%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL863^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 08:14:37 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 23
% Syntax : Number of formulae : 288 ( 25 unt; 0 typ; 17 def)
% Number of atoms : 3107 ( 540 equ; 0 cnn)
% Maximal formula atoms : 10 ( 10 avg)
% Number of connectives : 3309 ( 266 ~; 698 |; 130 &;1883 @)
% ( 21 <=>; 124 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 80 ( 80 >; 0 *; 0 +; 0 <<)
% Number of symbols : 81 ( 76 usr; 32 con; 0-4 aty)
% ( 171 !!; 15 ??; 0 @@+; 0 @@-)
% Number of variables : 497 ( 0 sgn 232 !; 5 ?; 497 :)
% 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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
vIMP: $o > $o > $o ).
thf(func_def_34,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
vAND: $o > $o > $o ).
thf(func_def_39,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_41,type,
vNOT: $o > $o ).
thf(func_def_42,type,
vOR: $o > $o > $o ).
thf(func_def_43,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_44,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
sK0: $i > $i > $o ).
thf(func_def_59,type,
sK12: $i > $i ).
thf(func_def_60,type,
sK13: $i > $i ).
thf(f18,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f20,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) )
= mserial ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mserial) ).
thf(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i,X3: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f22,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X3: $i,X2: $i,X1: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X2 @ X3 ) ) )
= meuclidean ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',meuclidean) ).
thf(f32,conjecture,
! [X0: $i > $i > $o] :
( ( ( meuclidean @ X0 )
& ( mreflexive @ X0 ) )
<=> ( ( mserial @ X0 )
& ( msymmetric @ X0 )
& ( mtransitive @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( ( meuclidean @ X0 )
& ( mreflexive @ X0 ) )
<=> ( ( mserial @ X0 )
& ( msymmetric @ X0 )
& ( mtransitive @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f45,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
inference(rectify,[],[f18]) ).
thf(f46,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f45]) ).
thf(f55,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X1 )
& ( X0 @ X3 @ X2 ) )
=> ( X0 @ X2 @ X1 ) ) )
= meuclidean ),
inference(rectify,[],[f22]) ).
thf(f56,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f59,plain,
~ ! [X0: $i > $i > $o] :
( ( ( meuclidean @ X0 )
& ( mreflexive @ X0 ) )
<=> ( ( mserial @ X0 )
& ( msymmetric @ X0 )
& ( mtransitive @ X0 ) ) ),
inference(rectify,[],[f33]) ).
thf(f60,plain,
~ ! [X0: $i > $i > $o] :
( ( ( ( msymmetric @ X0 )
= $true )
& ( ( mserial @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true ) )
<=> ( ( ( meuclidean @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f59]) ).
thf(f61,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) )
= mserial ),
inference(rectify,[],[f20]) ).
thf(f62,plain,
( mserial
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f61]) ).
thf(f72,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f73,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f72]) ).
thf(f76,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X1 )
& ( X0 @ X1 @ X3 ) )
=> ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f77,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f76]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( ( ( msymmetric @ X0 )
= $true )
& ( ( mserial @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true ) )
<~> ( ( ( meuclidean @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) ) ),
inference(ennf_transformation,[],[f60]) ).
thf(f88,plain,
? [X0: $i > $i > $o] :
( ( ( ( meuclidean @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true )
| ( ( msymmetric @ X0 )
!= $true )
| ( ( mserial @ X0 )
!= $true )
| ( ( mtransitive @ X0 )
!= $true ) )
& ( ( ( ( meuclidean @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) )
| ( ( ( msymmetric @ X0 )
= $true )
& ( ( mserial @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f87]) ).
thf(f89,plain,
? [X0: $i > $i > $o] :
( ( ( ( meuclidean @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true )
| ( ( msymmetric @ X0 )
!= $true )
| ( ( mserial @ X0 )
!= $true )
| ( ( mtransitive @ X0 )
!= $true ) )
& ( ( ( ( meuclidean @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) )
| ( ( ( msymmetric @ X0 )
= $true )
& ( ( mserial @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true ) ) ) ),
inference(flattening,[],[f88]) ).
thf(f90,plain,
( ( ( $true
!= ( meuclidean @ sK0 ) )
| ( ( mreflexive @ sK0 )
!= $true )
| ( $true
!= ( msymmetric @ sK0 ) )
| ( $true
!= ( mserial @ sK0 ) )
| ( ( mtransitive @ sK0 )
!= $true ) )
& ( ( ( $true
= ( meuclidean @ sK0 ) )
& ( ( mreflexive @ sK0 )
= $true ) )
| ( ( $true
= ( msymmetric @ sK0 ) )
& ( $true
= ( mserial @ sK0 ) )
& ( ( mtransitive @ 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,[],[f62]) ).
thf(f97,plain,
( ( ( mreflexive @ sK0 )
= $true )
| ( $true
= ( mserial @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f98,plain,
( ( ( mreflexive @ sK0 )
= $true )
| ( $true
= ( msymmetric @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f99,plain,
( ( $true
= ( meuclidean @ sK0 ) )
| ( ( mtransitive @ sK0 )
= $true ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f101,plain,
( ( $true
= ( meuclidean @ sK0 ) )
| ( $true
= ( msymmetric @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f102,plain,
( ( $true
!= ( meuclidean @ sK0 ) )
| ( ( mreflexive @ sK0 )
!= $true )
| ( $true
!= ( msymmetric @ sK0 ) )
| ( $true
!= ( mserial @ sK0 ) )
| ( ( mtransitive @ sK0 )
!= $true ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f109,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f73]) ).
thf(f110,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f113,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f116,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f77]) ).
thf(f140,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ sK0 )
!= $true )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
@ sK0 )
!= $true )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ sK0 )
!= $true )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) )
@ sK0 ) )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 )
!= $true ) ),
inference(definition_unfolding,[],[f102,f113,f110,f109,f94,f116]) ).
thf(f141,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ sK0 )
= $true )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
@ sK0 )
= $true ) ),
inference(definition_unfolding,[],[f101,f113,f109]) ).
thf(f143,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ sK0 )
= $true )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
@ sK0 )
= $true ) ),
inference(definition_unfolding,[],[f99,f113,f116]) ).
thf(f144,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 )
= $true )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ sK0 )
= $true ) ),
inference(definition_unfolding,[],[f98,f110,f109]) ).
thf(f145,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 )
= $true )
| ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f97,f110,f94]) ).
thf(f147,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f148,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f147]) ).
thf(f149,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y1 @ Y2 ) ) ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ X2 @ Y0 )
& ( sK0 @ X2 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( sK0 @ X1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( sK0 @ X1 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ X2 @ Y0 )
& ( sK0 @ X2 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( sK0 @ X1 @ Y0 ) )
@ X4 ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ X2 @ Y0 )
& ( sK0 @ X2 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ X2 @ X3 )
& ( sK0 @ X2 @ Y0 ) )
=> ( sK0 @ X3 @ Y0 ) ) ) )
| ( ( ( sK0 @ X4 @ X1 )
=> ( sK0 @ X1 @ X4 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f154,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( ( sK0 @ X4 @ X1 )
=> ( sK0 @ X1 @ X4 ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( ( sK0 @ X2 @ X3 )
& ( sK0 @ X2 @ Y0 ) )
=> ( sK0 @ X3 @ Y0 ) )
@ X5 )
= $true ) ),
inference(pi_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( sK0 @ X4 @ X1 )
= $false )
| ( $true
= ( sK0 @ X1 @ X4 ) )
| ( ( ^ [Y0: $i] :
( ( ( sK0 @ X2 @ X3 )
& ( sK0 @ X2 @ Y0 ) )
=> ( sK0 @ X3 @ Y0 ) )
@ X5 )
= $true ) ),
inference(imp_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ( ( sK0 @ X2 @ X3 )
& ( sK0 @ X2 @ X5 ) )
=> ( sK0 @ X3 @ X5 ) ) )
| ( ( sK0 @ X4 @ X1 )
= $false )
| ( $true
= ( sK0 @ X1 @ X4 ) ) ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f157,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( sK0 @ X3 @ X5 ) )
| ( $true
= ( sK0 @ X1 @ X4 ) )
| ( ( sK0 @ X4 @ X1 )
= $false )
| ( $false
= ( ( sK0 @ X2 @ X3 )
& ( sK0 @ X2 @ X5 ) ) ) ),
inference(imp_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( sK0 @ X2 @ X5 ) )
| ( $false
= ( sK0 @ X2 @ X3 ) )
| ( ( sK0 @ X4 @ X1 )
= $false )
| ( $true
= ( sK0 @ X3 @ X5 ) )
| ( $true
= ( sK0 @ X1 @ X4 ) ) ),
inference(and_proxy_clausification,[],[f157]) ).
thf(f169,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f170,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK0 @ X2 @ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( sK0 @ X1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f173,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( sK0 @ X1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( sK0 @ X2 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK0 @ X2 @ X2 ) )
| ( $true
= ( ( sK0 @ X3 @ X1 )
=> ( sK0 @ X1 @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f175,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( ( sK0 @ X1 @ X3 )
= $true )
| ( $true
= ( sK0 @ X2 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f174]) ).
thf(f176,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
!= $true )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f177,plain,
( ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK1 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(sigma_proxy_clausification,[],[f176]) ).
thf(f178,plain,
( ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y1 @ Y2 ) ) ) )
@ sK2 )
= $false )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f177]) ).
thf(f179,plain,
( ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK1 ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y1 @ Y2 ) ) ) )
@ sK2 )
= $false )
| ( $false
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ sK3 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f178]) ).
thf(f180,plain,
( ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y1 @ Y2 ) ) ) )
@ sK2 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( $false
= ( ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) )
@ sK4 ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y1 @ Y2 ) ) ) )
@ sK2 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ sK3 ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
@ sK5 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f180]) ).
thf(f182,plain,
( ( $false
= ( ?? @ $i @ ( sK0 @ sK4 ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK1 )
=> ( sK0 @ sK1 @ Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK5 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ sK5 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ sK2 @ Y0 )
& ( sK0 @ sK2 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ sK2 @ Y0 )
& ( sK0 @ sK2 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK5 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ sK5 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK1 )
=> ( sK0 @ sK1 @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ sK2 @ Y0 )
& ( sK0 @ sK2 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK6 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK1 )
=> ( sK0 @ sK1 @ Y0 ) ) ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK5 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ sK5 ) ) ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ sK2 @ Y0 )
& ( sK0 @ sK2 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK1 )
=> ( sK0 @ sK1 @ Y0 ) )
@ sK7 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK5 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ sK5 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK1 )
=> ( sK0 @ sK1 @ Y0 ) )
@ sK7 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ sK2 @ Y0 )
& ( sK0 @ sK2 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK6 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK5 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ sK5 ) ) )
@ sK8 ) ) ),
inference(sigma_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK8 @ Y0 ) )
=> ( sK0 @ sK8 @ sK5 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK2 @ sK6 )
& ( sK0 @ sK2 @ Y0 ) )
=> ( sK0 @ sK6 @ Y0 ) ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK7 @ sK1 )
=> ( sK0 @ sK1 @ sK7 ) ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f186]) ).
thf(f188,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( ( sK0 @ sK7 @ sK1 )
=> ( sK0 @ sK1 @ sK7 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK8 @ Y0 ) )
=> ( sK0 @ sK8 @ sK5 ) )
@ sK9 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK2 @ sK6 )
& ( sK0 @ sK2 @ Y0 ) )
=> ( sK0 @ sK6 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK2 @ sK6 )
& ( sK0 @ sK2 @ Y0 ) )
=> ( sK0 @ sK6 @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK8 @ Y0 ) )
=> ( sK0 @ sK8 @ sK5 ) )
@ sK9 ) )
| ( $false
= ( sK0 @ sK1 @ sK7 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK8 @ Y0 ) )
=> ( sK0 @ sK8 @ sK5 ) )
@ sK9 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK2 @ sK6 )
& ( sK0 @ sK2 @ Y0 ) )
=> ( sK0 @ sK6 @ Y0 ) ) ) )
| ( $true
= ( sK0 @ sK7 @ sK1 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f188]) ).
thf(f191,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK2 @ sK6 )
& ( sK0 @ sK2 @ Y0 ) )
=> ( sK0 @ sK6 @ Y0 ) )
@ sK10 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( sK0 @ sK7 @ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK8 @ Y0 ) )
=> ( sK0 @ sK8 @ sK5 ) )
@ sK9 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK5 )
& ( sK0 @ sK8 @ sK9 ) )
=> ( sK0 @ sK8 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $true
= ( sK0 @ sK7 @ sK1 ) )
| ( ( ( ( sK0 @ sK2 @ sK6 )
& ( sK0 @ sK2 @ sK10 ) )
=> ( sK0 @ sK6 @ sK10 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f193,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK8 @ sK5 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( sK0 @ sK7 @ sK1 ) )
| ( ( ( ( sK0 @ sK2 @ sK6 )
& ( sK0 @ sK2 @ sK10 ) )
=> ( sK0 @ sK6 @ sK10 ) )
= $false )
| ( $false
= ( sK0 @ sK4 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X1: $i] :
( ( $true
= ( ( sK0 @ sK9 @ sK5 )
& ( sK0 @ sK8 @ sK9 ) ) )
| ( $true
= ( sK0 @ sK7 @ sK1 ) )
| ( ( ( ( sK0 @ sK2 @ sK6 )
& ( sK0 @ sK2 @ sK10 ) )
=> ( sK0 @ sK6 @ sK10 ) )
= $false )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f192]) ).
thf(f195,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( sK0 @ sK7 @ sK1 ) )
| ( $true
= ( sK0 @ sK8 @ sK9 ) )
| ( ( ( ( sK0 @ sK2 @ sK6 )
& ( sK0 @ sK2 @ sK10 ) )
=> ( sK0 @ sK6 @ sK10 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK7 @ sK1 ) )
| ( ( ( ( sK0 @ sK2 @ sK6 )
& ( sK0 @ sK2 @ sK10 ) )
=> ( sK0 @ sK6 @ sK10 ) )
= $false )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( sK0 @ sK9 @ sK5 ) ) ),
inference(and_proxy_clausification,[],[f194]) ).
thf(f197,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( sK0 @ sK7 @ sK1 ) )
| ( ( sK0 @ sK6 @ sK10 )
= $false )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $true
= ( sK0 @ sK9 @ sK5 ) ) ),
inference(imp_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $true
= ( sK0 @ sK9 @ sK5 ) )
| ( ( ( sK0 @ sK2 @ sK6 )
& ( sK0 @ sK2 @ sK10 ) )
= $true )
| ( $true
= ( sK0 @ sK7 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f196]) ).
thf(f199,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $true
= ( sK0 @ sK9 @ sK5 ) )
| ( $true
= ( sK0 @ sK7 @ sK1 ) )
| ( $true
= ( sK0 @ sK2 @ sK10 ) ) ),
inference(and_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $true
= ( sK0 @ sK2 @ sK6 ) )
| ( $true
= ( sK0 @ sK9 @ sK5 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( sK0 @ sK7 @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f198]) ).
thf(f201,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( ( sK0 @ sK6 @ sK10 )
= $false )
| ( $true
= ( sK0 @ sK7 @ sK1 ) )
| ( $true
= ( sK0 @ sK8 @ sK9 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f195]) ).
thf(f202,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( ( ( sK0 @ sK2 @ sK6 )
& ( sK0 @ sK2 @ sK10 ) )
= $true )
| ( $true
= ( sK0 @ sK7 @ sK1 ) )
| ( $true
= ( sK0 @ sK8 @ sK9 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f195]) ).
thf(f203,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK2 @ sK10 ) )
| ( $true
= ( sK0 @ sK7 @ sK1 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( sK0 @ sK8 @ sK9 ) ) ),
inference(and_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $true
= ( sK0 @ sK2 @ sK6 ) )
| ( $true
= ( sK0 @ sK7 @ sK1 ) )
| ( $true
= ( sK0 @ sK8 @ sK9 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f202]) ).
thf(f205,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( sK0 @ sK8 @ sK5 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $true
= ( sK0 @ sK7 @ sK1 ) )
| ( ( sK0 @ sK6 @ sK10 )
= $false ) ),
inference(imp_proxy_clausification,[],[f193]) ).
thf(f206,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( sK0 @ sK8 @ sK5 ) )
| ( $true
= ( sK0 @ sK7 @ sK1 ) )
| ( ( ( sK0 @ sK2 @ sK6 )
& ( sK0 @ sK2 @ sK10 ) )
= $true )
| ( $false
= ( sK0 @ sK4 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f193]) ).
thf(f207,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK2 @ sK10 ) )
| ( $false
= ( sK0 @ sK8 @ sK5 ) )
| ( $true
= ( sK0 @ sK7 @ sK1 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $true
= ( sK0 @ sK7 @ sK1 ) )
| ( $true
= ( sK0 @ sK2 @ sK6 ) )
| ( $false
= ( sK0 @ sK8 @ sK5 ) ) ),
inference(and_proxy_clausification,[],[f206]) ).
thf(f209,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK2 @ sK6 )
& ( sK0 @ sK2 @ Y0 ) )
=> ( sK0 @ sK6 @ Y0 ) )
@ sK11 ) )
| ( $false
= ( sK0 @ sK1 @ sK7 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK8 @ Y0 ) )
=> ( sK0 @ sK8 @ sK5 ) )
@ sK9 ) ) ),
inference(sigma_proxy_clausification,[],[f189]) ).
thf(f210,plain,
! [X1: $i] :
( ( $false
= ( ( ( sK0 @ sK2 @ sK6 )
& ( sK0 @ sK2 @ sK11 ) )
=> ( sK0 @ sK6 @ sK11 ) ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK5 )
& ( sK0 @ sK8 @ sK9 ) )
=> ( sK0 @ sK8 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( sK0 @ sK1 @ sK7 ) ) ),
inference(beta-eta_normalization,[],[f209]) ).
thf(f211,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( sK0 @ sK1 @ sK7 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK5 )
& ( sK0 @ sK8 @ sK9 ) )
=> ( sK0 @ sK8 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK6 @ sK11 ) ) ),
inference(imp_proxy_clausification,[],[f210]) ).
thf(f212,plain,
! [X1: $i] :
( ( $true
= ( ( sK0 @ sK2 @ sK6 )
& ( sK0 @ sK2 @ sK11 ) ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $false
= ( sK0 @ sK1 @ sK7 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK5 )
& ( sK0 @ sK8 @ sK9 ) )
=> ( sK0 @ sK8 @ sK5 ) ) ) ),
inference(imp_proxy_clausification,[],[f210]) ).
thf(f213,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK1 @ sK7 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( ( sK0 @ sK2 @ sK11 )
= $true )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK5 )
& ( sK0 @ sK8 @ sK9 ) )
=> ( sK0 @ sK8 @ sK5 ) ) ) ),
inference(and_proxy_clausification,[],[f212]) ).
thf(f214,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK1 @ sK7 ) )
| ( $true
= ( sK0 @ sK2 @ sK6 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK5 )
& ( sK0 @ sK8 @ sK9 ) )
=> ( sK0 @ sK8 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f212]) ).
thf(f215,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( sK0 @ sK2 @ sK6 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $false
= ( sK0 @ sK1 @ sK7 ) )
| ( $false
= ( sK0 @ sK8 @ sK5 ) ) ),
inference(imp_proxy_clausification,[],[f214]) ).
thf(f216,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK1 @ sK7 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $true
= ( ( sK0 @ sK9 @ sK5 )
& ( sK0 @ sK8 @ sK9 ) ) )
| ( $true
= ( sK0 @ sK2 @ sK6 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f214]) ).
thf(f217,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $true
= ( sK0 @ sK2 @ sK6 ) )
| ( $false
= ( sK0 @ sK1 @ sK7 ) )
| ( $true
= ( sK0 @ sK8 @ sK9 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f216]) ).
thf(f218,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK2 @ sK6 ) )
| ( $false
= ( sK0 @ sK1 @ sK7 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $true
= ( sK0 @ sK9 @ sK5 ) ) ),
inference(and_proxy_clausification,[],[f216]) ).
thf(f219,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( ( sK0 @ sK2 @ sK11 )
= $true )
| ( $false
= ( sK0 @ sK8 @ sK5 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( sK0 @ sK1 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f213]) ).
thf(f220,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK9 @ sK5 )
& ( sK0 @ sK8 @ sK9 ) ) )
| ( ( sK0 @ sK2 @ sK11 )
= $true )
| ( $false
= ( sK0 @ sK1 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f213]) ).
thf(f221,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK8 @ sK9 ) )
| ( ( sK0 @ sK2 @ sK11 )
= $true )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( sK0 @ sK1 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f220]) ).
thf(f222,plain,
! [X1: $i] :
( ( ( sK0 @ sK2 @ sK11 )
= $true )
| ( $false
= ( sK0 @ sK1 @ sK7 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( sK0 @ sK9 @ sK5 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f220]) ).
thf(f223,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $false
= ( sK0 @ sK1 @ sK7 ) )
| ( $false
= ( sK0 @ sK6 @ sK11 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( sK0 @ sK8 @ sK5 ) ) ),
inference(imp_proxy_clausification,[],[f211]) ).
thf(f224,plain,
! [X1: $i] :
( ( $true
= ( ( sK0 @ sK9 @ sK5 )
& ( sK0 @ sK8 @ sK9 ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( sK0 @ sK6 @ sK11 ) )
| ( $false
= ( sK0 @ sK1 @ sK7 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f211]) ).
thf(f225,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( sK0 @ sK8 @ sK9 ) )
| ( $false
= ( sK0 @ sK1 @ sK7 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $false
= ( sK0 @ sK6 @ sK11 ) ) ),
inference(and_proxy_clausification,[],[f224]) ).
thf(f226,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK6 @ sK11 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $false
= ( sK0 @ sK1 @ sK7 ) )
| ( $true
= ( sK0 @ sK9 @ sK5 ) ) ),
inference(and_proxy_clausification,[],[f224]) ).
thf(f227,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f145]) ).
thf(f228,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK0 @ X1 @ X1 ) )
| ( $true
= ( ?? @ $i @ ( sK0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f229]) ).
thf(f231,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK0 @ X2 @ ( sK12 @ X2 ) ) )
| ( $true
= ( sK0 @ X1 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f230]) ).
thf(f232,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f233,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y1 @ Y2 ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y1 @ Y2 ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f233]) ).
thf(f235,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ X1 @ Y0 )
& ( sK0 @ X1 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ X2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ X2 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f234]) ).
thf(f236,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ X2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ X2 ) ) ) )
= $true )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ X1 @ Y0 )
& ( sK0 @ X1 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f235]) ).
thf(f237,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ X1 @ Y0 )
& ( sK0 @ X1 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ X3 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ X2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ X2 ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f236]) ).
thf(f238,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X2 )
& ( sK0 @ X4 @ Y0 ) )
=> ( sK0 @ X4 @ X2 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ X1 @ X3 )
& ( sK0 @ X1 @ Y0 ) )
=> ( sK0 @ X3 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f237]) ).
thf(f239,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X2 )
& ( sK0 @ X4 @ Y0 ) )
=> ( sK0 @ X4 @ X2 ) )
@ X5 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ X1 @ X3 )
& ( sK0 @ X1 @ Y0 ) )
=> ( sK0 @ X3 @ Y0 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f238]) ).
thf(f240,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ X1 @ X3 )
& ( sK0 @ X1 @ Y0 ) )
=> ( sK0 @ X3 @ Y0 ) )
@ X6 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X2 )
& ( sK0 @ X4 @ Y0 ) )
=> ( sK0 @ X4 @ X2 ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f239]) ).
thf(f241,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ( ( sK0 @ X1 @ X3 )
& ( sK0 @ X1 @ X6 ) )
=> ( sK0 @ X3 @ X6 ) ) )
| ( $true
= ( ( ( sK0 @ X5 @ X2 )
& ( sK0 @ X4 @ X5 ) )
=> ( sK0 @ X4 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f240]) ).
thf(f242,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ( ( sK0 @ X5 @ X2 )
& ( sK0 @ X4 @ X5 ) )
=> ( sK0 @ X4 @ X2 ) ) )
| ( ( ( sK0 @ X1 @ X3 )
& ( sK0 @ X1 @ X6 ) )
= $false )
| ( ( sK0 @ X3 @ X6 )
= $true ) ),
inference(imp_proxy_clausification,[],[f241]) ).
thf(f243,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( ( ( sK0 @ X1 @ X3 )
& ( sK0 @ X1 @ X6 ) )
= $false )
| ( ( sK0 @ X3 @ X6 )
= $true )
| ( $true
= ( sK0 @ X4 @ X2 ) )
| ( $false
= ( ( sK0 @ X5 @ X2 )
& ( sK0 @ X4 @ X5 ) ) ) ),
inference(imp_proxy_clausification,[],[f242]) ).
thf(f244,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( ( sK0 @ X5 @ X2 )
& ( sK0 @ X4 @ X5 ) ) )
| ( $false
= ( sK0 @ X1 @ X6 ) )
| ( ( sK0 @ X3 @ X6 )
= $true )
| ( $true
= ( sK0 @ X4 @ X2 ) )
| ( ( sK0 @ X1 @ X3 )
= $false ) ),
inference(and_proxy_clausification,[],[f243]) ).
thf(f245,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( sK0 @ X5 @ X2 ) )
| ( ( sK0 @ X3 @ X6 )
= $true )
| ( $true
= ( sK0 @ X4 @ X2 ) )
| ( $false
= ( sK0 @ X4 @ X5 ) )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( $false
= ( sK0 @ X1 @ X6 ) ) ),
inference(and_proxy_clausification,[],[f244]) ).
thf(f258,definition,
( spl14_1
<=> ! [X4: $i,X1: $i] :
( ( ( sK0 @ X4 @ X1 )
= $false )
| ( $true
= ( sK0 @ X1 @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
thf(f259,plain,
( ! [X1: $i,X4: $i] :
( ( $true
= ( sK0 @ X1 @ X4 ) )
| ( ( sK0 @ X4 @ X1 )
= $false ) )
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f258]) ).
thf(f261,definition,
( spl14_2
<=> ! [X2: $i,X5: $i,X3: $i] :
( ( $false
= ( sK0 @ X2 @ X5 ) )
| ( $true
= ( sK0 @ X3 @ X5 ) )
| ( $false
= ( sK0 @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
thf(f262,plain,
( ! [X2: $i,X3: $i,X5: $i] :
( ( $false
= ( sK0 @ X2 @ X5 ) )
| ( $true
= ( sK0 @ X3 @ X5 ) )
| ( $false
= ( sK0 @ X2 @ X3 ) ) )
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f261]) ).
thf(f263,plain,
( spl14_1
| spl14_2 ),
inference(avatar_split_clause,[],[f158,f261,f258]) ).
thf(f265,definition,
( spl14_3
<=> ! [X2: $i] :
( $true
= ( sK0 @ X2 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
thf(f266,plain,
( ! [X2: $i] :
( $true
= ( sK0 @ X2 @ X2 ) )
| ~ spl14_3 ),
inference(avatar_component_clause,[],[f265]) ).
thf(f268,definition,
( spl14_4
<=> ! [X4: $i,X1: $i,X3: $i] :
( ( $true
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X3 @ X4 ) )
| ( ( sK0 @ X4 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition]) ).
thf(f269,plain,
( ! [X3: $i,X1: $i,X4: $i] :
( ( ( sK0 @ X4 @ X1 )
= $false )
| ( $false
= ( sK0 @ X3 @ X4 ) )
| ( $true
= ( sK0 @ X3 @ X1 ) ) )
| ~ spl14_4 ),
inference(avatar_component_clause,[],[f268]) ).
thf(f271,plain,
( spl14_1
| spl14_3 ),
inference(avatar_split_clause,[],[f175,f265,f258]) ).
thf(f273,definition,
( spl14_5
<=> ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_5])],[avatar_definition]) ).
thf(f275,plain,
( ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ~ spl14_5 ),
inference(avatar_component_clause,[],[f273]) ).
thf(f277,definition,
( spl14_6
<=> ( $true
= ( sK0 @ sK7 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_6])],[avatar_definition]) ).
thf(f279,plain,
( ( $true
= ( sK0 @ sK7 @ sK1 ) )
| ~ spl14_6 ),
inference(avatar_component_clause,[],[f277]) ).
thf(f281,definition,
( spl14_7
<=> ( $true
= ( sK0 @ sK2 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_7])],[avatar_definition]) ).
thf(f283,plain,
( ( $true
= ( sK0 @ sK2 @ sK6 ) )
| ~ spl14_7 ),
inference(avatar_component_clause,[],[f281]) ).
thf(f285,definition,
( spl14_8
<=> ! [X1: $i] :
( $false
= ( sK0 @ sK4 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_8])],[avatar_definition]) ).
thf(f286,plain,
( ! [X1: $i] :
( $false
= ( sK0 @ sK4 @ X1 ) )
| ~ spl14_8 ),
inference(avatar_component_clause,[],[f285]) ).
thf(f288,definition,
( spl14_9
<=> ( $true
= ( sK0 @ sK9 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_9])],[avatar_definition]) ).
thf(f290,plain,
( ( $true
= ( sK0 @ sK9 @ sK5 ) )
| ~ spl14_9 ),
inference(avatar_component_clause,[],[f288]) ).
thf(f291,plain,
( spl14_5
| spl14_6
| spl14_7
| spl14_8
| spl14_9 ),
inference(avatar_split_clause,[],[f200,f288,f285,f281,f277,f273]) ).
thf(f293,definition,
( spl14_10
<=> ( $true
= ( sK0 @ sK2 @ sK10 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_10])],[avatar_definition]) ).
thf(f295,plain,
( ( $true
= ( sK0 @ sK2 @ sK10 ) )
| ~ spl14_10 ),
inference(avatar_component_clause,[],[f293]) ).
thf(f296,plain,
( spl14_9
| spl14_8
| spl14_10
| spl14_5
| spl14_6 ),
inference(avatar_split_clause,[],[f199,f277,f273,f293,f285,f288]) ).
thf(f298,definition,
( spl14_11
<=> ( ( sK0 @ sK6 @ sK10 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl14_11])],[avatar_definition]) ).
thf(f300,plain,
( ( ( sK0 @ sK6 @ sK10 )
= $false )
| ~ spl14_11 ),
inference(avatar_component_clause,[],[f298]) ).
thf(f301,plain,
( spl14_5
| spl14_9
| spl14_8
| spl14_11
| spl14_6 ),
inference(avatar_split_clause,[],[f197,f277,f298,f285,f288,f273]) ).
thf(f303,definition,
( spl14_12
<=> ( $true
= ( sK0 @ sK8 @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_12])],[avatar_definition]) ).
thf(f305,plain,
( ( $true
= ( sK0 @ sK8 @ sK9 ) )
| ~ spl14_12 ),
inference(avatar_component_clause,[],[f303]) ).
thf(f306,plain,
( spl14_7
| spl14_5
| spl14_12
| spl14_8
| spl14_6 ),
inference(avatar_split_clause,[],[f204,f277,f285,f303,f273,f281]) ).
thf(f307,plain,
( spl14_12
| spl14_6
| spl14_10
| spl14_5
| spl14_8 ),
inference(avatar_split_clause,[],[f203,f285,f273,f293,f277,f303]) ).
thf(f308,plain,
( spl14_12
| spl14_5
| spl14_8
| spl14_6
| spl14_11 ),
inference(avatar_split_clause,[],[f201,f298,f277,f285,f273,f303]) ).
thf(f310,definition,
( spl14_13
<=> ( $false
= ( sK0 @ sK8 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_13])],[avatar_definition]) ).
thf(f312,plain,
( ( $false
= ( sK0 @ sK8 @ sK5 ) )
| ~ spl14_13 ),
inference(avatar_component_clause,[],[f310]) ).
thf(f313,plain,
( spl14_5
| spl14_7
| spl14_6
| spl14_8
| spl14_13 ),
inference(avatar_split_clause,[],[f208,f310,f285,f277,f281,f273]) ).
thf(f314,plain,
( spl14_5
| spl14_8
| spl14_6
| spl14_10
| spl14_13 ),
inference(avatar_split_clause,[],[f207,f310,f293,f277,f285,f273]) ).
thf(f315,plain,
( spl14_6
| spl14_5
| spl14_11
| spl14_13
| spl14_8 ),
inference(avatar_split_clause,[],[f205,f285,f310,f298,f273,f277]) ).
thf(f317,definition,
( spl14_14
<=> ( $false
= ( sK0 @ sK1 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_14])],[avatar_definition]) ).
thf(f319,plain,
( ( $false
= ( sK0 @ sK1 @ sK7 ) )
| ~ spl14_14 ),
inference(avatar_component_clause,[],[f317]) ).
thf(f320,plain,
( spl14_14
| spl14_8
| spl14_5
| spl14_7
| spl14_9 ),
inference(avatar_split_clause,[],[f218,f288,f281,f273,f285,f317]) ).
thf(f321,plain,
( spl14_14
| spl14_8
| spl14_7
| spl14_5
| spl14_12 ),
inference(avatar_split_clause,[],[f217,f303,f273,f281,f285,f317]) ).
thf(f322,plain,
( spl14_5
| spl14_7
| spl14_8
| spl14_14
| spl14_13 ),
inference(avatar_split_clause,[],[f215,f310,f317,f285,f281,f273]) ).
thf(f324,definition,
( spl14_15
<=> ( ( sK0 @ sK2 @ sK11 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl14_15])],[avatar_definition]) ).
thf(f326,plain,
( ( ( sK0 @ sK2 @ sK11 )
= $true )
| ~ spl14_15 ),
inference(avatar_component_clause,[],[f324]) ).
thf(f327,plain,
( spl14_5
| spl14_14
| spl14_15
| spl14_9
| spl14_8 ),
inference(avatar_split_clause,[],[f222,f285,f288,f324,f317,f273]) ).
thf(f328,plain,
( spl14_12
| spl14_5
| spl14_8
| spl14_14
| spl14_15 ),
inference(avatar_split_clause,[],[f221,f324,f317,f285,f273,f303]) ).
thf(f329,plain,
( spl14_8
| spl14_14
| spl14_5
| spl14_15
| spl14_13 ),
inference(avatar_split_clause,[],[f219,f310,f324,f273,f317,f285]) ).
thf(f331,definition,
( spl14_16
<=> ( $false
= ( sK0 @ sK6 @ sK11 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_16])],[avatar_definition]) ).
thf(f333,plain,
( ( $false
= ( sK0 @ sK6 @ sK11 ) )
| ~ spl14_16 ),
inference(avatar_component_clause,[],[f331]) ).
thf(f334,plain,
( spl14_8
| spl14_9
| spl14_5
| spl14_16
| spl14_14 ),
inference(avatar_split_clause,[],[f226,f317,f331,f273,f288,f285]) ).
thf(f335,plain,
( spl14_5
| spl14_14
| spl14_12
| spl14_8
| spl14_16 ),
inference(avatar_split_clause,[],[f225,f331,f285,f303,f317,f273]) ).
thf(f336,plain,
( spl14_16
| spl14_13
| spl14_8
| spl14_14
| spl14_5 ),
inference(avatar_split_clause,[],[f223,f273,f317,f285,f310,f331]) ).
thf(f338,definition,
( spl14_17
<=> ! [X2: $i] :
( $true
= ( sK0 @ X2 @ ( sK12 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_17])],[avatar_definition]) ).
thf(f339,plain,
( ! [X2: $i] :
( $true
= ( sK0 @ X2 @ ( sK12 @ X2 ) ) )
| ~ spl14_17 ),
inference(avatar_component_clause,[],[f338]) ).
thf(f340,plain,
( spl14_3
| spl14_17 ),
inference(avatar_split_clause,[],[f231,f338,f265]) ).
thf(f341,plain,
( spl14_4
| spl14_2 ),
inference(avatar_split_clause,[],[f245,f261,f268]) ).
thf(f346,plain,
( ( $false = $true )
| ~ spl14_3
| ~ spl14_5 ),
inference(forward_demodulation,[],[f275,f266]) ).
thf(f347,plain,
( $false
| ~ spl14_3
| ~ spl14_5 ),
inference(trivial_inequality_removal,[],[f346]) ).
thf(f348,plain,
( ~ spl14_3
| ~ spl14_5 ),
inference(avatar_contradiction_clause,[],[f347]) ).
thf(f356,plain,
( ! [X0: $i,X1: $i] :
( ( $false = $true )
| ( $true
= ( sK0 @ X1 @ X0 ) )
| ( ( sK0 @ X0 @ X1 )
= $false ) )
| ~ spl14_2
| ~ spl14_3 ),
inference(constrained_superposition,[],[f266,f262]) ).
thf(f365,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( sK0 @ X1 @ X0 ) )
| ( ( sK0 @ X0 @ X1 )
= $false ) )
| ~ spl14_2
| ~ spl14_3 ),
inference(trivial_inequality_removal,[],[f356]) ).
thf(f371,plain,
( spl14_1
| ~ spl14_2
| ~ spl14_3 ),
inference(avatar_split_clause,[],[f365,f265,f261,f258]) ).
thf(f372,plain,
( ( $false = $true )
| ~ spl14_3
| ~ spl14_8 ),
inference(constrained_superposition,[],[f286,f266]) ).
thf(f380,plain,
( $false
| ~ spl14_3
| ~ spl14_8 ),
inference(trivial_inequality_removal,[],[f372]) ).
thf(f381,plain,
( ~ spl14_3
| ~ spl14_8 ),
inference(avatar_contradiction_clause,[],[f380]) ).
thf(f383,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK8 ) )
| ( $false = $true )
| ( $false
= ( sK0 @ X0 @ sK5 ) ) )
| ~ spl14_2
| ~ spl14_13 ),
inference(constrained_superposition,[],[f262,f312]) ).
thf(f384,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK8 ) )
| ( $false
= ( sK0 @ X0 @ sK5 ) ) )
| ~ spl14_2
| ~ spl14_13 ),
inference(trivial_inequality_removal,[],[f383]) ).
thf(f431,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK5 ) )
| ( $false = $true )
| ( $false
= ( sK0 @ sK8 @ X0 ) ) )
| ~ spl14_1
| ~ spl14_2
| ~ spl14_13 ),
inference(constrained_superposition,[],[f384,f259]) ).
thf(f437,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ sK8 @ X0 ) )
| ( $false
= ( sK0 @ X0 @ sK5 ) ) )
| ~ spl14_1
| ~ spl14_2
| ~ spl14_13 ),
inference(trivial_inequality_removal,[],[f431]) ).
thf(f520,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK8 @ sK9 ) )
| ~ spl14_1
| ~ spl14_2
| ~ spl14_9
| ~ spl14_13 ),
inference(constrained_superposition,[],[f437,f290]) ).
thf(f530,plain,
( ( $false
= ( sK0 @ sK8 @ sK9 ) )
| ~ spl14_1
| ~ spl14_2
| ~ spl14_9
| ~ spl14_13 ),
inference(trivial_inequality_removal,[],[f520]) ).
thf(f545,plain,
( ( $false = $true )
| ~ spl14_1
| ~ spl14_2
| ~ spl14_9
| ~ spl14_12
| ~ spl14_13 ),
inference(forward_demodulation,[],[f530,f305]) ).
thf(f546,plain,
( $false
| ~ spl14_1
| ~ spl14_2
| ~ spl14_9
| ~ spl14_12
| ~ spl14_13 ),
inference(trivial_inequality_removal,[],[f545]) ).
thf(f547,plain,
( ~ spl14_1
| ~ spl14_2
| ~ spl14_9
| ~ spl14_12
| ~ spl14_13 ),
inference(avatar_contradiction_clause,[],[f546]) ).
thf(f558,plain,
( ( $false = $true )
| ( $true
= ( sK0 @ sK1 @ sK7 ) )
| ~ spl14_1
| ~ spl14_6 ),
inference(constrained_superposition,[],[f279,f259]) ).
thf(f569,plain,
( ( $true
= ( sK0 @ sK1 @ sK7 ) )
| ~ spl14_1
| ~ spl14_6 ),
inference(trivial_inequality_removal,[],[f558]) ).
thf(f573,plain,
( ( $false = $true )
| ~ spl14_1
| ~ spl14_6
| ~ spl14_14 ),
inference(forward_demodulation,[],[f569,f319]) ).
thf(f574,plain,
( $false
| ~ spl14_1
| ~ spl14_6
| ~ spl14_14 ),
inference(trivial_inequality_removal,[],[f573]) ).
thf(f575,plain,
( ~ spl14_1
| ~ spl14_6
| ~ spl14_14 ),
inference(avatar_contradiction_clause,[],[f574]) ).
thf(f577,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK6 ) )
| ( $false
= ( sK0 @ X0 @ sK10 ) )
| ( $false = $true ) )
| ~ spl14_2
| ~ spl14_11 ),
inference(constrained_superposition,[],[f262,f300]) ).
thf(f578,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK10 ) )
| ( $false
= ( sK0 @ X0 @ sK6 ) ) )
| ~ spl14_2
| ~ spl14_11 ),
inference(trivial_inequality_removal,[],[f577]) ).
thf(f687,plain,
( ( $false
= ( sK0 @ sK2 @ sK6 ) )
| ( $false = $true )
| ~ spl14_2
| ~ spl14_10
| ~ spl14_11 ),
inference(constrained_superposition,[],[f578,f295]) ).
thf(f699,plain,
( ( $false
= ( sK0 @ sK2 @ sK6 ) )
| ~ spl14_2
| ~ spl14_10
| ~ spl14_11 ),
inference(trivial_inequality_removal,[],[f687]) ).
thf(f703,plain,
( ( $false = $true )
| ~ spl14_2
| ~ spl14_7
| ~ spl14_10
| ~ spl14_11 ),
inference(forward_demodulation,[],[f699,f283]) ).
thf(f704,plain,
( $false
| ~ spl14_2
| ~ spl14_7
| ~ spl14_10
| ~ spl14_11 ),
inference(trivial_inequality_removal,[],[f703]) ).
thf(f705,plain,
( ~ spl14_2
| ~ spl14_7
| ~ spl14_10
| ~ spl14_11 ),
inference(avatar_contradiction_clause,[],[f704]) ).
thf(f714,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK6 ) )
| ( $false = $true )
| ( $false
= ( sK0 @ X0 @ sK11 ) ) )
| ~ spl14_2
| ~ spl14_16 ),
inference(constrained_superposition,[],[f262,f333]) ).
thf(f715,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK11 ) )
| ( $false
= ( sK0 @ X0 @ sK6 ) ) )
| ~ spl14_2
| ~ spl14_16 ),
inference(trivial_inequality_removal,[],[f714]) ).
thf(f756,plain,
( ( $false
= ( sK0 @ sK2 @ sK6 ) )
| ( $false = $true )
| ~ spl14_2
| ~ spl14_15
| ~ spl14_16 ),
inference(constrained_superposition,[],[f326,f715]) ).
thf(f764,plain,
( ( $false
= ( sK0 @ sK2 @ sK6 ) )
| ~ spl14_2
| ~ spl14_15
| ~ spl14_16 ),
inference(trivial_inequality_removal,[],[f756]) ).
thf(f768,plain,
( ( $false = $true )
| ~ spl14_2
| ~ spl14_7
| ~ spl14_15
| ~ spl14_16 ),
inference(forward_demodulation,[],[f764,f283]) ).
thf(f769,plain,
( $false
| ~ spl14_2
| ~ spl14_7
| ~ spl14_15
| ~ spl14_16 ),
inference(trivial_inequality_removal,[],[f768]) ).
thf(f770,plain,
( ~ spl14_2
| ~ spl14_7
| ~ spl14_15
| ~ spl14_16 ),
inference(avatar_contradiction_clause,[],[f769]) ).
thf(f825,plain,
( ( $false = $true )
| ~ spl14_8
| ~ spl14_17 ),
inference(constrained_superposition,[],[f339,f286]) ).
thf(f837,plain,
( $false
| ~ spl14_8
| ~ spl14_17 ),
inference(trivial_inequality_removal,[],[f825]) ).
thf(f838,plain,
( ~ spl14_8
| ~ spl14_17 ),
inference(avatar_contradiction_clause,[],[f837]) ).
thf(f878,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $true
= ( sK0 @ X0 @ X2 ) )
| ( $false = $true )
| ( $false
= ( sK0 @ X1 @ X2 ) ) )
| ~ spl14_1
| ~ spl14_4 ),
inference(constrained_superposition,[],[f259,f269]) ).
thf(f920,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $true
= ( sK0 @ X0 @ X2 ) ) )
| ~ spl14_1
| ~ spl14_4 ),
inference(trivial_inequality_removal,[],[f878]) ).
thf(f948,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( sK0 @ X0 @ sK3 ) )
| ( $false
= ( sK0 @ X0 @ sK3 ) ) )
| ~ spl14_2
| ~ spl14_5 ),
inference(constrained_superposition,[],[f262,f275]) ).
thf(f951,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( sK0 @ X0 @ sK3 ) ) )
| ~ spl14_2
| ~ spl14_5 ),
inference(duplicate_literal_removal,[],[f948]) ).
thf(f952,plain,
( ! [X0: $i] :
( $false
= ( sK0 @ X0 @ sK3 ) )
| ~ spl14_2
| ~ spl14_5 ),
inference(trivial_inequality_removal,[],[f951]) ).
thf(f960,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( sK0 @ sK3 @ X0 ) ) )
| ~ spl14_1
| ~ spl14_2
| ~ spl14_5 ),
inference(constrained_superposition,[],[f259,f952]) ).
thf(f965,plain,
( ! [X0: $i] :
( $false
= ( sK0 @ sK3 @ X0 ) )
| ~ spl14_1
| ~ spl14_2
| ~ spl14_5 ),
inference(trivial_inequality_removal,[],[f960]) ).
thf(f972,plain,
( ( $false = $true )
| ~ spl14_1
| ~ spl14_2
| ~ spl14_5
| ~ spl14_17 ),
inference(constrained_superposition,[],[f965,f339]) ).
thf(f983,plain,
( $false
| ~ spl14_1
| ~ spl14_2
| ~ spl14_5
| ~ spl14_17 ),
inference(trivial_inequality_removal,[],[f972]) ).
thf(f984,plain,
( ~ spl14_1
| ~ spl14_2
| ~ spl14_5
| ~ spl14_17 ),
inference(avatar_contradiction_clause,[],[f983]) ).
thf(f989,plain,
( spl14_2
| ~ spl14_1
| ~ spl14_4 ),
inference(avatar_split_clause,[],[f920,f268,f258,f261]) ).
cnf(s1,plain,
( spl14_1
| spl14_2 ),
inference(sat_conversion,[],[f263]) ).
cnf(s3,plain,
( spl14_1
| spl14_3 ),
inference(sat_conversion,[],[f271]) ).
cnf(s4,plain,
( spl14_5
| spl14_6
| spl14_7
| spl14_8
| spl14_9 ),
inference(sat_conversion,[],[f291]) ).
cnf(s5,plain,
( spl14_5
| spl14_6
| spl14_8
| spl14_9
| spl14_10 ),
inference(sat_conversion,[],[f296]) ).
cnf(s6,plain,
( spl14_5
| spl14_6
| spl14_8
| spl14_9
| spl14_11 ),
inference(sat_conversion,[],[f301]) ).
cnf(s7,plain,
( spl14_5
| spl14_6
| spl14_7
| spl14_8
| spl14_12 ),
inference(sat_conversion,[],[f306]) ).
cnf(s8,plain,
( spl14_5
| spl14_6
| spl14_8
| spl14_10
| spl14_12 ),
inference(sat_conversion,[],[f307]) ).
cnf(s9,plain,
( spl14_5
| spl14_6
| spl14_8
| spl14_11
| spl14_12 ),
inference(sat_conversion,[],[f308]) ).
cnf(s10,plain,
( spl14_5
| spl14_6
| spl14_7
| spl14_8
| spl14_13 ),
inference(sat_conversion,[],[f313]) ).
cnf(s11,plain,
( spl14_5
| spl14_6
| spl14_8
| spl14_10
| spl14_13 ),
inference(sat_conversion,[],[f314]) ).
cnf(s12,plain,
( spl14_5
| spl14_6
| spl14_8
| spl14_11
| spl14_13 ),
inference(sat_conversion,[],[f315]) ).
cnf(s13,plain,
( spl14_5
| spl14_7
| spl14_8
| spl14_9
| spl14_14 ),
inference(sat_conversion,[],[f320]) ).
cnf(s14,plain,
( spl14_5
| spl14_7
| spl14_8
| spl14_12
| spl14_14 ),
inference(sat_conversion,[],[f321]) ).
cnf(s15,plain,
( spl14_5
| spl14_7
| spl14_8
| spl14_13
| spl14_14 ),
inference(sat_conversion,[],[f322]) ).
cnf(s16,plain,
( spl14_5
| spl14_8
| spl14_9
| spl14_14
| spl14_15 ),
inference(sat_conversion,[],[f327]) ).
cnf(s17,plain,
( spl14_5
| spl14_8
| spl14_12
| spl14_14
| spl14_15 ),
inference(sat_conversion,[],[f328]) ).
cnf(s18,plain,
( spl14_5
| spl14_8
| spl14_13
| spl14_14
| spl14_15 ),
inference(sat_conversion,[],[f329]) ).
cnf(s19,plain,
( spl14_5
| spl14_8
| spl14_9
| spl14_14
| spl14_16 ),
inference(sat_conversion,[],[f334]) ).
cnf(s20,plain,
( spl14_5
| spl14_8
| spl14_12
| spl14_14
| spl14_16 ),
inference(sat_conversion,[],[f335]) ).
cnf(s21,plain,
( spl14_5
| spl14_8
| spl14_13
| spl14_14
| spl14_16 ),
inference(sat_conversion,[],[f336]) ).
cnf(s22,plain,
( spl14_3
| spl14_17 ),
inference(sat_conversion,[],[f340]) ).
cnf(s23,plain,
( spl14_2
| spl14_4 ),
inference(sat_conversion,[],[f341]) ).
cnf(s25,plain,
( ~ spl14_3
| ~ spl14_5 ),
inference(sat_conversion,[],[f348]) ).
cnf(s26,plain,
( spl14_1
| ~ spl14_2
| ~ spl14_3 ),
inference(sat_conversion,[],[f371]) ).
cnf(s29,plain,
( ~ spl14_3
| ~ spl14_8 ),
inference(sat_conversion,[],[f381]) ).
cnf(s33,plain,
( ~ spl14_1
| ~ spl14_2
| ~ spl14_9
| ~ spl14_12
| ~ spl14_13 ),
inference(sat_conversion,[],[f547]) ).
cnf(s35,plain,
( ~ spl14_1
| ~ spl14_6
| ~ spl14_14 ),
inference(sat_conversion,[],[f575]) ).
cnf(s37,plain,
( ~ spl14_2
| ~ spl14_7
| ~ spl14_10
| ~ spl14_11 ),
inference(sat_conversion,[],[f705]) ).
cnf(s39,plain,
( ~ spl14_2
| ~ spl14_7
| ~ spl14_15
| ~ spl14_16 ),
inference(sat_conversion,[],[f770]) ).
cnf(s43,plain,
( ~ spl14_8
| ~ spl14_17 ),
inference(sat_conversion,[],[f838]) ).
cnf(s45,plain,
( ~ spl14_1
| ~ spl14_2
| ~ spl14_5
| ~ spl14_17 ),
inference(sat_conversion,[],[f984]) ).
cnf(s46,plain,
( ~ spl14_1
| spl14_2
| ~ spl14_4 ),
inference(sat_conversion,[],[f989]) ).
cnf(s48,plain,
spl14_1,
inference(rat,[],[s26,s1,s3]) ).
cnf(s49,plain,
( spl14_7
| spl14_6
| ~ spl14_3
| ~ spl14_2 ),
inference(rat,[],[s33,s4,s7,s10,s29,s25,s48]) ).
cnf(s50,plain,
( spl14_13
| spl14_6
| ~ spl14_3
| ~ spl14_2 ),
inference(rat,[],[s37,s11,s12,s29,s25,s49]) ).
cnf(s51,plain,
( spl14_12
| spl14_6
| ~ spl14_3
| ~ spl14_2 ),
inference(rat,[],[s37,s8,s9,s29,s25,s49]) ).
cnf(s52,plain,
( spl14_6
| ~ spl14_3
| ~ spl14_2 ),
inference(rat,[],[s37,s5,s6,s33,s51,s50,s49,s29,s25,s48]) ).
cnf(s53,plain,
( spl14_13
| ~ spl14_7
| ~ spl14_3
| ~ spl14_2 ),
inference(rat,[],[s39,s18,s21,s29,s25,s35,s52,s48]) ).
cnf(s54,plain,
( spl14_12
| ~ spl14_7
| ~ spl14_3
| ~ spl14_2 ),
inference(rat,[],[s39,s17,s20,s29,s25,s35,s52,s48]) ).
cnf(s55,plain,
( ~ spl14_7
| ~ spl14_3
| ~ spl14_2 ),
inference(rat,[],[s39,s16,s19,s33,s54,s53,s29,s25,s35,s52,s48]) ).
cnf(s56,plain,
( ~ spl14_3
| ~ spl14_2 ),
inference(rat,[],[s33,s13,s14,s15,s55,s35,s52,s25,s29,s48]) ).
cnf(s57,plain,
( spl14_6
| spl14_13
| ~ spl14_7
| ~ spl14_2 ),
inference(rat,[],[s37,s11,s12,s43,s45,s22,s56,s48]) ).
cnf(s58,plain,
( spl14_13
| ~ spl14_7
| ~ spl14_2 ),
inference(rat,[],[s39,s18,s21,s35,s57,s43,s45,s22,s56,s48]) ).
cnf(s59,plain,
( spl14_6
| spl14_12
| ~ spl14_7
| ~ spl14_2 ),
inference(rat,[],[s37,s8,s9,s43,s45,s22,s56,s48]) ).
cnf(s60,plain,
( spl14_12
| ~ spl14_7
| ~ spl14_2 ),
inference(rat,[],[s39,s17,s20,s35,s59,s43,s45,s22,s56,s48]) ).
cnf(s61,plain,
( spl14_6
| ~ spl14_7
| ~ spl14_2 ),
inference(rat,[],[s37,s5,s6,s43,s45,s22,s56,s33,s60,s58,s48]) ).
cnf(s62,plain,
( ~ spl14_7
| ~ spl14_2 ),
inference(rat,[],[s39,s16,s19,s35,s61,s33,s60,s58,s43,s45,s22,s56,s48]) ).
cnf(s63,plain,
( spl14_13
| spl14_7
| spl14_8
| spl14_5 ),
inference(rat,[],[s35,s10,s15,s48]) ).
cnf(s64,plain,
( spl14_12
| spl14_7
| spl14_8
| spl14_5 ),
inference(rat,[],[s35,s7,s14,s48]) ).
cnf(s65,plain,
( spl14_9
| spl14_7
| spl14_8
| spl14_5 ),
inference(rat,[],[s35,s4,s13,s48]) ).
cnf(s66,plain,
~ spl14_2,
inference(rat,[],[s65,s33,s64,s63,s62,s45,s43,s22,s56,s48]) ).
cnf(s68,plain,
spl14_4,
inference(rat,[],[s23,s66]) ).
cnf(s69,plain,
$false,
inference(rat,[],[s46,s48,s66,s68]) ).
thf(f990,plain,
$false,
inference(avatar_sat_refutation,[],[s69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL863^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n011.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 10:14:01 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 Running higher-order theorem proving
% 0.08/0.22 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
% 0.20/0.28 % (4091270)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (4091275)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2459501460:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28 % (4091276)lrs+10_16_si=on:nwc=1.5:random_seed=3081463242:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.28 % (4091278)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=328808854: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)
% 0.20/0.28 % (4091275) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4091270-4091275"...
% 0.20/0.28 % (4091281)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.28 % (4091281)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
% 0.20/0.28 % (4091276)Instruction limit reached!
% 0.20/0.28 % (4091276)------------------------------
% 0.20/0.28 % (4091276)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (4091276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (4091276)CaDiCaL version: 2.1.3
% 0.20/0.28 % (4091276)Termination reason: Instruction limit
% 0.20/0.28 % (4091276)Termination phase: Saturation
% 0.20/0.28 % (4091276)Time elapsed: 0.011 s
% 0.20/0.28 % (4091276)Peak memory usage: 12 MB
% 0.20/0.28 % (4091276)Instructions burned: 20 (million)
% 0.20/0.28 % (4091275)...printing done.
% 0.20/0.28 % (4091277)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3656138293:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.28 % (4091279)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3388675370:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.28 % (4091280)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1426553659:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.28 % (4091281)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=3422758669:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.28 % (4091275)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.29 % (4091275)------------------------------
% 0.20/0.29 % (4091275)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (4091275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (4091275)CaDiCaL version: 2.1.3
% 0.20/0.29 % (4091275)Termination reason: Refutation
% 0.20/0.29 % (4091275)Time elapsed: 0.020 s
% 0.20/0.29 % (4091275)Peak memory usage: 13 MB
% 0.20/0.29 % (4091275)Instructions burned: 67 (million)
% 0.20/0.29 % (4091270)Success in time 0.055 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------