%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO064^4.001 : 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 : n019.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 08:46:26 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 15
% Syntax : Number of formulae : 118 ( 66 unt; 0 typ; 4 def)
% Number of atoms : 807 ( 158 equ; 0 cnn)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 921 ( 39 ~; 117 |; 13 &; 625 @)
% ( 4 <=>; 68 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 81 ( 81 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 41 usr; 10 con; 0-4 aty)
% ( 55 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 244 ( 0 sgn 72 !; 0 ?; 244 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
irel: $i > $i > $o ).
thf(func_def_2,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
iatom: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
inot: ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
itrue: $i > $o ).
thf(func_def_10,type,
ifalse: $i > $o ).
thf(func_def_11,type,
iand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
ior: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
iimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
iimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
iequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_16,type,
ixor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
ivalid: ( $i > $o ) > $o ).
thf(func_def_18,type,
isatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
icountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_20,type,
iinvalid: ( $i > $o ) > $o ).
thf(func_def_21,type,
a: $i > $o ).
thf(func_def_22,type,
b: $i > $o ).
thf(func_def_23,type,
c: $i > $o ).
thf(func_def_26,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_27,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_29,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_30,type,
vOR: $o > $o > $o ).
thf(func_def_31,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_32,type,
vAND: $o > $o > $o ).
thf(func_def_33,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_34,type,
vIMP: $o > $o > $o ).
thf(func_def_35,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X0: $i] : ( irel @ X0 @ X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',refl_axiom) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mor) ).
thf(f5,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mand) ).
thf(f7,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox_s4 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mbox_s4) ).
thf(f8,axiom,
( iatom
= ( ^ [X0: $i > $o] : X0 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iatom) ).
thf(f12,axiom,
( iand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iand) ).
thf(f13,axiom,
( ior
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mbox_s4 @ X0 ) @ ( mbox_s4 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',ior) ).
thf(f18,axiom,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(f22,axiom,
ivalid @ ( iatom @ c ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom1) ).
thf(f23,axiom,
ivalid @ ( ior @ ( ior @ ( iatom @ b ) @ ( iatom @ a ) ) @ ( iatom @ b ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom2) ).
thf(f24,conjecture,
ivalid @ ( ior @ ( iatom @ a ) @ ( iand @ ( iatom @ b ) @ ( iatom @ c ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f25,negated_conjecture,
~ ( ivalid @ ( ior @ ( iatom @ a ) @ ( iand @ ( iatom @ b ) @ ( iatom @ c ) ) ) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
thf(f28,plain,
ivalid @ ( ior @ ( ior @ ( iatom @ b ) @ ( iatom @ a ) ) @ ( iatom @ b ) ),
inference(rectify,[],[f23]) ).
thf(f29,plain,
( ( ivalid @ ( ior @ ( ior @ ( iatom @ b ) @ ( iatom @ a ) ) @ ( iatom @ b ) ) )
= $true ),
inference(fool_elimination,[],[f28]) ).
thf(f32,plain,
~ ( ivalid @ ( ior @ ( iatom @ a ) @ ( iand @ ( iatom @ b ) @ ( iatom @ c ) ) ) ),
inference(rectify,[],[f25]) ).
thf(f33,plain,
( ( ivalid @ ( ior @ ( iatom @ a ) @ ( iand @ ( iatom @ b ) @ ( iatom @ c ) ) ) )
!= $true ),
inference(fool_elimination,[],[f32]) ).
thf(f34,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f36,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f37,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f38,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
inference(rectify,[],[f5]) ).
thf(f39,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f41,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f42,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox_s4 ),
inference(rectify,[],[f7]) ).
thf(f43,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f44,plain,
ivalid @ ( iatom @ c ),
inference(rectify,[],[f22]) ).
thf(f45,plain,
( ( ivalid @ ( iatom @ c ) )
= $true ),
inference(fool_elimination,[],[f44]) ).
thf(f51,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f53,plain,
! [X0: $i] : ( irel @ X0 @ X0 ),
inference(rectify,[],[f1]) ).
thf(f54,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f53]) ).
thf(f55,plain,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f56,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f62,plain,
( ( ivalid @ ( ior @ ( iatom @ a ) @ ( iand @ ( iatom @ b ) @ ( iatom @ c ) ) ) )
!= $true ),
inference(flattening,[],[f33]) ).
thf(f66,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f67,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f68,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f71,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f73,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f54]) ).
thf(f82,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f83,plain,
( ( ivalid @ ( iatom @ c ) )
= $true ),
inference(cnf_transformation,[],[f45]) ).
thf(f85,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f87,plain,
( ( ivalid @ ( ior @ ( ior @ ( iatom @ b ) @ ( iatom @ a ) ) @ ( iatom @ b ) ) )
= $true ),
inference(cnf_transformation,[],[f29]) ).
thf(f88,plain,
( ( ivalid @ ( ior @ ( iatom @ a ) @ ( iand @ ( iatom @ b ) @ ( iatom @ c ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f62]) ).
thf(f89,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f95,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2 @ Y4 ) )
@ Y0
@ Y1 ) ) ),
inference(definition_unfolding,[],[f89,f82]) ).
thf(f96,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f85,f68,f66,f66]) ).
thf(f101,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ c ) ) ),
inference(definition_unfolding,[],[f83,f67,f71]) ).
thf(f102,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b )
@ ( ^ [Y0: $i > $o] : Y0
@ a ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b ) ) )
= $true ),
inference(definition_unfolding,[],[f87,f67,f96,f96,f71,f71,f71]) ).
thf(f103,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2 @ Y4 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o] : Y0
@ b )
@ ( ^ [Y0: $i > $o] : Y0
@ c ) ) ) ) ),
inference(definition_unfolding,[],[f88,f67,f96,f71,f95,f71,f71]) ).
thf(f104,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( c @ Y1 )
& ( b @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f103]) ).
thf(f105,plain,
( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( c @ Y1 )
& ( b @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f104]) ).
thf(f106,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( c @ Y0 )
& ( b @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( a @ Y0 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f105]) ).
thf(f107,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( a @ Y0 ) ) ) ),
inference(or_proxy_clausification,[],[f106]) ).
thf(f108,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( c @ Y0 )
& ( b @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f106]) ).
thf(f109,plain,
( $false
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( c @ Y0 )
& ( b @ Y0 ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f108]) ).
thf(f110,plain,
( ( ( irel @ sK0 @ sK1 )
=> ( ( c @ sK1 )
& ( b @ sK1 ) ) )
= $false ),
inference(beta-eta_normalization,[],[f109]) ).
thf(f111,plain,
( ( ( c @ sK1 )
& ( b @ sK1 ) )
= $false ),
inference(imp_proxy_clausification,[],[f110]) ).
thf(f112,plain,
( ( irel @ sK0 @ sK1 )
= $true ),
inference(imp_proxy_clausification,[],[f110]) ).
thf(f113,plain,
( ( $false
= ( c @ sK1 ) )
| ( $false
= ( b @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f111]) ).
thf(f114,plain,
( $false
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( a @ Y0 ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f107]) ).
thf(f115,plain,
( $false
= ( ( irel @ sK0 @ sK2 )
=> ( a @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f114]) ).
thf(f116,plain,
( ( a @ sK2 )
= $false ),
inference(imp_proxy_clausification,[],[f115]) ).
thf(f117,plain,
( ( irel @ sK0 @ sK2 )
= $true ),
inference(imp_proxy_clausification,[],[f115]) ).
thf(f118,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f102]) ).
thf(f119,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b @ Y2 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f118]) ).
thf(f120,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f119]) ).
thf(f121,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) ) )
= $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f120]) ).
thf(f122,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f121]) ).
thf(f123,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) )
@ X3 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f122]) ).
thf(f124,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) ) ) ) )
| ( $true
= ( ( irel @ X1 @ X3 )
=> ( b @ X3 ) ) ) ),
inference(beta-eta_normalization,[],[f123]) ).
thf(f125,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( irel @ X1 @ X3 )
=> ( b @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f124]) ).
thf(f126,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) ) ) )
| ( $true
= ( ( irel @ X1 @ X3 )
=> ( b @ X3 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a @ Y0 ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f125]) ).
thf(f127,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) )
@ X4 )
= $true )
| ( $true
= ( ( irel @ X1 @ X3 )
=> ( b @ X3 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a @ Y0 ) ) )
= $true )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f126]) ).
thf(f128,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a @ Y0 ) ) )
= $true )
| ( ( b @ X3 )
= $true )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) )
@ X4 )
= $true )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f127]) ).
thf(f129,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( b @ X3 )
= $true )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( b @ Y0 ) )
@ X4 )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a @ Y0 ) )
@ X5 ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(pi_proxy_clausification,[],[f128]) ).
thf(f130,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( ( irel @ X2 @ X4 )
=> ( b @ X4 ) )
= $true )
| ( $true
= ( ( irel @ X2 @ X5 )
=> ( a @ X5 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( b @ X3 )
= $true ) ),
inference(beta-eta_normalization,[],[f129]) ).
thf(f131,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
= ( ( irel @ X2 @ X5 )
=> ( a @ X5 ) ) )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( b @ X3 )
= $true )
| ( $true
= ( b @ X4 ) )
| ( ( irel @ X2 @ X4 )
= $false ) ),
inference(imp_proxy_clausification,[],[f130]) ).
thf(f132,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( irel @ X2 @ X5 )
= $false )
| ( ( irel @ X2 @ X4 )
= $false )
| ( ( irel @ X1 @ X3 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( b @ X3 )
= $true )
| ( ( a @ X5 )
= $true )
| ( $true
= ( b @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f131]) ).
thf(f133,plain,
( ( !! @ $i @ c )
= $true ),
inference(beta-eta_normalization,[],[f101]) ).
thf(f134,plain,
! [X1: $i] :
( $true
= ( c @ X1 ) ),
inference(pi_proxy_clausification,[],[f133]) ).
thf(f136,definition,
( spl3_1
<=> ( $false
= ( c @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f138,plain,
( ( $false
= ( c @ sK1 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f136]) ).
thf(f140,definition,
( spl3_2
<=> ( $false
= ( b @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f142,plain,
( ( $false
= ( b @ sK1 ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f140]) ).
thf(f143,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f113,f140,f136]) ).
thf(f154,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( irel @ X1 @ sK0 ) )
| ( $true
= ( b @ X2 ) )
| ( $true = $false )
| ( ( irel @ sK0 @ X0 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( b @ X0 ) )
| ( $true
= ( a @ sK2 ) ) ),
inference(constrained_superposition,[],[f132,f117]) ).
thf(f213,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false
= ( irel @ X1 @ sK0 ) )
| ( $true
= ( b @ X0 ) )
| ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( a @ sK2 ) )
| ( $true
= ( b @ X2 ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f154]) ).
thf(f232,definition,
( spl3_3
<=> ! [X2: $i,X1: $i] :
( ( $false
= ( irel @ X1 @ sK0 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( b @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
thf(f233,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( irel @ X1 @ sK0 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( b @ X2 ) ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[],[f232]) ).
thf(f235,definition,
( spl3_4
<=> ! [X0: $i] :
( ( $true
= ( b @ X0 ) )
| ( ( irel @ sK0 @ X0 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
thf(f236,plain,
( ! [X0: $i] :
( ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( b @ X0 ) ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f235]) ).
thf(f264,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( b @ X0 ) )
| ( $true = $false )
| ( $false
= ( irel @ X1 @ sK0 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( ( irel @ sK0 @ X0 )
= $false )
| ( $true
= ( b @ X2 ) ) ),
inference(forward_demodulation,[],[f213,f116]) ).
thf(f265,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( b @ X2 ) )
| ( $false
= ( irel @ X1 @ sK0 ) )
| ( $true
= ( b @ X0 ) )
| ( ( irel @ sK0 @ X0 )
= $false )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f264]) ).
thf(f279,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[],[f265,f235,f232]) ).
thf(f282,plain,
( ( $false
= ( irel @ sK0 @ sK0 ) )
| ( $true
= ( b @ sK1 ) )
| ( $true = $false )
| ~ spl3_3 ),
inference(constrained_superposition,[],[f233,f112]) ).
thf(f302,plain,
( ( $false
= ( irel @ sK0 @ sK0 ) )
| ( $true
= ( b @ sK1 ) )
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f282]) ).
thf(f316,plain,
( ( $true = $false )
| ( $true
= ( b @ sK1 ) )
| ~ spl3_3 ),
inference(forward_demodulation,[],[f302,f73]) ).
thf(f317,plain,
( ( $true
= ( b @ sK1 ) )
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f316]) ).
thf(f322,plain,
( ( $true = $false )
| ~ spl3_2
| ~ spl3_3 ),
inference(forward_demodulation,[],[f317,f142]) ).
thf(f323,plain,
( $false
| ~ spl3_2
| ~ spl3_3 ),
inference(trivial_inequality_removal,[],[f322]) ).
thf(f324,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(avatar_contradiction_clause,[],[f323]) ).
thf(f325,plain,
( ( $true = $false )
| ( $true
= ( b @ sK1 ) )
| ~ spl3_4 ),
inference(constrained_superposition,[],[f236,f112]) ).
thf(f338,plain,
( ( $true
= ( b @ sK1 ) )
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f325]) ).
thf(f344,plain,
( ( $true = $false )
| ~ spl3_2
| ~ spl3_4 ),
inference(forward_demodulation,[],[f338,f142]) ).
thf(f345,plain,
( $false
| ~ spl3_2
| ~ spl3_4 ),
inference(trivial_inequality_removal,[],[f344]) ).
thf(f346,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[],[f345]) ).
thf(f347,plain,
( ( $true = $false )
| ~ spl3_1 ),
inference(forward_demodulation,[],[f138,f134]) ).
thf(f348,plain,
( $false
| ~ spl3_1 ),
inference(trivial_inequality_removal,[],[f347]) ).
thf(f349,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[],[f348]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f143]) ).
cnf(s10,plain,
( spl3_3
| spl3_4 ),
inference(sat_conversion,[],[f279]) ).
cnf(s17,plain,
( ~ spl3_2
| ~ spl3_3 ),
inference(sat_conversion,[],[f324]) ).
cnf(s20,plain,
( ~ spl3_2
| ~ spl3_4 ),
inference(sat_conversion,[],[f346]) ).
cnf(s22,plain,
~ spl3_1,
inference(sat_conversion,[],[f349]) ).
cnf(s23,plain,
spl3_2,
inference(rat,[],[s1,s22]) ).
cnf(s24,plain,
~ spl3_4,
inference(rat,[],[s20,s23]) ).
cnf(s25,plain,
~ spl3_3,
inference(rat,[],[s17,s23]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s10,s24,s25]) ).
thf(f350,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO064^4.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n019.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 16:26:33 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.29 % (1002325)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (1002334)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3112224056:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (1002336)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.29 % (1002336)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
% 0.21/0.29 % (1002331)lrs+10_16_si=on:nwc=1.5:random_seed=3458666887:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (1002330)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1826601454:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (1002332)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1148018834:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (1002334)Instruction limit reached!
% 0.21/0.29 % (1002334)------------------------------
% 0.21/0.29 % (1002334)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (1002334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (1002334)CaDiCaL version: 2.1.3
% 0.21/0.29 % (1002334)Termination reason: Instruction limit
% 0.21/0.29 % (1002334)Termination phase: Saturation
% 0.21/0.29 % (1002334)Time elapsed: 0.007 s
% 0.21/0.29 % (1002334)Peak memory usage: 12 MB
% 0.21/0.29 % (1002334)Instructions burned: 25 (million)
% 0.21/0.29 % (1002333)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=2189562145: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)
% 0.21/0.29 % (1002335)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1382019115:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (1002336)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=771661867:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (1002332)Instruction limit reached!
% 0.21/0.29 % (1002332)------------------------------
% 0.21/0.29 % (1002332)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (1002332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (1002332)CaDiCaL version: 2.1.3
% 0.21/0.29 % (1002332)Termination reason: Instruction limit
% 0.21/0.29 % (1002332)Termination phase: Saturation
% 0.21/0.29 % (1002332)Time elapsed: 0.002 s
% 0.21/0.29 % (1002332)Peak memory usage: 11 MB
% 0.21/0.29 % (1002332)Instructions burned: 4 (million)
% 0.21/0.29 % (1002331)Instruction limit reached!
% 0.21/0.29 % (1002331)------------------------------
% 0.21/0.29 % (1002331)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (1002331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (1002331)CaDiCaL version: 2.1.3
% 0.21/0.29 % (1002331)Termination reason: Instruction limit
% 0.21/0.29 % (1002331)Termination phase: Saturation
% 0.21/0.29 % (1002331)Time elapsed: 0.009 s
% 0.21/0.29 % (1002331)Peak memory usage: 12 MB
% 0.21/0.29 % (1002331)Instructions burned: 18 (million)
% 0.21/0.29 % (1002330) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1002325-1002330"...
% 0.21/0.29 % (1002336) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1002325-1002336"...
% 0.21/0.29 % (1002335) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1002325-1002335"...
% 0.21/0.29 % (1002330)...printing done.
% 0.21/0.29 % (1002330)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.29 % (1002330)------------------------------
% 0.21/0.29 % (1002330)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (1002330)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (1002330)CaDiCaL version: 2.1.3
% 0.21/0.29 % (1002330)Termination reason: Refutation
% 0.21/0.29 % (1002330)Time elapsed: 0.014 s
% 0.21/0.29 % (1002330)Peak memory usage: 13 MB
% 0.21/0.29 % (1002330)Instructions burned: 25 (million)
% 0.21/0.29 % (1002325)Success in time 0.044 s
% 0.21/0.29 % Vampire exiting
%------------------------------------------------------------------------------