%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN978^4 : 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 : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:41:44 AM UTC 2026
% Result : Theorem 0.21s 0.27s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 16
% Syntax : Number of formulae : 122 ( 61 unt; 0 typ; 4 def)
% Number of atoms : 796 ( 132 equ; 0 cnn)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 1069 ( 88 ~; 100 |; 26 &; 709 @)
% ( 4 <=>; 77 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 139 ( 139 >; 0 *; 0 +; 0 <<)
% Number of symbols : 45 ( 41 usr; 11 con; 0-4 aty)
% ( 65 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 290 ( 0 sgn 34 !; 0 ?; 290 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_27,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_29,type,
vIMP: $o > $o > $o ).
thf(func_def_30,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_31,type,
vOR: $o > $o > $o ).
thf(func_def_32,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
vNOT: $o > $o ).
thf(func_def_34,type,
vAND: $o > $o > $o ).
thf(f2,axiom,
! [X2: $i,X0: $i,X1: $i] :
( ( ( irel @ X0 @ X1 )
& ( irel @ X1 @ X2 ) )
=> ( irel @ X0 @ X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',trans_axiom) ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
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(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mimplies) ).
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,
( ( ^ [X0: $i > $o] : X0 )
= iatom ),
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(f14,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mimplies @ ( mbox_s4 @ X0 ) @ ( mbox_s4 @ X1 ) ) )
= iimplies ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iimplies) ).
thf(f16,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( iand @ ( iimplies @ X0 @ X1 ) @ ( iimplies @ X1 @ X0 ) ) )
= iequiv ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iequiv) ).
thf(f18,axiom,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(f22,conjecture,
ivalid @ ( iimplies @ ( iand @ ( iatom @ a ) @ ( iatom @ b ) ) @ ( iequiv @ ( iatom @ a ) @ ( iatom @ b ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
thf(f23,negated_conjecture,
~ ( ivalid @ ( iimplies @ ( iand @ ( iatom @ a ) @ ( iatom @ b ) ) @ ( iequiv @ ( iatom @ a ) @ ( iatom @ b ) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
thf(f24,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f25,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( irel @ X1 @ X2 )
& ( irel @ X2 @ X0 ) )
=> ( irel @ X1 @ X0 ) ),
inference(rectify,[],[f2]) ).
thf(f26,plain,
! [X0: $i,X2: $i,X1: $i] :
( ( ( ( irel @ X1 @ X2 )
= $true )
& ( $true
= ( irel @ X2 @ X0 ) ) )
=> ( $true
= ( irel @ X1 @ X0 ) ) ),
inference(fool_elimination,[],[f25]) ).
thf(f30,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox_s4 ),
inference(rectify,[],[f7]) ).
thf(f31,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f32,plain,
~ ( ivalid @ ( iimplies @ ( iand @ ( iatom @ a ) @ ( iatom @ b ) ) @ ( iequiv @ ( iatom @ a ) @ ( iatom @ b ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f33,plain,
( ( ivalid @ ( iimplies @ ( iand @ ( iatom @ a ) @ ( iatom @ b ) ) @ ( iequiv @ ( iatom @ a ) @ ( iatom @ b ) ) ) )
!= $true ),
inference(fool_elimination,[],[f32]) ).
thf(f34,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f35,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f37,plain,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f38,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f37]) ).
thf(f40,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f41,plain,
( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( iand @ ( iimplies @ Y0 @ Y1 ) @ ( iimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f48,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
inference(rectify,[],[f5]) ).
thf(f49,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f50,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f53,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f54,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f55,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f56,plain,
( ( ivalid @ ( iimplies @ ( iand @ ( iatom @ a ) @ ( iatom @ b ) ) @ ( iequiv @ ( iatom @ a ) @ ( iatom @ b ) ) ) )
!= $true ),
inference(flattening,[],[f33]) ).
thf(f57,plain,
! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( irel @ X1 @ X0 ) )
| ( ( irel @ X1 @ X2 )
!= $true )
| ( $true
!= ( irel @ X2 @ X0 ) ) ),
inference(ennf_transformation,[],[f26]) ).
thf(f58,plain,
! [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( irel @ X1 @ X0 ) )
| ( $true
!= ( irel @ X2 @ X0 ) )
| ( ( irel @ X1 @ X2 )
!= $true ) ),
inference(flattening,[],[f57]) ).
thf(f59,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( irel @ X2 @ X0 ) )
| ( $true
!= ( irel @ X1 @ X0 ) )
| ( ( irel @ X2 @ X1 )
!= $true ) ),
inference(rectify,[],[f58]) ).
thf(f60,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f65,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( irel @ X1 @ X0 ) )
| ( ( irel @ X2 @ X1 )
!= $true )
| ( $true
= ( irel @ X2 @ X0 ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f67,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f68,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f69,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f70,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f71,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f73,plain,
( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( iand @ ( iimplies @ Y0 @ Y1 ) @ ( iimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f74,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f75,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f77,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f80,plain,
( ( ivalid @ ( iimplies @ ( iand @ ( iatom @ a ) @ ( iatom @ b ) ) @ ( iequiv @ ( iatom @ a ) @ ( iatom @ b ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f56]) ).
thf(f84,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f68,f69,f70]) ).
thf(f87,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,[],[f74,f67]) ).
thf(f89,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [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,[],[f75,f84,f60,f60]) ).
thf(f91,plain,
( iequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
& ( Y4 @ Y6 ) )
@ Y2
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f73,f87,f89,f89]) ).
thf(f93,plain,
( $true
!= ( ^ [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 > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [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 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o] : Y0
@ b ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
& ( Y4 @ Y6 ) )
@ Y2
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
( !! @ $i
@ ^ [Y6: $i] :
( ( irel @ Y5 @ Y6 )
=> ( Y4 @ Y6 ) ) )
@ Y3 ) )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a )
@ ( ^ [Y0: $i > $o] : Y0
@ b ) ) ) ) ),
inference(definition_unfolding,[],[f80,f77,f89,f87,f71,f71,f91,f71,f71]) ).
thf(f94,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( b @ Y1 )
& ( a @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f93]) ).
thf(f95,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( b @ Y1 )
& ( a @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b @ Y2 ) ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f94]) ).
thf(f96,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( a @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f95]) ).
thf(f97,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f96]) ).
thf(f98,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( a @ Y0 ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f96]) ).
thf(f99,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( a @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f98]) ).
thf(f100,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( a @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f99]) ).
thf(f101,plain,
! [X1: $i] :
( $true
= ( ( irel @ sK0 @ X1 )
=> ( ( b @ X1 )
& ( a @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f100]) ).
thf(f102,plain,
! [X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( ( b @ X1 )
& ( a @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f101]) ).
thf(f103,plain,
! [X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( a @ X1 ) ) ),
inference(and_proxy_clausification,[],[f102]) ).
thf(f104,plain,
! [X1: $i] :
( ( ( irel @ sK0 @ X1 )
= $false )
| ( $true
= ( b @ X1 ) ) ),
inference(and_proxy_clausification,[],[f102]) ).
thf(f105,plain,
( ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f97]) ).
thf(f106,plain,
( $false
= ( ( irel @ sK0 @ sK1 )
=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( b @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( a @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( a @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( b @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f105]) ).
thf(f107,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( b @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( a @ Y0 ) ) ) )
& ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( a @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( b @ Y0 ) ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f106]) ).
thf(f108,plain,
( $true
= ( irel @ sK0 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f106]) ).
thf(f109,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( a @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( b @ Y0 ) ) ) )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( b @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( a @ Y0 ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f107]) ).
thf(f110,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( b @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( a @ Y0 ) ) ) )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( b @ Y0 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f109]) ).
thf(f127,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( a @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( b @ Y0 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f110]) ).
thf(f136,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( b @ Y0 ) ) )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( a @ Y0 ) )
@ sK4 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f127]) ).
thf(f137,plain,
( ( ( ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( b @ Y0 ) )
@ sK5 )
= $false )
| ( ( ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( a @ Y0 ) )
@ sK4 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f136]) ).
thf(f138,plain,
( ( ( ( irel @ sK1 @ sK4 )
=> ( a @ sK4 ) )
= $false )
| ( ( ( irel @ sK1 @ sK5 )
=> ( b @ sK5 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f137]) ).
thf(f139,plain,
( ( ( ( irel @ sK1 @ sK5 )
=> ( b @ sK5 ) )
= $false )
| ( $false
= ( a @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f138]) ).
thf(f140,plain,
( ( ( ( irel @ sK1 @ sK5 )
=> ( b @ sK5 ) )
= $false )
| ( $true
= ( irel @ sK1 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f138]) ).
thf(f141,plain,
( ( $true
= ( irel @ sK1 @ sK4 ) )
| ( ( b @ sK5 )
= $false ) ),
inference(imp_proxy_clausification,[],[f140]) ).
thf(f142,plain,
( ( $true
= ( irel @ sK1 @ sK5 ) )
| ( $true
= ( irel @ sK1 @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f140]) ).
thf(f143,plain,
( ( $false
= ( a @ sK4 ) )
| ( ( b @ sK5 )
= $false ) ),
inference(imp_proxy_clausification,[],[f139]) ).
thf(f144,plain,
( ( $true
= ( irel @ sK1 @ sK5 ) )
| ( $false
= ( a @ sK4 ) ) ),
inference(imp_proxy_clausification,[],[f139]) ).
thf(f173,definition,
( spl6_7
<=> ( $true
= ( irel @ sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
thf(f175,plain,
( ( $true
= ( irel @ sK1 @ sK5 ) )
| ~ spl6_7 ),
inference(avatar_component_clause,[],[f173]) ).
thf(f177,definition,
( spl6_8
<=> ( $true
= ( irel @ sK1 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
thf(f179,plain,
( ( $true
= ( irel @ sK1 @ sK4 ) )
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f177]) ).
thf(f180,plain,
( spl6_7
| spl6_8 ),
inference(avatar_split_clause,[],[f142,f177,f173]) ).
thf(f182,definition,
( spl6_9
<=> ( ( b @ sK5 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition]) ).
thf(f184,plain,
( ( ( b @ sK5 )
= $false )
| ~ spl6_9 ),
inference(avatar_component_clause,[],[f182]) ).
thf(f185,plain,
( spl6_8
| spl6_9 ),
inference(avatar_split_clause,[],[f141,f182,f177]) ).
thf(f187,definition,
( spl6_10
<=> ( $false
= ( a @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition]) ).
thf(f189,plain,
( ( $false
= ( a @ sK4 ) )
| ~ spl6_10 ),
inference(avatar_component_clause,[],[f187]) ).
thf(f190,plain,
( spl6_10
| spl6_7 ),
inference(avatar_split_clause,[],[f144,f173,f187]) ).
thf(f191,plain,
( spl6_10
| spl6_9 ),
inference(avatar_split_clause,[],[f143,f182,f187]) ).
thf(f226,plain,
( ! [X0: $i] :
( ( ( irel @ X0 @ sK1 )
!= $true )
| ( $true
= ( irel @ X0 @ sK5 ) )
| ( $true != $true ) )
| ~ spl6_7 ),
inference(constrained_superposition,[],[f65,f175]) ).
thf(f228,plain,
( ! [X0: $i] :
( ( ( irel @ X0 @ sK1 )
!= $true )
| ( $true
= ( irel @ X0 @ sK5 ) ) )
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f226]) ).
thf(f239,plain,
( ( $true != $true )
| ( $true
= ( irel @ sK0 @ sK5 ) )
| ~ spl6_7 ),
inference(constrained_superposition,[],[f228,f108]) ).
thf(f240,plain,
( ( $true
= ( irel @ sK0 @ sK5 ) )
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f239]) ).
thf(f244,plain,
( ( $true
= ( b @ sK5 ) )
| ( $true = $false )
| ~ spl6_7 ),
inference(constrained_superposition,[],[f104,f240]) ).
thf(f249,plain,
( ( $true
= ( b @ sK5 ) )
| ~ spl6_7 ),
inference(trivial_inequality_removal,[],[f244]) ).
thf(f255,plain,
( ( $true = $false )
| ~ spl6_7
| ~ spl6_9 ),
inference(forward_demodulation,[],[f249,f184]) ).
thf(f256,plain,
( $false
| ~ spl6_7
| ~ spl6_9 ),
inference(trivial_inequality_removal,[],[f255]) ).
thf(f257,plain,
( ~ spl6_7
| ~ spl6_9 ),
inference(avatar_contradiction_clause,[],[f256]) ).
thf(f261,plain,
( ! [X0: $i] :
( ( $true
= ( irel @ X0 @ sK4 ) )
| ( ( irel @ X0 @ sK1 )
!= $true )
| ( $true != $true ) )
| ~ spl6_8 ),
inference(constrained_superposition,[],[f65,f179]) ).
thf(f262,plain,
( ! [X0: $i] :
( ( ( irel @ X0 @ sK1 )
!= $true )
| ( $true
= ( irel @ X0 @ sK4 ) ) )
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f261]) ).
thf(f303,plain,
( ( $true != $true )
| ( $true
= ( irel @ sK0 @ sK4 ) )
| ~ spl6_8 ),
inference(constrained_superposition,[],[f262,f108]) ).
thf(f304,plain,
( ( $true
= ( irel @ sK0 @ sK4 ) )
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f303]) ).
thf(f309,plain,
( ( $true = $false )
| ( $true
= ( a @ sK4 ) )
| ~ spl6_8 ),
inference(constrained_superposition,[],[f103,f304]) ).
thf(f312,plain,
( ( $true
= ( a @ sK4 ) )
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f309]) ).
thf(f316,plain,
( ( $true = $false )
| ~ spl6_8
| ~ spl6_10 ),
inference(forward_demodulation,[],[f312,f189]) ).
thf(f317,plain,
( $false
| ~ spl6_8
| ~ spl6_10 ),
inference(trivial_inequality_removal,[],[f316]) ).
thf(f318,plain,
( ~ spl6_8
| ~ spl6_10 ),
inference(avatar_contradiction_clause,[],[f317]) ).
cnf(s6,plain,
( spl6_7
| spl6_8 ),
inference(sat_conversion,[],[f180]) ).
cnf(s7,plain,
( spl6_8
| spl6_9 ),
inference(sat_conversion,[],[f185]) ).
cnf(s8,plain,
( spl6_7
| spl6_10 ),
inference(sat_conversion,[],[f190]) ).
cnf(s9,plain,
( spl6_9
| spl6_10 ),
inference(sat_conversion,[],[f191]) ).
cnf(s11,plain,
( ~ spl6_7
| ~ spl6_9 ),
inference(sat_conversion,[],[f257]) ).
cnf(s16,plain,
( ~ spl6_8
| ~ spl6_10 ),
inference(sat_conversion,[],[f318]) ).
cnf(s18,plain,
spl6_7,
inference(rat,[],[s16,s6,s8]) ).
cnf(s19,plain,
~ spl6_9,
inference(rat,[],[s11,s18]) ).
cnf(s20,plain,
spl6_10,
inference(rat,[],[s9,s19]) ).
cnf(s21,plain,
spl6_8,
inference(rat,[],[s7,s19]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s16,s20,s21]) ).
thf(f322,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN978^4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n018.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:21:42 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.21/0.27 % (286324)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.27 % (286329)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=238168041:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.27 % (286329) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-286324-286329"...
% 0.21/0.27 % (286335)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.27 % (286335)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
% 0.21/0.27 % (286329)...printing done.
% 0.21/0.27 % (286329)Refutation found. Thanks to Tanya!
% 0.21/0.27 % SZS status Theorem for theBenchmark
% 0.21/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.27 % (286329)------------------------------
% 0.21/0.27 % (286329)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.27 % (286329)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.27 % (286329)CaDiCaL version: 2.1.3
% 0.21/0.27 % (286329)Termination reason: Refutation
% 0.21/0.27 % (286329)Time elapsed: 0.006 s
% 0.21/0.27 % (286329)Peak memory usage: 13 MB
% 0.21/0.27 % (286329)Instructions burned: 20 (million)
% 0.21/0.27 % (286324)Success in time 0.028 s
% 0.21/0.27 % Vampire exiting
%------------------------------------------------------------------------------