%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n009.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 08:48:51 AM UTC 2026
% Result : Theorem 0.09s 0.26s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 14
% Syntax : Number of formulae : 111 ( 66 unt; 0 typ; 3 def)
% Number of atoms : 777 ( 159 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 898 ( 27 ~; 108 |; 13 &; 625 @)
% ( 3 <=>; 66 =>; 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 : 44 ( 40 usr; 9 con; 0-4 aty)
% ( 56 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 246 ( 0 sgn 74 !; 0 ?; 246 :)
% 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,
vNOT: $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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $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] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mor) ).
thf(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',mand) ).
thf(f7,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
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(f26,plain,
! [X0: $i] : ( irel @ X0 @ X0 ),
inference(rectify,[],[f1]) ).
thf(f27,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f26]) ).
thf(f32,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f33,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f34,plain,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f35,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f37,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f38,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f37]) ).
thf(f39,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f42,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f43,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f48,plain,
( ivalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f49,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f56,plain,
ivalid @ ( iatom @ c ),
inference(rectify,[],[f22]) ).
thf(f57,plain,
( ( ivalid @ ( iatom @ c ) )
= $true ),
inference(fool_elimination,[],[f56]) ).
thf(f58,plain,
ivalid @ ( ior @ ( ior @ ( iatom @ b ) @ ( iatom @ a ) ) @ ( iatom @ b ) ),
inference(rectify,[],[f23]) ).
thf(f59,plain,
( ( ivalid @ ( ior @ ( ior @ ( iatom @ b ) @ ( iatom @ a ) ) @ ( iatom @ b ) ) )
= $true ),
inference(fool_elimination,[],[f58]) ).
thf(f60,plain,
~ ( ivalid @ ( ior @ ( iatom @ a ) @ ( iand @ ( iatom @ b ) @ ( iatom @ c ) ) ) ),
inference(rectify,[],[f25]) ).
thf(f61,plain,
( ( ivalid @ ( ior @ ( iatom @ a ) @ ( iand @ ( iatom @ b ) @ ( iatom @ c ) ) ) )
!= $true ),
inference(fool_elimination,[],[f60]) ).
thf(f62,plain,
( ( ivalid @ ( ior @ ( iatom @ a ) @ ( iand @ ( iatom @ b ) @ ( iatom @ c ) ) ) )
!= $true ),
inference(flattening,[],[f61]) ).
thf(f65,plain,
! [X0: $i] :
( ( irel @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f27]) ).
thf(f68,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f69,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f35]) ).
thf(f71,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f72,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f76,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f77,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f82,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f49]) ).
thf(f86,plain,
( ( ivalid @ ( iatom @ c ) )
= $true ),
inference(cnf_transformation,[],[f57]) ).
thf(f87,plain,
( ( ivalid @ ( ior @ ( ior @ ( iatom @ b ) @ ( iatom @ a ) ) @ ( iatom @ b ) ) )
= $true ),
inference(cnf_transformation,[],[f59]) ).
thf(f88,plain,
( ( ivalid @ ( ior @ ( iatom @ a ) @ ( iand @ ( iatom @ b ) @ ( iatom @ c ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f62]) ).
thf(f94,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ Y0
@ Y1 ) ) ),
inference(definition_unfolding,[],[f76,f69]) ).
thf(f95,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ 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,[],[f77,f68,f71,f71]) ).
thf(f100,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ c ) ) ),
inference(definition_unfolding,[],[f86,f82,f72]) ).
thf(f101,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ 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] :
( ( Y2 @ Y4 )
| ( Y3 @ 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 ) ) ) ),
inference(definition_unfolding,[],[f87,f82,f95,f95,f72,f72,f72]) ).
thf(f102,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ 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] :
( ( Y2 @ Y4 )
& ( Y3 @ Y4 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o] : Y0
@ b )
@ ( ^ [Y0: $i > $o] : Y0
@ c ) ) ) ) ),
inference(definition_unfolding,[],[f88,f82,f95,f72,f94,f72,f72]) ).
thf(f103,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( b @ Y1 )
& ( c @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f102]) ).
thf(f104,plain,
( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( b @ Y1 )
& ( c @ Y1 ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f103]) ).
thf(f105,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( a @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( c @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f104]) ).
thf(f106,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( c @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f105]) ).
thf(f107,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( a @ Y0 ) ) ) ),
inference(or_proxy_clausification,[],[f105]) ).
thf(f108,plain,
( $false
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( a @ Y0 ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f107]) ).
thf(f109,plain,
( $false
= ( ( irel @ sK0 @ sK1 )
=> ( a @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f108]) ).
thf(f110,plain,
( $false
= ( a @ sK1 ) ),
inference(imp_proxy_clausification,[],[f109]) ).
thf(f111,plain,
( $true
= ( irel @ sK0 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f109]) ).
thf(f112,plain,
( $false
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( b @ Y0 )
& ( c @ Y0 ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f106]) ).
thf(f113,plain,
( $false
= ( ( irel @ sK0 @ sK2 )
=> ( ( b @ sK2 )
& ( c @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f112]) ).
thf(f114,plain,
( $false
= ( ( b @ sK2 )
& ( c @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f113]) ).
thf(f115,plain,
( $true
= ( irel @ sK0 @ sK2 ) ),
inference(imp_proxy_clausification,[],[f113]) ).
thf(f116,plain,
( ( $false
= ( c @ sK2 ) )
| ( $false
= ( b @ sK2 ) ) ),
inference(and_proxy_clausification,[],[f114]) ).
thf(f117,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f101]) ).
thf(f118,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f117]) ).
thf(f119,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f118]) ).
thf(f120,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f119]) ).
thf(f121,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) )
@ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f120]) ).
thf(f122,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( b @ Y0 ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f121]) ).
thf(f123,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X2 )
=> ( b @ X2 ) ) )
| ( $true
= ( ( irel @ X1 @ X3 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( b @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( a @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f122]) ).
thf(f124,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( ( irel @ X1 @ X3 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( b @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( a @ Y0 ) ) ) ) ) )
| ( $true
= ( b @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f123]) ).
thf(f125,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $true
= ( b @ X2 ) )
| ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( b @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( a @ Y0 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f124]) ).
thf(f126,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $true
= ( b @ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( a @ Y0 ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( b @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f125]) ).
thf(f127,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $true
= ( b @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( a @ Y0 ) )
@ X4 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( b @ Y0 ) ) ) ) ),
inference(pi_proxy_clausification,[],[f126]) ).
thf(f128,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $true
= ( b @ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( a @ Y0 ) )
@ X4 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( b @ Y0 ) )
@ X5 ) ) ),
inference(pi_proxy_clausification,[],[f127]) ).
thf(f129,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $true
= ( b @ X2 ) )
| ( $true
= ( ( irel @ X3 @ X4 )
=> ( a @ X4 ) ) )
| ( $true
= ( ( irel @ X3 @ X5 )
=> ( b @ X5 ) ) ) ),
inference(beta-eta_normalization,[],[f128]) ).
thf(f130,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $true
= ( b @ X2 ) )
| ( $false
= ( irel @ X3 @ X4 ) )
| ( $true
= ( ( irel @ X3 @ X5 )
=> ( b @ X5 ) ) )
| ( $true
= ( a @ X4 ) ) ),
inference(imp_proxy_clausification,[],[f129]) ).
thf(f131,plain,
! [X2: $i,X3: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( irel @ X3 @ X5 ) )
| ( $false
= ( irel @ X3 @ X4 ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( b @ X2 ) )
| ( $true
= ( a @ X4 ) )
| ( $true
= ( b @ X5 ) ) ),
inference(imp_proxy_clausification,[],[f130]) ).
thf(f132,plain,
( $true
= ( !! @ $i @ c ) ),
inference(beta-eta_normalization,[],[f100]) ).
thf(f133,plain,
! [X1: $i] :
( $true
= ( c @ X1 ) ),
inference(pi_proxy_clausification,[],[f132]) ).
thf(f135,definition,
( spl3_1
<=> ( $false
= ( b @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
thf(f137,plain,
( ( $false
= ( b @ sK2 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[],[f135]) ).
thf(f139,definition,
( spl3_2
<=> ( $false
= ( c @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
thf(f141,plain,
( ( $false
= ( c @ sK2 ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[],[f139]) ).
thf(f142,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[],[f116,f139,f135]) ).
thf(f154,plain,
( ( $true = $false )
| ~ spl3_2 ),
inference(constrained_superposition,[],[f133,f141]) ).
thf(f158,plain,
( $false
| ~ spl3_2 ),
inference(trivial_inequality_removal,[],[f154]) ).
thf(f159,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[],[f158]) ).
thf(f215,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( ( irel @ X0 @ X1 )
= $false )
| ( ( irel @ X0 @ X2 )
= $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( b @ X1 ) )
| ( $true
= ( a @ X2 ) )
| ( $true
= ( b @ X1 ) ) ),
inference(equality_factoring,[],[f131]) ).
thf(f220,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $false != $false )
| ( ( irel @ X0 @ X1 )
= $false )
| ( ( irel @ X0 @ X2 )
= $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( b @ X1 ) )
| ( $true
= ( a @ X2 ) ) ),
inference(duplicate_literal_removal,[],[f215]) ).
thf(f221,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( irel @ X0 @ X1 )
= $false )
| ( ( irel @ X0 @ X2 )
= $false )
| ( ( irel @ X0 @ X0 )
= $false )
| ( $true
= ( b @ X1 ) )
| ( $true
= ( a @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f220]) ).
thf(f258,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X0 @ X1 )
= $false )
| ( ( irel @ X0 @ X2 )
= $false )
| ( $true
= ( b @ X1 ) )
| ( $true
= ( a @ X2 ) ) ),
inference(forward_demodulation,[],[f221,f65]) ).
thf(f259,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( irel @ X0 @ X2 )
= $false )
| ( ( irel @ X0 @ X1 )
= $false )
| ( $true
= ( b @ X1 ) )
| ( $true
= ( a @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f258]) ).
thf(f290,definition,
( spl3_7
<=> ! [X0: $i] :
( ( $false
= ( irel @ sK0 @ X0 ) )
| ( $true
= ( b @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl3_7])],[avatar_definition]) ).
thf(f291,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK0 @ X0 ) )
| ( $true
= ( b @ X0 ) ) )
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f290]) ).
thf(f358,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ X0 ) )
| ( $true
= ( b @ X0 ) )
| ( $true
= ( a @ sK1 ) ) ),
inference(constrained_superposition,[],[f111,f259]) ).
thf(f375,plain,
! [X0: $i] :
( ( $false
= ( irel @ sK0 @ X0 ) )
| ( $true
= ( b @ X0 ) )
| ( $true
= ( a @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f358]) ).
thf(f389,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK0 @ X0 ) )
| ( $true
= ( b @ X0 ) ) ),
inference(forward_demodulation,[],[f375,f110]) ).
thf(f390,plain,
! [X0: $i] :
( ( $false
= ( irel @ sK0 @ X0 ) )
| ( $true
= ( b @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f389]) ).
thf(f398,plain,
spl3_7,
inference(avatar_split_clause,[],[f390,f290]) ).
thf(f401,plain,
( ( $true = $false )
| ( $true
= ( b @ sK2 ) )
| ~ spl3_7 ),
inference(constrained_superposition,[],[f291,f115]) ).
thf(f414,plain,
( ( $true
= ( b @ sK2 ) )
| ~ spl3_7 ),
inference(trivial_inequality_removal,[],[f401]) ).
thf(f421,plain,
( ( $true = $false )
| ~ spl3_1
| ~ spl3_7 ),
inference(forward_demodulation,[],[f414,f137]) ).
thf(f422,plain,
( $false
| ~ spl3_1
| ~ spl3_7 ),
inference(trivial_inequality_removal,[],[f421]) ).
thf(f423,plain,
( ~ spl3_1
| ~ spl3_7 ),
inference(avatar_contradiction_clause,[],[f422]) ).
cnf(s1,plain,
( spl3_1
| spl3_2 ),
inference(sat_conversion,[],[f142]) ).
cnf(s3,plain,
~ spl3_2,
inference(sat_conversion,[],[f159]) ).
cnf(s21,plain,
spl3_7,
inference(sat_conversion,[],[f398]) ).
cnf(s26,plain,
( ~ spl3_1
| ~ spl3_7 ),
inference(sat_conversion,[],[f423]) ).
cnf(s28,plain,
~ spl3_1,
inference(rat,[],[s26,s21]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s1,s3,s28]) ).
thf(f424,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.09/0.17 % Computer : n009.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 16:26:30 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 Running first-order model finding
% 0.09/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.26 % (14894)Will run a generic schedule for satisfiability detection.
% 0.09/0.26 % (14899)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3716860555_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.26 % (14902)dis+10_1_sil=32000:sp=arity:random_seed=3211637095:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.26 % (14904)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1931783534:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.26 % (14901)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3051115826:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.26 % (14903)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3268454104:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.26 % (14905)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4098008804:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.26 % (14903)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.26 % Exception at run slice level
% 0.09/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.09/0.26 % (14900)% WARNING: option uhcvi not known.
% 0.09/0.26 % (14900)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3955540995:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.26 % (14900)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.26 % (14900)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.09/0.26 % (14902) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-14894-14902"...
% 0.09/0.26 % (14904) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-14894-14904"...
% 0.09/0.26 % (14900) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-14894-14900"...
% 0.09/0.26 % (14905) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-14894-14905"...
% 0.09/0.26 % (14902)...printing done.
% 0.09/0.26 % (14902)Refutation found. Thanks to Tanya!
% 0.09/0.26 % SZS status Theorem for theBenchmark
% 0.09/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.26 % (14902)------------------------------
% 0.09/0.26 % (14902)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.26 % (14902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.26 % (14902)CaDiCaL version: 2.1.3
% 0.09/0.26 % (14902)Termination reason: Refutation
% 0.09/0.26 % (14902)Time elapsed: 0.016 s
% 0.09/0.26 % (14902)Peak memory usage: 12 MB
% 0.09/0.26 % (14902)Instructions burned: 30 (million)
% 0.09/0.26 % (14894)Success in time 0.053 s
% 0.09/0.26 % Vampire exiting
%------------------------------------------------------------------------------