%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL860^1 : 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 : n009.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 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 20
% Syntax : Number of formulae : 243 ( 40 unt; 0 typ; 15 def)
% Number of atoms : 2350 ( 383 equ; 0 cnn)
% Maximal formula atoms : 12 ( 9 avg)
% Number of connectives : 2284 ( 183 ~; 479 |; 112 &;1290 @)
% ( 19 <=>; 81 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 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 : 76 ( 72 usr; 29 con; 0-4 aty)
% ( 119 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 240 ( 0 sgn 60 !; 3 ?; 240 :)
% 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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_36,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_38,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_39,type,
vNOT: $o > $o ).
thf(func_def_40,type,
vIMP: $o > $o > $o ).
thf(func_def_41,type,
vAND: $o > $o > $o ).
thf(func_def_42,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vOR: $o > $o > $o ).
thf(func_def_44,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
sK0: $i > $i > $o ).
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,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
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/sandbox2/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f22,axiom,
( meuclidean
= ( ^ [X0: $i > $i > $o] :
! [X2: $i,X3: $i,X1: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',meuclidean) ).
thf(f32,conjecture,
! [X0: $i > $i > $o] :
( ( ( meuclidean @ X0 )
& ( mreflexive @ X0 ) )
<=> ( ( meuclidean @ X0 )
& ( mreflexive @ X0 )
& ( msymmetric @ X0 )
& ( mtransitive @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( ( meuclidean @ X0 )
& ( mreflexive @ X0 ) )
<=> ( ( meuclidean @ X0 )
& ( mreflexive @ X0 )
& ( msymmetric @ X0 )
& ( mtransitive @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f49,plain,
~ ! [X0: $i > $i > $o] :
( ( ( meuclidean @ X0 )
& ( mreflexive @ X0 ) )
<=> ( ( meuclidean @ X0 )
& ( mreflexive @ X0 )
& ( msymmetric @ X0 )
& ( mtransitive @ X0 ) ) ),
inference(rectify,[],[f33]) ).
thf(f50,plain,
~ ! [X0: $i > $i > $o] :
( ( ( ( meuclidean @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true ) )
<=> ( ( ( mreflexive @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f53,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f54,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f73,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(f74,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,[],[f73]) ).
thf(f75,plain,
( meuclidean
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X2 )
& ( X0 @ X3 @ X1 ) )
=> ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f22]) ).
thf(f76,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f75]) ).
thf(f80,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
=> ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f81,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f80]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( ( ( meuclidean @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true ) )
<~> ( ( ( mreflexive @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) ) ),
inference(ennf_transformation,[],[f50]) ).
thf(f88,plain,
? [X0: $i > $i > $o] :
( ( ( ( mreflexive @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true )
| ( ( msymmetric @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true )
| ( ( mtransitive @ X0 )
!= $true ) )
& ( ( ( ( mreflexive @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) )
| ( ( ( meuclidean @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f87]) ).
thf(f89,plain,
? [X0: $i > $i > $o] :
( ( ( ( mreflexive @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true )
| ( ( msymmetric @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true )
| ( ( mtransitive @ X0 )
!= $true ) )
& ( ( ( ( mreflexive @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) )
| ( ( ( meuclidean @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true ) ) ) ),
inference(flattening,[],[f88]) ).
thf(f90,plain,
( ( ( ( mreflexive @ sK0 )
!= $true )
| ( $true
!= ( meuclidean @ sK0 ) )
| ( $true
!= ( meuclidean @ sK0 ) )
| ( $true
!= ( msymmetric @ sK0 ) )
| ( ( mreflexive @ sK0 )
!= $true )
| ( $true
!= ( mtransitive @ sK0 ) ) )
& ( ( ( ( mreflexive @ sK0 )
= $true )
& ( $true
= ( meuclidean @ sK0 ) ) )
| ( ( $true
= ( meuclidean @ sK0 ) )
& ( $true
= ( msymmetric @ sK0 ) )
& ( ( mreflexive @ sK0 )
= $true )
& ( $true
= ( mtransitive @ sK0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f89]) ).
thf(f99,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,[],[f74]) ).
thf(f109,plain,
( ( $true
= ( meuclidean @ sK0 ) )
| ( $true
= ( meuclidean @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f111,plain,
( ( ( mreflexive @ sK0 )
= $true )
| ( ( mreflexive @ sK0 )
= $true ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f114,plain,
( ( ( mreflexive @ sK0 )
!= $true )
| ( $true
!= ( meuclidean @ sK0 ) )
| ( $true
!= ( meuclidean @ sK0 ) )
| ( $true
!= ( msymmetric @ sK0 ) )
| ( ( mreflexive @ sK0 )
!= $true )
| ( $true
!= ( mtransitive @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f115,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f76]) ).
thf(f118,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f125,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f142,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 )
!= $true )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK0 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK0 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
@ sK0 ) )
| ( ( ^ [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 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ sK0 )
!= $true ) ),
inference(definition_unfolding,[],[f114,f118,f115,f115,f125,f118,f99]) ).
thf(f145,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 )
= $true )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 )
= $true ) ),
inference(definition_unfolding,[],[f111,f118,f118]) ).
thf(f147,plain,
( ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK0 ) )
| ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f109,f115,f115]) ).
thf(f151,plain,
( ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK0 ) )
| ( ( ^ [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] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 )
!= $true )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
@ sK0 ) ) ),
inference(duplicate_literal_removal,[],[f142]) ).
thf(f152,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
!= $true )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) )
!= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) )
!= $true ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
( ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) )
!= $true )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ sK1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) )
!= $true ) ),
inference(sigma_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ sK1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) )
!= $true )
| ( ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ sK2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) )
!= $true ) ),
inference(sigma_proxy_clausification,[],[f153]) ).
thf(f155,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ sK1 ) )
| ( ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ sK2 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
@ sK3 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) )
!= $true ) ),
inference(sigma_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
@ sK3 ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) )
@ sK4 )
= $false )
| ( ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ sK2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f155]) ).
thf(f157,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ sK4 @ Y1 )
& ( sK0 @ sK4 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK3 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ sK3 ) ) ) )
= $false )
| ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK1 @ Y0 )
=> ( sK0 @ Y0 @ sK1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f158,plain,
( ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK1 @ Y0 )
=> ( sK0 @ Y0 @ sK1 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK3 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ sK3 ) ) ) )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ sK4 @ Y1 )
& ( sK0 @ sK4 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK3 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ sK3 ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK0 @ sK1 @ Y0 )
=> ( sK0 @ Y0 @ sK1 ) )
@ sK6 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ sK4 @ Y1 )
& ( sK0 @ sK4 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( ( ( ^ [Y0: $i] :
( ( sK0 @ sK1 @ Y0 )
=> ( sK0 @ Y0 @ sK1 ) )
@ sK6 )
= $false )
| ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ sK3 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ sK3 ) ) )
@ sK7 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ sK4 @ Y1 )
& ( sK0 @ sK4 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( ( ( sK0 @ sK1 @ sK6 )
=> ( sK0 @ sK6 @ sK1 ) )
= $false )
| ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK3 )
& ( sK0 @ sK7 @ Y0 ) )
=> ( sK0 @ sK7 @ sK3 ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK4 @ Y0 )
& ( sK0 @ sK4 @ sK5 ) )
=> ( sK0 @ Y0 @ sK5 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f162,plain,
( ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK3 )
& ( sK0 @ sK7 @ Y0 ) )
=> ( sK0 @ sK7 @ sK3 ) ) )
= $false )
| ( $false
= ( sK0 @ sK6 @ sK1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK4 @ Y0 )
& ( sK0 @ sK4 @ sK5 ) )
=> ( sK0 @ Y0 @ sK5 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK3 )
& ( sK0 @ sK7 @ Y0 ) )
=> ( sK0 @ sK7 @ sK3 ) ) )
= $false )
| ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK4 @ Y0 )
& ( sK0 @ sK4 @ sK5 ) )
=> ( sK0 @ Y0 @ sK5 ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f161]) ).
thf(f164,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK4 @ Y0 )
& ( sK0 @ sK4 @ sK5 ) )
=> ( sK0 @ Y0 @ sK5 ) ) )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK3 )
& ( sK0 @ sK7 @ Y0 ) )
=> ( sK0 @ sK7 @ sK3 ) )
@ sK8 ) )
| ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( $true
= ( sK0 @ sK1 @ sK6 ) ) ),
inference(sigma_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( ( ^ [Y0: $i] :
( ( ( sK0 @ sK4 @ Y0 )
& ( sK0 @ sK4 @ sK5 ) )
=> ( sK0 @ Y0 @ sK5 ) )
@ sK9 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK3 )
& ( sK0 @ sK7 @ Y0 ) )
=> ( sK0 @ sK7 @ sK3 ) )
@ sK8 ) ) ),
inference(sigma_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( $false
= ( ( ( sK0 @ sK4 @ sK9 )
& ( sK0 @ sK4 @ sK5 ) )
=> ( sK0 @ sK9 @ sK5 ) ) )
| ( ( ( ( sK0 @ sK8 @ sK3 )
& ( sK0 @ sK7 @ sK8 ) )
=> ( sK0 @ sK7 @ sK3 ) )
= $false )
| ( $true
= ( sK0 @ sK1 @ sK6 ) ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
( ( $false
= ( sK0 @ sK9 @ sK5 ) )
| ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ( ( ( ( sK0 @ sK8 @ sK3 )
& ( sK0 @ sK7 @ sK8 ) )
=> ( sK0 @ sK7 @ sK3 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( $true
= ( ( sK0 @ sK4 @ sK9 )
& ( sK0 @ sK4 @ sK5 ) ) )
| ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ( ( ( ( sK0 @ sK8 @ sK3 )
& ( sK0 @ sK7 @ sK8 ) )
=> ( sK0 @ sK7 @ sK3 ) )
= $false )
| ( $false
= ( sK0 @ sK2 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f166]) ).
thf(f169,plain,
( ( $true
= ( sK0 @ sK4 @ sK5 ) )
| ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ( ( ( ( sK0 @ sK8 @ sK3 )
& ( sK0 @ sK7 @ sK8 ) )
=> ( sK0 @ sK7 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( $true
= ( sK0 @ sK4 @ sK9 ) )
| ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( ( ( ( sK0 @ sK8 @ sK3 )
& ( sK0 @ sK7 @ sK8 ) )
=> ( sK0 @ sK7 @ sK3 ) )
= $false ) ),
inference(and_proxy_clausification,[],[f168]) ).
thf(f171,plain,
( ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( $true
= ( sK0 @ sK4 @ sK9 ) )
| ( $false
= ( sK0 @ sK7 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ( $true
= ( sK0 @ sK4 @ sK9 ) )
| ( ( ( sK0 @ sK8 @ sK3 )
& ( sK0 @ sK7 @ sK8 ) )
= $true )
| ( $false
= ( sK0 @ sK2 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f170]) ).
thf(f173,plain,
( ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ( ( sK0 @ sK7 @ sK8 )
= $true )
| ( $true
= ( sK0 @ sK4 @ sK9 ) )
| ( $false
= ( sK0 @ sK2 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( $true
= ( sK0 @ sK4 @ sK9 ) )
| ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ( $false
= ( sK0 @ sK2 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f172]) ).
thf(f175,plain,
( ( $false
= ( sK0 @ sK7 @ sK3 ) )
| ( $true
= ( sK0 @ sK4 @ sK5 ) )
| ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ( $false
= ( sK0 @ sK2 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f169]) ).
thf(f176,plain,
( ( $true
= ( sK0 @ sK4 @ sK5 ) )
| ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ( ( ( sK0 @ sK8 @ sK3 )
& ( sK0 @ sK7 @ sK8 ) )
= $true )
| ( $false
= ( sK0 @ sK2 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f169]) ).
thf(f177,plain,
( ( $true
= ( sK0 @ sK4 @ sK5 ) )
| ( ( sK0 @ sK7 @ sK8 )
= $true )
| ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( $true
= ( sK0 @ sK1 @ sK6 ) ) ),
inference(and_proxy_clausification,[],[f176]) ).
thf(f178,plain,
( ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ( $true
= ( sK0 @ sK4 @ sK5 ) )
| ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( $true
= ( sK0 @ sK8 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f176]) ).
thf(f179,plain,
( ( $false
= ( sK0 @ sK9 @ sK5 ) )
| ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( $false
= ( sK0 @ sK7 @ sK3 ) )
| ( $true
= ( sK0 @ sK1 @ sK6 ) ) ),
inference(imp_proxy_clausification,[],[f167]) ).
thf(f180,plain,
( ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ( $false
= ( sK0 @ sK9 @ sK5 ) )
| ( ( ( sK0 @ sK8 @ sK3 )
& ( sK0 @ sK7 @ sK8 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f167]) ).
thf(f181,plain,
( ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( ( sK0 @ sK7 @ sK8 )
= $true )
| ( $false
= ( sK0 @ sK9 @ sK5 ) ) ),
inference(and_proxy_clausification,[],[f180]) ).
thf(f182,plain,
( ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( $false
= ( sK0 @ sK9 @ sK5 ) ) ),
inference(and_proxy_clausification,[],[f180]) ).
thf(f183,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK4 @ Y0 )
& ( sK0 @ sK4 @ sK5 ) )
=> ( sK0 @ Y0 @ sK5 ) ) )
= $false )
| ( $false
= ( sK0 @ sK6 @ sK1 ) )
| ( ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK3 )
& ( sK0 @ sK7 @ Y0 ) )
=> ( sK0 @ sK7 @ sK3 ) )
@ sK10 )
= $false )
| ( $false
= ( sK0 @ sK2 @ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f162]) ).
thf(f184,plain,
( ( $false
= ( sK0 @ sK6 @ sK1 ) )
| ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK3 )
& ( sK0 @ sK7 @ Y0 ) )
=> ( sK0 @ sK7 @ sK3 ) )
@ sK10 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK4 @ Y0 )
& ( sK0 @ sK4 @ sK5 ) )
=> ( sK0 @ Y0 @ sK5 ) )
@ sK11 ) ) ),
inference(sigma_proxy_clausification,[],[f183]) ).
thf(f185,plain,
( ( $false
= ( sK0 @ sK6 @ sK1 ) )
| ( $false
= ( ( ( sK0 @ sK4 @ sK11 )
& ( sK0 @ sK4 @ sK5 ) )
=> ( sK0 @ sK11 @ sK5 ) ) )
| ( $false
= ( ( ( sK0 @ sK10 @ sK3 )
& ( sK0 @ sK7 @ sK10 ) )
=> ( sK0 @ sK7 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK2 @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f184]) ).
thf(f186,plain,
( ( $false
= ( sK0 @ sK11 @ sK5 ) )
| ( $false
= ( ( ( sK0 @ sK10 @ sK3 )
& ( sK0 @ sK7 @ sK10 ) )
=> ( sK0 @ sK7 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( $false
= ( sK0 @ sK6 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f185]) ).
thf(f187,plain,
( ( $false
= ( sK0 @ sK6 @ sK1 ) )
| ( $false
= ( ( ( sK0 @ sK10 @ sK3 )
& ( sK0 @ sK7 @ sK10 ) )
=> ( sK0 @ sK7 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( $true
= ( ( sK0 @ sK4 @ sK11 )
& ( sK0 @ sK4 @ sK5 ) ) ) ),
inference(imp_proxy_clausification,[],[f185]) ).
thf(f188,plain,
( ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( $false
= ( sK0 @ sK7 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK4 @ sK11 )
& ( sK0 @ sK4 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK6 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f187]) ).
thf(f189,plain,
( ( $true
= ( ( sK0 @ sK4 @ sK11 )
& ( sK0 @ sK4 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK6 @ sK1 ) )
| ( ( ( sK0 @ sK10 @ sK3 )
& ( sK0 @ sK7 @ sK10 ) )
= $true )
| ( $false
= ( sK0 @ sK2 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f187]) ).
thf(f190,plain,
( ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( $false
= ( sK0 @ sK6 @ sK1 ) )
| ( $true
= ( sK0 @ sK4 @ sK5 ) )
| ( ( ( sK0 @ sK10 @ sK3 )
& ( sK0 @ sK7 @ sK10 ) )
= $true ) ),
inference(and_proxy_clausification,[],[f189]) ).
thf(f191,plain,
( ( $false
= ( sK0 @ sK6 @ sK1 ) )
| ( ( ( sK0 @ sK10 @ sK3 )
& ( sK0 @ sK7 @ sK10 ) )
= $true )
| ( ( sK0 @ sK4 @ sK11 )
= $true )
| ( $false
= ( sK0 @ sK2 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f189]) ).
thf(f192,plain,
( ( $true
= ( sK0 @ sK7 @ sK10 ) )
| ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( $false
= ( sK0 @ sK6 @ sK1 ) )
| ( ( sK0 @ sK4 @ sK11 )
= $true ) ),
inference(and_proxy_clausification,[],[f191]) ).
thf(f193,plain,
( ( ( sK0 @ sK10 @ sK3 )
= $true )
| ( $false
= ( sK0 @ sK6 @ sK1 ) )
| ( ( sK0 @ sK4 @ sK11 )
= $true )
| ( $false
= ( sK0 @ sK2 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f191]) ).
thf(f194,plain,
( ( $true
= ( sK0 @ sK4 @ sK5 ) )
| ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( $true
= ( sK0 @ sK7 @ sK10 ) )
| ( $false
= ( sK0 @ sK6 @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f190]) ).
thf(f195,plain,
( ( $false
= ( sK0 @ sK6 @ sK1 ) )
| ( ( sK0 @ sK10 @ sK3 )
= $true )
| ( $true
= ( sK0 @ sK4 @ sK5 ) )
| ( $false
= ( sK0 @ sK2 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f190]) ).
thf(f196,plain,
( ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( $true
= ( sK0 @ sK4 @ sK5 ) )
| ( $false
= ( sK0 @ sK6 @ sK1 ) )
| ( $false
= ( sK0 @ sK7 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f188]) ).
thf(f197,plain,
( ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( $false
= ( sK0 @ sK7 @ sK3 ) )
| ( $false
= ( sK0 @ sK6 @ sK1 ) )
| ( ( sK0 @ sK4 @ sK11 )
= $true ) ),
inference(and_proxy_clausification,[],[f188]) ).
thf(f198,plain,
( ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( $false
= ( sK0 @ sK7 @ sK3 ) )
| ( $false
= ( sK0 @ sK6 @ sK1 ) )
| ( $false
= ( sK0 @ sK11 @ sK5 ) ) ),
inference(imp_proxy_clausification,[],[f186]) ).
thf(f199,plain,
( ( $false
= ( sK0 @ sK11 @ sK5 ) )
| ( ( ( sK0 @ sK10 @ sK3 )
& ( sK0 @ sK7 @ sK10 ) )
= $true )
| ( $false
= ( sK0 @ sK6 @ sK1 ) )
| ( $false
= ( sK0 @ sK2 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f186]) ).
thf(f200,plain,
( ( $false
= ( sK0 @ sK11 @ sK5 ) )
| ( $true
= ( sK0 @ sK7 @ sK10 ) )
| ( $false
= ( sK0 @ sK6 @ sK1 ) )
| ( $false
= ( sK0 @ sK2 @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f199]) ).
thf(f201,plain,
( ( $false
= ( sK0 @ sK11 @ sK5 ) )
| ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ( $false
= ( sK0 @ sK6 @ sK1 ) )
| ( ( sK0 @ sK10 @ sK3 )
= $true ) ),
inference(and_proxy_clausification,[],[f199]) ).
thf(f202,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK0 ) ),
inference(duplicate_literal_removal,[],[f147]) ).
thf(f203,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f202]) ).
thf(f204,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ X1 @ Y1 )
& ( sK0 @ X1 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f204]) ).
thf(f206,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ X1 @ Y1 )
& ( sK0 @ X1 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ X1 @ Y0 )
& ( sK0 @ X1 @ X2 ) )
=> ( sK0 @ Y0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f206]) ).
thf(f208,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( sK0 @ X1 @ Y0 )
& ( sK0 @ X1 @ X2 ) )
=> ( sK0 @ Y0 @ X2 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( sK0 @ X1 @ X3 )
& ( sK0 @ X1 @ X2 ) )
=> ( sK0 @ X3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f208]) ).
thf(f210,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( sK0 @ X3 @ X2 )
= $true )
| ( $false
= ( ( sK0 @ X1 @ X3 )
& ( sK0 @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f209]) ).
thf(f211,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( sK0 @ X3 @ X2 )
= $true )
| ( ( sK0 @ X1 @ X2 )
= $false )
| ( ( sK0 @ X1 @ X3 )
= $false ) ),
inference(and_proxy_clausification,[],[f210]) ).
thf(f229,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 )
= $true ),
inference(duplicate_literal_removal,[],[f145]) ).
thf(f230,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f229]) ).
thf(f231,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f230]) ).
thf(f232,plain,
! [X1: $i] :
( ( sK0 @ X1 @ X1 )
= $true ),
inference(beta-eta_normalization,[],[f231]) ).
thf(f280,definition,
( spl12_1
<=> ( $true
= ( sK0 @ sK8 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
thf(f282,plain,
( ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f280]) ).
thf(f284,definition,
( spl12_2
<=> ( $false
= ( sK0 @ sK2 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
thf(f286,plain,
( ( $false
= ( sK0 @ sK2 @ sK2 ) )
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f284]) ).
thf(f288,definition,
( spl12_3
<=> ( $true
= ( sK0 @ sK1 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
thf(f290,plain,
( ( $true
= ( sK0 @ sK1 @ sK6 ) )
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f288]) ).
thf(f292,definition,
( spl12_4
<=> ( $true
= ( sK0 @ sK4 @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
thf(f294,plain,
( ( $true
= ( sK0 @ sK4 @ sK9 ) )
| ~ spl12_4 ),
inference(avatar_component_clause,[],[f292]) ).
thf(f295,plain,
( spl12_1
| spl12_2
| spl12_3
| spl12_4 ),
inference(avatar_split_clause,[],[f174,f292,f288,f284,f280]) ).
thf(f297,definition,
( spl12_5
<=> ( ( sK0 @ sK7 @ sK8 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
thf(f299,plain,
( ( ( sK0 @ sK7 @ sK8 )
= $true )
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f297]) ).
thf(f300,plain,
( spl12_3
| spl12_5
| spl12_4
| spl12_2 ),
inference(avatar_split_clause,[],[f173,f284,f292,f297,f288]) ).
thf(f302,definition,
( spl12_6
<=> ( $false
= ( sK0 @ sK7 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_6])],[avatar_definition]) ).
thf(f304,plain,
( ( $false
= ( sK0 @ sK7 @ sK3 ) )
| ~ spl12_6 ),
inference(avatar_component_clause,[],[f302]) ).
thf(f305,plain,
( spl12_2
| spl12_4
| spl12_6
| spl12_3 ),
inference(avatar_split_clause,[],[f171,f288,f302,f292,f284]) ).
thf(f307,definition,
( spl12_7
<=> ( $true
= ( sK0 @ sK4 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_7])],[avatar_definition]) ).
thf(f309,plain,
( ( $true
= ( sK0 @ sK4 @ sK5 ) )
| ~ spl12_7 ),
inference(avatar_component_clause,[],[f307]) ).
thf(f310,plain,
( spl12_2
| spl12_7
| spl12_1
| spl12_3 ),
inference(avatar_split_clause,[],[f178,f288,f280,f307,f284]) ).
thf(f311,plain,
( spl12_3
| spl12_7
| spl12_2
| spl12_5 ),
inference(avatar_split_clause,[],[f177,f297,f284,f307,f288]) ).
thf(f312,plain,
( spl12_6
| spl12_7
| spl12_2
| spl12_3 ),
inference(avatar_split_clause,[],[f175,f288,f284,f307,f302]) ).
thf(f314,definition,
( spl12_8
<=> ( $false
= ( sK0 @ sK9 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_8])],[avatar_definition]) ).
thf(f316,plain,
( ( $false
= ( sK0 @ sK9 @ sK5 ) )
| ~ spl12_8 ),
inference(avatar_component_clause,[],[f314]) ).
thf(f317,plain,
( spl12_1
| spl12_8
| spl12_2
| spl12_3 ),
inference(avatar_split_clause,[],[f182,f288,f284,f314,f280]) ).
thf(f318,plain,
( spl12_2
| spl12_3
| spl12_8
| spl12_5 ),
inference(avatar_split_clause,[],[f181,f297,f314,f288,f284]) ).
thf(f319,plain,
( spl12_3
| spl12_6
| spl12_8
| spl12_2 ),
inference(avatar_split_clause,[],[f179,f284,f314,f302,f288]) ).
thf(f321,definition,
( spl12_9
<=> ( ( sK0 @ sK4 @ sK11 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl12_9])],[avatar_definition]) ).
thf(f323,plain,
( ( ( sK0 @ sK4 @ sK11 )
= $true )
| ~ spl12_9 ),
inference(avatar_component_clause,[],[f321]) ).
thf(f325,definition,
( spl12_10
<=> ( ( sK0 @ sK10 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl12_10])],[avatar_definition]) ).
thf(f327,plain,
( ( ( sK0 @ sK10 @ sK3 )
= $true )
| ~ spl12_10 ),
inference(avatar_component_clause,[],[f325]) ).
thf(f329,definition,
( spl12_11
<=> ( $false
= ( sK0 @ sK6 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_11])],[avatar_definition]) ).
thf(f331,plain,
( ( $false
= ( sK0 @ sK6 @ sK1 ) )
| ~ spl12_11 ),
inference(avatar_component_clause,[],[f329]) ).
thf(f332,plain,
( spl12_9
| spl12_2
| spl12_10
| spl12_11 ),
inference(avatar_split_clause,[],[f193,f329,f325,f284,f321]) ).
thf(f334,definition,
( spl12_12
<=> ( $true
= ( sK0 @ sK7 @ sK10 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_12])],[avatar_definition]) ).
thf(f336,plain,
( ( $true
= ( sK0 @ sK7 @ sK10 ) )
| ~ spl12_12 ),
inference(avatar_component_clause,[],[f334]) ).
thf(f337,plain,
( spl12_11
| spl12_2
| spl12_12
| spl12_9 ),
inference(avatar_split_clause,[],[f192,f321,f334,f284,f329]) ).
thf(f338,plain,
( spl12_10
| spl12_2
| spl12_11
| spl12_7 ),
inference(avatar_split_clause,[],[f195,f307,f329,f284,f325]) ).
thf(f339,plain,
( spl12_2
| spl12_7
| spl12_12
| spl12_11 ),
inference(avatar_split_clause,[],[f194,f329,f334,f307,f284]) ).
thf(f340,plain,
( spl12_9
| spl12_6
| spl12_2
| spl12_11 ),
inference(avatar_split_clause,[],[f197,f329,f284,f302,f321]) ).
thf(f341,plain,
( spl12_11
| spl12_6
| spl12_7
| spl12_2 ),
inference(avatar_split_clause,[],[f196,f284,f307,f302,f329]) ).
thf(f343,definition,
( spl12_13
<=> ( $false
= ( sK0 @ sK11 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_13])],[avatar_definition]) ).
thf(f345,plain,
( ( $false
= ( sK0 @ sK11 @ sK5 ) )
| ~ spl12_13 ),
inference(avatar_component_clause,[],[f343]) ).
thf(f346,plain,
( spl12_10
| spl12_13
| spl12_2
| spl12_11 ),
inference(avatar_split_clause,[],[f201,f329,f284,f343,f325]) ).
thf(f347,plain,
( spl12_2
| spl12_11
| spl12_12
| spl12_13 ),
inference(avatar_split_clause,[],[f200,f343,f334,f329,f284]) ).
thf(f348,plain,
( spl12_13
| spl12_11
| spl12_2
| spl12_6 ),
inference(avatar_split_clause,[],[f198,f302,f284,f329,f343]) ).
thf(f350,definition,
( spl12_14
<=> ! [X2: $i,X3: $i] :
( ( $false
= ( sK0 @ X2 @ X3 ) )
| ( ( sK0 @ X3 @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl12_14])],[avatar_definition]) ).
thf(f351,plain,
( ! [X2: $i,X3: $i] :
( ( $false
= ( sK0 @ X2 @ X3 ) )
| ( ( sK0 @ X3 @ X2 )
= $true ) )
| ~ spl12_14 ),
inference(avatar_component_clause,[],[f350]) ).
thf(f353,definition,
( spl12_15
<=> ! [X1: $i] :
( ( sK0 @ X1 @ X1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl12_15])],[avatar_definition]) ).
thf(f354,plain,
( ! [X1: $i] :
( ( sK0 @ X1 @ X1 )
= $true )
| ~ spl12_15 ),
inference(avatar_component_clause,[],[f353]) ).
thf(f360,plain,
spl12_15,
inference(avatar_split_clause,[],[f232,f353]) ).
thf(f361,plain,
( ( $false = $true )
| ~ spl12_2
| ~ spl12_15 ),
inference(forward_demodulation,[],[f286,f354]) ).
thf(f362,plain,
( $false
| ~ spl12_2
| ~ spl12_15 ),
inference(trivial_inequality_removal,[],[f361]) ).
thf(f363,plain,
( ~ spl12_2
| ~ spl12_15 ),
inference(avatar_contradiction_clause,[],[f362]) ).
thf(f371,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X0 @ X1 ) )
| ( ( sK0 @ X1 @ X0 )
= $true )
| ( $false = $true ) )
| ~ spl12_15 ),
inference(constrained_superposition,[],[f354,f211]) ).
thf(f381,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X0 @ X1 ) )
| ( ( sK0 @ X1 @ X0 )
= $true ) )
| ~ spl12_15 ),
inference(trivial_inequality_removal,[],[f371]) ).
thf(f386,plain,
( spl12_14
| ~ spl12_15 ),
inference(avatar_split_clause,[],[f381,f353,f350]) ).
thf(f387,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 @ sK5 )
= $false )
| ( ( sK0 @ X0 @ sK9 )
= $false )
| ( $false = $true ) )
| ~ spl12_8 ),
inference(constrained_superposition,[],[f316,f211]) ).
thf(f389,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 @ sK9 )
= $false )
| ( ( sK0 @ X0 @ sK5 )
= $false ) )
| ~ spl12_8 ),
inference(trivial_inequality_removal,[],[f387]) ).
thf(f408,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK1 @ sK6 ) )
| ~ spl12_11
| ~ spl12_14 ),
inference(constrained_superposition,[],[f351,f331]) ).
thf(f416,plain,
( ( $false
= ( sK0 @ sK1 @ sK6 ) )
| ~ spl12_11
| ~ spl12_14 ),
inference(trivial_inequality_removal,[],[f408]) ).
thf(f442,plain,
( ( $false
= ( sK0 @ sK4 @ sK5 ) )
| ( $false = $true )
| ~ spl12_4
| ~ spl12_8 ),
inference(constrained_superposition,[],[f294,f389]) ).
thf(f447,plain,
( ( $false
= ( sK0 @ sK4 @ sK5 ) )
| ~ spl12_4
| ~ spl12_8 ),
inference(trivial_inequality_removal,[],[f442]) ).
thf(f454,plain,
( ( $false = $true )
| ~ spl12_4
| ~ spl12_7
| ~ spl12_8 ),
inference(forward_demodulation,[],[f447,f309]) ).
thf(f455,plain,
( $false
| ~ spl12_4
| ~ spl12_7
| ~ spl12_8 ),
inference(trivial_inequality_removal,[],[f454]) ).
thf(f456,plain,
( ~ spl12_4
| ~ spl12_7
| ~ spl12_8 ),
inference(avatar_contradiction_clause,[],[f455]) ).
thf(f457,plain,
( ( $false = $true )
| ~ spl12_3
| ~ spl12_11
| ~ spl12_14 ),
inference(forward_demodulation,[],[f290,f416]) ).
thf(f458,plain,
( $false
| ~ spl12_3
| ~ spl12_11
| ~ spl12_14 ),
inference(trivial_inequality_removal,[],[f457]) ).
thf(f459,plain,
( ~ spl12_3
| ~ spl12_11
| ~ spl12_14 ),
inference(avatar_contradiction_clause,[],[f458]) ).
thf(f463,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( sK0 @ X0 @ sK11 ) )
| ( ( sK0 @ X0 @ sK5 )
= $false ) )
| ~ spl12_13 ),
inference(constrained_superposition,[],[f211,f345]) ).
thf(f466,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK11 ) )
| ( ( sK0 @ X0 @ sK5 )
= $false ) )
| ~ spl12_13 ),
inference(trivial_inequality_removal,[],[f463]) ).
thf(f499,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK4 @ sK5 ) )
| ~ spl12_9
| ~ spl12_13 ),
inference(constrained_superposition,[],[f323,f466]) ).
thf(f502,plain,
( ( $false
= ( sK0 @ sK4 @ sK5 ) )
| ~ spl12_9
| ~ spl12_13 ),
inference(trivial_inequality_removal,[],[f499]) ).
thf(f511,plain,
( ( $false = $true )
| ~ spl12_7
| ~ spl12_9
| ~ spl12_13 ),
inference(forward_demodulation,[],[f502,f309]) ).
thf(f512,plain,
( $false
| ~ spl12_7
| ~ spl12_9
| ~ spl12_13 ),
inference(trivial_inequality_removal,[],[f511]) ).
thf(f513,plain,
( ~ spl12_7
| ~ spl12_9
| ~ spl12_13 ),
inference(avatar_contradiction_clause,[],[f512]) ).
thf(f517,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 @ sK3 )
= $false )
| ( ( sK0 @ X0 @ sK7 )
= $false )
| ( $false = $true ) )
| ~ spl12_6 ),
inference(constrained_superposition,[],[f211,f304]) ).
thf(f520,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 @ sK7 )
= $false )
| ( ( sK0 @ X0 @ sK3 )
= $false ) )
| ~ spl12_6 ),
inference(trivial_inequality_removal,[],[f517]) ).
thf(f554,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 @ sK3 )
= $false )
| ( $false
= ( sK0 @ sK7 @ X0 ) )
| ( $false = $true ) )
| ~ spl12_6
| ~ spl12_14 ),
inference(constrained_superposition,[],[f351,f520]) ).
thf(f558,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 @ sK3 )
= $false )
| ( $false
= ( sK0 @ sK7 @ X0 ) ) )
| ~ spl12_6
| ~ spl12_14 ),
inference(trivial_inequality_removal,[],[f554]) ).
thf(f1368,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK7 @ sK10 ) )
| ~ spl12_6
| ~ spl12_10
| ~ spl12_14 ),
inference(constrained_superposition,[],[f327,f558]) ).
thf(f1384,plain,
( ( $false
= ( sK0 @ sK7 @ sK10 ) )
| ~ spl12_6
| ~ spl12_10
| ~ spl12_14 ),
inference(trivial_inequality_removal,[],[f1368]) ).
thf(f1403,plain,
( ( $false = $true )
| ~ spl12_6
| ~ spl12_10
| ~ spl12_12
| ~ spl12_14 ),
inference(forward_demodulation,[],[f1384,f336]) ).
thf(f1404,plain,
( $false
| ~ spl12_6
| ~ spl12_10
| ~ spl12_12
| ~ spl12_14 ),
inference(trivial_inequality_removal,[],[f1403]) ).
thf(f1405,plain,
( ~ spl12_6
| ~ spl12_10
| ~ spl12_12
| ~ spl12_14 ),
inference(avatar_contradiction_clause,[],[f1404]) ).
thf(f1421,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK7 @ sK8 ) )
| ~ spl12_1
| ~ spl12_6
| ~ spl12_14 ),
inference(constrained_superposition,[],[f558,f282]) ).
thf(f1431,plain,
( ( $false
= ( sK0 @ sK7 @ sK8 ) )
| ~ spl12_1
| ~ spl12_6
| ~ spl12_14 ),
inference(trivial_inequality_removal,[],[f1421]) ).
thf(f1437,plain,
( ( $false = $true )
| ~ spl12_1
| ~ spl12_5
| ~ spl12_6
| ~ spl12_14 ),
inference(forward_demodulation,[],[f1431,f299]) ).
thf(f1438,plain,
( $false
| ~ spl12_1
| ~ spl12_5
| ~ spl12_6
| ~ spl12_14 ),
inference(trivial_inequality_removal,[],[f1437]) ).
thf(f1439,plain,
( ~ spl12_1
| ~ spl12_5
| ~ spl12_6
| ~ spl12_14 ),
inference(avatar_contradiction_clause,[],[f1438]) ).
cnf(s1,plain,
( spl12_1
| spl12_2
| spl12_3
| spl12_4 ),
inference(sat_conversion,[],[f295]) ).
cnf(s2,plain,
( spl12_2
| spl12_3
| spl12_4
| spl12_5 ),
inference(sat_conversion,[],[f300]) ).
cnf(s3,plain,
( spl12_2
| spl12_3
| spl12_4
| spl12_6 ),
inference(sat_conversion,[],[f305]) ).
cnf(s4,plain,
( spl12_1
| spl12_2
| spl12_3
| spl12_7 ),
inference(sat_conversion,[],[f310]) ).
cnf(s5,plain,
( spl12_2
| spl12_3
| spl12_5
| spl12_7 ),
inference(sat_conversion,[],[f311]) ).
cnf(s6,plain,
( spl12_2
| spl12_3
| spl12_6
| spl12_7 ),
inference(sat_conversion,[],[f312]) ).
cnf(s7,plain,
( spl12_1
| spl12_2
| spl12_3
| spl12_8 ),
inference(sat_conversion,[],[f317]) ).
cnf(s8,plain,
( spl12_2
| spl12_3
| spl12_5
| spl12_8 ),
inference(sat_conversion,[],[f318]) ).
cnf(s9,plain,
( spl12_2
| spl12_3
| spl12_6
| spl12_8 ),
inference(sat_conversion,[],[f319]) ).
cnf(s10,plain,
( spl12_2
| spl12_9
| spl12_10
| spl12_11 ),
inference(sat_conversion,[],[f332]) ).
cnf(s11,plain,
( spl12_2
| spl12_9
| spl12_11
| spl12_12 ),
inference(sat_conversion,[],[f337]) ).
cnf(s12,plain,
( spl12_2
| spl12_7
| spl12_10
| spl12_11 ),
inference(sat_conversion,[],[f338]) ).
cnf(s13,plain,
( spl12_2
| spl12_7
| spl12_11
| spl12_12 ),
inference(sat_conversion,[],[f339]) ).
cnf(s14,plain,
( spl12_2
| spl12_6
| spl12_9
| spl12_11 ),
inference(sat_conversion,[],[f340]) ).
cnf(s15,plain,
( spl12_2
| spl12_6
| spl12_7
| spl12_11 ),
inference(sat_conversion,[],[f341]) ).
cnf(s16,plain,
( spl12_2
| spl12_10
| spl12_11
| spl12_13 ),
inference(sat_conversion,[],[f346]) ).
cnf(s17,plain,
( spl12_2
| spl12_11
| spl12_12
| spl12_13 ),
inference(sat_conversion,[],[f347]) ).
cnf(s18,plain,
( spl12_2
| spl12_6
| spl12_11
| spl12_13 ),
inference(sat_conversion,[],[f348]) ).
cnf(s21,plain,
spl12_15,
inference(sat_conversion,[],[f360]) ).
cnf(s22,plain,
( ~ spl12_2
| ~ spl12_15 ),
inference(sat_conversion,[],[f363]) ).
cnf(s23,plain,
( spl12_14
| ~ spl12_15 ),
inference(sat_conversion,[],[f386]) ).
cnf(s28,plain,
( ~ spl12_4
| ~ spl12_7
| ~ spl12_8 ),
inference(sat_conversion,[],[f456]) ).
cnf(s29,plain,
( ~ spl12_3
| ~ spl12_11
| ~ spl12_14 ),
inference(sat_conversion,[],[f459]) ).
cnf(s31,plain,
( ~ spl12_7
| ~ spl12_9
| ~ spl12_13 ),
inference(sat_conversion,[],[f513]) ).
cnf(s47,plain,
( ~ spl12_6
| ~ spl12_10
| ~ spl12_12
| ~ spl12_14 ),
inference(sat_conversion,[],[f1405]) ).
cnf(s49,plain,
( ~ spl12_1
| ~ spl12_5
| ~ spl12_6
| ~ spl12_14 ),
inference(sat_conversion,[],[f1439]) ).
cnf(s50,plain,
spl12_14,
inference(rat,[],[s23,s21]) ).
cnf(s51,plain,
~ spl12_2,
inference(rat,[],[s22,s21]) ).
cnf(s53,plain,
( spl12_6
| spl12_11
| spl12_13 ),
inference(rat,[],[s18,s51]) ).
cnf(s54,plain,
( spl12_11
| spl12_12
| spl12_13 ),
inference(rat,[],[s17,s51]) ).
cnf(s55,plain,
( spl12_10
| spl12_11
| spl12_13 ),
inference(rat,[],[s16,s51]) ).
cnf(s56,plain,
( spl12_6
| spl12_7
| spl12_11 ),
inference(rat,[],[s15,s51]) ).
cnf(s57,plain,
( spl12_6
| spl12_9
| spl12_11 ),
inference(rat,[],[s14,s51]) ).
cnf(s58,plain,
( spl12_7
| spl12_11
| spl12_12 ),
inference(rat,[],[s13,s51]) ).
cnf(s59,plain,
( spl12_7
| spl12_10
| spl12_11 ),
inference(rat,[],[s12,s51]) ).
cnf(s60,plain,
( spl12_9
| spl12_11
| spl12_12 ),
inference(rat,[],[s11,s51]) ).
cnf(s61,plain,
( spl12_9
| spl12_10
| spl12_11 ),
inference(rat,[],[s10,s51]) ).
cnf(s62,plain,
( spl12_3
| spl12_6
| spl12_8 ),
inference(rat,[],[s9,s51]) ).
cnf(s63,plain,
( spl12_3
| spl12_5
| spl12_8 ),
inference(rat,[],[s8,s51]) ).
cnf(s64,plain,
( spl12_1
| spl12_3
| spl12_8 ),
inference(rat,[],[s7,s51]) ).
cnf(s65,plain,
( spl12_3
| spl12_6
| spl12_7 ),
inference(rat,[],[s6,s51]) ).
cnf(s66,plain,
( spl12_3
| spl12_5
| spl12_7 ),
inference(rat,[],[s5,s51]) ).
cnf(s67,plain,
( spl12_1
| spl12_3
| spl12_7 ),
inference(rat,[],[s4,s51]) ).
cnf(s68,plain,
( spl12_3
| spl12_4
| spl12_6 ),
inference(rat,[],[s3,s51]) ).
cnf(s69,plain,
( spl12_3
| spl12_4
| spl12_5 ),
inference(rat,[],[s2,s51]) ).
cnf(s70,plain,
( spl12_1
| spl12_3
| spl12_4 ),
inference(rat,[],[s1,s51]) ).
cnf(s71,plain,
( spl12_3
| spl12_1 ),
inference(rat,[],[s28,s70,s67,s64]) ).
cnf(s72,plain,
( spl12_6
| ~ spl12_7
| spl12_11 ),
inference(rat,[],[s31,s57,s53]) ).
cnf(s73,plain,
( spl12_13
| ~ spl12_6
| spl12_11 ),
inference(rat,[],[s47,s55,s54,s50]) ).
cnf(s74,plain,
( ~ spl12_7
| spl12_11 ),
inference(rat,[],[s47,s61,s60,s31,s73,s72,s50]) ).
cnf(s75,plain,
( spl12_7
| spl12_11 ),
inference(rat,[],[s47,s59,s58,s56,s50]) ).
cnf(s76,plain,
spl12_11,
inference(rat,[],[s75,s74]) ).
cnf(s77,plain,
~ spl12_3,
inference(rat,[],[s29,s50,s76]) ).
cnf(s78,plain,
spl12_1,
inference(rat,[],[s71,s77]) ).
cnf(s79,plain,
( spl12_5
| ~ spl12_7 ),
inference(rat,[],[s28,s69,s63,s77]) ).
cnf(s80,plain,
~ spl12_7,
inference(rat,[],[s28,s68,s62,s49,s79,s77,s78,s50]) ).
cnf(s81,plain,
spl12_6,
inference(rat,[],[s65,s77,s80]) ).
cnf(s82,plain,
spl12_5,
inference(rat,[],[s66,s77,s80]) ).
cnf(s83,plain,
$false,
inference(rat,[],[s49,s50,s78,s81,s82]) ).
thf(f1440,plain,
$false,
inference(avatar_sat_refutation,[],[s83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL860^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n009.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 10:13:45 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.21/0.30 % (3809140)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.30 % (3809145)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1169619668:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.30 % (3809146)lrs+10_16_si=on:nwc=1.5:random_seed=644068931:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.30 % (3809147)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=190464326:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.30 % (3809147)Instruction limit reached!
% 0.21/0.30 % (3809147)------------------------------
% 0.21/0.30 % (3809147)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (3809147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (3809147)CaDiCaL version: 2.1.3
% 0.21/0.30 % (3809147)Termination reason: Instruction limit
% 0.21/0.30 % (3809147)Termination phase: Clausification
% 0.21/0.30 % (3809147)Time elapsed: 0.002 s
% 0.21/0.30 % (3809147)Peak memory usage: 10 MB
% 0.21/0.30 % (3809147)Instructions burned: 4 (million)
% 0.21/0.30 % (3809151)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.30 % (3809151)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.30 % (3809146)Instruction limit reached!
% 0.21/0.30 % (3809146)------------------------------
% 0.21/0.30 % (3809146)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (3809146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (3809146)CaDiCaL version: 2.1.3
% 0.21/0.30 % (3809146)Termination reason: Instruction limit
% 0.21/0.30 % (3809146)Termination phase: Saturation
% 0.21/0.30 % (3809146)Time elapsed: 0.009 s
% 0.21/0.30 % (3809146)Peak memory usage: 12 MB
% 0.21/0.30 % (3809146)Instructions burned: 18 (million)
% 0.21/0.30 % (3809150)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4178038798:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.30 % (3809151)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=550604275:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.30 % (3809148)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=1175821598:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.30 % (3809145) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3809140-3809145"...
% 0.21/0.30 % (3809149)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1797105942:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.30 % (3809151) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3809140-3809151"...
% 0.21/0.30 % (3809145)...printing done.
% 0.21/0.30 % (3809155)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=48444022:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.30 % (3809145)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.30 % (3809145)------------------------------
% 0.21/0.30 % (3809145)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (3809145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (3809145)CaDiCaL version: 2.1.3
% 0.21/0.30 % (3809145)Termination reason: Refutation
% 0.21/0.30 % (3809145)Time elapsed: 0.029 s
% 0.21/0.30 % (3809145)Peak memory usage: 13 MB
% 0.21/0.30 % (3809145)Instructions burned: 92 (million)
% 0.21/0.30 % (3809140)Success in time 0.055 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------