%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL862^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:14:37 AM UTC 2026
% Result : Theorem 0.23s 0.30s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 29
% Syntax : Number of formulae : 242 ( 40 unt; 0 typ; 24 def)
% Number of atoms : 1595 ( 327 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 1725 ( 205 ~; 314 |; 80 &; 915 @)
% ( 24 <=>; 68 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 94 ( 94 >; 0 *; 0 +; 0 <<)
% Number of symbols : 82 ( 78 usr; 35 con; 0-4 aty)
% ( 118 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 276 ( 0 sgn 98 !; 3 ?; 276 :)
% 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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
vIMP: $o > $o > $o ).
thf(func_def_34,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_38,type,
vOR: $o > $o > $o ).
thf(func_def_41,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
vAND: $o > $o > $o ).
thf(func_def_43,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_46,type,
vNOT: $o > $o ).
thf(func_def_47,type,
sK0: $i > $i > $o ).
thf(func_def_48,type,
sF1: $o ).
thf(func_def_49,type,
sF2: $o ).
thf(func_def_50,type,
sF3: $o ).
thf(func_def_51,type,
sF4: $o ).
thf(f18,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(f19,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) )
= msymmetric ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X2: $i,X3: $i,X1: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f22,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X2: $i,X3: $i,X1: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X2 @ X3 ) ) )
= meuclidean ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',meuclidean) ).
thf(f32,conjecture,
! [X0: $i > $i > $o] :
( ( ( meuclidean @ X0 )
& ( mreflexive @ X0 ) )
<=> ( ( mtransitive @ X0 )
& ( mreflexive @ X0 )
& ( msymmetric @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( ( meuclidean @ X0 )
& ( mreflexive @ X0 ) )
<=> ( ( mtransitive @ X0 )
& ( mreflexive @ X0 )
& ( msymmetric @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f34,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
=> ( X0 @ X1 @ X2 ) ) )
= msymmetric ),
inference(rectify,[],[f19]) ).
thf(f35,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f38,plain,
~ ! [X0: $i > $i > $o] :
( ( ( meuclidean @ X0 )
& ( mreflexive @ X0 ) )
<=> ( ( mtransitive @ X0 )
& ( mreflexive @ X0 )
& ( msymmetric @ X0 ) ) ),
inference(rectify,[],[f33]) ).
thf(f39,plain,
~ ! [X0: $i > $i > $o] :
( ( ( ( mreflexive @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) )
<=> ( ( ( mtransitive @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f55,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X2 )
& ( X0 @ X3 @ X1 ) )
=> ( X0 @ X1 @ X2 ) ) )
= meuclidean ),
inference(rectify,[],[f22]) ).
thf(f56,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f68,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
inference(rectify,[],[f18]) ).
thf(f69,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f68]) ).
thf(f70,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X1 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X3 @ X2 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f71,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f70]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( ( ( mreflexive @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) )
<~> ( ( ( mtransitive @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) ) ),
inference(ennf_transformation,[],[f39]) ).
thf(f88,plain,
? [X0: $i > $i > $o] :
( ( ( ( mtransitive @ X0 )
!= $true )
| ( ( msymmetric @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true ) )
& ( ( ( ( mtransitive @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) )
| ( ( ( mreflexive @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f87]) ).
thf(f89,plain,
? [X0: $i > $i > $o] :
( ( ( ( mtransitive @ X0 )
!= $true )
| ( ( msymmetric @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true ) )
& ( ( ( ( mtransitive @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) )
| ( ( ( mreflexive @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) ) ) ),
inference(flattening,[],[f88]) ).
thf(f90,plain,
( ( ( ( mtransitive @ sK0 )
!= $true )
| ( ( msymmetric @ sK0 )
!= $true )
| ( ( mreflexive @ sK0 )
!= $true )
| ( ( mreflexive @ sK0 )
!= $true )
| ( $true
!= ( meuclidean @ sK0 ) ) )
& ( ( ( ( mtransitive @ sK0 )
= $true )
& ( ( msymmetric @ sK0 )
= $true )
& ( ( mreflexive @ sK0 )
= $true ) )
| ( ( ( mreflexive @ sK0 )
= $true )
& ( $true
= ( meuclidean @ sK0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f89]) ).
thf(f101,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f109,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f111,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f71]) ).
thf(f117,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f120,plain,
( ( ( mreflexive @ sK0 )
= $true )
| ( ( mreflexive @ sK0 )
= $true ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f121,plain,
( ( ( msymmetric @ sK0 )
= $true )
| ( $true
= ( meuclidean @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f123,plain,
( ( ( mtransitive @ sK0 )
= $true )
| ( $true
= ( meuclidean @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f125,plain,
( ( ( mtransitive @ sK0 )
!= $true )
| ( ( msymmetric @ sK0 )
!= $true )
| ( ( mreflexive @ sK0 )
!= $true )
| ( ( mreflexive @ sK0 )
!= $true )
| ( $true
!= ( meuclidean @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f140,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
@ sK0 )
!= $true )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
@ sK0 )
!= $true )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ 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 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK0 )
!= $true ) ),
inference(definition_unfolding,[],[f125,f111,f109,f117,f117,f101]) ).
thf(f142,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
@ sK0 )
= $true )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK0 )
= $true ) ),
inference(definition_unfolding,[],[f123,f111,f101]) ).
thf(f144,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
@ sK0 )
= $true )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK0 )
= $true ) ),
inference(definition_unfolding,[],[f121,f109,f101]) ).
thf(f145,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 )
= $true )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 )
= $true ) ),
inference(definition_unfolding,[],[f120,f117,f117]) ).
thf(f147,definition,
( sF1
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
@ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f148,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
@ sK0 )
= sF1 ),
inference(reorient_equations,[],[f147]) ).
thf(f149,definition,
( sF2
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
@ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f150,definition,
( sF3
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f151,definition,
( sF4
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f152,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK0 )
= sF4 ),
inference(reorient_equations,[],[f151]) ).
thf(f153,plain,
( ( sF3 != $true )
| ( sF2 != $true )
| ( sF1 != $true )
| ( $true != sF4 )
| ( sF3 != $true ) ),
inference(definition_folding,[],[f140,f152,f150,f150,f149,f148]) ).
thf(f155,plain,
( ( $true = sF4 )
| ( sF1 = $true ) ),
inference(definition_folding,[],[f142,f152,f148]) ).
thf(f157,plain,
( ( sF2 = $true )
| ( $true = sF4 ) ),
inference(definition_folding,[],[f144,f152,f149]) ).
thf(f158,plain,
( ( sF3 = $true )
| ( sF3 = $true ) ),
inference(definition_folding,[],[f145,f150,f150]) ).
thf(f160,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
@ sK0 )
= $true )
| ( $false = sF1 ) ),
inference(iff_proxy_clausification,[],[f148]) ).
thf(f161,plain,
( ( $false
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
@ sK0 ) )
| ( sF1 = $true ) ),
inference(iff_proxy_clausification,[],[f148]) ).
thf(f162,plain,
( ( sF1 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
@ sK5 ) )
| ( sF1 = $true ) ),
inference(sigma_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ sK5 @ Y1 ) )
=> ( sK0 @ sK5 @ Y0 ) ) ) ) )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ sK5 @ Y1 ) )
=> ( sK0 @ sK5 @ Y0 ) ) )
@ sK6 ) )
| ( sF1 = $true ) ),
inference(sigma_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( ( sF1 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK6 )
& ( sK0 @ sK5 @ Y0 ) )
=> ( sK0 @ sK5 @ sK6 ) ) ) ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK6 )
& ( sK0 @ sK5 @ Y0 ) )
=> ( sK0 @ sK5 @ sK6 ) )
@ sK7 ) )
| ( sF1 = $true ) ),
inference(sigma_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( $false
= ( ( ( sK0 @ sK7 @ sK6 )
& ( sK0 @ sK5 @ sK7 ) )
=> ( sK0 @ sK5 @ sK6 ) ) )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
( ( sF1 = $true )
| ( $false
= ( sK0 @ sK5 @ sK6 ) ) ),
inference(imp_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( $true
= ( ( sK0 @ sK7 @ sK6 )
& ( sK0 @ sK5 @ sK7 ) ) )
| ( sF1 = $true ) ),
inference(imp_proxy_clausification,[],[f168]) ).
thf(f171,plain,
( ( sF1 = $true )
| ( ( sK0 @ sK5 @ sK7 )
= $true ) ),
inference(and_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( sF1 = $true )
| ( ( sK0 @ sK7 @ sK6 )
= $true ) ),
inference(and_proxy_clausification,[],[f170]) ).
thf(f173,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
= $true )
| ( $false = sF1 ) ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f174,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
@ X1 ) )
| ( $false = sF1 ) ),
inference(pi_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X1: $i] :
( ( $false = sF1 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ X1 @ Y1 ) )
=> ( sK0 @ X1 @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ X1 @ Y1 ) )
=> ( sK0 @ X1 @ Y0 ) ) )
@ X2 ) )
| ( $false = sF1 ) ),
inference(pi_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X2: $i,X1: $i] :
( ( $false = sF1 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X2 )
& ( sK0 @ X1 @ Y0 ) )
=> ( sK0 @ X1 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f176]) ).
thf(f178,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X2 )
& ( sK0 @ X1 @ Y0 ) )
=> ( sK0 @ X1 @ X2 ) )
@ X3 ) )
| ( $false = sF1 ) ),
inference(pi_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = sF1 )
| ( ( ( ( sK0 @ X3 @ X2 )
& ( sK0 @ X1 @ X3 ) )
=> ( sK0 @ X1 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f178]) ).
thf(f180,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = sF1 )
| ( ( sK0 @ X1 @ X2 )
= $true )
| ( $false
= ( ( sK0 @ X3 @ X2 )
& ( sK0 @ X1 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X3 ) )
| ( ( sK0 @ X1 @ X2 )
= $true )
| ( $false
= ( sK0 @ X3 @ X2 ) )
| ( $false = sF1 ) ),
inference(and_proxy_clausification,[],[f180]) ).
thf(f182,plain,
( ( $false = sF4 )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK0 )
= $true ) ),
inference(iff_proxy_clausification,[],[f152]) ).
thf(f183,plain,
( ( $true = sF4 )
| ( $false
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK0 ) ) ),
inference(iff_proxy_clausification,[],[f152]) ).
thf(f184,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) ) )
| ( $true = sF4 ) ),
inference(beta-eta_normalization,[],[f183]) ).
thf(f185,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) )
@ sK8 ) )
| ( $true = sF4 ) ),
inference(sigma_proxy_clausification,[],[f184]) ).
thf(f186,plain,
( ( $true = sF4 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ sK8 @ Y1 )
& ( sK0 @ sK8 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f187,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ sK8 @ Y1 )
& ( sK0 @ sK8 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ sK9 ) )
| ( $true = sF4 ) ),
inference(sigma_proxy_clausification,[],[f186]) ).
thf(f188,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK8 @ Y0 )
& ( sK0 @ sK8 @ sK9 ) )
=> ( sK0 @ Y0 @ sK9 ) ) ) )
| ( $true = sF4 ) ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f189,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK8 @ Y0 )
& ( sK0 @ sK8 @ sK9 ) )
=> ( sK0 @ Y0 @ sK9 ) )
@ sK10 ) )
| ( $true = sF4 ) ),
inference(sigma_proxy_clausification,[],[f188]) ).
thf(f190,plain,
( ( $true = sF4 )
| ( $false
= ( ( ( sK0 @ sK8 @ sK10 )
& ( sK0 @ sK8 @ sK9 ) )
=> ( sK0 @ sK10 @ sK9 ) ) ) ),
inference(beta-eta_normalization,[],[f189]) ).
thf(f191,plain,
( ( $true = sF4 )
| ( $false
= ( sK0 @ sK10 @ sK9 ) ) ),
inference(imp_proxy_clausification,[],[f190]) ).
thf(f192,plain,
( ( $true = sF4 )
| ( $true
= ( ( sK0 @ sK8 @ sK10 )
& ( sK0 @ sK8 @ sK9 ) ) ) ),
inference(imp_proxy_clausification,[],[f190]) ).
thf(f193,plain,
( ( $true = sF4 )
| ( ( sK0 @ sK8 @ sK9 )
= $true ) ),
inference(and_proxy_clausification,[],[f192]) ).
thf(f194,plain,
( ( $true
= ( sK0 @ sK8 @ sK10 ) )
| ( $true = sF4 ) ),
inference(and_proxy_clausification,[],[f192]) ).
thf(f195,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) ) )
= $true )
| ( $false = sF4 ) ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f196,plain,
! [X1: $i] :
( ( $false = sF4 )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y2 @ Y1 ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X1: $i] :
( ( $false = sF4 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ X1 @ Y1 )
& ( sK0 @ X1 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f196]) ).
thf(f198,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ X1 @ Y1 )
& ( sK0 @ X1 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ X2 )
= $true )
| ( $false = sF4 ) ),
inference(pi_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X2: $i,X1: $i] :
( ( $false = sF4 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ X1 @ Y0 )
& ( sK0 @ X1 @ X2 ) )
=> ( sK0 @ Y0 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f198]) ).
thf(f200,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = sF4 )
| ( ( ^ [Y0: $i] :
( ( ( sK0 @ X1 @ Y0 )
& ( sK0 @ X1 @ X2 ) )
=> ( sK0 @ Y0 @ X2 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( ( sK0 @ X1 @ X3 )
& ( sK0 @ X1 @ X2 ) )
=> ( sK0 @ X3 @ X2 ) )
= $true )
| ( $false = sF4 ) ),
inference(beta-eta_normalization,[],[f200]) ).
thf(f202,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( sK0 @ X1 @ X3 )
& ( sK0 @ X1 @ X2 ) ) )
| ( ( sK0 @ X3 @ X2 )
= $true )
| ( $false = sF4 ) ),
inference(imp_proxy_clausification,[],[f201]) ).
thf(f203,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( sK0 @ X3 @ X2 )
= $true )
| ( ( sK0 @ X1 @ X2 )
= $false )
| ( $false = sF4 )
| ( $false
= ( sK0 @ X1 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f202]) ).
thf(f204,plain,
sF3 = $true,
inference(duplicate_literal_removal,[],[f158]) ).
thf(f205,plain,
( ( $true != sF4 )
| ( sF3 != $true )
| ( sF2 != $true )
| ( sF1 != $true ) ),
inference(duplicate_literal_removal,[],[f153]) ).
thf(f207,plain,
( ( $false = sF3 )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 )
= $true ) ),
inference(iff_proxy_clausification,[],[f150]) ).
thf(f208,plain,
( ( $false = sF3 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f207]) ).
thf(f209,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ X1 )
= $true )
| ( $false = sF3 ) ),
inference(pi_proxy_clausification,[],[f208]) ).
thf(f210,plain,
! [X1: $i] :
( ( $false = sF3 )
| ( $true
= ( sK0 @ X1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f209]) ).
thf(f214,plain,
( ( sF2 = $true )
| ( $false
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
@ sK0 ) ) ),
inference(iff_proxy_clausification,[],[f149]) ).
thf(f215,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
@ sK0 )
= $true )
| ( $false = sF2 ) ),
inference(iff_proxy_clausification,[],[f149]) ).
thf(f216,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
= $true )
| ( $false = sF2 ) ),
inference(beta-eta_normalization,[],[f215]) ).
thf(f217,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ X1 )
= $true )
| ( $false = sF2 ) ),
inference(pi_proxy_clausification,[],[f216]) ).
thf(f218,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
=> ( sK0 @ Y0 @ X1 ) ) )
= $true )
| ( $false = sF2 ) ),
inference(beta-eta_normalization,[],[f217]) ).
thf(f219,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK0 @ X1 @ Y0 )
=> ( sK0 @ Y0 @ X1 ) )
@ X2 )
= $true )
| ( $false = sF2 ) ),
inference(pi_proxy_clausification,[],[f218]) ).
thf(f220,plain,
! [X2: $i,X1: $i] :
( ( ( ( sK0 @ X1 @ X2 )
=> ( sK0 @ X2 @ X1 ) )
= $true )
| ( $false = sF2 ) ),
inference(beta-eta_normalization,[],[f219]) ).
thf(f221,plain,
! [X2: $i,X1: $i] :
( ( $false = sF2 )
| ( ( sK0 @ X2 @ X1 )
= $true )
| ( ( sK0 @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f220]) ).
thf(f222,plain,
( ( sF2 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f214]) ).
thf(f223,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y0 @ Y1 )
=> ( sK0 @ Y1 @ Y0 ) ) )
@ sK12 ) )
| ( sF2 = $true ) ),
inference(sigma_proxy_clausification,[],[f222]) ).
thf(f224,plain,
( ( sF2 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ sK12 @ Y0 )
=> ( sK0 @ Y0 @ sK12 ) ) ) ) ),
inference(beta-eta_normalization,[],[f223]) ).
thf(f225,plain,
( ( sF2 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ sK12 @ Y0 )
=> ( sK0 @ Y0 @ sK12 ) )
@ sK13 ) ) ),
inference(sigma_proxy_clausification,[],[f224]) ).
thf(f226,plain,
( ( $false
= ( ( sK0 @ sK12 @ sK13 )
=> ( sK0 @ sK13 @ sK12 ) ) )
| ( sF2 = $true ) ),
inference(beta-eta_normalization,[],[f225]) ).
thf(f227,plain,
( ( $false
= ( sK0 @ sK13 @ sK12 ) )
| ( sF2 = $true ) ),
inference(imp_proxy_clausification,[],[f226]) ).
thf(f228,plain,
( ( sF2 = $true )
| ( ( sK0 @ sK12 @ sK13 )
= $true ) ),
inference(imp_proxy_clausification,[],[f226]) ).
thf(f230,definition,
( spl14_1
<=> ( $true = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
thf(f232,plain,
( ( $true = sF4 )
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f230]) ).
thf(f234,definition,
( spl14_2
<=> ( sF3 = $true ) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
thf(f236,plain,
( ( sF3 = $true )
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f234]) ).
thf(f239,definition,
( spl14_3
<=> ( ( sK0 @ sK7 @ sK6 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
thf(f241,plain,
( ( ( sK0 @ sK7 @ sK6 )
= $true )
| ~ spl14_3 ),
inference(avatar_component_clause,[],[f239]) ).
thf(f243,definition,
( spl14_4
<=> ( sF1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition]) ).
thf(f245,plain,
( ( sF1 = $true )
| ~ spl14_4 ),
inference(avatar_component_clause,[],[f243]) ).
thf(f246,plain,
( spl14_3
| spl14_4 ),
inference(avatar_split_clause,[],[f172,f243,f239]) ).
thf(f248,definition,
( spl14_5
<=> ( ( sK0 @ sK5 @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl14_5])],[avatar_definition]) ).
thf(f250,plain,
( ( ( sK0 @ sK5 @ sK7 )
= $true )
| ~ spl14_5 ),
inference(avatar_component_clause,[],[f248]) ).
thf(f251,plain,
( spl14_5
| spl14_4 ),
inference(avatar_split_clause,[],[f171,f243,f248]) ).
thf(f253,definition,
( spl14_6
<=> ( $false
= ( sK0 @ sK5 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_6])],[avatar_definition]) ).
thf(f255,plain,
( ( $false
= ( sK0 @ sK5 @ sK6 ) )
| ~ spl14_6 ),
inference(avatar_component_clause,[],[f253]) ).
thf(f256,plain,
( spl14_6
| spl14_4 ),
inference(avatar_split_clause,[],[f169,f243,f253]) ).
thf(f258,definition,
( spl14_7
<=> ( $false = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl14_7])],[avatar_definition]) ).
thf(f260,plain,
( ( $false = sF1 )
| ~ spl14_7 ),
inference(avatar_component_clause,[],[f258]) ).
thf(f262,definition,
( spl14_8
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $false
= ( sK0 @ X1 @ X3 ) )
| ( $false
= ( sK0 @ X3 @ X2 ) )
| ( ( sK0 @ X1 @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl14_8])],[avatar_definition]) ).
thf(f263,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X3 @ X2 ) )
| ( $false
= ( sK0 @ X1 @ X3 ) )
| ( ( sK0 @ X1 @ X2 )
= $true ) )
| ~ spl14_8 ),
inference(avatar_component_clause,[],[f262]) ).
thf(f264,plain,
( spl14_7
| spl14_8 ),
inference(avatar_split_clause,[],[f181,f262,f258]) ).
thf(f266,definition,
( spl14_9
<=> ( sF2 = $true ) ),
introduced(definition,[new_symbols(definition,[spl14_9])],[avatar_definition]) ).
thf(f268,plain,
( ( sF2 = $true )
| ~ spl14_9 ),
inference(avatar_component_clause,[],[f266]) ).
thf(f270,plain,
( spl14_1
| spl14_9 ),
inference(avatar_split_clause,[],[f157,f266,f230]) ).
thf(f272,definition,
( spl14_10
<=> ( $true
= ( sK0 @ sK8 @ sK10 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_10])],[avatar_definition]) ).
thf(f274,plain,
( ( $true
= ( sK0 @ sK8 @ sK10 ) )
| ~ spl14_10 ),
inference(avatar_component_clause,[],[f272]) ).
thf(f275,plain,
( spl14_10
| spl14_1 ),
inference(avatar_split_clause,[],[f194,f230,f272]) ).
thf(f277,definition,
( spl14_11
<=> ( ( sK0 @ sK8 @ sK9 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl14_11])],[avatar_definition]) ).
thf(f279,plain,
( ( ( sK0 @ sK8 @ sK9 )
= $true )
| ~ spl14_11 ),
inference(avatar_component_clause,[],[f277]) ).
thf(f280,plain,
( spl14_11
| spl14_1 ),
inference(avatar_split_clause,[],[f193,f230,f277]) ).
thf(f282,definition,
( spl14_12
<=> ( $false
= ( sK0 @ sK10 @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_12])],[avatar_definition]) ).
thf(f284,plain,
( ( $false
= ( sK0 @ sK10 @ sK9 ) )
| ~ spl14_12 ),
inference(avatar_component_clause,[],[f282]) ).
thf(f285,plain,
( spl14_12
| spl14_1 ),
inference(avatar_split_clause,[],[f191,f230,f282]) ).
thf(f287,definition,
( spl14_13
<=> ( $false = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl14_13])],[avatar_definition]) ).
thf(f289,plain,
( ( $false = sF4 )
| ~ spl14_13 ),
inference(avatar_component_clause,[],[f287]) ).
thf(f291,definition,
( spl14_14
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( ( sK0 @ X3 @ X2 )
= $true )
| ( $false
= ( sK0 @ X1 @ X3 ) )
| ( ( sK0 @ X1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl14_14])],[avatar_definition]) ).
thf(f292,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X3 ) )
| ( ( sK0 @ X1 @ X2 )
= $false )
| ( ( sK0 @ X3 @ X2 )
= $true ) )
| ~ spl14_14 ),
inference(avatar_component_clause,[],[f291]) ).
thf(f293,plain,
( spl14_13
| spl14_14 ),
inference(avatar_split_clause,[],[f203,f291,f287]) ).
thf(f294,plain,
spl14_2,
inference(avatar_split_clause,[],[f204,f234]) ).
thf(f295,plain,
( ~ spl14_2
| ~ spl14_4
| ~ spl14_9
| ~ spl14_1 ),
inference(avatar_split_clause,[],[f205,f230,f266,f243,f234]) ).
thf(f297,definition,
( spl14_15
<=> ( $false = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl14_15])],[avatar_definition]) ).
thf(f299,plain,
( ( $false = sF3 )
| ~ spl14_15 ),
inference(avatar_component_clause,[],[f297]) ).
thf(f301,definition,
( spl14_16
<=> ! [X1: $i] :
( $true
= ( sK0 @ X1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_16])],[avatar_definition]) ).
thf(f302,plain,
( ! [X1: $i] :
( $true
= ( sK0 @ X1 @ X1 ) )
| ~ spl14_16 ),
inference(avatar_component_clause,[],[f301]) ).
thf(f303,plain,
( spl14_15
| spl14_16 ),
inference(avatar_split_clause,[],[f210,f301,f297]) ).
thf(f310,definition,
( spl14_18
<=> ! [X2: $i,X1: $i] :
( ( ( sK0 @ X2 @ X1 )
= $true )
| ( ( sK0 @ X1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl14_18])],[avatar_definition]) ).
thf(f311,plain,
( ! [X2: $i,X1: $i] :
( ( ( sK0 @ X2 @ X1 )
= $true )
| ( ( sK0 @ X1 @ X2 )
= $false ) )
| ~ spl14_18 ),
inference(avatar_component_clause,[],[f310]) ).
thf(f313,definition,
( spl14_19
<=> ( $false = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl14_19])],[avatar_definition]) ).
thf(f315,plain,
( ( $false = sF2 )
| ~ spl14_19 ),
inference(avatar_component_clause,[],[f313]) ).
thf(f316,plain,
( spl14_18
| spl14_19 ),
inference(avatar_split_clause,[],[f221,f313,f310]) ).
thf(f318,definition,
( spl14_20
<=> ( ( sK0 @ sK12 @ sK13 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl14_20])],[avatar_definition]) ).
thf(f320,plain,
( ( ( sK0 @ sK12 @ sK13 )
= $true )
| ~ spl14_20 ),
inference(avatar_component_clause,[],[f318]) ).
thf(f321,plain,
( spl14_9
| spl14_20 ),
inference(avatar_split_clause,[],[f228,f318,f266]) ).
thf(f323,definition,
( spl14_21
<=> ( $false
= ( sK0 @ sK13 @ sK12 ) ) ),
introduced(definition,[new_symbols(definition,[spl14_21])],[avatar_definition]) ).
thf(f325,plain,
( ( $false
= ( sK0 @ sK13 @ sK12 ) )
| ~ spl14_21 ),
inference(avatar_component_clause,[],[f323]) ).
thf(f326,plain,
( spl14_21
| spl14_9 ),
inference(avatar_split_clause,[],[f227,f266,f323]) ).
thf(f327,plain,
( spl14_4
| spl14_1 ),
inference(avatar_split_clause,[],[f155,f230,f243]) ).
thf(f330,plain,
( ( $false = $true )
| ~ spl14_2
| ~ spl14_15 ),
inference(forward_demodulation,[],[f299,f236]) ).
thf(f331,plain,
( $false
| ~ spl14_2
| ~ spl14_15 ),
inference(trivial_inequality_removal,[],[f330]) ).
thf(f332,plain,
( ~ spl14_2
| ~ spl14_15 ),
inference(avatar_contradiction_clause,[],[f331]) ).
thf(f334,plain,
( ( $false = $true )
| ~ spl14_4
| ~ spl14_7 ),
inference(forward_demodulation,[],[f245,f260]) ).
thf(f335,plain,
( $false
| ~ spl14_4
| ~ spl14_7 ),
inference(trivial_inequality_removal,[],[f334]) ).
thf(f336,plain,
( ~ spl14_4
| ~ spl14_7 ),
inference(avatar_contradiction_clause,[],[f335]) ).
thf(f352,plain,
( ( $false
= ( sK0 @ sK9 @ sK10 ) )
| ( $false = $true )
| ~ spl14_12
| ~ spl14_18 ),
inference(constrained_superposition,[],[f311,f284]) ).
thf(f355,plain,
( ( $false
= ( sK0 @ sK9 @ sK10 ) )
| ~ spl14_12
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f352]) ).
thf(f365,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( sK0 @ X0 @ sK8 ) )
| ( $true
= ( sK0 @ X0 @ sK10 ) ) )
| ~ spl14_8
| ~ spl14_10 ),
inference(constrained_superposition,[],[f263,f274]) ).
thf(f376,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ X0 @ sK10 ) )
| ( $false
= ( sK0 @ X0 @ sK8 ) ) )
| ~ spl14_8
| ~ spl14_10 ),
inference(trivial_inequality_removal,[],[f365]) ).
thf(f410,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK9 @ sK8 ) )
| ~ spl14_8
| ~ spl14_10
| ~ spl14_12
| ~ spl14_18 ),
inference(constrained_superposition,[],[f355,f376]) ).
thf(f413,plain,
( ( $false
= ( sK0 @ sK9 @ sK8 ) )
| ~ spl14_8
| ~ spl14_10
| ~ spl14_12
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f410]) ).
thf(f417,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK8 @ sK9 ) )
| ~ spl14_8
| ~ spl14_10
| ~ spl14_12
| ~ spl14_18 ),
inference(constrained_superposition,[],[f413,f311]) ).
thf(f421,plain,
( ( $false
= ( sK0 @ sK8 @ sK9 ) )
| ~ spl14_8
| ~ spl14_10
| ~ spl14_12
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f417]) ).
thf(f426,plain,
( ( $false = $true )
| ~ spl14_8
| ~ spl14_10
| ~ spl14_11
| ~ spl14_12
| ~ spl14_18 ),
inference(forward_demodulation,[],[f421,f279]) ).
thf(f427,plain,
( $false
| ~ spl14_8
| ~ spl14_10
| ~ spl14_11
| ~ spl14_12
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f426]) ).
thf(f428,plain,
( ~ spl14_8
| ~ spl14_10
| ~ spl14_11
| ~ spl14_12
| ~ spl14_18 ),
inference(avatar_contradiction_clause,[],[f427]) ).
thf(f429,plain,
( ( $false = $true )
| ~ spl14_9
| ~ spl14_19 ),
inference(forward_demodulation,[],[f315,f268]) ).
thf(f430,plain,
( $false
| ~ spl14_9
| ~ spl14_19 ),
inference(trivial_inequality_removal,[],[f429]) ).
thf(f431,plain,
( ~ spl14_9
| ~ spl14_19 ),
inference(avatar_contradiction_clause,[],[f430]) ).
thf(f432,plain,
( ( $false = $true )
| ~ spl14_1
| ~ spl14_13 ),
inference(forward_demodulation,[],[f232,f289]) ).
thf(f433,plain,
( $false
| ~ spl14_1
| ~ spl14_13 ),
inference(trivial_inequality_removal,[],[f432]) ).
thf(f434,plain,
( ~ spl14_1
| ~ spl14_13 ),
inference(avatar_contradiction_clause,[],[f433]) ).
thf(f452,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( ( sK0 @ sK13 @ X0 )
= $true )
| ( $false
= ( sK0 @ sK12 @ X0 ) ) )
| ~ spl14_14
| ~ spl14_20 ),
inference(constrained_superposition,[],[f292,f320]) ).
thf(f461,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ sK12 @ X0 ) )
| ( ( sK0 @ sK13 @ X0 )
= $true ) )
| ~ spl14_14
| ~ spl14_20 ),
inference(trivial_inequality_removal,[],[f452]) ).
thf(f482,plain,
( ( ( sK0 @ sK13 @ sK12 )
= $true )
| ( $false = $true )
| ~ spl14_14
| ~ spl14_16
| ~ spl14_20 ),
inference(constrained_superposition,[],[f461,f302]) ).
thf(f492,plain,
( ( ( sK0 @ sK13 @ sK12 )
= $true )
| ~ spl14_14
| ~ spl14_16
| ~ spl14_20 ),
inference(trivial_inequality_removal,[],[f482]) ).
thf(f502,plain,
( ( $false = $true )
| ~ spl14_14
| ~ spl14_16
| ~ spl14_20
| ~ spl14_21 ),
inference(forward_demodulation,[],[f492,f325]) ).
thf(f503,plain,
( $false
| ~ spl14_14
| ~ spl14_16
| ~ spl14_20
| ~ spl14_21 ),
inference(trivial_inequality_removal,[],[f502]) ).
thf(f504,plain,
( ~ spl14_14
| ~ spl14_16
| ~ spl14_20
| ~ spl14_21 ),
inference(avatar_contradiction_clause,[],[f503]) ).
thf(f521,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X1 @ X0 ) )
| ( $false = $true )
| ( $false
= ( sK0 @ X0 @ X2 ) )
| ( ( sK0 @ X1 @ X2 )
= $true ) )
| ~ spl14_14
| ~ spl14_18 ),
inference(constrained_superposition,[],[f311,f292]) ).
thf(f531,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X0 @ X2 ) )
| ( ( sK0 @ X1 @ X2 )
= $true )
| ( $false
= ( sK0 @ X1 @ X0 ) ) )
| ~ spl14_14
| ~ spl14_18 ),
inference(trivial_inequality_removal,[],[f521]) ).
thf(f538,plain,
( spl14_8
| ~ spl14_14
| ~ spl14_18 ),
inference(avatar_split_clause,[],[f531,f310,f291,f262]) ).
thf(f578,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK7 ) )
| ( $false = $true )
| ( ( sK0 @ X0 @ sK6 )
= $true ) )
| ~ spl14_3
| ~ spl14_8 ),
inference(constrained_superposition,[],[f241,f263]) ).
thf(f596,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK7 ) )
| ( ( sK0 @ X0 @ sK6 )
= $true ) )
| ~ spl14_3
| ~ spl14_8 ),
inference(trivial_inequality_removal,[],[f578]) ).
thf(f1255,plain,
( ( $true
= ( sK0 @ sK5 @ sK6 ) )
| ( $false = $true )
| ~ spl14_3
| ~ spl14_5
| ~ spl14_8 ),
inference(constrained_superposition,[],[f596,f250]) ).
thf(f1284,plain,
( ( $true
= ( sK0 @ sK5 @ sK6 ) )
| ~ spl14_3
| ~ spl14_5
| ~ spl14_8 ),
inference(trivial_inequality_removal,[],[f1255]) ).
thf(f1299,plain,
( ( $false = $true )
| ~ spl14_3
| ~ spl14_5
| ~ spl14_6
| ~ spl14_8 ),
inference(forward_demodulation,[],[f1284,f255]) ).
thf(f1300,plain,
( $false
| ~ spl14_3
| ~ spl14_5
| ~ spl14_6
| ~ spl14_8 ),
inference(trivial_inequality_removal,[],[f1299]) ).
thf(f1301,plain,
( ~ spl14_3
| ~ spl14_5
| ~ spl14_6
| ~ spl14_8 ),
inference(avatar_contradiction_clause,[],[f1300]) ).
cnf(s2,plain,
( spl14_3
| spl14_4 ),
inference(sat_conversion,[],[f246]) ).
cnf(s3,plain,
( spl14_4
| spl14_5 ),
inference(sat_conversion,[],[f251]) ).
cnf(s4,plain,
( spl14_4
| spl14_6 ),
inference(sat_conversion,[],[f256]) ).
cnf(s5,plain,
( spl14_7
| spl14_8 ),
inference(sat_conversion,[],[f264]) ).
cnf(s7,plain,
( spl14_1
| spl14_9 ),
inference(sat_conversion,[],[f270]) ).
cnf(s8,plain,
( spl14_1
| spl14_10 ),
inference(sat_conversion,[],[f275]) ).
cnf(s9,plain,
( spl14_1
| spl14_11 ),
inference(sat_conversion,[],[f280]) ).
cnf(s10,plain,
( spl14_1
| spl14_12 ),
inference(sat_conversion,[],[f285]) ).
cnf(s11,plain,
( spl14_13
| spl14_14 ),
inference(sat_conversion,[],[f293]) ).
cnf(s12,plain,
spl14_2,
inference(sat_conversion,[],[f294]) ).
cnf(s13,plain,
( ~ spl14_1
| ~ spl14_2
| ~ spl14_4
| ~ spl14_9 ),
inference(sat_conversion,[],[f295]) ).
cnf(s14,plain,
( spl14_15
| spl14_16 ),
inference(sat_conversion,[],[f303]) ).
cnf(s16,plain,
( spl14_18
| spl14_19 ),
inference(sat_conversion,[],[f316]) ).
cnf(s17,plain,
( spl14_9
| spl14_20 ),
inference(sat_conversion,[],[f321]) ).
cnf(s18,plain,
( spl14_9
| spl14_21 ),
inference(sat_conversion,[],[f326]) ).
cnf(s19,plain,
( spl14_1
| spl14_4 ),
inference(sat_conversion,[],[f327]) ).
cnf(s21,plain,
( ~ spl14_2
| ~ spl14_15 ),
inference(sat_conversion,[],[f332]) ).
cnf(s22,plain,
( ~ spl14_4
| ~ spl14_7 ),
inference(sat_conversion,[],[f336]) ).
cnf(s24,plain,
( ~ spl14_8
| ~ spl14_10
| ~ spl14_11
| ~ spl14_12
| ~ spl14_18 ),
inference(sat_conversion,[],[f428]) ).
cnf(s25,plain,
( ~ spl14_9
| ~ spl14_19 ),
inference(sat_conversion,[],[f431]) ).
cnf(s26,plain,
( ~ spl14_1
| ~ spl14_13 ),
inference(sat_conversion,[],[f434]) ).
cnf(s29,plain,
( ~ spl14_14
| ~ spl14_16
| ~ spl14_20
| ~ spl14_21 ),
inference(sat_conversion,[],[f504]) ).
cnf(s32,plain,
( spl14_8
| ~ spl14_14
| ~ spl14_18 ),
inference(sat_conversion,[],[f538]) ).
cnf(s59,plain,
( ~ spl14_3
| ~ spl14_5
| ~ spl14_6
| ~ spl14_8 ),
inference(sat_conversion,[],[f1301]) ).
cnf(s60,plain,
~ spl14_15,
inference(rat,[],[s21,s12]) ).
cnf(s61,plain,
spl14_16,
inference(rat,[],[s14,s60]) ).
cnf(s62,plain,
spl14_1,
inference(rat,[],[s24,s16,s5,s25,s22,s7,s8,s9,s10,s19]) ).
cnf(s63,plain,
~ spl14_13,
inference(rat,[],[s26,s62]) ).
cnf(s64,plain,
spl14_14,
inference(rat,[],[s11,s63]) ).
cnf(s65,plain,
spl14_9,
inference(rat,[],[s29,s17,s18,s61,s64]) ).
cnf(s66,plain,
~ spl14_19,
inference(rat,[],[s25,s65]) ).
cnf(s67,plain,
~ spl14_4,
inference(rat,[],[s13,s62,s12,s65]) ).
cnf(s68,plain,
spl14_18,
inference(rat,[],[s16,s66]) ).
cnf(s69,plain,
spl14_6,
inference(rat,[],[s4,s67]) ).
cnf(s70,plain,
spl14_5,
inference(rat,[],[s3,s67]) ).
cnf(s71,plain,
spl14_3,
inference(rat,[],[s2,s67]) ).
cnf(s72,plain,
spl14_8,
inference(rat,[],[s32,s64,s68]) ).
cnf(s73,plain,
$false,
inference(rat,[],[s59,s72,s71,s69,s70]) ).
thf(f1302,plain,
$false,
inference(avatar_sat_refutation,[],[s73]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n002.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 10:15:53 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.23/0.30 % (1090305)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.30 % (1090316)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.30 % (1090316)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.23/0.30 % (1090316)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3373943917:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.30 % (1090310)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3271127841:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.30 % (1090311)lrs+10_16_si=on:nwc=1.5:random_seed=769719595:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.30 % (1090312)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2034281537:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.30 % (1090314)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=741870206:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.30 % (1090313)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2093439068:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.23/0.30 % (1090315)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3912964158:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.30 % (1090312)Instruction limit reached!
% 0.23/0.30 % (1090312)------------------------------
% 0.23/0.30 % (1090312)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (1090312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (1090312)CaDiCaL version: 2.1.3
% 0.23/0.30 % (1090312)Termination reason: Instruction limit
% 0.23/0.30 % (1090312)Termination phase: Preprocessing 3
% 0.23/0.30 % (1090312)Time elapsed: 0.002 s
% 0.23/0.30 % (1090312)Peak memory usage: 10 MB
% 0.23/0.30 % (1090312)Instructions burned: 4 (million)
% 0.23/0.30 % (1090316) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1090305-1090316"...
% 0.23/0.30 % (1090311)Instruction limit reached!
% 0.23/0.30 % (1090311)------------------------------
% 0.23/0.30 % (1090311)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (1090311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (1090311)CaDiCaL version: 2.1.3
% 0.23/0.30 % (1090311)Termination reason: Instruction limit
% 0.23/0.30 % (1090311)Termination phase: Saturation
% 0.23/0.30 % (1090311)Time elapsed: 0.010 s
% 0.23/0.30 % (1090311)Peak memory usage: 12 MB
% 0.23/0.30 % (1090311)Instructions burned: 19 (million)
% 0.23/0.30 % (1090316)...printing done.
% 0.23/0.30 % (1090316)Refutation found. Thanks to Tanya!
% 0.23/0.30 % SZS status Theorem for theBenchmark
% 0.23/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.30 % (1090316)------------------------------
% 0.23/0.30 % (1090316)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.30 % (1090316)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.30 % (1090316)CaDiCaL version: 2.1.3
% 0.23/0.30 % (1090316)Termination reason: Refutation
% 0.23/0.30 % (1090316)Time elapsed: 0.019 s
% 0.23/0.30 % (1090316)Peak memory usage: 13 MB
% 0.23/0.30 % (1090316)Instructions burned: 66 (million)
% 0.23/0.30 % (1090305)Success in time 0.044 s
% 0.23/0.30 % Vampire exiting
%------------------------------------------------------------------------------