%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO404^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:49:53 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 21
% Syntax : Number of formulae : 254 ( 43 unt; 0 typ; 13 def)
% Number of atoms : 2795 ( 468 equ; 0 cnn)
% Maximal formula atoms : 14 ( 11 avg)
% Number of connectives : 3405 ( 761 ~; 854 |; 0 &;1660 @)
% ( 13 <=>; 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 : 73 ( 69 usr; 22 con; 0-4 aty)
% ( 117 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 402 ( 0 sgn 90 !; 0 ?; 402 :)
% 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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_40,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_41,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vNOT: $o > $o ).
thf(func_def_43,type,
vOR: $o > $o > $o ).
thf(func_def_44,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vIMP: $o > $o > $o ).
thf(func_def_49,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_50,type,
vAND: $o > $o > $o ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_k
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_k @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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(f38,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f39,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f40,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f41,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f42,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f43,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f45,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f79,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f80,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f79]) ).
thf(f87,plain,
( mbox_k
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_k @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f88,plain,
( mbox_k
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f87]) ).
thf(f90,plain,
~ ( mvalid @ ( mequiv @ ( mand @ ( mbox_k @ ( mimplies @ q @ p ) ) @ ( mbox_k @ ( mimplies @ ( mnot @ q ) @ p ) ) ) @ ( mbox_k @ p ) ) ),
inference(rectify,[],[f35]) ).
thf(f91,plain,
( ( mvalid @ ( mequiv @ ( mand @ ( mbox_k @ ( mimplies @ q @ p ) ) @ ( mbox_k @ ( mimplies @ ( mnot @ q ) @ p ) ) ) @ ( mbox_k @ p ) ) )
!= $true ),
inference(fool_elimination,[],[f90]) ).
thf(f92,plain,
( ( mvalid @ ( mequiv @ ( mand @ ( mbox_k @ ( mimplies @ q @ p ) ) @ ( mbox_k @ ( mimplies @ ( mnot @ q ) @ p ) ) ) @ ( mbox_k @ p ) ) )
!= $true ),
inference(flattening,[],[f91]) ).
thf(f95,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f96,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f97,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f98,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f100,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f120,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f80]) ).
thf(f124,plain,
( mbox_k
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f126,plain,
( ( mvalid @ ( mequiv @ ( mand @ ( mbox_k @ ( mimplies @ q @ p ) ) @ ( mbox_k @ ( mimplies @ ( mnot @ q ) @ p ) ) ) @ ( mbox_k @ p ) ) )
!= $true ),
inference(cnf_transformation,[],[f92]) ).
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] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f97,f95,f96,f95,f95]) ).
thf(f130,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f98,f96,f95]) ).
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] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f100,f129,f130,f130]) ).
thf(f139,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ q
@ p ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ q )
@ p ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_k @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p ) ) ) ),
inference(definition_unfolding,[],[f126,f120,f132,f129,f124,f130,f124,f130,f95,f124]) ).
thf(f140,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( q @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( q @ Y1 )
| ( p @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( q @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( q @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f141,plain,
( $false
= ( ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( q @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( q @ Y1 )
| ( p @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ( q @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_k @ Y0 @ Y1 )
| ~ ~ ( q @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f140]) ).
thf(f142,plain,
( $false
= ( ~ ( ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f143,plain,
( $true
= ( ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f142]) ).
thf(f144,plain,
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f143]) ).
thf(f145,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f144]) ).
thf(f146,plain,
( ( $false
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f145]) ).
thf(f148,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f147]) ).
thf(f149,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f149]) ).
thf(f151,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f150]) ).
thf(f153,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f154]) ).
thf(f157,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_k @ sK0 @ X1 )
| ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 )
| ~ ( q @ X2 )
| ( p @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 )
| ~ ( q @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( q @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 ) ) )
| ( $true
= ( ~ ( q @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 ) ) )
| ( $true
= ( ~ ( q @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $true
= ( ~ ( q @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $false
= ( q @ X2 ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f155]) ).
thf(f167,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_k @ sK0 @ X1 )
| ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 )
| ~ ~ ( q @ X2 )
| ( p @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 )
| ~ ~ ( q @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ~ ( q @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 ) ) )
| ( $true
= ( ~ ~ ( q @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X2 ) ) )
| ( $true
= ( ~ ~ ( q @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $true
= ( ~ ~ ( q @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $false
= ( ~ ( q @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $true
= ( q @ X2 ) ) ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f151]) ).
thf(f177,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_k @ sK0 @ X1 )
| ( p @ X1 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK1 )
| ( p @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f176]) ).
thf(f178,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK1 )
| ( p @ sK1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( p @ sK1 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK1 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f178]) ).
thf(f181,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( p @ sK1 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f184,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f146]) ).
thf(f185,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f186,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f185]) ).
thf(f187,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $true
= ( ~ ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f186]) ).
thf(f188,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f189,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f188]) ).
thf(f190,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f188]) ).
thf(f191,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f192,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f191]) ).
thf(f194,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f195,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_k @ sK0 @ sK2 )
| ~ ~ ( q @ sK2 )
| ( p @ sK2 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 )
| ~ ( q @ X1 )
| ( p @ X1 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( q @ sK3 )
| ( p @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f198]) ).
thf(f200,plain,
! [X1: $i] :
( ( $false
= ( ~ ~ ( q @ sK2 )
| ( p @ sK2 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 )
| ~ ( q @ X1 )
| ( p @ X1 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( q @ sK3 )
| ( p @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_k @ sK0 @ sK2 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 )
| ~ ( q @ X1 )
| ( p @ X1 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( q @ sK3 )
| ( p @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f199]) ).
thf(f202,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 )
| ~ ( q @ X1 )
| ( p @ X1 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( q @ sK3 )
| ( p @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f201]) ).
thf(f203,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( ~ ( q @ X1 )
| ( p @ X1 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( q @ sK3 )
| ( p @ sK3 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( q @ sK3 )
| ( p @ sK3 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ( q @ sK3 )
| ( p @ sK3 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f204]) ).
thf(f207,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( rel_k @ sK0 @ sK3 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( rel_k @ sK0 @ sK3 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( rel_k @ sK0 @ sK3 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f208]) ).
thf(f210,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( p @ sK3 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f205]) ).
thf(f215,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( p @ sK3 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f210]) ).
thf(f216,plain,
! [X1: $i] :
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( p @ sK3 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f215]) ).
thf(f217,plain,
! [X1: $i] :
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 )
| ~ ( q @ X1 )
| ( p @ X1 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( q @ sK3 )
| ( p @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f200]) ).
thf(f235,plain,
! [X1: $i] :
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( ~ ( q @ X1 )
| ( p @ X1 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( q @ sK3 )
| ( p @ sK3 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f217]) ).
thf(f236,plain,
! [X1: $i] :
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 )
| ~ ( q @ sK3 )
| ( p @ sK3 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f235]) ).
thf(f237,plain,
! [X1: $i] :
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ( q @ sK3 )
| ( p @ sK3 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f236]) ).
thf(f238,plain,
! [X1: $i] :
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK3 ) ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f236]) ).
thf(f239,plain,
! [X1: $i] :
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( rel_k @ sK0 @ sK3 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f238]) ).
thf(f240,plain,
! [X1: $i] :
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( rel_k @ sK0 @ sK3 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f239]) ).
thf(f241,plain,
! [X1: $i] :
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( rel_k @ sK0 @ sK3 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f240]) ).
thf(f242,plain,
! [X1: $i] :
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( p @ sK3 ) )
| ( $true
= ( ~ ( rel_k @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f237]) ).
thf(f247,plain,
! [X1: $i] :
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( p @ sK3 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f242]) ).
thf(f248,plain,
! [X1: $i] :
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( p @ sK3 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $false
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f247]) ).
thf(f312,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK5 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f189]) ).
thf(f313,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK5 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f312]) ).
thf(f314,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ~ ( q @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_k @ sK0 @ Y0 )
| ~ ( q @ Y0 )
| ( p @ Y0 ) )
@ sK6 ) ) ),
inference(sigma_proxy_clausification,[],[f313]) ).
thf(f315,plain,
( ( $false
= ( ~ ( rel_k @ sK0 @ sK2 )
| ~ ~ ( q @ sK2 )
| ( p @ sK2 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK5 )
| ( p @ sK5 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK6 )
| ~ ( q @ sK6 )
| ( p @ sK6 ) ) ) ),
inference(beta-eta_normalization,[],[f314]) ).
thf(f316,plain,
( ( $false
= ( ~ ~ ( q @ sK2 )
| ( p @ sK2 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK5 )
| ( p @ sK5 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK6 )
| ~ ( q @ sK6 )
| ( p @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f315]) ).
thf(f317,plain,
( ( $false
= ( ~ ( rel_k @ sK0 @ sK2 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK5 )
| ( p @ sK5 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK6 )
| ~ ( q @ sK6 )
| ( p @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f315]) ).
thf(f318,plain,
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK5 )
| ( p @ sK5 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK6 )
| ~ ( q @ sK6 )
| ( p @ sK6 ) ) ) ),
inference(not_proxy_clausification,[],[f317]) ).
thf(f319,plain,
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $false
= ( p @ sK5 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK6 )
| ~ ( q @ sK6 )
| ( p @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f318]) ).
thf(f320,plain,
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK5 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK6 )
| ~ ( q @ sK6 )
| ( p @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f318]) ).
thf(f321,plain,
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( rel_k @ sK0 @ sK5 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK6 )
| ~ ( q @ sK6 )
| ( p @ sK6 ) ) ) ),
inference(not_proxy_clausification,[],[f320]) ).
thf(f322,plain,
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( rel_k @ sK0 @ sK5 ) )
| ( $false
= ( ~ ( q @ sK6 )
| ( p @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f321]) ).
thf(f323,plain,
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( rel_k @ sK0 @ sK5 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f321]) ).
thf(f324,plain,
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( rel_k @ sK0 @ sK5 ) )
| ( $true
= ( rel_k @ sK0 @ sK6 ) ) ),
inference(not_proxy_clausification,[],[f323]) ).
thf(f325,plain,
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $true
= ( rel_k @ sK0 @ sK5 ) )
| ( $false
= ( p @ sK6 ) ) ),
inference(or_proxy_clausification,[],[f322]) ).
thf(f328,plain,
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $false
= ( p @ sK5 ) )
| ( $false
= ( ~ ( q @ sK6 )
| ( p @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f319]) ).
thf(f329,plain,
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $false
= ( p @ sK5 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f319]) ).
thf(f330,plain,
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $false
= ( p @ sK5 ) )
| ( $true
= ( rel_k @ sK0 @ sK6 ) ) ),
inference(not_proxy_clausification,[],[f329]) ).
thf(f331,plain,
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ( $false
= ( p @ sK5 ) )
| ( $false
= ( p @ sK6 ) ) ),
inference(or_proxy_clausification,[],[f328]) ).
thf(f334,plain,
( ( $false
= ( p @ sK2 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK5 )
| ( p @ sK5 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK6 )
| ~ ( q @ sK6 )
| ( p @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f316]) ).
thf(f353,plain,
( ( $false
= ( p @ sK2 ) )
| ( $false
= ( p @ sK5 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK6 )
| ~ ( q @ sK6 )
| ( p @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f334]) ).
thf(f354,plain,
( ( $false
= ( p @ sK2 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK5 ) ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK6 )
| ~ ( q @ sK6 )
| ( p @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f334]) ).
thf(f355,plain,
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( rel_k @ sK0 @ sK5 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK6 )
| ~ ( q @ sK6 )
| ( p @ sK6 ) ) ) ),
inference(not_proxy_clausification,[],[f354]) ).
thf(f356,plain,
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( rel_k @ sK0 @ sK5 ) )
| ( $false
= ( ~ ( q @ sK6 )
| ( p @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f355]) ).
thf(f357,plain,
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( rel_k @ sK0 @ sK5 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f355]) ).
thf(f358,plain,
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( rel_k @ sK0 @ sK5 ) )
| ( $true
= ( rel_k @ sK0 @ sK6 ) ) ),
inference(not_proxy_clausification,[],[f357]) ).
thf(f359,plain,
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( rel_k @ sK0 @ sK5 ) )
| ( $false
= ( p @ sK6 ) ) ),
inference(or_proxy_clausification,[],[f356]) ).
thf(f362,plain,
( ( $false
= ( p @ sK2 ) )
| ( $false
= ( p @ sK5 ) )
| ( $false
= ( ~ ( q @ sK6 )
| ( p @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f353]) ).
thf(f363,plain,
( ( $false
= ( p @ sK2 ) )
| ( $false
= ( p @ sK5 ) )
| ( $false
= ( ~ ( rel_k @ sK0 @ sK6 ) ) ) ),
inference(or_proxy_clausification,[],[f353]) ).
thf(f364,plain,
( ( $false
= ( p @ sK2 ) )
| ( $false
= ( p @ sK5 ) )
| ( $true
= ( rel_k @ sK0 @ sK6 ) ) ),
inference(not_proxy_clausification,[],[f363]) ).
thf(f365,plain,
( ( $false
= ( p @ sK2 ) )
| ( $false
= ( p @ sK5 ) )
| ( $false
= ( p @ sK6 ) ) ),
inference(or_proxy_clausification,[],[f362]) ).
thf(f369,definition,
( spl7_1
<=> ! [X2: $i] :
( ( $true
= ( p @ X2 ) )
| ( $false
= ( q @ X2 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
thf(f370,plain,
( ! [X2: $i] :
( ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $false
= ( q @ X2 ) )
| ( $true
= ( p @ X2 ) ) )
| ~ spl7_1 ),
inference(avatar_component_clause,[],[f369]) ).
thf(f372,definition,
( spl7_2
<=> ! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_k @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
thf(f373,plain,
( ! [X1: $i] :
( ( $false
= ( rel_k @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) ) )
| ~ spl7_2 ),
inference(avatar_component_clause,[],[f372]) ).
thf(f374,plain,
( spl7_1
| spl7_2 ),
inference(avatar_split_clause,[],[f165,f372,f369]) ).
thf(f376,definition,
( spl7_3
<=> ! [X2: $i] :
( ( $true
= ( p @ X2 ) )
| ( $true
= ( q @ X2 ) )
| ( $false
= ( rel_k @ sK0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
thf(f377,plain,
( ! [X2: $i] :
( ( $false
= ( rel_k @ sK0 @ X2 ) )
| ( $true
= ( q @ X2 ) )
| ( $true
= ( p @ X2 ) ) )
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f376]) ).
thf(f378,plain,
( spl7_3
| spl7_2 ),
inference(avatar_split_clause,[],[f175,f372,f376]) ).
thf(f380,definition,
( spl7_4
<=> ( $true
= ( rel_k @ sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
thf(f382,plain,
( ( $true
= ( rel_k @ sK0 @ sK1 ) )
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f380]) ).
thf(f383,plain,
( spl7_4
| spl7_2 ),
inference(avatar_split_clause,[],[f182,f372,f380]) ).
thf(f385,definition,
( spl7_5
<=> ( $false
= ( p @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
thf(f387,plain,
( ( $false
= ( p @ sK1 ) )
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f385]) ).
thf(f388,plain,
( spl7_5
| spl7_2 ),
inference(avatar_split_clause,[],[f183,f372,f385]) ).
thf(f390,definition,
( spl7_6
<=> ( $true
= ( rel_k @ sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
thf(f392,plain,
( ( $true
= ( rel_k @ sK0 @ sK3 ) )
| ~ spl7_6 ),
inference(avatar_component_clause,[],[f390]) ).
thf(f394,definition,
( spl7_7
<=> ( $true
= ( rel_k @ sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
thf(f396,plain,
( ( $true
= ( rel_k @ sK0 @ sK2 ) )
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f394]) ).
thf(f397,plain,
( spl7_6
| spl7_1
| spl7_7 ),
inference(avatar_split_clause,[],[f209,f394,f369,f390]) ).
thf(f404,definition,
( spl7_9
<=> ( $false
= ( p @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_9])],[avatar_definition]) ).
thf(f406,plain,
( ( $false
= ( p @ sK3 ) )
| ~ spl7_9 ),
inference(avatar_component_clause,[],[f404]) ).
thf(f407,plain,
( spl7_9
| spl7_1
| spl7_7 ),
inference(avatar_split_clause,[],[f216,f394,f369,f404]) ).
thf(f416,definition,
( spl7_11
<=> ( $false
= ( p @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_11])],[avatar_definition]) ).
thf(f418,plain,
( ( $false
= ( p @ sK2 ) )
| ~ spl7_11 ),
inference(avatar_component_clause,[],[f416]) ).
thf(f419,plain,
( spl7_6
| spl7_1
| spl7_11 ),
inference(avatar_split_clause,[],[f241,f416,f369,f390]) ).
thf(f421,plain,
( spl7_9
| spl7_1
| spl7_11 ),
inference(avatar_split_clause,[],[f248,f416,f369,f404]) ).
thf(f444,definition,
( spl7_15
<=> ( $true
= ( rel_k @ sK0 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_15])],[avatar_definition]) ).
thf(f446,plain,
( ( $true
= ( rel_k @ sK0 @ sK6 ) )
| ~ spl7_15 ),
inference(avatar_component_clause,[],[f444]) ).
thf(f448,definition,
( spl7_16
<=> ( $true
= ( rel_k @ sK0 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_16])],[avatar_definition]) ).
thf(f450,plain,
( ( $true
= ( rel_k @ sK0 @ sK5 ) )
| ~ spl7_16 ),
inference(avatar_component_clause,[],[f448]) ).
thf(f451,plain,
( spl7_15
| spl7_16
| spl7_7 ),
inference(avatar_split_clause,[],[f324,f394,f448,f444]) ).
thf(f458,definition,
( spl7_18
<=> ( $false
= ( p @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_18])],[avatar_definition]) ).
thf(f460,plain,
( ( $false
= ( p @ sK6 ) )
| ~ spl7_18 ),
inference(avatar_component_clause,[],[f458]) ).
thf(f461,plain,
( spl7_18
| spl7_16
| spl7_7 ),
inference(avatar_split_clause,[],[f325,f394,f448,f458]) ).
thf(f463,definition,
( spl7_19
<=> ( $false
= ( p @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl7_19])],[avatar_definition]) ).
thf(f465,plain,
( ( $false
= ( p @ sK5 ) )
| ~ spl7_19 ),
inference(avatar_component_clause,[],[f463]) ).
thf(f466,plain,
( spl7_15
| spl7_19
| spl7_7 ),
inference(avatar_split_clause,[],[f330,f394,f463,f444]) ).
thf(f468,plain,
( spl7_18
| spl7_19
| spl7_7 ),
inference(avatar_split_clause,[],[f331,f394,f463,f458]) ).
thf(f475,plain,
( spl7_15
| spl7_16
| spl7_11 ),
inference(avatar_split_clause,[],[f358,f416,f448,f444]) ).
thf(f477,plain,
( spl7_18
| spl7_16
| spl7_11 ),
inference(avatar_split_clause,[],[f359,f416,f448,f458]) ).
thf(f478,plain,
( spl7_15
| spl7_19
| spl7_11 ),
inference(avatar_split_clause,[],[f364,f416,f463,f444]) ).
thf(f480,plain,
( spl7_18
| spl7_19
| spl7_11 ),
inference(avatar_split_clause,[],[f365,f416,f463,f458]) ).
thf(f492,plain,
( ( $true = $false )
| ( $true
= ( p @ sK2 ) )
| ~ spl7_2
| ~ spl7_7 ),
inference(constrained_superposition,[],[f373,f396]) ).
thf(f497,plain,
( ( $true
= ( p @ sK2 ) )
| ~ spl7_2
| ~ spl7_7 ),
inference(trivial_inequality_removal,[],[f492]) ).
thf(f501,plain,
( ( $true = $false )
| ~ spl7_2
| ~ spl7_7
| ~ spl7_11 ),
inference(forward_demodulation,[],[f497,f418]) ).
thf(f502,plain,
( $false
| ~ spl7_2
| ~ spl7_7
| ~ spl7_11 ),
inference(trivial_inequality_removal,[],[f501]) ).
thf(f503,plain,
( ~ spl7_2
| ~ spl7_7
| ~ spl7_11 ),
inference(avatar_contradiction_clause,[],[f502]) ).
thf(f505,plain,
( ( $true = $false )
| ( $true
= ( p @ sK3 ) )
| ~ spl7_2
| ~ spl7_6 ),
inference(constrained_superposition,[],[f373,f392]) ).
thf(f506,plain,
( ( $true
= ( p @ sK3 ) )
| ~ spl7_2
| ~ spl7_6 ),
inference(trivial_inequality_removal,[],[f505]) ).
thf(f520,plain,
( ( $true = $false )
| ( $true
= ( p @ sK6 ) )
| ~ spl7_2
| ~ spl7_15 ),
inference(constrained_superposition,[],[f373,f446]) ).
thf(f521,plain,
( ( $true
= ( p @ sK6 ) )
| ~ spl7_2
| ~ spl7_15 ),
inference(trivial_inequality_removal,[],[f520]) ).
thf(f525,plain,
( ( $true = $false )
| ~ spl7_2
| ~ spl7_6
| ~ spl7_9 ),
inference(forward_demodulation,[],[f506,f406]) ).
thf(f526,plain,
( $false
| ~ spl7_2
| ~ spl7_6
| ~ spl7_9 ),
inference(trivial_inequality_removal,[],[f525]) ).
thf(f527,plain,
( ~ spl7_2
| ~ spl7_6
| ~ spl7_9 ),
inference(avatar_contradiction_clause,[],[f526]) ).
thf(f537,plain,
( ( $true = $false )
| ~ spl7_2
| ~ spl7_15
| ~ spl7_18 ),
inference(forward_demodulation,[],[f521,f460]) ).
thf(f538,plain,
( $false
| ~ spl7_2
| ~ spl7_15
| ~ spl7_18 ),
inference(trivial_inequality_removal,[],[f537]) ).
thf(f539,plain,
( ~ spl7_2
| ~ spl7_15
| ~ spl7_18 ),
inference(avatar_contradiction_clause,[],[f538]) ).
thf(f545,plain,
( ( $true = $false )
| ( $true
= ( p @ sK5 ) )
| ~ spl7_2
| ~ spl7_16 ),
inference(constrained_superposition,[],[f450,f373]) ).
thf(f548,plain,
( ( $true
= ( p @ sK5 ) )
| ~ spl7_2
| ~ spl7_16 ),
inference(trivial_inequality_removal,[],[f545]) ).
thf(f552,plain,
( ( $true = $false )
| ~ spl7_2
| ~ spl7_16
| ~ spl7_19 ),
inference(forward_demodulation,[],[f548,f465]) ).
thf(f553,plain,
( $false
| ~ spl7_2
| ~ spl7_16
| ~ spl7_19 ),
inference(trivial_inequality_removal,[],[f552]) ).
thf(f554,plain,
( ~ spl7_2
| ~ spl7_16
| ~ spl7_19 ),
inference(avatar_contradiction_clause,[],[f553]) ).
thf(f563,plain,
( ( $true = $false )
| ( $false
= ( q @ sK1 ) )
| ( $true
= ( p @ sK1 ) )
| ~ spl7_1
| ~ spl7_4 ),
inference(constrained_superposition,[],[f382,f370]) ).
thf(f570,plain,
( ( $false
= ( q @ sK1 ) )
| ( $true
= ( p @ sK1 ) )
| ~ spl7_1
| ~ spl7_4 ),
inference(trivial_inequality_removal,[],[f563]) ).
thf(f576,plain,
( ( $true = $false )
| ( $false
= ( q @ sK1 ) )
| ~ spl7_1
| ~ spl7_4
| ~ spl7_5 ),
inference(forward_demodulation,[],[f570,f387]) ).
thf(f577,plain,
( ( $false
= ( q @ sK1 ) )
| ~ spl7_1
| ~ spl7_4
| ~ spl7_5 ),
inference(trivial_inequality_removal,[],[f576]) ).
thf(f584,plain,
( ( $true = $false )
| ( $true
= ( q @ sK1 ) )
| ( $true
= ( p @ sK1 ) )
| ~ spl7_3
| ~ spl7_4 ),
inference(constrained_superposition,[],[f377,f382]) ).
thf(f597,plain,
( ( $true
= ( q @ sK1 ) )
| ( $true
= ( p @ sK1 ) )
| ~ spl7_3
| ~ spl7_4 ),
inference(trivial_inequality_removal,[],[f584]) ).
thf(f604,plain,
( ( $true = $false )
| ( $true
= ( p @ sK1 ) )
| ~ spl7_1
| ~ spl7_3
| ~ spl7_4
| ~ spl7_5 ),
inference(forward_demodulation,[],[f597,f577]) ).
thf(f605,plain,
( ( $true
= ( p @ sK1 ) )
| ~ spl7_1
| ~ spl7_3
| ~ spl7_4
| ~ spl7_5 ),
inference(trivial_inequality_removal,[],[f604]) ).
thf(f609,plain,
( ( $true = $false )
| ~ spl7_1
| ~ spl7_3
| ~ spl7_4
| ~ spl7_5 ),
inference(forward_demodulation,[],[f605,f387]) ).
thf(f610,plain,
( $false
| ~ spl7_1
| ~ spl7_3
| ~ spl7_4
| ~ spl7_5 ),
inference(trivial_inequality_removal,[],[f609]) ).
thf(f611,plain,
( ~ spl7_1
| ~ spl7_3
| ~ spl7_4
| ~ spl7_5 ),
inference(avatar_contradiction_clause,[],[f610]) ).
cnf(s1,plain,
( spl7_1
| spl7_2 ),
inference(sat_conversion,[],[f374]) ).
cnf(s2,plain,
( spl7_2
| spl7_3 ),
inference(sat_conversion,[],[f378]) ).
cnf(s3,plain,
( spl7_2
| spl7_4 ),
inference(sat_conversion,[],[f383]) ).
cnf(s4,plain,
( spl7_2
| spl7_5 ),
inference(sat_conversion,[],[f388]) ).
cnf(s5,plain,
( spl7_1
| spl7_6
| spl7_7 ),
inference(sat_conversion,[],[f397]) ).
cnf(s7,plain,
( spl7_1
| spl7_7
| spl7_9 ),
inference(sat_conversion,[],[f407]) ).
cnf(s11,plain,
( spl7_1
| spl7_6
| spl7_11 ),
inference(sat_conversion,[],[f419]) ).
cnf(s13,plain,
( spl7_1
| spl7_9
| spl7_11 ),
inference(sat_conversion,[],[f421]) ).
cnf(s23,plain,
( spl7_7
| spl7_15
| spl7_16 ),
inference(sat_conversion,[],[f451]) ).
cnf(s25,plain,
( spl7_7
| spl7_16
| spl7_18 ),
inference(sat_conversion,[],[f461]) ).
cnf(s26,plain,
( spl7_7
| spl7_15
| spl7_19 ),
inference(sat_conversion,[],[f466]) ).
cnf(s28,plain,
( spl7_7
| spl7_18
| spl7_19 ),
inference(sat_conversion,[],[f468]) ).
cnf(s35,plain,
( spl7_11
| spl7_15
| spl7_16 ),
inference(sat_conversion,[],[f475]) ).
cnf(s37,plain,
( spl7_11
| spl7_16
| spl7_18 ),
inference(sat_conversion,[],[f477]) ).
cnf(s38,plain,
( spl7_11
| spl7_15
| spl7_19 ),
inference(sat_conversion,[],[f478]) ).
cnf(s40,plain,
( spl7_11
| spl7_18
| spl7_19 ),
inference(sat_conversion,[],[f480]) ).
cnf(s42,plain,
( ~ spl7_2
| ~ spl7_7
| ~ spl7_11 ),
inference(sat_conversion,[],[f503]) ).
cnf(s43,plain,
( ~ spl7_2
| ~ spl7_6
| ~ spl7_9 ),
inference(sat_conversion,[],[f527]) ).
cnf(s45,plain,
( ~ spl7_2
| ~ spl7_15
| ~ spl7_18 ),
inference(sat_conversion,[],[f539]) ).
cnf(s47,plain,
( ~ spl7_2
| ~ spl7_16
| ~ spl7_19 ),
inference(sat_conversion,[],[f554]) ).
cnf(s49,plain,
( ~ spl7_1
| ~ spl7_3
| ~ spl7_4
| ~ spl7_5 ),
inference(sat_conversion,[],[f611]) ).
cnf(s50,plain,
( spl7_6
| spl7_1 ),
inference(rat,[],[s42,s5,s11,s1]) ).
cnf(s51,plain,
spl7_1,
inference(rat,[],[s42,s7,s13,s43,s50,s1]) ).
cnf(s53,plain,
( spl7_15
| spl7_11
| ~ spl7_2 ),
inference(rat,[],[s47,s38,s35]) ).
cnf(s54,plain,
( spl7_11
| ~ spl7_2 ),
inference(rat,[],[s47,s37,s40,s45,s53]) ).
cnf(s55,plain,
( spl7_15
| ~ spl7_2 ),
inference(rat,[],[s47,s26,s23,s42,s54]) ).
cnf(s56,plain,
( ~ spl7_11
| ~ spl7_2 ),
inference(rat,[],[s47,s25,s28,s45,s55,s42]) ).
cnf(s57,plain,
~ spl7_2,
inference(rat,[],[s56,s54]) ).
cnf(s58,plain,
spl7_5,
inference(rat,[],[s4,s57]) ).
cnf(s59,plain,
spl7_4,
inference(rat,[],[s3,s57]) ).
cnf(s60,plain,
spl7_3,
inference(rat,[],[s2,s57]) ).
cnf(s61,plain,
$false,
inference(rat,[],[s49,s60,s51,s58,s59]) ).
thf(f612,plain,
$false,
inference(avatar_sat_refutation,[],[s61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO404^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n007.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 16:48:56 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.27 % (3632778)Will run a generic schedule for satisfiability detection.
% 0.19/0.27 % (3632786)dis+10_1_sil=32000:sp=arity:random_seed=1222453202:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.27 % (3632784)% WARNING: option uhcvi not known.
% 0.19/0.27 % (3632784)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=720030799:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.27 % (3632787)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1194729996:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.27 % (3632786) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3632778-3632786"...
% 0.19/0.27 % (3632785)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2456854483:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.27 % (3632783)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2045301137_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.27 % (3632787)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.27 % (3632784)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.27 % (3632784)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.27 % (3632789)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2315768717:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.27 % Exception at run slice level
% 0.19/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.27 % (3632786)...printing done.
% 0.19/0.27 % (3632786)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.28 % (3632786)------------------------------
% 0.19/0.28 % (3632786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (3632786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (3632786)CaDiCaL version: 2.1.3
% 0.19/0.28 % (3632786)Termination reason: Refutation
% 0.19/0.28 % (3632786)Time elapsed: 0.012 s
% 0.19/0.28 % (3632786)Peak memory usage: 13 MB
% 0.19/0.28 % (3632786)Instructions burned: 41 (million)
% 0.19/0.28 % (3632778)Success in time 0.042 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------