%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO462^3 : 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 : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:47:54 AM UTC 2026
% Result : Theorem 0.18s 0.28s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 14
% Syntax : Number of formulae : 152 ( 48 unt; 0 typ; 6 def)
% Number of atoms : 1173 ( 198 equ; 0 cnn)
% Maximal formula atoms : 11 ( 7 avg)
% Number of connectives : 1530 ( 305 ~; 324 |; 0 &; 831 @)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 116 ( 116 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 59 usr; 12 con; 0-4 aty)
% ( 64 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 288 ( 0 sgn 44 !; 0 ?; 288 :)
% 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_m: $i > $i > $o ).
thf(func_def_33,type,
mbox_m: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_m: ( $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,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_40,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_45,type,
vNOT: $o > $o ).
thf(func_def_46,type,
vOR: $o > $o > $o ).
thf(func_def_47,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_49,type,
vIMP: $o > $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/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_m @ X1 @ X2 ) ) )
= mbox_m ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^3.ax',mbox_m) ).
thf(f35,conjecture,
mvalid @ ( mimplies @ ( mbox_m @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_m @ p ) @ ( mbox_m @ q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f36,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_m @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_m @ p ) @ ( mbox_m @ q ) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
thf(f38,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f51,plain,
~ ( mvalid @ ( mimplies @ ( mbox_m @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_m @ p ) @ ( mbox_m @ q ) ) ) ),
inference(rectify,[],[f36]) ).
thf(f52,plain,
( ( mvalid @ ( mimplies @ ( mbox_m @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_m @ p ) @ ( mbox_m @ q ) ) ) )
!= $true ),
inference(fool_elimination,[],[f51]) ).
thf(f58,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f69,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f70,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f71,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f72,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f79,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f83,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f84,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f88,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_m @ X1 @ X2 ) ) )
= mbox_m ),
inference(rectify,[],[f32]) ).
thf(f89,plain,
( mbox_m
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_m @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f88]) ).
thf(f95,plain,
( ( mvalid @ ( mimplies @ ( mbox_m @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_m @ p ) @ ( mbox_m @ q ) ) ) )
!= $true ),
inference(flattening,[],[f52]) ).
thf(f98,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f106,plain,
( mbox_m
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_m @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f89]) ).
thf(f109,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f110,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f117,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f79]) ).
thf(f124,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f125,plain,
( ( mvalid @ ( mimplies @ ( mbox_m @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_m @ p ) @ ( mbox_m @ q ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f95]) ).
thf(f129,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f133,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,[],[f117,f129,f124,f129,f129]) ).
thf(f134,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,[],[f110,f124,f129]) ).
thf(f136,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,[],[f109,f133,f134,f134]) ).
thf(f144,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_m @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ p
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_m @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_m @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f125,f98,f134,f106,f136,f136,f106,f106]) ).
thf(f148,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_m @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_m @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_m @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_m @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_m @ Y0 @ Y1 )
| ~ ( ~ ( ( p @ Y1 )
| ~ ( q @ Y1 ) )
| ~ ( ( q @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f149,plain,
( ( ^ [Y0: $i] :
( ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_m @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_m @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_m @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_m @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_m @ Y0 @ Y1 )
| ~ ( ~ ( ( p @ Y1 )
| ~ ( q @ Y1 ) )
| ~ ( ( q @ Y1 )
| ~ ( p @ Y1 ) ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f148]) ).
thf(f150,plain,
( ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ~ ( ~ ( ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( ( q @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ~ ( ~ ( ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( ( q @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f150]) ).
thf(f153,plain,
( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $true )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f153]) ).
thf(f155,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
= $false )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f155]) ).
thf(f158,plain,
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK1 )
= $false ) ),
inference(not_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f159]) ).
thf(f162,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK2 )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( ( ( ~ ( rel_m @ sK0 @ sK1 )
| ( q @ sK1 ) )
= $false )
| ( ( ~ ( rel_m @ sK0 @ sK2 )
| ( p @ sK2 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
( ( ( ~ ( rel_m @ sK0 @ sK2 )
| ( p @ sK2 ) )
= $false )
| ( ( q @ sK1 )
= $false ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( ( ( ~ ( rel_m @ sK0 @ sK1 ) )
= $false )
| ( ( ~ ( rel_m @ sK0 @ sK2 )
| ( p @ sK2 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f166,plain,
( ( ( ~ ( rel_m @ sK0 @ sK2 )
| ( p @ sK2 ) )
= $false )
| ( ( rel_m @ sK0 @ sK1 )
= $true ) ),
inference(not_proxy_clausification,[],[f165]) ).
thf(f167,plain,
( ( ( p @ sK2 )
= $false )
| ( ( rel_m @ sK0 @ sK1 )
= $true ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( ( ~ ( rel_m @ sK0 @ sK2 ) )
= $false )
| ( ( rel_m @ sK0 @ sK1 )
= $true ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f169,plain,
( ( $true
= ( rel_m @ sK0 @ sK2 ) )
| ( ( rel_m @ sK0 @ sK1 )
= $true ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( ( p @ sK2 )
= $false )
| ( ( q @ sK1 )
= $false ) ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f171,plain,
( ( ( ~ ( rel_m @ sK0 @ sK2 ) )
= $false )
| ( ( q @ sK1 )
= $false ) ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f172,plain,
( ( ( q @ sK1 )
= $false )
| ( $true
= ( rel_m @ sK0 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK1 )
= $false ) ),
inference(not_proxy_clausification,[],[f160]) ).
thf(f174,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X1: $i] :
( ( ( ~ ( rel_m @ sK0 @ X1 )
| ( q @ X1 ) )
= $true )
| ( ( ~ ( rel_m @ sK0 @ sK1 )
| ( q @ sK1 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
! [X1: $i] :
( ( ( q @ X1 )
= $true )
| ( ( ~ ( rel_m @ sK0 @ X1 ) )
= $true )
| ( ( ~ ( rel_m @ sK0 @ sK1 )
| ( q @ sK1 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( ( ( ~ ( rel_m @ sK0 @ sK1 )
| ( q @ sK1 ) )
= $false )
| ( ( q @ X1 )
= $true )
| ( ( rel_m @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X1: $i] :
( ( ( q @ sK1 )
= $false )
| ( ( q @ X1 )
= $true )
| ( ( rel_m @ sK0 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X1: $i] :
( ( ( rel_m @ sK0 @ X1 )
= $false )
| ( ( q @ X1 )
= $true )
| ( ( ~ ( rel_m @ sK0 @ sK1 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f180,plain,
! [X1: $i] :
( ( ( rel_m @ sK0 @ sK1 )
= $true )
| ( ( q @ X1 )
= $true )
| ( ( rel_m @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
= $true )
| ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f156]) ).
thf(f182,plain,
! [X1: $i] :
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f195,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f196,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X2 )
= $true )
| ( ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_m @ sK0 @ X1 )
| ( p @ X1 ) ) )
| ( ( ~ ( rel_m @ sK0 @ X2 )
| ( q @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f196]) ).
thf(f198,plain,
! [X2: $i,X1: $i] :
( ( ( p @ X1 )
= $true )
| ( ( ~ ( rel_m @ sK0 @ X1 ) )
= $true )
| ( ( ~ ( rel_m @ sK0 @ X2 )
| ( q @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X2: $i,X1: $i] :
( ( ( rel_m @ sK0 @ X1 )
= $false )
| ( ( ~ ( rel_m @ sK0 @ X2 )
| ( q @ X2 ) )
= $true )
| ( ( p @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X2: $i,X1: $i] :
( ( ( rel_m @ sK0 @ X1 )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( q @ X2 )
= $true )
| ( ( ~ ( rel_m @ sK0 @ X2 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X2: $i,X1: $i] :
( ( ( q @ X2 )
= $true )
| ( ( p @ X1 )
= $true )
| ( ( rel_m @ sK0 @ X2 )
= $false )
| ( ( rel_m @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f200]) ).
thf(f202,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ~ ( ~ ( ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( ( q @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f151]) ).
thf(f203,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ~ ( ~ ( ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( ( q @ Y0 )
| ~ ( p @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X1: $i] :
( ( ~ ( rel_m @ sK0 @ X1 )
| ~ ( ~ ( ( p @ X1 )
| ~ ( q @ X1 ) )
| ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f203]) ).
thf(f205,plain,
! [X1: $i] :
( ( ( ~ ( rel_m @ sK0 @ X1 ) )
= $true )
| ( ( ~ ( ~ ( ( p @ X1 )
| ~ ( q @ X1 ) )
| ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X1: $i] :
( ( ( rel_m @ sK0 @ X1 )
= $false )
| ( ( ~ ( ~ ( ( p @ X1 )
| ~ ( q @ X1 ) )
| ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X1: $i] :
( ( ( rel_m @ sK0 @ X1 )
= $false )
| ( ( ~ ( ( p @ X1 )
| ~ ( q @ X1 ) )
| ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X1: $i] :
( ( ( rel_m @ sK0 @ X1 )
= $false )
| ( ( ~ ( ( q @ X1 )
| ~ ( p @ X1 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X1: $i] :
( ( ( ~ ( ( p @ X1 )
| ~ ( q @ X1 ) ) )
= $false )
| ( ( rel_m @ sK0 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f207]) ).
thf(f210,plain,
! [X1: $i] :
( ( ( rel_m @ sK0 @ X1 )
= $false )
| ( ( ( p @ X1 )
| ~ ( q @ X1 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f209]) ).
thf(f211,plain,
! [X1: $i] :
( ( ( rel_m @ sK0 @ X1 )
= $false )
| ( ( p @ X1 )
= $true )
| ( ( ~ ( q @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f210]) ).
thf(f212,plain,
! [X1: $i] :
( ( ( rel_m @ sK0 @ X1 )
= $false )
| ( ( q @ X1 )
= $false )
| ( ( p @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f211]) ).
thf(f213,plain,
! [X1: $i] :
( ( ( rel_m @ sK0 @ X1 )
= $false )
| ( ( ( q @ X1 )
| ~ ( p @ X1 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f208]) ).
thf(f214,plain,
! [X1: $i] :
( ( ( ~ ( p @ X1 ) )
= $true )
| ( ( q @ X1 )
= $true )
| ( ( rel_m @ sK0 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f213]) ).
thf(f215,plain,
! [X1: $i] :
( ( ( rel_m @ sK0 @ X1 )
= $false )
| ( ( p @ X1 )
= $false )
| ( ( q @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f214]) ).
thf(f217,definition,
( spl4_1
<=> ( ( rel_m @ sK0 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f219,plain,
( ( ( rel_m @ sK0 @ sK1 )
= $true )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f217]) ).
thf(f221,definition,
( spl4_2
<=> ( $true
= ( rel_m @ sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f223,plain,
( ( $true
= ( rel_m @ sK0 @ sK2 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f221]) ).
thf(f224,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f169,f221,f217]) ).
thf(f226,definition,
( spl4_3
<=> ( ( p @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f228,plain,
( ( ( p @ sK2 )
= $false )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f226]) ).
thf(f229,plain,
( spl4_1
| spl4_3 ),
inference(avatar_split_clause,[],[f167,f226,f217]) ).
thf(f231,definition,
( spl4_4
<=> ( ( q @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f233,plain,
( ( ( q @ sK1 )
= $false )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f231]) ).
thf(f234,plain,
( spl4_2
| spl4_4 ),
inference(avatar_split_clause,[],[f172,f231,f221]) ).
thf(f235,plain,
( spl4_4
| spl4_3 ),
inference(avatar_split_clause,[],[f170,f226,f231]) ).
thf(f237,definition,
( spl4_5
<=> ! [X1: $i] :
( ( ( q @ X1 )
= $true )
| ( ( rel_m @ sK0 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f238,plain,
( ! [X1: $i] :
( ( ( rel_m @ sK0 @ X1 )
= $false )
| ( ( q @ X1 )
= $true ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f237]) ).
thf(f239,plain,
( spl4_5
| spl4_1 ),
inference(avatar_split_clause,[],[f180,f217,f237]) ).
thf(f240,plain,
( spl4_5
| spl4_4 ),
inference(avatar_split_clause,[],[f178,f231,f237]) ).
thf(f246,definition,
( spl4_7
<=> ! [X1: $i] :
( ( ( rel_m @ sK0 @ X1 )
= $false )
| ( ( p @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
thf(f247,plain,
( ! [X1: $i] :
( ( ( rel_m @ sK0 @ X1 )
= $false )
| ( ( p @ X1 )
= $true ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f246]) ).
thf(f254,plain,
( spl4_5
| spl4_7 ),
inference(avatar_split_clause,[],[f201,f246,f237]) ).
thf(f256,plain,
( ( ( q @ sK2 )
= $false )
| ( $true = $false )
| ( ( p @ sK2 )
= $true )
| ~ spl4_2 ),
inference(constrained_superposition,[],[f212,f223]) ).
thf(f257,plain,
( ( ( q @ sK2 )
= $false )
| ( ( p @ sK2 )
= $true )
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f256]) ).
thf(f259,plain,
( ( ( q @ sK2 )
= $false )
| ( $true = $false )
| ~ spl4_2
| ~ spl4_3 ),
inference(forward_demodulation,[],[f257,f228]) ).
thf(f260,plain,
( ( ( q @ sK2 )
= $false )
| ~ spl4_2
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f259]) ).
thf(f263,plain,
( ( $true = $false )
| ( $true
= ( q @ sK2 ) )
| ~ spl4_2
| ~ spl4_5 ),
inference(constrained_superposition,[],[f238,f223]) ).
thf(f266,plain,
( ( $true
= ( q @ sK2 ) )
| ~ spl4_2
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f263]) ).
thf(f270,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5 ),
inference(forward_demodulation,[],[f266,f260]) ).
thf(f271,plain,
( $false
| ~ spl4_2
| ~ spl4_3
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f270]) ).
thf(f272,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f271]) ).
thf(f275,plain,
( ( $true = $false )
| ( ( q @ sK1 )
= $true )
| ~ spl4_1
| ~ spl4_5 ),
inference(constrained_superposition,[],[f238,f219]) ).
thf(f279,plain,
( ( ( q @ sK1 )
= $true )
| ~ spl4_1
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f275]) ).
thf(f284,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_4
| ~ spl4_5 ),
inference(forward_demodulation,[],[f279,f233]) ).
thf(f285,plain,
( $false
| ~ spl4_1
| ~ spl4_4
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f284]) ).
thf(f286,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f285]) ).
thf(f289,plain,
( ( $true = $false )
| ( ( p @ sK1 )
= $true )
| ~ spl4_1
| ~ spl4_7 ),
inference(constrained_superposition,[],[f219,f247]) ).
thf(f291,plain,
( ( ( p @ sK1 )
= $true )
| ~ spl4_1
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f289]) ).
thf(f293,plain,
( ( $true = $false )
| ( ( q @ sK1 )
= $true )
| ( ( p @ sK1 )
= $false )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f215,f219]) ).
thf(f297,plain,
( ( ( p @ sK1 )
= $false )
| ( ( q @ sK1 )
= $true )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f293]) ).
thf(f300,plain,
( ( ( q @ sK1 )
= $true )
| ( $true = $false )
| ~ spl4_1
| ~ spl4_7 ),
inference(forward_demodulation,[],[f297,f291]) ).
thf(f301,plain,
( ( ( q @ sK1 )
= $true )
| ~ spl4_1
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f300]) ).
thf(f305,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_4
| ~ spl4_7 ),
inference(forward_demodulation,[],[f301,f233]) ).
thf(f306,plain,
( $false
| ~ spl4_1
| ~ spl4_4
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f305]) ).
thf(f307,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_7 ),
inference(avatar_contradiction_clause,[],[f306]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f224]) ).
cnf(s2,plain,
( spl4_1
| spl4_3 ),
inference(sat_conversion,[],[f229]) ).
cnf(s3,plain,
( spl4_2
| spl4_4 ),
inference(sat_conversion,[],[f234]) ).
cnf(s4,plain,
( spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f235]) ).
cnf(s5,plain,
( spl4_1
| spl4_5 ),
inference(sat_conversion,[],[f239]) ).
cnf(s6,plain,
( spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f240]) ).
cnf(s9,plain,
( spl4_5
| spl4_7 ),
inference(sat_conversion,[],[f254]) ).
cnf(s11,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_5 ),
inference(sat_conversion,[],[f272]) ).
cnf(s13,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_5 ),
inference(sat_conversion,[],[f286]) ).
cnf(s15,plain,
( ~ spl4_1
| ~ spl4_4
| ~ spl4_7 ),
inference(sat_conversion,[],[f307]) ).
cnf(s16,plain,
spl4_1,
inference(rat,[],[s11,s1,s2,s5]) ).
cnf(s17,plain,
spl4_5,
inference(rat,[],[s15,s6,s9,s16]) ).
cnf(s18,plain,
~ spl4_4,
inference(rat,[],[s13,s16,s17]) ).
cnf(s19,plain,
spl4_3,
inference(rat,[],[s4,s18]) ).
cnf(s20,plain,
spl4_2,
inference(rat,[],[s3,s18]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s11,s17,s20,s19]) ).
thf(f308,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO462^3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n016.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 17:03:51 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running higher-order theorem proving
% 0.07/0.22 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
% 0.18/0.28 % (623660)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.18/0.28 % (623668)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=2382143844:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.18/0.28 % (623671)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.18/0.28 % (623671)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
% 0.18/0.28 % (623665)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1115603156:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.18/0.28 % (623666)lrs+10_16_si=on:nwc=1.5:random_seed=1498801499:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.18/0.28 % (623667)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3722644256:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.18/0.28 % (623669)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1315387395:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.18/0.28 % (623670)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=469788271:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.18/0.28 % (623671)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=2345696905:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.18/0.28 % (623667)Instruction limit reached!
% 0.18/0.28 % (623667)------------------------------
% 0.18/0.28 % (623667)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.28 % (623667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.28 % (623667)CaDiCaL version: 2.1.3
% 0.18/0.28 % (623667)Termination reason: Instruction limit
% 0.18/0.28 % (623667)Termination phase: shuffling
% 0.18/0.28 % (623667)Time elapsed: 0.002 s
% 0.18/0.28 % (623667)Peak memory usage: 10 MB
% 0.18/0.28 % (623667)Instructions burned: 4 (million)
% 0.18/0.28 % (623665) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-623660-623665"...
% 0.18/0.28 % (623666) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-623660-623666"...
% 0.18/0.28 % (623670) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-623660-623670"...
% 0.18/0.28 % (623665)...printing done.
% 0.18/0.28 % (623669)Instruction limit reached!
% 0.18/0.28 % (623669)------------------------------
% 0.18/0.28 % (623669)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.28 % (623669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.28 % (623669)CaDiCaL version: 2.1.3
% 0.18/0.28 % (623669)Termination reason: Instruction limit
% 0.18/0.28 % (623669)Termination phase: Saturation
% 0.18/0.28 % (623669)Time elapsed: 0.014 s
% 0.18/0.28 % (623669)Peak memory usage: 11 MB
% 0.18/0.28 % (623671) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-623660-623671"...
% 0.18/0.28 % (623669)Instructions burned: 25 (million)
% 0.18/0.28 % (623665)Refutation found. Thanks to Tanya!
% 0.18/0.28 % SZS status Theorem for theBenchmark
% 0.18/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.28 % (623665)------------------------------
% 0.18/0.28 % (623665)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.28 % (623665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.28 % (623665)CaDiCaL version: 2.1.3
% 0.18/0.28 % (623665)Termination reason: Refutation
% 0.18/0.28 % (623665)Time elapsed: 0.013 s
% 0.18/0.28 % (623665)Peak memory usage: 13 MB
% 0.18/0.28 % (623665)Instructions burned: 24 (million)
% 0.18/0.28 % (623660)Success in time 0.052 s
% 0.18/0.28 % Vampire exiting
%------------------------------------------------------------------------------