%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL866^1 : 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 : n013.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 08:14:38 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 15
% Syntax : Number of formulae : 198 ( 36 unt; 0 typ; 11 def)
% Number of atoms : 1815 ( 296 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 1857 ( 132 ~; 306 |; 101 &;1108 @)
% ( 15 <=>; 84 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 66 ( 66 >; 0 *; 0 +; 0 <<)
% Number of symbols : 70 ( 66 usr; 23 con; 0-4 aty)
% ( 110 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 219 ( 0 sgn 56 !; 3 ?; 219 :)
% 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,
vAND: $o > $o > $o ).
thf(func_def_35,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_40,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_41,type,
vNOT: $o > $o ).
thf(func_def_42,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_43,type,
vOR: $o > $o > $o ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
sK0: $i > $i > $o ).
thf(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X3: $i,X2: $i,X1: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f22,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X3: $i,X1: $i,X2: $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] :
( ( ( msymmetric @ X0 )
& ( meuclidean @ X0 ) )
<=> ( ( msymmetric @ X0 )
& ( mtransitive @ X0 )
& ( meuclidean @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( ( msymmetric @ X0 )
& ( meuclidean @ X0 ) )
<=> ( ( msymmetric @ X0 )
& ( mtransitive @ X0 )
& ( meuclidean @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f34,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X2 )
& ( X0 @ X2 @ X1 ) )
=> ( X0 @ X3 @ X1 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f35,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f45,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
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(f60,plain,
~ ! [X0: $i > $i > $o] :
( ( ( msymmetric @ X0 )
& ( meuclidean @ X0 ) )
<=> ( ( msymmetric @ X0 )
& ( mtransitive @ X0 )
& ( meuclidean @ X0 ) ) ),
inference(rectify,[],[f33]) ).
thf(f61,plain,
~ ! [X0: $i > $i > $o] :
( ( ( ( meuclidean @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true ) )
<=> ( ( ( msymmetric @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f60]) ).
thf(f72,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X1 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X3 @ X1 ) ) )
= meuclidean ),
inference(rectify,[],[f22]) ).
thf(f73,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f72]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( ( ( meuclidean @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true ) )
<~> ( ( ( msymmetric @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) ) ),
inference(ennf_transformation,[],[f61]) ).
thf(f88,plain,
? [X0: $i > $i > $o] :
( ( ( ( msymmetric @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true )
| ( ( mtransitive @ X0 )
!= $true )
| ( ( msymmetric @ X0 )
!= $true ) )
& ( ( ( ( msymmetric @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) )
| ( ( ( meuclidean @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f87]) ).
thf(f89,plain,
? [X0: $i > $i > $o] :
( ( ( ( msymmetric @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true )
| ( ( mtransitive @ X0 )
!= $true )
| ( ( msymmetric @ X0 )
!= $true ) )
& ( ( ( ( msymmetric @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) )
| ( ( ( meuclidean @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true ) ) ) ),
inference(flattening,[],[f88]) ).
thf(f90,plain,
( ( ( $true
!= ( msymmetric @ sK0 ) )
| ( ( meuclidean @ sK0 )
!= $true )
| ( ( meuclidean @ sK0 )
!= $true )
| ( $true
!= ( mtransitive @ sK0 ) )
| ( $true
!= ( msymmetric @ sK0 ) ) )
& ( ( ( $true
= ( msymmetric @ sK0 ) )
& ( ( meuclidean @ sK0 )
= $true ) )
| ( ( ( meuclidean @ sK0 )
= $true )
& ( $true
= ( mtransitive @ sK0 ) )
& ( $true
= ( msymmetric @ sK0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f89]) ).
thf(f100,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f73]) ).
thf(f103,plain,
( ( ( meuclidean @ sK0 )
= $true )
| ( ( meuclidean @ sK0 )
= $true ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f104,plain,
( ( $true
= ( msymmetric @ sK0 ) )
| ( $true
= ( msymmetric @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f107,plain,
( ( $true
!= ( msymmetric @ sK0 ) )
| ( ( meuclidean @ sK0 )
!= $true )
| ( ( meuclidean @ sK0 )
!= $true )
| ( $true
!= ( mtransitive @ sK0 ) )
| ( $true
!= ( msymmetric @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f109,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f111,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f140,plain,
( ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ sK0 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
@ sK0 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ 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] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f107,f109,f100,f100,f111,f109]) ).
thf(f143,plain,
( ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ sK0 ) )
| ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f104,f109,f109]) ).
thf(f144,plain,
( ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
@ sK0 ) )
| ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f103,f100,f100]) ).
thf(f159,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
@ sK0 ) ),
inference(duplicate_literal_removal,[],[f144]) ).
thf(f160,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ X1 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ X1 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ X1 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ X1 @ Y1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ X2 @ X1 )
& ( sK0 @ X2 @ Y0 ) )
=> ( sK0 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ X2 @ X1 )
& ( sK0 @ X2 @ Y0 ) )
=> ( sK0 @ X1 @ Y0 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( sK0 @ X2 @ X1 )
& ( sK0 @ X2 @ X3 ) )
=> ( sK0 @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( sK0 @ X2 @ X1 )
& ( sK0 @ X2 @ X3 ) ) )
| ( ( sK0 @ X1 @ X3 )
= $true ) ),
inference(imp_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X2 @ X3 ) )
| ( ( sK0 @ X1 @ X3 )
= $true ) ),
inference(and_proxy_clausification,[],[f167]) ).
thf(f193,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ sK0 ) ),
inference(duplicate_literal_removal,[],[f143]) ).
thf(f194,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f193]) ).
thf(f195,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( sK0 @ X1 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f195]) ).
thf(f197,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( sK0 @ X1 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( sK0 @ X2 @ X1 )
=> ( sK0 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f197]) ).
thf(f199,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( sK0 @ X2 @ X1 ) )
| ( ( sK0 @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f198]) ).
thf(f214,plain,
( ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ sK0 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
@ sK0 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
@ sK0 ) ) ),
inference(duplicate_literal_removal,[],[f140]) ).
thf(f215,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
!= $true )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f214]) ).
thf(f216,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK1 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f215]) ).
thf(f217,plain,
( ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f216]) ).
thf(f218,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) )
@ sK3 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ Y2 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f217]) ).
thf(f219,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK1 )
=> ( sK0 @ sK1 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ sK2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ sK2 @ Y1 ) ) ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ sK3 @ Y0 ) )
=> ( sK0 @ sK3 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f218]) ).
thf(f220,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ sK3 @ Y0 ) )
=> ( sK0 @ sK3 @ Y1 ) ) ) ) )
| ( ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK1 )
=> ( sK0 @ sK1 @ Y0 ) )
@ sK4 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ sK2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ sK2 @ Y1 ) ) ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f219]) ).
thf(f221,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ sK2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ sK2 @ Y1 ) ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ sK3 @ Y0 ) )
=> ( sK0 @ sK3 @ Y1 ) ) )
@ sK5 )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK1 )
=> ( sK0 @ sK1 @ Y0 ) )
@ sK4 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f220]) ).
thf(f222,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ sK2 )
& ( sK0 @ Y0 @ Y1 ) )
=> ( sK0 @ sK2 @ Y1 ) ) )
@ sK6 ) )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ sK3 @ Y0 ) )
=> ( sK0 @ sK3 @ Y1 ) ) )
@ sK5 )
= $false )
| ( ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ sK1 )
=> ( sK0 @ sK1 @ Y0 ) )
@ sK4 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f221]) ).
thf(f223,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK5 @ Y0 )
& ( sK0 @ sK3 @ sK5 ) )
=> ( sK0 @ sK3 @ Y0 ) ) ) )
| ( ( ( sK0 @ sK4 @ sK1 )
=> ( sK0 @ sK1 @ sK4 ) )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK6 @ sK2 )
& ( sK0 @ sK6 @ Y0 ) )
=> ( sK0 @ sK2 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f222]) ).
thf(f224,plain,
( ( ( ( sK0 @ sK4 @ sK1 )
=> ( sK0 @ sK1 @ sK4 ) )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK5 @ Y0 )
& ( sK0 @ sK3 @ sK5 ) )
=> ( sK0 @ sK3 @ Y0 ) )
@ sK7 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK6 @ sK2 )
& ( sK0 @ sK6 @ Y0 ) )
=> ( sK0 @ sK2 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f223]) ).
thf(f225,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK6 @ sK2 )
& ( sK0 @ sK6 @ Y0 ) )
=> ( sK0 @ sK2 @ Y0 ) ) ) )
| ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK5 @ Y0 )
& ( sK0 @ sK3 @ sK5 ) )
=> ( sK0 @ sK3 @ Y0 ) )
@ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f224]) ).
thf(f226,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK5 @ Y0 )
& ( sK0 @ sK3 @ sK5 ) )
=> ( sK0 @ sK3 @ Y0 ) )
@ sK7 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK6 @ sK2 )
& ( sK0 @ sK6 @ Y0 ) )
=> ( sK0 @ sK2 @ Y0 ) ) ) )
| ( ( sK0 @ sK4 @ sK1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f224]) ).
thf(f227,plain,
( ( ( sK0 @ sK4 @ sK1 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK5 @ Y0 )
& ( sK0 @ sK3 @ sK5 ) )
=> ( sK0 @ sK3 @ Y0 ) )
@ sK7 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK6 @ sK2 )
& ( sK0 @ sK6 @ Y0 ) )
=> ( sK0 @ sK2 @ Y0 ) )
@ sK8 ) ) ),
inference(sigma_proxy_clausification,[],[f226]) ).
thf(f228,plain,
( ( $false
= ( ( ( sK0 @ sK6 @ sK2 )
& ( sK0 @ sK6 @ sK8 ) )
=> ( sK0 @ sK2 @ sK8 ) ) )
| ( ( sK0 @ sK4 @ sK1 )
= $true )
| ( ( ( ( sK0 @ sK5 @ sK7 )
& ( sK0 @ sK3 @ sK5 ) )
=> ( sK0 @ sK3 @ sK7 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f227]) ).
thf(f229,plain,
( ( $false
= ( sK0 @ sK2 @ sK8 ) )
| ( ( sK0 @ sK4 @ sK1 )
= $true )
| ( ( ( ( sK0 @ sK5 @ sK7 )
& ( sK0 @ sK3 @ sK5 ) )
=> ( sK0 @ sK3 @ sK7 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f228]) ).
thf(f230,plain,
( ( ( ( ( sK0 @ sK5 @ sK7 )
& ( sK0 @ sK3 @ sK5 ) )
=> ( sK0 @ sK3 @ sK7 ) )
= $false )
| ( ( sK0 @ sK4 @ sK1 )
= $true )
| ( $true
= ( ( sK0 @ sK6 @ sK2 )
& ( sK0 @ sK6 @ sK8 ) ) ) ),
inference(imp_proxy_clausification,[],[f228]) ).
thf(f231,plain,
( ( ( sK0 @ sK4 @ sK1 )
= $true )
| ( ( sK0 @ sK3 @ sK7 )
= $false )
| ( $true
= ( ( sK0 @ sK6 @ sK2 )
& ( sK0 @ sK6 @ sK8 ) ) ) ),
inference(imp_proxy_clausification,[],[f230]) ).
thf(f232,plain,
( ( ( sK0 @ sK4 @ sK1 )
= $true )
| ( $true
= ( ( sK0 @ sK6 @ sK2 )
& ( sK0 @ sK6 @ sK8 ) ) )
| ( $true
= ( ( sK0 @ sK5 @ sK7 )
& ( sK0 @ sK3 @ sK5 ) ) ) ),
inference(imp_proxy_clausification,[],[f230]) ).
thf(f233,plain,
( ( ( sK0 @ sK4 @ sK1 )
= $true )
| ( ( sK0 @ sK6 @ sK8 )
= $true )
| ( $true
= ( ( sK0 @ sK5 @ sK7 )
& ( sK0 @ sK3 @ sK5 ) ) ) ),
inference(and_proxy_clausification,[],[f232]) ).
thf(f234,plain,
( ( $true
= ( ( sK0 @ sK5 @ sK7 )
& ( sK0 @ sK3 @ sK5 ) ) )
| ( ( sK0 @ sK4 @ sK1 )
= $true )
| ( ( sK0 @ sK6 @ sK2 )
= $true ) ),
inference(and_proxy_clausification,[],[f232]) ).
thf(f235,plain,
( ( ( sK0 @ sK4 @ sK1 )
= $true )
| ( ( sK0 @ sK6 @ sK2 )
= $true )
| ( ( sK0 @ sK3 @ sK5 )
= $true ) ),
inference(and_proxy_clausification,[],[f234]) ).
thf(f236,plain,
( ( ( sK0 @ sK6 @ sK2 )
= $true )
| ( $true
= ( sK0 @ sK5 @ sK7 ) )
| ( ( sK0 @ sK4 @ sK1 )
= $true ) ),
inference(and_proxy_clausification,[],[f234]) ).
thf(f237,plain,
( ( ( sK0 @ sK6 @ sK8 )
= $true )
| ( ( sK0 @ sK4 @ sK1 )
= $true )
| ( ( sK0 @ sK3 @ sK5 )
= $true ) ),
inference(and_proxy_clausification,[],[f233]) ).
thf(f238,plain,
( ( $true
= ( sK0 @ sK5 @ sK7 ) )
| ( ( sK0 @ sK4 @ sK1 )
= $true )
| ( ( sK0 @ sK6 @ sK8 )
= $true ) ),
inference(and_proxy_clausification,[],[f233]) ).
thf(f239,plain,
( ( ( sK0 @ sK6 @ sK8 )
= $true )
| ( ( sK0 @ sK3 @ sK7 )
= $false )
| ( ( sK0 @ sK4 @ sK1 )
= $true ) ),
inference(and_proxy_clausification,[],[f231]) ).
thf(f240,plain,
( ( ( sK0 @ sK4 @ sK1 )
= $true )
| ( ( sK0 @ sK3 @ sK7 )
= $false )
| ( ( sK0 @ sK6 @ sK2 )
= $true ) ),
inference(and_proxy_clausification,[],[f231]) ).
thf(f241,plain,
( ( $false
= ( sK0 @ sK2 @ sK8 ) )
| ( ( sK0 @ sK4 @ sK1 )
= $true )
| ( ( sK0 @ sK3 @ sK7 )
= $false ) ),
inference(imp_proxy_clausification,[],[f229]) ).
thf(f242,plain,
( ( $true
= ( ( sK0 @ sK5 @ sK7 )
& ( sK0 @ sK3 @ sK5 ) ) )
| ( ( sK0 @ sK4 @ sK1 )
= $true )
| ( $false
= ( sK0 @ sK2 @ sK8 ) ) ),
inference(imp_proxy_clausification,[],[f229]) ).
thf(f243,plain,
( ( ( sK0 @ sK4 @ sK1 )
= $true )
| ( ( sK0 @ sK3 @ sK5 )
= $true )
| ( $false
= ( sK0 @ sK2 @ sK8 ) ) ),
inference(and_proxy_clausification,[],[f242]) ).
thf(f244,plain,
( ( ( sK0 @ sK4 @ sK1 )
= $true )
| ( $true
= ( sK0 @ sK5 @ sK7 ) )
| ( $false
= ( sK0 @ sK2 @ sK8 ) ) ),
inference(and_proxy_clausification,[],[f242]) ).
thf(f245,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ sK5 @ Y0 )
& ( sK0 @ sK3 @ sK5 ) )
=> ( sK0 @ sK3 @ Y0 ) )
@ sK7 ) )
| ( ( ^ [Y0: $i] :
( ( ( sK0 @ sK6 @ sK2 )
& ( sK0 @ sK6 @ Y0 ) )
=> ( sK0 @ sK2 @ Y0 ) )
@ sK9 )
= $false )
| ( $false
= ( sK0 @ sK1 @ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f225]) ).
thf(f246,plain,
( ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( ( ( ( sK0 @ sK5 @ sK7 )
& ( sK0 @ sK3 @ sK5 ) )
=> ( sK0 @ sK3 @ sK7 ) )
= $false )
| ( $false
= ( ( ( sK0 @ sK6 @ sK2 )
& ( sK0 @ sK6 @ sK9 ) )
=> ( sK0 @ sK2 @ sK9 ) ) ) ),
inference(beta-eta_normalization,[],[f245]) ).
thf(f247,plain,
( ( ( sK0 @ sK3 @ sK7 )
= $false )
| ( $false
= ( ( ( sK0 @ sK6 @ sK2 )
& ( sK0 @ sK6 @ sK9 ) )
=> ( sK0 @ sK2 @ sK9 ) ) )
| ( $false
= ( sK0 @ sK1 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f246]) ).
thf(f248,plain,
( ( $false
= ( ( ( sK0 @ sK6 @ sK2 )
& ( sK0 @ sK6 @ sK9 ) )
=> ( sK0 @ sK2 @ sK9 ) ) )
| ( $true
= ( ( sK0 @ sK5 @ sK7 )
& ( sK0 @ sK3 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK1 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f246]) ).
thf(f249,plain,
( ( $true
= ( ( sK0 @ sK5 @ sK7 )
& ( sK0 @ sK3 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( $false
= ( sK0 @ sK2 @ sK9 ) ) ),
inference(imp_proxy_clausification,[],[f248]) ).
thf(f250,plain,
( ( ( ( sK0 @ sK6 @ sK2 )
& ( sK0 @ sK6 @ sK9 ) )
= $true )
| ( $true
= ( ( sK0 @ sK5 @ sK7 )
& ( sK0 @ sK3 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK1 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f248]) ).
thf(f251,plain,
( ( ( sK0 @ sK6 @ sK9 )
= $true )
| ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( ( sK0 @ sK5 @ sK7 )
& ( sK0 @ sK3 @ sK5 ) ) ) ),
inference(and_proxy_clausification,[],[f250]) ).
thf(f252,plain,
( ( $true
= ( ( sK0 @ sK5 @ sK7 )
& ( sK0 @ sK3 @ sK5 ) ) )
| ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( ( sK0 @ sK6 @ sK2 )
= $true ) ),
inference(and_proxy_clausification,[],[f250]) ).
thf(f253,plain,
( ( ( sK0 @ sK6 @ sK2 )
= $true )
| ( ( sK0 @ sK3 @ sK5 )
= $true )
| ( $false
= ( sK0 @ sK1 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f252]) ).
thf(f254,plain,
( ( $true
= ( sK0 @ sK5 @ sK7 ) )
| ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( ( sK0 @ sK6 @ sK2 )
= $true ) ),
inference(and_proxy_clausification,[],[f252]) ).
thf(f255,plain,
( ( ( sK0 @ sK3 @ sK5 )
= $true )
| ( ( sK0 @ sK6 @ sK9 )
= $true )
| ( $false
= ( sK0 @ sK1 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f251]) ).
thf(f256,plain,
( ( ( sK0 @ sK6 @ sK9 )
= $true )
| ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK5 @ sK7 ) ) ),
inference(and_proxy_clausification,[],[f251]) ).
thf(f257,plain,
( ( ( sK0 @ sK3 @ sK5 )
= $true )
| ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( $false
= ( sK0 @ sK2 @ sK9 ) ) ),
inference(and_proxy_clausification,[],[f249]) ).
thf(f258,plain,
( ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( $true
= ( sK0 @ sK5 @ sK7 ) )
| ( $false
= ( sK0 @ sK2 @ sK9 ) ) ),
inference(and_proxy_clausification,[],[f249]) ).
thf(f259,plain,
( ( $false
= ( sK0 @ sK2 @ sK9 ) )
| ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( ( sK0 @ sK3 @ sK7 )
= $false ) ),
inference(imp_proxy_clausification,[],[f247]) ).
thf(f260,plain,
( ( ( ( sK0 @ sK6 @ sK2 )
& ( sK0 @ sK6 @ sK9 ) )
= $true )
| ( ( sK0 @ sK3 @ sK7 )
= $false )
| ( $false
= ( sK0 @ sK1 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f247]) ).
thf(f261,plain,
( ( ( sK0 @ sK3 @ sK7 )
= $false )
| ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ( ( sK0 @ sK6 @ sK9 )
= $true ) ),
inference(and_proxy_clausification,[],[f260]) ).
thf(f262,plain,
( ( ( sK0 @ sK6 @ sK2 )
= $true )
| ( ( sK0 @ sK3 @ sK7 )
= $false )
| ( $false
= ( sK0 @ sK1 @ sK4 ) ) ),
inference(and_proxy_clausification,[],[f260]) ).
thf(f267,definition,
( spl10_2
<=> ! [X2: $i,X3: $i] :
( ( ( sK0 @ X2 @ X3 )
= $true )
| ( ( sK0 @ X3 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
thf(f268,plain,
( ! [X2: $i,X3: $i] :
( ( ( sK0 @ X3 @ X2 )
= $false )
| ( ( sK0 @ X2 @ X3 )
= $true ) )
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f267]) ).
thf(f270,plain,
spl10_2,
inference(avatar_split_clause,[],[f199,f267]) ).
thf(f272,definition,
( spl10_3
<=> ( $true
= ( sK0 @ sK5 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
thf(f274,plain,
( ( $true
= ( sK0 @ sK5 @ sK7 ) )
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f272]) ).
thf(f276,definition,
( spl10_4
<=> ( ( sK0 @ sK6 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
thf(f278,plain,
( ( ( sK0 @ sK6 @ sK2 )
= $true )
| ~ spl10_4 ),
inference(avatar_component_clause,[],[f276]) ).
thf(f280,definition,
( spl10_5
<=> ( ( sK0 @ sK4 @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition]) ).
thf(f282,plain,
( ( ( sK0 @ sK4 @ sK1 )
= $true )
| ~ spl10_5 ),
inference(avatar_component_clause,[],[f280]) ).
thf(f283,plain,
( spl10_3
| spl10_4
| spl10_5 ),
inference(avatar_split_clause,[],[f236,f280,f276,f272]) ).
thf(f285,definition,
( spl10_6
<=> ( ( sK0 @ sK3 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl10_6])],[avatar_definition]) ).
thf(f287,plain,
( ( ( sK0 @ sK3 @ sK5 )
= $true )
| ~ spl10_6 ),
inference(avatar_component_clause,[],[f285]) ).
thf(f288,plain,
( spl10_4
| spl10_6
| spl10_5 ),
inference(avatar_split_clause,[],[f235,f280,f285,f276]) ).
thf(f290,definition,
( spl10_7
<=> ( ( sK0 @ sK6 @ sK8 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl10_7])],[avatar_definition]) ).
thf(f292,plain,
( ( ( sK0 @ sK6 @ sK8 )
= $true )
| ~ spl10_7 ),
inference(avatar_component_clause,[],[f290]) ).
thf(f293,plain,
( spl10_5
| spl10_7
| spl10_3 ),
inference(avatar_split_clause,[],[f238,f272,f290,f280]) ).
thf(f294,plain,
( spl10_6
| spl10_7
| spl10_5 ),
inference(avatar_split_clause,[],[f237,f280,f290,f285]) ).
thf(f296,definition,
( spl10_8
<=> ( ( sK0 @ sK3 @ sK7 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl10_8])],[avatar_definition]) ).
thf(f298,plain,
( ( ( sK0 @ sK3 @ sK7 )
= $false )
| ~ spl10_8 ),
inference(avatar_component_clause,[],[f296]) ).
thf(f299,plain,
( spl10_5
| spl10_4
| spl10_8 ),
inference(avatar_split_clause,[],[f240,f296,f276,f280]) ).
thf(f300,plain,
( spl10_7
| spl10_8
| spl10_5 ),
inference(avatar_split_clause,[],[f239,f280,f296,f290]) ).
thf(f302,definition,
( spl10_9
<=> ( $false
= ( sK0 @ sK2 @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_9])],[avatar_definition]) ).
thf(f304,plain,
( ( $false
= ( sK0 @ sK2 @ sK8 ) )
| ~ spl10_9 ),
inference(avatar_component_clause,[],[f302]) ).
thf(f305,plain,
( spl10_3
| spl10_9
| spl10_5 ),
inference(avatar_split_clause,[],[f244,f280,f302,f272]) ).
thf(f306,plain,
( spl10_9
| spl10_6
| spl10_5 ),
inference(avatar_split_clause,[],[f243,f280,f285,f302]) ).
thf(f307,plain,
( spl10_8
| spl10_9
| spl10_5 ),
inference(avatar_split_clause,[],[f241,f280,f302,f296]) ).
thf(f309,definition,
( spl10_10
<=> ( $false
= ( sK0 @ sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_10])],[avatar_definition]) ).
thf(f311,plain,
( ( $false
= ( sK0 @ sK1 @ sK4 ) )
| ~ spl10_10 ),
inference(avatar_component_clause,[],[f309]) ).
thf(f312,plain,
( spl10_3
| spl10_4
| spl10_10 ),
inference(avatar_split_clause,[],[f254,f309,f276,f272]) ).
thf(f313,plain,
( spl10_4
| spl10_10
| spl10_6 ),
inference(avatar_split_clause,[],[f253,f285,f309,f276]) ).
thf(f315,definition,
( spl10_11
<=> ( ( sK0 @ sK6 @ sK9 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl10_11])],[avatar_definition]) ).
thf(f317,plain,
( ( ( sK0 @ sK6 @ sK9 )
= $true )
| ~ spl10_11 ),
inference(avatar_component_clause,[],[f315]) ).
thf(f318,plain,
( spl10_11
| spl10_3
| spl10_10 ),
inference(avatar_split_clause,[],[f256,f309,f272,f315]) ).
thf(f319,plain,
( spl10_11
| spl10_10
| spl10_6 ),
inference(avatar_split_clause,[],[f255,f285,f309,f315]) ).
thf(f321,definition,
( spl10_12
<=> ( $false
= ( sK0 @ sK2 @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_12])],[avatar_definition]) ).
thf(f323,plain,
( ( $false
= ( sK0 @ sK2 @ sK9 ) )
| ~ spl10_12 ),
inference(avatar_component_clause,[],[f321]) ).
thf(f324,plain,
( spl10_10
| spl10_3
| spl10_12 ),
inference(avatar_split_clause,[],[f258,f321,f272,f309]) ).
thf(f325,plain,
( spl10_10
| spl10_6
| spl10_12 ),
inference(avatar_split_clause,[],[f257,f321,f285,f309]) ).
thf(f326,plain,
( spl10_8
| spl10_10
| spl10_4 ),
inference(avatar_split_clause,[],[f262,f276,f309,f296]) ).
thf(f327,plain,
( spl10_8
| spl10_11
| spl10_10 ),
inference(avatar_split_clause,[],[f261,f309,f315,f296]) ).
thf(f328,plain,
( spl10_10
| spl10_12
| spl10_8 ),
inference(avatar_split_clause,[],[f259,f296,f321,f309]) ).
thf(f346,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK3 ) )
| ( $false
= ( sK0 @ X0 @ sK7 ) )
| ( $false = $true ) )
| ~ spl10_8 ),
inference(constrained_superposition,[],[f298,f168]) ).
thf(f354,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK7 ) )
| ( $false
= ( sK0 @ X0 @ sK3 ) ) )
| ~ spl10_8 ),
inference(trivial_inequality_removal,[],[f346]) ).
thf(f431,plain,
( ( $false
= ( sK0 @ sK5 @ sK3 ) )
| ( $false = $true )
| ~ spl10_3
| ~ spl10_8 ),
inference(constrained_superposition,[],[f274,f354]) ).
thf(f438,plain,
( ( $false
= ( sK0 @ sK5 @ sK3 ) )
| ~ spl10_3
| ~ spl10_8 ),
inference(trivial_inequality_removal,[],[f431]) ).
thf(f461,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK8 ) )
| ( $false
= ( sK0 @ X0 @ sK2 ) )
| ( $false = $true ) )
| ~ spl10_9 ),
inference(constrained_superposition,[],[f304,f168]) ).
thf(f463,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK8 ) )
| ( $false
= ( sK0 @ X0 @ sK2 ) ) )
| ~ spl10_9 ),
inference(trivial_inequality_removal,[],[f461]) ).
thf(f558,plain,
( ( ( sK0 @ sK3 @ sK5 )
= $false )
| ( $false = $true )
| ~ spl10_2
| ~ spl10_3
| ~ spl10_8 ),
inference(constrained_superposition,[],[f268,f438]) ).
thf(f561,plain,
( ( ( sK0 @ sK3 @ sK5 )
= $false )
| ~ spl10_2
| ~ spl10_3
| ~ spl10_8 ),
inference(trivial_inequality_removal,[],[f558]) ).
thf(f566,plain,
( ( $false = $true )
| ~ spl10_2
| ~ spl10_3
| ~ spl10_6
| ~ spl10_8 ),
inference(forward_demodulation,[],[f561,f287]) ).
thf(f567,plain,
( $false
| ~ spl10_2
| ~ spl10_3
| ~ spl10_6
| ~ spl10_8 ),
inference(trivial_inequality_removal,[],[f566]) ).
thf(f568,plain,
( ~ spl10_2
| ~ spl10_3
| ~ spl10_6
| ~ spl10_8 ),
inference(avatar_contradiction_clause,[],[f567]) ).
thf(f637,plain,
( ( $false
= ( sK0 @ sK6 @ sK2 ) )
| ( $false = $true )
| ~ spl10_7
| ~ spl10_9 ),
inference(constrained_superposition,[],[f463,f292]) ).
thf(f646,plain,
( ( $false
= ( sK0 @ sK6 @ sK2 ) )
| ~ spl10_7
| ~ spl10_9 ),
inference(trivial_inequality_removal,[],[f637]) ).
thf(f656,plain,
( ( $false = $true )
| ~ spl10_4
| ~ spl10_7
| ~ spl10_9 ),
inference(forward_demodulation,[],[f646,f278]) ).
thf(f657,plain,
( $false
| ~ spl10_4
| ~ spl10_7
| ~ spl10_9 ),
inference(trivial_inequality_removal,[],[f656]) ).
thf(f658,plain,
( ~ spl10_4
| ~ spl10_7
| ~ spl10_9 ),
inference(avatar_contradiction_clause,[],[f657]) ).
thf(f684,plain,
( ( $false = $true )
| ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ~ spl10_2
| ~ spl10_5 ),
inference(constrained_superposition,[],[f268,f282]) ).
thf(f693,plain,
( ( $true
= ( sK0 @ sK1 @ sK4 ) )
| ~ spl10_2
| ~ spl10_5 ),
inference(trivial_inequality_removal,[],[f684]) ).
thf(f697,plain,
( ( $false = $true )
| ~ spl10_2
| ~ spl10_5
| ~ spl10_10 ),
inference(forward_demodulation,[],[f693,f311]) ).
thf(f698,plain,
( $false
| ~ spl10_2
| ~ spl10_5
| ~ spl10_10 ),
inference(trivial_inequality_removal,[],[f697]) ).
thf(f699,plain,
( ~ spl10_2
| ~ spl10_5
| ~ spl10_10 ),
inference(avatar_contradiction_clause,[],[f698]) ).
thf(f702,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK2 ) )
| ( $false
= ( sK0 @ X0 @ sK9 ) )
| ( $false = $true ) )
| ~ spl10_12 ),
inference(constrained_superposition,[],[f168,f323]) ).
thf(f703,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK9 ) )
| ( $false
= ( sK0 @ X0 @ sK2 ) ) )
| ~ spl10_12 ),
inference(trivial_inequality_removal,[],[f702]) ).
thf(f826,plain,
( ( $false = $true )
| ( $false
= ( sK0 @ sK6 @ sK2 ) )
| ~ spl10_11
| ~ spl10_12 ),
inference(constrained_superposition,[],[f317,f703]) ).
thf(f830,plain,
( ( $false
= ( sK0 @ sK6 @ sK2 ) )
| ~ spl10_11
| ~ spl10_12 ),
inference(trivial_inequality_removal,[],[f826]) ).
thf(f848,plain,
( ( $false = $true )
| ~ spl10_4
| ~ spl10_11
| ~ spl10_12 ),
inference(forward_demodulation,[],[f830,f278]) ).
thf(f849,plain,
( $false
| ~ spl10_4
| ~ spl10_11
| ~ spl10_12 ),
inference(trivial_inequality_removal,[],[f848]) ).
thf(f850,plain,
( ~ spl10_4
| ~ spl10_11
| ~ spl10_12 ),
inference(avatar_contradiction_clause,[],[f849]) ).
cnf(s2,plain,
spl10_2,
inference(sat_conversion,[],[f270]) ).
cnf(s3,plain,
( spl10_3
| spl10_4
| spl10_5 ),
inference(sat_conversion,[],[f283]) ).
cnf(s4,plain,
( spl10_4
| spl10_5
| spl10_6 ),
inference(sat_conversion,[],[f288]) ).
cnf(s5,plain,
( spl10_3
| spl10_5
| spl10_7 ),
inference(sat_conversion,[],[f293]) ).
cnf(s6,plain,
( spl10_5
| spl10_6
| spl10_7 ),
inference(sat_conversion,[],[f294]) ).
cnf(s7,plain,
( spl10_4
| spl10_5
| spl10_8 ),
inference(sat_conversion,[],[f299]) ).
cnf(s8,plain,
( spl10_5
| spl10_7
| spl10_8 ),
inference(sat_conversion,[],[f300]) ).
cnf(s9,plain,
( spl10_3
| spl10_5
| spl10_9 ),
inference(sat_conversion,[],[f305]) ).
cnf(s10,plain,
( spl10_5
| spl10_6
| spl10_9 ),
inference(sat_conversion,[],[f306]) ).
cnf(s11,plain,
( spl10_5
| spl10_8
| spl10_9 ),
inference(sat_conversion,[],[f307]) ).
cnf(s12,plain,
( spl10_3
| spl10_4
| spl10_10 ),
inference(sat_conversion,[],[f312]) ).
cnf(s13,plain,
( spl10_4
| spl10_6
| spl10_10 ),
inference(sat_conversion,[],[f313]) ).
cnf(s14,plain,
( spl10_3
| spl10_10
| spl10_11 ),
inference(sat_conversion,[],[f318]) ).
cnf(s15,plain,
( spl10_6
| spl10_10
| spl10_11 ),
inference(sat_conversion,[],[f319]) ).
cnf(s16,plain,
( spl10_3
| spl10_10
| spl10_12 ),
inference(sat_conversion,[],[f324]) ).
cnf(s17,plain,
( spl10_6
| spl10_10
| spl10_12 ),
inference(sat_conversion,[],[f325]) ).
cnf(s18,plain,
( spl10_4
| spl10_8
| spl10_10 ),
inference(sat_conversion,[],[f326]) ).
cnf(s19,plain,
( spl10_8
| spl10_10
| spl10_11 ),
inference(sat_conversion,[],[f327]) ).
cnf(s20,plain,
( spl10_8
| spl10_10
| spl10_12 ),
inference(sat_conversion,[],[f328]) ).
cnf(s30,plain,
( ~ spl10_2
| ~ spl10_3
| ~ spl10_6
| ~ spl10_8 ),
inference(sat_conversion,[],[f568]) ).
cnf(s37,plain,
( ~ spl10_4
| ~ spl10_7
| ~ spl10_9 ),
inference(sat_conversion,[],[f658]) ).
cnf(s43,plain,
( ~ spl10_2
| ~ spl10_5
| ~ spl10_10 ),
inference(sat_conversion,[],[f699]) ).
cnf(s50,plain,
( ~ spl10_4
| ~ spl10_11
| ~ spl10_12 ),
inference(sat_conversion,[],[f850]) ).
cnf(s55,plain,
( spl10_4
| spl10_3 ),
inference(rat,[],[s43,s3,s12,s2]) ).
cnf(s56,plain,
( spl10_10
| spl10_3 ),
inference(rat,[],[s50,s14,s16,s55]) ).
cnf(s57,plain,
spl10_3,
inference(rat,[],[s37,s5,s9,s43,s56,s55,s2]) ).
cnf(s58,plain,
( spl10_12
| spl10_10 ),
inference(rat,[],[s30,s17,s20,s57,s2]) ).
cnf(s59,plain,
( spl10_11
| spl10_10 ),
inference(rat,[],[s30,s19,s15,s57,s2]) ).
cnf(s60,plain,
( spl10_10
| ~ spl10_4 ),
inference(rat,[],[s59,s50,s58]) ).
cnf(s61,plain,
( spl10_8
| ~ spl10_4 ),
inference(rat,[],[s37,s8,s11,s43,s60,s2]) ).
cnf(s62,plain,
~ spl10_4,
inference(rat,[],[s37,s6,s10,s30,s61,s43,s60,s2,s57]) ).
cnf(s63,plain,
spl10_5,
inference(rat,[],[s30,s4,s7,s2,s57,s62]) ).
cnf(s64,plain,
~ spl10_10,
inference(rat,[],[s43,s2,s63]) ).
cnf(s65,plain,
spl10_8,
inference(rat,[],[s18,s62,s64]) ).
cnf(s66,plain,
spl10_6,
inference(rat,[],[s13,s62,s64]) ).
cnf(s69,plain,
$false,
inference(rat,[],[s30,s57,s2,s65,s66]) ).
thf(f857,plain,
$false,
inference(avatar_sat_refutation,[],[s69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL866^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n013.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 10:17:36 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.24 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
% 0.21/0.30 % (1909748)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.30 % (1909753)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3670820071:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.30 % (1909759)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.30 % (1909759)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
% 0.21/0.30 % (1909757)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1874308230:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.30 % (1909755)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1427175928:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.30 % (1909754)lrs+10_16_si=on:nwc=1.5:random_seed=718222400:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.30 % (1909756)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=1332342844: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)
% 0.21/0.30 % (1909758)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2725304102:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.30 % (1909759)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=2173165468:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.30 % (1909755)Instruction limit reached!
% 0.21/0.30 % (1909755)------------------------------
% 0.21/0.30 % (1909755)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (1909755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (1909755)CaDiCaL version: 2.1.3
% 0.21/0.30 % (1909755)Termination reason: Instruction limit
% 0.21/0.30 % (1909755)Termination phase: Property scanning
% 0.21/0.30 % (1909755)Time elapsed: 0.002 s
% 0.21/0.30 % (1909755)Peak memory usage: 10 MB
% 0.21/0.30 % (1909755)Instructions burned: 4 (million)
% 0.21/0.30 % (1909753) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1909748-1909753"...
% 0.21/0.30 % (1909753)...printing done.
% 0.21/0.30 % (1909753)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.30 % (1909753)------------------------------
% 0.21/0.30 % (1909753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (1909753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (1909753)CaDiCaL version: 2.1.3
% 0.21/0.30 % (1909753)Termination reason: Refutation
% 0.21/0.30 % (1909753)Time elapsed: 0.015 s
% 0.21/0.30 % (1909753)Peak memory usage: 13 MB
% 0.21/0.30 % (1909753)Instructions burned: 52 (million)
% 0.21/0.30 % (1909748)Success in time 0.047 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------