%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL867^1 : 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 : n018.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 0.22s 0.34s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 22
% Syntax : Number of formulae : 183 ( 30 unt; 0 typ; 18 def)
% Number of atoms : 1235 ( 252 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 1388 ( 148 ~; 230 |; 69 &; 759 @)
% ( 19 <=>; 62 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 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 : 74 ( 70 usr; 27 con; 0-4 aty)
% ( 100 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 230 ( 0 sgn 84 !; 3 ?; 230 :)
% 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,
vIMP: $o > $o > $o ).
thf(func_def_37,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $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,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_45,type,
vNOT: $o > $o ).
thf(func_def_46,type,
vOR: $o > $o > $o ).
thf(func_def_47,type,
sK0: $i > $i > $o ).
thf(func_def_48,type,
sF1: $o ).
thf(func_def_49,type,
sF2: $o ).
thf(func_def_50,type,
sF3: $o ).
thf(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(f21,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X2: $i,X3: $i,X1: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) )
= mtransitive ),
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 @ X2 )
& ( X0 @ X1 @ X3 ) )
=> ( X0 @ X2 @ X3 ) ) )
= meuclidean ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',meuclidean) ).
thf(f32,conjecture,
! [X0: $i > $i > $o] :
( ( ( mtransitive @ X0 )
& ( msymmetric @ X0 ) )
<=> ( ( meuclidean @ X0 )
& ( msymmetric @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( ( mtransitive @ X0 )
& ( msymmetric @ X0 ) )
<=> ( ( meuclidean @ X0 )
& ( msymmetric @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f42,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) )
= msymmetric ),
inference(rectify,[],[f19]) ).
thf(f43,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f44,plain,
~ ! [X0: $i > $i > $o] :
( ( ( mtransitive @ X0 )
& ( msymmetric @ X0 ) )
<=> ( ( meuclidean @ X0 )
& ( msymmetric @ X0 ) ) ),
inference(rectify,[],[f33]) ).
thf(f45,plain,
~ ! [X0: $i > $i > $o] :
( ( ( ( mtransitive @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true ) )
<=> ( ( ( msymmetric @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f53,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X2 @ X1 ) )
=> ( X0 @ X3 @ X1 ) ) )
= meuclidean ),
inference(rectify,[],[f22]) ).
thf(f54,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f62,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X1 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X3 @ X2 ) ) )
= mtransitive ),
inference(rectify,[],[f21]) ).
thf(f63,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( ( ( msymmetric @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) )
<~> ( ( ( mtransitive @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true ) ) ),
inference(ennf_transformation,[],[f45]) ).
thf(f88,plain,
? [X0: $i > $i > $o] :
( ( ( ( mtransitive @ X0 )
!= $true )
| ( ( msymmetric @ X0 )
!= $true )
| ( ( msymmetric @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true ) )
& ( ( ( ( mtransitive @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true ) )
| ( ( ( msymmetric @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f87]) ).
thf(f89,plain,
? [X0: $i > $i > $o] :
( ( ( ( mtransitive @ X0 )
!= $true )
| ( ( msymmetric @ X0 )
!= $true )
| ( ( msymmetric @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true ) )
& ( ( ( ( mtransitive @ X0 )
= $true )
& ( ( msymmetric @ X0 )
= $true ) )
| ( ( ( msymmetric @ X0 )
= $true )
& ( ( meuclidean @ X0 )
= $true ) ) ) ),
inference(flattening,[],[f88]) ).
thf(f90,plain,
( ( ( ( mtransitive @ sK0 )
!= $true )
| ( ( msymmetric @ sK0 )
!= $true )
| ( ( msymmetric @ sK0 )
!= $true )
| ( ( meuclidean @ sK0 )
!= $true ) )
& ( ( ( ( mtransitive @ sK0 )
= $true )
& ( ( msymmetric @ sK0 )
= $true ) )
| ( ( ( msymmetric @ sK0 )
= $true )
& ( ( meuclidean @ sK0 )
= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f89]) ).
thf(f91,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f93,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f96,plain,
( ( ( msymmetric @ sK0 )
= $true )
| ( ( msymmetric @ sK0 )
= $true ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f97,plain,
( ( ( mtransitive @ sK0 )
= $true )
| ( ( meuclidean @ sK0 )
= $true ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f99,plain,
( ( ( mtransitive @ sK0 )
!= $true )
| ( ( msymmetric @ sK0 )
!= $true )
| ( ( msymmetric @ sK0 )
!= $true )
| ( ( meuclidean @ sK0 )
!= $true ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f120,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f138,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
@ sK0 )
!= $true )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ 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 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
@ sK0 )
!= $true ) ),
inference(definition_unfolding,[],[f99,f120,f93,f93,f91]) ).
thf(f140,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
@ sK0 )
= $true )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
@ sK0 )
= $true ) ),
inference(definition_unfolding,[],[f97,f120,f91]) ).
thf(f141,plain,
( ( ( ^ [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 )
= $true ) ),
inference(definition_unfolding,[],[f96,f93,f93]) ).
thf(f143,definition,
( sF1
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
@ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f144,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(f145,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ sK0 )
= sF2 ),
inference(reorient_equations,[],[f144]) ).
thf(f146,definition,
( sF3
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
@ sK0 ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f147,plain,
( ( sF3 != $true )
| ( sF1 != $true )
| ( sF2 != $true )
| ( sF2 != $true ) ),
inference(definition_folding,[],[f138,f146,f145,f145,f143]) ).
thf(f149,plain,
( ( sF1 = $true )
| ( sF3 = $true ) ),
inference(definition_folding,[],[f140,f146,f143]) ).
thf(f150,plain,
( ( sF2 = $true )
| ( sF2 = $true ) ),
inference(definition_folding,[],[f141,f145,f145]) ).
thf(f152,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ sK0 )
= $true )
| ( sF2 = $false ) ),
inference(iff_proxy_clausification,[],[f145]) ).
thf(f161,plain,
( ( sF2 = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f162,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 @ Y0 )
=> ( sK0 @ Y0 @ Y1 ) ) )
@ X1 )
= $true )
| ( sF2 = $false ) ),
inference(pi_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( sK0 @ X1 @ Y0 ) ) )
= $true )
| ( sF2 = $false ) ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
! [X2: $i,X1: $i] :
( ( sF2 = $false )
| ( ( ^ [Y0: $i] :
( ( sK0 @ Y0 @ X1 )
=> ( sK0 @ X1 @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X2: $i,X1: $i] :
( ( sF2 = $false )
| ( ( ( sK0 @ X2 @ X1 )
=> ( sK0 @ X1 @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f164]) ).
thf(f166,plain,
! [X2: $i,X1: $i] :
( ( ( sK0 @ X2 @ X1 )
= $false )
| ( sF2 = $false )
| ( ( sK0 @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f165]) ).
thf(f167,plain,
sF2 = $true,
inference(duplicate_literal_removal,[],[f150]) ).
thf(f168,plain,
( ( sF1 != $true )
| ( sF3 != $true )
| ( sF2 != $true ) ),
inference(duplicate_literal_removal,[],[f147]) ).
thf(f169,plain,
( ( sF1 = $true )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
@ sK0 )
= $false ) ),
inference(iff_proxy_clausification,[],[f143]) ).
thf(f170,plain,
( ( sF1 = $false )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
@ sK0 )
= $true ) ),
inference(iff_proxy_clausification,[],[f143]) ).
thf(f171,plain,
( ( sF1 = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f172,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
@ X1 )
= $true )
| ( sF1 = $false ) ),
inference(pi_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ X1 @ Y1 ) )
=> ( sK0 @ X1 @ Y0 ) ) ) )
= $true )
| ( sF1 = $false ) ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f174,plain,
! [X2: $i,X1: $i] :
( ( sF1 = $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ X1 @ Y1 ) )
=> ( sK0 @ X1 @ Y0 ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X2 )
& ( sK0 @ X1 @ Y0 ) )
=> ( sK0 @ X1 @ X2 ) ) )
= $true )
| ( sF1 = $false ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X2 )
& ( sK0 @ X1 @ Y0 ) )
=> ( sK0 @ X1 @ X2 ) )
@ X3 )
= $true )
| ( sF1 = $false ) ),
inference(pi_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( ( sK0 @ X3 @ X2 )
& ( sK0 @ X1 @ X3 ) )
=> ( sK0 @ X1 @ X2 ) )
= $true )
| ( sF1 = $false ) ),
inference(beta-eta_normalization,[],[f176]) ).
thf(f178,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( sK0 @ X1 @ X2 )
= $true )
| ( sF1 = $false )
| ( ( ( sK0 @ X3 @ X2 )
& ( sK0 @ X1 @ X3 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF1 = $false )
| ( ( sK0 @ X1 @ X2 )
= $true )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( ( sK0 @ X3 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f178]) ).
thf(f180,plain,
( ( sF1 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f181,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y0 @ Y2 ) )
=> ( sK0 @ Y0 @ Y1 ) ) ) )
@ sK6 )
= $false )
| ( sF1 = $true ) ),
inference(sigma_proxy_clausification,[],[f180]) ).
thf(f182,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ sK6 @ Y1 ) )
=> ( sK0 @ sK6 @ Y0 ) ) ) )
= $false )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f183,plain,
( ( sF1 = $true )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ sK6 @ Y1 ) )
=> ( sK0 @ sK6 @ Y0 ) ) )
@ sK7 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f182]) ).
thf(f184,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK7 )
& ( sK0 @ sK6 @ Y0 ) )
=> ( sK0 @ sK6 @ sK7 ) ) ) )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f183]) ).
thf(f185,plain,
( ( sF1 = $true )
| ( ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK7 )
& ( sK0 @ sK6 @ Y0 ) )
=> ( sK0 @ sK6 @ sK7 ) )
@ sK8 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f184]) ).
thf(f186,plain,
( ( sF1 = $true )
| ( ( ( ( sK0 @ sK8 @ sK7 )
& ( sK0 @ sK6 @ sK8 ) )
=> ( sK0 @ sK6 @ sK7 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f187,plain,
( ( sF1 = $true )
| ( ( sK0 @ sK6 @ sK7 )
= $false ) ),
inference(imp_proxy_clausification,[],[f186]) ).
thf(f188,plain,
( ( sF1 = $true )
| ( ( ( sK0 @ sK8 @ sK7 )
& ( sK0 @ sK6 @ sK8 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f186]) ).
thf(f189,plain,
( ( ( sK0 @ sK6 @ sK8 )
= $true )
| ( sF1 = $true ) ),
inference(and_proxy_clausification,[],[f188]) ).
thf(f190,plain,
( ( ( sK0 @ sK8 @ sK7 )
= $true )
| ( sF1 = $true ) ),
inference(and_proxy_clausification,[],[f188]) ).
thf(f191,plain,
( ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
@ sK0 )
= $false )
| ( sF3 = $true ) ),
inference(iff_proxy_clausification,[],[f146]) ).
thf(f192,plain,
( ( sF3 = $false )
| ( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
@ sK0 )
= $true ) ),
inference(iff_proxy_clausification,[],[f146]) ).
thf(f193,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) ) )
= $true )
| ( sF3 = $false ) ),
inference(beta-eta_normalization,[],[f192]) ).
thf(f194,plain,
! [X1: $i] :
( ( sF3 = $false )
| ( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ X1 @ Y1 ) ) ) )
= $true )
| ( sF3 = $false ) ),
inference(beta-eta_normalization,[],[f194]) ).
thf(f196,plain,
! [X2: $i,X1: $i] :
( ( sF3 = $false )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ X1 @ Y1 ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X2: $i,X1: $i] :
( ( sF3 = $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ X2 @ Y0 )
& ( sK0 @ X2 @ X1 ) )
=> ( sK0 @ X1 @ Y0 ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f196]) ).
thf(f198,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( sF3 = $false )
| ( ( ^ [Y0: $i] :
( ( ( sK0 @ X2 @ Y0 )
& ( sK0 @ X2 @ X1 ) )
=> ( sK0 @ X1 @ Y0 ) )
@ X3 )
= $true ) ),
inference(pi_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( ( sK0 @ X2 @ X3 )
& ( sK0 @ X2 @ X1 ) )
=> ( sK0 @ X1 @ X3 ) )
= $true )
| ( sF3 = $false ) ),
inference(beta-eta_normalization,[],[f198]) ).
thf(f200,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( sK0 @ X1 @ X3 )
= $true )
| ( sF3 = $false )
| ( ( ( sK0 @ X2 @ X3 )
& ( sK0 @ X2 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( sK0 @ X1 @ X3 )
= $true )
| ( sF3 = $false )
| ( ( sK0 @ X2 @ X3 )
= $false )
| ( ( sK0 @ X2 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f200]) ).
thf(f202,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) ) )
= $false )
| ( sF3 = $true ) ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f203,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y1 @ Y2 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y0 @ Y2 ) ) ) )
@ sK9 )
= $false )
| ( sF3 = $true ) ),
inference(sigma_proxy_clausification,[],[f202]) ).
thf(f204,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y0 @ sK9 ) )
=> ( sK0 @ sK9 @ Y1 ) ) ) )
= $false )
| ( sF3 = $true ) ),
inference(beta-eta_normalization,[],[f203]) ).
thf(f205,plain,
( ( sF3 = $true )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK0 @ Y0 @ sK9 ) )
=> ( sK0 @ sK9 @ Y1 ) ) )
@ sK10 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f204]) ).
thf(f206,plain,
( ( sF3 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ sK10 @ Y0 )
& ( sK0 @ sK10 @ sK9 ) )
=> ( sK0 @ sK9 @ Y0 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f205]) ).
thf(f207,plain,
( ( sF3 = $true )
| ( ( ^ [Y0: $i] :
( ( ( sK0 @ sK10 @ Y0 )
& ( sK0 @ sK10 @ sK9 ) )
=> ( sK0 @ sK9 @ Y0 ) )
@ sK11 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f206]) ).
thf(f208,plain,
( ( $false
= ( ( ( sK0 @ sK10 @ sK11 )
& ( sK0 @ sK10 @ sK9 ) )
=> ( sK0 @ sK9 @ sK11 ) ) )
| ( sF3 = $true ) ),
inference(beta-eta_normalization,[],[f207]) ).
thf(f209,plain,
( ( ( sK0 @ sK9 @ sK11 )
= $false )
| ( sF3 = $true ) ),
inference(imp_proxy_clausification,[],[f208]) ).
thf(f210,plain,
( ( ( ( sK0 @ sK10 @ sK11 )
& ( sK0 @ sK10 @ sK9 ) )
= $true )
| ( sF3 = $true ) ),
inference(imp_proxy_clausification,[],[f208]) ).
thf(f211,plain,
( ( ( sK0 @ sK10 @ sK9 )
= $true )
| ( sF3 = $true ) ),
inference(and_proxy_clausification,[],[f210]) ).
thf(f212,plain,
( ( sF3 = $true )
| ( ( sK0 @ sK10 @ sK11 )
= $true ) ),
inference(and_proxy_clausification,[],[f210]) ).
thf(f218,definition,
( spl12_2
<=> ( sF2 = $true ) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
thf(f220,plain,
( ( sF2 = $true )
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f218]) ).
thf(f228,definition,
( spl12_4
<=> ! [X2: $i,X1: $i] :
( ( ( sK0 @ X2 @ X1 )
= $false )
| ( ( sK0 @ X1 @ X2 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
thf(f229,plain,
( ! [X2: $i,X1: $i] :
( ( ( sK0 @ X2 @ X1 )
= $false )
| ( ( sK0 @ X1 @ X2 )
= $true ) )
| ~ spl12_4 ),
inference(avatar_component_clause,[],[f228]) ).
thf(f231,definition,
( spl12_5
<=> ( sF2 = $false ) ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
thf(f233,plain,
( ( sF2 = $false )
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f231]) ).
thf(f234,plain,
( spl12_4
| spl12_5 ),
inference(avatar_split_clause,[],[f166,f231,f228]) ).
thf(f235,plain,
spl12_2,
inference(avatar_split_clause,[],[f167,f218]) ).
thf(f237,definition,
( spl12_6
<=> ( sF1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl12_6])],[avatar_definition]) ).
thf(f238,plain,
( ( sF1 = $true )
| ~ spl12_6 ),
inference(avatar_component_clause,[],[f237]) ).
thf(f241,definition,
( spl12_7
<=> ( sF3 = $true ) ),
introduced(definition,[new_symbols(definition,[spl12_7])],[avatar_definition]) ).
thf(f242,plain,
( ( sF3 = $true )
| ~ spl12_7 ),
inference(avatar_component_clause,[],[f241]) ).
thf(f244,plain,
( ~ spl12_6
| ~ spl12_2
| ~ spl12_7 ),
inference(avatar_split_clause,[],[f168,f241,f218,f237]) ).
thf(f246,plain,
( spl12_6
| spl12_7 ),
inference(avatar_split_clause,[],[f149,f241,f237]) ).
thf(f248,definition,
( spl12_8
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( ( sK0 @ X1 @ X2 )
= $true )
| ( ( sK0 @ X3 @ X2 )
= $false )
| ( ( sK0 @ X1 @ X3 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl12_8])],[avatar_definition]) ).
thf(f249,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( sK0 @ X3 @ X2 )
= $false )
| ( ( sK0 @ X1 @ X3 )
= $false )
| ( ( sK0 @ X1 @ X2 )
= $true ) )
| ~ spl12_8 ),
inference(avatar_component_clause,[],[f248]) ).
thf(f251,definition,
( spl12_9
<=> ( sF1 = $false ) ),
introduced(definition,[new_symbols(definition,[spl12_9])],[avatar_definition]) ).
thf(f253,plain,
( ( sF1 = $false )
| ~ spl12_9 ),
inference(avatar_component_clause,[],[f251]) ).
thf(f254,plain,
( spl12_8
| spl12_9 ),
inference(avatar_split_clause,[],[f179,f251,f248]) ).
thf(f256,definition,
( spl12_10
<=> ( ( sK0 @ sK8 @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl12_10])],[avatar_definition]) ).
thf(f258,plain,
( ( ( sK0 @ sK8 @ sK7 )
= $true )
| ~ spl12_10 ),
inference(avatar_component_clause,[],[f256]) ).
thf(f259,plain,
( spl12_10
| spl12_6 ),
inference(avatar_split_clause,[],[f190,f237,f256]) ).
thf(f261,definition,
( spl12_11
<=> ( ( sK0 @ sK6 @ sK8 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl12_11])],[avatar_definition]) ).
thf(f263,plain,
( ( ( sK0 @ sK6 @ sK8 )
= $true )
| ~ spl12_11 ),
inference(avatar_component_clause,[],[f261]) ).
thf(f264,plain,
( spl12_6
| spl12_11 ),
inference(avatar_split_clause,[],[f189,f261,f237]) ).
thf(f266,definition,
( spl12_12
<=> ( ( sK0 @ sK6 @ sK7 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl12_12])],[avatar_definition]) ).
thf(f268,plain,
( ( ( sK0 @ sK6 @ sK7 )
= $false )
| ~ spl12_12 ),
inference(avatar_component_clause,[],[f266]) ).
thf(f269,plain,
( spl12_6
| spl12_12 ),
inference(avatar_split_clause,[],[f187,f266,f237]) ).
thf(f272,definition,
( spl12_13
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( ( sK0 @ X1 @ X3 )
= $true )
| ( ( sK0 @ X2 @ X1 )
= $false )
| ( ( sK0 @ X2 @ X3 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl12_13])],[avatar_definition]) ).
thf(f273,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( ( sK0 @ X2 @ X3 )
= $false )
| ( ( sK0 @ X2 @ X1 )
= $false )
| ( ( sK0 @ X1 @ X3 )
= $true ) )
| ~ spl12_13 ),
inference(avatar_component_clause,[],[f272]) ).
thf(f275,definition,
( spl12_14
<=> ( sF3 = $false ) ),
introduced(definition,[new_symbols(definition,[spl12_14])],[avatar_definition]) ).
thf(f277,plain,
( ( sF3 = $false )
| ~ spl12_14 ),
inference(avatar_component_clause,[],[f275]) ).
thf(f278,plain,
( spl12_13
| spl12_14 ),
inference(avatar_split_clause,[],[f201,f275,f272]) ).
thf(f280,definition,
( spl12_15
<=> ( ( sK0 @ sK10 @ sK11 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl12_15])],[avatar_definition]) ).
thf(f282,plain,
( ( ( sK0 @ sK10 @ sK11 )
= $true )
| ~ spl12_15 ),
inference(avatar_component_clause,[],[f280]) ).
thf(f283,plain,
( spl12_7
| spl12_15 ),
inference(avatar_split_clause,[],[f212,f280,f241]) ).
thf(f285,definition,
( spl12_16
<=> ( ( sK0 @ sK10 @ sK9 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl12_16])],[avatar_definition]) ).
thf(f287,plain,
( ( ( sK0 @ sK10 @ sK9 )
= $true )
| ~ spl12_16 ),
inference(avatar_component_clause,[],[f285]) ).
thf(f288,plain,
( spl12_16
| spl12_7 ),
inference(avatar_split_clause,[],[f211,f241,f285]) ).
thf(f290,definition,
( spl12_17
<=> ( ( sK0 @ sK9 @ sK11 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl12_17])],[avatar_definition]) ).
thf(f292,plain,
( ( ( sK0 @ sK9 @ sK11 )
= $false )
| ~ spl12_17 ),
inference(avatar_component_clause,[],[f290]) ).
thf(f293,plain,
( spl12_7
| spl12_17 ),
inference(avatar_split_clause,[],[f209,f290,f241]) ).
thf(f310,plain,
( ( ( sK0 @ sK8 @ sK6 )
= $true )
| ( $false = $true )
| ~ spl12_4
| ~ spl12_11 ),
inference(constrained_superposition,[],[f229,f263]) ).
thf(f318,plain,
( ( ( sK0 @ sK8 @ sK6 )
= $true )
| ~ spl12_4
| ~ spl12_11 ),
inference(trivial_inequality_removal,[],[f310]) ).
thf(f371,plain,
( ! [X0: $i] :
( ( ( sK0 @ sK8 @ X0 )
= $false )
| ( $false = $true )
| ( ( sK0 @ X0 @ sK7 )
= $true ) )
| ~ spl12_10
| ~ spl12_13 ),
inference(constrained_superposition,[],[f258,f273]) ).
thf(f376,plain,
( ! [X0: $i] :
( ( ( sK0 @ sK8 @ X0 )
= $false )
| ( ( sK0 @ X0 @ sK7 )
= $true ) )
| ~ spl12_10
| ~ spl12_13 ),
inference(trivial_inequality_removal,[],[f371]) ).
thf(f433,plain,
( ( $false = $true )
| ( ( sK0 @ sK6 @ sK7 )
= $true )
| ~ spl12_4
| ~ spl12_10
| ~ spl12_11
| ~ spl12_13 ),
inference(constrained_superposition,[],[f318,f376]) ).
thf(f439,plain,
( ( ( sK0 @ sK6 @ sK7 )
= $true )
| ~ spl12_4
| ~ spl12_10
| ~ spl12_11
| ~ spl12_13 ),
inference(trivial_inequality_removal,[],[f433]) ).
thf(f446,plain,
( ( $false = $true )
| ~ spl12_4
| ~ spl12_10
| ~ spl12_11
| ~ spl12_12
| ~ spl12_13 ),
inference(forward_demodulation,[],[f439,f268]) ).
thf(f447,plain,
( $false
| ~ spl12_4
| ~ spl12_10
| ~ spl12_11
| ~ spl12_12
| ~ spl12_13 ),
inference(trivial_inequality_removal,[],[f446]) ).
thf(f448,plain,
( ~ spl12_4
| ~ spl12_10
| ~ spl12_11
| ~ spl12_12
| ~ spl12_13 ),
inference(avatar_contradiction_clause,[],[f447]) ).
thf(f449,plain,
( ( $false = $true )
| ~ spl12_7
| ~ spl12_14 ),
inference(forward_demodulation,[],[f277,f242]) ).
thf(f450,plain,
( $false
| ~ spl12_7
| ~ spl12_14 ),
inference(trivial_inequality_removal,[],[f449]) ).
thf(f451,plain,
( ~ spl12_7
| ~ spl12_14 ),
inference(avatar_contradiction_clause,[],[f450]) ).
thf(f452,plain,
( ( $false = $true )
| ~ spl12_2
| ~ spl12_5 ),
inference(forward_demodulation,[],[f233,f220]) ).
thf(f453,plain,
( $false
| ~ spl12_2
| ~ spl12_5 ),
inference(trivial_inequality_removal,[],[f452]) ).
thf(f454,plain,
( ~ spl12_2
| ~ spl12_5 ),
inference(avatar_contradiction_clause,[],[f453]) ).
thf(f456,plain,
( ( $false = $true )
| ~ spl12_6
| ~ spl12_9 ),
inference(forward_demodulation,[],[f238,f253]) ).
thf(f457,plain,
( $false
| ~ spl12_6
| ~ spl12_9 ),
inference(trivial_inequality_removal,[],[f456]) ).
thf(f458,plain,
( ~ spl12_6
| ~ spl12_9 ),
inference(avatar_contradiction_clause,[],[f457]) ).
thf(f475,plain,
( ( ( sK0 @ sK9 @ sK10 )
= $true )
| ( $false = $true )
| ~ spl12_4
| ~ spl12_16 ),
inference(constrained_superposition,[],[f229,f287]) ).
thf(f483,plain,
( ( ( sK0 @ sK9 @ sK10 )
= $true )
| ~ spl12_4
| ~ spl12_16 ),
inference(trivial_inequality_removal,[],[f475]) ).
thf(f492,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 @ sK10 )
= $false )
| ( ( sK0 @ X0 @ sK11 )
= $true )
| ( $false = $true ) )
| ~ spl12_8
| ~ spl12_15 ),
inference(constrained_superposition,[],[f249,f282]) ).
thf(f500,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 @ sK11 )
= $true )
| ( ( sK0 @ X0 @ sK10 )
= $false ) )
| ~ spl12_8
| ~ spl12_15 ),
inference(trivial_inequality_removal,[],[f492]) ).
thf(f532,plain,
( ( $false = $true )
| ( ( sK0 @ sK9 @ sK10 )
= $false )
| ~ spl12_8
| ~ spl12_15
| ~ spl12_17 ),
inference(constrained_superposition,[],[f500,f292]) ).
thf(f541,plain,
( ( ( sK0 @ sK9 @ sK10 )
= $false )
| ~ spl12_8
| ~ spl12_15
| ~ spl12_17 ),
inference(trivial_inequality_removal,[],[f532]) ).
thf(f547,plain,
( ( $false = $true )
| ~ spl12_4
| ~ spl12_8
| ~ spl12_15
| ~ spl12_16
| ~ spl12_17 ),
inference(forward_demodulation,[],[f541,f483]) ).
thf(f548,plain,
( $false
| ~ spl12_4
| ~ spl12_8
| ~ spl12_15
| ~ spl12_16
| ~ spl12_17 ),
inference(trivial_inequality_removal,[],[f547]) ).
thf(f549,plain,
( ~ spl12_4
| ~ spl12_8
| ~ spl12_15
| ~ spl12_16
| ~ spl12_17 ),
inference(avatar_contradiction_clause,[],[f548]) ).
cnf(s3,plain,
( spl12_4
| spl12_5 ),
inference(sat_conversion,[],[f234]) ).
cnf(s4,plain,
spl12_2,
inference(sat_conversion,[],[f235]) ).
cnf(s5,plain,
( ~ spl12_2
| ~ spl12_6
| ~ spl12_7 ),
inference(sat_conversion,[],[f244]) ).
cnf(s7,plain,
( spl12_6
| spl12_7 ),
inference(sat_conversion,[],[f246]) ).
cnf(s8,plain,
( spl12_8
| spl12_9 ),
inference(sat_conversion,[],[f254]) ).
cnf(s9,plain,
( spl12_6
| spl12_10 ),
inference(sat_conversion,[],[f259]) ).
cnf(s10,plain,
( spl12_6
| spl12_11 ),
inference(sat_conversion,[],[f264]) ).
cnf(s11,plain,
( spl12_6
| spl12_12 ),
inference(sat_conversion,[],[f269]) ).
cnf(s13,plain,
( spl12_13
| spl12_14 ),
inference(sat_conversion,[],[f278]) ).
cnf(s14,plain,
( spl12_7
| spl12_15 ),
inference(sat_conversion,[],[f283]) ).
cnf(s15,plain,
( spl12_7
| spl12_16 ),
inference(sat_conversion,[],[f288]) ).
cnf(s16,plain,
( spl12_7
| spl12_17 ),
inference(sat_conversion,[],[f293]) ).
cnf(s21,plain,
( ~ spl12_4
| ~ spl12_10
| ~ spl12_11
| ~ spl12_12
| ~ spl12_13 ),
inference(sat_conversion,[],[f448]) ).
cnf(s22,plain,
( ~ spl12_7
| ~ spl12_14 ),
inference(sat_conversion,[],[f451]) ).
cnf(s23,plain,
( ~ spl12_2
| ~ spl12_5 ),
inference(sat_conversion,[],[f454]) ).
cnf(s24,plain,
( ~ spl12_6
| ~ spl12_9 ),
inference(sat_conversion,[],[f458]) ).
cnf(s27,plain,
( ~ spl12_4
| ~ spl12_8
| ~ spl12_15
| ~ spl12_16
| ~ spl12_17 ),
inference(sat_conversion,[],[f549]) ).
cnf(s28,plain,
~ spl12_5,
inference(rat,[],[s23,s4]) ).
cnf(s29,plain,
spl12_4,
inference(rat,[],[s3,s28]) ).
cnf(s30,plain,
spl12_6,
inference(rat,[],[s13,s22,s21,s7,s9,s10,s11,s29]) ).
cnf(s31,plain,
~ spl12_9,
inference(rat,[],[s24,s30]) ).
cnf(s32,plain,
~ spl12_7,
inference(rat,[],[s5,s4,s30]) ).
cnf(s33,plain,
spl12_8,
inference(rat,[],[s8,s31]) ).
cnf(s35,plain,
spl12_17,
inference(rat,[],[s16,s32]) ).
cnf(s36,plain,
spl12_16,
inference(rat,[],[s15,s32]) ).
cnf(s37,plain,
spl12_15,
inference(rat,[],[s14,s32]) ).
cnf(s38,plain,
$false,
inference(rat,[],[s27,s35,s36,s29,s37,s33]) ).
thf(f550,plain,
$false,
inference(avatar_sat_refutation,[],[s38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL867^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n018.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 10:18:11 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.25 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
% 0.22/0.34 % (4086792)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.34 % (4086798)lrs+10_16_si=on:nwc=1.5:random_seed=202099395:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.34 % (4086803)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.34 % (4086803)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
% 0.22/0.34 % (4086798)Instruction limit reached!
% 0.22/0.34 % (4086798)------------------------------
% 0.22/0.34 % (4086798)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (4086798)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (4086798)CaDiCaL version: 2.1.3
% 0.22/0.34 % (4086798)Termination reason: Instruction limit
% 0.22/0.34 % (4086798)Termination phase: Saturation
% 0.22/0.34 % (4086798)Time elapsed: 0.009 s
% 0.22/0.34 % (4086798)Peak memory usage: 12 MB
% 0.22/0.34 % (4086798)Instructions burned: 19 (million)
% 0.22/0.34 % (4086802)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=722672469:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.34 % (4086799)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3578306736:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.34 % (4086801)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3856697515:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.34 % (4086797)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3573007197:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.34 % (4086800)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=818897660: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)
% 0.22/0.34 % (4086803)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=3716011189:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.34 % (4086799)Instruction limit reached!
% 0.22/0.34 % (4086799)------------------------------
% 0.22/0.34 % (4086799)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (4086799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (4086799)CaDiCaL version: 2.1.3
% 0.22/0.34 % (4086799)Termination reason: Instruction limit
% 0.22/0.34 % (4086799)Termination phase: Property scanning
% 0.22/0.34 % (4086799)Time elapsed: 0.003 s
% 0.22/0.34 % (4086799)Peak memory usage: 9 MB
% 0.22/0.34 % (4086799)Instructions burned: 3 (million)
% 0.22/0.34 % (4086805)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2784913222:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.34 % (4086805)Instruction limit reached!
% 0.22/0.34 % (4086805)------------------------------
% 0.22/0.34 % (4086805)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (4086805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (4086805)CaDiCaL version: 2.1.3
% 0.22/0.34 % (4086805)Termination reason: Instruction limit
% 0.22/0.34 % (4086805)Termination phase: Function definition elimination
% 0.22/0.34 % (4086805)Time elapsed: 0.003 s
% 0.22/0.34 % (4086805)Peak memory usage: 10 MB
% 0.22/0.34 % (4086805)Instructions burned: 6 (million)
% 0.22/0.34 % (4086803) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4086792-4086803"...
% 0.22/0.34 % (4086801)Instruction limit reached!
% 0.22/0.34 % (4086801)------------------------------
% 0.22/0.34 % (4086801)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (4086801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (4086801)CaDiCaL version: 2.1.3
% 0.22/0.34 % (4086801)Termination reason: Instruction limit
% 0.22/0.34 % (4086801)Termination phase: Saturation
% 0.22/0.34 % (4086801)Time elapsed: 0.024 s
% 0.22/0.34 % (4086801)Peak memory usage: 11 MB
% 0.22/0.34 % (4086801)Instructions burned: 24 (million)
% 0.22/0.34 % (4086803)...printing done.
% 0.22/0.34 % (4086803)Refutation found. Thanks to Tanya!
% 0.22/0.34 % SZS status Theorem for theBenchmark
% 0.22/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.34 % (4086803)------------------------------
% 0.22/0.34 % (4086803)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.34 % (4086803)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.34 % (4086803)CaDiCaL version: 2.1.3
% 0.22/0.34 % (4086803)Termination reason: Refutation
% 0.22/0.34 % (4086803)Time elapsed: 0.028 s
% 0.22/0.34 % (4086803)Peak memory usage: 13 MB
% 0.22/0.34 % (4086803)Instructions burned: 29 (million)
% 0.22/0.34 % (4086792)Success in time 0.083 s
% 0.22/0.34 % Vampire exiting
%------------------------------------------------------------------------------