%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO060^4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:46:25 AM UTC 2026
% Result : Theorem 0.39s 0.34s
% Output : Refutation 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 15
% Syntax : Number of formulae : 146 ( 64 unt; 0 typ; 6 def)
% Number of atoms : 1048 ( 214 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 1274 ( 106 ~; 167 |; 0 &; 828 @)
% ( 6 <=>; 94 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 71 ( 71 >; 0 *; 0 +; 0 <<)
% Number of symbols : 48 ( 44 usr; 12 con; 0-4 aty)
% ( 73 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 285 ( 0 sgn 96 !; 0 ?; 285 :)
% 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,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_28,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_29,type,
vNOT: $o > $o ).
thf(func_def_30,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
vAND: $o > $o > $o ).
thf(func_def_32,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_33,type,
vOR: $o > $o > $o ).
thf(func_def_34,type,
vIMP: $o > $o > $o ).
thf(func_def_35,type,
sK0: $i > $i ).
thf(func_def_36,type,
sK1: $i > $i ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mor) ).
thf(f7,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',mbox_s4) ).
thf(f8,axiom,
( ( ^ [X0: $i > $o] : X0 )
= iatom ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',iatom) ).
thf(f9,axiom,
( inot
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s4 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',inot) ).
thf(f13,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mbox_s4 @ X0 ) @ ( mbox_s4 @ X1 ) ) )
= ior ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',ior) ).
thf(f18,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= ivalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(f22,axiom,
ivalid @ ( ior @ ( inot @ ( iatom @ a ) ) @ ( inot @ ( iatom @ b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1) ).
thf(f23,conjecture,
ivalid @ ( ior @ ( inot @ ( iatom @ b ) ) @ ( inot @ ( iatom @ a ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f24,negated_conjecture,
~ ( ivalid @ ( ior @ ( inot @ ( iatom @ b ) ) @ ( inot @ ( iatom @ a ) ) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
thf(f28,plain,
ivalid @ ( ior @ ( inot @ ( iatom @ a ) ) @ ( inot @ ( iatom @ b ) ) ),
inference(rectify,[],[f22]) ).
thf(f29,plain,
( ( ivalid @ ( ior @ ( inot @ ( iatom @ a ) ) @ ( inot @ ( iatom @ b ) ) ) )
= $true ),
inference(fool_elimination,[],[f28]) ).
thf(f32,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f33,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= ivalid ),
inference(rectify,[],[f18]) ).
thf(f34,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f38,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f39,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f40,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f41,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f42,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
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(f45,plain,
~ ( ivalid @ ( ior @ ( inot @ ( iatom @ b ) ) @ ( inot @ ( iatom @ a ) ) ) ),
inference(rectify,[],[f24]) ).
thf(f46,plain,
( ( ivalid @ ( ior @ ( inot @ ( iatom @ b ) ) @ ( inot @ ( iatom @ a ) ) ) )
!= $true ),
inference(fool_elimination,[],[f45]) ).
thf(f48,plain,
( inot
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f56,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f59,plain,
( ( ivalid @ ( ior @ ( inot @ ( iatom @ b ) ) @ ( inot @ ( iatom @ a ) ) ) )
!= $true ),
inference(flattening,[],[f46]) ).
thf(f62,plain,
( ( ivalid @ ( ior @ ( inot @ ( iatom @ b ) ) @ ( inot @ ( iatom @ a ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f59]) ).
thf(f66,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f68,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f70,plain,
( inot
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f72,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f76,plain,
( ( ivalid @ ( ior @ ( inot @ ( iatom @ a ) ) @ ( inot @ ( iatom @ b ) ) ) )
= $true ),
inference(cnf_transformation,[],[f29]) ).
thf(f78,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f80,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f81,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f85,plain,
( inot
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f70,f81,f80]) ).
thf(f87,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,[],[f72,f78,f80,f80]) ).
thf(f91,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] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ Y0 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ Y0 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a ) ) ) ) ),
inference(definition_unfolding,[],[f62,f66,f87,f85,f68,f85,f68]) ).
thf(f92,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] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ Y0 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ a ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ Y0 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ b ) ) ) ) ),
inference(definition_unfolding,[],[f76,f66,f87,f85,f68,f85,f68]) ).
thf(f93,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f92]) ).
thf(f94,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f93]) ).
thf(f95,plain,
! [X1: $i] :
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f94]) ).
thf(f96,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f95]) ).
thf(f97,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f96]) ).
thf(f98,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) )
@ X2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f97]) ).
thf(f99,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ( irel @ X1 @ X3 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( b @ Y0 ) ) ) ) )
| ( ( ( irel @ X1 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a @ Y0 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f98]) ).
thf(f100,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( b @ Y0 ) ) ) ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( ( ( irel @ X1 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a @ Y0 ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f99]) ).
thf(f101,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( b @ Y0 ) ) ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( ( ( irel @ X1 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a @ Y0 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f100]) ).
thf(f102,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X1 @ X3 ) )
| ( ( ( irel @ X1 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a @ Y0 ) ) ) )
= $true )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( b @ Y0 ) )
@ ( sK0 @ X3 ) ) ) ),
inference(sigma_proxy_clausification,[],[f101]) ).
thf(f103,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X1 @ X3 ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a @ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( b @ Y0 ) )
@ ( sK0 @ X3 ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f102]) ).
thf(f104,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a @ Y0 ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( b @ Y0 ) )
@ ( sK0 @ X3 ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f103]) ).
thf(f105,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( irel @ X3 @ Y0 )
=> ( b @ Y0 ) )
@ ( sK0 @ X3 ) ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( irel @ X2 @ Y0 )
=> ( a @ Y0 ) )
@ ( sK1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f104]) ).
thf(f106,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( irel @ X3 @ ( sK0 @ X3 ) )
=> ( b @ ( sK0 @ X3 ) ) ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $false
= ( ( irel @ X2 @ ( sK1 @ X2 ) )
=> ( a @ ( sK1 @ X2 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f105]) ).
thf(f107,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( b @ ( sK0 @ X3 ) ) )
| ( $false
= ( ( irel @ X2 @ ( sK1 @ X2 ) )
=> ( a @ ( sK1 @ X2 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f106]) ).
thf(f108,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( irel @ X2 @ ( sK1 @ X2 ) )
=> ( a @ ( sK1 @ X2 ) ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $true
= ( irel @ X3 @ ( sK0 @ X3 ) ) )
| ( $false
= ( irel @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f106]) ).
thf(f109,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( irel @ X3 @ ( sK0 @ X3 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( a @ ( sK1 @ X2 ) ) )
| ( $false
= ( irel @ X1 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f108]) ).
thf(f110,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( irel @ X3 @ ( sK0 @ X3 ) ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( $true
= ( irel @ X2 @ ( sK1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f108]) ).
thf(f111,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( irel @ X1 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( b @ ( sK0 @ X3 ) ) )
| ( $false
= ( a @ ( sK1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f107]) ).
thf(f112,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( irel @ X2 @ ( sK1 @ X2 ) ) )
| ( $false
= ( irel @ X1 @ X3 ) )
| ( ( irel @ X1 @ X2 )
= $false )
| ( $false
= ( b @ ( sK0 @ X3 ) ) ) ),
inference(imp_proxy_clausification,[],[f107]) ).
thf(f113,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b @ Y2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f91]) ).
thf(f114,plain,
( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( a @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( b @ Y2 ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f113]) ).
thf(f115,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f114]) ).
thf(f116,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f115]) ).
thf(f117,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f115]) ).
thf(f118,plain,
( $false
= ( ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( a @ Y1 ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f117]) ).
thf(f119,plain,
( $false
= ( ( irel @ sK2 @ sK3 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f118]) ).
thf(f120,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a @ Y0 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f119]) ).
thf(f121,plain,
( $true
= ( irel @ sK2 @ sK3 ) ),
inference(imp_proxy_clausification,[],[f119]) ).
thf(f122,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a @ Y0 ) ) )
= $true ),
inference(not_proxy_clausification,[],[f120]) ).
thf(f123,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( irel @ sK3 @ Y0 )
=> ( a @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f122]) ).
thf(f124,plain,
! [X1: $i] :
( $true
= ( ( irel @ sK3 @ X1 )
=> ( a @ X1 ) ) ),
inference(beta-eta_normalization,[],[f123]) ).
thf(f125,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK3 @ X1 ) )
| ( $true
= ( a @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f124]) ).
thf(f126,plain,
( $false
= ( ^ [Y0: $i] :
( ( irel @ sK2 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( b @ Y1 ) ) ) )
@ sK4 ) ),
inference(sigma_proxy_clausification,[],[f116]) ).
thf(f127,plain,
( $false
= ( ( irel @ sK2 @ sK4 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK4 @ Y0 )
=> ( b @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f126]) ).
thf(f128,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK4 @ Y0 )
=> ( b @ Y0 ) ) ) )
= $false ),
inference(imp_proxy_clausification,[],[f127]) ).
thf(f129,plain,
( $true
= ( irel @ sK2 @ sK4 ) ),
inference(imp_proxy_clausification,[],[f127]) ).
thf(f130,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK4 @ Y0 )
=> ( b @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f128]) ).
thf(f131,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( irel @ sK4 @ Y0 )
=> ( b @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f130]) ).
thf(f132,plain,
! [X1: $i] :
( $true
= ( ( irel @ sK4 @ X1 )
=> ( b @ X1 ) ) ),
inference(beta-eta_normalization,[],[f131]) ).
thf(f133,plain,
! [X1: $i] :
( ( $false
= ( irel @ sK4 @ X1 ) )
| ( ( b @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f132]) ).
thf(f135,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( a @ ( sK1 @ X0 ) )
= $false )
| ( $false
= ( irel @ sK2 @ X0 ) )
| ( $false
= ( b @ ( sK0 @ sK4 ) ) ) ),
inference(superposition,[],[f111,f129]) ).
thf(f140,plain,
! [X0: $i] :
( ( ( a @ ( sK1 @ X0 ) )
= $false )
| ( $false
= ( b @ ( sK0 @ sK4 ) ) )
| ( $false
= ( irel @ sK2 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f135]) ).
thf(f145,definition,
( spl5_1
<=> ! [X0: $i] :
( ( ( a @ ( sK1 @ X0 ) )
= $false )
| ( $false
= ( irel @ sK2 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f146,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK2 @ X0 ) )
| ( ( a @ ( sK1 @ X0 ) )
= $false ) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f145]) ).
thf(f148,definition,
( spl5_2
<=> ( $false
= ( b @ ( sK0 @ sK4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f150,plain,
( ( $false
= ( b @ ( sK0 @ sK4 ) ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f148]) ).
thf(f151,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f140,f148,f145]) ).
thf(f164,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( irel @ X0 @ X1 )
= $false )
| ( $false
= ( irel @ X0 @ sK4 ) )
| ( $true
= ( b @ ( sK0 @ sK4 ) ) )
| ( $false
= ( a @ ( sK1 @ X1 ) ) ) ),
inference(superposition,[],[f133,f109]) ).
thf(f166,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( b @ ( sK0 @ sK4 ) ) )
| ( $false
= ( a @ ( sK1 @ X1 ) ) )
| ( $false
= ( irel @ X0 @ sK4 ) )
| ( ( irel @ X0 @ X1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f164]) ).
thf(f172,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( a @ ( sK1 @ X1 ) ) )
| ( $false
= ( irel @ X0 @ sK4 ) )
| ( $true = $false )
| ( ( irel @ X0 @ X1 )
= $false ) )
| ~ spl5_2 ),
inference(forward_demodulation,[],[f166,f150]) ).
thf(f173,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( irel @ X0 @ sK4 ) )
| ( ( irel @ X0 @ X1 )
= $false )
| ( $false
= ( a @ ( sK1 @ X1 ) ) ) )
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f172]) ).
thf(f189,plain,
! [X0: $i,X1: $i] :
( ( ( irel @ X0 @ sK3 )
= $false )
| ( $true = $false )
| ( ( irel @ X0 @ X1 )
= $false )
| ( ( a @ ( sK1 @ sK3 ) )
= $true )
| ( $false
= ( b @ ( sK0 @ X1 ) ) ) ),
inference(superposition,[],[f125,f112]) ).
thf(f194,plain,
! [X0: $i,X1: $i] :
( ( ( irel @ X0 @ sK3 )
= $false )
| ( ( a @ ( sK1 @ sK3 ) )
= $true )
| ( ( irel @ X0 @ X1 )
= $false )
| ( $false
= ( b @ ( sK0 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[],[f189]) ).
thf(f199,definition,
( spl5_6
<=> ( ( a @ ( sK1 @ sK3 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
thf(f201,plain,
( ( ( a @ ( sK1 @ sK3 ) )
= $true )
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f199]) ).
thf(f203,definition,
( spl5_7
<=> ! [X0: $i,X1: $i] :
( ( $false
= ( b @ ( sK0 @ X1 ) ) )
| ( ( irel @ X0 @ sK3 )
= $false )
| ( ( irel @ X0 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
thf(f204,plain,
( ! [X0: $i,X1: $i] :
( ( ( irel @ X0 @ sK3 )
= $false )
| ( $false
= ( b @ ( sK0 @ X1 ) ) )
| ( ( irel @ X0 @ X1 )
= $false ) )
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f203]) ).
thf(f206,plain,
( spl5_7
| spl5_6 ),
inference(avatar_split_clause,[],[f194,f199,f203]) ).
thf(f221,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( b @ ( sK0 @ sK4 ) ) )
| ( $false
= ( irel @ X0 @ sK4 ) )
| ( $true
= ( irel @ X1 @ ( sK1 @ X1 ) ) )
| ( ( irel @ X0 @ X1 )
= $false )
| ( $true = $false ) ),
inference(superposition,[],[f133,f110]) ).
thf(f226,plain,
! [X0: $i,X1: $i] :
( ( ( irel @ X0 @ X1 )
= $false )
| ( $true
= ( irel @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( irel @ X0 @ sK4 ) )
| ( $true
= ( b @ ( sK0 @ sK4 ) ) ) ),
inference(trivial_inequality_removal,[],[f221]) ).
thf(f234,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ sK2 @ X0 ) )
| ( ( a @ ( sK1 @ X0 ) )
= $false ) )
| ~ spl5_2 ),
inference(superposition,[],[f129,f173]) ).
thf(f236,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK2 @ X0 ) )
| ( ( a @ ( sK1 @ X0 ) )
= $false ) )
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f234]) ).
thf(f239,plain,
( spl5_1
| ~ spl5_2 ),
inference(avatar_split_clause,[],[f236,f148,f145]) ).
thf(f249,definition,
( spl5_12
<=> ( $true
= ( b @ ( sK0 @ sK4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_12])],[avatar_definition]) ).
thf(f251,plain,
( ( $true
= ( b @ ( sK0 @ sK4 ) ) )
| ~ spl5_12 ),
inference(avatar_component_clause,[],[f249]) ).
thf(f253,definition,
( spl5_13
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( irel @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( irel @ X0 @ sK4 ) )
| ( ( irel @ X0 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl5_13])],[avatar_definition]) ).
thf(f254,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( irel @ X1 @ ( sK1 @ X1 ) ) )
| ( $false
= ( irel @ X0 @ sK4 ) )
| ( ( irel @ X0 @ X1 )
= $false ) )
| ~ spl5_13 ),
inference(avatar_component_clause,[],[f253]) ).
thf(f260,plain,
( spl5_12
| spl5_13 ),
inference(avatar_split_clause,[],[f226,f253,f249]) ).
thf(f263,plain,
( ( $true = $false )
| ( ( a @ ( sK1 @ sK3 ) )
= $false )
| ~ spl5_1 ),
inference(superposition,[],[f146,f121]) ).
thf(f275,plain,
( ( ( a @ ( sK1 @ sK3 ) )
= $false )
| ~ spl5_1 ),
inference(trivial_inequality_removal,[],[f263]) ).
thf(f328,plain,
( ( $true = $false )
| ~ spl5_1
| ~ spl5_6 ),
inference(superposition,[],[f201,f275]) ).
thf(f331,plain,
( $false
| ~ spl5_1
| ~ spl5_6 ),
inference(trivial_inequality_removal,[],[f328]) ).
thf(f332,plain,
( ~ spl5_1
| ~ spl5_6 ),
inference(avatar_contradiction_clause,[],[f331]) ).
thf(f334,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK2 @ X0 ) )
| ( $false
= ( b @ ( sK0 @ X0 ) ) )
| ( $true = $false ) )
| ~ spl5_7 ),
inference(superposition,[],[f204,f121]) ).
thf(f337,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ sK2 @ X0 ) )
| ( $false
= ( b @ ( sK0 @ X0 ) ) ) )
| ~ spl5_7 ),
inference(trivial_inequality_removal,[],[f334]) ).
thf(f348,plain,
( ( $false
= ( b @ ( sK0 @ sK4 ) ) )
| ( $true = $false )
| ~ spl5_7 ),
inference(superposition,[],[f129,f337]) ).
thf(f354,plain,
( ( $false
= ( b @ ( sK0 @ sK4 ) ) )
| ~ spl5_7 ),
inference(trivial_inequality_removal,[],[f348]) ).
thf(f380,plain,
( spl5_2
| ~ spl5_7 ),
inference(avatar_split_clause,[],[f354,f203,f148]) ).
thf(f381,plain,
( ( $true = $false )
| ~ spl5_2
| ~ spl5_12 ),
inference(superposition,[],[f150,f251]) ).
thf(f385,plain,
( $false
| ~ spl5_2
| ~ spl5_12 ),
inference(trivial_inequality_removal,[],[f381]) ).
thf(f386,plain,
( ~ spl5_2
| ~ spl5_12 ),
inference(avatar_contradiction_clause,[],[f385]) ).
thf(f408,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ X0 @ sK4 ) )
| ( ( irel @ X0 @ sK3 )
= $false )
| ( ( a @ ( sK1 @ sK3 ) )
= $true ) )
| ~ spl5_13 ),
inference(superposition,[],[f254,f125]) ).
thf(f422,plain,
( ! [X0: $i] :
( ( ( a @ ( sK1 @ sK3 ) )
= $true )
| ( ( irel @ X0 @ sK3 )
= $false )
| ( $false
= ( irel @ X0 @ sK4 ) ) )
| ~ spl5_13 ),
inference(trivial_inequality_removal,[],[f408]) ).
thf(f434,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( irel @ X0 @ sK4 ) )
| ( ( irel @ X0 @ sK3 )
= $false ) )
| ~ spl5_1
| ~ spl5_13 ),
inference(forward_demodulation,[],[f422,f275]) ).
thf(f435,plain,
( ! [X0: $i] :
( ( $false
= ( irel @ X0 @ sK4 ) )
| ( ( irel @ X0 @ sK3 )
= $false ) )
| ~ spl5_1
| ~ spl5_13 ),
inference(trivial_inequality_removal,[],[f434]) ).
thf(f440,plain,
( ( $true = $false )
| ( ( irel @ sK2 @ sK3 )
= $false )
| ~ spl5_1
| ~ spl5_13 ),
inference(superposition,[],[f129,f435]) ).
thf(f441,plain,
( ( ( irel @ sK2 @ sK3 )
= $false )
| ~ spl5_1
| ~ spl5_13 ),
inference(trivial_inequality_removal,[],[f440]) ).
thf(f475,plain,
( ( $true = $false )
| ~ spl5_1
| ~ spl5_13 ),
inference(superposition,[],[f121,f441]) ).
thf(f478,plain,
( $false
| ~ spl5_1
| ~ spl5_13 ),
inference(trivial_inequality_removal,[],[f475]) ).
thf(f479,plain,
( ~ spl5_1
| ~ spl5_13 ),
inference(avatar_contradiction_clause,[],[f478]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f151]) ).
cnf(s8,plain,
( spl5_6
| spl5_7 ),
inference(sat_conversion,[],[f206]) ).
cnf(s11,plain,
( spl5_1
| ~ spl5_2 ),
inference(sat_conversion,[],[f239]) ).
cnf(s16,plain,
( spl5_12
| spl5_13 ),
inference(sat_conversion,[],[f260]) ).
cnf(s27,plain,
( ~ spl5_1
| ~ spl5_6 ),
inference(sat_conversion,[],[f332]) ).
cnf(s36,plain,
( spl5_2
| ~ spl5_7 ),
inference(sat_conversion,[],[f380]) ).
cnf(s39,plain,
( ~ spl5_2
| ~ spl5_12 ),
inference(sat_conversion,[],[f386]) ).
cnf(s44,plain,
( ~ spl5_1
| ~ spl5_13 ),
inference(sat_conversion,[],[f479]) ).
cnf(s45,plain,
spl5_1,
inference(rat,[],[s1,s11]) ).
cnf(s46,plain,
~ spl5_13,
inference(rat,[],[s44,s45]) ).
cnf(s47,plain,
~ spl5_6,
inference(rat,[],[s27,s45]) ).
cnf(s49,plain,
spl5_12,
inference(rat,[],[s16,s46]) ).
cnf(s50,plain,
spl5_7,
inference(rat,[],[s8,s47]) ).
cnf(s51,plain,
~ spl5_2,
inference(rat,[],[s39,s49]) ).
cnf(s52,plain,
$false,
inference(rat,[],[s36,s50,s51]) ).
thf(f480,plain,
$false,
inference(avatar_sat_refutation,[],[s52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO060^4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n016.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 16:30:35 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 Running higher-order theorem proving
% 0.10/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.39/0.32 % (561810)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.39/0.32 % (561823)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=321928049:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.39/0.32 % (561824)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.39/0.32 % (561824)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
% 0.39/0.32 % (561818)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4114032174:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.39/0.32 % (561820)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=861010497:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.39/0.32 % (561822)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1086904366:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.39/0.32 % (561821)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=3286479159: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)
% 0.39/0.32 % (561824)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=366681781:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.39/0.32 % (561819)lrs+10_16_si=on:nwc=1.5:random_seed=529810151:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.39/0.32 % (561820)Instruction limit reached!
% 0.39/0.32 % (561820)------------------------------
% 0.39/0.32 % (561820)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.32 % (561820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.32 % (561820)CaDiCaL version: 2.1.3
% 0.39/0.32 % (561820)Termination reason: Instruction limit
% 0.39/0.32 % (561820)Termination phase: Saturation
% 0.39/0.32 % (561820)Time elapsed: 0.003 s
% 0.39/0.32 % (561820)Peak memory usage: 12 MB
% 0.39/0.32 % (561820)Instructions burned: 6 (million)
% 0.39/0.32 % (561819)Instruction limit reached!
% 0.39/0.32 % (561819)------------------------------
% 0.39/0.32 % (561819)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.32 % (561819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.32 % (561819)CaDiCaL version: 2.1.3
% 0.39/0.32 % (561819)Termination reason: Instruction limit
% 0.39/0.32 % (561819)Termination phase: Saturation
% 0.39/0.32 % (561819)Time elapsed: 0.011 s
% 0.39/0.32 % (561819)Peak memory usage: 12 MB
% 0.39/0.32 % (561819)Instructions burned: 19 (million)
% 0.39/0.32 % (561823)Instruction limit reached!
% 0.39/0.32 % (561823)------------------------------
% 0.39/0.32 % (561823)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.32 % (561823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.32 % (561823)CaDiCaL version: 2.1.3
% 0.39/0.32 % (561823)Termination reason: Instruction limit
% 0.39/0.32 % (561823)Termination phase: Saturation
% 0.39/0.32 % (561823)Time elapsed: 0.022 s
% 0.39/0.32 % (561823)Peak memory usage: 12 MB
% 0.39/0.32 % (561823)Instructions burned: 79 (million)
% 0.39/0.32 % (561822)Instruction limit reached!
% 0.39/0.32 % (561822)------------------------------
% 0.39/0.32 % (561822)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.32 % (561822)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.32 % (561822)CaDiCaL version: 2.1.3
% 0.39/0.32 % (561822)Termination reason: Instruction limit
% 0.39/0.32 % (561822)Termination phase: Saturation
% 0.39/0.32 % (561822)Time elapsed: 0.014 s
% 0.39/0.32 % (561822)Peak memory usage: 11 MB
% 0.39/0.32 % (561822)Instructions burned: 24 (million)
% 0.39/0.32 % (561840)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2705122463:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.39/0.32 % (561841)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=4036098124:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.39/0.32 % (561840)Instruction limit reached!
% 0.39/0.34 % (561840)------------------------------
% 0.39/0.34 % (561840)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.34 % (561840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.34 % (561840)CaDiCaL version: 2.1.3
% 0.39/0.34 % (561840)Termination reason: Instruction limit
% 0.39/0.34 % (561840)Termination phase: Saturation
% 0.39/0.34 % (561840)Time elapsed: 0.002 s
% 0.39/0.34 % (561840)Peak memory usage: 10 MB
% 0.39/0.34 % (561840)Instructions burned: 4 (million)
% 0.39/0.34 % (561841)Instruction limit reached!
% 0.39/0.34 % (561841)------------------------------
% 0.39/0.34 % (561841)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.34 % (561841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.34 % (561841)CaDiCaL version: 2.1.3
% 0.39/0.34 % (561841)Termination reason: Instruction limit
% 0.39/0.34 % (561841)Termination phase: Saturation
% 0.39/0.34 % (561841)Time elapsed: 0.002 s
% 0.39/0.34 % (561841)Peak memory usage: 11 MB
% 0.39/0.34 % (561841)Instructions burned: 7 (million)
% 0.39/0.34 % (561842)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.39/0.34 % (561842)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3783788762:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.39/0.34 % (561843)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2921688608:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.39/0.34 % (561847)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=4291492533:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.39/0.34 % (561842)Instruction limit reached!
% 0.39/0.34 % (561842)------------------------------
% 0.39/0.34 % (561842)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.34 % (561842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.34 % (561842)CaDiCaL version: 2.1.3
% 0.39/0.34 % (561842)Termination reason: Instruction limit
% 0.39/0.34 % (561842)Termination phase: Saturation
% 0.39/0.34 % (561842)Time elapsed: 0.004 s
% 0.39/0.34 % (561842)Peak memory usage: 12 MB
% 0.39/0.34 % (561842)Instructions burned: 8 (million)
% 0.39/0.34 % (561843)Instruction limit reached!
% 0.39/0.34 % (561843)------------------------------
% 0.39/0.34 % (561843)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.34 % (561843)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.34 % (561843)CaDiCaL version: 2.1.3
% 0.39/0.34 % (561843)Termination reason: Instruction limit
% 0.39/0.34 % (561843)Termination phase: Saturation
% 0.39/0.34 % (561843)Time elapsed: 0.007 s
% 0.39/0.34 % (561843)Peak memory usage: 12 MB
% 0.39/0.34 % (561843)Instructions burned: 13 (million)
% 0.39/0.34 % (561846)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
% 0.39/0.34 % (561846)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.39/0.34 % (561818)Instruction limit reached!
% 0.39/0.34 % (561818)------------------------------
% 0.39/0.34 % (561818)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.34 % (561818)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.34 % (561818)CaDiCaL version: 2.1.3
% 0.39/0.34 % (561818)Termination reason: Instruction limit
% 0.39/0.34 % (561818)Termination phase: Saturation
% 0.39/0.34 % (561818)Time elapsed: 0.043 s
% 0.39/0.34 % (561818)Peak memory usage: 12 MB
% 0.39/0.34 % (561818)Instructions burned: 88 (million)
% 0.39/0.34 % (561846)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3851176800:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.39/0.34 % (561852)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.39/0.34 % (561851)lrs+10_1_si=on:cs=on:random_seed=1953626284:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.39/0.34 % (561846)Instruction limit reached!
% 0.39/0.34 % (561846)------------------------------
% 0.39/0.34 % (561846)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.34 % (561846)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.34 % (561846)CaDiCaL version: 2.1.3
% 0.39/0.34 % (561846)Termination reason: Instruction limit
% 0.39/0.34 % (561846)Termination phase: Saturation
% 0.39/0.34 % (561846)Time elapsed: 0.014 s
% 0.39/0.34 % (561846)Peak memory usage: 12 MB
% 0.39/0.34 % (561846)Instructions burned: 28 (million)
% 0.39/0.34 % (561852)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=3512351815:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.39/0.34 % (561851)Instruction limit reached!
% 0.39/0.34 % (561851)------------------------------
% 0.39/0.34 % (561851)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.34 % (561851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.34 % (561851)CaDiCaL version: 2.1.3
% 0.39/0.34 % (561851)Termination reason: Instruction limit
% 0.39/0.34 % (561851)Termination phase: Saturation
% 0.39/0.34 % (561851)Time elapsed: 0.004 s
% 0.39/0.34 % (561851)Peak memory usage: 11 MB
% 0.39/0.34 % (561851)Instructions burned: 9 (million)
% 0.39/0.34 % (561847)Instruction limit reached!
% 0.39/0.34 % (561847)------------------------------
% 0.39/0.34 % (561847)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.34 % (561847)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.34 % (561847)CaDiCaL version: 2.1.3
% 0.39/0.34 % (561847)Termination reason: Instruction limit
% 0.39/0.34 % (561847)Termination phase: Saturation
% 0.39/0.34 % (561847)Time elapsed: 0.024 s
% 0.39/0.34 % (561847)Peak memory usage: 12 MB
% 0.39/0.34 % (561847)Instructions burned: 86 (million)
% 0.39/0.34 % (561852)Instruction limit reached!
% 0.39/0.34 % (561852)------------------------------
% 0.39/0.34 % (561852)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.34 % (561852)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.34 % (561852)CaDiCaL version: 2.1.3
% 0.39/0.34 % (561852)Termination reason: Instruction limit
% 0.39/0.34 % (561852)Termination phase: shuffling
% 0.39/0.34 % (561852)Time elapsed: 0.002 s
% 0.39/0.34 % (561852)Peak memory usage: 10 MB
% 0.39/0.34 % (561852)Instructions burned: 4 (million)
% 0.39/0.34 % (561853)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=108980373:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.39/0.34 % (561853)Refutation not found, incomplete strategy
% 0.39/0.34 % (561853)------------------------------
% 0.39/0.34 % (561853)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.34 % (561853)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.34 % (561853)CaDiCaL version: 2.1.3
% 0.39/0.34 % (561853)Termination reason: Refutation not found, incomplete strategy
% 0.39/0.34 % (561853)Time elapsed: 0.002 s
% 0.39/0.34 % (561853)Peak memory usage: 12 MB
% 0.39/0.34 % (561853)Instructions burned: 3 (million)
% 0.39/0.34 % (561853)------------------------------
% 0.39/0.34 % (561853)------------------------------
% 0.39/0.34 % (561860)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1495176726:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.39/0.34 % (561860)Instruction limit reached!
% 0.39/0.34 % (561860)------------------------------
% 0.39/0.34 % (561860)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.34 % (561860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.34 % (561860)CaDiCaL version: 2.1.3
% 0.39/0.34 % (561860)Termination reason: Instruction limit
% 0.39/0.34 % (561860)Termination phase: Saturation
% 0.39/0.34 % (561860)Time elapsed: 0.004 s
% 0.39/0.34 % (561860)Peak memory usage: 12 MB
% 0.39/0.34 % (561860)Instructions burned: 14 (million)
% 0.39/0.34 % (561857)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1851827701:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.39/0.34 % (561858)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=748582224:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.39/0.34 % (561861)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=3562197121:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 0.39/0.34 % (561857)Refutation not found, incomplete strategy
% 0.39/0.34 % (561857)------------------------------
% 0.39/0.34 % (561857)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.34 % (561857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.34 % (561857)CaDiCaL version: 2.1.3
% 0.39/0.34 % (561857)Termination reason: Refutation not found, incomplete strategy
% 0.39/0.34 % (561857)Time elapsed: 0.002 s
% 0.39/0.34 % (561857)Peak memory usage: 12 MB
% 0.39/0.34 % (561857)Instructions burned: 3 (million)
% 0.39/0.34 % (561857)------------------------------
% 0.39/0.34 % (561857)------------------------------
% 0.39/0.34 % (561824)Instruction limit reached!
% 0.39/0.34 % (561824)------------------------------
% 0.39/0.34 % (561824)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.34 % (561824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.34 % (561824)CaDiCaL version: 2.1.3
% 0.39/0.34 % (561824)Termination reason: Instruction limit
% 0.39/0.34 % (561824)Termination phase: Saturation
% 0.39/0.34 % (561824)Time elapsed: 0.081 s
% 0.39/0.34 % (561824)Peak memory usage: 12 MB
% 0.39/0.34 % (561824)Instructions burned: 157 (million)
% 0.39/0.34 % (561862)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=1969477581:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/14Mi)
% 0.39/0.34 % (561862)Instruction limit reached!
% 0.39/0.34 % (561862)------------------------------
% 0.39/0.34 % (561862)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.34 % (561862)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.34 % (561862)CaDiCaL version: 2.1.3
% 0.39/0.34 % (561862)Termination reason: Instruction limit
% 0.39/0.34 % (561862)Termination phase: Saturation
% 0.39/0.34 % (561862)Time elapsed: 0.007 s
% 0.39/0.34 % (561862)Peak memory usage: 12 MB
% 0.39/0.34 % (561862)Instructions burned: 14 (million)
% 0.39/0.34 % (561868)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=2118633135:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 0.39/0.34 % (561858)Instruction limit reached!
% 0.39/0.34 % (561858)------------------------------
% 0.39/0.34 % (561858)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.34 % (561858)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.34 % (561858)CaDiCaL version: 2.1.3
% 0.39/0.34 % (561858)Termination reason: Instruction limit
% 0.39/0.34 % (561858)Termination phase: Saturation
% 0.39/0.34 % (561858)Time elapsed: 0.015 s
% 0.39/0.34 % (561858)Peak memory usage: 12 MB
% 0.39/0.34 % (561858)Instructions burned: 26 (million)
% 0.39/0.34 % (561864)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1615865411:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.39/0.34 % (561861) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-561810-561861"...
% 0.39/0.34 % (561864)Instruction limit reached!
% 0.39/0.34 % (561864)------------------------------
% 0.39/0.34 % (561864)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.34 % (561864)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.34 % (561864)CaDiCaL version: 2.1.3
% 0.39/0.34 % (561864)Termination reason: Instruction limit
% 0.39/0.34 % (561864)Termination phase: Function definition elimination
% 0.39/0.34 % (561864)Time elapsed: 0.002 s
% 0.39/0.34 % (561864)Peak memory usage: 10 MB
% 0.39/0.34 % (561864)Instructions burned: 3 (million)
% 0.39/0.34 % (561868)Instruction limit reached!
% 0.39/0.34 % (561868)------------------------------
% 0.39/0.34 % (561868)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.34 % (561868)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.34 % (561868)CaDiCaL version: 2.1.3
% 0.39/0.34 % (561868)Termination reason: Instruction limit
% 0.39/0.34 % (561868)Termination phase: Saturation
% 0.39/0.34 % (561868)Time elapsed: 0.008 s
% 0.39/0.34 % (561868)Peak memory usage: 12 MB
% 0.39/0.34 % (561868)Instructions burned: 28 (million)
% 0.39/0.34 % (561861)...printing done.
% 0.39/0.34 % (561869)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=2161523271:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 0.39/0.34 % (561861)Refutation found. Thanks to Tanya!
% 0.39/0.34 % SZS status Theorem for theBenchmark
% 0.39/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.39/0.34 % (561861)------------------------------
% 0.39/0.34 % (561861)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.39/0.34 % (561861)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.39/0.34 % (561861)CaDiCaL version: 2.1.3
% 0.39/0.34 % (561861)Termination reason: Refutation
% 0.39/0.34 % (561861)Time elapsed: 0.019 s
% 0.39/0.34 % (561861)Peak memory usage: 13 MB
% 0.39/0.34 % (561861)Instructions burned: 36 (million)
% 0.39/0.34 % (561810)Success in time 0.124 s
% 0.39/0.34 % Vampire exiting
%------------------------------------------------------------------------------