%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL864^1 : 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 0.22s 0.38s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 23
% Syntax : Number of formulae : 287 ( 45 unt; 0 typ; 17 def)
% Number of atoms : 2998 ( 523 equ; 0 cnn)
% Maximal formula atoms : 12 ( 10 avg)
% Number of connectives : 3095 ( 258 ~; 657 |; 123 &;1753 @)
% ( 21 <=>; 104 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 94 ( 94 >; 0 *; 0 +; 0 <<)
% Number of symbols : 81 ( 76 usr; 32 con; 0-4 aty)
% ( 159 !!; 19 ??; 0 @@+; 0 @@-)
% Number of variables : 429 ( 0 sgn 174 !; 5 ?; 429 :)
% 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 ) )
<=> ( ( meuclidean @ 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 ) )
<=> ( ( meuclidean @ 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 ) )
<=> ( ( meuclidean @ X0 )
& ( msymmetric @ X0 )
& ( mtransitive @ X0 )
& ( mserial @ X0 ) ) ),
inference(rectify,[],[f33]) ).
thf(f86,plain,
~ ! [X0: $i > $i > $o] :
( ( ( ( meuclidean @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) )
<=> ( ( ( meuclidean @ 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 ) )
<~> ( ( ( meuclidean @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true )
& ( ( mserial @ X0 )
= $true ) ) ),
inference(ennf_transformation,[],[f86]) ).
thf(f88,plain,
? [X0: $i > $i > $o] :
( ( ( ( meuclidean @ X0 )
!= $true )
| ( ( msymmetric @ X0 )
!= $true )
| ( ( mtransitive @ X0 )
!= $true )
| ( ( mserial @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true ) )
& ( ( ( ( meuclidean @ 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] :
( ( ( ( meuclidean @ X0 )
!= $true )
| ( ( msymmetric @ X0 )
!= $true )
| ( ( mtransitive @ X0 )
!= $true )
| ( ( mserial @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true ) )
& ( ( ( ( meuclidean @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true )
& ( ( mserial @ X0 )
= $true ) )
| ( ( ( meuclidean @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) ) ) ),
inference(flattening,[],[f88]) ).
thf(f90,plain,
( ( ( $true
!= ( meuclidean @ sK0 ) )
| ( $true
!= ( msymmetric @ sK0 ) )
| ( $true
!= ( mtransitive @ sK0 ) )
| ( $true
!= ( mserial @ sK0 ) )
| ( $true
!= ( meuclidean @ sK0 ) )
| ( $true
!= ( mreflexive @ sK0 ) ) )
& ( ( ( $true
= ( meuclidean @ 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(f126,plain,
( ( $true
= ( msymmetric @ sK0 ) )
| ( $true
= ( mreflexive @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f129,plain,
( ( $true
= ( meuclidean @ sK0 ) )
| ( $true
= ( meuclidean @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f130,plain,
( ( $true
!= ( meuclidean @ sK0 ) )
| ( $true
!= ( msymmetric @ sK0 ) )
| ( $true
!= ( mtransitive @ sK0 ) )
| ( $true
!= ( mserial @ sK0 ) )
| ( $true
!= ( meuclidean @ sK0 ) )
| ( $true
!= ( mreflexive @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f142,plain,
( ( $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] :
( !! @ $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,[],[f130,f112,f109,f111,f110,f112,f108]) ).
thf(f143,plain,
( ( $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] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f129,f112,f112]) ).
thf(f146,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(f148,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(f150,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(f151,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f150]) ).
thf(f152,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(pi_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ?? @ $i @ ( sK0 @ X1 ) ) )
| ( $true
= ( sK0 @ X2 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f155,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( sK0 @ X1 @ ( sK1 @ X1 ) ) )
| ( $true
= ( sK0 @ X2 @ X2 ) ) ),
inference(sigma_proxy_clausification,[],[f154]) ).
thf(f167,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,[],[f148]) ).
thf(f168,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,[],[f167]) ).
thf(f169,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,[],[f168]) ).
thf(f170,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,[],[f169]) ).
thf(f171,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,[],[f170]) ).
thf(f172,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,[],[f171]) ).
thf(f173,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,[],[f172]) ).
thf(f174,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,[],[f173]) ).
thf(f175,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,[],[f174]) ).
thf(f176,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,[],[f175]) ).
thf(f191,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,[],[f146]) ).
thf(f192,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,[],[f191]) ).
thf(f193,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,[],[f192]) ).
thf(f194,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( sK0 @ X1 @ Y0 ) ) ) )
| ( $true
= ( sK0 @ X2 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f193]) ).
thf(f195,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,[],[f194]) ).
thf(f196,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( sK0 @ X3 @ X1 )
=> ( sK0 @ X1 @ X3 ) ) )
| ( $true
= ( sK0 @ X2 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f195]) ).
thf(f197,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $true
= ( sK0 @ X2 @ X2 ) )
| ( $true
= ( sK0 @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f196]) ).
thf(f220,plain,
( $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(duplicate_literal_removal,[],[f143]) ).
thf(f221,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f220]) ).
thf(f222,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f221]) ).
thf(f223,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f222]) ).
thf(f224,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f223]) ).
thf(f225,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X2 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f224]) ).
thf(f226,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X2 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ X2 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( sK0 @ X3 @ X2 )
& ( sK0 @ X3 @ X1 ) )
=> ( sK0 @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f226]) ).
thf(f228,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( sK0 @ X3 @ X2 )
& ( sK0 @ X3 @ X1 ) ) )
| ( $true
= ( sK0 @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $true
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f228]) ).
thf(f230,plain,
( ( $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] :
( !! @ $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] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) ) ),
inference(duplicate_literal_removal,[],[f142]) ).
thf(f231,plain,
( ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
| ( $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] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f230]) ).
thf(f232,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
@ sK3 ) )
| ( $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] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(sigma_proxy_clausification,[],[f231]) ).
thf(f233,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK4 ) )
| ( $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] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(sigma_proxy_clausification,[],[f232]) ).
thf(f234,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK5 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(sigma_proxy_clausification,[],[f233]) ).
thf(f235,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) )
@ sK6 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(sigma_proxy_clausification,[],[f234]) ).
thf(f236,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) )
@ sK6 ) )
| ( $false
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f235]) ).
thf(f237,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK4 )
=> ( sK0 @ sK4 @ Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK5 ) )
=> ( sK0 @ Y1 @ sK5 ) ) ) ) )
| ( $false
= ( ?? @ $i @ ( sK0 @ sK6 ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(beta-eta_normalization,[],[f236]) ).
thf(f238,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) ) )
@ sK8 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK4 )
=> ( sK0 @ sK4 @ Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK5 ) )
=> ( sK0 @ Y1 @ sK5 ) ) ) ) )
| ( $false
= ( ?? @ $i @ ( sK0 @ sK6 ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f237]) ).
thf(f239,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) ) )
@ sK8 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK4 )
=> ( sK0 @ sK4 @ Y0 ) )
@ sK9 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK5 ) )
=> ( sK0 @ Y1 @ sK5 ) ) ) ) )
| ( $false
= ( ?? @ $i @ ( sK0 @ sK6 ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f238]) ).
thf(f240,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) ) )
@ sK8 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK4 )
=> ( sK0 @ sK4 @ Y0 ) )
@ sK9 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK5 ) )
=> ( sK0 @ Y1 @ sK5 ) ) )
@ sK10 ) )
| ( $false
= ( ?? @ $i @ ( sK0 @ sK6 ) ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f239]) ).
thf(f241,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) ) )
@ sK8 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK4 )
=> ( sK0 @ sK4 @ Y0 ) )
@ sK9 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK5 ) )
=> ( sK0 @ Y1 @ sK5 ) ) )
@ sK10 ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(pi_proxy_clausification,[],[f240]) ).
thf(f242,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK8 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ sK8 @ sK3 ) ) ) )
| ( $false
= ( ( sK0 @ sK9 @ sK4 )
=> ( sK0 @ sK4 @ sK9 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK10 )
& ( sK0 @ sK10 @ sK5 ) )
=> ( sK0 @ Y0 @ sK5 ) ) ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(beta-eta_normalization,[],[f241]) ).
thf(f243,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK8 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ sK8 @ sK3 ) )
@ sK11 ) )
| ( $false
= ( ( sK0 @ sK9 @ sK4 )
=> ( sK0 @ sK4 @ sK9 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK10 )
& ( sK0 @ sK10 @ sK5 ) )
=> ( sK0 @ Y0 @ sK5 ) ) ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f242]) ).
thf(f244,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK8 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ sK8 @ sK3 ) )
@ sK11 ) )
| ( $false
= ( sK0 @ sK4 @ sK9 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK10 )
& ( sK0 @ sK10 @ sK5 ) )
=> ( sK0 @ Y0 @ sK5 ) ) ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f243]) ).
thf(f245,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK8 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ sK8 @ sK3 ) )
@ sK11 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK10 )
& ( sK0 @ sK10 @ sK5 ) )
=> ( sK0 @ Y0 @ sK5 ) ) ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f243]) ).
thf(f246,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK8 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ sK8 @ sK3 ) )
@ sK11 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK10 )
& ( sK0 @ sK10 @ sK5 ) )
=> ( sK0 @ Y0 @ sK5 ) )
@ sK12 ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f245]) ).
thf(f247,plain,
! [X1: $i] :
( ( $false
= ( ( ( sK0 @ sK11 @ sK8 )
& ( sK0 @ sK11 @ sK3 ) )
=> ( sK0 @ sK8 @ sK3 ) ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $false
= ( ( ( sK0 @ sK12 @ sK10 )
& ( sK0 @ sK10 @ sK5 ) )
=> ( sK0 @ sK12 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(beta-eta_normalization,[],[f246]) ).
thf(f248,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK8 @ sK3 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $false
= ( ( ( sK0 @ sK12 @ sK10 )
& ( sK0 @ sK10 @ sK5 ) )
=> ( sK0 @ sK12 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f247]) ).
thf(f249,plain,
! [X1: $i] :
( ( $true
= ( ( sK0 @ sK11 @ sK8 )
& ( sK0 @ sK11 @ sK3 ) ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $false
= ( ( ( sK0 @ sK12 @ sK10 )
& ( sK0 @ sK10 @ sK5 ) )
=> ( sK0 @ sK12 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f247]) ).
thf(f250,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK11 @ sK3 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $false
= ( ( ( sK0 @ sK12 @ sK10 )
& ( sK0 @ sK10 @ sK5 ) )
=> ( sK0 @ sK12 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f249]) ).
thf(f251,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK11 @ sK8 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $false
= ( ( ( sK0 @ sK12 @ sK10 )
& ( sK0 @ sK10 @ sK5 ) )
=> ( sK0 @ sK12 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f249]) ).
thf(f252,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK11 @ sK8 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $false
= ( sK0 @ sK12 @ sK5 ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f251]) ).
thf(f253,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK11 @ sK8 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $true
= ( ( sK0 @ sK12 @ sK10 )
& ( sK0 @ sK10 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f251]) ).
thf(f254,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK11 @ sK8 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $true
= ( sK0 @ sK10 @ sK5 ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f253]) ).
thf(f255,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK11 @ sK8 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $true
= ( sK0 @ sK12 @ sK10 ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f253]) ).
thf(f256,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK11 @ sK3 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $false
= ( sK0 @ sK12 @ sK5 ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f250]) ).
thf(f257,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK11 @ sK3 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $true
= ( ( sK0 @ sK12 @ sK10 )
& ( sK0 @ sK10 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f250]) ).
thf(f258,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK11 @ sK3 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $true
= ( sK0 @ sK10 @ sK5 ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f257]) ).
thf(f259,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK11 @ sK3 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $true
= ( sK0 @ sK12 @ sK10 ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f257]) ).
thf(f260,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK8 @ sK3 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $false
= ( sK0 @ sK12 @ sK5 ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f248]) ).
thf(f261,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK8 @ sK3 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $true
= ( ( sK0 @ sK12 @ sK10 )
& ( sK0 @ sK10 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f248]) ).
thf(f262,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK8 @ sK3 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $true
= ( sK0 @ sK10 @ sK5 ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f261]) ).
thf(f263,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK8 @ sK3 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ( $true
= ( sK0 @ sK12 @ sK10 ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f261]) ).
thf(f264,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK8 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ sK8 @ sK3 ) )
@ sK11 ) )
| ( $false
= ( sK0 @ sK4 @ sK9 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK10 )
& ( sK0 @ sK10 @ sK5 ) )
=> ( sK0 @ Y0 @ sK5 ) )
@ sK13 ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f244]) ).
thf(f265,plain,
! [X1: $i] :
( ( $false
= ( ( ( sK0 @ sK11 @ sK8 )
& ( sK0 @ sK11 @ sK3 ) )
=> ( sK0 @ sK8 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK4 @ sK9 ) )
| ( $false
= ( ( ( sK0 @ sK13 @ sK10 )
& ( sK0 @ sK10 @ sK5 ) )
=> ( sK0 @ sK13 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(beta-eta_normalization,[],[f264]) ).
thf(f266,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK8 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ sK9 ) )
| ( $false
= ( ( ( sK0 @ sK13 @ sK10 )
& ( sK0 @ sK10 @ sK5 ) )
=> ( sK0 @ sK13 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f265]) ).
thf(f267,plain,
! [X1: $i] :
( ( $true
= ( ( sK0 @ sK11 @ sK8 )
& ( sK0 @ sK11 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK4 @ sK9 ) )
| ( $false
= ( ( ( sK0 @ sK13 @ sK10 )
& ( sK0 @ sK10 @ sK5 ) )
=> ( sK0 @ sK13 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f265]) ).
thf(f268,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK11 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ sK9 ) )
| ( $false
= ( ( ( sK0 @ sK13 @ sK10 )
& ( sK0 @ sK10 @ sK5 ) )
=> ( sK0 @ sK13 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f267]) ).
thf(f269,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK11 @ sK8 ) )
| ( $false
= ( sK0 @ sK4 @ sK9 ) )
| ( $false
= ( ( ( sK0 @ sK13 @ sK10 )
& ( sK0 @ sK10 @ sK5 ) )
=> ( sK0 @ sK13 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f267]) ).
thf(f270,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK11 @ sK8 ) )
| ( $false
= ( sK0 @ sK4 @ sK9 ) )
| ( $false
= ( sK0 @ sK13 @ sK5 ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f269]) ).
thf(f271,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK11 @ sK8 ) )
| ( $false
= ( sK0 @ sK4 @ sK9 ) )
| ( $true
= ( ( sK0 @ sK13 @ sK10 )
& ( sK0 @ sK10 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f269]) ).
thf(f272,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK11 @ sK8 ) )
| ( $false
= ( sK0 @ sK4 @ sK9 ) )
| ( $true
= ( sK0 @ sK10 @ sK5 ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f271]) ).
thf(f273,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK11 @ sK8 ) )
| ( $false
= ( sK0 @ sK4 @ sK9 ) )
| ( $true
= ( sK0 @ sK13 @ sK10 ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f271]) ).
thf(f274,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK11 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ sK9 ) )
| ( $false
= ( sK0 @ sK13 @ sK5 ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f268]) ).
thf(f275,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK11 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ sK9 ) )
| ( $true
= ( ( sK0 @ sK13 @ sK10 )
& ( sK0 @ sK10 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f268]) ).
thf(f276,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK11 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ sK9 ) )
| ( $true
= ( sK0 @ sK10 @ sK5 ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f275]) ).
thf(f277,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ sK11 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ sK9 ) )
| ( $true
= ( sK0 @ sK13 @ sK10 ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f275]) ).
thf(f278,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK8 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ sK9 ) )
| ( $false
= ( sK0 @ sK13 @ sK5 ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f266]) ).
thf(f279,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK8 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ sK9 ) )
| ( $true
= ( ( sK0 @ sK13 @ sK10 )
& ( sK0 @ sK10 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f266]) ).
thf(f280,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK8 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ sK9 ) )
| ( $true
= ( sK0 @ sK10 @ sK5 ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f279]) ).
thf(f281,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK8 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ sK9 ) )
| ( $true
= ( sK0 @ sK13 @ sK10 ) )
| ( $false
= ( sK0 @ sK6 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f279]) ).
thf(f283,definition,
( spl14_1
<=> ! [X2: $i] :
( $true
= ( sK0 @ X2 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
thf(f284,plain,
( ! [X2: $i] :
( $true
= ( sK0 @ X2 @ X2 ) )
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f283]) ).
thf(f286,definition,
( spl14_2
<=> ! [X1: $i] :
( $true
= ( sK0 @ X1 @ ( sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
thf(f287,plain,
( ! [X1: $i] :
( $true
= ( sK0 @ X1 @ ( sK1 @ X1 ) ) )
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f286]) ).
thf(f288,plain,
( spl14_1
| spl14_2 ),
inference(avatar_split_clause,[],[f155,f286,f283]) ).
thf(f290,definition,
( spl14_3
<=> ! [X2: $i,X3: $i,X4: $i] :
( ( $false
= ( sK0 @ X4 @ X2 ) )
| ( $false
= ( sK0 @ X4 @ X3 ) )
| ( $true
= ( sK0 @ X3 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
thf(f291,plain,
( ! [X2: $i,X3: $i,X4: $i] :
( ( $false
= ( sK0 @ X4 @ X2 ) )
| ( $false
= ( sK0 @ X4 @ X3 ) )
| ( $true
= ( sK0 @ X3 @ X2 ) ) )
| ~ spl14_3 ),
inference(avatar_component_clause,[],[f290]) ).
thf(f297,definition,
( spl14_5
<=> ! [X4: $i,X1: $i,X3: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X4 @ X3 ) )
| ( $true
= ( sK0 @ X4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_5])],[avatar_definition]) ).
thf(f298,plain,
( ! [X3: $i,X1: $i,X4: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X4 @ X3 ) )
| ( $true
= ( sK0 @ X4 @ X1 ) ) )
| ~ spl14_5 ),
inference(avatar_component_clause,[],[f297]) ).
thf(f299,plain,
( spl14_1
| spl14_5 ),
inference(avatar_split_clause,[],[f176,f297,f283]) ).
thf(f302,definition,
( spl14_6
<=> ! [X1: $i,X3: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $true
= ( sK0 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl14_6])],[avatar_definition]) ).
thf(f303,plain,
( ! [X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $true
= ( sK0 @ X1 @ X3 ) ) )
| ~ spl14_6 ),
inference(avatar_component_clause,[],[f302]) ).
thf(f304,plain,
( spl14_1
| spl14_6 ),
inference(avatar_split_clause,[],[f197,f302,f283]) ).
thf(f307,plain,
spl14_3,
inference(avatar_split_clause,[],[f229,f290]) ).
thf(f309,definition,
( spl14_7
<=> ( $false
= ( sK0 @ sK7 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_7])],[avatar_definition]) ).
thf(f311,plain,
( ( $false
= ( sK0 @ sK7 @ sK7 ) )
| ~ spl14_7 ),
inference(avatar_component_clause,[],[f309]) ).
thf(f313,definition,
( spl14_8
<=> ! [X1: $i] :
( $false
= ( sK0 @ sK6 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_8])],[avatar_definition]) ).
thf(f314,plain,
( ! [X1: $i] :
( $false
= ( sK0 @ sK6 @ X1 ) )
| ~ spl14_8 ),
inference(avatar_component_clause,[],[f313]) ).
thf(f316,definition,
( spl14_9
<=> ( $true
= ( sK0 @ sK12 @ sK10 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_9])],[avatar_definition]) ).
thf(f318,plain,
( ( $true
= ( sK0 @ sK12 @ sK10 ) )
| ~ spl14_9 ),
inference(avatar_component_clause,[],[f316]) ).
thf(f320,definition,
( spl14_10
<=> ( $true
= ( sK0 @ sK9 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_10])],[avatar_definition]) ).
thf(f322,plain,
( ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ~ spl14_10 ),
inference(avatar_component_clause,[],[f320]) ).
thf(f324,definition,
( spl14_11
<=> ( $true
= ( sK0 @ sK11 @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_11])],[avatar_definition]) ).
thf(f326,plain,
( ( $true
= ( sK0 @ sK11 @ sK8 ) )
| ~ spl14_11 ),
inference(avatar_component_clause,[],[f324]) ).
thf(f327,plain,
( spl14_7
| spl14_8
| spl14_9
| spl14_10
| spl14_11 ),
inference(avatar_split_clause,[],[f255,f324,f320,f316,f313,f309]) ).
thf(f329,definition,
( spl14_12
<=> ( $true
= ( sK0 @ sK10 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_12])],[avatar_definition]) ).
thf(f331,plain,
( ( $true
= ( sK0 @ sK10 @ sK5 ) )
| ~ spl14_12 ),
inference(avatar_component_clause,[],[f329]) ).
thf(f332,plain,
( spl14_7
| spl14_8
| spl14_12
| spl14_10
| spl14_11 ),
inference(avatar_split_clause,[],[f254,f324,f320,f329,f313,f309]) ).
thf(f334,definition,
( spl14_13
<=> ( $false
= ( sK0 @ sK12 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_13])],[avatar_definition]) ).
thf(f336,plain,
( ( $false
= ( sK0 @ sK12 @ sK5 ) )
| ~ spl14_13 ),
inference(avatar_component_clause,[],[f334]) ).
thf(f337,plain,
( spl14_7
| spl14_8
| spl14_13
| spl14_10
| spl14_11 ),
inference(avatar_split_clause,[],[f252,f324,f320,f334,f313,f309]) ).
thf(f339,definition,
( spl14_14
<=> ( $true
= ( sK0 @ sK11 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_14])],[avatar_definition]) ).
thf(f341,plain,
( ( $true
= ( sK0 @ sK11 @ sK3 ) )
| ~ spl14_14 ),
inference(avatar_component_clause,[],[f339]) ).
thf(f342,plain,
( spl14_7
| spl14_8
| spl14_9
| spl14_10
| spl14_14 ),
inference(avatar_split_clause,[],[f259,f339,f320,f316,f313,f309]) ).
thf(f343,plain,
( spl14_7
| spl14_8
| spl14_12
| spl14_10
| spl14_14 ),
inference(avatar_split_clause,[],[f258,f339,f320,f329,f313,f309]) ).
thf(f344,plain,
( spl14_7
| spl14_8
| spl14_13
| spl14_10
| spl14_14 ),
inference(avatar_split_clause,[],[f256,f339,f320,f334,f313,f309]) ).
thf(f346,definition,
( spl14_15
<=> ( $false
= ( sK0 @ sK8 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_15])],[avatar_definition]) ).
thf(f348,plain,
( ( $false
= ( sK0 @ sK8 @ sK3 ) )
| ~ spl14_15 ),
inference(avatar_component_clause,[],[f346]) ).
thf(f349,plain,
( spl14_7
| spl14_8
| spl14_9
| spl14_10
| spl14_15 ),
inference(avatar_split_clause,[],[f263,f346,f320,f316,f313,f309]) ).
thf(f350,plain,
( spl14_7
| spl14_8
| spl14_12
| spl14_10
| spl14_15 ),
inference(avatar_split_clause,[],[f262,f346,f320,f329,f313,f309]) ).
thf(f351,plain,
( spl14_7
| spl14_8
| spl14_13
| spl14_10
| spl14_15 ),
inference(avatar_split_clause,[],[f260,f346,f320,f334,f313,f309]) ).
thf(f353,definition,
( spl14_16
<=> ( $true
= ( sK0 @ sK13 @ sK10 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_16])],[avatar_definition]) ).
thf(f355,plain,
( ( $true
= ( sK0 @ sK13 @ sK10 ) )
| ~ spl14_16 ),
inference(avatar_component_clause,[],[f353]) ).
thf(f357,definition,
( spl14_17
<=> ( $false
= ( sK0 @ sK4 @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_17])],[avatar_definition]) ).
thf(f359,plain,
( ( $false
= ( sK0 @ sK4 @ sK9 ) )
| ~ spl14_17 ),
inference(avatar_component_clause,[],[f357]) ).
thf(f360,plain,
( spl14_7
| spl14_8
| spl14_16
| spl14_17
| spl14_11 ),
inference(avatar_split_clause,[],[f273,f324,f357,f353,f313,f309]) ).
thf(f361,plain,
( spl14_7
| spl14_8
| spl14_12
| spl14_17
| spl14_11 ),
inference(avatar_split_clause,[],[f272,f324,f357,f329,f313,f309]) ).
thf(f363,definition,
( spl14_18
<=> ( $false
= ( sK0 @ sK13 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_18])],[avatar_definition]) ).
thf(f365,plain,
( ( $false
= ( sK0 @ sK13 @ sK5 ) )
| ~ spl14_18 ),
inference(avatar_component_clause,[],[f363]) ).
thf(f366,plain,
( spl14_7
| spl14_8
| spl14_18
| spl14_17
| spl14_11 ),
inference(avatar_split_clause,[],[f270,f324,f357,f363,f313,f309]) ).
thf(f367,plain,
( spl14_7
| spl14_8
| spl14_16
| spl14_17
| spl14_14 ),
inference(avatar_split_clause,[],[f277,f339,f357,f353,f313,f309]) ).
thf(f368,plain,
( spl14_7
| spl14_8
| spl14_12
| spl14_17
| spl14_14 ),
inference(avatar_split_clause,[],[f276,f339,f357,f329,f313,f309]) ).
thf(f369,plain,
( spl14_7
| spl14_8
| spl14_18
| spl14_17
| spl14_14 ),
inference(avatar_split_clause,[],[f274,f339,f357,f363,f313,f309]) ).
thf(f370,plain,
( spl14_7
| spl14_8
| spl14_16
| spl14_17
| spl14_15 ),
inference(avatar_split_clause,[],[f281,f346,f357,f353,f313,f309]) ).
thf(f371,plain,
( spl14_7
| spl14_8
| spl14_12
| spl14_17
| spl14_15 ),
inference(avatar_split_clause,[],[f280,f346,f357,f329,f313,f309]) ).
thf(f372,plain,
( spl14_7
| spl14_8
| spl14_18
| spl14_17
| spl14_15 ),
inference(avatar_split_clause,[],[f278,f346,f357,f363,f313,f309]) ).
thf(f409,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK4 @ sK9 ) )
| ~ spl14_6
| ~ spl14_10 ),
inference(constrained_superposition,[],[f303,f322]) ).
thf(f410,plain,
( ( $true
= ( sK0 @ sK4 @ sK9 ) )
| ~ spl14_6
| ~ spl14_10 ),
inference(trivial_inequality_removal,[],[f409]) ).
thf(f449,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X0 @ X2 ) )
| ( $true
= ( sK0 @ X1 @ X2 ) ) )
| ~ spl14_3
| ~ spl14_6 ),
inference(constrained_superposition,[],[f303,f291]) ).
thf(f463,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK7 ) )
| ( $false
= ( sK0 @ X0 @ sK7 ) ) )
| ~ spl14_3
| ~ spl14_7 ),
inference(constrained_superposition,[],[f311,f291]) ).
thf(f490,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK7 ) ) )
| ~ spl14_3
| ~ spl14_7 ),
inference(duplicate_literal_removal,[],[f463]) ).
thf(f491,plain,
( ! [X0: $i] :
( $false
= ( sK0 @ X0 @ sK7 ) )
| ~ spl14_3
| ~ spl14_7 ),
inference(trivial_inequality_removal,[],[f490]) ).
thf(f499,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X0 @ X2 ) )
| ( $true
= ( sK0 @ X1 @ X2 ) ) )
| ~ spl14_3
| ~ spl14_6 ),
inference(trivial_inequality_removal,[],[f449]) ).
thf(f535,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ sK7 @ X0 ) ) )
| ~ spl14_3
| ~ spl14_6
| ~ spl14_7 ),
inference(constrained_superposition,[],[f303,f491]) ).
thf(f536,plain,
( ! [X0: $i] :
( $false
= ( sK0 @ sK7 @ X0 ) )
| ~ spl14_3
| ~ spl14_6
| ~ spl14_7 ),
inference(trivial_inequality_removal,[],[f535]) ).
thf(f540,plain,
( ( $true = $false )
| ~ spl14_2
| ~ spl14_3
| ~ spl14_6
| ~ spl14_7 ),
inference(constrained_superposition,[],[f536,f287]) ).
thf(f552,plain,
( $false
| ~ spl14_2
| ~ spl14_3
| ~ spl14_6
| ~ spl14_7 ),
inference(trivial_inequality_removal,[],[f540]) ).
thf(f553,plain,
( ~ spl14_2
| ~ spl14_3
| ~ spl14_6
| ~ spl14_7 ),
inference(avatar_contradiction_clause,[],[f552]) ).
thf(f554,plain,
( ( $true = $false )
| ~ spl14_1
| ~ spl14_3
| ~ spl14_7 ),
inference(constrained_superposition,[],[f284,f491]) ).
thf(f556,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $true
= ( sK0 @ X1 @ X0 ) ) )
| ~ spl14_1
| ~ spl14_3 ),
inference(constrained_superposition,[],[f284,f291]) ).
thf(f572,plain,
( $false
| ~ spl14_1
| ~ spl14_3
| ~ spl14_7 ),
inference(trivial_inequality_removal,[],[f554]) ).
thf(f573,plain,
( ~ spl14_1
| ~ spl14_3
| ~ spl14_7 ),
inference(avatar_contradiction_clause,[],[f572]) ).
thf(f582,plain,
( ( $true = $false )
| ~ spl14_1
| ~ spl14_8 ),
inference(constrained_superposition,[],[f314,f284]) ).
thf(f594,plain,
( $false
| ~ spl14_1
| ~ spl14_8 ),
inference(trivial_inequality_removal,[],[f582]) ).
thf(f595,plain,
( ~ spl14_1
| ~ spl14_8 ),
inference(avatar_contradiction_clause,[],[f594]) ).
thf(f597,plain,
( ( $true = $false )
| ~ spl14_6
| ~ spl14_10
| ~ spl14_17 ),
inference(constrained_superposition,[],[f359,f410]) ).
thf(f603,plain,
( $false
| ~ spl14_6
| ~ spl14_10
| ~ spl14_17 ),
inference(trivial_inequality_removal,[],[f597]) ).
thf(f604,plain,
( ~ spl14_6
| ~ spl14_10
| ~ spl14_17 ),
inference(avatar_contradiction_clause,[],[f603]) ).
thf(f609,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK5 ) )
| ( $false
= ( sK0 @ X0 @ sK13 ) ) )
| ~ spl14_3
| ~ spl14_18 ),
inference(constrained_superposition,[],[f291,f365]) ).
thf(f612,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK13 ) )
| ( $false
= ( sK0 @ X0 @ sK5 ) ) )
| ~ spl14_3
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f609]) ).
thf(f632,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK10 @ sK13 ) )
| ~ spl14_6
| ~ spl14_16 ),
inference(constrained_superposition,[],[f303,f355]) ).
thf(f633,plain,
( ( $true
= ( sK0 @ sK10 @ sK13 ) )
| ~ spl14_6
| ~ spl14_16 ),
inference(trivial_inequality_removal,[],[f632]) ).
thf(f1048,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK10 @ sK5 ) )
| ~ spl14_3
| ~ spl14_6
| ~ spl14_16
| ~ spl14_18 ),
inference(constrained_superposition,[],[f633,f612]) ).
thf(f1049,plain,
( ( $false
= ( sK0 @ sK10 @ sK5 ) )
| ~ spl14_3
| ~ spl14_6
| ~ spl14_16
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f1048]) ).
thf(f1062,plain,
( ( $true = $false )
| ~ spl14_3
| ~ spl14_6
| ~ spl14_12
| ~ spl14_16
| ~ spl14_18 ),
inference(constrained_superposition,[],[f1049,f331]) ).
thf(f1072,plain,
( $false
| ~ spl14_3
| ~ spl14_6
| ~ spl14_12
| ~ spl14_16
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f1062]) ).
thf(f1073,plain,
( ~ spl14_3
| ~ spl14_6
| ~ spl14_12
| ~ spl14_16
| ~ spl14_18 ),
inference(avatar_contradiction_clause,[],[f1072]) ).
thf(f1130,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK3 ) )
| ( $false
= ( sK0 @ sK8 @ X0 ) ) )
| ~ spl14_5
| ~ spl14_15 ),
inference(constrained_superposition,[],[f298,f348]) ).
thf(f1133,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK3 ) )
| ( $false
= ( sK0 @ sK8 @ X0 ) ) )
| ~ spl14_5
| ~ spl14_15 ),
inference(trivial_inequality_removal,[],[f1130]) ).
thf(f1148,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK8 @ sK11 ) )
| ~ spl14_6
| ~ spl14_11 ),
inference(constrained_superposition,[],[f303,f326]) ).
thf(f1149,plain,
( ( $true
= ( sK0 @ sK8 @ sK11 ) )
| ~ spl14_6
| ~ spl14_11 ),
inference(trivial_inequality_removal,[],[f1148]) ).
thf(f1378,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK5 ) )
| ( $false
= ( sK0 @ sK12 @ X0 ) ) )
| ~ spl14_5
| ~ spl14_13 ),
inference(constrained_superposition,[],[f298,f336]) ).
thf(f1381,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK5 ) )
| ( $false
= ( sK0 @ sK12 @ X0 ) ) )
| ~ spl14_5
| ~ spl14_13 ),
inference(trivial_inequality_removal,[],[f1378]) ).
thf(f1566,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK8 @ sK11 ) )
| ~ spl14_5
| ~ spl14_14
| ~ spl14_15 ),
inference(constrained_superposition,[],[f341,f1133]) ).
thf(f1577,plain,
( ( $false
= ( sK0 @ sK8 @ sK11 ) )
| ~ spl14_5
| ~ spl14_14
| ~ spl14_15 ),
inference(trivial_inequality_removal,[],[f1566]) ).
thf(f1596,plain,
( ( $true = $false )
| ~ spl14_5
| ~ spl14_6
| ~ spl14_11
| ~ spl14_14
| ~ spl14_15 ),
inference(constrained_superposition,[],[f1577,f1149]) ).
thf(f1606,plain,
( $false
| ~ spl14_5
| ~ spl14_6
| ~ spl14_11
| ~ spl14_14
| ~ spl14_15 ),
inference(trivial_inequality_removal,[],[f1596]) ).
thf(f1607,plain,
( ~ spl14_5
| ~ spl14_6
| ~ spl14_11
| ~ spl14_14
| ~ spl14_15 ),
inference(avatar_contradiction_clause,[],[f1606]) ).
thf(f1796,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK10 @ sK5 ) )
| ~ spl14_5
| ~ spl14_9
| ~ spl14_13 ),
inference(constrained_superposition,[],[f318,f1381]) ).
thf(f1797,plain,
( ( $false
= ( sK0 @ sK10 @ sK5 ) )
| ~ spl14_5
| ~ spl14_9
| ~ spl14_13 ),
inference(trivial_inequality_removal,[],[f1796]) ).
thf(f1823,plain,
( ( $true = $false )
| ~ spl14_5
| ~ spl14_9
| ~ spl14_12
| ~ spl14_13 ),
inference(constrained_superposition,[],[f1797,f331]) ).
thf(f1837,plain,
( $false
| ~ spl14_5
| ~ spl14_9
| ~ spl14_12
| ~ spl14_13 ),
inference(trivial_inequality_removal,[],[f1823]) ).
thf(f1838,plain,
( ~ spl14_5
| ~ spl14_9
| ~ spl14_12
| ~ spl14_13 ),
inference(avatar_contradiction_clause,[],[f1837]) ).
thf(f1843,plain,
( spl14_5
| ~ spl14_3
| ~ spl14_6 ),
inference(avatar_split_clause,[],[f499,f302,f290,f297]) ).
thf(f1995,plain,
( ( $true = $false )
| ~ spl14_2
| ~ spl14_8 ),
inference(constrained_superposition,[],[f287,f314]) ).
thf(f2001,plain,
( $false
| ~ spl14_2
| ~ spl14_8 ),
inference(trivial_inequality_removal,[],[f1995]) ).
thf(f2002,plain,
( ~ spl14_2
| ~ spl14_8 ),
inference(avatar_contradiction_clause,[],[f2001]) ).
thf(f2005,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $true
= ( sK0 @ X1 @ X0 ) ) )
| ~ spl14_1
| ~ spl14_3 ),
inference(trivial_inequality_removal,[],[f556]) ).
thf(f2120,plain,
( spl14_6
| ~ spl14_1
| ~ spl14_3 ),
inference(avatar_split_clause,[],[f2005,f290,f283,f302]) ).
cnf(s1,plain,
( spl14_1
| spl14_2 ),
inference(sat_conversion,[],[f288]) ).
cnf(s3,plain,
( spl14_1
| spl14_5 ),
inference(sat_conversion,[],[f299]) ).
cnf(s5,plain,
( spl14_1
| spl14_6 ),
inference(sat_conversion,[],[f304]) ).
cnf(s8,plain,
spl14_3,
inference(sat_conversion,[],[f307]) ).
cnf(s9,plain,
( spl14_7
| spl14_8
| spl14_9
| spl14_10
| spl14_11 ),
inference(sat_conversion,[],[f327]) ).
cnf(s10,plain,
( spl14_7
| spl14_8
| spl14_10
| spl14_11
| spl14_12 ),
inference(sat_conversion,[],[f332]) ).
cnf(s11,plain,
( spl14_7
| spl14_8
| spl14_10
| spl14_11
| spl14_13 ),
inference(sat_conversion,[],[f337]) ).
cnf(s12,plain,
( spl14_7
| spl14_8
| spl14_9
| spl14_10
| spl14_14 ),
inference(sat_conversion,[],[f342]) ).
cnf(s13,plain,
( spl14_7
| spl14_8
| spl14_10
| spl14_12
| spl14_14 ),
inference(sat_conversion,[],[f343]) ).
cnf(s14,plain,
( spl14_7
| spl14_8
| spl14_10
| spl14_13
| spl14_14 ),
inference(sat_conversion,[],[f344]) ).
cnf(s15,plain,
( spl14_7
| spl14_8
| spl14_9
| spl14_10
| spl14_15 ),
inference(sat_conversion,[],[f349]) ).
cnf(s16,plain,
( spl14_7
| spl14_8
| spl14_10
| spl14_12
| spl14_15 ),
inference(sat_conversion,[],[f350]) ).
cnf(s17,plain,
( spl14_7
| spl14_8
| spl14_10
| spl14_13
| spl14_15 ),
inference(sat_conversion,[],[f351]) ).
cnf(s18,plain,
( spl14_7
| spl14_8
| spl14_11
| spl14_16
| spl14_17 ),
inference(sat_conversion,[],[f360]) ).
cnf(s19,plain,
( spl14_7
| spl14_8
| spl14_11
| spl14_12
| spl14_17 ),
inference(sat_conversion,[],[f361]) ).
cnf(s20,plain,
( spl14_7
| spl14_8
| spl14_11
| spl14_17
| spl14_18 ),
inference(sat_conversion,[],[f366]) ).
cnf(s21,plain,
( spl14_7
| spl14_8
| spl14_14
| spl14_16
| spl14_17 ),
inference(sat_conversion,[],[f367]) ).
cnf(s22,plain,
( spl14_7
| spl14_8
| spl14_12
| spl14_14
| spl14_17 ),
inference(sat_conversion,[],[f368]) ).
cnf(s23,plain,
( spl14_7
| spl14_8
| spl14_14
| spl14_17
| spl14_18 ),
inference(sat_conversion,[],[f369]) ).
cnf(s24,plain,
( spl14_7
| spl14_8
| spl14_15
| spl14_16
| spl14_17 ),
inference(sat_conversion,[],[f370]) ).
cnf(s25,plain,
( spl14_7
| spl14_8
| spl14_12
| spl14_15
| spl14_17 ),
inference(sat_conversion,[],[f371]) ).
cnf(s26,plain,
( spl14_7
| spl14_8
| spl14_15
| spl14_17
| spl14_18 ),
inference(sat_conversion,[],[f372]) ).
cnf(s29,plain,
( ~ spl14_2
| ~ spl14_3
| ~ spl14_6
| ~ spl14_7 ),
inference(sat_conversion,[],[f553]) ).
cnf(s33,plain,
( ~ spl14_1
| ~ spl14_3
| ~ spl14_7 ),
inference(sat_conversion,[],[f573]) ).
cnf(s35,plain,
( ~ spl14_1
| ~ spl14_8 ),
inference(sat_conversion,[],[f595]) ).
cnf(s37,plain,
( ~ spl14_6
| ~ spl14_10
| ~ spl14_17 ),
inference(sat_conversion,[],[f604]) ).
cnf(s43,plain,
( ~ spl14_3
| ~ spl14_6
| ~ spl14_12
| ~ spl14_16
| ~ spl14_18 ),
inference(sat_conversion,[],[f1073]) ).
cnf(s47,plain,
( ~ spl14_5
| ~ spl14_6
| ~ spl14_11
| ~ spl14_14
| ~ spl14_15 ),
inference(sat_conversion,[],[f1607]) ).
cnf(s51,plain,
( ~ spl14_5
| ~ spl14_9
| ~ spl14_12
| ~ spl14_13 ),
inference(sat_conversion,[],[f1838]) ).
cnf(s52,plain,
( ~ spl14_3
| spl14_5
| ~ spl14_6 ),
inference(sat_conversion,[],[f1843]) ).
cnf(s57,plain,
( ~ spl14_2
| ~ spl14_8 ),
inference(sat_conversion,[],[f2002]) ).
cnf(s58,plain,
( ~ spl14_1
| ~ spl14_3
| spl14_6 ),
inference(sat_conversion,[],[f2120]) ).
cnf(s62,plain,
( spl14_10
| spl14_9
| spl14_1 ),
inference(rat,[],[s47,s9,s12,s15,s3,s57,s29,s1,s5,s8]) ).
cnf(s63,plain,
( spl14_15
| spl14_17
| spl14_1 ),
inference(rat,[],[s43,s25,s24,s26,s57,s29,s1,s5,s8]) ).
cnf(s64,plain,
( spl14_14
| spl14_17
| spl14_1 ),
inference(rat,[],[s43,s22,s21,s23,s57,s29,s1,s5,s8]) ).
cnf(s65,plain,
( spl14_17
| spl14_1 ),
inference(rat,[],[s43,s18,s19,s20,s47,s64,s63,s3,s57,s29,s1,s5,s8]) ).
cnf(s66,plain,
( spl14_15
| spl14_1 ),
inference(rat,[],[s51,s17,s16,s3,s57,s29,s1,s62,s37,s65,s5,s8]) ).
cnf(s67,plain,
( spl14_14
| spl14_1 ),
inference(rat,[],[s51,s13,s14,s3,s57,s29,s1,s62,s37,s65,s5,s8]) ).
cnf(s68,plain,
spl14_1,
inference(rat,[],[s51,s11,s10,s47,s67,s66,s62,s37,s65,s29,s57,s1,s3,s5,s8]) ).
cnf(s69,plain,
spl14_6,
inference(rat,[],[s58,s8,s68]) ).
cnf(s70,plain,
~ spl14_8,
inference(rat,[],[s35,s68]) ).
cnf(s71,plain,
~ spl14_7,
inference(rat,[],[s33,s8,s68]) ).
cnf(s72,plain,
spl14_5,
inference(rat,[],[s52,s8,s69]) ).
cnf(s73,plain,
( spl14_15
| spl14_17 ),
inference(rat,[],[s43,s25,s24,s26,s71,s70,s69,s8]) ).
cnf(s74,plain,
( spl14_14
| spl14_17 ),
inference(rat,[],[s43,s22,s21,s23,s71,s70,s69,s8]) ).
cnf(s75,plain,
( spl14_11
| spl14_17 ),
inference(rat,[],[s43,s18,s19,s20,s71,s70,s69,s8]) ).
cnf(s76,plain,
spl14_17,
inference(rat,[],[s75,s47,s74,s73,s69,s72]) ).
cnf(s77,plain,
~ spl14_10,
inference(rat,[],[s37,s69,s76]) ).
cnf(s78,plain,
spl14_9,
inference(rat,[],[s47,s9,s12,s15,s69,s72,s77,s70,s71]) ).
cnf(s79,plain,
spl14_13,
inference(rat,[],[s47,s11,s14,s17,s69,s72,s70,s71,s77]) ).
cnf(s80,plain,
~ spl14_12,
inference(rat,[],[s51,s78,s72,s79]) ).
cnf(s81,plain,
spl14_11,
inference(rat,[],[s10,s71,s70,s77,s80]) ).
cnf(s82,plain,
spl14_15,
inference(rat,[],[s16,s71,s70,s77,s80]) ).
cnf(s83,plain,
spl14_14,
inference(rat,[],[s13,s71,s70,s77,s80]) ).
cnf(s84,plain,
$false,
inference(rat,[],[s47,s82,s72,s69,s81,s83]) ).
thf(f2121,plain,
$false,
inference(avatar_sat_refutation,[],[s84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL864^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n008.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 10:15:54 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 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
% 0.22/0.38 % (2956012)Will run a generic schedule for satisfiability detection.
% 0.22/0.38 % (2956017)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3985997335_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.38 % Exception at run slice level
% 0.22/0.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.38 % (2956018)% WARNING: option uhcvi not known.
% 0.22/0.38 % (2956018)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3469969893:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.38 % (2956019)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2492029529:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.38 % (2956020)dis+10_1_sil=32000:sp=arity:random_seed=3710337884:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.38 % (2956021)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2846603336:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.38 % (2956018)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.38 % (2956021)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.38 % (2956018)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.22/0.38 % (2956025)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1835565689:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.22/0.38 % Exception at run slice level
% 0.22/0.38 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.22/0.38 % (2956022)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3899952442:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.38 % (2956023)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=914163266:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.38 % (2956031)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=947759271:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.38 % (2956020)Instruction limit reached!
% 0.22/0.38 % (2956020)------------------------------
% 0.22/0.38 % (2956020)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.38 % (2956020)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.38 % (2956020)CaDiCaL version: 2.1.3
% 0.22/0.38 % (2956020)Termination reason: Instruction limit
% 0.22/0.38 % (2956020)Termination phase: Saturation
% 0.22/0.38 % (2956020)Time elapsed: 0.047 s
% 0.22/0.38 % (2956020)Peak memory usage: 12 MB
% 0.22/0.38 % (2956020)Instructions burned: 104 (million)
% 0.22/0.38 % (2956031)Instruction limit reached!
% 0.22/0.38 % (2956031)------------------------------
% 0.22/0.38 % (2956031)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.38 % (2956031)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.38 % (2956031)CaDiCaL version: 2.1.3
% 0.22/0.38 % (2956031)Termination reason: Instruction limit
% 0.22/0.38 % (2956031)Termination phase: Saturation
% 0.22/0.38 % (2956031)Time elapsed: 0.032 s
% 0.22/0.38 % (2956031)Peak memory usage: 12 MB
% 0.22/0.38 % (2956031)Instructions burned: 131 (million)
% 0.22/0.38 % (2956021)Instruction limit reached!
% 0.22/0.38 % (2956021)------------------------------
% 0.22/0.38 % (2956021)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.38 % (2956021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.38 % (2956021)CaDiCaL version: 2.1.3
% 0.22/0.38 % (2956021)Termination reason: Instruction limit
% 0.22/0.38 % (2956021)Termination phase: Saturation
% 0.22/0.38 % (2956021)Time elapsed: 0.052 s
% 0.22/0.38 % (2956021)Peak memory usage: 12 MB
% 0.22/0.38 % (2956021)Instructions burned: 116 (million)
% 0.22/0.38 % (2956036)ott-21_1_sil=16000:fs=off:random_seed=2325219299:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.22/0.38 % (2956035)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=187320129:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.22/0.38 % (2956023) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2956012-2956023"...
% 0.22/0.38 % (2956035)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.22/0.38 % (2956035)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.22/0.38 % (2956037)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=686987671:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 0.22/0.38 % (2956022)Instruction limit reached!
% 0.22/0.38 % (2956022)------------------------------
% 0.22/0.38 % (2956022)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.38 % (2956022)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.38 % (2956022)CaDiCaL version: 2.1.3
% 0.22/0.38 % (2956022)Termination reason: Instruction limit
% 0.22/0.38 % (2956022)Termination phase: Saturation
% 0.22/0.38 % (2956022)Time elapsed: 0.059 s
% 0.22/0.38 % (2956022)Peak memory usage: 12 MB
% 0.22/0.38 % (2956022)Instructions burned: 133 (million)
% 0.22/0.38 % (2956023)...printing done.
% 0.22/0.38 % (2956023)Refutation found. Thanks to Tanya!
% 0.22/0.38 % SZS status Theorem for theBenchmark
% 0.22/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.38 % (2956023)------------------------------
% 0.22/0.38 % (2956023)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.38 % (2956023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.38 % (2956023)CaDiCaL version: 2.1.3
% 0.22/0.38 % (2956023)Termination reason: Refutation
% 0.22/0.38 % (2956023)Time elapsed: 0.066 s
% 0.22/0.38 % (2956023)Peak memory usage: 13 MB
% 0.22/0.38 % (2956023)Instructions burned: 118 (million)
% 0.22/0.38 % (2956012)Success in time 0.122 s
% 0.22/0.38 % Vampire exiting
%------------------------------------------------------------------------------