%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL864^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 0.20s 0.33s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 31
% Syntax : Number of formulae : 238 ( 44 unt; 0 typ; 25 def)
% Number of atoms : 1476 ( 315 equ; 0 cnn)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 1592 ( 209 ~; 291 |; 70 &; 827 @)
% ( 24 <=>; 52 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 110 ( 110 >; 0 *; 0 +; 0 <<)
% Number of symbols : 84 ( 79 usr; 36 con; 0-4 aty)
% ( 105 !!; 13 ??; 0 @@+; 0 @@-)
% Number of variables : 265 ( 0 sgn 86 !; 5 ?; 265 :)
% 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,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_35,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_36,type,
vNOT: $o > $o ).
thf(func_def_37,type,
vIMP: $o > $o > $o ).
thf(func_def_38,type,
vAND: $o > $o > $o ).
thf(func_def_39,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vOR: $o > $o > $o ).
thf(func_def_42,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_43,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
sK0: $i > $i > $o ).
thf(func_def_48,type,
sF1: $o ).
thf(func_def_49,type,
sF2: $o ).
thf(func_def_50,type,
sF3: $o ).
thf(func_def_51,type,
sF4: $o ).
thf(func_def_52,type,
sF5: $o ).
thf(func_def_62,type,
sK15: $i > $i ).
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] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) )
= msymmetric ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f20,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) )
= mserial ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mserial) ).
thf(f21,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) )
= mtransitive ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f22,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i,X3: $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 )
& ( mserial @ X0 )
& ( mtransitive @ X0 )
& ( msymmetric @ X0 ) )
<=> ( ( meuclidean @ X0 )
& ( mreflexive @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( ( meuclidean @ X0 )
& ( mserial @ X0 )
& ( mtransitive @ X0 )
& ( msymmetric @ X0 ) )
<=> ( ( meuclidean @ X0 )
& ( mreflexive @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f38,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X2 @ X1 ) )
=> ( X0 @ X2 @ X3 ) ) )
= mtransitive ),
inference(rectify,[],[f21]) ).
thf(f39,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f49,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
inference(rectify,[],[f18]) ).
thf(f50,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f59,plain,
~ ! [X0: $i > $i > $o] :
( ( ( meuclidean @ X0 )
& ( mserial @ X0 )
& ( mtransitive @ X0 )
& ( msymmetric @ X0 ) )
<=> ( ( meuclidean @ X0 )
& ( mreflexive @ X0 ) ) ),
inference(rectify,[],[f33]) ).
thf(f60,plain,
~ ! [X0: $i > $i > $o] :
( ( ( ( msymmetric @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true )
& ( ( mserial @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) )
<=> ( ( ( meuclidean @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f59]) ).
thf(f63,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) )
= msymmetric ),
inference(rectify,[],[f19]) ).
thf(f64,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f65,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X2 @ X1 ) )
=> ( X0 @ X1 @ X3 ) ) )
= meuclidean ),
inference(rectify,[],[f22]) ).
thf(f66,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f65]) ).
thf(f67,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] :
? [X2: $i] : ( X0 @ X1 @ X2 ) )
= mserial ),
inference(rectify,[],[f20]) ).
thf(f68,plain,
( mserial
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f67]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( ( ( msymmetric @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true )
& ( ( mserial @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) )
<~> ( ( ( meuclidean @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) ) ),
inference(ennf_transformation,[],[f60]) ).
thf(f88,plain,
? [X0: $i > $i > $o] :
( ( ( ( meuclidean @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true )
| ( ( msymmetric @ X0 )
!= $true )
| ( ( mtransitive @ X0 )
!= $true )
| ( ( mserial @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true ) )
& ( ( ( ( meuclidean @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) )
| ( ( ( msymmetric @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true )
& ( ( mserial @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f87]) ).
thf(f89,plain,
? [X0: $i > $i > $o] :
( ( ( ( meuclidean @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true )
| ( ( msymmetric @ X0 )
!= $true )
| ( ( mtransitive @ X0 )
!= $true )
| ( ( mserial @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true ) )
& ( ( ( ( meuclidean @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) )
| ( ( ( msymmetric @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true )
& ( ( mserial @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) ) ) ),
inference(flattening,[],[f88]) ).
thf(f90,plain,
( ( ( ( meuclidean @ sK0 )
!= $true )
| ( $true
!= ( mreflexive @ sK0 ) )
| ( ( msymmetric @ sK0 )
!= $true )
| ( ( mtransitive @ sK0 )
!= $true )
| ( ( mserial @ sK0 )
!= $true )
| ( ( meuclidean @ sK0 )
!= $true ) )
& ( ( ( ( meuclidean @ sK0 )
= $true )
& ( $true
= ( mreflexive @ sK0 ) ) )
| ( ( ( msymmetric @ sK0 )
= $true )
& ( ( mtransitive @ sK0 )
= $true )
& ( ( mserial @ sK0 )
= $true )
& ( ( meuclidean @ sK0 )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f89]) ).
thf(f92,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f99,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f105,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f108,plain,
( ( $true
= ( mreflexive @ sK0 ) )
| ( ( mserial @ sK0 )
= $true ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f110,plain,
( ( $true
= ( mreflexive @ sK0 ) )
| ( ( msymmetric @ sK0 )
= $true ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f111,plain,
( ( ( meuclidean @ sK0 )
= $true )
| ( ( meuclidean @ sK0 )
= $true ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f115,plain,
( ( ( meuclidean @ sK0 )
!= $true )
| ( $true
!= ( mreflexive @ sK0 ) )
| ( ( msymmetric @ sK0 )
!= $true )
| ( ( mtransitive @ sK0 )
!= $true )
| ( ( mserial @ sK0 )
!= $true )
| ( ( meuclidean @ sK0 )
!= $true ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f122,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f126,plain,
( mserial
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f142,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( 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] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ sK0 )
!= $true )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ sK0 )
!= $true )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) )
@ sK0 ) )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK0 )
!= $true ) ),
inference(definition_unfolding,[],[f115,f105,f122,f99,f92,f126,f105]) ).
thf(f146,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK0 )
= $true )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK0 )
= $true ) ),
inference(definition_unfolding,[],[f111,f105,f105]) ).
thf(f147,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 )
= $true )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ sK0 )
= $true ) ),
inference(definition_unfolding,[],[f110,f122,f99]) ).
thf(f149,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 )
= $true )
| ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f108,f122,f126]) ).
thf(f151,definition,
( sF1
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f152,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK0 )
= sF1 ),
inference(reorient_equations,[],[f151]) ).
thf(f153,definition,
( sF2
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f154,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 )
= sF2 ),
inference(reorient_equations,[],[f153]) ).
thf(f155,definition,
( sF3
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f156,definition,
( sF4
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f157,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ sK0 )
= sF4 ),
inference(reorient_equations,[],[f156]) ).
thf(f158,definition,
( sF5
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) )
@ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f159,plain,
( ( sF3 != $true )
| ( $true != sF2 )
| ( sF4 != $true )
| ( $true != sF5 )
| ( $true != sF1 )
| ( $true != sF1 ) ),
inference(definition_folding,[],[f142,f152,f158,f157,f155,f154,f152]) ).
thf(f163,plain,
( ( $true = sF1 )
| ( $true = sF1 ) ),
inference(definition_folding,[],[f146,f152,f152]) ).
thf(f164,plain,
( ( $true = sF2 )
| ( sF3 = $true ) ),
inference(definition_folding,[],[f147,f155,f154]) ).
thf(f166,plain,
( ( $true = sF2 )
| ( $true = sF5 ) ),
inference(definition_folding,[],[f149,f158,f154]) ).
thf(f168,plain,
( ( sF4 != $true )
| ( $true != sF2 )
| ( $true != sF5 )
| ( sF3 != $true )
| ( $true != sF1 ) ),
inference(duplicate_literal_removal,[],[f159]) ).
thf(f169,plain,
( ( $false = sF1 )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK0 )
= $true ) ),
inference(iff_proxy_clausification,[],[f152]) ).
thf(f182,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) )
= $true )
| ( $false = sF1 ) ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f183,plain,
! [X1: $i] :
( ( $false = sF1 )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X1: $i] :
( ( $false = sF1 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ Y1 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f183]) ).
thf(f185,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ Y1 @ X1 ) ) )
@ X2 )
= $true )
| ( $false = sF1 ) ),
inference(pi_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X2: $i,X1: $i] :
( ( $false = sF1 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ X2 @ Y0 )
& ( sK0 @ X2 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f187,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( ( sK0 @ X2 @ Y0 )
& ( sK0 @ X2 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) )
@ X3 )
= $true )
| ( $false = sF1 ) ),
inference(pi_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = sF1 )
| ( ( ( ( sK0 @ X2 @ X3 )
& ( sK0 @ X2 @ X1 ) )
=> ( sK0 @ X3 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f189,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( sK0 @ X2 @ X3 )
& ( sK0 @ X2 @ X1 ) ) )
| ( $false = sF1 )
| ( ( sK0 @ X3 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X1 ) )
| ( ( sK0 @ X2 @ X3 )
= $false )
| ( $false = sF1 )
| ( ( sK0 @ X3 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f189]) ).
thf(f192,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ sK0 )
= $false )
| ( sF4 = $true ) ),
inference(iff_proxy_clausification,[],[f157]) ).
thf(f193,plain,
( ( sF4 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f192]) ).
thf(f194,plain,
( ( sF4 = $true )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
@ sK9 ) ) ),
inference(sigma_proxy_clausification,[],[f193]) ).
thf(f195,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y1 @ sK9 ) )
=> ( sK0 @ Y0 @ sK9 ) ) ) ) )
| ( sF4 = $true ) ),
inference(beta-eta_normalization,[],[f194]) ).
thf(f196,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y1 @ sK9 ) )
=> ( sK0 @ Y0 @ sK9 ) ) )
@ sK10 ) )
| ( sF4 = $true ) ),
inference(sigma_proxy_clausification,[],[f195]) ).
thf(f197,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK10 @ Y0 )
& ( sK0 @ Y0 @ sK9 ) )
=> ( sK0 @ sK10 @ sK9 ) ) ) )
| ( sF4 = $true ) ),
inference(beta-eta_normalization,[],[f196]) ).
thf(f198,plain,
( ( sF4 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK10 @ Y0 )
& ( sK0 @ Y0 @ sK9 ) )
=> ( sK0 @ sK10 @ sK9 ) )
@ sK11 ) ) ),
inference(sigma_proxy_clausification,[],[f197]) ).
thf(f199,plain,
( ( $false
= ( ( ( sK0 @ sK10 @ sK11 )
& ( sK0 @ sK11 @ sK9 ) )
=> ( sK0 @ sK10 @ sK9 ) ) )
| ( sF4 = $true ) ),
inference(beta-eta_normalization,[],[f198]) ).
thf(f200,plain,
( ( ( sK0 @ sK10 @ sK9 )
= $false )
| ( sF4 = $true ) ),
inference(imp_proxy_clausification,[],[f199]) ).
thf(f201,plain,
( ( ( ( sK0 @ sK10 @ sK11 )
& ( sK0 @ sK11 @ sK9 ) )
= $true )
| ( sF4 = $true ) ),
inference(imp_proxy_clausification,[],[f199]) ).
thf(f202,plain,
( ( ( sK0 @ sK11 @ sK9 )
= $true )
| ( sF4 = $true ) ),
inference(and_proxy_clausification,[],[f201]) ).
thf(f203,plain,
( ( sF4 = $true )
| ( $true
= ( sK0 @ sK10 @ sK11 ) ) ),
inference(and_proxy_clausification,[],[f201]) ).
thf(f213,plain,
$true = sF1,
inference(duplicate_literal_removal,[],[f163]) ).
thf(f214,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ sK0 )
= $false )
| ( sF3 = $true ) ),
inference(iff_proxy_clausification,[],[f155]) ).
thf(f215,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ sK0 )
= $true )
| ( sF3 = $false ) ),
inference(iff_proxy_clausification,[],[f155]) ).
thf(f216,plain,
( ( sF3 = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f215]) ).
thf(f217,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ X1 )
= $true )
| ( sF3 = $false ) ),
inference(pi_proxy_clausification,[],[f216]) ).
thf(f218,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( sK0 @ X1 @ Y0 ) ) )
= $true )
| ( sF3 = $false ) ),
inference(beta-eta_normalization,[],[f217]) ).
thf(f219,plain,
! [X2: $i,X1: $i] :
( ( sF3 = $false )
| ( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( sK0 @ X1 @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f218]) ).
thf(f220,plain,
! [X2: $i,X1: $i] :
( ( ( ( sK0 @ X2 @ X1 )
=> ( sK0 @ X1 @ X2 ) )
= $true )
| ( sF3 = $false ) ),
inference(beta-eta_normalization,[],[f219]) ).
thf(f221,plain,
! [X2: $i,X1: $i] :
( ( sF3 = $false )
| ( ( sK0 @ X1 @ X2 )
= $true )
| ( $false
= ( sK0 @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f220]) ).
thf(f222,plain,
( ( sF3 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f214]) ).
thf(f223,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK12 )
= $false )
| ( sF3 = $true ) ),
inference(sigma_proxy_clausification,[],[f222]) ).
thf(f224,plain,
( ( sF3 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK12 )
=> ( sK0 @ sK12 @ Y0 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f223]) ).
thf(f225,plain,
( ( sF3 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK12 )
=> ( sK0 @ sK12 @ Y0 ) )
@ sK13 ) ) ),
inference(sigma_proxy_clausification,[],[f224]) ).
thf(f226,plain,
( ( $false
= ( ( sK0 @ sK13 @ sK12 )
=> ( sK0 @ sK12 @ sK13 ) ) )
| ( sF3 = $true ) ),
inference(beta-eta_normalization,[],[f225]) ).
thf(f227,plain,
( ( sF3 = $true )
| ( $false
= ( sK0 @ sK12 @ sK13 ) ) ),
inference(imp_proxy_clausification,[],[f226]) ).
thf(f228,plain,
( ( sF3 = $true )
| ( ( sK0 @ sK13 @ sK12 )
= $true ) ),
inference(imp_proxy_clausification,[],[f226]) ).
thf(f229,plain,
( ( $false = sF2 )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 )
= $true ) ),
inference(iff_proxy_clausification,[],[f154]) ).
thf(f230,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 )
= $false )
| ( $true = sF2 ) ),
inference(iff_proxy_clausification,[],[f154]) ).
thf(f231,plain,
( ( $true = sF2 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f230]) ).
thf(f232,plain,
( ( $true = sF2 )
| ( $false
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ sK14 ) ) ),
inference(sigma_proxy_clausification,[],[f231]) ).
thf(f233,plain,
( ( $true = sF2 )
| ( $false
= ( sK0 @ sK14 @ sK14 ) ) ),
inference(beta-eta_normalization,[],[f232]) ).
thf(f234,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) )
| ( $false = sF2 ) ),
inference(beta-eta_normalization,[],[f229]) ).
thf(f235,plain,
! [X1: $i] :
( ( $false = sF2 )
| ( $true
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f234]) ).
thf(f236,plain,
! [X1: $i] :
( ( $true
= ( sK0 @ X1 @ X1 ) )
| ( $false = sF2 ) ),
inference(beta-eta_normalization,[],[f235]) ).
thf(f237,plain,
( ( $true = sF5 )
| ( $false
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) )
@ sK0 ) ) ),
inference(iff_proxy_clausification,[],[f158]) ).
thf(f238,plain,
( ( $false = sF5 )
| ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y1 @ Y2 ) ) )
@ sK0 ) ) ),
inference(iff_proxy_clausification,[],[f158]) ).
thf(f239,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) ) )
| ( $false = sF5 ) ),
inference(beta-eta_normalization,[],[f238]) ).
thf(f240,plain,
! [X1: $i] :
( ( $false = sF5 )
| ( ( ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f239]) ).
thf(f241,plain,
! [X1: $i] :
( ( $false = sF5 )
| ( ( ?? @ $i @ ( sK0 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f240]) ).
thf(f242,plain,
! [X1: $i] :
( ( $false = sF5 )
| ( ( sK0 @ X1 @ ( sK15 @ X1 ) )
= $true ) ),
inference(sigma_proxy_clausification,[],[f241]) ).
thf(f243,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) ) ) )
| ( $true = sF5 ) ),
inference(beta-eta_normalization,[],[f237]) ).
thf(f244,plain,
( ( $false
= ( ^ [Y0: $i] : ( ?? @ $i @ ( sK0 @ Y0 ) )
@ sK16 ) )
| ( $true = sF5 ) ),
inference(sigma_proxy_clausification,[],[f243]) ).
thf(f245,plain,
( ( $true = sF5 )
| ( $false
= ( ?? @ $i @ ( sK0 @ sK16 ) ) ) ),
inference(beta-eta_normalization,[],[f244]) ).
thf(f246,plain,
! [X1: $i] :
( ( $true = sF5 )
| ( $false
= ( sK0 @ sK16 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f245]) ).
thf(f248,definition,
( spl17_1
<=> ( sF3 = $true ) ),
introduced(definition,[new_symbols(definition,[spl17_1])],[avatar_definition]) ).
thf(f249,plain,
( ( sF3 = $true )
| ~ spl17_1 ),
inference(avatar_component_clause,[],[f248]) ).
thf(f252,definition,
( spl17_2
<=> ( sF4 = $true ) ),
introduced(definition,[new_symbols(definition,[spl17_2])],[avatar_definition]) ).
thf(f256,definition,
( spl17_3
<=> ( $true = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl17_3])],[avatar_definition]) ).
thf(f257,plain,
( ( $true = sF2 )
| ~ spl17_3 ),
inference(avatar_component_clause,[],[f256]) ).
thf(f260,definition,
( spl17_4
<=> ( $true = sF5 ) ),
introduced(definition,[new_symbols(definition,[spl17_4])],[avatar_definition]) ).
thf(f261,plain,
( ( $true = sF5 )
| ~ spl17_4 ),
inference(avatar_component_clause,[],[f260]) ).
thf(f264,definition,
( spl17_5
<=> ( $true = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl17_5])],[avatar_definition]) ).
thf(f265,plain,
( ( $true = sF1 )
| ~ spl17_5 ),
inference(avatar_component_clause,[],[f264]) ).
thf(f267,plain,
( ~ spl17_1
| ~ spl17_2
| ~ spl17_3
| ~ spl17_4
| ~ spl17_5 ),
inference(avatar_split_clause,[],[f168,f264,f260,f256,f252,f248]) ).
thf(f269,plain,
( spl17_3
| spl17_4 ),
inference(avatar_split_clause,[],[f166,f260,f256]) ).
thf(f287,definition,
( spl17_9
<=> ( $false = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl17_9])],[avatar_definition]) ).
thf(f289,plain,
( ( $false = sF1 )
| ~ spl17_9 ),
inference(avatar_component_clause,[],[f287]) ).
thf(f291,definition,
( spl17_10
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( $false
= ( sK0 @ X2 @ X1 ) )
| ( ( sK0 @ X3 @ X1 )
= $true )
| ( ( sK0 @ X2 @ X3 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl17_10])],[avatar_definition]) ).
thf(f292,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X1 ) )
| ( ( sK0 @ X2 @ X3 )
= $false )
| ( ( sK0 @ X3 @ X1 )
= $true ) )
| ~ spl17_10 ),
inference(avatar_component_clause,[],[f291]) ).
thf(f293,plain,
( spl17_9
| spl17_10 ),
inference(avatar_split_clause,[],[f190,f291,f287]) ).
thf(f295,definition,
( spl17_11
<=> ( $true
= ( sK0 @ sK10 @ sK11 ) ) ),
introduced(definition,[new_symbols(definition,[spl17_11])],[avatar_definition]) ).
thf(f297,plain,
( ( $true
= ( sK0 @ sK10 @ sK11 ) )
| ~ spl17_11 ),
inference(avatar_component_clause,[],[f295]) ).
thf(f298,plain,
( spl17_11
| spl17_2 ),
inference(avatar_split_clause,[],[f203,f252,f295]) ).
thf(f300,definition,
( spl17_12
<=> ( ( sK0 @ sK11 @ sK9 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl17_12])],[avatar_definition]) ).
thf(f302,plain,
( ( ( sK0 @ sK11 @ sK9 )
= $true )
| ~ spl17_12 ),
inference(avatar_component_clause,[],[f300]) ).
thf(f303,plain,
( spl17_2
| spl17_12 ),
inference(avatar_split_clause,[],[f202,f300,f252]) ).
thf(f305,definition,
( spl17_13
<=> ( ( sK0 @ sK10 @ sK9 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl17_13])],[avatar_definition]) ).
thf(f307,plain,
( ( ( sK0 @ sK10 @ sK9 )
= $false )
| ~ spl17_13 ),
inference(avatar_component_clause,[],[f305]) ).
thf(f308,plain,
( spl17_2
| spl17_13 ),
inference(avatar_split_clause,[],[f200,f305,f252]) ).
thf(f319,plain,
( spl17_1
| spl17_3 ),
inference(avatar_split_clause,[],[f164,f256,f248]) ).
thf(f320,plain,
spl17_5,
inference(avatar_split_clause,[],[f213,f264]) ).
thf(f322,definition,
( spl17_16
<=> ! [X2: $i,X1: $i] :
( ( ( sK0 @ X1 @ X2 )
= $true )
| ( $false
= ( sK0 @ X2 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl17_16])],[avatar_definition]) ).
thf(f323,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X1 ) )
| ( ( sK0 @ X1 @ X2 )
= $true ) )
| ~ spl17_16 ),
inference(avatar_component_clause,[],[f322]) ).
thf(f325,definition,
( spl17_17
<=> ( sF3 = $false ) ),
introduced(definition,[new_symbols(definition,[spl17_17])],[avatar_definition]) ).
thf(f327,plain,
( ( sF3 = $false )
| ~ spl17_17 ),
inference(avatar_component_clause,[],[f325]) ).
thf(f328,plain,
( spl17_16
| spl17_17 ),
inference(avatar_split_clause,[],[f221,f325,f322]) ).
thf(f330,definition,
( spl17_18
<=> ( ( sK0 @ sK13 @ sK12 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl17_18])],[avatar_definition]) ).
thf(f332,plain,
( ( ( sK0 @ sK13 @ sK12 )
= $true )
| ~ spl17_18 ),
inference(avatar_component_clause,[],[f330]) ).
thf(f333,plain,
( spl17_18
| spl17_1 ),
inference(avatar_split_clause,[],[f228,f248,f330]) ).
thf(f335,definition,
( spl17_19
<=> ( $false
= ( sK0 @ sK12 @ sK13 ) ) ),
introduced(definition,[new_symbols(definition,[spl17_19])],[avatar_definition]) ).
thf(f337,plain,
( ( $false
= ( sK0 @ sK12 @ sK13 ) )
| ~ spl17_19 ),
inference(avatar_component_clause,[],[f335]) ).
thf(f338,plain,
( spl17_19
| spl17_1 ),
inference(avatar_split_clause,[],[f227,f248,f335]) ).
thf(f340,definition,
( spl17_20
<=> ( $false
= ( sK0 @ sK14 @ sK14 ) ) ),
introduced(definition,[new_symbols(definition,[spl17_20])],[avatar_definition]) ).
thf(f342,plain,
( ( $false
= ( sK0 @ sK14 @ sK14 ) )
| ~ spl17_20 ),
inference(avatar_component_clause,[],[f340]) ).
thf(f343,plain,
( spl17_20
| spl17_3 ),
inference(avatar_split_clause,[],[f233,f256,f340]) ).
thf(f345,definition,
( spl17_21
<=> ( $false = sF2 ) ),
introduced(definition,[new_symbols(definition,[spl17_21])],[avatar_definition]) ).
thf(f347,plain,
( ( $false = sF2 )
| ~ spl17_21 ),
inference(avatar_component_clause,[],[f345]) ).
thf(f349,definition,
( spl17_22
<=> ! [X1: $i] :
( $true
= ( sK0 @ X1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl17_22])],[avatar_definition]) ).
thf(f350,plain,
( ! [X1: $i] :
( $true
= ( sK0 @ X1 @ X1 ) )
| ~ spl17_22 ),
inference(avatar_component_clause,[],[f349]) ).
thf(f351,plain,
( spl17_21
| spl17_22 ),
inference(avatar_split_clause,[],[f236,f349,f345]) ).
thf(f353,definition,
( spl17_23
<=> ! [X1: $i] :
( ( sK0 @ X1 @ ( sK15 @ X1 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl17_23])],[avatar_definition]) ).
thf(f354,plain,
( ! [X1: $i] :
( ( sK0 @ X1 @ ( sK15 @ X1 ) )
= $true )
| ~ spl17_23 ),
inference(avatar_component_clause,[],[f353]) ).
thf(f356,definition,
( spl17_24
<=> ( $false = sF5 ) ),
introduced(definition,[new_symbols(definition,[spl17_24])],[avatar_definition]) ).
thf(f358,plain,
( ( $false = sF5 )
| ~ spl17_24 ),
inference(avatar_component_clause,[],[f356]) ).
thf(f359,plain,
( spl17_23
| spl17_24 ),
inference(avatar_split_clause,[],[f242,f356,f353]) ).
thf(f361,definition,
( spl17_25
<=> ! [X1: $i] :
( $false
= ( sK0 @ sK16 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl17_25])],[avatar_definition]) ).
thf(f362,plain,
( ! [X1: $i] :
( $false
= ( sK0 @ sK16 @ X1 ) )
| ~ spl17_25 ),
inference(avatar_component_clause,[],[f361]) ).
thf(f363,plain,
( spl17_25
| spl17_4 ),
inference(avatar_split_clause,[],[f246,f260,f361]) ).
thf(f365,plain,
( ( $false = $true )
| ~ spl17_5
| ~ spl17_9 ),
inference(forward_demodulation,[],[f289,f265]) ).
thf(f366,plain,
( $false
| ~ spl17_5
| ~ spl17_9 ),
inference(trivial_inequality_removal,[],[f365]) ).
thf(f367,plain,
( ~ spl17_5
| ~ spl17_9 ),
inference(avatar_contradiction_clause,[],[f366]) ).
thf(f390,plain,
( ( $false = $true )
| ~ spl17_3
| ~ spl17_21 ),
inference(forward_demodulation,[],[f347,f257]) ).
thf(f391,plain,
( $false
| ~ spl17_3
| ~ spl17_21 ),
inference(trivial_inequality_removal,[],[f390]) ).
thf(f392,plain,
( ~ spl17_3
| ~ spl17_21 ),
inference(avatar_contradiction_clause,[],[f391]) ).
thf(f407,plain,
( ( $false = $true )
| ( ( sK0 @ sK12 @ sK13 )
= $true )
| ~ spl17_16
| ~ spl17_18 ),
inference(constrained_superposition,[],[f332,f323]) ).
thf(f417,plain,
( ( ( sK0 @ sK12 @ sK13 )
= $true )
| ~ spl17_16
| ~ spl17_18 ),
inference(trivial_inequality_removal,[],[f407]) ).
thf(f422,plain,
( ( $false = $true )
| ~ spl17_16
| ~ spl17_18
| ~ spl17_19 ),
inference(forward_demodulation,[],[f417,f337]) ).
thf(f423,plain,
( $false
| ~ spl17_16
| ~ spl17_18
| ~ spl17_19 ),
inference(trivial_inequality_removal,[],[f422]) ).
thf(f424,plain,
( ~ spl17_16
| ~ spl17_18
| ~ spl17_19 ),
inference(avatar_contradiction_clause,[],[f423]) ).
thf(f428,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 @ sK9 )
= $true )
| ( $false
= ( sK0 @ sK11 @ X0 ) )
| ( $false = $true ) )
| ~ spl17_10
| ~ spl17_12 ),
inference(constrained_superposition,[],[f292,f302]) ).
thf(f431,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK0 @ X0 @ X1 )
= $false )
| ( $true
= ( sK0 @ X1 @ X0 ) )
| ( $false = $true ) )
| ~ spl17_10
| ~ spl17_22 ),
inference(constrained_superposition,[],[f350,f292]) ).
thf(f436,plain,
( ! [X0: $i,X1: $i] :
( ( $false != $false )
| ( $true
= ( sK0 @ X1 @ X1 ) )
| ( ( sK0 @ X0 @ X1 )
= $false ) )
| ~ spl17_10 ),
inference(equality_factoring,[],[f292]) ).
thf(f438,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ sK11 @ X0 ) )
| ( ( sK0 @ X0 @ sK9 )
= $true ) )
| ~ spl17_10
| ~ spl17_12 ),
inference(trivial_inequality_removal,[],[f428]) ).
thf(f442,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK0 @ X0 @ X1 )
= $false )
| ( $true
= ( sK0 @ X1 @ X0 ) ) )
| ~ spl17_10
| ~ spl17_22 ),
inference(trivial_inequality_removal,[],[f431]) ).
thf(f448,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( sK0 @ X1 @ X1 ) )
| ( ( sK0 @ X0 @ X1 )
= $false ) )
| ~ spl17_10 ),
inference(trivial_inequality_removal,[],[f436]) ).
thf(f450,plain,
( spl17_16
| ~ spl17_10
| ~ spl17_22 ),
inference(avatar_split_clause,[],[f442,f349,f291,f322]) ).
thf(f451,plain,
( ( $false = $true )
| ~ spl17_1
| ~ spl17_17 ),
inference(forward_demodulation,[],[f249,f327]) ).
thf(f452,plain,
( $false
| ~ spl17_1
| ~ spl17_17 ),
inference(trivial_inequality_removal,[],[f451]) ).
thf(f453,plain,
( ~ spl17_1
| ~ spl17_17 ),
inference(avatar_contradiction_clause,[],[f452]) ).
thf(f459,plain,
( ( $false = $true )
| ( $true
= ( sK0 @ sK11 @ sK10 ) )
| ~ spl17_11
| ~ spl17_16 ),
inference(constrained_superposition,[],[f323,f297]) ).
thf(f464,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ ( sK15 @ X0 ) @ X0 ) )
| ( $false = $true ) )
| ~ spl17_16
| ~ spl17_23 ),
inference(constrained_superposition,[],[f354,f323]) ).
thf(f470,plain,
( ! [X0: $i] :
( $true
= ( sK0 @ ( sK15 @ X0 ) @ X0 ) )
| ~ spl17_16
| ~ spl17_23 ),
inference(trivial_inequality_removal,[],[f464]) ).
thf(f474,plain,
( ( $true
= ( sK0 @ sK11 @ sK10 ) )
| ~ spl17_11
| ~ spl17_16 ),
inference(trivial_inequality_removal,[],[f459]) ).
thf(f571,plain,
( ( $false = $true )
| ( ( sK0 @ sK10 @ sK9 )
= $true )
| ~ spl17_10
| ~ spl17_11
| ~ spl17_12
| ~ spl17_16 ),
inference(constrained_superposition,[],[f438,f474]) ).
thf(f590,plain,
( ( ( sK0 @ sK10 @ sK9 )
= $true )
| ~ spl17_10
| ~ spl17_11
| ~ spl17_12
| ~ spl17_16 ),
inference(trivial_inequality_removal,[],[f571]) ).
thf(f608,plain,
( ( $false = $true )
| ~ spl17_10
| ~ spl17_11
| ~ spl17_12
| ~ spl17_13
| ~ spl17_16 ),
inference(forward_demodulation,[],[f590,f307]) ).
thf(f609,plain,
( $false
| ~ spl17_10
| ~ spl17_11
| ~ spl17_12
| ~ spl17_13
| ~ spl17_16 ),
inference(trivial_inequality_removal,[],[f608]) ).
thf(f610,plain,
( ~ spl17_10
| ~ spl17_11
| ~ spl17_12
| ~ spl17_13
| ~ spl17_16 ),
inference(avatar_contradiction_clause,[],[f609]) ).
thf(f619,plain,
( ( $false = $true )
| ~ spl17_22
| ~ spl17_25 ),
inference(constrained_superposition,[],[f362,f350]) ).
thf(f628,plain,
( $false
| ~ spl17_22
| ~ spl17_25 ),
inference(trivial_inequality_removal,[],[f619]) ).
thf(f629,plain,
( ~ spl17_22
| ~ spl17_25 ),
inference(avatar_contradiction_clause,[],[f628]) ).
thf(f641,plain,
( ( $false = $true )
| ~ spl17_4
| ~ spl17_24 ),
inference(forward_demodulation,[],[f261,f358]) ).
thf(f642,plain,
( $false
| ~ spl17_4
| ~ spl17_24 ),
inference(trivial_inequality_removal,[],[f641]) ).
thf(f643,plain,
( ~ spl17_4
| ~ spl17_24 ),
inference(avatar_contradiction_clause,[],[f642]) ).
thf(f706,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( ( sK0 @ X0 @ sK14 )
= $false ) )
| ~ spl17_10
| ~ spl17_20 ),
inference(constrained_superposition,[],[f342,f448]) ).
thf(f711,plain,
( ! [X0: $i] :
( ( sK0 @ X0 @ sK14 )
= $false )
| ~ spl17_10
| ~ spl17_20 ),
inference(trivial_inequality_removal,[],[f706]) ).
thf(f721,plain,
( ( $false = $true )
| ~ spl17_10
| ~ spl17_16
| ~ spl17_20
| ~ spl17_23 ),
inference(constrained_superposition,[],[f470,f711]) ).
thf(f729,plain,
( $false
| ~ spl17_10
| ~ spl17_16
| ~ spl17_20
| ~ spl17_23 ),
inference(trivial_inequality_removal,[],[f721]) ).
thf(f730,plain,
( ~ spl17_10
| ~ spl17_16
| ~ spl17_20
| ~ spl17_23 ),
inference(avatar_contradiction_clause,[],[f729]) ).
cnf(s1,plain,
( ~ spl17_1
| ~ spl17_2
| ~ spl17_3
| ~ spl17_4
| ~ spl17_5 ),
inference(sat_conversion,[],[f267]) ).
cnf(s3,plain,
( spl17_3
| spl17_4 ),
inference(sat_conversion,[],[f269]) ).
cnf(s8,plain,
( spl17_9
| spl17_10 ),
inference(sat_conversion,[],[f293]) ).
cnf(s9,plain,
( spl17_2
| spl17_11 ),
inference(sat_conversion,[],[f298]) ).
cnf(s10,plain,
( spl17_2
| spl17_12 ),
inference(sat_conversion,[],[f303]) ).
cnf(s11,plain,
( spl17_2
| spl17_13 ),
inference(sat_conversion,[],[f308]) ).
cnf(s15,plain,
( spl17_1
| spl17_3 ),
inference(sat_conversion,[],[f319]) ).
cnf(s16,plain,
spl17_5,
inference(sat_conversion,[],[f320]) ).
cnf(s17,plain,
( spl17_16
| spl17_17 ),
inference(sat_conversion,[],[f328]) ).
cnf(s18,plain,
( spl17_1
| spl17_18 ),
inference(sat_conversion,[],[f333]) ).
cnf(s19,plain,
( spl17_1
| spl17_19 ),
inference(sat_conversion,[],[f338]) ).
cnf(s20,plain,
( spl17_3
| spl17_20 ),
inference(sat_conversion,[],[f343]) ).
cnf(s21,plain,
( spl17_21
| spl17_22 ),
inference(sat_conversion,[],[f351]) ).
cnf(s22,plain,
( spl17_23
| spl17_24 ),
inference(sat_conversion,[],[f359]) ).
cnf(s23,plain,
( spl17_4
| spl17_25 ),
inference(sat_conversion,[],[f363]) ).
cnf(s25,plain,
( ~ spl17_5
| ~ spl17_9 ),
inference(sat_conversion,[],[f367]) ).
cnf(s28,plain,
( ~ spl17_3
| ~ spl17_21 ),
inference(sat_conversion,[],[f392]) ).
cnf(s30,plain,
( ~ spl17_16
| ~ spl17_18
| ~ spl17_19 ),
inference(sat_conversion,[],[f424]) ).
cnf(s31,plain,
( ~ spl17_10
| spl17_16
| ~ spl17_22 ),
inference(sat_conversion,[],[f450]) ).
cnf(s33,plain,
( ~ spl17_1
| ~ spl17_17 ),
inference(sat_conversion,[],[f453]) ).
cnf(s36,plain,
( ~ spl17_10
| ~ spl17_11
| ~ spl17_12
| ~ spl17_13
| ~ spl17_16 ),
inference(sat_conversion,[],[f610]) ).
cnf(s39,plain,
( ~ spl17_22
| ~ spl17_25 ),
inference(sat_conversion,[],[f629]) ).
cnf(s43,plain,
( ~ spl17_4
| ~ spl17_24 ),
inference(sat_conversion,[],[f643]) ).
cnf(s47,plain,
( ~ spl17_10
| ~ spl17_16
| ~ spl17_20
| ~ spl17_23 ),
inference(sat_conversion,[],[f730]) ).
cnf(s48,plain,
~ spl17_9,
inference(rat,[],[s25,s16]) ).
cnf(s49,plain,
spl17_10,
inference(rat,[],[s8,s48]) ).
cnf(s50,plain,
( ~ spl17_1
| ~ spl17_2
| ~ spl17_3
| ~ spl17_4 ),
inference(rat,[],[s1,s16]) ).
cnf(s51,plain,
spl17_1,
inference(rat,[],[s21,s31,s28,s30,s15,s18,s19,s49]) ).
cnf(s52,plain,
~ spl17_17,
inference(rat,[],[s33,s51]) ).
cnf(s53,plain,
spl17_16,
inference(rat,[],[s17,s52]) ).
cnf(s54,plain,
spl17_2,
inference(rat,[],[s36,s9,s10,s11,s49,s53]) ).
cnf(s57,plain,
~ spl17_3,
inference(rat,[],[s39,s23,s21,s50,s28,s51,s54]) ).
cnf(s59,plain,
spl17_20,
inference(rat,[],[s20,s57]) ).
cnf(s60,plain,
spl17_4,
inference(rat,[],[s3,s57]) ).
cnf(s62,plain,
~ spl17_23,
inference(rat,[],[s47,s53,s49,s59]) ).
cnf(s63,plain,
~ spl17_24,
inference(rat,[],[s43,s60]) ).
cnf(s64,plain,
$false,
inference(rat,[],[s22,s63,s62]) ).
thf(f731,plain,
$false,
inference(avatar_sat_refutation,[],[s64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL864^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 % Computer : n003.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 10:16:47 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.25 Running higher-order theorem proving
% 0.20/0.27 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
% 0.20/0.33 % (2327324)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.33 % (2327333)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2697940059:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.33 % (2327335)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.33 % (2327335)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
% 0.20/0.33 % (2327329)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=214949187:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.33 % (2327330)lrs+10_16_si=on:nwc=1.5:random_seed=4158570817:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.33 % (2327331)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3293359260:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.33 % (2327334)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2358806742:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.33 % (2327333)Instruction limit reached!
% 0.20/0.33 % (2327333)------------------------------
% 0.20/0.33 % (2327333)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (2327333)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (2327333)CaDiCaL version: 2.1.3
% 0.20/0.33 % (2327333)Termination reason: Instruction limit
% 0.20/0.33 % (2327333)Termination phase: Saturation
% 0.20/0.33 % (2327333)Time elapsed: 0.008 s
% 0.20/0.33 % (2327333)Peak memory usage: 12 MB
% 0.20/0.33 % (2327333)Instructions burned: 26 (million)
% 0.20/0.33 % (2327332)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=2970397684: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)
% 0.20/0.33 % (2327335)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=3519043643:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.33 % (2327331)Instruction limit reached!
% 0.20/0.33 % (2327331)------------------------------
% 0.20/0.33 % (2327331)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (2327331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (2327331)CaDiCaL version: 2.1.3
% 0.20/0.33 % (2327331)Termination reason: Instruction limit
% 0.20/0.33 % (2327331)Termination phase: Property scanning
% 0.20/0.33 % (2327331)Time elapsed: 0.003 s
% 0.20/0.33 % (2327331)Peak memory usage: 10 MB
% 0.20/0.33 % (2327331)Instructions burned: 7 (million)
% 0.20/0.33 % (2327330)Instruction limit reached!
% 0.20/0.33 % (2327330)------------------------------
% 0.20/0.33 % (2327330)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (2327330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (2327330)CaDiCaL version: 2.1.3
% 0.20/0.33 % (2327330)Termination reason: Instruction limit
% 0.20/0.33 % (2327330)Termination phase: Saturation
% 0.20/0.33 % (2327330)Time elapsed: 0.010 s
% 0.20/0.33 % (2327330)Peak memory usage: 12 MB
% 0.20/0.33 % (2327330)Instructions burned: 19 (million)
% 0.20/0.33 % (2327343)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4887161:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.33 % (2327343)Instruction limit reached!
% 0.20/0.33 % (2327343)------------------------------
% 0.20/0.33 % (2327343)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (2327343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (2327343)CaDiCaL version: 2.1.3
% 0.20/0.33 % (2327343)Termination reason: Instruction limit
% 0.20/0.33 % (2327343)Termination phase: shuffling
% 0.20/0.33 % (2327343)Time elapsed: 0.0000 s
% 0.20/0.33 % (2327343)Peak memory usage: 9 MB
% 0.20/0.33 % (2327343)Instructions burned: 2 (million)
% 0.20/0.33 % (2327335) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2327324-2327335"...
% 0.20/0.33 % (2327347)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3162170492:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/0.33 % (2327344)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=886433839:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.33 % (2327329) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2327324-2327329"...
% 0.20/0.33 % (2327335)...printing done.
% 0.20/0.33 % (2327335)Refutation found. Thanks to Tanya!
% 0.20/0.33 % SZS status Theorem for theBenchmark
% 0.20/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.34 % (2327335)------------------------------
% 0.20/0.34 % (2327335)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (2327335)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (2327335)CaDiCaL version: 2.1.3
% 0.20/0.34 % (2327335)Termination reason: Refutation
% 0.20/0.34 % (2327335)Time elapsed: 0.021 s
% 0.20/0.34 % (2327335)Peak memory usage: 13 MB
% 0.20/0.34 % (2327335)Instructions burned: 37 (million)
% 0.20/0.34 % (2327324)Success in time 0.055 s
% 0.20/0.34 % Vampire exiting
%------------------------------------------------------------------------------