%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL862^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 0.20s 0.34s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 21
% Syntax : Number of formulae : 275 ( 35 unt; 0 typ; 16 def)
% Number of atoms : 2726 ( 459 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 2858 ( 216 ~; 576 |; 129 &;1645 @)
% ( 20 <=>; 115 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 78 ( 78 >; 0 *; 0 +; 0 <<)
% Number of symbols : 77 ( 73 usr; 30 con; 0-4 aty)
% ( 156 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 389 ( 0 sgn 159 !; 3 ?; 389 :)
% 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(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(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/sandbox/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/sandbox/benchmark/Axioms/LCL013^0.ax',meuclidean) ).
thf(f32,conjecture,
! [X0: $i > $i > $o] :
( ( ( meuclidean @ X0 )
& ( mreflexive @ X0 ) )
<=> ( ( msymmetric @ X0 )
& ( mtransitive @ X0 )
& ( mreflexive @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( ( meuclidean @ X0 )
& ( mreflexive @ X0 ) )
<=> ( ( msymmetric @ X0 )
& ( mtransitive @ X0 )
& ( mreflexive @ 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(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 )
& ( mreflexive @ X0 ) ) ),
inference(rectify,[],[f33]) ).
thf(f86,plain,
~ ! [X0: $i > $i > $o] :
( ( ( ( meuclidean @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) )
<=> ( ( ( msymmetric @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true )
& ( ( mreflexive @ 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 )
& ( ( mreflexive @ X0 )
= $true ) ) ),
inference(ennf_transformation,[],[f86]) ).
thf(f88,plain,
? [X0: $i > $i > $o] :
( ( ( ( msymmetric @ X0 )
!= $true )
| ( ( mtransitive @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true ) )
& ( ( ( ( msymmetric @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true )
& ( ( mreflexive @ 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 )
| ( ( mreflexive @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true ) )
& ( ( ( ( msymmetric @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) )
| ( ( ( meuclidean @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) ) ) ),
inference(flattening,[],[f88]) ).
thf(f90,plain,
( ( ( $true
!= ( msymmetric @ sK0 ) )
| ( $true
!= ( mtransitive @ sK0 ) )
| ( $true
!= ( mreflexive @ sK0 ) )
| ( $true
!= ( meuclidean @ sK0 ) )
| ( $true
!= ( mreflexive @ sK0 ) ) )
& ( ( ( $true
= ( msymmetric @ sK0 ) )
& ( $true
= ( mtransitive @ sK0 ) )
& ( $true
= ( mreflexive @ 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(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
= ( mreflexive @ sK0 ) )
| ( $true
= ( mreflexive @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f125,plain,
( ( $true
= ( mtransitive @ sK0 ) )
| ( $true
= ( meuclidean @ 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
!= ( mreflexive @ 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] : ( Y0 @ Y1 @ 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 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f128,f109,f111,f108,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(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(f146,plain,
( ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) )
| ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f122,f108,f108]) ).
thf(f147,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) ),
inference(duplicate_literal_removal,[],[f146]) ).
thf(f148,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f149,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X1: $i] :
( $true
= ( sK0 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f171,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(f172,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,[],[f171]) ).
thf(f173,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,[],[f172]) ).
thf(f174,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,[],[f173]) ).
thf(f175,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,[],[f174]) ).
thf(f176,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,[],[f175]) ).
thf(f177,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,[],[f176]) ).
thf(f178,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,[],[f177]) ).
thf(f179,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,[],[f178]) ).
thf(f180,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,[],[f179]) ).
thf(f181,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,[],[f180]) ).
thf(f182,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,[],[f181]) ).
thf(f183,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,[],[f182]) ).
thf(f184,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,[],[f183]) ).
thf(f192,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(f193,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,[],[f192]) ).
thf(f194,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,[],[f193]) ).
thf(f195,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,[],[f194]) ).
thf(f196,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,[],[f195]) ).
thf(f197,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,[],[f196]) ).
thf(f198,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,[],[f197]) ).
thf(f199,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,[],[f198]) ).
thf(f200,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,[],[f199]) ).
thf(f201,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,[],[f200]) ).
thf(f202,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,[],[f201]) ).
thf(f203,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,[],[f202]) ).
thf(f204,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] : ( Y0 @ Y1 @ 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(duplicate_literal_removal,[],[f140]) ).
thf(f205,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] : ( sK0 @ Y0 @ Y0 ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f204]) ).
thf(f206,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK1 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f205]) ).
thf(f207,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK2 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f206]) ).
thf(f208,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ sK3 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f207]) ).
thf(f209,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f208]) ).
thf(f210,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK1 )
=> ( sK0 @ sK1 @ Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK2 ) )
=> ( sK0 @ Y1 @ sK2 ) ) ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ sK4 ) )
=> ( sK0 @ Y0 @ sK4 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f209]) ).
thf(f211,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK1 )
=> ( sK0 @ sK1 @ Y0 ) )
@ sK5 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK2 ) )
=> ( sK0 @ Y1 @ sK2 ) ) ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ sK4 ) )
=> ( sK0 @ Y0 @ sK4 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f210]) ).
thf(f212,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK1 )
=> ( sK0 @ sK1 @ Y0 ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK2 ) )
=> ( sK0 @ Y1 @ sK2 ) ) )
@ sK6 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ sK4 ) )
=> ( sK0 @ Y0 @ sK4 ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f211]) ).
thf(f213,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK1 )
=> ( sK0 @ sK1 @ Y0 ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK2 ) )
=> ( sK0 @ Y1 @ sK2 ) ) )
@ sK6 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ sK4 ) )
=> ( sK0 @ Y0 @ sK4 ) ) )
@ sK7 ) ) ),
inference(sigma_proxy_clausification,[],[f212]) ).
thf(f214,plain,
( ( $false
= ( ( sK0 @ sK5 @ sK1 )
=> ( sK0 @ sK1 @ sK5 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) )
=> ( sK0 @ Y0 @ sK2 ) ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK7 )
& ( sK0 @ Y0 @ sK4 ) )
=> ( sK0 @ sK7 @ sK4 ) ) ) ) ),
inference(beta-eta_normalization,[],[f213]) ).
thf(f215,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) )
=> ( sK0 @ Y0 @ sK2 ) ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK7 )
& ( sK0 @ Y0 @ sK4 ) )
=> ( sK0 @ sK7 @ sK4 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f214]) ).
thf(f216,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) )
=> ( sK0 @ Y0 @ sK2 ) ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK7 )
& ( sK0 @ Y0 @ sK4 ) )
=> ( sK0 @ sK7 @ sK4 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f214]) ).
thf(f217,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) )
=> ( sK0 @ Y0 @ sK2 ) )
@ sK8 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK7 )
& ( sK0 @ Y0 @ sK4 ) )
=> ( sK0 @ sK7 @ sK4 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f216]) ).
thf(f218,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) )
=> ( sK0 @ Y0 @ sK2 ) )
@ sK8 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK7 )
& ( sK0 @ Y0 @ sK4 ) )
=> ( sK0 @ sK7 @ sK4 ) )
@ sK9 ) ) ),
inference(sigma_proxy_clausification,[],[f217]) ).
thf(f219,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( ( ( sK0 @ sK8 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) )
=> ( sK0 @ sK8 @ sK2 ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK7 )
& ( sK0 @ sK9 @ sK4 ) )
=> ( sK0 @ sK7 @ sK4 ) ) ) ),
inference(beta-eta_normalization,[],[f218]) ).
thf(f220,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( sK0 @ sK8 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK7 )
& ( sK0 @ sK9 @ sK4 ) )
=> ( sK0 @ sK7 @ sK4 ) ) ) ),
inference(imp_proxy_clausification,[],[f219]) ).
thf(f221,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $true
= ( ( sK0 @ sK8 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK7 )
& ( sK0 @ sK9 @ sK4 ) )
=> ( sK0 @ sK7 @ sK4 ) ) ) ),
inference(imp_proxy_clausification,[],[f219]) ).
thf(f222,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK7 )
& ( sK0 @ sK9 @ sK4 ) )
=> ( sK0 @ sK7 @ sK4 ) ) ) ),
inference(and_proxy_clausification,[],[f221]) ).
thf(f223,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $true
= ( sK0 @ sK8 @ sK6 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK7 )
& ( sK0 @ sK9 @ sK4 ) )
=> ( sK0 @ sK7 @ sK4 ) ) ) ),
inference(and_proxy_clausification,[],[f221]) ).
thf(f224,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $true
= ( sK0 @ sK8 @ sK6 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( sK0 @ sK7 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f223]) ).
thf(f225,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $true
= ( sK0 @ sK8 @ sK6 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK9 @ sK7 )
& ( sK0 @ sK9 @ sK4 ) ) ) ),
inference(imp_proxy_clausification,[],[f223]) ).
thf(f226,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $true
= ( sK0 @ sK8 @ sK6 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f225]) ).
thf(f227,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $true
= ( sK0 @ sK8 @ sK6 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( sK0 @ sK9 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f225]) ).
thf(f228,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( sK0 @ sK7 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f222]) ).
thf(f229,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK9 @ sK7 )
& ( sK0 @ sK9 @ sK4 ) ) ) ),
inference(imp_proxy_clausification,[],[f222]) ).
thf(f230,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f229]) ).
thf(f231,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( sK0 @ sK9 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f229]) ).
thf(f232,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( sK0 @ sK8 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( sK0 @ sK7 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f220]) ).
thf(f233,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( sK0 @ sK8 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK9 @ sK7 )
& ( sK0 @ sK9 @ sK4 ) ) ) ),
inference(imp_proxy_clausification,[],[f220]) ).
thf(f234,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( sK0 @ sK8 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( sK0 @ sK9 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f233]) ).
thf(f235,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( sK0 @ sK8 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( sK0 @ sK9 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f233]) ).
thf(f236,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) )
=> ( sK0 @ Y0 @ sK2 ) )
@ sK10 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK7 )
& ( sK0 @ Y0 @ sK4 ) )
=> ( sK0 @ sK7 @ sK4 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f215]) ).
thf(f237,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) )
=> ( sK0 @ Y0 @ sK2 ) )
@ sK10 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK7 )
& ( sK0 @ Y0 @ sK4 ) )
=> ( sK0 @ sK7 @ sK4 ) )
@ sK11 ) ) ),
inference(sigma_proxy_clausification,[],[f236]) ).
thf(f238,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ( $false
= ( ( ( sK0 @ sK10 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) )
=> ( sK0 @ sK10 @ sK2 ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK11 @ sK7 )
& ( sK0 @ sK11 @ sK4 ) )
=> ( sK0 @ sK7 @ sK4 ) ) ) ),
inference(beta-eta_normalization,[],[f237]) ).
thf(f239,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK10 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK11 @ sK7 )
& ( sK0 @ sK11 @ sK4 ) )
=> ( sK0 @ sK7 @ sK4 ) ) ) ),
inference(imp_proxy_clausification,[],[f238]) ).
thf(f240,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ( $true
= ( ( sK0 @ sK10 @ sK6 )
& ( sK0 @ sK6 @ sK2 ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK11 @ sK7 )
& ( sK0 @ sK11 @ sK4 ) )
=> ( sK0 @ sK7 @ sK4 ) ) ) ),
inference(imp_proxy_clausification,[],[f238]) ).
thf(f241,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK11 @ sK7 )
& ( sK0 @ sK11 @ sK4 ) )
=> ( sK0 @ sK7 @ sK4 ) ) ) ),
inference(and_proxy_clausification,[],[f240]) ).
thf(f242,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ( $true
= ( sK0 @ sK10 @ sK6 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( ( ( sK0 @ sK11 @ sK7 )
& ( sK0 @ sK11 @ sK4 ) )
=> ( sK0 @ sK7 @ sK4 ) ) ) ),
inference(and_proxy_clausification,[],[f240]) ).
thf(f243,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ( $true
= ( sK0 @ sK10 @ sK6 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( sK0 @ sK7 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f242]) ).
thf(f244,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ( $true
= ( sK0 @ sK10 @ sK6 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK11 @ sK7 )
& ( sK0 @ sK11 @ sK4 ) ) ) ),
inference(imp_proxy_clausification,[],[f242]) ).
thf(f245,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ( $true
= ( sK0 @ sK10 @ sK6 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( sK0 @ sK11 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f244]) ).
thf(f246,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ( $true
= ( sK0 @ sK10 @ sK6 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( sK0 @ sK11 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f244]) ).
thf(f247,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( sK0 @ sK7 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f241]) ).
thf(f248,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK11 @ sK7 )
& ( sK0 @ sK11 @ sK4 ) ) ) ),
inference(imp_proxy_clausification,[],[f241]) ).
thf(f249,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( sK0 @ sK11 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f248]) ).
thf(f250,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( sK0 @ sK11 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f248]) ).
thf(f251,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK10 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $false
= ( sK0 @ sK7 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f239]) ).
thf(f252,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK10 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( ( sK0 @ sK11 @ sK7 )
& ( sK0 @ sK11 @ sK4 ) ) ) ),
inference(imp_proxy_clausification,[],[f239]) ).
thf(f253,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK10 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( sK0 @ sK11 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f252]) ).
thf(f254,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ( $false
= ( sK0 @ sK10 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ( $true
= ( sK0 @ sK11 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f252]) ).
thf(f256,definition,
( spl12_1
<=> ! [X6: $i,X2: $i,X4: $i] :
( ( $false
= ( sK0 @ X6 @ X2 ) )
| ( $false
= ( sK0 @ X6 @ X4 ) )
| ( $true
= ( sK0 @ X4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
thf(f257,plain,
( ! [X2: $i,X6: $i,X4: $i] :
( ( $false
= ( sK0 @ X6 @ X2 ) )
| ( $false
= ( sK0 @ X6 @ X4 ) )
| ( $true
= ( sK0 @ X4 @ X2 ) ) )
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f256]) ).
thf(f259,definition,
( spl12_2
<=> ! [X5: $i,X1: $i,X3: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X5 @ X3 ) )
| ( $true
= ( sK0 @ X5 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
thf(f260,plain,
( ! [X3: $i,X1: $i,X5: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X5 @ X3 ) )
| ( $true
= ( sK0 @ X5 @ X1 ) ) )
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f259]) ).
thf(f261,plain,
( spl12_1
| spl12_2 ),
inference(avatar_split_clause,[],[f184,f259,f256]) ).
thf(f263,definition,
( spl12_3
<=> ! [X1: $i,X3: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $true
= ( sK0 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
thf(f264,plain,
( ! [X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $true
= ( sK0 @ X1 @ X3 ) ) )
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f263]) ).
thf(f265,plain,
( spl12_1
| spl12_3 ),
inference(avatar_split_clause,[],[f203,f263,f256]) ).
thf(f267,definition,
( spl12_4
<=> ( $true
= ( sK0 @ sK9 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
thf(f269,plain,
( ( $true
= ( sK0 @ sK9 @ sK7 ) )
| ~ spl12_4 ),
inference(avatar_component_clause,[],[f267]) ).
thf(f271,definition,
( spl12_5
<=> ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
thf(f273,plain,
( ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f271]) ).
thf(f275,definition,
( spl12_6
<=> ( $true
= ( sK0 @ sK8 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_6])],[avatar_definition]) ).
thf(f277,plain,
( ( $true
= ( sK0 @ sK8 @ sK6 ) )
| ~ spl12_6 ),
inference(avatar_component_clause,[],[f275]) ).
thf(f279,definition,
( spl12_7
<=> ( $true
= ( sK0 @ sK5 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_7])],[avatar_definition]) ).
thf(f281,plain,
( ( $true
= ( sK0 @ sK5 @ sK1 ) )
| ~ spl12_7 ),
inference(avatar_component_clause,[],[f279]) ).
thf(f282,plain,
( spl12_4
| spl12_5
| spl12_6
| spl12_7 ),
inference(avatar_split_clause,[],[f227,f279,f275,f271,f267]) ).
thf(f284,definition,
( spl12_8
<=> ( $true
= ( sK0 @ sK9 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_8])],[avatar_definition]) ).
thf(f286,plain,
( ( $true
= ( sK0 @ sK9 @ sK4 ) )
| ~ spl12_8 ),
inference(avatar_component_clause,[],[f284]) ).
thf(f287,plain,
( spl12_8
| spl12_5
| spl12_6
| spl12_7 ),
inference(avatar_split_clause,[],[f226,f279,f275,f271,f284]) ).
thf(f289,definition,
( spl12_9
<=> ( $false
= ( sK0 @ sK7 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_9])],[avatar_definition]) ).
thf(f291,plain,
( ( $false
= ( sK0 @ sK7 @ sK4 ) )
| ~ spl12_9 ),
inference(avatar_component_clause,[],[f289]) ).
thf(f292,plain,
( spl12_9
| spl12_5
| spl12_6
| spl12_7 ),
inference(avatar_split_clause,[],[f224,f279,f275,f271,f289]) ).
thf(f294,definition,
( spl12_10
<=> ( $true
= ( sK0 @ sK6 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_10])],[avatar_definition]) ).
thf(f296,plain,
( ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ~ spl12_10 ),
inference(avatar_component_clause,[],[f294]) ).
thf(f297,plain,
( spl12_4
| spl12_5
| spl12_10
| spl12_7 ),
inference(avatar_split_clause,[],[f231,f279,f294,f271,f267]) ).
thf(f298,plain,
( spl12_8
| spl12_5
| spl12_10
| spl12_7 ),
inference(avatar_split_clause,[],[f230,f279,f294,f271,f284]) ).
thf(f299,plain,
( spl12_9
| spl12_5
| spl12_10
| spl12_7 ),
inference(avatar_split_clause,[],[f228,f279,f294,f271,f289]) ).
thf(f301,definition,
( spl12_11
<=> ( $false
= ( sK0 @ sK8 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_11])],[avatar_definition]) ).
thf(f303,plain,
( ( $false
= ( sK0 @ sK8 @ sK2 ) )
| ~ spl12_11 ),
inference(avatar_component_clause,[],[f301]) ).
thf(f304,plain,
( spl12_4
| spl12_5
| spl12_11
| spl12_7 ),
inference(avatar_split_clause,[],[f235,f279,f301,f271,f267]) ).
thf(f305,plain,
( spl12_8
| spl12_5
| spl12_11
| spl12_7 ),
inference(avatar_split_clause,[],[f234,f279,f301,f271,f284]) ).
thf(f306,plain,
( spl12_9
| spl12_5
| spl12_11
| spl12_7 ),
inference(avatar_split_clause,[],[f232,f279,f301,f271,f289]) ).
thf(f308,definition,
( spl12_12
<=> ( $true
= ( sK0 @ sK11 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_12])],[avatar_definition]) ).
thf(f310,plain,
( ( $true
= ( sK0 @ sK11 @ sK7 ) )
| ~ spl12_12 ),
inference(avatar_component_clause,[],[f308]) ).
thf(f312,definition,
( spl12_13
<=> ( $true
= ( sK0 @ sK10 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_13])],[avatar_definition]) ).
thf(f314,plain,
( ( $true
= ( sK0 @ sK10 @ sK6 ) )
| ~ spl12_13 ),
inference(avatar_component_clause,[],[f312]) ).
thf(f316,definition,
( spl12_14
<=> ( $false
= ( sK0 @ sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_14])],[avatar_definition]) ).
thf(f318,plain,
( ( $false
= ( sK0 @ sK1 @ sK5 ) )
| ~ spl12_14 ),
inference(avatar_component_clause,[],[f316]) ).
thf(f319,plain,
( spl12_12
| spl12_5
| spl12_13
| spl12_14 ),
inference(avatar_split_clause,[],[f246,f316,f312,f271,f308]) ).
thf(f321,definition,
( spl12_15
<=> ( $true
= ( sK0 @ sK11 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_15])],[avatar_definition]) ).
thf(f323,plain,
( ( $true
= ( sK0 @ sK11 @ sK4 ) )
| ~ spl12_15 ),
inference(avatar_component_clause,[],[f321]) ).
thf(f324,plain,
( spl12_15
| spl12_5
| spl12_13
| spl12_14 ),
inference(avatar_split_clause,[],[f245,f316,f312,f271,f321]) ).
thf(f325,plain,
( spl12_9
| spl12_5
| spl12_13
| spl12_14 ),
inference(avatar_split_clause,[],[f243,f316,f312,f271,f289]) ).
thf(f326,plain,
( spl12_12
| spl12_5
| spl12_10
| spl12_14 ),
inference(avatar_split_clause,[],[f250,f316,f294,f271,f308]) ).
thf(f327,plain,
( spl12_15
| spl12_5
| spl12_10
| spl12_14 ),
inference(avatar_split_clause,[],[f249,f316,f294,f271,f321]) ).
thf(f328,plain,
( spl12_9
| spl12_5
| spl12_10
| spl12_14 ),
inference(avatar_split_clause,[],[f247,f316,f294,f271,f289]) ).
thf(f330,definition,
( spl12_16
<=> ( $false
= ( sK0 @ sK10 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_16])],[avatar_definition]) ).
thf(f332,plain,
( ( $false
= ( sK0 @ sK10 @ sK2 ) )
| ~ spl12_16 ),
inference(avatar_component_clause,[],[f330]) ).
thf(f333,plain,
( spl12_12
| spl12_5
| spl12_16
| spl12_14 ),
inference(avatar_split_clause,[],[f254,f316,f330,f271,f308]) ).
thf(f334,plain,
( spl12_15
| spl12_5
| spl12_16
| spl12_14 ),
inference(avatar_split_clause,[],[f253,f316,f330,f271,f321]) ).
thf(f335,plain,
( spl12_9
| spl12_5
| spl12_16
| spl12_14 ),
inference(avatar_split_clause,[],[f251,f316,f330,f271,f289]) ).
thf(f353,plain,
( ( $true = $false )
| ~ spl12_5 ),
inference(constrained_superposition,[],[f273,f150]) ).
thf(f359,plain,
( $false
| ~ spl12_5 ),
inference(trivial_inequality_removal,[],[f353]) ).
thf(f360,plain,
~ spl12_5,
inference(avatar_contradiction_clause,[],[f359]) ).
thf(f367,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK1 @ sK5 ) )
| ~ spl12_3
| ~ spl12_7 ),
inference(constrained_superposition,[],[f264,f281]) ).
thf(f368,plain,
( ( $true
= ( sK0 @ sK1 @ sK5 ) )
| ~ spl12_3
| ~ spl12_7 ),
inference(trivial_inequality_removal,[],[f367]) ).
thf(f385,plain,
( ( $true = $false )
| ~ spl12_3
| ~ spl12_7
| ~ spl12_14 ),
inference(constrained_superposition,[],[f368,f318]) ).
thf(f389,plain,
( $false
| ~ spl12_3
| ~ spl12_7
| ~ spl12_14 ),
inference(trivial_inequality_removal,[],[f385]) ).
thf(f390,plain,
( ~ spl12_3
| ~ spl12_7
| ~ spl12_14 ),
inference(avatar_contradiction_clause,[],[f389]) ).
thf(f396,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK7 @ sK11 ) )
| ~ spl12_3
| ~ spl12_12 ),
inference(constrained_superposition,[],[f264,f310]) ).
thf(f397,plain,
( ( $true
= ( sK0 @ sK7 @ sK11 ) )
| ~ spl12_3
| ~ spl12_12 ),
inference(trivial_inequality_removal,[],[f396]) ).
thf(f451,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $true
= ( sK0 @ X0 @ X2 ) ) )
| ~ spl12_2
| ~ spl12_3 ),
inference(constrained_superposition,[],[f264,f260]) ).
thf(f473,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK4 ) )
| ( $false
= ( sK0 @ sK7 @ X0 ) ) )
| ~ spl12_2
| ~ spl12_9 ),
inference(constrained_superposition,[],[f291,f260]) ).
thf(f486,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK4 ) )
| ( $false
= ( sK0 @ sK7 @ X0 ) ) )
| ~ spl12_2
| ~ spl12_9 ),
inference(trivial_inequality_removal,[],[f473]) ).
thf(f501,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X1 @ X2 ) )
| ( $true
= ( sK0 @ X0 @ X2 ) ) )
| ~ spl12_2
| ~ spl12_3 ),
inference(trivial_inequality_removal,[],[f451]) ).
thf(f544,plain,
( spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(avatar_split_clause,[],[f501,f263,f259,f256]) ).
thf(f554,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK7 @ sK11 ) )
| ~ spl12_2
| ~ spl12_9
| ~ spl12_15 ),
inference(constrained_superposition,[],[f323,f486]) ).
thf(f561,plain,
( ( $false
= ( sK0 @ sK7 @ sK11 ) )
| ~ spl12_2
| ~ spl12_9
| ~ spl12_15 ),
inference(trivial_inequality_removal,[],[f554]) ).
thf(f603,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $true
= ( sK0 @ X1 @ X0 ) ) )
| ~ spl12_1 ),
inference(constrained_superposition,[],[f150,f257]) ).
thf(f625,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X0 @ X2 ) )
| ( $true
= ( sK0 @ X1 @ X2 ) ) )
| ~ spl12_1
| ~ spl12_3 ),
inference(constrained_superposition,[],[f264,f257]) ).
thf(f689,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK0 @ X0 @ X2 ) )
| ( $true
= ( sK0 @ X1 @ X2 ) ) )
| ~ spl12_1
| ~ spl12_3 ),
inference(trivial_inequality_removal,[],[f625]) ).
thf(f706,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $true
= ( sK0 @ X1 @ X0 ) ) )
| ~ spl12_1 ),
inference(trivial_inequality_removal,[],[f603]) ).
thf(f742,plain,
( ( $true = $false )
| ~ spl12_2
| ~ spl12_3
| ~ spl12_9
| ~ spl12_12
| ~ spl12_15 ),
inference(constrained_superposition,[],[f561,f397]) ).
thf(f750,plain,
( $false
| ~ spl12_2
| ~ spl12_3
| ~ spl12_9
| ~ spl12_12
| ~ spl12_15 ),
inference(trivial_inequality_removal,[],[f742]) ).
thf(f751,plain,
( ~ spl12_2
| ~ spl12_3
| ~ spl12_9
| ~ spl12_12
| ~ spl12_15 ),
inference(avatar_contradiction_clause,[],[f750]) ).
thf(f759,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK2 ) )
| ( $false
= ( sK0 @ sK10 @ X0 ) ) )
| ~ spl12_2
| ~ spl12_16 ),
inference(constrained_superposition,[],[f260,f332]) ).
thf(f762,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK2 ) )
| ( $false
= ( sK0 @ sK10 @ X0 ) ) )
| ~ spl12_2
| ~ spl12_16 ),
inference(trivial_inequality_removal,[],[f759]) ).
thf(f1201,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK6 @ sK2 ) )
| ~ spl12_2
| ~ spl12_13
| ~ spl12_16 ),
inference(constrained_superposition,[],[f314,f762]) ).
thf(f1202,plain,
( ( $false
= ( sK0 @ sK6 @ sK2 ) )
| ~ spl12_2
| ~ spl12_13
| ~ spl12_16 ),
inference(trivial_inequality_removal,[],[f1201]) ).
thf(f1227,plain,
( ( $true = $false )
| ~ spl12_2
| ~ spl12_10
| ~ spl12_13
| ~ spl12_16 ),
inference(constrained_superposition,[],[f1202,f296]) ).
thf(f1239,plain,
( $false
| ~ spl12_2
| ~ spl12_10
| ~ spl12_13
| ~ spl12_16 ),
inference(trivial_inequality_removal,[],[f1227]) ).
thf(f1240,plain,
( ~ spl12_2
| ~ spl12_10
| ~ spl12_13
| ~ spl12_16 ),
inference(avatar_contradiction_clause,[],[f1239]) ).
thf(f1258,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK2 ) )
| ( $false
= ( sK0 @ sK8 @ X0 ) ) )
| ~ spl12_2
| ~ spl12_11 ),
inference(constrained_superposition,[],[f260,f303]) ).
thf(f1261,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK2 ) )
| ( $false
= ( sK0 @ sK8 @ X0 ) ) )
| ~ spl12_2
| ~ spl12_11 ),
inference(trivial_inequality_removal,[],[f1258]) ).
thf(f1784,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK6 @ sK2 ) )
| ~ spl12_2
| ~ spl12_6
| ~ spl12_11 ),
inference(constrained_superposition,[],[f277,f1261]) ).
thf(f1785,plain,
( ( $false
= ( sK0 @ sK6 @ sK2 ) )
| ~ spl12_2
| ~ spl12_6
| ~ spl12_11 ),
inference(trivial_inequality_removal,[],[f1784]) ).
thf(f1859,plain,
( ( $true = $false )
| ~ spl12_2
| ~ spl12_6
| ~ spl12_10
| ~ spl12_11 ),
inference(constrained_superposition,[],[f1785,f296]) ).
thf(f1873,plain,
( $false
| ~ spl12_2
| ~ spl12_6
| ~ spl12_10
| ~ spl12_11 ),
inference(trivial_inequality_removal,[],[f1859]) ).
thf(f1874,plain,
( ~ spl12_2
| ~ spl12_6
| ~ spl12_10
| ~ spl12_11 ),
inference(avatar_contradiction_clause,[],[f1873]) ).
thf(f1969,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK7 @ sK9 ) )
| ~ spl12_3
| ~ spl12_4 ),
inference(constrained_superposition,[],[f264,f269]) ).
thf(f1974,plain,
( ( $true
= ( sK0 @ sK7 @ sK9 ) )
| ~ spl12_3
| ~ spl12_4 ),
inference(trivial_inequality_removal,[],[f1969]) ).
thf(f2001,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK7 @ sK9 ) )
| ~ spl12_2
| ~ spl12_8
| ~ spl12_9 ),
inference(constrained_superposition,[],[f486,f286]) ).
thf(f2002,plain,
( ( $false
= ( sK0 @ sK7 @ sK9 ) )
| ~ spl12_2
| ~ spl12_8
| ~ spl12_9 ),
inference(trivial_inequality_removal,[],[f2001]) ).
thf(f2386,plain,
( ( $true = $false )
| ~ spl12_2
| ~ spl12_3
| ~ spl12_4
| ~ spl12_8
| ~ spl12_9 ),
inference(constrained_superposition,[],[f2002,f1974]) ).
thf(f2396,plain,
( $false
| ~ spl12_2
| ~ spl12_3
| ~ spl12_4
| ~ spl12_8
| ~ spl12_9 ),
inference(trivial_inequality_removal,[],[f2386]) ).
thf(f2397,plain,
( ~ spl12_2
| ~ spl12_3
| ~ spl12_4
| ~ spl12_8
| ~ spl12_9 ),
inference(avatar_contradiction_clause,[],[f2396]) ).
thf(f2417,plain,
( spl12_3
| ~ spl12_1 ),
inference(avatar_split_clause,[],[f706,f256,f263]) ).
thf(f2469,plain,
( spl12_2
| ~ spl12_1
| ~ spl12_3 ),
inference(avatar_split_clause,[],[f689,f263,f256,f259]) ).
cnf(s1,plain,
( spl12_1
| spl12_2 ),
inference(sat_conversion,[],[f261]) ).
cnf(s2,plain,
( spl12_1
| spl12_3 ),
inference(sat_conversion,[],[f265]) ).
cnf(s3,plain,
( spl12_4
| spl12_5
| spl12_6
| spl12_7 ),
inference(sat_conversion,[],[f282]) ).
cnf(s4,plain,
( spl12_5
| spl12_6
| spl12_7
| spl12_8 ),
inference(sat_conversion,[],[f287]) ).
cnf(s5,plain,
( spl12_5
| spl12_6
| spl12_7
| spl12_9 ),
inference(sat_conversion,[],[f292]) ).
cnf(s6,plain,
( spl12_4
| spl12_5
| spl12_7
| spl12_10 ),
inference(sat_conversion,[],[f297]) ).
cnf(s7,plain,
( spl12_5
| spl12_7
| spl12_8
| spl12_10 ),
inference(sat_conversion,[],[f298]) ).
cnf(s8,plain,
( spl12_5
| spl12_7
| spl12_9
| spl12_10 ),
inference(sat_conversion,[],[f299]) ).
cnf(s9,plain,
( spl12_4
| spl12_5
| spl12_7
| spl12_11 ),
inference(sat_conversion,[],[f304]) ).
cnf(s10,plain,
( spl12_5
| spl12_7
| spl12_8
| spl12_11 ),
inference(sat_conversion,[],[f305]) ).
cnf(s11,plain,
( spl12_5
| spl12_7
| spl12_9
| spl12_11 ),
inference(sat_conversion,[],[f306]) ).
cnf(s12,plain,
( spl12_5
| spl12_12
| spl12_13
| spl12_14 ),
inference(sat_conversion,[],[f319]) ).
cnf(s13,plain,
( spl12_5
| spl12_13
| spl12_14
| spl12_15 ),
inference(sat_conversion,[],[f324]) ).
cnf(s14,plain,
( spl12_5
| spl12_9
| spl12_13
| spl12_14 ),
inference(sat_conversion,[],[f325]) ).
cnf(s15,plain,
( spl12_5
| spl12_10
| spl12_12
| spl12_14 ),
inference(sat_conversion,[],[f326]) ).
cnf(s16,plain,
( spl12_5
| spl12_10
| spl12_14
| spl12_15 ),
inference(sat_conversion,[],[f327]) ).
cnf(s17,plain,
( spl12_5
| spl12_9
| spl12_10
| spl12_14 ),
inference(sat_conversion,[],[f328]) ).
cnf(s18,plain,
( spl12_5
| spl12_12
| spl12_14
| spl12_16 ),
inference(sat_conversion,[],[f333]) ).
cnf(s19,plain,
( spl12_5
| spl12_14
| spl12_15
| spl12_16 ),
inference(sat_conversion,[],[f334]) ).
cnf(s20,plain,
( spl12_5
| spl12_9
| spl12_14
| spl12_16 ),
inference(sat_conversion,[],[f335]) ).
cnf(s22,plain,
~ spl12_5,
inference(sat_conversion,[],[f360]) ).
cnf(s24,plain,
( ~ spl12_3
| ~ spl12_7
| ~ spl12_14 ),
inference(sat_conversion,[],[f390]) ).
cnf(s25,plain,
( spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(sat_conversion,[],[f544]) ).
cnf(s28,plain,
( ~ spl12_2
| ~ spl12_3
| ~ spl12_9
| ~ spl12_12
| ~ spl12_15 ),
inference(sat_conversion,[],[f751]) ).
cnf(s34,plain,
( ~ spl12_2
| ~ spl12_10
| ~ spl12_13
| ~ spl12_16 ),
inference(sat_conversion,[],[f1240]) ).
cnf(s43,plain,
( ~ spl12_2
| ~ spl12_6
| ~ spl12_10
| ~ spl12_11 ),
inference(sat_conversion,[],[f1874]) ).
cnf(s45,plain,
( ~ spl12_2
| ~ spl12_3
| ~ spl12_4
| ~ spl12_8
| ~ spl12_9 ),
inference(sat_conversion,[],[f2397]) ).
cnf(s46,plain,
( ~ spl12_1
| spl12_3 ),
inference(sat_conversion,[],[f2417]) ).
cnf(s48,plain,
( ~ spl12_1
| spl12_2
| ~ spl12_3 ),
inference(sat_conversion,[],[f2469]) ).
cnf(s50,plain,
( spl12_9
| spl12_14
| spl12_16 ),
inference(rat,[],[s20,s22]) ).
cnf(s51,plain,
( spl12_14
| spl12_15
| spl12_16 ),
inference(rat,[],[s19,s22]) ).
cnf(s52,plain,
( spl12_12
| spl12_14
| spl12_16 ),
inference(rat,[],[s18,s22]) ).
cnf(s53,plain,
( spl12_9
| spl12_10
| spl12_14 ),
inference(rat,[],[s17,s22]) ).
cnf(s54,plain,
( spl12_10
| spl12_14
| spl12_15 ),
inference(rat,[],[s16,s22]) ).
cnf(s55,plain,
( spl12_10
| spl12_12
| spl12_14 ),
inference(rat,[],[s15,s22]) ).
cnf(s56,plain,
( spl12_9
| spl12_13
| spl12_14 ),
inference(rat,[],[s14,s22]) ).
cnf(s57,plain,
( spl12_13
| spl12_14
| spl12_15 ),
inference(rat,[],[s13,s22]) ).
cnf(s58,plain,
( spl12_12
| spl12_13
| spl12_14 ),
inference(rat,[],[s12,s22]) ).
cnf(s59,plain,
( spl12_7
| spl12_9
| spl12_11 ),
inference(rat,[],[s11,s22]) ).
cnf(s60,plain,
( spl12_7
| spl12_8
| spl12_11 ),
inference(rat,[],[s10,s22]) ).
cnf(s61,plain,
( spl12_4
| spl12_7
| spl12_11 ),
inference(rat,[],[s9,s22]) ).
cnf(s62,plain,
( spl12_7
| spl12_9
| spl12_10 ),
inference(rat,[],[s8,s22]) ).
cnf(s63,plain,
( spl12_7
| spl12_8
| spl12_10 ),
inference(rat,[],[s7,s22]) ).
cnf(s64,plain,
( spl12_4
| spl12_7
| spl12_10 ),
inference(rat,[],[s6,s22]) ).
cnf(s65,plain,
( spl12_6
| spl12_7
| spl12_9 ),
inference(rat,[],[s5,s22]) ).
cnf(s66,plain,
( spl12_6
| spl12_7
| spl12_8 ),
inference(rat,[],[s4,s22]) ).
cnf(s67,plain,
( spl12_4
| spl12_6
| spl12_7 ),
inference(rat,[],[s3,s22]) ).
cnf(s68,plain,
spl12_1,
inference(rat,[],[s25,s1,s2]) ).
cnf(s69,plain,
spl12_3,
inference(rat,[],[s46,s68]) ).
cnf(s70,plain,
spl12_2,
inference(rat,[],[s48,s68,s69]) ).
cnf(s71,plain,
( spl12_9
| spl12_14 ),
inference(rat,[],[s34,s56,s53,s50,s70]) ).
cnf(s72,plain,
( spl12_16
| spl12_14 ),
inference(rat,[],[s28,s52,s51,s71,s69,s70]) ).
cnf(s73,plain,
( spl12_13
| spl12_14 ),
inference(rat,[],[s28,s58,s57,s71,s69,s70]) ).
cnf(s74,plain,
spl12_14,
inference(rat,[],[s28,s55,s54,s34,s73,s72,s71,s69,s70]) ).
cnf(s75,plain,
~ spl12_7,
inference(rat,[],[s24,s69,s74]) ).
cnf(s76,plain,
spl12_4,
inference(rat,[],[s43,s67,s64,s61,s70,s75]) ).
cnf(s77,plain,
spl12_6,
inference(rat,[],[s45,s66,s65,s69,s70,s76,s75]) ).
cnf(s78,plain,
spl12_8,
inference(rat,[],[s43,s63,s60,s70,s77,s75]) ).
cnf(s79,plain,
~ spl12_9,
inference(rat,[],[s45,s76,s70,s69,s78]) ).
cnf(s80,plain,
spl12_11,
inference(rat,[],[s59,s75,s79]) ).
cnf(s81,plain,
spl12_10,
inference(rat,[],[s62,s75,s79]) ).
cnf(s82,plain,
$false,
inference(rat,[],[s43,s77,s70,s80,s81]) ).
thf(f2470,plain,
$false,
inference(avatar_sat_refutation,[],[s82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL862^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n020.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 10:14:04 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.33 % (868407)Will run a generic schedule for satisfiability detection.
% 0.20/0.33 % (868412)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1484577441_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.33 % Exception at run slice level
% 0.20/0.33 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.33 % (868413)% WARNING: option uhcvi not known.
% 0.20/0.33 % (868413)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4158921845:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.33 % (868414)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4339222:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.33 % (868415)dis+10_1_sil=32000:sp=arity:random_seed=1504528117:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.33 % (868416)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2892040470:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.33 % (868417)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2456486870:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.33 % (868418)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3238476649:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.33 % (868413)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.33 % (868416)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.33 % (868413)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.33 % (868420)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2284325478:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.33 % Exception at run slice level
% 0.20/0.33 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.33 % (868428)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1750570011:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.33 % (868415)Instruction limit reached!
% 0.20/0.33 % (868415)------------------------------
% 0.20/0.33 % (868415)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (868415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (868415)CaDiCaL version: 2.1.3
% 0.20/0.33 % (868415)Termination reason: Instruction limit
% 0.20/0.33 % (868415)Termination phase: Saturation
% 0.20/0.33 % (868415)Time elapsed: 0.045 s
% 0.20/0.33 % (868415)Peak memory usage: 12 MB
% 0.20/0.33 % (868415)Instructions burned: 103 (million)
% 0.20/0.33 % (868428)Instruction limit reached!
% 0.20/0.33 % (868428)------------------------------
% 0.20/0.33 % (868428)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (868428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (868428)CaDiCaL version: 2.1.3
% 0.20/0.33 % (868428)Termination reason: Instruction limit
% 0.20/0.33 % (868428)Termination phase: Saturation
% 0.20/0.33 % (868428)Time elapsed: 0.031 s
% 0.20/0.33 % (868428)Peak memory usage: 12 MB
% 0.20/0.33 % (868428)Instructions burned: 134 (million)
% 0.20/0.33 % (868416)Instruction limit reached!
% 0.20/0.33 % (868416)------------------------------
% 0.20/0.33 % (868416)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (868416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (868416)CaDiCaL version: 2.1.3
% 0.20/0.34 % (868416)Termination reason: Instruction limit
% 0.20/0.34 % (868416)Termination phase: Saturation
% 0.20/0.34 % (868416)Time elapsed: 0.051 s
% 0.20/0.34 % (868416)Peak memory usage: 12 MB
% 0.20/0.34 % (868416)Instructions burned: 118 (million)
% 0.20/0.34 % (868417)Instruction limit reached!
% 0.20/0.34 % (868417)------------------------------
% 0.20/0.34 % (868417)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (868417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (868417)CaDiCaL version: 2.1.3
% 0.20/0.34 % (868417)Termination reason: Instruction limit
% 0.20/0.34 % (868417)Termination phase: Saturation
% 0.20/0.34 % (868417)Time elapsed: 0.056 s
% 0.20/0.34 % (868417)Peak memory usage: 12 MB
% 0.20/0.34 % (868417)Instructions burned: 131 (million)
% 0.20/0.34 % (868418) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-868407-868418"...
% 0.20/0.34 % (868431)ott-21_1_sil=16000:fs=off:random_seed=2734139152:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.20/0.34 % (868418)...printing done.
% 0.20/0.34 % (868430)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=2728212130:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.20/0.34 % (868418)Refutation found. Thanks to Tanya!
% 0.20/0.34 % SZS status Theorem for theBenchmark
% 0.20/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.34 % (868418)------------------------------
% 0.20/0.34 % (868418)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (868418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (868418)CaDiCaL version: 2.1.3
% 0.20/0.34 % (868418)Termination reason: Refutation
% 0.20/0.34 % (868418)Time elapsed: 0.063 s
% 0.20/0.34 % (868418)Peak memory usage: 13 MB
% 0.20/0.34 % (868418)Instructions burned: 129 (million)
% 0.20/0.34 % (868407)Success in time 0.1 s
% 0.20/0.34 % Vampire exiting
%------------------------------------------------------------------------------