%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL865^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:14:38 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 15
% Syntax : Number of formulae : 164 ( 35 unt; 0 typ; 10 def)
% Number of atoms : 1378 ( 268 equ; 0 cnn)
% Maximal formula atoms : 10 ( 8 avg)
% Number of connectives : 1544 ( 128 ~; 248 |; 62 &; 921 @)
% ( 14 <=>; 56 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 78 ( 78 >; 0 *; 0 +; 0 <<)
% Number of symbols : 70 ( 65 usr; 21 con; 0-4 aty)
% ( 98 !!; 16 ??; 0 @@+; 0 @@-)
% Number of variables : 266 ( 0 sgn 99 !; 5 ?; 266 :)
% 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,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_35,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_36,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_37,type,
vAND: $o > $o > $o ).
thf(func_def_38,type,
vIMP: $o > $o > $o ).
thf(func_def_39,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_42,type,
vNOT: $o > $o ).
thf(func_def_43,type,
vOR: $o > $o > $o ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
sK0: $i > $i > $o ).
thf(func_def_55,type,
sK8: $i > $i ).
thf(func_def_56,type,
sK9: $i > $i ).
thf(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(f19,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) )
= msymmetric ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f20,axiom,
( mserial
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mserial) ).
thf(f22,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X3: $i,X1: $i,X2: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X2 @ X3 ) ) )
= meuclidean ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',meuclidean) ).
thf(f32,conjecture,
! [X0: $i > $i > $o] :
( ( ( mreflexive @ X0 )
& ( meuclidean @ X0 ) )
<=> ( ( mserial @ X0 )
& ( meuclidean @ X0 )
& ( msymmetric @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( ( mreflexive @ X0 )
& ( meuclidean @ X0 ) )
<=> ( ( mserial @ X0 )
& ( meuclidean @ X0 )
& ( msymmetric @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f46,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
=> ( X0 @ X1 @ X2 ) ) )
= msymmetric ),
inference(rectify,[],[f19]) ).
thf(f47,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f48,plain,
( mserial
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) ) ),
inference(rectify,[],[f20]) ).
thf(f49,plain,
( mserial
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f56,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f57,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f56]) ).
thf(f69,plain,
~ ! [X0: $i > $i > $o] :
( ( ( mreflexive @ X0 )
& ( meuclidean @ X0 ) )
<=> ( ( mserial @ X0 )
& ( meuclidean @ X0 )
& ( msymmetric @ X0 ) ) ),
inference(rectify,[],[f33]) ).
thf(f70,plain,
~ ! [X0: $i > $i > $o] :
( ( ( ( mserial @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true ) )
<=> ( ( ( mreflexive @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f73,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X1 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X3 @ X1 ) ) )
= meuclidean ),
inference(rectify,[],[f22]) ).
thf(f74,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f73]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( ( ( mserial @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true ) )
<~> ( ( ( mreflexive @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) ) ),
inference(ennf_transformation,[],[f70]) ).
thf(f88,plain,
? [X0: $i > $i > $o] :
( ( ( ( mreflexive @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true )
| ( ( mserial @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true )
| ( ( msymmetric @ X0 )
!= $true ) )
& ( ( ( ( mreflexive @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) )
| ( ( ( mserial @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f87]) ).
thf(f89,plain,
? [X0: $i > $i > $o] :
( ( ( ( mreflexive @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true )
| ( ( mserial @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true )
| ( ( msymmetric @ X0 )
!= $true ) )
& ( ( ( ( mreflexive @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) )
| ( ( ( mserial @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true ) ) ) ),
inference(flattening,[],[f88]) ).
thf(f90,plain,
( ( ( ( mreflexive @ sK0 )
!= $true )
| ( $true
!= ( meuclidean @ sK0 ) )
| ( ( mserial @ sK0 )
!= $true )
| ( $true
!= ( meuclidean @ sK0 ) )
| ( ( msymmetric @ sK0 )
!= $true ) )
& ( ( ( ( mreflexive @ sK0 )
= $true )
& ( $true
= ( meuclidean @ sK0 ) ) )
| ( ( ( mserial @ sK0 )
= $true )
& ( $true
= ( meuclidean @ sK0 ) )
& ( ( msymmetric @ sK0 )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f89]) ).
thf(f94,plain,
( mserial
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f99,plain,
( ( $true
= ( meuclidean @ sK0 ) )
| ( $true
= ( meuclidean @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f101,plain,
( ( ( mreflexive @ sK0 )
= $true )
| ( ( msymmetric @ sK0 )
= $true ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f103,plain,
( ( ( mreflexive @ sK0 )
= $true )
| ( ( mserial @ sK0 )
= $true ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f104,plain,
( ( ( mreflexive @ sK0 )
!= $true )
| ( $true
!= ( meuclidean @ sK0 ) )
| ( ( mserial @ sK0 )
!= $true )
| ( $true
!= ( meuclidean @ sK0 ) )
| ( ( msymmetric @ sK0 )
!= $true ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f106,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f109,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f116,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f57]) ).
thf(f140,plain,
( ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
@ sK0 ) )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
@ sK0 )
!= $true )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
@ sK0 ) )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) )
@ sK0 )
!= $true ) ),
inference(definition_unfolding,[],[f104,f116,f109,f94,f109,f106]) ).
thf(f141,plain,
( ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) )
@ sK0 )
= $true ) ),
inference(definition_unfolding,[],[f103,f116,f94]) ).
thf(f143,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
@ sK0 )
= $true )
| ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f101,f116,f106]) ).
thf(f145,plain,
( ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
@ sK0 ) )
| ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f99,f109,f109]) ).
thf(f147,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
@ sK0 )
!= $true )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
@ sK0 ) )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) )
@ sK0 )
!= $true )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) ) ),
inference(duplicate_literal_removal,[],[f140]) ).
thf(f148,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) )
!= $true )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f149,plain,
( ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) ) )
| ( ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ sK1 )
= $false )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f148]) ).
thf(f150,plain,
( ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) ) ) )
| ( ( ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) )
@ sK2 )
= $false )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) )
| ( ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ sK1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f149]) ).
thf(f151,plain,
( ( ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ sK1 )
= $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) )
@ sK3 )
= $false )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) )
| ( ( ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) )
@ sK2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ sK4 ) )
| ( ( ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) )
@ sK2 )
= $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) )
@ sK3 )
= $false )
| ( ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ sK1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK0 @ Y0 @ sK4 ) ) )
= $false )
| ( $false
= ( ?? @ $i @ ( sK0 @ sK2 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ sK3 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ sK3 @ Y1 ) ) ) )
= $false )
| ( ( sK0 @ sK1 @ sK1 )
= $false ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f154,plain,
( ( ( sK0 @ sK1 @ sK1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK0 @ Y0 @ sK4 ) )
@ sK5 )
= $false )
| ( $false
= ( ?? @ $i @ ( sK0 @ sK2 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ sK3 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ sK3 @ Y1 ) ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ sK3 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ sK3 @ Y1 ) ) ) )
= $false )
| ( ( sK0 @ sK2 @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK0 @ Y0 @ sK4 ) )
@ sK5 )
= $false )
| ( ( sK0 @ sK1 @ sK1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X1: $i] :
( ( ( sK0 @ sK2 @ X1 )
= $false )
| ( ( sK0 @ sK1 @ sK1 )
= $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ sK3 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ sK3 @ Y1 ) ) )
@ sK6 )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK0 @ Y0 @ sK4 ) )
@ sK5 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X1: $i] :
( ( ( sK0 @ sK2 @ X1 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK6 @ sK3 )
& ( sK0 @ sK6 @ Y0 ) )
=> ( sK0 @ sK3 @ Y0 ) ) )
= $false )
| ( ( ( sK0 @ sK4 @ sK5 )
=> ( sK0 @ sK5 @ sK4 ) )
= $false )
| ( ( sK0 @ sK1 @ sK1 )
= $false ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
! [X1: $i] :
( ( ( ( sK0 @ sK4 @ sK5 )
=> ( sK0 @ sK5 @ sK4 ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( ( sK0 @ sK6 @ sK3 )
& ( sK0 @ sK6 @ Y0 ) )
=> ( sK0 @ sK3 @ Y0 ) )
@ sK7 )
= $false )
| ( ( sK0 @ sK1 @ sK1 )
= $false )
| ( ( sK0 @ sK2 @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( ( sK0 @ sK6 @ sK3 )
& ( sK0 @ sK6 @ Y0 ) )
=> ( sK0 @ sK3 @ Y0 ) )
@ sK7 )
= $false )
| ( ( sK0 @ sK5 @ sK4 )
= $false )
| ( ( sK0 @ sK1 @ sK1 )
= $false )
| ( ( sK0 @ sK2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X1: $i] :
( ( ( sK0 @ sK1 @ sK1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( ( sK0 @ sK6 @ sK3 )
& ( sK0 @ sK6 @ Y0 ) )
=> ( sK0 @ sK3 @ Y0 ) )
@ sK7 )
= $false )
| ( ( sK0 @ sK2 @ X1 )
= $false )
| ( ( sK0 @ sK4 @ sK5 )
= $true ) ),
inference(imp_proxy_clausification,[],[f158]) ).
thf(f161,plain,
! [X1: $i] :
( ( ( sK0 @ sK1 @ sK1 )
= $false )
| ( ( ( ( sK0 @ sK6 @ sK3 )
& ( sK0 @ sK6 @ sK7 ) )
=> ( sK0 @ sK3 @ sK7 ) )
= $false )
| ( ( sK0 @ sK2 @ X1 )
= $false )
| ( ( sK0 @ sK4 @ sK5 )
= $true ) ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f162,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK7 ) )
| ( ( sK0 @ sK1 @ sK1 )
= $false )
| ( ( sK0 @ sK2 @ X1 )
= $false )
| ( ( sK0 @ sK4 @ sK5 )
= $true ) ),
inference(imp_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X1: $i] :
( ( ( sK0 @ sK4 @ sK5 )
= $true )
| ( ( sK0 @ sK2 @ X1 )
= $false )
| ( ( ( sK0 @ sK6 @ sK3 )
& ( sK0 @ sK6 @ sK7 ) )
= $true )
| ( ( sK0 @ sK1 @ sK1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f161]) ).
thf(f164,plain,
! [X1: $i] :
( ( ( sK0 @ sK2 @ X1 )
= $false )
| ( ( sK0 @ sK1 @ sK1 )
= $false )
| ( ( sK0 @ sK4 @ sK5 )
= $true )
| ( ( sK0 @ sK6 @ sK7 )
= $true ) ),
inference(and_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X1: $i] :
( ( ( sK0 @ sK1 @ sK1 )
= $false )
| ( $true
= ( sK0 @ sK6 @ sK3 ) )
| ( ( sK0 @ sK2 @ X1 )
= $false )
| ( ( sK0 @ sK4 @ sK5 )
= $true ) ),
inference(and_proxy_clausification,[],[f163]) ).
thf(f166,plain,
! [X1: $i] :
( ( ( sK0 @ sK2 @ X1 )
= $false )
| ( ( sK0 @ sK5 @ sK4 )
= $false )
| ( ( sK0 @ sK1 @ sK1 )
= $false )
| ( ( ( ( sK0 @ sK6 @ sK3 )
& ( sK0 @ sK6 @ sK7 ) )
=> ( sK0 @ sK3 @ sK7 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f167,plain,
! [X1: $i] :
( ( ( sK0 @ sK2 @ X1 )
= $false )
| ( ( sK0 @ sK5 @ sK4 )
= $false )
| ( ( sK0 @ sK1 @ sK1 )
= $false )
| ( $false
= ( sK0 @ sK3 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( ( ( ( sK0 @ sK6 @ sK3 )
& ( sK0 @ sK6 @ sK7 ) )
= $true )
| ( ( sK0 @ sK1 @ sK1 )
= $false )
| ( ( sK0 @ sK5 @ sK4 )
= $false )
| ( ( sK0 @ sK2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f166]) ).
thf(f169,plain,
! [X1: $i] :
( ( ( sK0 @ sK1 @ sK1 )
= $false )
| ( ( sK0 @ sK2 @ X1 )
= $false )
| ( ( sK0 @ sK6 @ sK7 )
= $true )
| ( ( sK0 @ sK5 @ sK4 )
= $false ) ),
inference(and_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X1: $i] :
( ( ( sK0 @ sK5 @ sK4 )
= $false )
| ( ( sK0 @ sK2 @ X1 )
= $false )
| ( $true
= ( sK0 @ sK6 @ sK3 ) )
| ( ( sK0 @ sK1 @ sK1 )
= $false ) ),
inference(and_proxy_clausification,[],[f168]) ).
thf(f171,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
@ sK0 ) ),
inference(duplicate_literal_removal,[],[f145]) ).
thf(f172,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f173,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ X1 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ X1 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f175,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ X1 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ X1 @ Y1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ X2 @ X1 )
& ( sK0 @ X2 @ Y0 ) )
=> ( sK0 @ X1 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f177,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( sK0 @ X2 @ X1 )
& ( sK0 @ X2 @ Y0 ) )
=> ( sK0 @ X1 @ Y0 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( sK0 @ X2 @ X1 )
& ( sK0 @ X2 @ X3 ) )
=> ( sK0 @ X1 @ X3 ) )
= $true ),
inference(beta-eta_normalization,[],[f177]) ).
thf(f179,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( sK0 @ X2 @ X1 )
& ( sK0 @ X2 @ X3 ) )
= $false )
| ( ( sK0 @ X1 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( sK0 @ X2 @ X1 )
= $false )
| ( ( sK0 @ X1 @ X3 )
= $true )
| ( ( sK0 @ X2 @ X3 )
= $false ) ),
inference(and_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f182,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) )
= $true )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
=> ( sK0 @ Y0 @ X1 ) ) )
= $true )
| ( ( sK0 @ X2 @ X2 )
= $true ) ),
inference(beta-eta_normalization,[],[f183]) ).
thf(f185,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( sK0 @ X2 @ X2 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
=> ( sK0 @ Y0 @ X1 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( sK0 @ X2 @ X2 )
= $true )
| ( ( ( sK0 @ X1 @ X3 )
=> ( sK0 @ X3 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f187,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK0 @ X3 @ X1 ) )
| ( ( sK0 @ X2 @ X2 )
= $true )
| ( ( sK0 @ X1 @ X3 )
= $false ) ),
inference(imp_proxy_clausification,[],[f186]) ).
thf(f221,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f222,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ X1 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f221]) ).
thf(f223,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f222]) ).
thf(f224,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ X1 @ X1 )
= $true )
| ( ( ?? @ $i @ ( sK0 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f223]) ).
thf(f225,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK0 @ X2 @ ( sK9 @ X2 ) ) )
| ( ( sK0 @ X1 @ X1 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f224]) ).
thf(f227,definition,
( spl10_1
<=> ( ( sK0 @ sK4 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
thf(f229,plain,
( ( ( sK0 @ sK4 @ sK5 )
= $true )
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f227]) ).
thf(f231,definition,
( spl10_2
<=> ( ( sK0 @ sK1 @ sK1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
thf(f233,plain,
( ( ( sK0 @ sK1 @ sK1 )
= $false )
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f231]) ).
thf(f235,definition,
( spl10_3
<=> ! [X1: $i] :
( ( sK0 @ sK2 @ X1 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
thf(f236,plain,
( ! [X1: $i] :
( ( sK0 @ sK2 @ X1 )
= $false )
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f235]) ).
thf(f238,definition,
( spl10_4
<=> ( $true
= ( sK0 @ sK6 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
thf(f240,plain,
( ( $true
= ( sK0 @ sK6 @ sK3 ) )
| ~ spl10_4 ),
inference(avatar_component_clause,[],[f238]) ).
thf(f241,plain,
( spl10_1
| spl10_2
| spl10_3
| spl10_4 ),
inference(avatar_split_clause,[],[f165,f238,f235,f231,f227]) ).
thf(f243,definition,
( spl10_5
<=> ( ( sK0 @ sK6 @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition]) ).
thf(f245,plain,
( ( ( sK0 @ sK6 @ sK7 )
= $true )
| ~ spl10_5 ),
inference(avatar_component_clause,[],[f243]) ).
thf(f246,plain,
( spl10_3
| spl10_1
| spl10_5
| spl10_2 ),
inference(avatar_split_clause,[],[f164,f231,f243,f227,f235]) ).
thf(f248,definition,
( spl10_6
<=> ( $false
= ( sK0 @ sK3 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition]) ).
thf(f250,plain,
( ( $false
= ( sK0 @ sK3 @ sK7 ) )
| ~ spl10_6 ),
inference(avatar_component_clause,[],[f248]) ).
thf(f251,plain,
( spl10_1
| spl10_6
| spl10_2
| spl10_3 ),
inference(avatar_split_clause,[],[f162,f235,f231,f248,f227]) ).
thf(f253,definition,
( spl10_7
<=> ( ( sK0 @ sK5 @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl10_7])],[avatar_definition]) ).
thf(f255,plain,
( ( ( sK0 @ sK5 @ sK4 )
= $false )
| ~ spl10_7 ),
inference(avatar_component_clause,[],[f253]) ).
thf(f256,plain,
( spl10_3
| spl10_7
| spl10_4
| spl10_2 ),
inference(avatar_split_clause,[],[f170,f231,f238,f253,f235]) ).
thf(f257,plain,
( spl10_7
| spl10_3
| spl10_2
| spl10_5 ),
inference(avatar_split_clause,[],[f169,f243,f231,f235,f253]) ).
thf(f258,plain,
( spl10_7
| spl10_3
| spl10_2
| spl10_6 ),
inference(avatar_split_clause,[],[f167,f248,f231,f235,f253]) ).
thf(f260,definition,
( spl10_8
<=> ! [X2: $i] :
( ( sK0 @ X2 @ X2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl10_8])],[avatar_definition]) ).
thf(f261,plain,
( ! [X2: $i] :
( ( sK0 @ X2 @ X2 )
= $true )
| ~ spl10_8 ),
inference(avatar_component_clause,[],[f260]) ).
thf(f263,definition,
( spl10_9
<=> ! [X1: $i,X3: $i] :
( ( $true
= ( sK0 @ X3 @ X1 ) )
| ( ( sK0 @ X1 @ X3 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl10_9])],[avatar_definition]) ).
thf(f264,plain,
( ! [X3: $i,X1: $i] :
( ( ( sK0 @ X1 @ X3 )
= $false )
| ( $true
= ( sK0 @ X3 @ X1 ) ) )
| ~ spl10_9 ),
inference(avatar_component_clause,[],[f263]) ).
thf(f265,plain,
( spl10_8
| spl10_9 ),
inference(avatar_split_clause,[],[f187,f263,f260]) ).
thf(f267,definition,
( spl10_10
<=> ! [X2: $i] :
( $true
= ( sK0 @ X2 @ ( sK9 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_10])],[avatar_definition]) ).
thf(f268,plain,
( ! [X2: $i] :
( $true
= ( sK0 @ X2 @ ( sK9 @ X2 ) ) )
| ~ spl10_10 ),
inference(avatar_component_clause,[],[f267]) ).
thf(f269,plain,
( spl10_10
| spl10_8 ),
inference(avatar_split_clause,[],[f225,f260,f267]) ).
thf(f270,plain,
( ( $true = $false )
| ~ spl10_2
| ~ spl10_8 ),
inference(forward_demodulation,[],[f233,f261]) ).
thf(f271,plain,
( $false
| ~ spl10_2
| ~ spl10_8 ),
inference(trivial_inequality_removal,[],[f270]) ).
thf(f272,plain,
( ~ spl10_2
| ~ spl10_8 ),
inference(avatar_contradiction_clause,[],[f271]) ).
thf(f297,plain,
! [X0: $i,X1: $i] :
( ( ( sK0 @ X1 @ X1 )
= $true )
| ( ( sK0 @ X0 @ X1 )
= $false )
| ( $false != $false ) ),
inference(equality_factoring,[],[f180]) ).
thf(f314,plain,
! [X0: $i,X1: $i] :
( ( ( sK0 @ X0 @ X1 )
= $false )
| ( ( sK0 @ X1 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[],[f297]) ).
thf(f347,plain,
( ( $true = $false )
| ~ spl10_3
| ~ spl10_10 ),
inference(constrained_superposition,[],[f236,f268]) ).
thf(f359,plain,
( $false
| ~ spl10_3
| ~ spl10_10 ),
inference(trivial_inequality_removal,[],[f347]) ).
thf(f360,plain,
( ~ spl10_3
| ~ spl10_10 ),
inference(avatar_contradiction_clause,[],[f359]) ).
thf(f366,plain,
( ( ( sK0 @ sK4 @ sK5 )
= $false )
| ( $true = $false )
| ~ spl10_7
| ~ spl10_9 ),
inference(constrained_superposition,[],[f255,f264]) ).
thf(f372,plain,
( ( ( sK0 @ sK4 @ sK5 )
= $false )
| ~ spl10_7
| ~ spl10_9 ),
inference(trivial_inequality_removal,[],[f366]) ).
thf(f376,plain,
( ( $true = $false )
| ~ spl10_1
| ~ spl10_7
| ~ spl10_9 ),
inference(forward_demodulation,[],[f372,f229]) ).
thf(f377,plain,
( $false
| ~ spl10_1
| ~ spl10_7
| ~ spl10_9 ),
inference(trivial_inequality_removal,[],[f376]) ).
thf(f378,plain,
( ~ spl10_1
| ~ spl10_7
| ~ spl10_9 ),
inference(avatar_contradiction_clause,[],[f377]) ).
thf(f381,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 @ sK3 )
= $false )
| ( ( sK0 @ X0 @ sK7 )
= $false )
| ( $true = $false ) )
| ~ spl10_6 ),
inference(constrained_superposition,[],[f180,f250]) ).
thf(f382,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 @ sK7 )
= $false )
| ( ( sK0 @ X0 @ sK3 )
= $false ) )
| ~ spl10_6 ),
inference(trivial_inequality_removal,[],[f381]) ).
thf(f409,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK0 @ X1 @ X1 )
= $true )
| ( ( sK0 @ X1 @ X0 )
= $false )
| ( $true = $false ) )
| ~ spl10_9 ),
inference(constrained_superposition,[],[f314,f264]) ).
thf(f421,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK0 @ X1 @ X0 )
= $false )
| ( ( sK0 @ X1 @ X1 )
= $true ) )
| ~ spl10_9 ),
inference(trivial_inequality_removal,[],[f409]) ).
thf(f434,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( sK0 @ X0 @ X0 )
= $true ) )
| ~ spl10_9
| ~ spl10_10 ),
inference(constrained_superposition,[],[f421,f268]) ).
thf(f459,plain,
( ! [X0: $i] :
( ( sK0 @ X0 @ X0 )
= $true )
| ~ spl10_9
| ~ spl10_10 ),
inference(trivial_inequality_removal,[],[f434]) ).
thf(f462,plain,
( spl10_8
| ~ spl10_9
| ~ spl10_10 ),
inference(avatar_split_clause,[],[f459,f267,f263,f260]) ).
thf(f466,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK0 @ X0 @ X1 )
= $false )
| ( ( sK0 @ X1 @ X0 )
= $true )
| ( $true = $false ) )
| ~ spl10_8 ),
inference(constrained_superposition,[],[f180,f261]) ).
thf(f468,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK0 @ X0 @ X1 )
= $false )
| ( ( sK0 @ X1 @ X0 )
= $true ) )
| ~ spl10_8 ),
inference(trivial_inequality_removal,[],[f466]) ).
thf(f481,plain,
( ( $true = $false )
| ( ( sK0 @ sK6 @ sK3 )
= $false )
| ~ spl10_5
| ~ spl10_6 ),
inference(constrained_superposition,[],[f382,f245]) ).
thf(f499,plain,
( ( ( sK0 @ sK6 @ sK3 )
= $false )
| ~ spl10_5
| ~ spl10_6 ),
inference(trivial_inequality_removal,[],[f481]) ).
thf(f503,plain,
( ( $true = $false )
| ~ spl10_4
| ~ spl10_5
| ~ spl10_6 ),
inference(forward_demodulation,[],[f499,f240]) ).
thf(f504,plain,
( $false
| ~ spl10_4
| ~ spl10_5
| ~ spl10_6 ),
inference(trivial_inequality_removal,[],[f503]) ).
thf(f505,plain,
( ~ spl10_4
| ~ spl10_5
| ~ spl10_6 ),
inference(avatar_contradiction_clause,[],[f504]) ).
thf(f506,plain,
( spl10_9
| ~ spl10_8 ),
inference(avatar_split_clause,[],[f468,f260,f263]) ).
thf(f517,plain,
( ( $true = $false )
| ~ spl10_3
| ~ spl10_8 ),
inference(constrained_superposition,[],[f236,f261]) ).
thf(f527,plain,
( $false
| ~ spl10_3
| ~ spl10_8 ),
inference(trivial_inequality_removal,[],[f517]) ).
thf(f528,plain,
( ~ spl10_3
| ~ spl10_8 ),
inference(avatar_contradiction_clause,[],[f527]) ).
cnf(s1,plain,
( spl10_1
| spl10_2
| spl10_3
| spl10_4 ),
inference(sat_conversion,[],[f241]) ).
cnf(s2,plain,
( spl10_1
| spl10_2
| spl10_3
| spl10_5 ),
inference(sat_conversion,[],[f246]) ).
cnf(s3,plain,
( spl10_1
| spl10_2
| spl10_3
| spl10_6 ),
inference(sat_conversion,[],[f251]) ).
cnf(s4,plain,
( spl10_2
| spl10_3
| spl10_4
| spl10_7 ),
inference(sat_conversion,[],[f256]) ).
cnf(s5,plain,
( spl10_2
| spl10_3
| spl10_5
| spl10_7 ),
inference(sat_conversion,[],[f257]) ).
cnf(s6,plain,
( spl10_2
| spl10_3
| spl10_6
| spl10_7 ),
inference(sat_conversion,[],[f258]) ).
cnf(s7,plain,
( spl10_8
| spl10_9 ),
inference(sat_conversion,[],[f265]) ).
cnf(s8,plain,
( spl10_8
| spl10_10 ),
inference(sat_conversion,[],[f269]) ).
cnf(s9,plain,
( ~ spl10_2
| ~ spl10_8 ),
inference(sat_conversion,[],[f272]) ).
cnf(s13,plain,
( ~ spl10_3
| ~ spl10_10 ),
inference(sat_conversion,[],[f360]) ).
cnf(s15,plain,
( ~ spl10_1
| ~ spl10_7
| ~ spl10_9 ),
inference(sat_conversion,[],[f378]) ).
cnf(s16,plain,
( spl10_8
| ~ spl10_9
| ~ spl10_10 ),
inference(sat_conversion,[],[f462]) ).
cnf(s19,plain,
( ~ spl10_4
| ~ spl10_5
| ~ spl10_6 ),
inference(sat_conversion,[],[f505]) ).
cnf(s20,plain,
( ~ spl10_8
| spl10_9 ),
inference(sat_conversion,[],[f506]) ).
cnf(s23,plain,
( ~ spl10_3
| ~ spl10_8 ),
inference(sat_conversion,[],[f528]) ).
cnf(s24,plain,
( spl10_3
| spl10_2
| spl10_1 ),
inference(rat,[],[s19,s1,s2,s3]) ).
cnf(s25,plain,
~ spl10_3,
inference(rat,[],[s8,s13,s23]) ).
cnf(s26,plain,
spl10_8,
inference(rat,[],[s16,s7,s8]) ).
cnf(s27,plain,
spl10_9,
inference(rat,[],[s20,s26]) ).
cnf(s28,plain,
~ spl10_2,
inference(rat,[],[s9,s26]) ).
cnf(s29,plain,
spl10_1,
inference(rat,[],[s24,s25,s28]) ).
cnf(s30,plain,
~ spl10_7,
inference(rat,[],[s15,s27,s29]) ).
cnf(s31,plain,
spl10_6,
inference(rat,[],[s6,s25,s28,s30]) ).
cnf(s32,plain,
spl10_5,
inference(rat,[],[s5,s25,s28,s30]) ).
cnf(s33,plain,
spl10_4,
inference(rat,[],[s4,s25,s28,s30]) ).
cnf(s34,plain,
$false,
inference(rat,[],[s19,s31,s32,s33]) ).
thf(f531,plain,
$false,
inference(avatar_sat_refutation,[],[s34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL865^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n018.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 10:19:56 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.30 % (4091657)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (4091665)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=1375356223:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.30 % (4091662)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1747293336:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (4091663)lrs+10_16_si=on:nwc=1.5:random_seed=4034515136:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.30 % (4091666)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3574469708:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.30 % (4091664)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1199298116:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.30 % (4091667)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=305753247:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.30 % (4091664)Instruction limit reached!
% 0.22/0.30 % (4091664)------------------------------
% 0.22/0.30 % (4091664)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (4091664)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (4091664)CaDiCaL version: 2.1.3
% 0.22/0.30 % (4091664)Termination reason: Instruction limit
% 0.22/0.30 % (4091664)Termination phase: Preprocessing 3
% 0.22/0.30 % (4091664)Time elapsed: 0.002 s
% 0.22/0.30 % (4091664)Peak memory usage: 10 MB
% 0.22/0.30 % (4091664)Instructions burned: 4 (million)
% 0.22/0.30 % (4091663)Instruction limit reached!
% 0.22/0.30 % (4091663)------------------------------
% 0.22/0.30 % (4091663)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (4091663)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (4091663)CaDiCaL version: 2.1.3
% 0.22/0.30 % (4091663)Termination reason: Instruction limit
% 0.22/0.30 % (4091663)Termination phase: Saturation
% 0.22/0.30 % (4091663)Time elapsed: 0.011 s
% 0.22/0.30 % (4091663)Peak memory usage: 12 MB
% 0.22/0.30 % (4091663)Instructions burned: 19 (million)
% 0.22/0.30 % (4091668)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.30 % (4091668)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.30 % (4091666)Instruction limit reached!
% 0.22/0.30 % (4091666)------------------------------
% 0.22/0.30 % (4091666)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (4091666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (4091666)CaDiCaL version: 2.1.3
% 0.22/0.30 % (4091666)Termination reason: Instruction limit
% 0.22/0.30 % (4091666)Termination phase: Saturation
% 0.22/0.30 % (4091666)Time elapsed: 0.014 s
% 0.22/0.30 % (4091666)Peak memory usage: 12 MB
% 0.22/0.30 % (4091666)Instructions burned: 25 (million)
% 0.22/0.30 % (4091662) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4091657-4091662"...
% 0.22/0.30 % (4091668)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=3105991342:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.30 % (4091662)...printing done.
% 0.22/0.30 % (4091662)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.30 % (4091662)------------------------------
% 0.22/0.30 % (4091662)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (4091662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (4091662)CaDiCaL version: 2.1.3
% 0.22/0.30 % (4091662)Termination reason: Refutation
% 0.22/0.30 % (4091662)Time elapsed: 0.019 s
% 0.22/0.30 % (4091662)Peak memory usage: 13 MB
% 0.22/0.30 % (4091662)Instructions burned: 35 (million)
% 0.22/0.30 % (4091657)Success in time 0.054 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------