%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL860^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 0.53s 0.32s
% Output : Refutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 19
% Syntax : Number of formulae : 236 ( 44 unt; 0 typ; 14 def)
% Number of atoms : 2313 ( 383 equ; 0 cnn)
% Maximal formula atoms : 12 ( 9 avg)
% Number of connectives : 2262 ( 173 ~; 478 |; 109 &;1285 @)
% ( 18 <=>; 82 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 78 ( 78 >; 0 *; 0 +; 0 <<)
% Number of symbols : 74 ( 70 usr; 27 con; 0-4 aty)
% ( 116 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 252 ( 0 sgn 74 !; 3 ?; 252 :)
% 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/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(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 )
& ( mreflexive @ 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 )
& ( 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 ) )
<=> ( ( meuclidean @ X0 )
& ( msymmetric @ X0 )
& ( mtransitive @ X0 )
& ( mreflexive @ 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 )
& ( ( mreflexive @ 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 )
& ( ( mreflexive @ X0 )
= $true ) ) ),
inference(ennf_transformation,[],[f86]) ).
thf(f88,plain,
? [X0: $i > $i > $o] :
( ( ( ( meuclidean @ X0 )
!= $true )
| ( ( msymmetric @ X0 )
!= $true )
| ( ( mtransitive @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true ) )
& ( ( ( ( meuclidean @ 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] :
( ( ( ( meuclidean @ X0 )
!= $true )
| ( ( msymmetric @ X0 )
!= $true )
| ( ( mtransitive @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true ) )
& ( ( ( ( meuclidean @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) )
| ( ( ( meuclidean @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) ) ) ),
inference(flattening,[],[f88]) ).
thf(f90,plain,
( ( ( $true
!= ( meuclidean @ sK0 ) )
| ( $true
!= ( msymmetric @ sK0 ) )
| ( $true
!= ( mtransitive @ sK0 ) )
| ( $true
!= ( mreflexive @ sK0 ) )
| ( $true
!= ( meuclidean @ sK0 ) )
| ( $true
!= ( mreflexive @ sK0 ) ) )
& ( ( ( $true
= ( meuclidean @ 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(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
!= ( mreflexive @ 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] : ( 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,[],[f130,f112,f109,f111,f108,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(f150,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(f151,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) ),
inference(duplicate_literal_removal,[],[f150]) ).
thf(f152,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X1: $i] :
( $true
= ( sK0 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f218,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(f219,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f218]) ).
thf(f220,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,[],[f219]) ).
thf(f221,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f220]) ).
thf(f222,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,[],[f221]) ).
thf(f223,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X2 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f222]) ).
thf(f224,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X2 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ X2 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f223]) ).
thf(f225,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( sK0 @ X3 @ X2 )
& ( sK0 @ X3 @ X1 ) )
=> ( sK0 @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f224]) ).
thf(f226,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( sK0 @ X3 @ X2 )
& ( sK0 @ X3 @ X1 ) ) )
| ( $true
= ( sK0 @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $true
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f226]) ).
thf(f228,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] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) ) ),
inference(duplicate_literal_removal,[],[f142]) ).
thf(f229,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] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f228]) ).
thf(f230,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
@ sK1 ) )
| ( $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 ) ) ) ),
inference(sigma_proxy_clausification,[],[f229]) ).
thf(f231,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK2 ) )
| ( $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(sigma_proxy_clausification,[],[f230]) ).
thf(f232,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK3 ) )
| ( $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 ) ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK3 ) )
| ( $false
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f232]) ).
thf(f234,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ sK1 ) )
=> ( sK0 @ Y0 @ sK1 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK2 )
=> ( sK0 @ sK2 @ Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ Y1 @ sK3 ) ) ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f233]) ).
thf(f235,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ sK1 ) )
=> ( sK0 @ Y0 @ sK1 ) ) )
@ sK5 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK2 )
=> ( sK0 @ sK2 @ Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ Y1 @ sK3 ) ) ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f234]) ).
thf(f236,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ sK1 ) )
=> ( sK0 @ Y0 @ sK1 ) ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK2 )
=> ( sK0 @ sK2 @ Y0 ) )
@ sK6 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ Y1 @ sK3 ) ) ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f235]) ).
thf(f237,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ sK1 ) )
=> ( sK0 @ Y0 @ sK1 ) ) )
@ sK5 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK2 )
=> ( sK0 @ sK2 @ Y0 ) )
@ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK3 ) )
=> ( sK0 @ Y1 @ sK3 ) ) )
@ sK7 ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f236]) ).
thf(f238,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ Y0 @ sK1 ) )
=> ( sK0 @ sK5 @ sK1 ) ) ) )
| ( $false
= ( ( sK0 @ sK6 @ sK2 )
=> ( sK0 @ sK2 @ sK6 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK7 )
& ( sK0 @ sK7 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f237]) ).
thf(f239,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ Y0 @ sK1 ) )
=> ( sK0 @ sK5 @ sK1 ) )
@ sK8 ) )
| ( $false
= ( ( sK0 @ sK6 @ sK2 )
=> ( sK0 @ sK2 @ sK6 ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK7 )
& ( sK0 @ sK7 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f238]) ).
thf(f240,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ Y0 @ sK1 ) )
=> ( sK0 @ sK5 @ sK1 ) )
@ sK8 ) )
| ( $false
= ( sK0 @ sK2 @ sK6 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK7 )
& ( sK0 @ sK7 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f239]) ).
thf(f241,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ Y0 @ sK1 ) )
=> ( sK0 @ sK5 @ sK1 ) )
@ sK8 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK7 )
& ( sK0 @ sK7 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f239]) ).
thf(f242,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ Y0 @ sK1 ) )
=> ( sK0 @ sK5 @ sK1 ) )
@ sK8 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK7 )
& ( sK0 @ sK7 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) )
@ sK9 ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f241]) ).
thf(f243,plain,
( ( $false
= ( ( ( sK0 @ sK8 @ sK5 )
& ( sK0 @ sK8 @ sK1 ) )
=> ( sK0 @ sK5 @ sK1 ) ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK7 )
& ( sK0 @ sK7 @ sK3 ) )
=> ( sK0 @ sK9 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f242]) ).
thf(f244,plain,
( ( $false
= ( sK0 @ sK5 @ sK1 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK7 )
& ( sK0 @ sK7 @ sK3 ) )
=> ( sK0 @ sK9 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f243]) ).
thf(f245,plain,
( ( $true
= ( ( sK0 @ sK8 @ sK5 )
& ( sK0 @ sK8 @ sK1 ) ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK7 )
& ( sK0 @ sK7 @ sK3 ) )
=> ( sK0 @ sK9 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f243]) ).
thf(f246,plain,
( ( $true
= ( sK0 @ sK8 @ sK1 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK7 )
& ( sK0 @ sK7 @ sK3 ) )
=> ( sK0 @ sK9 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f245]) ).
thf(f247,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $false
= ( ( ( sK0 @ sK9 @ sK7 )
& ( sK0 @ sK7 @ sK3 ) )
=> ( sK0 @ sK9 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f245]) ).
thf(f248,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $false
= ( sK0 @ sK9 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f247]) ).
thf(f249,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $true
= ( ( sK0 @ sK9 @ sK7 )
& ( sK0 @ sK7 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f247]) ).
thf(f250,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $true
= ( sK0 @ sK7 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f249]) ).
thf(f251,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $true
= ( sK0 @ sK9 @ sK7 ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f249]) ).
thf(f252,plain,
( ( $true
= ( sK0 @ sK8 @ sK1 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $false
= ( sK0 @ sK9 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f246]) ).
thf(f253,plain,
( ( $true
= ( sK0 @ sK8 @ sK1 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $true
= ( ( sK0 @ sK9 @ sK7 )
& ( sK0 @ sK7 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f246]) ).
thf(f254,plain,
( ( $true
= ( sK0 @ sK8 @ sK1 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $true
= ( sK0 @ sK7 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f253]) ).
thf(f255,plain,
( ( $true
= ( sK0 @ sK8 @ sK1 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $true
= ( sK0 @ sK9 @ sK7 ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f253]) ).
thf(f256,plain,
( ( $false
= ( sK0 @ sK5 @ sK1 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $false
= ( sK0 @ sK9 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f244]) ).
thf(f257,plain,
( ( $false
= ( sK0 @ sK5 @ sK1 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $true
= ( ( sK0 @ sK9 @ sK7 )
& ( sK0 @ sK7 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f244]) ).
thf(f258,plain,
( ( $false
= ( sK0 @ sK5 @ sK1 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $true
= ( sK0 @ sK7 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f257]) ).
thf(f259,plain,
( ( $false
= ( sK0 @ sK5 @ sK1 ) )
| ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ( $true
= ( sK0 @ sK9 @ sK7 ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f257]) ).
thf(f260,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ Y0 @ sK1 ) )
=> ( sK0 @ sK5 @ sK1 ) )
@ sK8 ) )
| ( $false
= ( sK0 @ sK2 @ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK7 )
& ( sK0 @ sK7 @ sK3 ) )
=> ( sK0 @ Y0 @ sK3 ) )
@ sK10 ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f240]) ).
thf(f261,plain,
( ( $false
= ( ( ( sK0 @ sK8 @ sK5 )
& ( sK0 @ sK8 @ sK1 ) )
=> ( sK0 @ sK5 @ sK1 ) ) )
| ( $false
= ( sK0 @ sK2 @ sK6 ) )
| ( $false
= ( ( ( sK0 @ sK10 @ sK7 )
& ( sK0 @ sK7 @ sK3 ) )
=> ( sK0 @ sK10 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f260]) ).
thf(f262,plain,
( ( $false
= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( sK0 @ sK2 @ sK6 ) )
| ( $false
= ( ( ( sK0 @ sK10 @ sK7 )
& ( sK0 @ sK7 @ sK3 ) )
=> ( sK0 @ sK10 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f261]) ).
thf(f263,plain,
( ( $true
= ( ( sK0 @ sK8 @ sK5 )
& ( sK0 @ sK8 @ sK1 ) ) )
| ( $false
= ( sK0 @ sK2 @ sK6 ) )
| ( $false
= ( ( ( sK0 @ sK10 @ sK7 )
& ( sK0 @ sK7 @ sK3 ) )
=> ( sK0 @ sK10 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f261]) ).
thf(f264,plain,
( ( $true
= ( sK0 @ sK8 @ sK1 ) )
| ( $false
= ( sK0 @ sK2 @ sK6 ) )
| ( $false
= ( ( ( sK0 @ sK10 @ sK7 )
& ( sK0 @ sK7 @ sK3 ) )
=> ( sK0 @ sK10 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f263]) ).
thf(f265,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ( $false
= ( sK0 @ sK2 @ sK6 ) )
| ( $false
= ( ( ( sK0 @ sK10 @ sK7 )
& ( sK0 @ sK7 @ sK3 ) )
=> ( sK0 @ sK10 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f263]) ).
thf(f266,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ( $false
= ( sK0 @ sK2 @ sK6 ) )
| ( $false
= ( sK0 @ sK10 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f265]) ).
thf(f267,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ( $false
= ( sK0 @ sK2 @ sK6 ) )
| ( $true
= ( ( sK0 @ sK10 @ sK7 )
& ( sK0 @ sK7 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f265]) ).
thf(f268,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ( $false
= ( sK0 @ sK2 @ sK6 ) )
| ( $true
= ( sK0 @ sK7 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f267]) ).
thf(f269,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ( $false
= ( sK0 @ sK2 @ sK6 ) )
| ( $true
= ( sK0 @ sK10 @ sK7 ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f267]) ).
thf(f270,plain,
( ( $true
= ( sK0 @ sK8 @ sK1 ) )
| ( $false
= ( sK0 @ sK2 @ sK6 ) )
| ( $false
= ( sK0 @ sK10 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f264]) ).
thf(f271,plain,
( ( $true
= ( sK0 @ sK8 @ sK1 ) )
| ( $false
= ( sK0 @ sK2 @ sK6 ) )
| ( $true
= ( ( sK0 @ sK10 @ sK7 )
& ( sK0 @ sK7 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f264]) ).
thf(f272,plain,
( ( $true
= ( sK0 @ sK8 @ sK1 ) )
| ( $false
= ( sK0 @ sK2 @ sK6 ) )
| ( $true
= ( sK0 @ sK7 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f271]) ).
thf(f273,plain,
( ( $true
= ( sK0 @ sK8 @ sK1 ) )
| ( $false
= ( sK0 @ sK2 @ sK6 ) )
| ( $true
= ( sK0 @ sK10 @ sK7 ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f271]) ).
thf(f274,plain,
( ( $false
= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( sK0 @ sK2 @ sK6 ) )
| ( $false
= ( sK0 @ sK10 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f262]) ).
thf(f275,plain,
( ( $false
= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( sK0 @ sK2 @ sK6 ) )
| ( $true
= ( ( sK0 @ sK10 @ sK7 )
& ( sK0 @ sK7 @ sK3 ) ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f262]) ).
thf(f276,plain,
( ( $false
= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( sK0 @ sK2 @ sK6 ) )
| ( $true
= ( sK0 @ sK7 @ sK3 ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f275]) ).
thf(f277,plain,
( ( $false
= ( sK0 @ sK5 @ sK1 ) )
| ( $false
= ( sK0 @ sK2 @ sK6 ) )
| ( $true
= ( sK0 @ sK10 @ sK7 ) )
| ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f275]) ).
thf(f279,definition,
( spl11_1
<=> ! [X6: $i,X2: $i,X4: $i] :
( ( $false
= ( sK0 @ X6 @ X2 ) )
| ( $false
= ( sK0 @ X6 @ X4 ) )
| ( $true
= ( sK0 @ X4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
thf(f280,plain,
( ! [X2: $i,X6: $i,X4: $i] :
( ( $false
= ( sK0 @ X6 @ X2 ) )
| ( $false
= ( sK0 @ X6 @ X4 ) )
| ( $true
= ( sK0 @ X4 @ X2 ) ) )
| ~ spl11_1 ),
inference(avatar_component_clause,[],[f279]) ).
thf(f282,definition,
( spl11_2
<=> ! [X5: $i,X1: $i,X3: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X5 @ X3 ) )
| ( $true
= ( sK0 @ X5 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
thf(f283,plain,
( ! [X3: $i,X1: $i,X5: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X5 @ X3 ) )
| ( $true
= ( sK0 @ X5 @ X1 ) ) )
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f282]) ).
thf(f286,definition,
( spl11_3
<=> ! [X1: $i,X3: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $true
= ( sK0 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
thf(f287,plain,
( ! [X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $true
= ( sK0 @ X1 @ X3 ) ) )
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f286]) ).
thf(f289,plain,
spl11_1,
inference(avatar_split_clause,[],[f227,f279]) ).
thf(f291,definition,
( spl11_4
<=> ( $false
= ( sK0 @ sK4 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition]) ).
thf(f293,plain,
( ( $false
= ( sK0 @ sK4 @ sK4 ) )
| ~ spl11_4 ),
inference(avatar_component_clause,[],[f291]) ).
thf(f295,definition,
( spl11_5
<=> ( $true
= ( sK0 @ sK9 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition]) ).
thf(f297,plain,
( ( $true
= ( sK0 @ sK9 @ sK7 ) )
| ~ spl11_5 ),
inference(avatar_component_clause,[],[f295]) ).
thf(f299,definition,
( spl11_6
<=> ( $true
= ( sK0 @ sK6 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition]) ).
thf(f301,plain,
( ( $true
= ( sK0 @ sK6 @ sK2 ) )
| ~ spl11_6 ),
inference(avatar_component_clause,[],[f299]) ).
thf(f303,definition,
( spl11_7
<=> ( $true
= ( sK0 @ sK8 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_7])],[avatar_definition]) ).
thf(f305,plain,
( ( $true
= ( sK0 @ sK8 @ sK5 ) )
| ~ spl11_7 ),
inference(avatar_component_clause,[],[f303]) ).
thf(f306,plain,
( spl11_4
| spl11_5
| spl11_6
| spl11_7 ),
inference(avatar_split_clause,[],[f251,f303,f299,f295,f291]) ).
thf(f308,definition,
( spl11_8
<=> ( $true
= ( sK0 @ sK7 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_8])],[avatar_definition]) ).
thf(f310,plain,
( ( $true
= ( sK0 @ sK7 @ sK3 ) )
| ~ spl11_8 ),
inference(avatar_component_clause,[],[f308]) ).
thf(f311,plain,
( spl11_4
| spl11_8
| spl11_6
| spl11_7 ),
inference(avatar_split_clause,[],[f250,f303,f299,f308,f291]) ).
thf(f313,definition,
( spl11_9
<=> ( $false
= ( sK0 @ sK9 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_9])],[avatar_definition]) ).
thf(f315,plain,
( ( $false
= ( sK0 @ sK9 @ sK3 ) )
| ~ spl11_9 ),
inference(avatar_component_clause,[],[f313]) ).
thf(f316,plain,
( spl11_4
| spl11_9
| spl11_6
| spl11_7 ),
inference(avatar_split_clause,[],[f248,f303,f299,f313,f291]) ).
thf(f318,definition,
( spl11_10
<=> ( $true
= ( sK0 @ sK8 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_10])],[avatar_definition]) ).
thf(f320,plain,
( ( $true
= ( sK0 @ sK8 @ sK1 ) )
| ~ spl11_10 ),
inference(avatar_component_clause,[],[f318]) ).
thf(f321,plain,
( spl11_4
| spl11_5
| spl11_6
| spl11_10 ),
inference(avatar_split_clause,[],[f255,f318,f299,f295,f291]) ).
thf(f322,plain,
( spl11_4
| spl11_8
| spl11_6
| spl11_10 ),
inference(avatar_split_clause,[],[f254,f318,f299,f308,f291]) ).
thf(f323,plain,
( spl11_4
| spl11_9
| spl11_6
| spl11_10 ),
inference(avatar_split_clause,[],[f252,f318,f299,f313,f291]) ).
thf(f325,definition,
( spl11_11
<=> ( $false
= ( sK0 @ sK5 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_11])],[avatar_definition]) ).
thf(f327,plain,
( ( $false
= ( sK0 @ sK5 @ sK1 ) )
| ~ spl11_11 ),
inference(avatar_component_clause,[],[f325]) ).
thf(f328,plain,
( spl11_4
| spl11_5
| spl11_6
| spl11_11 ),
inference(avatar_split_clause,[],[f259,f325,f299,f295,f291]) ).
thf(f329,plain,
( spl11_4
| spl11_8
| spl11_6
| spl11_11 ),
inference(avatar_split_clause,[],[f258,f325,f299,f308,f291]) ).
thf(f330,plain,
( spl11_4
| spl11_9
| spl11_6
| spl11_11 ),
inference(avatar_split_clause,[],[f256,f325,f299,f313,f291]) ).
thf(f332,definition,
( spl11_12
<=> ( $true
= ( sK0 @ sK10 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_12])],[avatar_definition]) ).
thf(f334,plain,
( ( $true
= ( sK0 @ sK10 @ sK7 ) )
| ~ spl11_12 ),
inference(avatar_component_clause,[],[f332]) ).
thf(f336,definition,
( spl11_13
<=> ( $false
= ( sK0 @ sK2 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_13])],[avatar_definition]) ).
thf(f338,plain,
( ( $false
= ( sK0 @ sK2 @ sK6 ) )
| ~ spl11_13 ),
inference(avatar_component_clause,[],[f336]) ).
thf(f339,plain,
( spl11_4
| spl11_12
| spl11_13
| spl11_7 ),
inference(avatar_split_clause,[],[f269,f303,f336,f332,f291]) ).
thf(f340,plain,
( spl11_4
| spl11_8
| spl11_13
| spl11_7 ),
inference(avatar_split_clause,[],[f268,f303,f336,f308,f291]) ).
thf(f342,definition,
( spl11_14
<=> ( $false
= ( sK0 @ sK10 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_14])],[avatar_definition]) ).
thf(f344,plain,
( ( $false
= ( sK0 @ sK10 @ sK3 ) )
| ~ spl11_14 ),
inference(avatar_component_clause,[],[f342]) ).
thf(f345,plain,
( spl11_4
| spl11_14
| spl11_13
| spl11_7 ),
inference(avatar_split_clause,[],[f266,f303,f336,f342,f291]) ).
thf(f346,plain,
( spl11_4
| spl11_12
| spl11_13
| spl11_10 ),
inference(avatar_split_clause,[],[f273,f318,f336,f332,f291]) ).
thf(f347,plain,
( spl11_4
| spl11_8
| spl11_13
| spl11_10 ),
inference(avatar_split_clause,[],[f272,f318,f336,f308,f291]) ).
thf(f348,plain,
( spl11_4
| spl11_14
| spl11_13
| spl11_10 ),
inference(avatar_split_clause,[],[f270,f318,f336,f342,f291]) ).
thf(f349,plain,
( spl11_4
| spl11_12
| spl11_13
| spl11_11 ),
inference(avatar_split_clause,[],[f277,f325,f336,f332,f291]) ).
thf(f350,plain,
( spl11_4
| spl11_8
| spl11_13
| spl11_11 ),
inference(avatar_split_clause,[],[f276,f325,f336,f308,f291]) ).
thf(f351,plain,
( spl11_4
| spl11_14
| spl11_13
| spl11_11 ),
inference(avatar_split_clause,[],[f274,f325,f336,f342,f291]) ).
thf(f352,plain,
( ( $true = $false )
| ~ spl11_4 ),
inference(constrained_superposition,[],[f293,f154]) ).
thf(f356,plain,
( $false
| ~ spl11_4 ),
inference(trivial_inequality_removal,[],[f352]) ).
thf(f357,plain,
~ spl11_4,
inference(avatar_contradiction_clause,[],[f356]) ).
thf(f370,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $true
= ( sK0 @ X1 @ X0 ) ) )
| ~ spl11_1 ),
inference(constrained_superposition,[],[f154,f280]) ).
thf(f393,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK1 ) )
| ( $false
= ( sK0 @ X0 @ sK5 ) ) )
| ~ spl11_1
| ~ spl11_11 ),
inference(constrained_superposition,[],[f327,f280]) ).
thf(f411,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK5 ) )
| ( $false
= ( sK0 @ X0 @ sK1 ) ) )
| ~ spl11_1
| ~ spl11_11 ),
inference(trivial_inequality_removal,[],[f393]) ).
thf(f425,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $true
= ( sK0 @ X1 @ X0 ) ) )
| ~ spl11_1 ),
inference(trivial_inequality_removal,[],[f370]) ).
thf(f437,plain,
( spl11_3
| ~ spl11_1 ),
inference(avatar_split_clause,[],[f425,f279,f286]) ).
thf(f455,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ X2 ) )
| ( $true
= ( sK0 @ X1 @ X2 ) )
| ( $false
= ( sK0 @ X1 @ X0 ) ) )
| ~ spl11_1
| ~ spl11_3 ),
inference(constrained_superposition,[],[f280,f287]) ).
thf(f472,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X0 @ X2 ) )
| ( $true
= ( sK0 @ X1 @ X2 ) )
| ( $false
= ( sK0 @ X1 @ X0 ) ) )
| ~ spl11_1
| ~ spl11_3 ),
inference(trivial_inequality_removal,[],[f455]) ).
thf(f487,plain,
( spl11_2
| ~ spl11_1
| ~ spl11_3 ),
inference(avatar_split_clause,[],[f472,f286,f279,f282]) ).
thf(f666,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK8 @ sK1 ) )
| ~ spl11_1
| ~ spl11_7
| ~ spl11_11 ),
inference(constrained_superposition,[],[f305,f411]) ).
thf(f667,plain,
( ( $false
= ( sK0 @ sK8 @ sK1 ) )
| ~ spl11_1
| ~ spl11_7
| ~ spl11_11 ),
inference(trivial_inequality_removal,[],[f666]) ).
thf(f680,plain,
( ( $true = $false )
| ~ spl11_1
| ~ spl11_7
| ~ spl11_10
| ~ spl11_11 ),
inference(constrained_superposition,[],[f667,f320]) ).
thf(f690,plain,
( $false
| ~ spl11_1
| ~ spl11_7
| ~ spl11_10
| ~ spl11_11 ),
inference(trivial_inequality_removal,[],[f680]) ).
thf(f691,plain,
( ~ spl11_1
| ~ spl11_7
| ~ spl11_10
| ~ spl11_11 ),
inference(avatar_contradiction_clause,[],[f690]) ).
thf(f704,plain,
( ( $true = $false )
| ( $true
= ( sK0 @ sK2 @ sK6 ) )
| ~ spl11_3
| ~ spl11_6 ),
inference(constrained_superposition,[],[f287,f301]) ).
thf(f705,plain,
( ( $true
= ( sK0 @ sK2 @ sK6 ) )
| ~ spl11_3
| ~ spl11_6 ),
inference(trivial_inequality_removal,[],[f704]) ).
thf(f729,plain,
( ( $true = $false )
| ~ spl11_3
| ~ spl11_6
| ~ spl11_13 ),
inference(constrained_superposition,[],[f705,f338]) ).
thf(f737,plain,
( $false
| ~ spl11_3
| ~ spl11_6
| ~ spl11_13 ),
inference(trivial_inequality_removal,[],[f729]) ).
thf(f738,plain,
( ~ spl11_3
| ~ spl11_6
| ~ spl11_13 ),
inference(avatar_contradiction_clause,[],[f737]) ).
thf(f746,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK3 ) )
| ( $false
= ( sK0 @ sK10 @ X0 ) ) )
| ~ spl11_2
| ~ spl11_14 ),
inference(constrained_superposition,[],[f283,f344]) ).
thf(f749,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK3 ) )
| ( $false
= ( sK0 @ sK10 @ X0 ) ) )
| ~ spl11_2
| ~ spl11_14 ),
inference(trivial_inequality_removal,[],[f746]) ).
thf(f1520,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK7 @ sK3 ) )
| ~ spl11_2
| ~ spl11_12
| ~ spl11_14 ),
inference(constrained_superposition,[],[f334,f749]) ).
thf(f1521,plain,
( ( $false
= ( sK0 @ sK7 @ sK3 ) )
| ~ spl11_2
| ~ spl11_12
| ~ spl11_14 ),
inference(trivial_inequality_removal,[],[f1520]) ).
thf(f1551,plain,
( ( $true = $false )
| ~ spl11_2
| ~ spl11_8
| ~ spl11_12
| ~ spl11_14 ),
inference(constrained_superposition,[],[f1521,f310]) ).
thf(f1565,plain,
( $false
| ~ spl11_2
| ~ spl11_8
| ~ spl11_12
| ~ spl11_14 ),
inference(trivial_inequality_removal,[],[f1551]) ).
thf(f1566,plain,
( ~ spl11_2
| ~ spl11_8
| ~ spl11_12
| ~ spl11_14 ),
inference(avatar_contradiction_clause,[],[f1565]) ).
thf(f1607,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK3 ) )
| ( $false
= ( sK0 @ sK9 @ X0 ) ) )
| ~ spl11_2
| ~ spl11_9 ),
inference(constrained_superposition,[],[f283,f315]) ).
thf(f1612,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK3 ) )
| ( $false
= ( sK0 @ sK9 @ X0 ) ) )
| ~ spl11_2
| ~ spl11_9 ),
inference(trivial_inequality_removal,[],[f1607]) ).
thf(f2271,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK7 @ sK3 ) )
| ~ spl11_2
| ~ spl11_5
| ~ spl11_9 ),
inference(constrained_superposition,[],[f297,f1612]) ).
thf(f2272,plain,
( ( $false
= ( sK0 @ sK7 @ sK3 ) )
| ~ spl11_2
| ~ spl11_5
| ~ spl11_9 ),
inference(trivial_inequality_removal,[],[f2271]) ).
thf(f2358,plain,
( ( $true = $false )
| ~ spl11_2
| ~ spl11_5
| ~ spl11_8
| ~ spl11_9 ),
inference(constrained_superposition,[],[f2272,f310]) ).
thf(f2374,plain,
( $false
| ~ spl11_2
| ~ spl11_5
| ~ spl11_8
| ~ spl11_9 ),
inference(trivial_inequality_removal,[],[f2358]) ).
thf(f2375,plain,
( ~ spl11_2
| ~ spl11_5
| ~ spl11_8
| ~ spl11_9 ),
inference(avatar_contradiction_clause,[],[f2374]) ).
cnf(s3,plain,
spl11_1,
inference(sat_conversion,[],[f289]) ).
cnf(s4,plain,
( spl11_4
| spl11_5
| spl11_6
| spl11_7 ),
inference(sat_conversion,[],[f306]) ).
cnf(s5,plain,
( spl11_4
| spl11_6
| spl11_7
| spl11_8 ),
inference(sat_conversion,[],[f311]) ).
cnf(s6,plain,
( spl11_4
| spl11_6
| spl11_7
| spl11_9 ),
inference(sat_conversion,[],[f316]) ).
cnf(s7,plain,
( spl11_4
| spl11_5
| spl11_6
| spl11_10 ),
inference(sat_conversion,[],[f321]) ).
cnf(s8,plain,
( spl11_4
| spl11_6
| spl11_8
| spl11_10 ),
inference(sat_conversion,[],[f322]) ).
cnf(s9,plain,
( spl11_4
| spl11_6
| spl11_9
| spl11_10 ),
inference(sat_conversion,[],[f323]) ).
cnf(s10,plain,
( spl11_4
| spl11_5
| spl11_6
| spl11_11 ),
inference(sat_conversion,[],[f328]) ).
cnf(s11,plain,
( spl11_4
| spl11_6
| spl11_8
| spl11_11 ),
inference(sat_conversion,[],[f329]) ).
cnf(s12,plain,
( spl11_4
| spl11_6
| spl11_9
| spl11_11 ),
inference(sat_conversion,[],[f330]) ).
cnf(s13,plain,
( spl11_4
| spl11_7
| spl11_12
| spl11_13 ),
inference(sat_conversion,[],[f339]) ).
cnf(s14,plain,
( spl11_4
| spl11_7
| spl11_8
| spl11_13 ),
inference(sat_conversion,[],[f340]) ).
cnf(s15,plain,
( spl11_4
| spl11_7
| spl11_13
| spl11_14 ),
inference(sat_conversion,[],[f345]) ).
cnf(s16,plain,
( spl11_4
| spl11_10
| spl11_12
| spl11_13 ),
inference(sat_conversion,[],[f346]) ).
cnf(s17,plain,
( spl11_4
| spl11_8
| spl11_10
| spl11_13 ),
inference(sat_conversion,[],[f347]) ).
cnf(s18,plain,
( spl11_4
| spl11_10
| spl11_13
| spl11_14 ),
inference(sat_conversion,[],[f348]) ).
cnf(s19,plain,
( spl11_4
| spl11_11
| spl11_12
| spl11_13 ),
inference(sat_conversion,[],[f349]) ).
cnf(s20,plain,
( spl11_4
| spl11_8
| spl11_11
| spl11_13 ),
inference(sat_conversion,[],[f350]) ).
cnf(s21,plain,
( spl11_4
| spl11_11
| spl11_13
| spl11_14 ),
inference(sat_conversion,[],[f351]) ).
cnf(s23,plain,
~ spl11_4,
inference(sat_conversion,[],[f357]) ).
cnf(s24,plain,
( ~ spl11_1
| spl11_3 ),
inference(sat_conversion,[],[f437]) ).
cnf(s27,plain,
( ~ spl11_1
| spl11_2
| ~ spl11_3 ),
inference(sat_conversion,[],[f487]) ).
cnf(s30,plain,
( ~ spl11_1
| ~ spl11_7
| ~ spl11_10
| ~ spl11_11 ),
inference(sat_conversion,[],[f691]) ).
cnf(s32,plain,
( ~ spl11_3
| ~ spl11_6
| ~ spl11_13 ),
inference(sat_conversion,[],[f738]) ).
cnf(s40,plain,
( ~ spl11_2
| ~ spl11_8
| ~ spl11_12
| ~ spl11_14 ),
inference(sat_conversion,[],[f1566]) ).
cnf(s49,plain,
( ~ spl11_2
| ~ spl11_5
| ~ spl11_8
| ~ spl11_9 ),
inference(sat_conversion,[],[f2375]) ).
cnf(s50,plain,
( spl11_11
| spl11_13
| spl11_14 ),
inference(rat,[],[s21,s23]) ).
cnf(s51,plain,
( spl11_8
| spl11_11
| spl11_13 ),
inference(rat,[],[s20,s23]) ).
cnf(s52,plain,
( spl11_11
| spl11_12
| spl11_13 ),
inference(rat,[],[s19,s23]) ).
cnf(s53,plain,
( spl11_10
| spl11_13
| spl11_14 ),
inference(rat,[],[s18,s23]) ).
cnf(s54,plain,
( spl11_8
| spl11_10
| spl11_13 ),
inference(rat,[],[s17,s23]) ).
cnf(s55,plain,
( spl11_10
| spl11_12
| spl11_13 ),
inference(rat,[],[s16,s23]) ).
cnf(s56,plain,
( spl11_7
| spl11_13
| spl11_14 ),
inference(rat,[],[s15,s23]) ).
cnf(s57,plain,
( spl11_7
| spl11_8
| spl11_13 ),
inference(rat,[],[s14,s23]) ).
cnf(s58,plain,
( spl11_7
| spl11_12
| spl11_13 ),
inference(rat,[],[s13,s23]) ).
cnf(s59,plain,
( spl11_6
| spl11_9
| spl11_11 ),
inference(rat,[],[s12,s23]) ).
cnf(s60,plain,
( spl11_6
| spl11_8
| spl11_11 ),
inference(rat,[],[s11,s23]) ).
cnf(s61,plain,
( spl11_5
| spl11_6
| spl11_11 ),
inference(rat,[],[s10,s23]) ).
cnf(s62,plain,
( spl11_6
| spl11_9
| spl11_10 ),
inference(rat,[],[s9,s23]) ).
cnf(s63,plain,
( spl11_6
| spl11_8
| spl11_10 ),
inference(rat,[],[s8,s23]) ).
cnf(s64,plain,
( spl11_5
| spl11_6
| spl11_10 ),
inference(rat,[],[s7,s23]) ).
cnf(s65,plain,
( spl11_6
| spl11_7
| spl11_9 ),
inference(rat,[],[s6,s23]) ).
cnf(s66,plain,
( spl11_6
| spl11_7
| spl11_8 ),
inference(rat,[],[s5,s23]) ).
cnf(s67,plain,
( spl11_5
| spl11_6
| spl11_7 ),
inference(rat,[],[s4,s23]) ).
cnf(s68,plain,
spl11_3,
inference(rat,[],[s24,s3]) ).
cnf(s69,plain,
spl11_2,
inference(rat,[],[s27,s3,s68]) ).
cnf(s70,plain,
( spl11_6
| spl11_5 ),
inference(rat,[],[s30,s67,s64,s61,s3]) ).
cnf(s71,plain,
( spl11_11
| spl11_13 ),
inference(rat,[],[s40,s50,s52,s51,s69]) ).
cnf(s72,plain,
( spl11_10
| spl11_13 ),
inference(rat,[],[s40,s55,s54,s53,s69]) ).
cnf(s73,plain,
( spl11_7
| spl11_13 ),
inference(rat,[],[s40,s58,s57,s56,s69]) ).
cnf(s74,plain,
spl11_13,
inference(rat,[],[s73,s30,s72,s71,s3]) ).
cnf(s75,plain,
~ spl11_6,
inference(rat,[],[s32,s68,s74]) ).
cnf(s76,plain,
spl11_5,
inference(rat,[],[s70,s75]) ).
cnf(s77,plain,
spl11_9,
inference(rat,[],[s30,s65,s62,s59,s3,s75]) ).
cnf(s78,plain,
~ spl11_8,
inference(rat,[],[s49,s76,s69,s77]) ).
cnf(s79,plain,
spl11_11,
inference(rat,[],[s60,s75,s78]) ).
cnf(s80,plain,
spl11_10,
inference(rat,[],[s63,s75,s78]) ).
cnf(s81,plain,
spl11_7,
inference(rat,[],[s66,s75,s78]) ).
cnf(s82,plain,
$false,
inference(rat,[],[s30,s79,s3,s81,s80]) ).
thf(f2381,plain,
$false,
inference(avatar_sat_refutation,[],[s82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL860^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n014.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 10:09:45 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.53/0.32 % (2479811)Will run a generic schedule for satisfiability detection.
% 0.53/0.32 % (2479820)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4031997008:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.53/0.32 % (2479820)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.53/0.32 % (2479817)% WARNING: option uhcvi not known.
% 0.53/0.32 % (2479819)dis+10_1_sil=32000:sp=arity:random_seed=1943610937:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.53/0.32 % (2479817)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=390403183:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.53/0.32 % (2479817)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.53/0.32 % (2479817)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.53/0.32 % (2479822)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2258124666:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.53/0.32 % (2479821)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=697540486:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.53/0.32 % (2479816)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2426108512_2999 on theBenchmark for (2999ds/0Mi)
% 0.53/0.32 % (2479818)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2799842118:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.53/0.32 % (2479820)Instruction limit reached!
% 0.53/0.32 % (2479820)------------------------------
% 0.53/0.32 % (2479820)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.32 % (2479820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.32 % (2479820)CaDiCaL version: 2.1.3
% 0.53/0.32 % (2479820)Termination reason: Instruction limit
% 0.53/0.32 % (2479820)Termination phase: Saturation
% 0.53/0.32 % (2479820)Time elapsed: 0.028 s
% 0.53/0.32 % (2479820)Peak memory usage: 12 MB
% 0.53/0.32 % (2479820)Instructions burned: 119 (million)
% 0.53/0.32 % Exception at run slice level
% 0.53/0.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.53/0.32 % (2479831)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3304122322:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.53/0.32 % (2479830)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1342775624:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.53/0.32 % (2479819)Instruction limit reached!
% 0.53/0.32 % (2479819)------------------------------
% 0.53/0.32 % (2479819)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.32 % (2479819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.32 % (2479819)CaDiCaL version: 2.1.3
% 0.53/0.32 % (2479819)Termination reason: Instruction limit
% 0.53/0.32 % (2479819)Termination phase: Saturation
% 0.53/0.32 % (2479819)Time elapsed: 0.047 s
% 0.53/0.32 % (2479819)Peak memory usage: 12 MB
% 0.53/0.32 % (2479819)Instructions burned: 105 (million)
% 0.53/0.32 % Exception at run slice level
% 0.53/0.32 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.53/0.32 % (2479822) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2479811-2479822"...
% 0.53/0.32 % (2479822)...printing done.
% 0.53/0.32 % (2479822)Refutation found. Thanks to Tanya!
% 0.53/0.32 % SZS status Theorem for theBenchmark
% 0.53/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.53/0.32 % (2479822)------------------------------
% 0.53/0.32 % (2479822)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.53/0.32 % (2479822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.53/0.32 % (2479822)CaDiCaL version: 2.1.3
% 0.53/0.32 % (2479822)Termination reason: Refutation
% 0.53/0.32 % (2479822)Time elapsed: 0.057 s
% 0.53/0.32 % (2479822)Peak memory usage: 13 MB
% 0.53/0.32 % (2479822)Instructions burned: 115 (million)
% 0.53/0.32 % (2479811)Success in time 0.098 s
% 0.53/0.32 % Vampire exiting
%------------------------------------------------------------------------------