%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL861^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n020.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 08:15:11 AM UTC 2026
% Result : Theorem 0.20s 0.33s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 13
% Syntax : Number of formulae : 150 ( 37 unt; 0 typ; 9 def)
% Number of atoms : 1271 ( 228 equ; 0 cnn)
% Maximal formula atoms : 10 ( 8 avg)
% Number of connectives : 1377 ( 109 ~; 220 |; 81 &; 816 @)
% ( 13 <=>; 49 =>; 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 : 66 ( 62 usr; 19 con; 0-4 aty)
% ( 88 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 197 ( 0 sgn 64 !; 3 ?; 197 :)
% 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,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_35,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_36,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
vNOT: $o > $o ).
thf(func_def_38,type,
vOR: $o > $o > $o ).
thf(func_def_39,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vIMP: $o > $o > $o ).
thf(func_def_44,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_45,type,
vAND: $o > $o > $o ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
sK0: $i > $i > $o ).
thf(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f22,axiom,
( meuclidean
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',meuclidean) ).
thf(f32,conjecture,
! [X0: $i > $i > $o] :
( ( ( meuclidean @ X0 )
& ( mreflexive @ X0 ) )
<=> ( ( meuclidean @ X0 )
& ( mtransitive @ X0 )
& ( mreflexive @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o] :
( ( ( meuclidean @ X0 )
& ( mreflexive @ X0 ) )
<=> ( ( meuclidean @ X0 )
& ( mtransitive @ X0 )
& ( mreflexive @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f57,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f58,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f63,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f64,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f65,plain,
( meuclidean
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f22]) ).
thf(f66,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f65]) ).
thf(f85,plain,
~ ! [X0: $i > $i > $o] :
( ( ( meuclidean @ X0 )
& ( mreflexive @ X0 ) )
<=> ( ( meuclidean @ X0 )
& ( mtransitive @ X0 )
& ( mreflexive @ X0 ) ) ),
inference(rectify,[],[f33]) ).
thf(f86,plain,
~ ! [X0: $i > $i > $o] :
( ( ( ( meuclidean @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) )
<=> ( ( ( meuclidean @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) ) ),
inference(fool_elimination,[],[f85]) ).
thf(f87,plain,
? [X0: $i > $i > $o] :
( ( ( ( meuclidean @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) )
<~> ( ( ( meuclidean @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) ) ),
inference(ennf_transformation,[],[f86]) ).
thf(f88,plain,
? [X0: $i > $i > $o] :
( ( ( ( meuclidean @ X0 )
!= $true )
| ( ( mtransitive @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true ) )
& ( ( ( ( meuclidean @ X0 )
= $true )
& ( ( mtransitive @ 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 )
| ( ( mtransitive @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true )
| ( ( meuclidean @ X0 )
!= $true )
| ( ( mreflexive @ X0 )
!= $true ) )
& ( ( ( ( meuclidean @ X0 )
= $true )
& ( ( mtransitive @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) )
| ( ( ( meuclidean @ X0 )
= $true )
& ( ( mreflexive @ X0 )
= $true ) ) ) ),
inference(flattening,[],[f88]) ).
thf(f90,plain,
( ( ( $true
!= ( meuclidean @ sK0 ) )
| ( $true
!= ( mtransitive @ sK0 ) )
| ( $true
!= ( mreflexive @ sK0 ) )
| ( $true
!= ( meuclidean @ sK0 ) )
| ( $true
!= ( mreflexive @ sK0 ) ) )
& ( ( ( $true
= ( meuclidean @ sK0 ) )
& ( $true
= ( mtransitive @ sK0 ) )
& ( $true
= ( mreflexive @ sK0 ) ) )
| ( ( $true
= ( meuclidean @ sK0 ) )
& ( $true
= ( mreflexive @ sK0 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f89]) ).
thf(f108,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f111,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f112,plain,
( meuclidean
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f122,plain,
( ( $true
= ( mreflexive @ sK0 ) )
| ( $true
= ( mreflexive @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f127,plain,
( ( $true
= ( meuclidean @ sK0 ) )
| ( $true
= ( meuclidean @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f128,plain,
( ( $true
!= ( meuclidean @ sK0 ) )
| ( $true
!= ( mtransitive @ sK0 ) )
| ( $true
!= ( mreflexive @ sK0 ) )
| ( $true
!= ( meuclidean @ sK0 ) )
| ( $true
!= ( mreflexive @ sK0 ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f140,plain,
( ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ sK0 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK0 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ sK0 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f128,f112,f111,f108,f112,f108]) ).
thf(f141,plain,
( ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ sK0 ) )
| ( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ sK0 ) ) ),
inference(definition_unfolding,[],[f127,f112,f112]) ).
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,[],[f122,f108,f108]) ).
thf(f147,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) ),
inference(duplicate_literal_removal,[],[f146]) ).
thf(f148,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f149,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f148]) ).
thf(f150,plain,
! [X1: $i] :
( $true
= ( sK0 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f195,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ sK0 ) ),
inference(duplicate_literal_removal,[],[f141]) ).
thf(f196,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f195]) ).
thf(f197,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f197]) ).
thf(f199,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ X1 ) )
=> ( sK0 @ Y0 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X2 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f199]) ).
thf(f201,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ X2 )
& ( sK0 @ Y0 @ X1 ) )
=> ( sK0 @ X2 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( sK0 @ X3 @ X2 )
& ( sK0 @ X3 @ X1 ) )
=> ( sK0 @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f201]) ).
thf(f203,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( sK0 @ X3 @ X2 )
& ( sK0 @ X3 @ X1 ) ) )
| ( $true
= ( sK0 @ X2 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $true
= ( sK0 @ X2 @ X1 ) )
| ( $false
= ( sK0 @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f203]) ).
thf(f205,plain,
( ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ sK0 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ sK0 ) )
| ( $true
!= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ sK0 ) ) ),
inference(duplicate_literal_removal,[],[f140]) ).
thf(f206,plain,
( ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f205]) ).
thf(f207,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
@ sK1 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(sigma_proxy_clausification,[],[f206]) ).
thf(f208,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK2 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(sigma_proxy_clausification,[],[f207]) ).
thf(f209,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y2 @ Y0 ) )
=> ( sK0 @ Y1 @ Y0 ) ) ) )
@ sK1 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK0 @ Y2 @ Y1 )
& ( sK0 @ Y1 @ Y0 ) )
=> ( sK0 @ Y2 @ Y0 ) ) ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] : ( sK0 @ Y0 @ Y0 )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f208]) ).
thf(f210,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ sK1 ) )
=> ( sK0 @ Y0 @ sK1 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK2 ) )
=> ( sK0 @ Y1 @ sK2 ) ) ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f209]) ).
thf(f211,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ sK1 ) )
=> ( sK0 @ Y0 @ sK1 ) ) )
@ sK4 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK2 ) )
=> ( sK0 @ Y1 @ sK2 ) ) ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f210]) ).
thf(f212,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y1 @ sK1 ) )
=> ( sK0 @ Y0 @ sK1 ) ) )
@ sK4 ) )
| ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK0 @ Y0 @ sK2 ) )
=> ( sK0 @ Y1 @ sK2 ) ) )
@ sK5 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f211]) ).
thf(f213,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK4 )
& ( sK0 @ Y0 @ sK1 ) )
=> ( sK0 @ sK4 @ sK1 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK5 @ sK2 ) )
=> ( sK0 @ Y0 @ sK2 ) ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f212]) ).
thf(f214,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK4 )
& ( sK0 @ Y0 @ sK1 ) )
=> ( sK0 @ sK4 @ sK1 ) )
@ sK6 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK5 @ sK2 ) )
=> ( sK0 @ Y0 @ sK2 ) ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f213]) ).
thf(f215,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK4 )
& ( sK0 @ Y0 @ sK1 ) )
=> ( sK0 @ sK4 @ sK1 ) )
@ sK6 ) )
| ( $false
= ( ^ [Y0: $i] :
( ( ( sK0 @ Y0 @ sK5 )
& ( sK0 @ sK5 @ sK2 ) )
=> ( sK0 @ Y0 @ sK2 ) )
@ sK7 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f214]) ).
thf(f216,plain,
( ( $false
= ( ( ( sK0 @ sK6 @ sK4 )
& ( sK0 @ sK6 @ sK1 ) )
=> ( sK0 @ sK4 @ sK1 ) ) )
| ( $false
= ( ( ( sK0 @ sK7 @ sK5 )
& ( sK0 @ sK5 @ sK2 ) )
=> ( sK0 @ sK7 @ sK2 ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(beta-eta_normalization,[],[f215]) ).
thf(f217,plain,
( ( $false
= ( sK0 @ sK4 @ sK1 ) )
| ( $false
= ( ( ( sK0 @ sK7 @ sK5 )
& ( sK0 @ sK5 @ sK2 ) )
=> ( sK0 @ sK7 @ sK2 ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f216]) ).
thf(f218,plain,
( ( $true
= ( ( sK0 @ sK6 @ sK4 )
& ( sK0 @ sK6 @ sK1 ) ) )
| ( $false
= ( ( ( sK0 @ sK7 @ sK5 )
& ( sK0 @ sK5 @ sK2 ) )
=> ( sK0 @ sK7 @ sK2 ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f216]) ).
thf(f219,plain,
( ( $true
= ( sK0 @ sK6 @ sK1 ) )
| ( $false
= ( ( ( sK0 @ sK7 @ sK5 )
& ( sK0 @ sK5 @ sK2 ) )
=> ( sK0 @ sK7 @ sK2 ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f218]) ).
thf(f220,plain,
( ( $true
= ( sK0 @ sK6 @ sK4 ) )
| ( $false
= ( ( ( sK0 @ sK7 @ sK5 )
& ( sK0 @ sK5 @ sK2 ) )
=> ( sK0 @ sK7 @ sK2 ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f218]) ).
thf(f221,plain,
( ( $true
= ( sK0 @ sK6 @ sK4 ) )
| ( $false
= ( sK0 @ sK7 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f220]) ).
thf(f222,plain,
( ( $true
= ( sK0 @ sK6 @ sK4 ) )
| ( $true
= ( ( sK0 @ sK7 @ sK5 )
& ( sK0 @ sK5 @ sK2 ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f220]) ).
thf(f223,plain,
( ( $true
= ( sK0 @ sK6 @ sK4 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f222]) ).
thf(f224,plain,
( ( $true
= ( sK0 @ sK6 @ sK4 ) )
| ( $true
= ( sK0 @ sK7 @ sK5 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f222]) ).
thf(f225,plain,
( ( $true
= ( sK0 @ sK6 @ sK1 ) )
| ( $false
= ( sK0 @ sK7 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f219]) ).
thf(f226,plain,
( ( $true
= ( sK0 @ sK6 @ sK1 ) )
| ( $true
= ( ( sK0 @ sK7 @ sK5 )
& ( sK0 @ sK5 @ sK2 ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f219]) ).
thf(f227,plain,
( ( $true
= ( sK0 @ sK6 @ sK1 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f226]) ).
thf(f228,plain,
( ( $true
= ( sK0 @ sK6 @ sK1 ) )
| ( $true
= ( sK0 @ sK7 @ sK5 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f226]) ).
thf(f229,plain,
( ( $false
= ( sK0 @ sK4 @ sK1 ) )
| ( $false
= ( sK0 @ sK7 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f217]) ).
thf(f230,plain,
( ( $false
= ( sK0 @ sK4 @ sK1 ) )
| ( $true
= ( ( sK0 @ sK7 @ sK5 )
& ( sK0 @ sK5 @ sK2 ) ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f217]) ).
thf(f231,plain,
( ( $false
= ( sK0 @ sK4 @ sK1 ) )
| ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f230]) ).
thf(f232,plain,
( ( $false
= ( sK0 @ sK4 @ sK1 ) )
| ( $true
= ( sK0 @ sK7 @ sK5 ) )
| ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f230]) ).
thf(f234,definition,
( spl8_1
<=> ! [X6: $i,X2: $i,X4: $i] :
( ( $false
= ( sK0 @ X6 @ X2 ) )
| ( $false
= ( sK0 @ X6 @ X4 ) )
| ( $true
= ( sK0 @ X4 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
thf(f235,plain,
( ! [X2: $i,X6: $i,X4: $i] :
( ( $false
= ( sK0 @ X6 @ X2 ) )
| ( $false
= ( sK0 @ X6 @ X4 ) )
| ( $true
= ( sK0 @ X4 @ X2 ) ) )
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f234]) ).
thf(f237,definition,
( spl8_2
<=> ! [X5: $i,X1: $i,X3: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X5 @ X3 ) )
| ( $true
= ( sK0 @ X5 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
thf(f238,plain,
( ! [X3: $i,X1: $i,X5: $i] :
( ( $false
= ( sK0 @ X3 @ X1 ) )
| ( $false
= ( sK0 @ X5 @ X3 ) )
| ( $true
= ( sK0 @ X5 @ X1 ) ) )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f237]) ).
thf(f240,plain,
spl8_1,
inference(avatar_split_clause,[],[f204,f234]) ).
thf(f242,definition,
( spl8_3
<=> ( $false
= ( sK0 @ sK3 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
thf(f244,plain,
( ( $false
= ( sK0 @ sK3 @ sK3 ) )
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f242]) ).
thf(f246,definition,
( spl8_4
<=> ( $true
= ( sK0 @ sK7 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
thf(f248,plain,
( ( $true
= ( sK0 @ sK7 @ sK5 ) )
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f246]) ).
thf(f250,definition,
( spl8_5
<=> ( $true
= ( sK0 @ sK6 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition]) ).
thf(f252,plain,
( ( $true
= ( sK0 @ sK6 @ sK4 ) )
| ~ spl8_5 ),
inference(avatar_component_clause,[],[f250]) ).
thf(f253,plain,
( spl8_3
| spl8_4
| spl8_5 ),
inference(avatar_split_clause,[],[f224,f250,f246,f242]) ).
thf(f255,definition,
( spl8_6
<=> ( $true
= ( sK0 @ sK5 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_6])],[avatar_definition]) ).
thf(f257,plain,
( ( $true
= ( sK0 @ sK5 @ sK2 ) )
| ~ spl8_6 ),
inference(avatar_component_clause,[],[f255]) ).
thf(f258,plain,
( spl8_3
| spl8_6
| spl8_5 ),
inference(avatar_split_clause,[],[f223,f250,f255,f242]) ).
thf(f260,definition,
( spl8_7
<=> ( $false
= ( sK0 @ sK7 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_7])],[avatar_definition]) ).
thf(f262,plain,
( ( $false
= ( sK0 @ sK7 @ sK2 ) )
| ~ spl8_7 ),
inference(avatar_component_clause,[],[f260]) ).
thf(f263,plain,
( spl8_3
| spl8_7
| spl8_5 ),
inference(avatar_split_clause,[],[f221,f250,f260,f242]) ).
thf(f265,definition,
( spl8_8
<=> ( $true
= ( sK0 @ sK6 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_8])],[avatar_definition]) ).
thf(f267,plain,
( ( $true
= ( sK0 @ sK6 @ sK1 ) )
| ~ spl8_8 ),
inference(avatar_component_clause,[],[f265]) ).
thf(f268,plain,
( spl8_3
| spl8_4
| spl8_8 ),
inference(avatar_split_clause,[],[f228,f265,f246,f242]) ).
thf(f269,plain,
( spl8_3
| spl8_6
| spl8_8 ),
inference(avatar_split_clause,[],[f227,f265,f255,f242]) ).
thf(f270,plain,
( spl8_3
| spl8_7
| spl8_8 ),
inference(avatar_split_clause,[],[f225,f265,f260,f242]) ).
thf(f272,definition,
( spl8_9
<=> ( $false
= ( sK0 @ sK4 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition]) ).
thf(f274,plain,
( ( $false
= ( sK0 @ sK4 @ sK1 ) )
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f272]) ).
thf(f275,plain,
( spl8_3
| spl8_4
| spl8_9 ),
inference(avatar_split_clause,[],[f232,f272,f246,f242]) ).
thf(f276,plain,
( spl8_3
| spl8_6
| spl8_9 ),
inference(avatar_split_clause,[],[f231,f272,f255,f242]) ).
thf(f277,plain,
( spl8_3
| spl8_7
| spl8_9 ),
inference(avatar_split_clause,[],[f229,f272,f260,f242]) ).
thf(f278,plain,
( ( $true = $false )
| ~ spl8_3 ),
inference(constrained_superposition,[],[f244,f150]) ).
thf(f282,plain,
( $false
| ~ spl8_3 ),
inference(trivial_inequality_removal,[],[f278]) ).
thf(f283,plain,
~ spl8_3,
inference(avatar_contradiction_clause,[],[f282]) ).
thf(f296,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $true
= ( sK0 @ X1 @ X0 ) ) )
| ~ spl8_1 ),
inference(constrained_superposition,[],[f150,f235]) ).
thf(f311,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK1 ) )
| ( $false
= ( sK0 @ X0 @ sK4 ) ) )
| ~ spl8_1
| ~ spl8_9 ),
inference(constrained_superposition,[],[f274,f235]) ).
thf(f324,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK4 ) )
| ( $false
= ( sK0 @ X0 @ sK1 ) ) )
| ~ spl8_1
| ~ spl8_9 ),
inference(trivial_inequality_removal,[],[f311]) ).
thf(f335,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X0 @ X1 ) )
| ( $true
= ( sK0 @ X1 @ X0 ) ) )
| ~ spl8_1 ),
inference(trivial_inequality_removal,[],[f296]) ).
thf(f361,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ X2 ) )
| ( $true
= ( sK0 @ X1 @ X2 ) )
| ( $false
= ( sK0 @ X1 @ X0 ) ) )
| ~ spl8_1 ),
inference(constrained_superposition,[],[f235,f335]) ).
thf(f373,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK0 @ X0 @ X2 ) )
| ( $true
= ( sK0 @ X1 @ X2 ) )
| ( $false
= ( sK0 @ X1 @ X0 ) ) )
| ~ spl8_1 ),
inference(trivial_inequality_removal,[],[f361]) ).
thf(f386,plain,
( spl8_2
| ~ spl8_1 ),
inference(avatar_split_clause,[],[f373,f234,f237]) ).
thf(f528,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK6 @ sK1 ) )
| ~ spl8_1
| ~ spl8_5
| ~ spl8_9 ),
inference(constrained_superposition,[],[f252,f324]) ).
thf(f529,plain,
( ( $false
= ( sK0 @ sK6 @ sK1 ) )
| ~ spl8_1
| ~ spl8_5
| ~ spl8_9 ),
inference(trivial_inequality_removal,[],[f528]) ).
thf(f542,plain,
( ( $true = $false )
| ~ spl8_1
| ~ spl8_5
| ~ spl8_8
| ~ spl8_9 ),
inference(constrained_superposition,[],[f529,f267]) ).
thf(f552,plain,
( $false
| ~ spl8_1
| ~ spl8_5
| ~ spl8_8
| ~ spl8_9 ),
inference(trivial_inequality_removal,[],[f542]) ).
thf(f553,plain,
( ~ spl8_1
| ~ spl8_5
| ~ spl8_8
| ~ spl8_9 ),
inference(avatar_contradiction_clause,[],[f552]) ).
thf(f561,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( sK0 @ X0 @ sK2 ) )
| ( $false
= ( sK0 @ sK7 @ X0 ) ) )
| ~ spl8_2
| ~ spl8_7 ),
inference(constrained_superposition,[],[f238,f262]) ).
thf(f564,plain,
( ! [X0: $i] :
( ( $false
= ( sK0 @ X0 @ sK2 ) )
| ( $false
= ( sK0 @ sK7 @ X0 ) ) )
| ~ spl8_2
| ~ spl8_7 ),
inference(trivial_inequality_removal,[],[f561]) ).
thf(f669,plain,
( ( $true = $false )
| ( $false
= ( sK0 @ sK5 @ sK2 ) )
| ~ spl8_2
| ~ spl8_4
| ~ spl8_7 ),
inference(constrained_superposition,[],[f248,f564]) ).
thf(f670,plain,
( ( $false
= ( sK0 @ sK5 @ sK2 ) )
| ~ spl8_2
| ~ spl8_4
| ~ spl8_7 ),
inference(trivial_inequality_removal,[],[f669]) ).
thf(f689,plain,
( ( $true = $false )
| ~ spl8_2
| ~ spl8_4
| ~ spl8_6
| ~ spl8_7 ),
inference(constrained_superposition,[],[f670,f257]) ).
thf(f699,plain,
( $false
| ~ spl8_2
| ~ spl8_4
| ~ spl8_6
| ~ spl8_7 ),
inference(trivial_inequality_removal,[],[f689]) ).
thf(f700,plain,
( ~ spl8_2
| ~ spl8_4
| ~ spl8_6
| ~ spl8_7 ),
inference(avatar_contradiction_clause,[],[f699]) ).
cnf(s2,plain,
spl8_1,
inference(sat_conversion,[],[f240]) ).
cnf(s3,plain,
( spl8_3
| spl8_4
| spl8_5 ),
inference(sat_conversion,[],[f253]) ).
cnf(s4,plain,
( spl8_3
| spl8_5
| spl8_6 ),
inference(sat_conversion,[],[f258]) ).
cnf(s5,plain,
( spl8_3
| spl8_5
| spl8_7 ),
inference(sat_conversion,[],[f263]) ).
cnf(s6,plain,
( spl8_3
| spl8_4
| spl8_8 ),
inference(sat_conversion,[],[f268]) ).
cnf(s7,plain,
( spl8_3
| spl8_6
| spl8_8 ),
inference(sat_conversion,[],[f269]) ).
cnf(s8,plain,
( spl8_3
| spl8_7
| spl8_8 ),
inference(sat_conversion,[],[f270]) ).
cnf(s9,plain,
( spl8_3
| spl8_4
| spl8_9 ),
inference(sat_conversion,[],[f275]) ).
cnf(s10,plain,
( spl8_3
| spl8_6
| spl8_9 ),
inference(sat_conversion,[],[f276]) ).
cnf(s11,plain,
( spl8_3
| spl8_7
| spl8_9 ),
inference(sat_conversion,[],[f277]) ).
cnf(s13,plain,
~ spl8_3,
inference(sat_conversion,[],[f283]) ).
cnf(s14,plain,
( ~ spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f386]) ).
cnf(s17,plain,
( ~ spl8_1
| ~ spl8_5
| ~ spl8_8
| ~ spl8_9 ),
inference(sat_conversion,[],[f553]) ).
cnf(s19,plain,
( ~ spl8_2
| ~ spl8_4
| ~ spl8_6
| ~ spl8_7 ),
inference(sat_conversion,[],[f700]) ).
cnf(s20,plain,
( spl8_7
| spl8_9 ),
inference(rat,[],[s11,s13]) ).
cnf(s21,plain,
( spl8_6
| spl8_9 ),
inference(rat,[],[s10,s13]) ).
cnf(s22,plain,
( spl8_4
| spl8_9 ),
inference(rat,[],[s9,s13]) ).
cnf(s23,plain,
( spl8_7
| spl8_8 ),
inference(rat,[],[s8,s13]) ).
cnf(s24,plain,
( spl8_6
| spl8_8 ),
inference(rat,[],[s7,s13]) ).
cnf(s25,plain,
( spl8_4
| spl8_8 ),
inference(rat,[],[s6,s13]) ).
cnf(s26,plain,
( spl8_5
| spl8_7 ),
inference(rat,[],[s5,s13]) ).
cnf(s27,plain,
( spl8_5
| spl8_6 ),
inference(rat,[],[s4,s13]) ).
cnf(s28,plain,
( spl8_4
| spl8_5 ),
inference(rat,[],[s3,s13]) ).
cnf(s29,plain,
spl8_2,
inference(rat,[],[s14,s2]) ).
cnf(s30,plain,
spl8_4,
inference(rat,[],[s17,s28,s25,s22,s2]) ).
cnf(s31,plain,
spl8_5,
inference(rat,[],[s19,s27,s26,s29,s30]) ).
cnf(s32,plain,
spl8_7,
inference(rat,[],[s17,s23,s20,s2,s31]) ).
cnf(s33,plain,
~ spl8_6,
inference(rat,[],[s19,s30,s29,s32]) ).
cnf(s34,plain,
spl8_9,
inference(rat,[],[s21,s33]) ).
cnf(s35,plain,
spl8_8,
inference(rat,[],[s24,s33]) ).
cnf(s36,plain,
$false,
inference(rat,[],[s17,s31,s2,s34,s35]) ).
thf(f704,plain,
$false,
inference(avatar_sat_refutation,[],[s36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL861^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n020.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
% 0.08/0.19 % DateTime : Tue Sep 29 10:13:34 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.33 % (867413)Will run a generic schedule for satisfiability detection.
% 0.20/0.33 % (867418)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2963506826_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.33 % Exception at run slice level
% 0.20/0.33 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.33 % (867420)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=62895508:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.33 % (867423)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=776788898:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.33 % (867419)% WARNING: option uhcvi not known.
% 0.20/0.33 % (867426)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3687476591:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.33 % Exception at run slice level
% 0.20/0.33 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.33 % (867421)dis+10_1_sil=32000:sp=arity:random_seed=35166439:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.33 % (867422)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2990634445:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.33 % (867422)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.33 % (867419)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3161724028:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.33 % (867430)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3649973825:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.33 % (867419)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.33 % (867424)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2065552823:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.33 % (867419)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.33 % (867430)Instruction limit reached!
% 0.20/0.33 % (867430)------------------------------
% 0.20/0.33 % (867430)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (867430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (867430)CaDiCaL version: 2.1.3
% 0.20/0.33 % (867430)Termination reason: Instruction limit
% 0.20/0.33 % (867430)Termination phase: Saturation
% 0.20/0.33 % (867430)Time elapsed: 0.032 s
% 0.20/0.33 % (867430)Peak memory usage: 12 MB
% 0.20/0.33 % (867430)Instructions burned: 135 (million)
% 0.20/0.33 % (867424) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-867413-867424"...
% 0.20/0.33 % (867423)Instruction limit reached!
% 0.20/0.33 % (867423)------------------------------
% 0.20/0.33 % (867423)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.33 % (867423)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.33 % (867423)CaDiCaL version: 2.1.3
% 0.20/0.33 % (867423)Termination reason: Instruction limit
% 0.20/0.33 % (867423)Termination phase: Saturation
% 0.20/0.33 % (867423)Time elapsed: 0.059 s
% 0.20/0.33 % (867423)Peak memory usage: 12 MB
% 0.20/0.33 % (867423)Instructions burned: 132 (million)
% 0.20/0.33 % (867436)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3398071229:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.20/0.33 % (867436)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.33 % (867436)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.33 % (867424)...printing done.
% 0.20/0.33 % (867424)Refutation found. Thanks to Tanya!
% 0.20/0.33 % SZS status Theorem for theBenchmark
% 0.20/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.34 % (867424)------------------------------
% 0.20/0.34 % (867424)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (867424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (867424)CaDiCaL version: 2.1.3
% 0.20/0.34 % (867424)Termination reason: Refutation
% 0.20/0.34 % (867424)Time elapsed: 0.042 s
% 0.20/0.34 % (867424)Peak memory usage: 13 MB
% 0.20/0.34 % (867424)Instructions burned: 39 (million)
% 0.20/0.34 % (867413)Success in time 0.102 s
% 0.20/0.34 % Vampire exiting
%------------------------------------------------------------------------------