%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO430^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 08:47:40 AM UTC 2026
% Result : Theorem 0.23s 0.37s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 13
% Syntax : Number of formulae : 142 ( 60 unt; 0 typ; 2 def)
% Number of atoms : 1180 ( 128 equ; 0 cnn)
% Maximal formula atoms : 10 ( 8 avg)
% Number of connectives : 2603 ( 585 ~; 372 |; 0 &;1389 @)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 121 ( 121 >; 0 *; 0 +; 0 <<)
% Number of symbols : 62 ( 58 usr; 11 con; 0-4 aty)
% ( 243 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 445 ( 0 sgn 24 !; 0 ?; 445 :)
% 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,
rel_b: $i > $i > $o ).
thf(func_def_33,type,
mbox_b: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_b: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_39,type,
vNOT: $o > $o ).
thf(func_def_40,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_43,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
vIMP: $o > $o > $o ).
thf(func_def_45,type,
vAND: $o > $o > $o ).
thf(func_def_46,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_49,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vOR: $o > $o > $o ).
thf(func_def_59,type,
sK8: $i > $i ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) )
= mand ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mequiv) ).
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(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_b
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_b @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^4.ax',mbox_b) ).
thf(f33,axiom,
( ( ^ [X0: $i > $o] : ( mnot @ ( mbox_b @ ( mnot @ X0 ) ) ) )
= mdia_b ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^4.ax',mdia_b) ).
thf(f35,axiom,
msymmetric @ rel_b,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^4.ax',a2) ).
thf(f36,conjecture,
mvalid @ ( mequiv @ ( mdia_b @ ( mbox_b @ p ) ) @ ( mdia_b @ ( mbox_b @ ( mdia_b @ ( mbox_b @ p ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f37,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mdia_b @ ( mbox_b @ p ) ) @ ( mdia_b @ ( mbox_b @ ( mdia_b @ ( mbox_b @ p ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f39,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f40,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f41,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f44,plain,
~ ( mvalid @ ( mequiv @ ( mdia_b @ ( mbox_b @ p ) ) @ ( mdia_b @ ( mbox_b @ ( mdia_b @ ( mbox_b @ p ) ) ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f45,plain,
( ( ~ ( mvalid @ ( mequiv @ ( mdia_b @ ( mbox_b @ p ) ) @ ( mdia_b @ ( mbox_b @ ( mdia_b @ ( mbox_b @ p ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f44]) ).
thf(f46,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f56,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f57,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f56]) ).
thf(f66,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f67,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) )
= msymmetric ),
inference(rectify,[],[f19]) ).
thf(f68,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f67]) ).
thf(f79,plain,
( mdia_b
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_b @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f89,plain,
msymmetric @ rel_b,
inference(rectify,[],[f35]) ).
thf(f90,plain,
( ( msymmetric @ rel_b )
= $true ),
inference(fool_elimination,[],[f89]) ).
thf(f91,plain,
( mbox_b
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_b @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f92,plain,
( mbox_b
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f91]) ).
thf(f97,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f98,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f97]) ).
thf(f99,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f57]) ).
thf(f100,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f101,plain,
( ( ~ ( mvalid @ ( mequiv @ ( mdia_b @ ( mbox_b @ p ) ) @ ( mdia_b @ ( mbox_b @ ( mdia_b @ ( mbox_b @ p ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f45]) ).
thf(f107,plain,
( ( msymmetric @ rel_b )
= $true ),
inference(cnf_transformation,[],[f90]) ).
thf(f108,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f98]) ).
thf(f110,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f116,plain,
( mdia_b
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_b @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f79]) ).
thf(f119,plain,
( mbox_b
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f121,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f126,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f132,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f137,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f110,f126,f108,f126,f126]) ).
thf(f138,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,[],[f121,f108,f126]) ).
thf(f140,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f132,f137,f138,f138]) ).
thf(f146,plain,
( mdia_b
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f116,f126,f119,f126]) ).
thf(f147,plain,
( ( ~ ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f101,f99,f140,f146,f119,f146,f119,f146,f119]) ).
thf(f148,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ rel_b ) ),
inference(definition_unfolding,[],[f107,f100]) ).
thf(f150,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_b @ Y1 @ Y0 )
=> ( rel_b @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f151,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_b @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_b @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f152,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_b @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_b @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f151]) ).
thf(f153,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_b @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_b @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(boolean_simplification,[],[f152]) ).
thf(f157,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_b @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_b @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f153]) ).
thf(f158,plain,
( ( ^ [Y0: $i] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_b @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_b @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( $false
= ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) )
| ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f165,definition,
( spl1_1
<=> ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f167,plain,
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f165]) ).
thf(f169,definition,
( spl1_2
<=> ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f171,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) )
= $true )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f169]) ).
thf(f172,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f161,f169,f165]) ).
thf(f173,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f174,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
= $false )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f176,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
= $true )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X1 )
= $true )
| ~ spl1_2 ),
inference(pi_proxy_clausification,[],[f176]) ).
thf(f178,plain,
( ! [X1: $i] :
( ( ~ ( rel_b @ sK0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ( p @ Y0 ) ) ) )
= $true )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f177]) ).
thf(f218,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) )
@ sK4 ) )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f174]) ).
thf(f219,plain,
( ( $false
= ( ~ ( rel_b @ sK0 @ sK4 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f218]) ).
thf(f220,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) )
= $false )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f219]) ).
thf(f221,plain,
( ( ( ~ ( rel_b @ sK0 @ sK4 ) )
= $false )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f219]) ).
thf(f224,plain,
( ( ( $false
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK4 @ Y0 )
| ( p @ Y0 ) ) ) )
= $true )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f178,f221]) ).
thf(f225,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK4 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f224]) ).
thf(f235,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK4 @ Y0 )
| ( p @ Y0 ) ) )
= $false )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f225]) ).
thf(f236,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_b @ sK4 @ Y0 )
| ( p @ Y0 ) )
@ sK5 )
= $false )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f235]) ).
thf(f237,plain,
( ( ( ~ ( rel_b @ sK4 @ sK5 )
| ( p @ sK5 ) )
= $false )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f236]) ).
thf(f238,plain,
( ( ( p @ sK5 )
= $false )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f237]) ).
thf(f239,plain,
( ( $false
= ( ~ ( rel_b @ sK4 @ sK5 ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f237]) ).
thf(f242,plain,
( ( ( rel_b @ sK4 @ sK5 )
= $true )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f239]) ).
thf(f250,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f220]) ).
thf(f252,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( rel_b @ sK4 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X1 )
= $true )
| ~ spl1_2 ),
inference(pi_proxy_clausification,[],[f250]) ).
thf(f253,plain,
( ! [X1: $i] :
( ( ~ ( rel_b @ sK4 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
= $true )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f252]) ).
thf(f256,plain,
( ( ( ~ $true
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
= $true )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f253,f242]) ).
thf(f258,plain,
( ( $true
= ( $false
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f256]) ).
thf(f259,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
= $true )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f258]) ).
thf(f320,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
= $false )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f259]) ).
thf(f321,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_b @ sK5 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ sK7 )
= $false )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f320]) ).
thf(f322,plain,
( ( ( ~ ( rel_b @ sK5 @ sK7 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK7 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f321]) ).
thf(f323,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK7 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f322]) ).
thf(f324,plain,
( ( $false
= ( ~ ( rel_b @ sK5 @ sK7 ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f322]) ).
thf(f325,plain,
( ( ( rel_b @ sK5 @ sK7 )
= $true )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f324]) ).
thf(f333,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK7 @ Y0 )
| ( p @ Y0 ) ) )
= $true )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f323]) ).
thf(f334,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( rel_b @ sK7 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ~ spl1_2 ),
inference(pi_proxy_clausification,[],[f333]) ).
thf(f335,plain,
( ! [X1: $i] :
( ( ~ ( rel_b @ sK7 @ X1 )
| ( p @ X1 ) )
= $true )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f334]) ).
thf(f339,plain,
( ( ( ~ ( rel_b @ sK7 @ sK5 )
| $false )
= $true )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f335,f238]) ).
thf(f342,plain,
( ( ( ~ ( rel_b @ sK7 @ sK5 ) )
= $true )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f339]) ).
thf(f352,plain,
( ( $false
= ( rel_b @ sK7 @ sK5 ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f342]) ).
thf(f378,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_b @ Y1 @ Y0 )
=> ( rel_b @ Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f150]) ).
thf(f379,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_b @ Y0 @ X1 )
=> ( rel_b @ X1 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f378]) ).
thf(f445,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel_b @ Y0 @ X1 )
=> ( rel_b @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f379]) ).
thf(f446,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel_b @ X2 @ X1 )
=> ( rel_b @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f445]) ).
thf(f480,plain,
( ( ( $true
=> ( rel_b @ sK7 @ sK5 ) )
= $true )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f446,f325]) ).
thf(f513,plain,
( ( ( rel_b @ sK7 @ sK5 )
= $true )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f480]) ).
thf(f519,plain,
( ( $false = $true )
| ~ spl1_2 ),
inference(forward_demodulation,[],[f513,f352]) ).
thf(f520,plain,
( $false
| ~ spl1_2 ),
inference(trivial_inequality_removal,[],[f519]) ).
thf(f521,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[],[f520]) ).
thf(f522,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f523,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
= $false )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f522]) ).
thf(f524,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f522]) ).
thf(f525,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ sK10 ) )
| ~ spl1_1 ),
inference(sigma_proxy_clausification,[],[f523]) ).
thf(f526,plain,
( ( $false
= ( ~ ( rel_b @ sK0 @ sK10 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK10 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f525]) ).
thf(f527,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK10 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f526]) ).
thf(f528,plain,
( ( $false
= ( ~ ( rel_b @ sK0 @ sK10 ) ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f526]) ).
thf(f529,plain,
( ( ( rel_b @ sK0 @ sK10 )
= $true )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f528]) ).
thf(f559,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f524]) ).
thf(f560,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_b @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_b @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) )
@ X1 ) )
| ~ spl1_1 ),
inference(pi_proxy_clausification,[],[f559]) ).
thf(f561,plain,
( ! [X1: $i] :
( ( ~ ( rel_b @ sK0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) )
= $true )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f560]) ).
thf(f573,plain,
( ( ( ~ $true
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK10 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) )
= $true )
| ~ spl1_1 ),
inference(constrained_superposition,[],[f561,f529]) ).
thf(f575,plain,
( ( ( $false
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK10 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) )
= $true )
| ~ spl1_1 ),
inference(boolean_simplification,[],[f573]) ).
thf(f576,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK10 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ) )
| ~ spl1_1 ),
inference(boolean_simplification,[],[f575]) ).
thf(f792,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK10 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f576]) ).
thf(f793,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_b @ sK10 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_b @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ sK12 )
= $false )
| ~ spl1_1 ),
inference(sigma_proxy_clausification,[],[f792]) ).
thf(f794,plain,
( ( $false
= ( ~ ( rel_b @ sK10 @ sK12 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK12 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f793]) ).
thf(f795,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK12 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
= $false )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f794]) ).
thf(f796,plain,
( ( $false
= ( ~ ( rel_b @ sK10 @ sK12 ) ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f794]) ).
thf(f806,plain,
( ( ( rel_b @ sK10 @ sK12 )
= $true )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f796]) ).
thf(f824,plain,
( ( ( $true
=> ( rel_b @ sK12 @ sK10 ) )
= $true )
| ~ spl1_1 ),
inference(constrained_superposition,[],[f446,f806]) ).
thf(f828,plain,
( ( ( rel_b @ sK12 @ sK10 )
= $true )
| ~ spl1_1 ),
inference(boolean_simplification,[],[f824]) ).
thf(f841,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK12 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
= $true )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f795]) ).
thf(f842,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( rel_b @ sK12 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_b @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X1 )
= $true )
| ~ spl1_1 ),
inference(pi_proxy_clausification,[],[f841]) ).
thf(f843,plain,
( ! [X1: $i] :
( ( ~ ( rel_b @ sK12 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ X1 @ Y0 )
| ( p @ Y0 ) ) ) )
= $true )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f842]) ).
thf(f846,plain,
( ( ( ~ $true
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK10 @ Y0 )
| ( p @ Y0 ) ) ) )
= $true )
| ~ spl1_1 ),
inference(constrained_superposition,[],[f843,f828]) ).
thf(f849,plain,
( ( $true
= ( $false
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK10 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ~ spl1_1 ),
inference(boolean_simplification,[],[f846]) ).
thf(f850,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_b @ sK10 @ Y0 )
| ( p @ Y0 ) ) ) )
= $true )
| ~ spl1_1 ),
inference(boolean_simplification,[],[f849]) ).
thf(f851,plain,
( ( $false = $true )
| ~ spl1_1 ),
inference(forward_demodulation,[],[f850,f527]) ).
thf(f852,plain,
( $false
| ~ spl1_1 ),
inference(trivial_inequality_removal,[],[f851]) ).
thf(f853,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f852]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f172]) ).
cnf(s3,plain,
~ spl1_2,
inference(sat_conversion,[],[f521]) ).
cnf(s4,plain,
~ spl1_1,
inference(sat_conversion,[],[f853]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s3,s4]) ).
thf(f854,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO430^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n007.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 16:49:41 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.25 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
% 0.23/0.37 % (3635384)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.37 % (3635395)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1262449860:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.37 % (3635396)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.37 % (3635396)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
% 0.23/0.37 % (3635392)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3734488716:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.37 % (3635391)lrs+10_16_si=on:nwc=1.5:random_seed=2075387239:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.37 % (3635390)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3736675280:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.37 % (3635393)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=2898133388: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)
% 0.23/0.37 % (3635394)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=63269871:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.37 % (3635396)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=2024145733:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.37 % (3635392)Instruction limit reached!
% 0.23/0.37 % (3635392)------------------------------
% 0.23/0.37 % (3635392)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (3635392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (3635392)CaDiCaL version: 2.1.3
% 0.23/0.37 % (3635392)Termination reason: Instruction limit
% 0.23/0.37 % (3635392)Termination phase: Property scanning
% 0.23/0.37 % (3635392)Time elapsed: 0.002 s
% 0.23/0.37 % (3635392)Peak memory usage: 10 MB
% 0.23/0.37 % (3635392)Instructions burned: 4 (million)
% 0.23/0.37 % (3635391)Instruction limit reached!
% 0.23/0.37 % (3635391)------------------------------
% 0.23/0.37 % (3635391)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (3635391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (3635391)CaDiCaL version: 2.1.3
% 0.23/0.37 % (3635391)Termination reason: Instruction limit
% 0.23/0.37 % (3635391)Termination phase: Saturation
% 0.23/0.37 % (3635391)Time elapsed: 0.009 s
% 0.23/0.37 % (3635391)Peak memory usage: 11 MB
% 0.23/0.37 % (3635391)Instructions burned: 18 (million)
% 0.23/0.37 % (3635395)Instruction limit reached!
% 0.23/0.37 % (3635395)------------------------------
% 0.23/0.37 % (3635395)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (3635395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (3635395)CaDiCaL version: 2.1.3
% 0.23/0.37 % (3635395)Termination reason: Instruction limit
% 0.23/0.37 % (3635395)Termination phase: Saturation
% 0.23/0.37 % (3635395)Time elapsed: 0.022 s
% 0.23/0.37 % (3635395)Peak memory usage: 12 MB
% 0.23/0.37 % (3635395)Instructions burned: 76 (million)
% 0.23/0.37 % (3635394)Instruction limit reached!
% 0.23/0.37 % (3635394)------------------------------
% 0.23/0.37 % (3635394)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (3635394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (3635394)CaDiCaL version: 2.1.3
% 0.23/0.37 % (3635394)Termination reason: Instruction limit
% 0.23/0.37 % (3635394)Termination phase: Saturation
% 0.23/0.37 % (3635394)Time elapsed: 0.014 s
% 0.23/0.37 % (3635394)Peak memory usage: 11 MB
% 0.23/0.37 % (3635394)Instructions burned: 25 (million)
% 0.23/0.37 % (3635412)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=535402711:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.23/0.37 % (3635418)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.23/0.37 % (3635412)Instruction limit reached!
% 0.23/0.37 % (3635412)------------------------------
% 0.23/0.37 % (3635412)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (3635412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (3635412)CaDiCaL version: 2.1.3
% 0.23/0.37 % (3635412)Termination reason: Instruction limit
% 0.23/0.37 % (3635412)Termination phase: Unused predicate definition removal
% 0.23/0.37 % (3635412)Time elapsed: 0.002 s
% 0.23/0.37 % (3635412)Peak memory usage: 10 MB
% 0.23/0.37 % (3635412)Instructions burned: 4 (million)
% 0.23/0.37 % (3635418)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2928268392:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.23/0.37 % (3635418)Instruction limit reached!
% 0.23/0.37 % (3635418)------------------------------
% 0.23/0.37 % (3635418)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (3635418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (3635418)CaDiCaL version: 2.1.3
% 0.23/0.37 % (3635418)Termination reason: Instruction limit
% 0.23/0.37 % (3635418)Termination phase: Saturation
% 0.23/0.37 % (3635418)Time elapsed: 0.002 s
% 0.23/0.37 % (3635418)Peak memory usage: 11 MB
% 0.23/0.37 % (3635418)Instructions burned: 8 (million)
% 0.23/0.37 % (3635415)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3170002386:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.23/0.37 % (3635415)Instruction limit reached!
% 0.23/0.37 % (3635415)------------------------------
% 0.23/0.37 % (3635415)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (3635415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (3635415)CaDiCaL version: 2.1.3
% 0.23/0.37 % (3635415)Termination reason: Instruction limit
% 0.23/0.37 % (3635415)Termination phase: Function definition elimination
% 0.23/0.37 % (3635415)Time elapsed: 0.003 s
% 0.23/0.37 % (3635415)Peak memory usage: 10 MB
% 0.23/0.37 % (3635415)Instructions burned: 6 (million)
% 0.23/0.37 % (3635419)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=701875990:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.23/0.37 % (3635428)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1264411591:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.23/0.37 % (3635425)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
% 0.23/0.37 % (3635425)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.23/0.37 % (3635419)Instruction limit reached!
% 0.23/0.37 % (3635419)------------------------------
% 0.23/0.37 % (3635419)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (3635419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (3635419)CaDiCaL version: 2.1.3
% 0.23/0.37 % (3635419)Termination reason: Instruction limit
% 0.23/0.37 % (3635419)Termination phase: Saturation
% 0.23/0.37 % (3635419)Time elapsed: 0.006 s
% 0.23/0.37 % (3635419)Peak memory usage: 11 MB
% 0.23/0.37 % (3635419)Instructions burned: 14 (million)
% 0.23/0.37 % (3635425)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1808616111:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.23/0.37 % (3635390)Instruction limit reached!
% 0.23/0.37 % (3635390)------------------------------
% 0.23/0.37 % (3635390)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (3635390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (3635390)CaDiCaL version: 2.1.3
% 0.23/0.37 % (3635390)Termination reason: Instruction limit
% 0.23/0.37 % (3635390)Termination phase: Saturation
% 0.23/0.37 % (3635390)Time elapsed: 0.047 s
% 0.23/0.37 % (3635390)Peak memory usage: 12 MB
% 0.23/0.37 % (3635390)Instructions burned: 94 (million)
% 0.23/0.37 % (3635432)lrs+10_1_si=on:cs=on:random_seed=2927906975:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.23/0.37 % (3635432)Instruction limit reached!
% 0.23/0.37 % (3635432)------------------------------
% 0.23/0.37 % (3635432)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (3635432)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (3635432)CaDiCaL version: 2.1.3
% 0.23/0.37 % (3635432)Termination reason: Instruction limit
% 0.23/0.37 % (3635432)Termination phase: Saturation
% 0.23/0.37 % (3635432)Time elapsed: 0.004 s
% 0.23/0.37 % (3635432)Peak memory usage: 11 MB
% 0.23/0.37 % (3635432)Instructions burned: 8 (million)
% 0.23/0.37 % (3635438)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.23/0.37 % (3635425)Instruction limit reached!
% 0.23/0.37 % (3635425)------------------------------
% 0.23/0.37 % (3635425)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (3635425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (3635425)CaDiCaL version: 2.1.3
% 0.23/0.37 % (3635425)Termination reason: Instruction limit
% 0.23/0.37 % (3635425)Termination phase: Saturation
% 0.23/0.37 % (3635425)Time elapsed: 0.012 s
% 0.23/0.37 % (3635425)Peak memory usage: 11 MB
% 0.23/0.37 % (3635425)Instructions burned: 28 (million)
% 0.23/0.37 % (3635428) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3635384-3635428"...
% 0.23/0.37 % (3635438)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=3059984306:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.23/0.37 % (3635396) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3635384-3635396"...
% 0.23/0.37 % (3635438)Instruction limit reached!
% 0.23/0.37 % (3635438)------------------------------
% 0.23/0.37 % (3635438)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (3635438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (3635438)CaDiCaL version: 2.1.3
% 0.23/0.37 % (3635438)Termination reason: Instruction limit
% 0.23/0.37 % (3635438)Termination phase: Property scanning
% 0.23/0.37 % (3635438)Time elapsed: 0.001 s
% 0.23/0.37 % (3635438)Peak memory usage: 9 MB
% 0.23/0.37 % (3635438)Instructions burned: 2 (million)
% 0.23/0.37 % (3635428)...printing done.
% 0.23/0.37 % (3635428)Refutation found. Thanks to Tanya!
% 0.23/0.37 % SZS status Theorem for theBenchmark
% 0.23/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.37 % (3635428)------------------------------
% 0.23/0.37 % (3635428)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.37 % (3635428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.37 % (3635428)CaDiCaL version: 2.1.3
% 0.23/0.37 % (3635428)Termination reason: Refutation
% 0.23/0.37 % (3635428)Time elapsed: 0.024 s
% 0.23/0.37 % (3635428)Peak memory usage: 13 MB
% 0.23/0.37 % (3635428)Instructions burned: 87 (million)
% 0.23/0.37 % (3635384)Success in time 0.109 s
% 0.23/0.37 % Vampire exiting
%------------------------------------------------------------------------------