%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL863^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 08:15:11 AM UTC 2026
% Result : Theorem 0.85s 0.44s
% Output : Refutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 25
% Syntax : Number of formulae : 308 ( 27 unt; 0 typ; 19 def)
% Number of atoms : 3324 ( 594 equ; 0 cnn)
% Maximal formula atoms : 10 ( 10 avg)
% Number of connectives : 3569 ( 268 ~; 723 |; 141 &;2072 @)
% ( 23 <=>; 134 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 84 ( 84 >; 0 *; 0 +; 0 <<)
% Number of symbols : 84 ( 79 usr; 35 con; 0-4 aty)
% ( 190 !!; 17 ??; 0 @@+; 0 @@-)
% Number of variables : 562 ( 0 sgn 271 !; 5 ?; 562 :)
% 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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_35,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_36,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
vNOT: $o > $o ).
thf(func_def_38,type,
vOR: $o > $o > $o ).
thf(func_def_39,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vIMP: $o > $o > $o ).
thf(func_def_44,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_45,type,
vAND: $o > $o > $o ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
sK0: $i > $i > $o ).
thf(func_def_48,type,
sK1: $i > $i ).
thf(func_def_49,type,
sK2: $i > $i ).
thf(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f20,axiom,
( mserial
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mserial) ).
thf(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f22,axiom,
( meuclidean
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $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 ) )
<=> ( ( msymmetric @ X0 )
& ( mtransitive @ X0 )
& ( mserial @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( ( meuclidean @ X0 )
& ( mreflexive @ X0 ) )
<=> ( ( msymmetric @ X0 )
& ( mtransitive @ X0 )
& ( mserial @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f57,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f58,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f59,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f60,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f59]) ).
thf(f61,plain,
( mserial
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) ) ),
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(f63,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f64,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f65,plain,
( meuclidean
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f22]) ).
thf(f66,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f65]) ).
thf(f85,plain,
~ ! [X0: $i > $i > $o] :
( ( ( meuclidean @ X0 )
& ( mreflexive @ X0 ) )
<=> ( ( msymmetric @ X0 )
& ( mtransitive @ X0 )
& ( mserial @ X0 ) ) ),
inference(rectify,[],[f33]) ).
thf(f86,plain,
~ ! [X0: $i > $i > $o] :
( ( ( ( meuclidean @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) )
<=> ( ( ( msymmetric @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true )
& ( ( mserial @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f85]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( ( ( meuclidean @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) )
<~> ( ( ( msymmetric @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true )
& ( ( mserial @ X0 )
= $true ) ) ),
inference(ennf_transformation,[],[f86]) ).
thf(f88,plain,
? [X0: $i > $i > $o] :
( ( ( ( msymmetric @ X0 )
!= $true )
| ( ( mtransitive @ X0 )
!= $true )
| ( ( mserial @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true ) )
& ( ( ( ( msymmetric @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true )
& ( ( mserial @ X0 )
= $true ) )
| ( ( ( meuclidean @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f87]) ).
thf(f89,plain,
? [X0: $i > $i > $o] :
( ( ( ( msymmetric @ X0 )
!= $true )
| ( ( mtransitive @ X0 )
!= $true )
| ( ( mserial @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true ) )
& ( ( ( ( msymmetric @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true )
& ( ( mserial @ X0 )
= $true ) )
| ( ( ( meuclidean @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) ) ) ),
inference(flattening,[],[f88]) ).
thf(f90,plain,
( ( ( $true
!= ( msymmetric @ sK0 ) )
| ( $true
!= ( mtransitive @ sK0 ) )
| ( $true
!= ( mserial @ sK0 ) )
| ( $true
!= ( meuclidean @ sK0 ) )
| ( $true
!= ( mreflexive @ sK0 ) ) )
& ( ( ( $true
= ( msymmetric @ sK0 ) )
& ( $true
= ( mtransitive @ sK0 ) )
& ( $true
= ( mserial @ sK0 ) ) )
| ( ( $true
= ( meuclidean @ sK0 ) )
& ( $true
= ( mreflexive @ sK0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f89]) ).
thf(f108,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f109,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f110,plain,
( mserial
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f111,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f112,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f122,plain,
( ( $true
= ( mserial @ sK0 ) )
| ( $true
= ( mreflexive @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f124,plain,
( ( $true
= ( mtransitive @ sK0 ) )
| ( $true
= ( mreflexive @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f125,plain,
( ( $true
= ( mtransitive @ sK0 ) )
| ( $true
= ( meuclidean @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f126,plain,
( ( $true
= ( msymmetric @ sK0 ) )
| ( $true
= ( mreflexive @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f127,plain,
( ( $true
= ( msymmetric @ sK0 ) )
| ( $true
= ( meuclidean @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f128,plain,
( ( $true
!= ( msymmetric @ sK0 ) )
| ( $true
!= ( mtransitive @ sK0 ) )
| ( $true
!= ( mserial @ sK0 ) )
| ( $true
!= ( meuclidean @ sK0 ) )
| ( $true
!= ( mreflexive @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f140,plain,
( ( $true
!= ( ^ [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 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK0 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) )
@ sK0 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ sK0 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f128,f109,f111,f110,f112,f108]) ).
thf(f141,plain,
( ( $true
= ( ^ [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 @ Y3 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f127,f109,f112]) ).
thf(f142,plain,
( ( $true
= ( ^ [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] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f126,f109,f108]) ).
thf(f143,plain,
( ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK0 ) )
| ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f125,f111,f112]) ).
thf(f144,plain,
( ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK0 ) )
| ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f124,f111,f108]) ).
thf(f146,plain,
( ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) )
@ sK0 ) )
| ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f122,f110,f108]) ).
thf(f147,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f148,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(pi_proxy_clausification,[],[f147]) ).
thf(f149,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ?? @ $i @ ( sK0 @ X1 ) ) )
| ( $true
= ( sK0 @ X2 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK0 @ X1 @ ( sK1 @ X1 ) ) )
| ( $true
= ( sK0 @ X2 @ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f150]) ).
thf(f163,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f164,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(pi_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ Y1 @ X1 ) ) ) ) )
| ( $true
= ( sK0 @ X2 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ Y1 @ X1 ) ) )
@ X3 ) )
| ( $true
= ( sK0 @ X2 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X3 )
& ( sK0 @ X3 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) ) ) )
| ( $true
= ( sK0 @ X2 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X3 )
& ( sK0 @ X3 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) )
@ X4 ) )
| ( $true
= ( sK0 @ X2 @ X2 ) ) ),
inference(pi_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ( ( sK0 @ X4 @ X3 )
& ( sK0 @ X3 @ X1 ) )
=> ( sK0 @ X4 @ X1 ) ) )
| ( $true
= ( sK0 @ X2 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f171,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( ( sK0 @ X4 @ X3 )
& ( sK0 @ X3 @ X1 ) ) )
| ( $true
= ( sK0 @ X2 @ X2 ) )
| ( $true
= ( sK0 @ X4 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $true
= ( sK0 @ X2 @ X2 ) )
| ( $true
= ( sK0 @ X4 @ X1 ) )
| ( $false
= ( sK0 @ X4 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f143]) ).
thf(f174,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ Y1 @ X1 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ X2 ) )
=> ( sK0 @ Y0 @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f177,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ Y1 @ X1 ) ) )
@ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ X2 ) )
=> ( sK0 @ Y0 @ X2 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ Y1 @ X1 ) ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ X2 ) )
=> ( sK0 @ Y0 @ X2 ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X3 )
& ( sK0 @ X3 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X4 )
& ( sK0 @ Y0 @ X2 ) )
=> ( sK0 @ X4 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f178]) ).
thf(f180,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X3 )
& ( sK0 @ X3 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) )
@ X5 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X4 )
& ( sK0 @ Y0 @ X2 ) )
=> ( sK0 @ X4 @ X2 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X3 )
& ( sK0 @ X3 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) )
@ X5 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X4 )
& ( sK0 @ Y0 @ X2 ) )
=> ( sK0 @ X4 @ X2 ) )
@ X6 ) ) ),
inference(pi_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $true
= ( ( ( sK0 @ X5 @ X3 )
& ( sK0 @ X3 @ X1 ) )
=> ( sK0 @ X5 @ X1 ) ) )
| ( $true
= ( ( ( sK0 @ X6 @ X4 )
& ( sK0 @ X6 @ X2 ) )
=> ( sK0 @ X4 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f183,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( ( sK0 @ X5 @ X3 )
& ( sK0 @ X3 @ X1 ) ) )
| ( $true
= ( ( ( sK0 @ X6 @ X4 )
& ( sK0 @ X6 @ X2 ) )
=> ( sK0 @ X4 @ X2 ) ) )
| ( $true
= ( sK0 @ X5 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $true
= ( ( ( sK0 @ X6 @ X4 )
& ( sK0 @ X6 @ X2 ) )
=> ( sK0 @ X4 @ X2 ) ) )
| ( $true
= ( sK0 @ X5 @ X1 ) )
| ( $false
= ( sK0 @ X5 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( ( sK0 @ X6 @ X4 )
& ( sK0 @ X6 @ X2 ) ) )
| ( $true
= ( sK0 @ X5 @ X1 ) )
| ( $false
= ( sK0 @ X5 @ X3 ) )
| ( $true
= ( sK0 @ X4 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X2: $i,X3: $i,X1: $i,X6: $i,X4: $i,X5: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X6 @ X2 ) )
| ( $true
= ( sK0 @ X5 @ X1 ) )
| ( $false
= ( sK0 @ X5 @ X3 ) )
| ( $true
= ( sK0 @ X4 @ X2 ) )
| ( $false
= ( sK0 @ X6 @ X4 ) ) ),
inference(and_proxy_clausification,[],[f185]) ).
thf(f187,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f142]) ).
thf(f188,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(pi_proxy_clausification,[],[f187]) ).
thf(f189,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,[],[f188]) ).
thf(f190,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( sK0 @ X1 @ Y0 ) ) ) )
| ( $true
= ( sK0 @ X2 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f189]) ).
thf(f191,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,[],[f190]) ).
thf(f192,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( sK0 @ X3 @ X1 )
=> ( sK0 @ X1 @ X3 ) ) )
| ( $true
= ( sK0 @ X2 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f193,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $true
= ( sK0 @ X2 @ X2 ) )
| ( $true
= ( sK0 @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f192]) ).
thf(f194,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f195,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 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( sK0 @ X1 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ X2 ) )
=> ( sK0 @ Y0 @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f196]) ).
thf(f198,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( sK0 @ X1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ X2 ) )
=> ( sK0 @ Y0 @ X2 ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( sK0 @ X1 @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ X2 ) )
=> ( sK0 @ Y0 @ X2 ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $true
= ( ( sK0 @ X3 @ X1 )
=> ( sK0 @ X1 @ X3 ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X4 )
& ( sK0 @ Y0 @ X2 ) )
=> ( sK0 @ X4 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f199]) ).
thf(f201,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X4 )
& ( sK0 @ Y0 @ X2 ) )
=> ( sK0 @ X4 @ X2 ) ) ) )
| ( $true
= ( sK0 @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X4 )
& ( sK0 @ Y0 @ X2 ) )
=> ( sK0 @ X4 @ X2 ) )
@ X5 ) )
| ( $true
= ( sK0 @ X1 @ X3 ) ) ),
inference(pi_proxy_clausification,[],[f201]) ).
thf(f203,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $true
= ( ( ( sK0 @ X5 @ X4 )
& ( sK0 @ X5 @ X2 ) )
=> ( sK0 @ X4 @ X2 ) ) )
| ( $true
= ( sK0 @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f202]) ).
thf(f204,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( ( sK0 @ X5 @ X4 )
& ( sK0 @ X5 @ X2 ) ) )
| ( $true
= ( sK0 @ X1 @ X3 ) )
| ( $true
= ( sK0 @ X4 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X5 @ X2 ) )
| ( $true
= ( sK0 @ X1 @ X3 ) )
| ( $true
= ( sK0 @ X4 @ X2 ) )
| ( $false
= ( sK0 @ X5 @ X4 ) ) ),
inference(and_proxy_clausification,[],[f204]) ).
thf(f206,plain,
( ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f207,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK3 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(sigma_proxy_clausification,[],[f206]) ).
thf(f208,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK4 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(sigma_proxy_clausification,[],[f207]) ).
thf(f209,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) )
@ sK5 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(sigma_proxy_clausification,[],[f208]) ).
thf(f210,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
@ sK6 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(sigma_proxy_clausification,[],[f209]) ).
thf(f211,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
@ sK6 ) )
| ( $false
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f210]) ).
thf(f212,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK3 )
=> ( sK0 @ sK3 @ Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK4 ) )
=> ( sK0 @ Y1 @ sK4 ) ) ) ) )
| ( $false
= ( ?? @ $i @ ( sK0 @ sK5 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ sK6 ) )
=> ( sK0 @ Y0 @ sK6 ) ) ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(beta-eta_normalization,[],[f211]) ).
thf(f213,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK3 )
=> ( sK0 @ sK3 @ Y0 ) )
@ sK8 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK4 ) )
=> ( sK0 @ Y1 @ sK4 ) ) ) ) )
| ( $false
= ( ?? @ $i @ ( sK0 @ sK5 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ sK6 ) )
=> ( sK0 @ Y0 @ sK6 ) ) ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f212]) ).
thf(f214,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK3 )
=> ( sK0 @ sK3 @ Y0 ) )
@ sK8 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK4 ) )
=> ( sK0 @ Y1 @ sK4 ) ) )
@ sK9 ) )
| ( $false
= ( ?? @ $i @ ( sK0 @ sK5 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ sK6 ) )
=> ( sK0 @ Y0 @ sK6 ) ) ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f213]) ).
thf(f215,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK3 )
=> ( sK0 @ sK3 @ Y0 ) )
@ sK8 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK4 ) )
=> ( sK0 @ Y1 @ sK4 ) ) )
@ sK9 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ sK6 ) )
=> ( sK0 @ Y0 @ sK6 ) ) ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(pi_proxy_clausification,[],[f214]) ).
thf(f216,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK3 )
=> ( sK0 @ sK3 @ Y0 ) )
@ sK8 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK4 ) )
=> ( sK0 @ Y1 @ sK4 ) ) )
@ sK9 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ sK6 ) )
=> ( sK0 @ Y0 @ sK6 ) ) )
@ sK10 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f215]) ).
thf(f217,plain,
! [X1: $i] :
( ( $false
= ( ( sK0 @ sK8 @ sK3 )
=> ( sK0 @ sK3 @ sK8 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK9 )
& ( sK0 @ sK9 @ sK4 ) )
=> ( sK0 @ Y0 @ sK4 ) ) ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK10 )
& ( sK0 @ Y0 @ sK6 ) )
=> ( sK0 @ sK10 @ sK6 ) ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(beta-eta_normalization,[],[f216]) ).
thf(f218,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK8 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK9 )
& ( sK0 @ sK9 @ sK4 ) )
=> ( sK0 @ Y0 @ sK4 ) ) ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK10 )
& ( sK0 @ Y0 @ sK6 ) )
=> ( sK0 @ sK10 @ sK6 ) ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f217]) ).
thf(f219,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK9 )
& ( sK0 @ sK9 @ sK4 ) )
=> ( sK0 @ Y0 @ sK4 ) ) ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK10 )
& ( sK0 @ Y0 @ sK6 ) )
=> ( sK0 @ sK10 @ sK6 ) ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f217]) ).
thf(f220,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK9 )
& ( sK0 @ sK9 @ sK4 ) )
=> ( sK0 @ Y0 @ sK4 ) )
@ sK11 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK10 )
& ( sK0 @ Y0 @ sK6 ) )
=> ( sK0 @ sK10 @ sK6 ) ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f219]) ).
thf(f221,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK9 )
& ( sK0 @ sK9 @ sK4 ) )
=> ( sK0 @ Y0 @ sK4 ) )
@ sK11 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK10 )
& ( sK0 @ Y0 @ sK6 ) )
=> ( sK0 @ sK10 @ sK6 ) )
@ sK12 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f220]) ).
thf(f222,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK11 @ sK9 )
& ( sK0 @ sK9 @ sK4 ) )
=> ( sK0 @ sK11 @ sK4 ) ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( ( ( sK0 @ sK12 @ sK10 )
& ( sK0 @ sK12 @ sK6 ) )
=> ( sK0 @ sK10 @ sK6 ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(beta-eta_normalization,[],[f221]) ).
thf(f223,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ( $false
= ( sK0 @ sK11 @ sK4 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( ( ( sK0 @ sK12 @ sK10 )
& ( sK0 @ sK12 @ sK6 ) )
=> ( sK0 @ sK10 @ sK6 ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f222]) ).
thf(f224,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK11 @ sK9 )
& ( sK0 @ sK9 @ sK4 ) ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( ( ( sK0 @ sK12 @ sK10 )
& ( sK0 @ sK12 @ sK6 ) )
=> ( sK0 @ sK10 @ sK6 ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f222]) ).
thf(f225,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( ( ( sK0 @ sK12 @ sK10 )
& ( sK0 @ sK12 @ sK6 ) )
=> ( sK0 @ sK10 @ sK6 ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f224]) ).
thf(f226,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ( $true
= ( sK0 @ sK11 @ sK9 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( ( ( sK0 @ sK12 @ sK10 )
& ( sK0 @ sK12 @ sK6 ) )
=> ( sK0 @ sK10 @ sK6 ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f224]) ).
thf(f227,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ( $true
= ( sK0 @ sK11 @ sK9 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( sK0 @ sK10 @ sK6 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f226]) ).
thf(f228,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ( $true
= ( sK0 @ sK11 @ sK9 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( ( sK0 @ sK12 @ sK10 )
& ( sK0 @ sK12 @ sK6 ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f226]) ).
thf(f229,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ( $true
= ( sK0 @ sK11 @ sK9 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK0 @ sK12 @ sK6 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ( $true
= ( sK0 @ sK11 @ sK9 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK0 @ sK12 @ sK10 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f228]) ).
thf(f231,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( sK0 @ sK10 @ sK6 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f225]) ).
thf(f232,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( ( sK0 @ sK12 @ sK10 )
& ( sK0 @ sK12 @ sK6 ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f225]) ).
thf(f233,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK0 @ sK12 @ sK6 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK0 @ sK12 @ sK10 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f232]) ).
thf(f235,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ( $false
= ( sK0 @ sK11 @ sK4 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( sK0 @ sK10 @ sK6 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f223]) ).
thf(f236,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ( $false
= ( sK0 @ sK11 @ sK4 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( ( sK0 @ sK12 @ sK10 )
& ( sK0 @ sK12 @ sK6 ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f223]) ).
thf(f237,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ( $false
= ( sK0 @ sK11 @ sK4 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK0 @ sK12 @ sK6 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f236]) ).
thf(f238,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ( $false
= ( sK0 @ sK11 @ sK4 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK0 @ sK12 @ sK10 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f236]) ).
thf(f239,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK8 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK9 )
& ( sK0 @ sK9 @ sK4 ) )
=> ( sK0 @ Y0 @ sK4 ) )
@ sK13 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK10 )
& ( sK0 @ Y0 @ sK6 ) )
=> ( sK0 @ sK10 @ sK6 ) ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f218]) ).
thf(f240,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK8 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK9 )
& ( sK0 @ sK9 @ sK4 ) )
=> ( sK0 @ Y0 @ sK4 ) )
@ sK13 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK10 )
& ( sK0 @ Y0 @ sK6 ) )
=> ( sK0 @ sK10 @ sK6 ) )
@ sK14 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f239]) ).
thf(f241,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK8 ) )
| ( $false
= ( ( ( sK0 @ sK13 @ sK9 )
& ( sK0 @ sK9 @ sK4 ) )
=> ( sK0 @ sK13 @ sK4 ) ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( ( ( sK0 @ sK14 @ sK10 )
& ( sK0 @ sK14 @ sK6 ) )
=> ( sK0 @ sK10 @ sK6 ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(beta-eta_normalization,[],[f240]) ).
thf(f242,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK8 ) )
| ( $false
= ( sK0 @ sK13 @ sK4 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( ( ( sK0 @ sK14 @ sK10 )
& ( sK0 @ sK14 @ sK6 ) )
=> ( sK0 @ sK10 @ sK6 ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f241]) ).
thf(f243,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK8 ) )
| ( $true
= ( ( sK0 @ sK13 @ sK9 )
& ( sK0 @ sK9 @ sK4 ) ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( ( ( sK0 @ sK14 @ sK10 )
& ( sK0 @ sK14 @ sK6 ) )
=> ( sK0 @ sK10 @ sK6 ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f241]) ).
thf(f244,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK8 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( ( ( sK0 @ sK14 @ sK10 )
& ( sK0 @ sK14 @ sK6 ) )
=> ( sK0 @ sK10 @ sK6 ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f243]) ).
thf(f245,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK8 ) )
| ( $true
= ( sK0 @ sK13 @ sK9 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( ( ( sK0 @ sK14 @ sK10 )
& ( sK0 @ sK14 @ sK6 ) )
=> ( sK0 @ sK10 @ sK6 ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f243]) ).
thf(f246,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK8 ) )
| ( $true
= ( sK0 @ sK13 @ sK9 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( sK0 @ sK10 @ sK6 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f245]) ).
thf(f247,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK8 ) )
| ( $true
= ( sK0 @ sK13 @ sK9 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( ( sK0 @ sK14 @ sK10 )
& ( sK0 @ sK14 @ sK6 ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f245]) ).
thf(f248,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK8 ) )
| ( $true
= ( sK0 @ sK13 @ sK9 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK0 @ sK14 @ sK6 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f247]) ).
thf(f249,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK8 ) )
| ( $true
= ( sK0 @ sK13 @ sK9 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK0 @ sK14 @ sK10 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f247]) ).
thf(f250,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK8 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( sK0 @ sK10 @ sK6 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f244]) ).
thf(f251,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK8 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( ( sK0 @ sK14 @ sK10 )
& ( sK0 @ sK14 @ sK6 ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f244]) ).
thf(f252,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK8 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK0 @ sK14 @ sK6 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f251]) ).
thf(f253,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK8 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK0 @ sK14 @ sK10 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f251]) ).
thf(f254,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK8 ) )
| ( $false
= ( sK0 @ sK13 @ sK4 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $false
= ( sK0 @ sK10 @ sK6 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f242]) ).
thf(f255,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK8 ) )
| ( $false
= ( sK0 @ sK13 @ sK4 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( ( sK0 @ sK14 @ sK10 )
& ( sK0 @ sK14 @ sK6 ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f242]) ).
thf(f256,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK8 ) )
| ( $false
= ( sK0 @ sK13 @ sK4 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK0 @ sK14 @ sK6 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f255]) ).
thf(f257,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK3 @ sK8 ) )
| ( $false
= ( sK0 @ sK13 @ sK4 ) )
| ( $false
= ( sK0 @ sK5 @ X1 ) )
| ( $true
= ( sK0 @ sK14 @ sK10 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f255]) ).
thf(f259,definition,
( spl15_1
<=> ! [X2: $i] :
( $true
= ( sK0 @ X2 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
thf(f260,plain,
( ! [X2: $i] :
( $true
= ( sK0 @ X2 @ X2 ) )
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f259]) ).
thf(f262,definition,
( spl15_2
<=> ! [X1: $i] :
( $true
= ( sK0 @ X1 @ ( sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
thf(f263,plain,
( ! [X1: $i] :
( $true
= ( sK0 @ X1 @ ( sK1 @ X1 ) ) )
| ~ spl15_2 ),
inference(avatar_component_clause,[],[f262]) ).
thf(f264,plain,
( spl15_1
| spl15_2 ),
inference(avatar_split_clause,[],[f151,f262,f259]) ).
thf(f266,definition,
( spl15_3
<=> ! [X2: $i,X3: $i,X4: $i] :
( ( $false
= ( sK0 @ X4 @ X2 ) )
| ( $false
= ( sK0 @ X4 @ X3 ) )
| ( $true
= ( sK0 @ X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
thf(f267,plain,
( ! [X2: $i,X3: $i,X4: $i] :
( ( $false
= ( sK0 @ X4 @ X2 ) )
| ( $false
= ( sK0 @ X4 @ X3 ) )
| ( $true
= ( sK0 @ X3 @ X2 ) ) )
| ~ spl15_3 ),
inference(avatar_component_clause,[],[f266]) ).
thf(f273,definition,
( spl15_5
<=> ! [X4: $i,X1: $i,X3: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X4 @ X3 ) )
| ( $true
= ( sK0 @ X4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl15_5])],[avatar_definition]) ).
thf(f274,plain,
( ! [X3: $i,X1: $i,X4: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X4 @ X3 ) )
| ( $true
= ( sK0 @ X4 @ X1 ) ) )
| ~ spl15_5 ),
inference(avatar_component_clause,[],[f273]) ).
thf(f275,plain,
( spl15_1
| spl15_5 ),
inference(avatar_split_clause,[],[f172,f273,f259]) ).
thf(f276,plain,
( spl15_3
| spl15_5 ),
inference(avatar_split_clause,[],[f186,f273,f266]) ).
thf(f278,definition,
( spl15_6
<=> ! [X1: $i,X3: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $true
= ( sK0 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl15_6])],[avatar_definition]) ).
thf(f279,plain,
( ! [X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $true
= ( sK0 @ X1 @ X3 ) ) )
| ~ spl15_6 ),
inference(avatar_component_clause,[],[f278]) ).
thf(f280,plain,
( spl15_1
| spl15_6 ),
inference(avatar_split_clause,[],[f193,f278,f259]) ).
thf(f281,plain,
( spl15_3
| spl15_6 ),
inference(avatar_split_clause,[],[f205,f278,f266]) ).
thf(f283,definition,
( spl15_7
<=> ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_7])],[avatar_definition]) ).
thf(f285,plain,
( ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ~ spl15_7 ),
inference(avatar_component_clause,[],[f283]) ).
thf(f287,definition,
( spl15_8
<=> ( $true
= ( sK0 @ sK12 @ sK10 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_8])],[avatar_definition]) ).
thf(f289,plain,
( ( $true
= ( sK0 @ sK12 @ sK10 ) )
| ~ spl15_8 ),
inference(avatar_component_clause,[],[f287]) ).
thf(f291,definition,
( spl15_9
<=> ! [X1: $i] :
( $false
= ( sK0 @ sK5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_9])],[avatar_definition]) ).
thf(f292,plain,
( ! [X1: $i] :
( $false
= ( sK0 @ sK5 @ X1 ) )
| ~ spl15_9 ),
inference(avatar_component_clause,[],[f291]) ).
thf(f294,definition,
( spl15_10
<=> ( $true
= ( sK0 @ sK11 @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_10])],[avatar_definition]) ).
thf(f296,plain,
( ( $true
= ( sK0 @ sK11 @ sK9 ) )
| ~ spl15_10 ),
inference(avatar_component_clause,[],[f294]) ).
thf(f298,definition,
( spl15_11
<=> ( $true
= ( sK0 @ sK8 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_11])],[avatar_definition]) ).
thf(f300,plain,
( ( $true
= ( sK0 @ sK8 @ sK3 ) )
| ~ spl15_11 ),
inference(avatar_component_clause,[],[f298]) ).
thf(f301,plain,
( spl15_7
| spl15_8
| spl15_9
| spl15_10
| spl15_11 ),
inference(avatar_split_clause,[],[f230,f298,f294,f291,f287,f283]) ).
thf(f303,definition,
( spl15_12
<=> ( $true
= ( sK0 @ sK12 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_12])],[avatar_definition]) ).
thf(f305,plain,
( ( $true
= ( sK0 @ sK12 @ sK6 ) )
| ~ spl15_12 ),
inference(avatar_component_clause,[],[f303]) ).
thf(f306,plain,
( spl15_7
| spl15_12
| spl15_9
| spl15_10
| spl15_11 ),
inference(avatar_split_clause,[],[f229,f298,f294,f291,f303,f283]) ).
thf(f308,definition,
( spl15_13
<=> ( $false
= ( sK0 @ sK10 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_13])],[avatar_definition]) ).
thf(f310,plain,
( ( $false
= ( sK0 @ sK10 @ sK6 ) )
| ~ spl15_13 ),
inference(avatar_component_clause,[],[f308]) ).
thf(f311,plain,
( spl15_7
| spl15_13
| spl15_9
| spl15_10
| spl15_11 ),
inference(avatar_split_clause,[],[f227,f298,f294,f291,f308,f283]) ).
thf(f313,definition,
( spl15_14
<=> ( $true
= ( sK0 @ sK9 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_14])],[avatar_definition]) ).
thf(f315,plain,
( ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ~ spl15_14 ),
inference(avatar_component_clause,[],[f313]) ).
thf(f316,plain,
( spl15_7
| spl15_8
| spl15_9
| spl15_14
| spl15_11 ),
inference(avatar_split_clause,[],[f234,f298,f313,f291,f287,f283]) ).
thf(f317,plain,
( spl15_7
| spl15_12
| spl15_9
| spl15_14
| spl15_11 ),
inference(avatar_split_clause,[],[f233,f298,f313,f291,f303,f283]) ).
thf(f318,plain,
( spl15_7
| spl15_13
| spl15_9
| spl15_14
| spl15_11 ),
inference(avatar_split_clause,[],[f231,f298,f313,f291,f308,f283]) ).
thf(f320,definition,
( spl15_15
<=> ( $false
= ( sK0 @ sK11 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_15])],[avatar_definition]) ).
thf(f322,plain,
( ( $false
= ( sK0 @ sK11 @ sK4 ) )
| ~ spl15_15 ),
inference(avatar_component_clause,[],[f320]) ).
thf(f323,plain,
( spl15_7
| spl15_8
| spl15_9
| spl15_15
| spl15_11 ),
inference(avatar_split_clause,[],[f238,f298,f320,f291,f287,f283]) ).
thf(f324,plain,
( spl15_7
| spl15_12
| spl15_9
| spl15_15
| spl15_11 ),
inference(avatar_split_clause,[],[f237,f298,f320,f291,f303,f283]) ).
thf(f325,plain,
( spl15_7
| spl15_13
| spl15_9
| spl15_15
| spl15_11 ),
inference(avatar_split_clause,[],[f235,f298,f320,f291,f308,f283]) ).
thf(f327,definition,
( spl15_16
<=> ( $true
= ( sK0 @ sK14 @ sK10 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_16])],[avatar_definition]) ).
thf(f329,plain,
( ( $true
= ( sK0 @ sK14 @ sK10 ) )
| ~ spl15_16 ),
inference(avatar_component_clause,[],[f327]) ).
thf(f331,definition,
( spl15_17
<=> ( $true
= ( sK0 @ sK13 @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_17])],[avatar_definition]) ).
thf(f333,plain,
( ( $true
= ( sK0 @ sK13 @ sK9 ) )
| ~ spl15_17 ),
inference(avatar_component_clause,[],[f331]) ).
thf(f335,definition,
( spl15_18
<=> ( $false
= ( sK0 @ sK3 @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_18])],[avatar_definition]) ).
thf(f337,plain,
( ( $false
= ( sK0 @ sK3 @ sK8 ) )
| ~ spl15_18 ),
inference(avatar_component_clause,[],[f335]) ).
thf(f338,plain,
( spl15_7
| spl15_16
| spl15_9
| spl15_17
| spl15_18 ),
inference(avatar_split_clause,[],[f249,f335,f331,f291,f327,f283]) ).
thf(f340,definition,
( spl15_19
<=> ( $true
= ( sK0 @ sK14 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_19])],[avatar_definition]) ).
thf(f342,plain,
( ( $true
= ( sK0 @ sK14 @ sK6 ) )
| ~ spl15_19 ),
inference(avatar_component_clause,[],[f340]) ).
thf(f343,plain,
( spl15_7
| spl15_19
| spl15_9
| spl15_17
| spl15_18 ),
inference(avatar_split_clause,[],[f248,f335,f331,f291,f340,f283]) ).
thf(f344,plain,
( spl15_7
| spl15_13
| spl15_9
| spl15_17
| spl15_18 ),
inference(avatar_split_clause,[],[f246,f335,f331,f291,f308,f283]) ).
thf(f345,plain,
( spl15_7
| spl15_16
| spl15_9
| spl15_14
| spl15_18 ),
inference(avatar_split_clause,[],[f253,f335,f313,f291,f327,f283]) ).
thf(f346,plain,
( spl15_7
| spl15_19
| spl15_9
| spl15_14
| spl15_18 ),
inference(avatar_split_clause,[],[f252,f335,f313,f291,f340,f283]) ).
thf(f347,plain,
( spl15_7
| spl15_13
| spl15_9
| spl15_14
| spl15_18 ),
inference(avatar_split_clause,[],[f250,f335,f313,f291,f308,f283]) ).
thf(f349,definition,
( spl15_20
<=> ( $false
= ( sK0 @ sK13 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl15_20])],[avatar_definition]) ).
thf(f351,plain,
( ( $false
= ( sK0 @ sK13 @ sK4 ) )
| ~ spl15_20 ),
inference(avatar_component_clause,[],[f349]) ).
thf(f352,plain,
( spl15_7
| spl15_16
| spl15_9
| spl15_20
| spl15_18 ),
inference(avatar_split_clause,[],[f257,f335,f349,f291,f327,f283]) ).
thf(f353,plain,
( spl15_7
| spl15_19
| spl15_9
| spl15_20
| spl15_18 ),
inference(avatar_split_clause,[],[f256,f335,f349,f291,f340,f283]) ).
thf(f354,plain,
( spl15_7
| spl15_13
| spl15_9
| spl15_20
| spl15_18 ),
inference(avatar_split_clause,[],[f254,f335,f349,f291,f308,f283]) ).
thf(f397,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK3 @ sK8 ) )
| ~ spl15_6
| ~ spl15_11 ),
inference(constrained_superposition,[],[f279,f300]) ).
thf(f398,plain,
( ( $true
= ( sK0 @ sK3 @ sK8 ) )
| ~ spl15_6
| ~ spl15_11 ),
inference(trivial_inequality_removal,[],[f397]) ).
thf(f441,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X0 @ X2 ) )
| ( $true
= ( sK0 @ X1 @ X2 ) ) )
| ~ spl15_3
| ~ spl15_6 ),
inference(constrained_superposition,[],[f279,f267]) ).
thf(f458,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK7 ) )
| ( $false
= ( sK0 @ X0 @ sK7 ) ) )
| ~ spl15_3
| ~ spl15_7 ),
inference(constrained_superposition,[],[f285,f267]) ).
thf(f474,plain,
( ! [X0: $i,X1: $i] :
( ( $false != $false )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $true
= ( sK0 @ X1 @ X1 ) ) )
| ~ spl15_3 ),
inference(equality_factoring,[],[f267]) ).
thf(f478,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $true
= ( sK0 @ X1 @ X1 ) ) )
| ~ spl15_3 ),
inference(trivial_inequality_removal,[],[f474]) ).
thf(f491,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK7 ) ) )
| ~ spl15_3
| ~ spl15_7 ),
inference(duplicate_literal_removal,[],[f458]) ).
thf(f492,plain,
( ! [X0: $i] :
( $false
= ( sK0 @ X0 @ sK7 ) )
| ~ spl15_3
| ~ spl15_7 ),
inference(trivial_inequality_removal,[],[f491]) ).
thf(f501,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X0 @ X2 ) )
| ( $true
= ( sK0 @ X1 @ X2 ) ) )
| ~ spl15_3
| ~ spl15_6 ),
inference(trivial_inequality_removal,[],[f441]) ).
thf(f537,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ sK7 @ X0 ) ) )
| ~ spl15_3
| ~ spl15_6
| ~ spl15_7 ),
inference(constrained_superposition,[],[f492,f279]) ).
thf(f580,plain,
( ( $true = $false )
| ~ spl15_6
| ~ spl15_11
| ~ spl15_18 ),
inference(constrained_superposition,[],[f337,f398]) ).
thf(f586,plain,
( $false
| ~ spl15_6
| ~ spl15_11
| ~ spl15_18 ),
inference(trivial_inequality_removal,[],[f580]) ).
thf(f587,plain,
( ~ spl15_6
| ~ spl15_11
| ~ spl15_18 ),
inference(avatar_contradiction_clause,[],[f586]) ).
thf(f592,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK6 ) )
| ( $false
= ( sK0 @ X0 @ sK10 ) ) )
| ~ spl15_3
| ~ spl15_13 ),
inference(constrained_superposition,[],[f267,f310]) ).
thf(f595,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK10 ) )
| ( $false
= ( sK0 @ X0 @ sK6 ) ) )
| ~ spl15_3
| ~ spl15_13 ),
inference(trivial_inequality_removal,[],[f592]) ).
thf(f637,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $true
= ( sK0 @ X0 @ X2 ) ) )
| ~ spl15_5
| ~ spl15_6 ),
inference(constrained_superposition,[],[f279,f274]) ).
thf(f684,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $true
= ( sK0 @ X0 @ X2 ) ) )
| ~ spl15_5
| ~ spl15_6 ),
inference(trivial_inequality_removal,[],[f637]) ).
thf(f802,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $true
= ( sK0 @ X1 @ X1 ) ) )
| ~ spl15_3
| ~ spl15_6 ),
inference(constrained_superposition,[],[f279,f478]) ).
thf(f828,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $true
= ( sK0 @ X1 @ X1 ) ) )
| ~ spl15_3
| ~ spl15_6 ),
inference(trivial_inequality_removal,[],[f802]) ).
thf(f918,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( sK0 @ X0 @ X0 ) ) )
| ~ spl15_2
| ~ spl15_3
| ~ spl15_6 ),
inference(constrained_superposition,[],[f263,f828]) ).
thf(f947,plain,
( ! [X0: $i] :
( $true
= ( sK0 @ X0 @ X0 ) )
| ~ spl15_2
| ~ spl15_3
| ~ spl15_6 ),
inference(trivial_inequality_removal,[],[f918]) ).
thf(f961,plain,
( spl15_1
| ~ spl15_2
| ~ spl15_3
| ~ spl15_6 ),
inference(avatar_split_clause,[],[f947,f278,f266,f262,f259]) ).
thf(f962,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $true
= ( sK0 @ X1 @ X0 ) ) )
| ~ spl15_1
| ~ spl15_3 ),
inference(constrained_superposition,[],[f260,f267]) ).
thf(f1325,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK14 @ sK6 ) )
| ~ spl15_3
| ~ spl15_13
| ~ spl15_16 ),
inference(constrained_superposition,[],[f329,f595]) ).
thf(f1326,plain,
( ( $false
= ( sK0 @ sK14 @ sK6 ) )
| ~ spl15_3
| ~ spl15_13
| ~ spl15_16 ),
inference(trivial_inequality_removal,[],[f1325]) ).
thf(f1340,plain,
( ( $true = $false )
| ~ spl15_3
| ~ spl15_13
| ~ spl15_16
| ~ spl15_19 ),
inference(constrained_superposition,[],[f1326,f342]) ).
thf(f1352,plain,
( $false
| ~ spl15_3
| ~ spl15_13
| ~ spl15_16
| ~ spl15_19 ),
inference(trivial_inequality_removal,[],[f1340]) ).
thf(f1353,plain,
( ~ spl15_3
| ~ spl15_13
| ~ spl15_16
| ~ spl15_19 ),
inference(avatar_contradiction_clause,[],[f1352]) ).
thf(f1375,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK12 @ sK6 ) )
| ~ spl15_3
| ~ spl15_8
| ~ spl15_13 ),
inference(constrained_superposition,[],[f595,f289]) ).
thf(f1376,plain,
( ( $false
= ( sK0 @ sK12 @ sK6 ) )
| ~ spl15_3
| ~ spl15_8
| ~ spl15_13 ),
inference(trivial_inequality_removal,[],[f1375]) ).
thf(f1570,plain,
( ( $true = $false )
| ~ spl15_3
| ~ spl15_8
| ~ spl15_12
| ~ spl15_13 ),
inference(constrained_superposition,[],[f1376,f305]) ).
thf(f1582,plain,
( $false
| ~ spl15_3
| ~ spl15_8
| ~ spl15_12
| ~ spl15_13 ),
inference(trivial_inequality_removal,[],[f1570]) ).
thf(f1583,plain,
( ~ spl15_3
| ~ spl15_8
| ~ spl15_12
| ~ spl15_13 ),
inference(avatar_contradiction_clause,[],[f1582]) ).
thf(f1587,plain,
( spl15_3
| ~ spl15_5
| ~ spl15_6 ),
inference(avatar_split_clause,[],[f684,f278,f273,f266]) ).
thf(f1716,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $true
= ( sK0 @ X1 @ X0 ) ) )
| ~ spl15_1
| ~ spl15_3 ),
inference(trivial_inequality_removal,[],[f962]) ).
thf(f1750,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK4 ) )
| ( $false
= ( sK0 @ sK11 @ X0 ) ) )
| ~ spl15_5
| ~ spl15_15 ),
inference(constrained_superposition,[],[f274,f322]) ).
thf(f1753,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK4 ) )
| ( $false
= ( sK0 @ sK11 @ X0 ) ) )
| ~ spl15_5
| ~ spl15_15 ),
inference(trivial_inequality_removal,[],[f1750]) ).
thf(f1951,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK4 ) )
| ( $false
= ( sK0 @ sK13 @ X0 ) ) )
| ~ spl15_5
| ~ spl15_20 ),
inference(constrained_superposition,[],[f351,f274]) ).
thf(f1999,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK9 @ sK4 ) )
| ~ spl15_5
| ~ spl15_10
| ~ spl15_15 ),
inference(constrained_superposition,[],[f296,f1753]) ).
thf(f2000,plain,
( ( $false
= ( sK0 @ sK9 @ sK4 ) )
| ~ spl15_5
| ~ spl15_10
| ~ spl15_15 ),
inference(trivial_inequality_removal,[],[f1999]) ).
thf(f2016,plain,
( ( $true = $false )
| ~ spl15_5
| ~ spl15_10
| ~ spl15_14
| ~ spl15_15 ),
inference(constrained_superposition,[],[f2000,f315]) ).
thf(f2026,plain,
( $false
| ~ spl15_5
| ~ spl15_10
| ~ spl15_14
| ~ spl15_15 ),
inference(trivial_inequality_removal,[],[f2016]) ).
thf(f2027,plain,
( ~ spl15_5
| ~ spl15_10
| ~ spl15_14
| ~ spl15_15 ),
inference(avatar_contradiction_clause,[],[f2026]) ).
thf(f2030,plain,
( spl15_5
| ~ spl15_3
| ~ spl15_6 ),
inference(avatar_split_clause,[],[f501,f278,f266,f273]) ).
thf(f2113,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK4 ) )
| ( $false
= ( sK0 @ sK13 @ X0 ) ) )
| ~ spl15_5
| ~ spl15_20 ),
inference(trivial_inequality_removal,[],[f1951]) ).
thf(f2351,plain,
( ( $true = $false )
| ~ spl15_1
| ~ spl15_9 ),
inference(constrained_superposition,[],[f292,f260]) ).
thf(f2371,plain,
( $false
| ~ spl15_1
| ~ spl15_9 ),
inference(trivial_inequality_removal,[],[f2351]) ).
thf(f2372,plain,
( ~ spl15_1
| ~ spl15_9 ),
inference(avatar_contradiction_clause,[],[f2371]) ).
thf(f2375,plain,
( spl15_6
| ~ spl15_1
| ~ spl15_3 ),
inference(avatar_split_clause,[],[f1716,f266,f259,f278]) ).
thf(f2474,plain,
( ! [X0: $i] :
( $false
= ( sK0 @ sK7 @ X0 ) )
| ~ spl15_3
| ~ spl15_6
| ~ spl15_7 ),
inference(trivial_inequality_removal,[],[f537]) ).
thf(f2648,plain,
( ( $true = $false )
| ~ spl15_1
| ~ spl15_3
| ~ spl15_6
| ~ spl15_7 ),
inference(constrained_superposition,[],[f260,f2474]) ).
thf(f2654,plain,
( $false
| ~ spl15_1
| ~ spl15_3
| ~ spl15_6
| ~ spl15_7 ),
inference(trivial_inequality_removal,[],[f2648]) ).
thf(f2655,plain,
( ~ spl15_1
| ~ spl15_3
| ~ spl15_6
| ~ spl15_7 ),
inference(avatar_contradiction_clause,[],[f2654]) ).
thf(f2890,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK9 @ sK4 ) )
| ~ spl15_5
| ~ spl15_17
| ~ spl15_20 ),
inference(constrained_superposition,[],[f333,f2113]) ).
thf(f2891,plain,
( ( $false
= ( sK0 @ sK9 @ sK4 ) )
| ~ spl15_5
| ~ spl15_17
| ~ spl15_20 ),
inference(trivial_inequality_removal,[],[f2890]) ).
thf(f2907,plain,
( ( $true = $false )
| ~ spl15_5
| ~ spl15_14
| ~ spl15_17
| ~ spl15_20 ),
inference(constrained_superposition,[],[f2891,f315]) ).
thf(f2917,plain,
( $false
| ~ spl15_5
| ~ spl15_14
| ~ spl15_17
| ~ spl15_20 ),
inference(trivial_inequality_removal,[],[f2907]) ).
thf(f2918,plain,
( ~ spl15_5
| ~ spl15_14
| ~ spl15_17
| ~ spl15_20 ),
inference(avatar_contradiction_clause,[],[f2917]) ).
cnf(s1,plain,
( spl15_1
| spl15_2 ),
inference(sat_conversion,[],[f264]) ).
cnf(s3,plain,
( spl15_1
| spl15_5 ),
inference(sat_conversion,[],[f275]) ).
cnf(s4,plain,
( spl15_3
| spl15_5 ),
inference(sat_conversion,[],[f276]) ).
cnf(s5,plain,
( spl15_1
| spl15_6 ),
inference(sat_conversion,[],[f280]) ).
cnf(s6,plain,
( spl15_3
| spl15_6 ),
inference(sat_conversion,[],[f281]) ).
cnf(s7,plain,
( spl15_7
| spl15_8
| spl15_9
| spl15_10
| spl15_11 ),
inference(sat_conversion,[],[f301]) ).
cnf(s8,plain,
( spl15_7
| spl15_9
| spl15_10
| spl15_11
| spl15_12 ),
inference(sat_conversion,[],[f306]) ).
cnf(s9,plain,
( spl15_7
| spl15_9
| spl15_10
| spl15_11
| spl15_13 ),
inference(sat_conversion,[],[f311]) ).
cnf(s10,plain,
( spl15_7
| spl15_8
| spl15_9
| spl15_11
| spl15_14 ),
inference(sat_conversion,[],[f316]) ).
cnf(s11,plain,
( spl15_7
| spl15_9
| spl15_11
| spl15_12
| spl15_14 ),
inference(sat_conversion,[],[f317]) ).
cnf(s12,plain,
( spl15_7
| spl15_9
| spl15_11
| spl15_13
| spl15_14 ),
inference(sat_conversion,[],[f318]) ).
cnf(s13,plain,
( spl15_7
| spl15_8
| spl15_9
| spl15_11
| spl15_15 ),
inference(sat_conversion,[],[f323]) ).
cnf(s14,plain,
( spl15_7
| spl15_9
| spl15_11
| spl15_12
| spl15_15 ),
inference(sat_conversion,[],[f324]) ).
cnf(s15,plain,
( spl15_7
| spl15_9
| spl15_11
| spl15_13
| spl15_15 ),
inference(sat_conversion,[],[f325]) ).
cnf(s16,plain,
( spl15_7
| spl15_9
| spl15_16
| spl15_17
| spl15_18 ),
inference(sat_conversion,[],[f338]) ).
cnf(s17,plain,
( spl15_7
| spl15_9
| spl15_17
| spl15_18
| spl15_19 ),
inference(sat_conversion,[],[f343]) ).
cnf(s18,plain,
( spl15_7
| spl15_9
| spl15_13
| spl15_17
| spl15_18 ),
inference(sat_conversion,[],[f344]) ).
cnf(s19,plain,
( spl15_7
| spl15_9
| spl15_14
| spl15_16
| spl15_18 ),
inference(sat_conversion,[],[f345]) ).
cnf(s20,plain,
( spl15_7
| spl15_9
| spl15_14
| spl15_18
| spl15_19 ),
inference(sat_conversion,[],[f346]) ).
cnf(s21,plain,
( spl15_7
| spl15_9
| spl15_13
| spl15_14
| spl15_18 ),
inference(sat_conversion,[],[f347]) ).
cnf(s22,plain,
( spl15_7
| spl15_9
| spl15_16
| spl15_18
| spl15_20 ),
inference(sat_conversion,[],[f352]) ).
cnf(s23,plain,
( spl15_7
| spl15_9
| spl15_18
| spl15_19
| spl15_20 ),
inference(sat_conversion,[],[f353]) ).
cnf(s24,plain,
( spl15_7
| spl15_9
| spl15_13
| spl15_18
| spl15_20 ),
inference(sat_conversion,[],[f354]) ).
cnf(s31,plain,
( ~ spl15_6
| ~ spl15_11
| ~ spl15_18 ),
inference(sat_conversion,[],[f587]) ).
cnf(s32,plain,
( spl15_1
| ~ spl15_2
| ~ spl15_3
| ~ spl15_6 ),
inference(sat_conversion,[],[f961]) ).
cnf(s35,plain,
( ~ spl15_3
| ~ spl15_13
| ~ spl15_16
| ~ spl15_19 ),
inference(sat_conversion,[],[f1353]) ).
cnf(s39,plain,
( ~ spl15_3
| ~ spl15_8
| ~ spl15_12
| ~ spl15_13 ),
inference(sat_conversion,[],[f1583]) ).
cnf(s40,plain,
( spl15_3
| ~ spl15_5
| ~ spl15_6 ),
inference(sat_conversion,[],[f1587]) ).
cnf(s47,plain,
( ~ spl15_5
| ~ spl15_10
| ~ spl15_14
| ~ spl15_15 ),
inference(sat_conversion,[],[f2027]) ).
cnf(s48,plain,
( ~ spl15_3
| spl15_5
| ~ spl15_6 ),
inference(sat_conversion,[],[f2030]) ).
cnf(s53,plain,
( ~ spl15_1
| ~ spl15_9 ),
inference(sat_conversion,[],[f2372]) ).
cnf(s54,plain,
( ~ spl15_1
| ~ spl15_3
| spl15_6 ),
inference(sat_conversion,[],[f2375]) ).
cnf(s61,plain,
( ~ spl15_1
| ~ spl15_3
| ~ spl15_6
| ~ spl15_7 ),
inference(sat_conversion,[],[f2655]) ).
cnf(s65,plain,
( ~ spl15_5
| ~ spl15_14
| ~ spl15_17
| ~ spl15_20 ),
inference(sat_conversion,[],[f2918]) ).
cnf(s66,plain,
spl15_1,
inference(rat,[],[s32,s40,s1,s3,s5]) ).
cnf(s67,plain,
~ spl15_9,
inference(rat,[],[s53,s66]) ).
cnf(s68,plain,
( spl15_13
| spl15_18
| ~ spl15_3 ),
inference(rat,[],[s65,s18,s21,s24,s61,s48,s54,s67,s66]) ).
cnf(s69,plain,
( spl15_20
| spl15_18
| ~ spl15_3 ),
inference(rat,[],[s35,s22,s23,s61,s54,s68,s67,s66]) ).
cnf(s70,plain,
( spl15_17
| spl15_18
| ~ spl15_3 ),
inference(rat,[],[s35,s16,s17,s61,s54,s68,s67,s66]) ).
cnf(s71,plain,
( spl15_18
| ~ spl15_3 ),
inference(rat,[],[s35,s19,s20,s65,s70,s69,s68,s61,s48,s54,s67,s66]) ).
cnf(s72,plain,
( spl15_8
| ~ spl15_3 ),
inference(rat,[],[s47,s7,s10,s13,s61,s48,s31,s71,s54,s67,s66]) ).
cnf(s73,plain,
( spl15_10
| ~ spl15_3 ),
inference(rat,[],[s39,s8,s9,s61,s31,s71,s54,s72,s67,s66]) ).
cnf(s74,plain,
( spl15_12
| ~ spl15_3 ),
inference(rat,[],[s47,s11,s14,s61,s48,s31,s71,s54,s73,s67,s66]) ).
cnf(s75,plain,
( ~ spl15_3
| ~ spl15_6 ),
inference(rat,[],[s47,s12,s15,s39,s74,s73,s72,s31,s71,s48,s61,s66,s67]) ).
cnf(s76,plain,
~ spl15_3,
inference(rat,[],[s75,s54,s66]) ).
cnf(s77,plain,
spl15_6,
inference(rat,[],[s6,s76]) ).
cnf(s78,plain,
spl15_5,
inference(rat,[],[s4,s76]) ).
cnf(s80,plain,
$false,
inference(rat,[],[s40,s76,s77,s78]) ).
thf(f2921,plain,
$false,
inference(avatar_sat_refutation,[],[s80]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.19 % Computer : n008.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 10:14:39 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.85/0.44 % (2955140)Will run a generic schedule for satisfiability detection.
% 0.85/0.44 % (2955146)% WARNING: option uhcvi not known.
% 0.85/0.44 % (2955146)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2872696231:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.85/0.44 % (2955145)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3639910885_2999 on theBenchmark for (2999ds/0Mi)
% 0.85/0.44 % (2955147)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3970098282:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.85/0.44 % (2955148)dis+10_1_sil=32000:sp=arity:random_seed=2449977444:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.85/0.44 % (2955146)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.85/0.44 % Exception at run slice level% (2955146)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.85/0.44
% 0.85/0.44 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.85/0.44 % (2955149)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=156429539:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.85/0.44 % (2955149)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.85/0.44 % (2955151)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=160789709:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.85/0.44 % (2955150)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2136613667:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.85/0.44 % (2955156)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3419824066:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.85/0.44 % Exception at run slice level
% 0.85/0.44 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.85/0.44 % (2955161)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2240254644:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.85/0.44 % (2955148)Instruction limit reached!
% 0.85/0.44 % (2955148)------------------------------
% 0.85/0.44 % (2955148)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.44 % (2955148)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.44 % (2955148)CaDiCaL version: 2.1.3
% 0.85/0.44 % (2955148)Termination reason: Instruction limit
% 0.85/0.44 % (2955148)Termination phase: Saturation
% 0.85/0.44 % (2955148)Time elapsed: 0.047 s
% 0.85/0.44 % (2955148)Peak memory usage: 12 MB
% 0.85/0.44 % (2955148)Instructions burned: 104 (million)
% 0.85/0.44 % (2955163)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=4273991499:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.85/0.44 % (2955163)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.85/0.44 % (2955163)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.85/0.44 % (2955149)Instruction limit reached!
% 0.85/0.44 % (2955149)------------------------------
% 0.85/0.44 % (2955149)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.44 % (2955149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.44 % (2955149)CaDiCaL version: 2.1.3
% 0.85/0.44 % (2955149)Termination reason: Instruction limit
% 0.85/0.44 % (2955149)Termination phase: Saturation
% 0.85/0.44 % (2955149)Time elapsed: 0.067 s
% 0.85/0.44 % (2955149)Peak memory usage: 12 MB
% 0.85/0.44 % (2955149)Instructions burned: 117 (million)
% 0.85/0.44 % (2955165)ott-21_1_sil=16000:fs=off:random_seed=2983329339:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 0.85/0.44 % (2955161)Instruction limit reached!
% 0.85/0.44 % (2955161)------------------------------
% 0.85/0.44 % (2955161)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.44 % (2955161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.44 % (2955161)CaDiCaL version: 2.1.3
% 0.85/0.44 % (2955161)Termination reason: Instruction limit
% 0.85/0.44 % (2955161)Termination phase: Saturation
% 0.85/0.44 % (2955161)Time elapsed: 0.061 s
% 0.85/0.44 % (2955161)Peak memory usage: 12 MB
% 0.85/0.44 % (2955161)Instructions burned: 133 (million)
% 0.85/0.44 % (2955167)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1088824407:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 0.85/0.44 % (2955150)Instruction limit reached!
% 0.85/0.44 % (2955150)------------------------------
% 0.85/0.44 % (2955150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.44 % (2955150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.44 % (2955150)CaDiCaL version: 2.1.3
% 0.85/0.44 % (2955150)Termination reason: Instruction limit
% 0.85/0.44 % (2955150)Termination phase: Saturation
% 0.85/0.44 % (2955150)Time elapsed: 0.120 s
% 0.85/0.44 % (2955150)Peak memory usage: 12 MB
% 0.85/0.44 % (2955150)Instructions burned: 134 (million)
% 0.85/0.44 % (2955151) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2955140-2955151"...
% 0.85/0.44 % (2955151)...printing done.
% 0.85/0.44 % (2955151)Refutation found. Thanks to Tanya!
% 0.85/0.44 % SZS status Theorem for theBenchmark
% 0.85/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.85/0.44 % (2955151)------------------------------
% 0.85/0.44 % (2955151)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.85/0.44 % (2955151)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.85/0.44 % (2955151)CaDiCaL version: 2.1.3
% 0.85/0.44 % (2955151)Termination reason: Refutation
% 0.85/0.44 % (2955151)Time elapsed: 0.141 s
% 0.85/0.44 % (2955151)Peak memory usage: 13 MB
% 0.85/0.44 % (2955151)Instructions burned: 157 (million)
% 0.85/0.44 % (2955140)Success in time 0.202 s
% 0.85/0.44 % Vampire exiting
%------------------------------------------------------------------------------