%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL859^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 0.22s 0.32s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 16
% Syntax : Number of formulae : 115 ( 32 unt; 0 typ; 12 def)
% Number of atoms : 733 ( 168 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 813 ( 96 ~; 124 |; 46 &; 443 @)
% ( 13 <=>; 30 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 72 ( 72 >; 0 *; 0 +; 0 <<)
% Number of symbols : 64 ( 60 usr; 17 con; 0-4 aty)
% ( 60 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 144 ( 0 sgn 46 !; 3 ?; 144 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_35,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_36,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_37,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
vIMP: $o > $o > $o ).
thf(func_def_39,type,
vAND: $o > $o > $o ).
thf(func_def_40,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vOR: $o > $o > $o ).
thf(func_def_42,type,
vNOT: $o > $o ).
thf(func_def_43,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,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(f18,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f22,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X3: $i,X2: $i,X1: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X2 @ X3 ) ) )
= meuclidean ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',meuclidean) ).
thf(f32,conjecture,
! [X0: $i > $i > $o] :
( ( ( mreflexive @ X0 )
& ( meuclidean @ X0 )
& ( msymmetric @ X0 ) )
<=> ( ( meuclidean @ X0 )
& ( mreflexive @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( ( mreflexive @ X0 )
& ( meuclidean @ X0 )
& ( msymmetric @ X0 ) )
<=> ( ( meuclidean @ X0 )
& ( mreflexive @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f40,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
inference(rectify,[],[f18]) ).
thf(f41,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f45,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) )
= msymmetric ),
inference(rectify,[],[f19]) ).
thf(f46,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f45]) ).
thf(f52,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X1 )
& ( X0 @ X3 @ X2 ) )
=> ( X0 @ X2 @ X1 ) ) )
= meuclidean ),
inference(rectify,[],[f22]) ).
thf(f53,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f52]) ).
thf(f81,plain,
~ ! [X0: $i > $i > $o] :
( ( ( mreflexive @ X0 )
& ( meuclidean @ X0 )
& ( msymmetric @ X0 ) )
<=> ( ( meuclidean @ X0 )
& ( mreflexive @ X0 ) ) ),
inference(rectify,[],[f33]) ).
thf(f82,plain,
~ ! [X0: $i > $i > $o] :
( ( ( ( meuclidean @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) )
<=> ( ( ( meuclidean @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( ( ( meuclidean @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) )
<~> ( ( ( meuclidean @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) ) ),
inference(ennf_transformation,[],[f82]) ).
thf(f88,plain,
? [X0: $i > $i > $o] :
( ( ( ( meuclidean @ X0 )
!= $true )
| ( ( msymmetric @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true ) )
& ( ( ( ( meuclidean @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) )
| ( ( ( meuclidean @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f87]) ).
thf(f89,plain,
? [X0: $i > $i > $o] :
( ( ( ( meuclidean @ X0 )
!= $true )
| ( ( msymmetric @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true ) )
& ( ( ( ( meuclidean @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) )
| ( ( ( meuclidean @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) ) ) ),
inference(flattening,[],[f88]) ).
thf(f90,plain,
( ( ( ( meuclidean @ sK0 )
!= $true )
| ( ( msymmetric @ sK0 )
!= $true )
| ( ( mreflexive @ sK0 )
!= $true )
| ( ( meuclidean @ sK0 )
!= $true )
| ( ( mreflexive @ sK0 )
!= $true ) )
& ( ( ( ( meuclidean @ sK0 )
= $true )
& ( ( msymmetric @ sK0 )
= $true )
& ( ( mreflexive @ sK0 )
= $true ) )
| ( ( ( meuclidean @ sK0 )
= $true )
& ( ( mreflexive @ sK0 )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f89]) ).
thf(f100,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f104,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f112,plain,
( ( ( mreflexive @ sK0 )
= $true )
| ( ( mreflexive @ sK0 )
= $true ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f117,plain,
( ( ( meuclidean @ sK0 )
= $true )
| ( ( meuclidean @ sK0 )
= $true ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f118,plain,
( ( ( meuclidean @ sK0 )
!= $true )
| ( ( msymmetric @ sK0 )
!= $true )
| ( ( mreflexive @ sK0 )
!= $true )
| ( ( meuclidean @ sK0 )
!= $true )
| ( ( mreflexive @ sK0 )
!= $true ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f128,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f140,plain,
( ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
@ 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] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
@ sK0 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f118,f104,f100,f128,f104,f128]) ).
thf(f141,plain,
( ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
@ sK0 ) )
| ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f117,f104,f104]) ).
thf(f146,plain,
( ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) )
| ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f112,f128,f128]) ).
thf(f147,definition,
( sF1
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
@ 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 @ Y1 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
@ sK0 )
= sF1 ),
inference(reorient_equations,[],[f147]) ).
thf(f149,definition,
( sF2
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ 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,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 )
= sF3 ),
inference(reorient_equations,[],[f150]) ).
thf(f152,plain,
( ( $true != sF3 )
| ( $true != sF3 )
| ( $true != sF1 )
| ( sF2 != $true )
| ( $true != sF1 ) ),
inference(definition_folding,[],[f140,f151,f148,f151,f149,f148]) ).
thf(f153,plain,
( ( $true = sF1 )
| ( $true = sF1 ) ),
inference(definition_folding,[],[f141,f148,f148]) ).
thf(f158,plain,
( ( $true = sF3 )
| ( $true = sF3 ) ),
inference(definition_folding,[],[f146,f151,f151]) ).
thf(f159,plain,
( ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
@ sK0 ) )
| ( $false = sF1 ) ),
inference(iff_proxy_clausification,[],[f148]) ).
thf(f172,plain,
( ( $false = sF1 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f173,plain,
! [X1: $i] :
( ( $false = sF1 )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y1 @ Y2 ) ) ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X1: $i] :
( ( $false = sF1 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ X1 @ Y0 )
& ( sK0 @ X1 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f175,plain,
! [X2: $i,X1: $i] :
( ( $false = sF1 )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ X1 @ Y0 )
& ( sK0 @ X1 @ Y1 ) )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X2: $i,X1: $i] :
( ( $false = sF1 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ X1 @ X2 )
& ( sK0 @ X1 @ Y0 ) )
=> ( sK0 @ X2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f177,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( ( sK0 @ X1 @ X2 )
& ( sK0 @ X1 @ Y0 ) )
=> ( sK0 @ X2 @ Y0 ) )
@ X3 )
= $true )
| ( $false = sF1 ) ),
inference(pi_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( ( sK0 @ X1 @ X2 )
& ( sK0 @ X1 @ X3 ) )
=> ( sK0 @ X2 @ X3 ) ) )
| ( $false = sF1 ) ),
inference(beta-eta_normalization,[],[f177]) ).
thf(f179,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false = sF1 )
| ( ( ( sK0 @ X1 @ X2 )
& ( sK0 @ X1 @ X3 ) )
= $false )
| ( $true
= ( sK0 @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( sK0 @ X1 @ X2 )
= $false )
| ( $false = sF1 )
| ( $false
= ( sK0 @ X1 @ X3 ) )
| ( $true
= ( sK0 @ X2 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( $false
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ sK0 ) )
| ( sF2 = $true ) ),
inference(iff_proxy_clausification,[],[f149]) ).
thf(f189,plain,
( ( sF2 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f190,plain,
( ( sF2 = $true )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK7 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f189]) ).
thf(f191,plain,
( ( sF2 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK7 )
=> ( sK0 @ sK7 @ Y0 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f190]) ).
thf(f192,plain,
( ( ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK7 )
=> ( sK0 @ sK7 @ Y0 ) )
@ sK8 )
= $false )
| ( sF2 = $true ) ),
inference(sigma_proxy_clausification,[],[f191]) ).
thf(f193,plain,
( ( sF2 = $true )
| ( ( ( sK0 @ sK8 @ sK7 )
=> ( sK0 @ sK7 @ sK8 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f192]) ).
thf(f194,plain,
( ( ( sK0 @ sK7 @ sK8 )
= $false )
| ( sF2 = $true ) ),
inference(imp_proxy_clausification,[],[f193]) ).
thf(f195,plain,
( ( sF2 = $true )
| ( ( sK0 @ sK8 @ sK7 )
= $true ) ),
inference(imp_proxy_clausification,[],[f193]) ).
thf(f196,plain,
( ( $true != sF3 )
| ( $true != sF1 )
| ( sF2 != $true ) ),
inference(duplicate_literal_removal,[],[f152]) ).
thf(f197,plain,
$true = sF1,
inference(duplicate_literal_removal,[],[f153]) ).
thf(f198,plain,
( ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) )
| ( $false = sF3 ) ),
inference(iff_proxy_clausification,[],[f151]) ).
thf(f203,plain,
( ( $false = sF3 )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f198]) ).
thf(f204,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ X1 ) )
| ( $false = sF3 ) ),
inference(pi_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X1: $i] :
( ( $false = sF3 )
| ( $true
= ( sK0 @ X1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f204]) ).
thf(f206,plain,
$true = sF3,
inference(duplicate_literal_removal,[],[f158]) ).
thf(f208,definition,
( spl10_1
<=> ( sF2 = $true ) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
thf(f212,definition,
( spl10_2
<=> ( $true = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
thf(f214,plain,
( ( $true = sF1 )
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f212]) ).
thf(f232,definition,
( spl10_6
<=> ( $false = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition]) ).
thf(f234,plain,
( ( $false = sF1 )
| ~ spl10_6 ),
inference(avatar_component_clause,[],[f232]) ).
thf(f236,definition,
( spl10_7
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( ( sK0 @ X1 @ X2 )
= $false )
| ( $true
= ( sK0 @ X2 @ X3 ) )
| ( $false
= ( sK0 @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_7])],[avatar_definition]) ).
thf(f237,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( sK0 @ X2 @ X3 ) )
| ( ( sK0 @ X1 @ X2 )
= $false )
| ( $false
= ( sK0 @ X1 @ X3 ) ) )
| ~ spl10_7 ),
inference(avatar_component_clause,[],[f236]) ).
thf(f238,plain,
( spl10_6
| spl10_7 ),
inference(avatar_split_clause,[],[f180,f236,f232]) ).
thf(f248,definition,
( spl10_10
<=> ( ( sK0 @ sK8 @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl10_10])],[avatar_definition]) ).
thf(f250,plain,
( ( ( sK0 @ sK8 @ sK7 )
= $true )
| ~ spl10_10 ),
inference(avatar_component_clause,[],[f248]) ).
thf(f251,plain,
( spl10_10
| spl10_1 ),
inference(avatar_split_clause,[],[f195,f208,f248]) ).
thf(f253,definition,
( spl10_11
<=> ( ( sK0 @ sK7 @ sK8 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl10_11])],[avatar_definition]) ).
thf(f255,plain,
( ( ( sK0 @ sK7 @ sK8 )
= $false )
| ~ spl10_11 ),
inference(avatar_component_clause,[],[f253]) ).
thf(f256,plain,
( spl10_11
| spl10_1 ),
inference(avatar_split_clause,[],[f194,f208,f253]) ).
thf(f258,definition,
( spl10_12
<=> ( $true = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl10_12])],[avatar_definition]) ).
thf(f259,plain,
( ( $true = sF3 )
| ~ spl10_12 ),
inference(avatar_component_clause,[],[f258]) ).
thf(f261,plain,
( ~ spl10_12
| ~ spl10_2
| ~ spl10_1 ),
inference(avatar_split_clause,[],[f196,f208,f212,f258]) ).
thf(f262,plain,
spl10_2,
inference(avatar_split_clause,[],[f197,f212]) ).
thf(f269,definition,
( spl10_14
<=> ! [X1: $i] :
( $true
= ( sK0 @ X1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_14])],[avatar_definition]) ).
thf(f270,plain,
( ! [X1: $i] :
( $true
= ( sK0 @ X1 @ X1 ) )
| ~ spl10_14 ),
inference(avatar_component_clause,[],[f269]) ).
thf(f272,definition,
( spl10_15
<=> ( $false = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl10_15])],[avatar_definition]) ).
thf(f274,plain,
( ( $false = sF3 )
| ~ spl10_15 ),
inference(avatar_component_clause,[],[f272]) ).
thf(f275,plain,
( spl10_14
| spl10_15 ),
inference(avatar_split_clause,[],[f205,f272,f269]) ).
thf(f278,plain,
spl10_12,
inference(avatar_split_clause,[],[f206,f258]) ).
thf(f280,plain,
( ( $true = $false )
| ~ spl10_2
| ~ spl10_6 ),
inference(forward_demodulation,[],[f234,f214]) ).
thf(f281,plain,
( $false
| ~ spl10_2
| ~ spl10_6 ),
inference(trivial_inequality_removal,[],[f280]) ).
thf(f282,plain,
( ~ spl10_2
| ~ spl10_6 ),
inference(avatar_contradiction_clause,[],[f281]) ).
thf(f314,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK7 ) )
| ( ( sK0 @ X0 @ sK8 )
= $false ) )
| ~ spl10_7
| ~ spl10_11 ),
inference(constrained_superposition,[],[f237,f255]) ).
thf(f318,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK7 ) )
| ( ( sK0 @ X0 @ sK8 )
= $false ) )
| ~ spl10_7
| ~ spl10_11 ),
inference(trivial_inequality_removal,[],[f314]) ).
thf(f327,plain,
( ( $false
= ( sK0 @ sK8 @ sK8 ) )
| ( $true = $false )
| ~ spl10_7
| ~ spl10_10
| ~ spl10_11 ),
inference(constrained_superposition,[],[f250,f318]) ).
thf(f334,plain,
( ( $false
= ( sK0 @ sK8 @ sK8 ) )
| ~ spl10_7
| ~ spl10_10
| ~ spl10_11 ),
inference(trivial_inequality_removal,[],[f327]) ).
thf(f338,plain,
( ( $true = $false )
| ~ spl10_7
| ~ spl10_10
| ~ spl10_11
| ~ spl10_14 ),
inference(forward_demodulation,[],[f334,f270]) ).
thf(f339,plain,
( $false
| ~ spl10_7
| ~ spl10_10
| ~ spl10_11
| ~ spl10_14 ),
inference(trivial_inequality_removal,[],[f338]) ).
thf(f340,plain,
( ~ spl10_7
| ~ spl10_10
| ~ spl10_11
| ~ spl10_14 ),
inference(avatar_contradiction_clause,[],[f339]) ).
thf(f341,plain,
( ( $true = $false )
| ~ spl10_12
| ~ spl10_15 ),
inference(forward_demodulation,[],[f274,f259]) ).
thf(f342,plain,
( $false
| ~ spl10_12
| ~ spl10_15 ),
inference(trivial_inequality_removal,[],[f341]) ).
thf(f343,plain,
( ~ spl10_12
| ~ spl10_15 ),
inference(avatar_contradiction_clause,[],[f342]) ).
cnf(s5,plain,
( spl10_6
| spl10_7 ),
inference(sat_conversion,[],[f238]) ).
cnf(s7,plain,
( spl10_1
| spl10_10 ),
inference(sat_conversion,[],[f251]) ).
cnf(s8,plain,
( spl10_1
| spl10_11 ),
inference(sat_conversion,[],[f256]) ).
cnf(s9,plain,
( ~ spl10_1
| ~ spl10_2
| ~ spl10_12 ),
inference(sat_conversion,[],[f261]) ).
cnf(s10,plain,
spl10_2,
inference(sat_conversion,[],[f262]) ).
cnf(s12,plain,
( spl10_14
| spl10_15 ),
inference(sat_conversion,[],[f275]) ).
cnf(s15,plain,
spl10_12,
inference(sat_conversion,[],[f278]) ).
cnf(s17,plain,
( ~ spl10_2
| ~ spl10_6 ),
inference(sat_conversion,[],[f282]) ).
cnf(s22,plain,
( ~ spl10_7
| ~ spl10_10
| ~ spl10_11
| ~ spl10_14 ),
inference(sat_conversion,[],[f340]) ).
cnf(s23,plain,
( ~ spl10_12
| ~ spl10_15 ),
inference(sat_conversion,[],[f343]) ).
cnf(s24,plain,
~ spl10_15,
inference(rat,[],[s23,s15]) ).
cnf(s25,plain,
spl10_14,
inference(rat,[],[s12,s24]) ).
cnf(s26,plain,
~ spl10_6,
inference(rat,[],[s17,s10]) ).
cnf(s27,plain,
~ spl10_1,
inference(rat,[],[s9,s15,s10]) ).
cnf(s29,plain,
spl10_11,
inference(rat,[],[s8,s27]) ).
cnf(s30,plain,
spl10_10,
inference(rat,[],[s7,s27]) ).
cnf(s31,plain,
~ spl10_7,
inference(rat,[],[s22,s25,s29,s30]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s5,s31,s26]) ).
thf(f344,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL859^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 % Computer : n001.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Tue Sep 29 10:17:52 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.32 % (1053257)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.32 % (1053264)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1803420158:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.32 % (1053264)Instruction limit reached!
% 0.22/0.32 % (1053264)------------------------------
% 0.22/0.32 % (1053264)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (1053264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (1053264)CaDiCaL version: 2.1.3
% 0.22/0.32 % (1053264)Termination reason: Instruction limit
% 0.22/0.32 % (1053264)Termination phase: Property scanning
% 0.22/0.32 % (1053264)Time elapsed: 0.001 s
% 0.22/0.32 % (1053264)Peak memory usage: 10 MB
% 0.22/0.32 % (1053264)Instructions burned: 3 (million)
% 0.22/0.32 % (1053263)lrs+10_16_si=on:nwc=1.5:random_seed=1063949746:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.32 % (1053266)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1473077792:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.32 % (1053265)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=3031717616: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)
% 0.22/0.32 % (1053270)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=712326290:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.32 % (1053268)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.32 % (1053268)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
% 0.22/0.32 % (1053262)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3760532985:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.32 % (1053270)Instruction limit reached!
% 0.22/0.32 % (1053270)------------------------------
% 0.22/0.32 % (1053270)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (1053270)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (1053270)CaDiCaL version: 2.1.3
% 0.22/0.32 % (1053270)Termination reason: Instruction limit
% 0.22/0.32 % (1053270)Termination phase: Property scanning
% 0.22/0.32 % (1053270)Time elapsed: 0.001 s
% 0.22/0.32 % (1053270)Peak memory usage: 10 MB
% 0.22/0.32 % (1053270)Instructions burned: 3 (million)
% 0.22/0.32 % (1053268)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=3814142484:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.32 % (1053263)Instruction limit reached!
% 0.22/0.32 % (1053263)------------------------------
% 0.22/0.32 % (1053263)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (1053263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (1053263)CaDiCaL version: 2.1.3
% 0.22/0.32 % (1053263)Termination reason: Instruction limit
% 0.22/0.32 % (1053263)Termination phase: Saturation
% 0.22/0.32 % (1053263)Time elapsed: 0.011 s
% 0.22/0.32 % (1053263)Peak memory usage: 12 MB
% 0.22/0.32 % (1053263)Instructions burned: 20 (million)
% 0.22/0.32 % (1053267)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=718831234:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.32 % (1053266)Instruction limit reached!
% 0.22/0.32 % (1053266)------------------------------
% 0.22/0.32 % (1053266)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (1053266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (1053266)CaDiCaL version: 2.1.3
% 0.22/0.32 % (1053266)Termination reason: Instruction limit
% 0.22/0.32 % (1053266)Termination phase: Saturation
% 0.22/0.32 % (1053266)Time elapsed: 0.014 s
% 0.22/0.32 % (1053266)Peak memory usage: 11 MB
% 0.22/0.32 % (1053266)Instructions burned: 25 (million)
% 0.22/0.32 % (1053276)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2341559318:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.32 % (1053268) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1053257-1053268"...
% 0.22/0.32 % (1053262) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1053257-1053262"...
% 0.22/0.32 % (1053276)Instruction limit reached!
% 0.22/0.32 % (1053276)------------------------------
% 0.22/0.32 % (1053276)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (1053276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (1053276)CaDiCaL version: 2.1.3
% 0.22/0.32 % (1053276)Termination reason: Instruction limit
% 0.22/0.32 % (1053276)Termination phase: Saturation
% 0.22/0.32 % (1053276)Time elapsed: 0.002 s
% 0.22/0.32 % (1053276)Peak memory usage: 12 MB
% 0.22/0.32 % (1053276)Instructions burned: 8 (million)
% 0.22/0.32 % (1053268)...printing done.
% 0.22/0.32 % (1053268)Refutation found. Thanks to Tanya!
% 0.22/0.32 % SZS status Theorem for theBenchmark
% 0.22/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.32 % (1053268)------------------------------
% 0.22/0.32 % (1053268)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (1053268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (1053268)CaDiCaL version: 2.1.3
% 0.22/0.32 % (1053268)Termination reason: Refutation
% 0.22/0.32 % (1053268)Time elapsed: 0.010 s
% 0.22/0.32 % (1053268)Peak memory usage: 13 MB
% 0.22/0.32 % (1053268)Instructions burned: 17 (million)
% 0.22/0.32 % (1053257)Success in time 0.069 s
% 0.22/0.32 % Vampire exiting
%------------------------------------------------------------------------------