( ( ~ ( rel_k @ sK0 @ sK3 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f196,plain,
( ( ( rel_k @ sK0 @ sK2 )
= $true )
| ( $false
= ( p @ sK1 ) )
| ( ( ~ ( rel_k @ sK0 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f194]) ).
thf(f197,plain,
( ( $false
= ( p @ sK1 ) )
| ( ( rel_k @ sK0 @ sK3 )
= $true )
| ( ( rel_k @ sK0 @ sK2 )
= $true ) ),
inference(not_proxy_clausification,[],[f196]) ).
thf(f200,plain,
( ( ( ( p @ sK3 )
| ~ ( rel_k @ sK0 @ sK3 ) )
= $false )
| ( ( ~ ( rel_k @ sK0 @ sK2 ) )
= $false )
| ( ( ~ ( rel_k @ sK0 @ sK1 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f201,plain,
( ( ( ~ ( rel_k @ sK0 @ sK1 ) )
= $false )
| ( $false
= ( ( p @ sK2 )
| ~ ~ ( q @ sK2 ) ) )
| ( ( ( p @ sK3 )
| ~ ( rel_k @ sK0 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f202,plain,
( ( $false
= ( ( p @ sK2 )
| ~ ~ ( q @ sK2 ) ) )
| ( ( ( p @ sK3 )
| ~ ( rel_k @ sK0 @ sK3 ) )
= $false )
| ( ( rel_k @ sK0 @ sK1 )
= $true ) ),
inference(not_proxy_clausification,[],[f201]) ).
thf(f204,plain,
( ( ( rel_k @ sK0 @ sK1 )
= $true )
| ( ( ( p @ sK3 )
| ~ ( rel_k @ sK0 @ sK3 ) )
= $false )
| ( $false
= ( p @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f202]) ).
thf(f205,plain,
( ( ( ~ ( rel_k @ sK0 @ sK3 ) )
= $false )
| ( ( rel_k @ sK0 @ sK1 )
= $true )
| ( $false
= ( p @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f204]) ).
thf(f206,plain,
( ( ( rel_k @ sK0 @ sK1 )
= $true )
| ( ( p @ sK3 )
= $false )
| ( $false
= ( p @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f204]) ).
thf(f207,plain,
( ( $false
= ( p @ sK2 ) )
| ( ( rel_k @ sK0 @ sK1 )
= $true )
| ( ( rel_k @ sK0 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f205]) ).
thf(f215,plain,
( ( ( ~ ( rel_k @ sK0 @ sK1 ) )
= $false )
| ( ( ~ ( rel_k @ sK0 @ sK2 ) )
= $false )
| ( ( ~ ( rel_k @ sK0 @ sK3 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f200]) ).
thf(f216,plain,
( ( ( ~ ( rel_k @ sK0 @ sK2 ) )
= $false )
| ( ( ~ ( rel_k @ sK0 @ sK1 ) )
= $false )
| ( ( p @ sK3 )
= $false ) ),
inference(or_proxy_clausification,[],[f200]) ).
thf(f217,plain,
( ( ( ~ ( rel_k @ sK0 @ sK1 ) )
= $false )
| ( ( p @ sK3 )
= $false )
| ( ( rel_k @ sK0 @ sK2 )
= $true ) ),
inference(not_proxy_clausification,[],[f216]) ).
thf(f218,plain,
( ( ( rel_k @ sK0 @ sK2 )
= $true )
| ( ( p @ sK3 )
= $false )
| ( ( rel_k @ sK0 @ sK1 )
= $true ) ),
inference(not_proxy_clausification,[],[f217]) ).
thf(f219,plain,
( ( ( rel_k @ sK0 @ sK1 )
= $true )
| ( ( ~ ( rel_k @ sK0 @ sK2 ) )
= $false )
| ( ( ~ ( rel_k @ sK0 @ sK3 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f215]) ).
thf(f220,plain,
( ( ( ~ ( rel_k @ sK0 @ sK3 ) )
= $false )
| ( ( rel_k @ sK0 @ sK1 )
= $true )
| ( ( rel_k @ sK0 @ sK2 )
= $true ) ),
inference(not_proxy_clausification,[],[f219]) ).
thf(f221,plain,
( ( ( rel_k @ sK0 @ sK2 )
= $true )
| ( ( rel_k @ sK0 @ sK1 )
= $true )
| ( ( rel_k @ sK0 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f220]) ).
thf(f353,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f146]) ).
thf(f354,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) )
| ( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f353]) ).
thf(f355,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f353]) ).
thf(f356,plain,
( ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ sK8 )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f355]) ).
thf(f357,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ sK8 )
= $false ) ),
inference(not_proxy_clausification,[],[f356]) ).
thf(f358,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ sK8 )
= $false ) ),
inference(pi_proxy_clausification,[],[f357]) ).
thf(f359,plain,
! [X1: $i] :
( ( $false
= ( ( p @ sK8 )
| ~ ( rel_k @ sK0 @ sK8 ) ) )
| ( ( ( p @ X1 )
| ~ ( rel_k @ sK0 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f358]) ).
thf(f360,plain,
! [X1: $i] :
( ( ( ( p @ X1 )
| ~ ( rel_k @ sK0 @ X1 ) )
= $true )
| ( ( ~ ( rel_k @ sK0 @ sK8 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f359]) ).
thf(f361,plain,
! [X1: $i] :
( ( ( ( p @ X1 )
| ~ ( rel_k @ sK0 @ X1 ) )
= $true )
| ( ( p @ sK8 )
= $false ) ),
inference(or_proxy_clausification,[],[f359]) ).
thf(f362,plain,
! [X1: $i] :
( ( ( ~ ( rel_k @ sK0 @ X1 ) )
= $true )
| ( ( p @ X1 )
= $true )
| ( ( p @ sK8 )
= $false ) ),
inference(or_proxy_clausification,[],[f361]) ).
thf(f363,plain,
! [X1: $i] :
( ( ( p @ X1 )
= $true )
| ( ( rel_k @ sK0 @ X1 )
= $false )
| ( ( p @ sK8 )
= $false ) ),
inference(not_proxy_clausification,[],[f362]) ).
thf(f364,plain,
! [X1: $i] :
( ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_k @ sK0 @ X1 ) )
= $true )
| ( ( ~ ( rel_k @ sK0 @ sK8 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f360]) ).
thf(f365,plain,
! [X1: $i] :
( ( ( ~ ( rel_k @ sK0 @ sK8 ) )
= $false )
| ( ( rel_k @ sK0 @ X1 )
= $false )
| ( ( p @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f364]) ).
thf(f366,plain,
! [X1: $i] :
( ( ( rel_k @ sK0 @ X1 )
= $false )
| ( ( p @ X1 )
= $true )
| ( $true
= ( rel_k @ sK0 @ sK8 ) ) ),
inference(not_proxy_clausification,[],[f365]) ).
thf(f367,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $true )
| ( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f354]) ).
thf(f368,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ X1 )
= $true )
| ( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f367]) ).
thf(f369,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ X1 )
= $true )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f368]) ).
thf(f370,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ X1 )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f369]) ).
thf(f371,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f370]) ).
thf(f372,plain,
! [X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f370]) ).
thf(f373,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f372]) ).
thf(f374,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f373]) ).
thf(f375,plain,
! [X2: $i,X1: $i] :
( ( ( ( p @ X2 )
| ~ ~ ( q @ X2 )
| ~ ( rel_k @ sK0 @ X2 ) )
= $true )
| ( ( ( p @ X1 )
| ~ ( rel_k @ sK0 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f374]) ).
thf(f376,plain,
! [X2: $i,X1: $i] :
( ( ( ( p @ X2 )
| ~ ~ ( q @ X2 ) )
= $true )
| ( ( ( p @ X1 )
| ~ ( rel_k @ sK0 @ X1 ) )
= $true )
| ( ( ~ ( rel_k @ sK0 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f375]) ).
thf(f377,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ~ ( q @ X2 ) )
= $true )
| ( ( ( p @ X1 )
| ~ ( rel_k @ sK0 @ X1 ) )
= $true )
| ( ( p @ X2 )
= $true )
| ( ( ~ ( rel_k @ sK0 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f376]) ).
thf(f378,plain,
! [X2: $i,X1: $i] :
( ( ( p @ X2 )
= $true )
| ( ( ( p @ X1 )
| ~ ( rel_k @ sK0 @ X1 ) )
= $true )
| ( ( ~ ( rel_k @ sK0 @ X2 ) )
= $true )
| ( ( ~ ( q @ X2 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f377]) ).
thf(f379,plain,
! [X2: $i,X1: $i] :
( ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_k @ sK0 @ X1 ) )
= $true )
| ( ( p @ X2 )
= $true )
| ( ( ~ ( rel_k @ sK0 @ X2 ) )
= $true )
| ( ( ~ ( q @ X2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f378]) ).
thf(f380,plain,
! [X2: $i,X1: $i] :
( ( ( rel_k @ sK0 @ X1 )
= $false )
| ( ( ~ ( q @ X2 ) )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( p @ X2 )
= $true )
| ( ( ~ ( rel_k @ sK0 @ X2 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f379]) ).
thf(f381,plain,
! [X2: $i,X1: $i] :
( ( ( p @ X1 )
= $true )
| ( ( q @ X2 )
= $true )
| ( ( p @ X2 )
= $true )
| ( ( rel_k @ sK0 @ X1 )
= $false )
| ( ( ~ ( rel_k @ sK0 @ X2 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f380]) ).
thf(f382,plain,
! [X2: $i,X1: $i] :
( ( ( rel_k @ sK0 @ X1 )
= $false )
| ( ( p @ X2 )
= $true )
| ( ( p @ X1 )
= $true )
| ( ( q @ X2 )
= $true )
| ( ( rel_k @ sK0 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f381]) ).
thf(f383,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f371]) ).
thf(f384,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( q @ Y0 )
| ~ ( rel_k @ sK0 @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f383]) ).
thf(f385,plain,
! [X2: $i,X1: $i] :
( ( ( ( p @ X2 )
| ~ ( q @ X2 )
| ~ ( rel_k @ sK0 @ X2 ) )
= $true )
| ( ( ( p @ X1 )
| ~ ( rel_k @ sK0 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f384]) ).
thf(f386,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( p @ X2 )
| ~ ( q @ X2 ) ) )
| ( ( ~ ( rel_k @ sK0 @ X2 ) )
= $true )
| ( ( ( p @ X1 )
| ~ ( rel_k @ sK0 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f385]) ).
thf(f387,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_k @ sK0 @ X2 ) )
= $true )
| ( ( ( p @ X1 )
| ~ ( rel_k @ sK0 @ X1 ) )
= $true )
| ( ( ~ ( q @ X2 ) )
= $true )
| ( ( p @ X2 )
= $true ) ),
inference(or_proxy_clausification,[],[f386]) ).
thf(f388,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( q @ X2 ) )
= $true )
| ( ( p @ X2 )
= $true )
| ( ( ( p @ X1 )
| ~ ( rel_k @ sK0 @ X1 ) )
= $true )
| ( ( rel_k @ sK0 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f387]) ).
thf(f389,plain,
! [X2: $i,X1: $i] :
( ( ( rel_k @ sK0 @ X2 )
= $false )
| ( ( ( p @ X1 )
| ~ ( rel_k @ sK0 @ X1 ) )
= $true )
| ( ( q @ X2 )
= $false )
| ( ( p @ X2 )
= $true ) ),
inference(not_proxy_clausification,[],[f388]) ).
thf(f390,plain,
! [X2: $i,X1: $i] :
( ( ( q @ X2 )
= $false )
| ( ( p @ X2 )
= $true )
| ( ( p @ X1 )
= $true )
| ( ( rel_k @ sK0 @ X2 )
= $false )
| ( ( ~ ( rel_k @ sK0 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f389]) ).
thf(f391,plain,
! [X2: $i,X1: $i] :
( ( ( rel_k @ sK0 @ X1 )
= $false )
| ( ( p @ X2 )
= $true )
| ( ( p @ X1 )
= $true )
| ( ( q @ X2 )
= $false )
| ( ( rel_k @ sK0 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f390]) ).
thf(f393,definition,
( spl9_1
<=> ( $false
= ( p @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
thf(f395,plain,
( ( $false
= ( p @ sK2 ) )
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f393]) ).
thf(f397,definition,
( spl9_2
<=> ( ( p @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
thf(f399,plain,
( ( ( p @ sK3 )
= $false )
| ~ spl9_2 ),
inference(avatar_component_clause,[],[f397]) ).
thf(f401,definition,
( spl9_3
<=> ( $false
= ( p @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_3])],[avatar_definition]) ).
thf(f403,plain,
( ( $false
= ( p @ sK1 ) )
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f401]) ).
thf(f404,plain,
( spl9_1
| spl9_2
| spl9_3 ),
inference(avatar_split_clause,[],[f168,f401,f397,f393]) ).
thf(f406,definition,
( spl9_4
<=> ( ( q @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
thf(f408,plain,
( ( ( q @ sK1 )
= $true )
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f406]) ).
thf(f409,plain,
( spl9_4
| spl9_2
| spl9_1 ),
inference(avatar_split_clause,[],[f169,f393,f397,f406]) ).
thf(f417,definition,
( spl9_6
<=> ( ( rel_k @ sK0 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition]) ).
thf(f419,plain,
( ( ( rel_k @ sK0 @ sK3 )
= $true )
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f417]) ).
thf(f420,plain,
( spl9_6
| spl9_1
| spl9_3 ),
inference(avatar_split_clause,[],[f180,f401,f393,f417]) ).
thf(f421,plain,
( spl9_4
| spl9_6
| spl9_1 ),
inference(avatar_split_clause,[],[f181,f393,f417,f406]) ).
thf(f425,definition,
( spl9_7
<=> ( ( rel_k @ sK0 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_7])],[avatar_definition]) ).
thf(f427,plain,
( ( ( rel_k @ sK0 @ sK2 )
= $true )
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f425]) ).
thf(f428,plain,
( spl9_2
| spl9_3
| spl9_7 ),
inference(avatar_split_clause,[],[f191,f425,f401,f397]) ).
thf(f430,plain,
( spl9_3
| spl9_7
| spl9_6 ),
inference(avatar_split_clause,[],[f197,f417,f425,f401]) ).
thf(f433,definition,
( spl9_8
<=> ( ( rel_k @ sK0 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_8])],[avatar_definition]) ).
thf(f435,plain,
( ( ( rel_k @ sK0 @ sK1 )
= $true )
| ~ spl9_8 ),
inference(avatar_component_clause,[],[f433]) ).
thf(f436,plain,
( spl9_2
| spl9_8
| spl9_1 ),
inference(avatar_split_clause,[],[f206,f393,f433,f397]) ).
thf(f437,plain,
( spl9_1
| spl9_8
| spl9_6 ),
inference(avatar_split_clause,[],[f207,f417,f433,f393]) ).
thf(f440,plain,
( spl9_8
| spl9_2
| spl9_7 ),
inference(avatar_split_clause,[],[f218,f425,f397,f433]) ).
thf(f441,plain,
( spl9_8
| spl9_7
| spl9_6 ),
inference(avatar_split_clause,[],[f221,f417,f425,f433]) ).
thf(f451,definition,
( spl9_11
<=> ! [X1: $i] :
( ( ( p @ X1 )
= $true )
| ( ( rel_k @ sK0 @ X1 )
= $false )
| ( ( q @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl9_11])],[avatar_definition]) ).
thf(f452,plain,
( ! [X1: $i] :
( ( ( rel_k @ sK0 @ X1 )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( q @ X1 )
= $true ) )
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f451]) ).
thf(f487,definition,
( spl9_18
<=> ! [X1: $i] :
( ( ( q @ X1 )
= $false )
| ( ( rel_k @ sK0 @ X1 )
= $false )
| ( ( p @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl9_18])],[avatar_definition]) ).
thf(f488,plain,
( ! [X1: $i] :
( ( ( rel_k @ sK0 @ X1 )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( q @ X1 )
= $false ) )
| ~ spl9_18 ),
inference(avatar_component_clause,[],[f487]) ).
thf(f515,definition,
( spl9_23
<=> ( ( p @ sK8 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl9_23])],[avatar_definition]) ).
thf(f517,plain,
( ( ( p @ sK8 )
= $false )
| ~ spl9_23 ),
inference(avatar_component_clause,[],[f515]) ).
thf(f519,definition,
( spl9_24
<=> ! [X1: $i] :
( ( ( p @ X1 )
= $true )
| ( ( rel_k @ sK0 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl9_24])],[avatar_definition]) ).
thf(f520,plain,
( ! [X1: $i] :
( ( ( rel_k @ sK0 @ X1 )
= $false )
| ( ( p @ X1 )
= $true ) )
| ~ spl9_24 ),
inference(avatar_component_clause,[],[f519]) ).
thf(f521,plain,
( spl9_23
| spl9_24 ),
inference(avatar_split_clause,[],[f363,f519,f515]) ).
thf(f523,definition,
( spl9_25
<=> ( $true
= ( rel_k @ sK0 @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_25])],[avatar_definition]) ).
thf(f525,plain,
( ( $true
= ( rel_k @ sK0 @ sK8 ) )
| ~ spl9_25 ),
inference(avatar_component_clause,[],[f523]) ).
thf(f526,plain,
( spl9_25
| spl9_24 ),
inference(avatar_split_clause,[],[f366,f519,f523]) ).
thf(f527,plain,
( spl9_24
| spl9_11 ),
inference(avatar_split_clause,[],[f382,f451,f519]) ).
thf(f528,plain,
( spl9_24
| spl9_18 ),
inference(avatar_split_clause,[],[f391,f487,f519]) ).
thf(f530,plain,
( ( $false = $true )
| ( ( p @ sK3 )
= $true )
| ~ spl9_6
| ~ spl9_24 ),
inference(constrained_superposition,[],[f520,f419]) ).
thf(f532,plain,
( ( ( p @ sK3 )
= $true )
| ~ spl9_6
| ~ spl9_24 ),
inference(trivial_inequality_removal,[],[f530]) ).
thf(f536,plain,
( ( $false = $true )
| ~ spl9_2
| ~ spl9_6
| ~ spl9_24 ),
inference(forward_demodulation,[],[f532,f399]) ).
thf(f537,plain,
( $false
| ~ spl9_2
| ~ spl9_6
| ~ spl9_24 ),
inference(trivial_inequality_removal,[],[f536]) ).
thf(f538,plain,
( ~ spl9_2
| ~ spl9_6
| ~ spl9_24 ),
inference(avatar_contradiction_clause,[],[f537]) ).
thf(f540,plain,
( ( $false = $true )
| ( ( p @ sK8 )
= $true )
| ( $true
= ( q @ sK8 ) )
| ~ spl9_11
| ~ spl9_25 ),
inference(constrained_superposition,[],[f452,f525]) ).
thf(f544,plain,
( ( ( p @ sK8 )
= $true )
| ( $true
= ( q @ sK8 ) )
| ~ spl9_11
| ~ spl9_25 ),
inference(trivial_inequality_removal,[],[f540]) ).
thf(f549,plain,
( ( $true
= ( q @ sK8 ) )
| ( $false = $true )
| ~ spl9_11
| ~ spl9_23
| ~ spl9_25 ),
inference(forward_demodulation,[],[f544,f517]) ).
thf(f550,plain,
( ( $true
= ( q @ sK8 ) )
| ~ spl9_11
| ~ spl9_23
| ~ spl9_25 ),
inference(trivial_inequality_removal,[],[f549]) ).
thf(f558,plain,
( ( $false = $true )
| ( ( p @ sK8 )
= $true )
| ( $false
= ( q @ sK8 ) )
| ~ spl9_18
| ~ spl9_25 ),
inference(constrained_superposition,[],[f525,f488]) ).
thf(f562,plain,
( ( $false
= ( q @ sK8 ) )
| ( ( p @ sK8 )
= $true )
| ~ spl9_18
| ~ spl9_25 ),
inference(trivial_inequality_removal,[],[f558]) ).
thf(f569,plain,
( ( $false = $true )
| ( ( p @ sK8 )
= $true )
| ~ spl9_11
| ~ spl9_18
| ~ spl9_23
| ~ spl9_25 ),
inference(forward_demodulation,[],[f562,f550]) ).
thf(f570,plain,
( ( ( p @ sK8 )
= $true )
| ~ spl9_11
| ~ spl9_18
| ~ spl9_23
| ~ spl9_25 ),
inference(trivial_inequality_removal,[],[f569]) ).
thf(f580,plain,
( ( $false = $true )
| ~ spl9_11
| ~ spl9_18
| ~ spl9_23
| ~ spl9_25 ),
inference(forward_demodulation,[],[f570,f517]) ).
thf(f581,plain,
( $false
| ~ spl9_11
| ~ spl9_18
| ~ spl9_23
| ~ spl9_25 ),
inference(trivial_inequality_removal,[],[f580]) ).
thf(f582,plain,
( ~ spl9_11
| ~ spl9_18
| ~ spl9_23
| ~ spl9_25 ),
inference(avatar_contradiction_clause,[],[f581]) ).
thf(f623,plain,
( ( ( p @ sK2 )
= $true )
| ( $false = $true )
| ~ spl9_7
| ~ spl9_24 ),
inference(constrained_superposition,[],[f520,f427]) ).
thf(f633,plain,
( ( ( p @ sK2 )
= $true )
| ~ spl9_7
| ~ spl9_24 ),
inference(trivial_inequality_removal,[],[f623]) ).
thf(f643,plain,
( ( $false = $true )
| ~ spl9_1
| ~ spl9_7
| ~ spl9_24 ),
inference(forward_demodulation,[],[f633,f395]) ).
thf(f644,plain,
( $false
| ~ spl9_1
| ~ spl9_7
| ~ spl9_24 ),
inference(trivial_inequality_removal,[],[f643]) ).
thf(f645,plain,
( ~ spl9_1
| ~ spl9_7
| ~ spl9_24 ),
inference(avatar_contradiction_clause,[],[f644]) ).
thf(f649,plain,
( ( $true
= ( p @ sK1 ) )
| ( $false = $true )
| ~ spl9_8
| ~ spl9_24 ),
inference(constrained_superposition,[],[f435,f520]) ).
thf(f650,plain,
( ( ( q @ sK1 )
= $false )
| ( $false = $true )
| ( $true
= ( p @ sK1 ) )
| ~ spl9_8
| ~ spl9_18 ),
inference(constrained_superposition,[],[f435,f488]) ).
thf(f655,plain,
( ( ( q @ sK1 )
= $false )
| ( $true
= ( p @ sK1 ) )
| ~ spl9_8
| ~ spl9_18 ),
inference(trivial_inequality_removal,[],[f650]) ).
thf(f656,plain,
( ( $true
= ( p @ sK1 ) )
| ~ spl9_8
| ~ spl9_24 ),
inference(trivial_inequality_removal,[],[f649]) ).
thf(f662,plain,
( ( $false = $true )
| ( $true
= ( p @ sK1 ) )
| ~ spl9_4
| ~ spl9_8
| ~ spl9_18 ),
inference(forward_demodulation,[],[f655,f408]) ).
thf(f663,plain,
( ( $true
= ( p @ sK1 ) )
| ~ spl9_4
| ~ spl9_8
| ~ spl9_18 ),
inference(trivial_inequality_removal,[],[f662]) ).
thf(f664,plain,
( ( $false = $true )
| ~ spl9_3
| ~ spl9_8
| ~ spl9_24 ),
inference(forward_demodulation,[],[f656,f403]) ).
thf(f665,plain,
( $false
| ~ spl9_3
| ~ spl9_8
| ~ spl9_24 ),
inference(trivial_inequality_removal,[],[f664]) ).
thf(f666,plain,
( ~ spl9_3
| ~ spl9_8
| ~ spl9_24 ),
inference(avatar_contradiction_clause,[],[f665]) ).
thf(f670,plain,
( ( $false = $true )
| ~ spl9_3
| ~ spl9_4
| ~ spl9_8
| ~ spl9_18 ),
inference(forward_demodulation,[],[f663,f403]) ).
thf(f671,plain,
( $false
| ~ spl9_3
| ~ spl9_4
| ~ spl9_8
| ~ spl9_18 ),
inference(trivial_inequality_removal,[],[f670]) ).
thf(f672,plain,
( ~ spl9_3
| ~ spl9_4
| ~ spl9_8
| ~ spl9_18 ),
inference(avatar_contradiction_clause,[],[f671]) ).
cnf(s1,plain,
( spl9_1
| spl9_2
| spl9_3 ),
inference(sat_conversion,[],[f404]) ).
cnf(s2,plain,
( spl9_1
| spl9_2
| spl9_4 ),
inference(sat_conversion,[],[f409]) ).
cnf(s5,plain,
( spl9_1
| spl9_3
| spl9_6 ),
inference(sat_conversion,[],[f420]) ).
cnf(s6,plain,
( spl9_1
| spl9_4
| spl9_6 ),
inference(sat_conversion,[],[f421]) ).
cnf(s9,plain,
( spl9_2
| spl9_3
| spl9_7 ),
inference(sat_conversion,[],[f428]) ).
cnf(s11,plain,
( spl9_3
| spl9_6
| spl9_7 ),
inference(sat_conversion,[],[f430]) ).
cnf(s13,plain,
( spl9_1
| spl9_2
| spl9_8 ),
inference(sat_conversion,[],[f436]) ).
cnf(s14,plain,
( spl9_1
| spl9_6
| spl9_8 ),
inference(sat_conversion,[],[f437]) ).
cnf(s17,plain,
( spl9_2
| spl9_7
| spl9_8 ),
inference(sat_conversion,[],[f440]) ).
cnf(s18,plain,
( spl9_6
| spl9_7
| spl9_8 ),
inference(sat_conversion,[],[f441]) ).
cnf(s37,plain,
( spl9_23
| spl9_24 ),
inference(sat_conversion,[],[f521]) ).
cnf(s38,plain,
( spl9_24
| spl9_25 ),
inference(sat_conversion,[],[f526]) ).
cnf(s39,plain,
( spl9_11
| spl9_24 ),
inference(sat_conversion,[],[f527]) ).
cnf(s40,plain,
( spl9_18
| spl9_24 ),
inference(sat_conversion,[],[f528]) ).
cnf(s42,plain,
( ~ spl9_2
| ~ spl9_6
| ~ spl9_24 ),
inference(sat_conversion,[],[f538]) ).
cnf(s46,plain,
( ~ spl9_11
| ~ spl9_18
| ~ spl9_23
| ~ spl9_25 ),
inference(sat_conversion,[],[f582]) ).
cnf(s54,plain,
( ~ spl9_1
| ~ spl9_7
| ~ spl9_24 ),
inference(sat_conversion,[],[f645]) ).
cnf(s56,plain,
( ~ spl9_3
| ~ spl9_8
| ~ spl9_24 ),
inference(sat_conversion,[],[f666]) ).
cnf(s58,plain,
( ~ spl9_3
| ~ spl9_4
| ~ spl9_8
| ~ spl9_18 ),
inference(sat_conversion,[],[f672]) ).
cnf(s59,plain,
( ~ spl9_4
| ~ spl9_8
| ~ spl9_3 ),
inference(rat,[],[s40,s56,s58]) ).
cnf(s60,plain,
( spl9_2
| spl9_1 ),
inference(rat,[],[s59,s1,s2,s13]) ).
cnf(s61,plain,
spl9_24,
inference(rat,[],[s46,s37,s38,s39,s40]) ).
cnf(s62,plain,
( spl9_6
| spl9_1 ),
inference(rat,[],[s59,s5,s6,s14]) ).
cnf(s63,plain,
spl9_1,
inference(rat,[],[s62,s42,s60,s61]) ).
cnf(s64,plain,
~ spl9_7,
inference(rat,[],[s54,s61,s63]) ).
cnf(s65,plain,
spl9_8,
inference(rat,[],[s42,s17,s18,s61,s64]) ).
cnf(s66,plain,
~ spl9_3,
inference(rat,[],[s56,s61,s65]) ).
cnf(s67,plain,
spl9_6,
inference(rat,[],[s11,s64,s66]) ).
cnf(s68,plain,
spl9_2,
inference(rat,[],[s9,s64,s66]) ).
cnf(s69,plain,
$false,
inference(rat,[],[s42,s61,s68,s67]) ).
thf(f673,plain,
$false,
inference(avatar_sat_refutation,[],[s69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO404^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n014.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 16:50:45 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.21/0.29 % (2920925)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (2920934)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4078773473:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (2920936)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.29 % (2920936)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
% 0.21/0.29 % (2920930)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2061327624:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (2920931)lrs+10_16_si=on:nwc=1.5:random_seed=2585209643:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (2920932)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3973571523:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (2920934)Instruction limit reached!
% 0.21/0.29 % (2920934)------------------------------
% 0.21/0.29 % (2920934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2920934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2920935)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1492687633:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (2920934)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2920934)Termination reason: Instruction limit
% 0.21/0.29 % (2920934)Termination phase: Saturation
% 0.21/0.29 % (2920934)Time elapsed: 0.007 s
% 0.21/0.29 % (2920934)Peak memory usage: 12 MB
% 0.21/0.29 % (2920934)Instructions burned: 25 (million)
% 0.21/0.29 % (2920933)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=1676228015: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)
% 0.21/0.29 % (2920936)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=838845244:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (2920932)Instruction limit reached!
% 0.21/0.29 % (2920932)------------------------------
% 0.21/0.29 % (2920932)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2920932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2920932)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2920932)Termination reason: Instruction limit
% 0.21/0.29 % (2920932)Termination phase: Property scanning
% 0.21/0.29 % (2920932)Time elapsed: 0.002 s
% 0.21/0.29 % (2920932)Peak memory usage: 10 MB
% 0.21/0.29 % (2920932)Instructions burned: 4 (million)
% 0.21/0.29 % (2920931)Instruction limit reached!
% 0.21/0.29 % (2920931)------------------------------
% 0.21/0.29 % (2920931)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2920931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2920931)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2920931)Termination reason: Instruction limit
% 0.21/0.29 % (2920931)Termination phase: Saturation
% 0.21/0.29 % (2920931)Time elapsed: 0.009 s
% 0.21/0.29 % (2920931)Peak memory usage: 12 MB
% 0.21/0.29 % (2920931)Instructions burned: 19 (million)
% 0.21/0.29 % (2920943)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2409475742:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.29 % (2920930) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2920925-2920930"...
% 0.21/0.29 % (2920935) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2920925-2920935"...
% 0.21/0.29 % (2920943)Instruction limit reached!
% 0.21/0.29 % (2920943)------------------------------
% 0.21/0.29 % (2920943)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2920943)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2920943)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2920943)Termination reason: Instruction limit
% 0.21/0.29 % (2920943)Termination phase: Preprocessing 1
% 0.21/0.29 % (2920943)Time elapsed: 0.001 s
% 0.21/0.29 % (2920943)Peak memory usage: 10 MB
% 0.21/0.29 % (2920943)Instructions burned: 4 (million)
% 0.21/0.29 % (2920936) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2920925-2920936"...
% 0.21/0.29 % (2920930)...printing done.
% 0.21/0.29 % (2920935)...printing done.
% 0.21/0.29 % (2920930)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.30 % (2920930)------------------------------
% 0.21/0.30 % (2920930)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (2920930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (2920930)CaDiCaL version: 2.1.3
% 0.21/0.30 % (2920930)Termination reason: Refutation
% 0.21/0.30 % (2920930)Time elapsed: 0.018 s
% 0.21/0.30 % (2920930)Peak memory usage: 13 MB
% 0.21/0.30 % (2920930)Instructions burned: 36 (million)
% 0.21/0.30 % (2920925)Success in time 0.051 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------