%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL878^1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 08:14:39 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 20
% Syntax : Number of formulae : 202 ( 32 unt; 0 typ; 13 def)
% Number of atoms : 1603 ( 341 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 1942 ( 364 ~; 471 |; 6 &;1009 @)
% ( 17 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 196 ( 196 >; 0 *; 0 +; 0 <<)
% Number of symbols : 73 ( 69 usr; 22 con; 0-4 aty)
% ( 70 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 393 ( 0 sgn 175 !; 10 ?; 393 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
db1:
!>[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,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_41,type,
vOR: $o > $o > $o ).
thf(func_def_42,type,
vNOT: $o > $o ).
thf(func_def_43,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
sK0: $i > $i > $o ).
thf(func_def_48,type,
sK1: $i > $i > $o ).
thf(func_def_52,type,
sK5: $i > $o ).
thf(func_def_55,type,
sK8: $i > $o ).
thf(func_def_57,type,
sK10: ( $i > $o ) > $i > $i ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f11,axiom,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mforall_prop) ).
thf(f16,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mbox) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,conjecture,
! [X0: $i > $i > $o,X1: $i > $i > $o] :
( ! [X4: $i,X3: $i] :
( ( X1 @ X3 @ X4 )
=> ( X0 @ X3 @ X4 ) )
<=> ( mvalid
@ ( mforall_prop
@ ^ [X2: $i > $o] : ( mimplies @ ( mbox @ X0 @ X2 ) @ ( mbox @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
thf(f33,negated_conjecture,
~ ! [X0: $i > $i > $o,X1: $i > $i > $o] :
( ! [X4: $i,X3: $i] :
( ( X1 @ X3 @ X4 )
=> ( X0 @ X3 @ X4 ) )
<=> ( mvalid
@ ( mforall_prop
@ ^ [X2: $i > $o] : ( mimplies @ ( mbox @ X0 @ X2 ) @ ( mbox @ X1 @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f47,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ~ ( X0 @ X2 @ X3 )
| ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f16]) ).
thf(f48,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f53,plain,
~ ! [X0: $i > $i > $o,X1: $i > $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X1 @ X3 @ X2 )
=> ( X0 @ X3 @ X2 ) )
<=> ( mvalid
@ ( mforall_prop
@ ^ [X4: $i > $o] : ( mimplies @ ( mbox @ X0 @ X4 ) @ ( mbox @ X1 @ X4 ) ) ) ) ),
inference(rectify,[],[f33]) ).
thf(f54,plain,
~ ! [X1: $i > $i > $o,X0: $i > $i > $o] :
( ( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ X0 @ Y0 ) @ ( mbox @ X1 @ Y0 ) ) ) )
= $true )
<=> ! [X2: $i,X3: $i] :
( ( ( X1 @ X3 @ X2 )
= $true )
=> ( ( X0 @ X3 @ X2 )
= $true ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f55,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f56,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f57,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f58,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f63,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f64,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f65,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f76,plain,
( mforall_prop
= ( ^ [X0: ( $i > $o ) > $i > $o,X1: $i] :
! [X2: $i > $o] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[],[f11]) ).
thf(f77,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f76]) ).
thf(f87,plain,
? [X0: $i > $i > $o,X1: $i > $i > $o] :
( ! [X3: $i,X2: $i] :
( ( ( X0 @ X3 @ X2 )
= $true )
| ( ( X1 @ X3 @ X2 )
!= $true ) )
<~> ( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ X0 @ Y0 ) @ ( mbox @ X1 @ Y0 ) ) ) )
= $true ) ),
inference(ennf_transformation,[],[f54]) ).
thf(f88,plain,
? [X0: $i > $i > $o,X1: $i > $i > $o] :
( ( ( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ X0 @ Y0 ) @ ( mbox @ X1 @ Y0 ) ) ) )
!= $true )
| ? [X3: $i,X2: $i] :
( ( ( X0 @ X3 @ X2 )
!= $true )
& ( ( X1 @ X3 @ X2 )
= $true ) ) )
& ( ( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ X0 @ Y0 ) @ ( mbox @ X1 @ Y0 ) ) ) )
= $true )
| ! [X3: $i,X2: $i] :
( ( ( X0 @ X3 @ X2 )
= $true )
| ( ( X1 @ X3 @ X2 )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f87]) ).
thf(f89,plain,
? [X0: $i > $i > $o,X1: $i > $i > $o] :
( ( ( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ X0 @ Y0 ) @ ( mbox @ X1 @ Y0 ) ) ) )
!= $true )
| ? [X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
!= $true )
& ( ( X1 @ X2 @ X3 )
= $true ) ) )
& ( ( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ X0 @ Y0 ) @ ( mbox @ X1 @ Y0 ) ) ) )
= $true )
| ! [X4: $i,X5: $i] :
( ( $true
= ( X0 @ X4 @ X5 ) )
| ( ( X1 @ X4 @ X5 )
!= $true ) ) ) ),
inference(rectify,[],[f88]) ).
thf(f90,plain,
( ( ( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ sK0 @ Y0 ) @ ( mbox @ sK1 @ Y0 ) ) ) )
!= $true )
| ( ( ( sK0 @ sK2 @ sK3 )
!= $true )
& ( ( sK1 @ sK2 @ sK3 )
= $true ) ) )
& ( ( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ sK0 @ Y0 ) @ ( mbox @ sK1 @ Y0 ) ) ) )
= $true )
| ! [X4: $i,X5: $i] :
( ( ( sK0 @ X4 @ X5 )
= $true )
| ( ( sK1 @ X4 @ X5 )
!= $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f89]) ).
thf(f96,plain,
! [X4: $i,X5: $i] :
( ( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ sK0 @ Y0 ) @ ( mbox @ sK1 @ Y0 ) ) ) )
= $true )
| ( ( sK0 @ X4 @ X5 )
= $true )
| ( ( sK1 @ X4 @ X5 )
!= $true ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f97,plain,
( ( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ sK0 @ Y0 ) @ ( mbox @ sK1 @ Y0 ) ) ) )
!= $true )
| ( ( sK1 @ sK2 @ sK3 )
= $true ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f98,plain,
( ( ( mvalid
@ ( mforall_prop
@ ^ [Y0: $i > $o] : ( mimplies @ ( mbox @ sK0 @ Y0 ) @ ( mbox @ sK1 @ Y0 ) ) ) )
!= $true )
| ( ( sK0 @ sK2 @ sK3 )
!= $true ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f100,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f65]) ).
thf(f106,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f113,plain,
( mforall_prop
= ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f77]) ).
thf(f114,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( Y0 @ Y2 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f116,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f123,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f128,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f100,f116,f123]) ).
thf(f136,plain,
( ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y4 @ Y5 )
| ( Y3 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK0
@ Y0 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK1
@ Y0 ) ) ) )
!= $true )
| ( ( sK0 @ sK2 @ sK3 )
!= $true ) ),
inference(definition_unfolding,[],[f98,f106,f113,f128,f114,f114]) ).
thf(f137,plain,
( ( ( sK1 @ sK2 @ sK3 )
= $true )
| ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y4 @ Y5 )
| ( Y3 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK0
@ Y0 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK1
@ Y0 ) ) ) )
!= $true ) ),
inference(definition_unfolding,[],[f97,f106,f113,f128,f114,f114]) ).
thf(f138,plain,
! [X4: $i,X5: $i] :
( ( ( sK1 @ X4 @ X5 )
!= $true )
| ( ( sK0 @ X4 @ X5 )
= $true )
| ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: ( $i > $o ) > $i > $o,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y4 @ Y5 )
| ( Y3 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK0
@ Y0 )
@ ( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( Y1 @ Y3 @ Y4 ) ) )
@ sK1
@ Y0 ) ) ) )
= $true ) ),
inference(definition_unfolding,[],[f96,f106,f113,f128,f114,f114]) ).
thf(f139,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK1 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) ) )
!= $true )
| ( ( sK1 @ sK2 @ sK3 )
= $true ) ),
inference(beta-eta_normalization,[],[f137]) ).
thf(f140,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK1 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) )
@ sK4 ) )
| ( ( sK1 @ sK2 @ sK3 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f139]) ).
thf(f141,plain,
( ( ( sK1 @ sK2 @ sK3 )
= $true )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK1 @ sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK0 @ sK4 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f140]) ).
thf(f142,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK1 @ sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK0 @ sK4 @ Y1 ) ) ) )
@ sK5 ) )
| ( ( sK1 @ sK2 @ sK3 )
= $true ) ),
inference(sigma_proxy_clausification,[],[f141]) ).
thf(f143,plain,
( ( ( sK1 @ sK2 @ sK3 )
= $true )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5 @ Y0 )
| ~ ( sK1 @ sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5 @ Y0 )
| ~ ( sK0 @ sK4 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f142]) ).
thf(f144,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5 @ Y0 )
| ~ ( sK0 @ sK4 @ Y0 ) ) ) )
= $false )
| ( ( sK1 @ sK2 @ sK3 )
= $true ) ),
inference(or_proxy_clausification,[],[f143]) ).
thf(f145,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5 @ Y0 )
| ~ ( sK1 @ sK4 @ Y0 ) ) )
= $false )
| ( ( sK1 @ sK2 @ sK3 )
= $true ) ),
inference(or_proxy_clausification,[],[f143]) ).
thf(f146,plain,
( ( ( sK1 @ sK2 @ sK3 )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( sK5 @ Y0 )
| ~ ( sK1 @ sK4 @ Y0 ) )
@ sK6 ) ) ),
inference(sigma_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( ( $false
= ( ( sK5 @ sK6 )
| ~ ( sK1 @ sK4 @ sK6 ) ) )
| ( ( sK1 @ sK2 @ sK3 )
= $true ) ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f148,plain,
( ( ( sK1 @ sK2 @ sK3 )
= $true )
| ( ( ~ ( sK1 @ sK4 @ sK6 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f147]) ).
thf(f149,plain,
( ( ( sK1 @ sK2 @ sK3 )
= $true )
| ( $false
= ( sK5 @ sK6 ) ) ),
inference(or_proxy_clausification,[],[f147]) ).
thf(f150,plain,
( ( ( sK1 @ sK4 @ sK6 )
= $true )
| ( ( sK1 @ sK2 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f148]) ).
thf(f151,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK5 @ Y0 )
| ~ ( sK0 @ sK4 @ Y0 ) ) )
= $true )
| ( ( sK1 @ sK2 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[],[f144]) ).
thf(f152,plain,
! [X1: $i] :
( ( ( sK1 @ sK2 @ sK3 )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK5 @ Y0 )
| ~ ( sK0 @ sK4 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f151]) ).
thf(f153,plain,
! [X1: $i] :
( ( $true
= ( ( sK5 @ X1 )
| ~ ( sK0 @ sK4 @ X1 ) ) )
| ( ( sK1 @ sK2 @ sK3 )
= $true ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f154,plain,
! [X1: $i] :
( ( $true
= ( sK5 @ X1 ) )
| ( $true
= ( ~ ( sK0 @ sK4 @ X1 ) ) )
| ( ( sK1 @ sK2 @ sK3 )
= $true ) ),
inference(or_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( ( sK1 @ sK2 @ sK3 )
= $true )
| ( $true
= ( sK5 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f154]) ).
thf(f156,plain,
( ( ( sK0 @ sK2 @ sK3 )
!= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK1 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) ) )
!= $true ) ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f157,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK1 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) )
@ sK7 ) )
| ( ( sK0 @ sK2 @ sK3 )
!= $true ) ),
inference(sigma_proxy_clausification,[],[f156]) ).
thf(f158,plain,
( ( ( sK0 @ sK2 @ sK3 )
!= $true )
| ( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK1 @ sK7 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK0 @ sK7 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f159,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK1 @ sK7 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK0 @ sK7 @ Y1 ) ) ) )
@ sK8 ) )
| ( ( sK0 @ sK2 @ sK3 )
!= $true ) ),
inference(sigma_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( ( ( sK0 @ sK2 @ sK3 )
!= $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK8 @ Y0 )
| ~ ( sK1 @ sK7 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK8 @ Y0 )
| ~ ( sK0 @ sK7 @ Y0 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
( ( ( sK0 @ sK2 @ sK3 )
!= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK8 @ Y0 )
| ~ ( sK0 @ sK7 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK8 @ Y0 )
| ~ ( sK1 @ sK7 @ Y0 ) ) ) )
| ( ( sK0 @ sK2 @ sK3 )
!= $true ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f163,plain,
( ( ( ^ [Y0: $i] :
( ( sK8 @ Y0 )
| ~ ( sK1 @ sK7 @ Y0 ) )
@ sK9 )
= $false )
| ( ( sK0 @ sK2 @ sK3 )
!= $true ) ),
inference(sigma_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $false
= ( ( sK8 @ sK9 )
| ~ ( sK1 @ sK7 @ sK9 ) ) )
| ( ( sK0 @ sK2 @ sK3 )
!= $true ) ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
( ( ( sK0 @ sK2 @ sK3 )
!= $true )
| ( $false
= ( ~ ( sK1 @ sK7 @ sK9 ) ) ) ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( ( $false
= ( sK8 @ sK9 ) )
| ( ( sK0 @ sK2 @ sK3 )
!= $true ) ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f167,plain,
( ( $true
= ( sK1 @ sK7 @ sK9 ) )
| ( ( sK0 @ sK2 @ sK3 )
!= $true ) ),
inference(not_proxy_clausification,[],[f165]) ).
thf(f168,plain,
( ( ( sK0 @ sK2 @ sK3 )
!= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK8 @ Y0 )
| ~ ( sK0 @ sK7 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f169,plain,
! [X1: $i] :
( ( ( sK0 @ sK2 @ sK3 )
!= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( sK8 @ Y0 )
| ~ ( sK0 @ sK7 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f168]) ).
thf(f170,plain,
! [X1: $i] :
( ( ( ( sK8 @ X1 )
| ~ ( sK0 @ sK7 @ X1 ) )
= $true )
| ( ( sK0 @ sK2 @ sK3 )
!= $true ) ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f171,plain,
! [X1: $i] :
( ( $true
= ( sK8 @ X1 ) )
| ( ( ~ ( sK0 @ sK7 @ X1 ) )
= $true )
| ( ( sK0 @ sK2 @ sK3 )
!= $true ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X1: $i] :
( ( $true
= ( sK8 @ X1 ) )
| ( ( sK0 @ sK2 @ sK3 )
!= $true )
| ( $false
= ( sK0 @ sK7 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X4: $i,X5: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK1 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) ) )
= $true )
| ( ( sK1 @ X4 @ X5 )
!= $true )
| ( ( sK0 @ X4 @ X5 )
= $true ) ),
inference(beta-eta_normalization,[],[f138]) ).
thf(f174,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( ( sK0 @ X4 @ X5 )
= $true )
| ( ( sK1 @ X4 @ X5 )
!= $true )
| ( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK1 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
| ~ ( sK0 @ Y0 @ Y2 ) ) ) ) )
@ X6 ) ) ),
inference(pi_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X6: $i,X4: $i,X5: $i] :
( ( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK1 @ X6 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK0 @ X6 @ Y1 ) ) ) ) ) )
| ( ( sK1 @ X4 @ X5 )
!= $true )
| ( ( sK0 @ X4 @ X5 )
= $true ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
! [X6: $i,X7: $i > $o,X4: $i,X5: $i] :
( ( $true
= ( ^ [Y0: $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK1 @ X6 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
| ~ ( sK0 @ X6 @ Y1 ) ) ) )
@ X7 ) )
| ( ( sK1 @ X4 @ X5 )
!= $true )
| ( ( sK0 @ X4 @ X5 )
= $true ) ),
inference(pi_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X6: $i,X7: $i > $o,X4: $i,X5: $i] :
( ( ( sK0 @ X4 @ X5 )
= $true )
| ( ( sK1 @ X4 @ X5 )
!= $true )
| ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X7 @ Y0 )
| ~ ( sK1 @ X6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X7 @ Y0 )
| ~ ( sK0 @ X6 @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f176]) ).
thf(f178,plain,
! [X6: $i,X7: $i > $o,X4: $i,X5: $i] :
( ( ( sK0 @ X4 @ X5 )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X7 @ Y0 )
| ~ ( sK1 @ X6 @ Y0 ) ) ) )
| ( ( sK1 @ X4 @ X5 )
!= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X7 @ Y0 )
| ~ ( sK0 @ X6 @ Y0 ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X8: $i,X6: $i,X7: $i > $o,X4: $i,X5: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X7 @ Y0 )
| ~ ( sK0 @ X6 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( X7 @ Y0 )
| ~ ( sK1 @ X6 @ Y0 ) )
@ X8 ) )
| ( ( sK1 @ X4 @ X5 )
!= $true )
| ( ( sK0 @ X4 @ X5 )
= $true ) ),
inference(pi_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X8: $i,X6: $i,X7: $i > $o,X4: $i,X5: $i] :
( ( ( sK0 @ X4 @ X5 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( X7 @ Y0 )
| ~ ( sK1 @ X6 @ Y0 ) )
@ X8 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X7 @ Y0 )
| ~ ( sK0 @ X6 @ Y0 ) ) ) )
| ( ( sK1 @ X4 @ X5 )
!= $true ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X8: $i,X6: $i,X7: $i > $o,X4: $i,X5: $i] :
( ( ( sK0 @ X4 @ X5 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( X7 @ Y0 )
| ~ ( sK1 @ X6 @ Y0 ) )
@ X8 ) )
| ( ( sK1 @ X4 @ X5 )
!= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( X7 @ Y0 )
| ~ ( sK0 @ X6 @ Y0 ) )
@ ( sK10 @ X7 @ X6 ) ) ) ),
inference(sigma_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X8: $i,X6: $i,X7: $i > $o,X4: $i,X5: $i] :
( ( ( sK1 @ X4 @ X5 )
!= $true )
| ( ( ( X7 @ ( sK10 @ X7 @ X6 ) )
| ~ ( sK0 @ X6 @ ( sK10 @ X7 @ X6 ) ) )
= $false )
| ( ( ( X7 @ X8 )
| ~ ( sK1 @ X6 @ X8 ) )
= $true )
| ( ( sK0 @ X4 @ X5 )
= $true ) ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f183,plain,
! [X8: $i,X6: $i,X7: $i > $o,X4: $i,X5: $i] :
( ( ( sK0 @ X4 @ X5 )
= $true )
| ( ( ( X7 @ X8 )
| ~ ( sK1 @ X6 @ X8 ) )
= $true )
| ( ( sK1 @ X4 @ X5 )
!= $true )
| ( ( ~ ( sK0 @ X6 @ ( sK10 @ X7 @ X6 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X8: $i,X6: $i,X7: $i > $o,X4: $i,X5: $i] :
( ( ( ( X7 @ X8 )
| ~ ( sK1 @ X6 @ X8 ) )
= $true )
| ( ( sK0 @ X4 @ X5 )
= $true )
| ( ( sK1 @ X4 @ X5 )
!= $true )
| ( ( X7 @ ( sK10 @ X7 @ X6 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f185,plain,
! [X8: $i,X6: $i,X7: $i > $o,X4: $i,X5: $i] :
( ( ( X7 @ X8 )
= $true )
| ( ( X7 @ ( sK10 @ X7 @ X6 ) )
= $false )
| ( ( sK0 @ X4 @ X5 )
= $true )
| ( ( ~ ( sK1 @ X6 @ X8 ) )
= $true )
| ( ( sK1 @ X4 @ X5 )
!= $true ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X8: $i,X6: $i,X7: $i > $o,X4: $i,X5: $i] :
( ( ( sK0 @ X4 @ X5 )
= $true )
| ( ( X7 @ ( sK10 @ X7 @ X6 ) )
= $false )
| ( ( X7 @ X8 )
= $true )
| ( $false
= ( sK1 @ X6 @ X8 ) )
| ( ( sK1 @ X4 @ X5 )
!= $true ) ),
inference(not_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X8: $i,X6: $i,X7: $i > $o,X4: $i,X5: $i] :
( ( ( ~ ( sK0 @ X6 @ ( sK10 @ X7 @ X6 ) ) )
= $false )
| ( ( sK1 @ X4 @ X5 )
!= $true )
| ( ( X7 @ X8 )
= $true )
| ( ( ~ ( sK1 @ X6 @ X8 ) )
= $true )
| ( ( sK0 @ X4 @ X5 )
= $true ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f188,plain,
! [X8: $i,X6: $i,X7: $i > $o,X4: $i,X5: $i] :
( ( $true
= ( sK0 @ X6 @ ( sK10 @ X7 @ X6 ) ) )
| ( ( sK1 @ X4 @ X5 )
!= $true )
| ( ( ~ ( sK1 @ X6 @ X8 ) )
= $true )
| ( ( X7 @ X8 )
= $true )
| ( ( sK0 @ X4 @ X5 )
= $true ) ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X8: $i,X6: $i,X7: $i > $o,X4: $i,X5: $i] :
( ( ( X7 @ X8 )
= $true )
| ( $false
= ( sK1 @ X6 @ X8 ) )
| ( ( sK1 @ X4 @ X5 )
!= $true )
| ( $true
= ( sK0 @ X6 @ ( sK10 @ X7 @ X6 ) ) )
| ( ( sK0 @ X4 @ X5 )
= $true ) ),
inference(not_proxy_clausification,[],[f188]) ).
thf(f191,definition,
( spl11_1
<=> ( ( sK1 @ sK2 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
thf(f193,plain,
( ( ( sK1 @ sK2 @ sK3 )
= $true )
| ~ spl11_1 ),
inference(avatar_component_clause,[],[f191]) ).
thf(f195,definition,
( spl11_2
<=> ( $false
= ( sK5 @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
thf(f197,plain,
( ( $false
= ( sK5 @ sK6 ) )
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f195]) ).
thf(f198,plain,
( spl11_1
| spl11_2 ),
inference(avatar_split_clause,[],[f149,f195,f191]) ).
thf(f200,definition,
( spl11_3
<=> ( ( sK1 @ sK4 @ sK6 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
thf(f202,plain,
( ( ( sK1 @ sK4 @ sK6 )
= $true )
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f200]) ).
thf(f203,plain,
( spl11_3
| spl11_1 ),
inference(avatar_split_clause,[],[f150,f191,f200]) ).
thf(f205,definition,
( spl11_4
<=> ! [X1: $i] :
( ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $true
= ( sK5 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition]) ).
thf(f206,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ sK4 @ X1 ) )
| ( $true
= ( sK5 @ X1 ) ) )
| ~ spl11_4 ),
inference(avatar_component_clause,[],[f205]) ).
thf(f207,plain,
( spl11_1
| spl11_4 ),
inference(avatar_split_clause,[],[f155,f205,f191]) ).
thf(f209,definition,
( spl11_5
<=> ( $false
= ( sK8 @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition]) ).
thf(f211,plain,
( ( $false
= ( sK8 @ sK9 ) )
| ~ spl11_5 ),
inference(avatar_component_clause,[],[f209]) ).
thf(f213,definition,
( spl11_6
<=> ( ( sK0 @ sK2 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition]) ).
thf(f215,plain,
( ( ( sK0 @ sK2 @ sK3 )
!= $true )
| spl11_6 ),
inference(avatar_component_clause,[],[f213]) ).
thf(f216,plain,
( spl11_5
| ~ spl11_6 ),
inference(avatar_split_clause,[],[f166,f213,f209]) ).
thf(f218,definition,
( spl11_7
<=> ( $true
= ( sK1 @ sK7 @ sK9 ) ) ),
introduced(definition,[new_symbols(definition,[spl11_7])],[avatar_definition]) ).
thf(f220,plain,
( ( $true
= ( sK1 @ sK7 @ sK9 ) )
| ~ spl11_7 ),
inference(avatar_component_clause,[],[f218]) ).
thf(f221,plain,
( spl11_7
| ~ spl11_6 ),
inference(avatar_split_clause,[],[f167,f213,f218]) ).
thf(f223,definition,
( spl11_8
<=> ! [X1: $i] :
( ( $true
= ( sK8 @ X1 ) )
| ( $false
= ( sK0 @ sK7 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_8])],[avatar_definition]) ).
thf(f224,plain,
( ! [X1: $i] :
( ( $false
= ( sK0 @ sK7 @ X1 ) )
| ( $true
= ( sK8 @ X1 ) ) )
| ~ spl11_8 ),
inference(avatar_component_clause,[],[f223]) ).
thf(f225,plain,
( spl11_8
| ~ spl11_6 ),
inference(avatar_split_clause,[],[f172,f213,f223]) ).
thf(f227,definition,
( spl11_9
<=> ! [X4: $i,X5: $i] :
( ( ( sK0 @ X4 @ X5 )
= $true )
| ( ( sK1 @ X4 @ X5 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl11_9])],[avatar_definition]) ).
thf(f228,plain,
( ! [X4: $i,X5: $i] :
( ( ( sK1 @ X4 @ X5 )
!= $true )
| ( ( sK0 @ X4 @ X5 )
= $true ) )
| ~ spl11_9 ),
inference(avatar_component_clause,[],[f227]) ).
thf(f230,definition,
( spl11_10
<=> ! [X6: $i,X7: $i > $o,X8: $i] :
( ( ( X7 @ ( sK10 @ X7 @ X6 ) )
= $false )
| ( $false
= ( sK1 @ X6 @ X8 ) )
| ( ( X7 @ X8 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl11_10])],[avatar_definition]) ).
thf(f231,plain,
( ! [X8: $i,X6: $i,X7: $i > $o] :
( ( ( X7 @ X8 )
= $true )
| ( ( X7 @ ( sK10 @ X7 @ X6 ) )
= $false )
| ( $false
= ( sK1 @ X6 @ X8 ) ) )
| ~ spl11_10 ),
inference(avatar_component_clause,[],[f230]) ).
thf(f232,plain,
( spl11_9
| spl11_10 ),
inference(avatar_split_clause,[],[f186,f230,f227]) ).
thf(f234,definition,
( spl11_11
<=> ! [X6: $i,X8: $i,X7: $i > $o] :
( ( ( X7 @ X8 )
= $true )
| ( $true
= ( sK0 @ X6 @ ( sK10 @ X7 @ X6 ) ) )
| ( $false
= ( sK1 @ X6 @ X8 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_11])],[avatar_definition]) ).
thf(f235,plain,
( ! [X8: $i,X6: $i,X7: $i > $o] :
( ( ( X7 @ X8 )
= $true )
| ( $false
= ( sK1 @ X6 @ X8 ) )
| ( $true
= ( sK0 @ X6 @ ( sK10 @ X7 @ X6 ) ) ) )
| ~ spl11_11 ),
inference(avatar_component_clause,[],[f234]) ).
thf(f236,plain,
( spl11_11
| spl11_9 ),
inference(avatar_split_clause,[],[f189,f227,f234]) ).
thf(f237,plain,
( ( $true != $true )
| ( $true
= ( sK0 @ sK4 @ sK6 ) )
| ~ spl11_3
| ~ spl11_9 ),
inference(constrained_superposition,[],[f228,f202]) ).
thf(f238,plain,
( ( $true
= ( sK0 @ sK4 @ sK6 ) )
| ~ spl11_3
| ~ spl11_9 ),
inference(trivial_inequality_removal,[],[f237]) ).
thf(f239,plain,
( ( $false = $true )
| ( ( sK5 @ sK6 )
= $true )
| ~ spl11_3
| ~ spl11_4
| ~ spl11_9 ),
inference(constrained_superposition,[],[f238,f206]) ).
thf(f242,plain,
( ( ( sK5 @ sK6 )
= $true )
| ~ spl11_3
| ~ spl11_4
| ~ spl11_9 ),
inference(trivial_inequality_removal,[],[f239]) ).
thf(f246,plain,
( ( $false = $true )
| ~ spl11_2
| ~ spl11_3
| ~ spl11_4
| ~ spl11_9 ),
inference(forward_demodulation,[],[f242,f197]) ).
thf(f247,plain,
( $false
| ~ spl11_2
| ~ spl11_3
| ~ spl11_4
| ~ spl11_9 ),
inference(trivial_inequality_removal,[],[f246]) ).
thf(f248,plain,
( ~ spl11_2
| ~ spl11_3
| ~ spl11_4
| ~ spl11_9 ),
inference(avatar_contradiction_clause,[],[f247]) ).
thf(f249,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK10
@ ^ [Y0: $i] : ( Y0 != X0 )
@ X1 )
= X0 )
| ( ( sK1 @ X1 @ X0 )
= $false ) )
| ~ spl11_10 ),
inference(leibniz_equality_elimination,[],[f231]) ).
thf(f294,plain,
( ! [X0: $i > $o,X1: $i] :
( ( $true
= ( sK5 @ ( sK10 @ X0 @ sK4 ) ) )
| ( ( X0 @ X1 )
= $true )
| ( $false = $true )
| ( $false
= ( sK1 @ sK4 @ X1 ) ) )
| ~ spl11_4
| ~ spl11_11 ),
inference(constrained_superposition,[],[f206,f235]) ).
thf(f304,plain,
( ! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
= $true )
| ( $false
= ( sK1 @ sK4 @ X1 ) )
| ( $true
= ( sK5 @ ( sK10 @ X0 @ sK4 ) ) ) )
| ~ spl11_4
| ~ spl11_11 ),
inference(trivial_inequality_removal,[],[f294]) ).
thf(f334,plain,
( ! [X0: $i,X1: $i] :
( ( ( sK1 @ sK4 @ X0 )
= $false )
| ( $false
= ( sK1 @ sK4 @ X1 ) )
| ( $true
= ( sK5 @ X0 ) )
| ( $false = $true )
| ( $true
= ( sK5 @ X1 ) ) )
| ~ spl11_4
| ~ spl11_10
| ~ spl11_11 ),
inference(constrained_superposition,[],[f231,f304]) ).
thf(f356,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( sK5 @ X1 ) )
| ( $false
= ( sK1 @ sK4 @ X1 ) )
| ( ( sK1 @ sK4 @ X0 )
= $false )
| ( $true
= ( sK5 @ X0 ) ) )
| ~ spl11_4
| ~ spl11_10
| ~ spl11_11 ),
inference(trivial_inequality_removal,[],[f334]) ).
thf(f361,definition,
( spl11_12
<=> ! [X0: $i] :
( ( ( sK1 @ sK4 @ X0 )
= $false )
| ( $true
= ( sK5 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_12])],[avatar_definition]) ).
thf(f362,plain,
( ! [X0: $i] :
( ( ( sK1 @ sK4 @ X0 )
= $false )
| ( $true
= ( sK5 @ X0 ) ) )
| ~ spl11_12 ),
inference(avatar_component_clause,[],[f361]) ).
thf(f378,plain,
( spl11_12
| spl11_12
| ~ spl11_4
| ~ spl11_10
| ~ spl11_11 ),
inference(avatar_split_clause,[],[f356,f234,f230,f205,f361,f361]) ).
thf(f391,plain,
( ( ( sK0 @ sK2 @ sK3 )
= $true )
| ( $true != $true )
| ~ spl11_1
| ~ spl11_9 ),
inference(constrained_superposition,[],[f228,f193]) ).
thf(f393,plain,
( ( ( sK0 @ sK2 @ sK3 )
= $true )
| ~ spl11_1
| ~ spl11_9 ),
inference(trivial_inequality_removal,[],[f391]) ).
thf(f395,plain,
( $false
| ~ spl11_1
| spl11_6
| ~ spl11_9 ),
inference(forward_subsumption_resolution,[],[f393,f215]) ).
thf(f396,plain,
( ~ spl11_1
| spl11_6
| ~ spl11_9 ),
inference(avatar_contradiction_clause,[],[f395]) ).
thf(f397,plain,
( ( ( sK0 @ sK7 @ sK9 )
= $true )
| ( $true != $true )
| ~ spl11_7
| ~ spl11_9 ),
inference(constrained_superposition,[],[f228,f220]) ).
thf(f398,plain,
( ( ( sK0 @ sK7 @ sK9 )
= $true )
| ~ spl11_7
| ~ spl11_9 ),
inference(trivial_inequality_removal,[],[f397]) ).
thf(f400,plain,
( ( $false = $true )
| ( ( sK8 @ sK9 )
= $true )
| ~ spl11_7
| ~ spl11_8
| ~ spl11_9 ),
inference(constrained_superposition,[],[f224,f398]) ).
thf(f404,plain,
( ( ( sK8 @ sK9 )
= $true )
| ~ spl11_7
| ~ spl11_8
| ~ spl11_9 ),
inference(trivial_inequality_removal,[],[f400]) ).
thf(f410,plain,
( ( $false = $true )
| ~ spl11_5
| ~ spl11_7
| ~ spl11_8
| ~ spl11_9 ),
inference(forward_demodulation,[],[f404,f211]) ).
thf(f411,plain,
( $false
| ~ spl11_5
| ~ spl11_7
| ~ spl11_8
| ~ spl11_9 ),
inference(trivial_inequality_removal,[],[f410]) ).
thf(f412,plain,
( ~ spl11_5
| ~ spl11_7
| ~ spl11_8
| ~ spl11_9 ),
inference(avatar_contradiction_clause,[],[f411]) ).
thf(f473,plain,
( ! [X0: $i > $o,X1: $i] :
( ( $false = $true )
| ( $true
= ( sK8 @ ( sK10 @ X0 @ sK7 ) ) )
| ( $false
= ( sK1 @ sK7 @ X1 ) )
| ( ( X0 @ X1 )
= $true ) )
| ~ spl11_8
| ~ spl11_11 ),
inference(constrained_superposition,[],[f235,f224]) ).
thf(f491,plain,
( ! [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
= $true )
| ( $false
= ( sK1 @ sK7 @ X1 ) )
| ( $true
= ( sK8 @ ( sK10 @ X0 @ sK7 ) ) ) )
| ~ spl11_8
| ~ spl11_11 ),
inference(trivial_inequality_removal,[],[f473]) ).
thf(f540,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( sK1 @ sK7 @ X0 ) )
| ( $true
= ( sK8 @ X1 ) )
| ( ( sK8 @ X0 )
= $true )
| ( $false = $true )
| ( $false
= ( sK1 @ sK7 @ X1 ) ) )
| ~ spl11_8
| ~ spl11_10
| ~ spl11_11 ),
inference(constrained_superposition,[],[f231,f491]) ).
thf(f559,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( sK1 @ sK7 @ X1 ) )
| ( ( sK8 @ X0 )
= $true )
| ( $true
= ( sK8 @ X1 ) )
| ( $false
= ( sK1 @ sK7 @ X0 ) ) )
| ~ spl11_8
| ~ spl11_10
| ~ spl11_11 ),
inference(trivial_inequality_removal,[],[f540]) ).
thf(f579,definition,
( spl11_21
<=> ! [X1: $i] :
( ( $false
= ( sK1 @ sK7 @ X1 ) )
| ( $true
= ( sK8 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl11_21])],[avatar_definition]) ).
thf(f580,plain,
( ! [X1: $i] :
( ( $false
= ( sK1 @ sK7 @ X1 ) )
| ( $true
= ( sK8 @ X1 ) ) )
| ~ spl11_21 ),
inference(avatar_component_clause,[],[f579]) ).
thf(f589,plain,
( spl11_21
| spl11_21
| ~ spl11_8
| ~ spl11_10
| ~ spl11_11 ),
inference(avatar_split_clause,[],[f559,f234,f230,f223,f579,f579]) ).
thf(f610,plain,
( ( ( sK8 @ sK9 )
= $true )
| ( $false = $true )
| ~ spl11_7
| ~ spl11_21 ),
inference(constrained_superposition,[],[f580,f220]) ).
thf(f617,plain,
( ( ( sK8 @ sK9 )
= $true )
| ~ spl11_7
| ~ spl11_21 ),
inference(trivial_inequality_removal,[],[f610]) ).
thf(f624,plain,
( ( $false = $true )
| ~ spl11_5
| ~ spl11_7
| ~ spl11_21 ),
inference(forward_demodulation,[],[f617,f211]) ).
thf(f625,plain,
( $false
| ~ spl11_5
| ~ spl11_7
| ~ spl11_21 ),
inference(trivial_inequality_removal,[],[f624]) ).
thf(f626,plain,
( ~ spl11_5
| ~ spl11_7
| ~ spl11_21 ),
inference(avatar_contradiction_clause,[],[f625]) ).
thf(f691,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK1 @ X1 @ X2 ) )
| ( $true
= ( ^ [Y0: $i] : ( Y0 != X0 )
@ X2 ) )
| ( ( sK1 @ X1 @ X0 )
= $false ) )
| ~ spl11_10
| ~ spl11_11 ),
inference(constrained_superposition,[],[f235,f249]) ).
thf(f694,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( sK1 @ X1 @ X2 ) )
| ( $true
= ( sK0 @ X1 @ X0 ) )
| ( ( sK1 @ X1 @ X0 )
= $false )
| ( $true
= ( X2 != X0 ) ) )
| ~ spl11_10
| ~ spl11_11 ),
inference(beta-eta_normalization,[],[f691]) ).
thf(f695,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK1 @ X1 @ X2 ) )
| ( ( sK1 @ X1 @ X0 )
= $false )
| ( $false
= ( X2 = X0 ) ) )
| ~ spl11_10
| ~ spl11_11 ),
inference(not_proxy_clausification,[],[f694]) ).
thf(f696,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( sK0 @ X1 @ X0 ) )
| ( $false
= ( sK1 @ X1 @ X2 ) )
| ( ( sK1 @ X1 @ X0 )
= $false )
| ( X0 != X2 ) )
| ~ spl11_10
| ~ spl11_11 ),
inference(equality_proxy_clausification,[],[f695]) ).
thf(f712,plain,
( ! [X0: $i] :
( ( sK3 != X0 )
| ( $false
= ( sK1 @ sK2 @ X0 ) )
| ( $true != $true )
| ( $false
= ( sK1 @ sK2 @ sK3 ) ) )
| spl11_6
| ~ spl11_10
| ~ spl11_11 ),
inference(constrained_superposition,[],[f215,f696]) ).
thf(f725,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ sK2 @ sK3 ) )
| ( $false
= ( sK1 @ sK2 @ X0 ) )
| ( sK3 != X0 ) )
| spl11_6
| ~ spl11_10
| ~ spl11_11 ),
inference(trivial_inequality_removal,[],[f712]) ).
thf(f731,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ sK2 @ X0 ) )
| ( sK3 != X0 )
| ( $false = $true ) )
| ~ spl11_1
| spl11_6
| ~ spl11_10
| ~ spl11_11 ),
inference(forward_demodulation,[],[f725,f193]) ).
thf(f732,plain,
( ! [X0: $i] :
( ( sK3 != X0 )
| ( $false
= ( sK1 @ sK2 @ X0 ) ) )
| ~ spl11_1
| spl11_6
| ~ spl11_10
| ~ spl11_11 ),
inference(trivial_inequality_removal,[],[f731]) ).
thf(f733,plain,
( ( $false
= ( sK1 @ sK2 @ sK3 ) )
| ( sK3 != sK3 )
| ~ spl11_1
| spl11_6
| ~ spl11_10
| ~ spl11_11 ),
inference(imitation,[],[f732]) ).
thf(f735,plain,
( ( $false
= ( sK1 @ sK2 @ sK3 ) )
| ~ spl11_1
| spl11_6
| ~ spl11_10
| ~ spl11_11 ),
inference(trivial_inequality_removal,[],[f733]) ).
thf(f739,plain,
( ( $false = $true )
| ~ spl11_1
| spl11_6
| ~ spl11_10
| ~ spl11_11 ),
inference(forward_demodulation,[],[f735,f193]) ).
thf(f740,plain,
( $false
| ~ spl11_1
| spl11_6
| ~ spl11_10
| ~ spl11_11 ),
inference(trivial_inequality_removal,[],[f739]) ).
thf(f741,plain,
( ~ spl11_1
| spl11_6
| ~ spl11_10
| ~ spl11_11 ),
inference(avatar_contradiction_clause,[],[f740]) ).
thf(f754,plain,
( ( ( sK5 @ sK6 )
= $true )
| ( $false = $true )
| ~ spl11_3
| ~ spl11_12 ),
inference(constrained_superposition,[],[f362,f202]) ).
thf(f756,plain,
( ( ( sK5 @ sK6 )
= $true )
| ~ spl11_3
| ~ spl11_12 ),
inference(trivial_inequality_removal,[],[f754]) ).
thf(f760,plain,
( ( $false = $true )
| ~ spl11_2
| ~ spl11_3
| ~ spl11_12 ),
inference(forward_demodulation,[],[f756,f197]) ).
thf(f761,plain,
( $false
| ~ spl11_2
| ~ spl11_3
| ~ spl11_12 ),
inference(trivial_inequality_removal,[],[f760]) ).
thf(f762,plain,
( ~ spl11_2
| ~ spl11_3
| ~ spl11_12 ),
inference(avatar_contradiction_clause,[],[f761]) ).
cnf(s1,plain,
( spl11_1
| spl11_2 ),
inference(sat_conversion,[],[f198]) ).
cnf(s2,plain,
( spl11_1
| spl11_3 ),
inference(sat_conversion,[],[f203]) ).
cnf(s3,plain,
( spl11_1
| spl11_4 ),
inference(sat_conversion,[],[f207]) ).
cnf(s4,plain,
( spl11_5
| ~ spl11_6 ),
inference(sat_conversion,[],[f216]) ).
cnf(s5,plain,
( ~ spl11_6
| spl11_7 ),
inference(sat_conversion,[],[f221]) ).
cnf(s6,plain,
( ~ spl11_6
| spl11_8 ),
inference(sat_conversion,[],[f225]) ).
cnf(s7,plain,
( spl11_9
| spl11_10 ),
inference(sat_conversion,[],[f232]) ).
cnf(s8,plain,
( spl11_9
| spl11_11 ),
inference(sat_conversion,[],[f236]) ).
cnf(s10,plain,
( ~ spl11_2
| ~ spl11_3
| ~ spl11_4
| ~ spl11_9 ),
inference(sat_conversion,[],[f248]) ).
cnf(s16,plain,
( spl11_12
| ~ spl11_10
| ~ spl11_11
| ~ spl11_4
| spl11_12 ),
inference(sat_conversion,[],[f378]) ).
cnf(s17,plain,
( ~ spl11_4
| ~ spl11_10
| ~ spl11_11
| spl11_12 ),
inference(rat,[],[s16]) ).
cnf(s18,plain,
( ~ spl11_1
| spl11_6
| ~ spl11_9 ),
inference(sat_conversion,[],[f396]) ).
cnf(s20,plain,
( ~ spl11_5
| ~ spl11_7
| ~ spl11_8
| ~ spl11_9 ),
inference(sat_conversion,[],[f412]) ).
cnf(s32,plain,
( spl11_21
| ~ spl11_10
| ~ spl11_11
| ~ spl11_8
| spl11_21 ),
inference(sat_conversion,[],[f589]) ).
cnf(s33,plain,
( ~ spl11_8
| ~ spl11_10
| ~ spl11_11
| spl11_21 ),
inference(rat,[],[s32]) ).
cnf(s38,plain,
( ~ spl11_5
| ~ spl11_7
| ~ spl11_21 ),
inference(sat_conversion,[],[f626]) ).
cnf(s44,plain,
( ~ spl11_1
| spl11_6
| ~ spl11_10
| ~ spl11_11 ),
inference(sat_conversion,[],[f741]) ).
cnf(s50,plain,
( ~ spl11_2
| ~ spl11_3
| ~ spl11_12 ),
inference(sat_conversion,[],[f762]) ).
cnf(s51,plain,
spl11_1,
inference(rat,[],[s17,s7,s8,s10,s50,s1,s2,s3]) ).
cnf(s53,plain,
( ~ spl11_10
| ~ spl11_11 ),
inference(rat,[],[s38,s33,s4,s5,s6,s44,s51]) ).
cnf(s54,plain,
spl11_9,
inference(rat,[],[s53,s7,s8]) ).
cnf(s55,plain,
spl11_6,
inference(rat,[],[s18,s51,s54]) ).
cnf(s56,plain,
spl11_8,
inference(rat,[],[s6,s55]) ).
cnf(s57,plain,
spl11_7,
inference(rat,[],[s5,s55]) ).
cnf(s58,plain,
spl11_5,
inference(rat,[],[s4,s55]) ).
cnf(s60,plain,
$false,
inference(rat,[],[s20,s54,s56,s57,s58]) ).
thf(f763,plain,
$false,
inference(avatar_sat_refutation,[],[s60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL878^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n020.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 10:23:21 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.30 % (879826)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.30 % (879831)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=552790771:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.30 % (879837)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 % (879837)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 % (879833)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1889098934:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.30 % (879832)lrs+10_16_si=on:nwc=1.5:random_seed=1781659830:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.30 % (879835)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=641891939:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.30 % (879837)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=3669988877:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.30 % (879834)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=605405002: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 % (879836)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3788714024:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.30 % (879833)Instruction limit reached!
% 0.21/0.30 % (879833)------------------------------
% 0.21/0.30 % (879833)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (879833)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (879833)CaDiCaL version: 2.1.3
% 0.21/0.30 % (879833)Termination reason: Instruction limit
% 0.21/0.30 % (879833)Termination phase: Preprocessing 3
% 0.21/0.30 % (879833)Time elapsed: 0.002 s
% 0.21/0.30 % (879833)Peak memory usage: 10 MB
% 0.21/0.30 % (879833)Instructions burned: 4 (million)
% 0.21/0.30 % (879831) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-879826-879831"...
% 0.21/0.30 % (879832)Instruction limit reached!
% 0.21/0.30 % (879832)------------------------------
% 0.21/0.30 % (879832)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (879832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (879832)CaDiCaL version: 2.1.3
% 0.21/0.30 % (879832)Termination reason: Instruction limit
% 0.21/0.30 % (879832)Termination phase: Saturation
% 0.21/0.30 % (879832)Time elapsed: 0.009 s
% 0.21/0.30 % (879832)Peak memory usage: 12 MB
% 0.21/0.30 % (879832)Instructions burned: 18 (million)
% 0.21/0.30 % (879831)...printing done.
% 0.21/0.30 % (879831)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 % (879831)------------------------------
% 0.21/0.30 % (879831)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (879831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (879831)CaDiCaL version: 2.1.3
% 0.21/0.30 % (879831)Termination reason: Refutation
% 0.21/0.30 % (879831)Time elapsed: 0.019 s
% 0.21/0.30 % (879831)Peak memory usage: 13 MB
% 0.21/0.30 % (879831)Instructions burned: 63 (million)
% 0.21/0.30 % (879826)Success in time 0.05 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------