%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN391^4 : 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 : n010.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 08:41:42 AM UTC 2026
% Result : Theorem 0.21s 0.32s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 15
% Syntax : Number of formulae : 121 ( 76 unt; 0 typ; 2 def)
% Number of atoms : 1220 ( 103 equ; 0 cnn)
% Maximal formula atoms : 29 ( 10 avg)
% Number of connectives : 2378 ( 149 ~; 122 |; 40 &;1544 @)
% ( 2 <=>; 265 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 150 ( 150 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 38 usr; 7 con; 0-4 aty)
% ( 256 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 485 ( 0 sgn 16 !; 0 ?; 485 :)
% 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,
p1: $i > $o ).
thf(func_def_22,type,
p2: $i > $o ).
thf(func_def_23,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_24,type,
vIMP: $o > $o > $o ).
thf(func_def_25,type,
vAND: $o > $o > $o ).
thf(func_def_26,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_27,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_29,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_32,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_33,type,
vNOT: $o > $o ).
thf(func_def_34,type,
vOR: $o > $o > $o ).
thf(func_def_35,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f1,axiom,
! [X0: $i] : ( irel @ X0 @ X0 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',refl_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,
( 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] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) ) ),
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,
( 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,
( ( ^ [X0: $i > $o] : X0 )
= iatom ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',iatom) ).
thf(f9,axiom,
( ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s4 @ X0 ) ) )
= inot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',inot) ).
thf(f12,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ X0 @ X1 ) )
= iand ),
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(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(f18,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= ivalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL010^0.ax',ivalid) ).
thf(f22,conjecture,
ivalid @ ( iimplies @ ( iand @ ( ior @ ( iatom @ p1 ) @ ( iatom @ p2 ) ) @ ( iand @ ( ior @ ( inot @ ( iatom @ p1 ) ) @ ( iatom @ p2 ) ) @ ( ior @ ( iatom @ p1 ) @ ( inot @ ( iatom @ p2 ) ) ) ) ) @ ( inot @ ( ior @ ( inot @ ( iatom @ p1 ) ) @ ( inot @ ( iatom @ p2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pel9) ).
thf(f23,negated_conjecture,
~ ( ivalid @ ( iimplies @ ( iand @ ( ior @ ( iatom @ p1 ) @ ( iatom @ p2 ) ) @ ( iand @ ( ior @ ( inot @ ( iatom @ p1 ) ) @ ( iatom @ p2 ) ) @ ( ior @ ( iatom @ p1 ) @ ( inot @ ( iatom @ p2 ) ) ) ) ) @ ( inot @ ( ior @ ( inot @ ( iatom @ p1 ) ) @ ( inot @ ( iatom @ p2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
thf(f26,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f27,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f28,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= ivalid ),
inference(rectify,[],[f18]) ).
thf(f29,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f30,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( irel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
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(f35,plain,
~ ( ivalid @ ( iimplies @ ( iand @ ( ior @ ( iatom @ p1 ) @ ( iatom @ p2 ) ) @ ( iand @ ( ior @ ( inot @ ( iatom @ p1 ) ) @ ( iatom @ p2 ) ) @ ( ior @ ( iatom @ p1 ) @ ( inot @ ( iatom @ p2 ) ) ) ) ) @ ( inot @ ( ior @ ( inot @ ( iatom @ p1 ) ) @ ( inot @ ( iatom @ p2 ) ) ) ) ) ),
inference(rectify,[],[f23]) ).
thf(f36,plain,
( $true
= ( ~ ( ivalid @ ( iimplies @ ( iand @ ( ior @ ( iatom @ p1 ) @ ( iatom @ p2 ) ) @ ( iand @ ( ior @ ( inot @ ( iatom @ p1 ) ) @ ( iatom @ p2 ) ) @ ( ior @ ( iatom @ p1 ) @ ( inot @ ( iatom @ p2 ) ) ) ) ) @ ( inot @ ( ior @ ( inot @ ( iatom @ p1 ) ) @ ( inot @ ( iatom @ p2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f35]) ).
thf(f37,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f38,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f37]) ).
thf(f39,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f46,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f47,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f48,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f49,plain,
! [X0: $i] : ( irel @ X0 @ X0 ),
inference(rectify,[],[f1]) ).
thf(f50,plain,
( ( !! @ $i
@ ^ [Y0: $i] : ( irel @ Y0 @ Y0 ) )
= $true ),
inference(fool_elimination,[],[f49]) ).
thf(f51,plain,
( inot
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f53,plain,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f54,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f56,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f12]) ).
thf(f58,plain,
( inot
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f60,plain,
( iimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mimplies @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f61,plain,
( iatom
= ( ^ [Y0: $i > $o] : Y0 ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f62,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f63,plain,
( $true
= ( ~ ( ivalid @ ( iimplies @ ( iand @ ( ior @ ( iatom @ p1 ) @ ( iatom @ p2 ) ) @ ( iand @ ( ior @ ( inot @ ( iatom @ p1 ) ) @ ( iatom @ p2 ) ) @ ( ior @ ( iatom @ p1 ) @ ( inot @ ( iatom @ p2 ) ) ) ) ) @ ( inot @ ( ior @ ( inot @ ( iatom @ p1 ) ) @ ( inot @ ( iatom @ p2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f64,plain,
( ior
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mbox_s4 @ Y0 ) @ ( mbox_s4 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f65,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f68,plain,
( ivalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f69,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f70,plain,
( iand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f71,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f74,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f38]) ).
thf(f77,plain,
( ( !! @ $i
@ ^ [Y0: $i] : ( irel @ Y0 @ Y0 ) )
= $true ),
inference(cnf_transformation,[],[f50]) ).
thf(f81,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,[],[f65,f71,f74]) ).
thf(f82,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,[],[f58,f74,f69]) ).
thf(f84,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,[],[f70,f62]) ).
thf(f85,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,[],[f64,f71,f69,f69]) ).
thf(f86,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,[],[f60,f81,f69,f69]) ).
thf(f90,plain,
( ( ~ ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $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,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
@ p1 )
@ ( ^ [Y0: $i > $o] : Y0
@ p2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
& ( Y2 @ Y4 ) )
@ 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] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ Y0 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p1 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p2 ) )
@ ( ^ [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
@ p1 )
@ ( ^ [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
@ p2 ) ) ) ) )
@ ( ^ [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,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] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ Y0 ) )
@ ( ^ [Y0: $i > $o] : Y0
@ p1 ) )
@ ( ^ [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
@ p2 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f63,f68,f86,f84,f85,f61,f61,f84,f85,f82,f61,f61,f85,f61,f82,f61,f82,f85,f82,f61,f82,f61]) ).
thf(f91,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( p2 @ Y3 ) ) ) ) ) )
& ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( p1 @ Y3 ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) )
& ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( p1 @ Y4 ) ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( p2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f90]) ).
thf(f92,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( irel @ Y0 @ Y0 )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f77]) ).
thf(f93,plain,
! [X1: $i] :
( ( irel @ X1 @ X1 )
= $true ),
inference(beta-eta_normalization,[],[f92]) ).
thf(f94,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( p2 @ Y3 ) ) ) ) ) )
& ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( p1 @ Y3 ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) )
& ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( p1 @ Y4 ) ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( p2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f91]) ).
thf(f95,plain,
( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( p2 @ Y3 ) ) ) ) ) )
& ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( p1 @ Y3 ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) )
& ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( p1 @ Y4 ) ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( irel @ Y3 @ Y4 )
=> ( p2 @ Y4 ) ) ) ) ) ) ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f94]) ).
thf(f96,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( p1 @ Y3 ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( p2 @ Y3 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f95]) ).
thf(f97,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( p1 @ Y3 ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( p2 @ Y3 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f96]) ).
thf(f98,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f96]) ).
thf(f99,plain,
( ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( p1 @ Y3 ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( irel @ Y2 @ Y3 )
=> ( p2 @ Y3 ) ) ) ) ) ) ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f97]) ).
thf(f100,plain,
( $false
= ( ( irel @ sK0 @ sK1 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f99]) ).
thf(f101,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f100]) ).
thf(f102,plain,
( ( irel @ sK0 @ sK1 )
= $true ),
inference(imp_proxy_clausification,[],[f100]) ).
thf(f105,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f101]) ).
thf(f106,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f105]) ).
thf(f107,plain,
! [X1: $i] :
( $true
= ( ( irel @ sK1 @ X1 )
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f106]) ).
thf(f109,plain,
( $true
= ( $true
=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) ) ) ),
inference(constrained_superposition,[],[f107,f93]) ).
thf(f110,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f109]) ).
thf(f111,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f110]) ).
thf(f113,definition,
( spl2_1
<=> ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
thf(f115,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f113]) ).
thf(f117,definition,
( spl2_2
<=> ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
thf(f118,plain,
( ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) )
| spl2_2 ),
inference(avatar_component_clause,[],[f117]) ).
thf(f119,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f117]) ).
thf(f120,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f111,f117,f113]) ).
thf(f121,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) )
@ X1 ) )
| ~ spl2_2 ),
inference(pi_proxy_clausification,[],[f119]) ).
thf(f122,plain,
( ! [X1: $i] :
( ( ( irel @ sK1 @ X1 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) ) ) )
= $true )
| ~ spl2_2 ),
inference(beta-eta_normalization,[],[f121]) ).
thf(f124,plain,
( ( ( $true
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p2 @ Y0 ) ) ) )
= $true )
| ~ spl2_2 ),
inference(constrained_superposition,[],[f122,f93]) ).
thf(f125,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p2 @ Y0 ) ) ) )
= $true )
| ~ spl2_2 ),
inference(boolean_simplification,[],[f124]) ).
thf(f126,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p2 @ Y0 ) ) ) )
| ~ spl2_2 ),
inference(not_proxy_clausification,[],[f125]) ).
thf(f180,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f98]) ).
thf(f181,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( irel @ sK0 @ Y0 )
=> ( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p2 @ Y2 ) ) ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( irel @ Y1 @ Y2 )
=> ( p1 @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) )
& ( ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X1: $i] :
( $true
= ( ( irel @ sK0 @ X1 )
=> ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f186,plain,
( $true
= ( $true
=> ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p2 @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ) ) ),
inference(constrained_superposition,[],[f182,f102]) ).
thf(f187,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p2 @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f186]) ).
thf(f189,plain,
( ( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p1 @ Y0 ) ) )
| $true )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p2 @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ) )
| ~ spl2_2 ),
inference(forward_demodulation,[],[f187,f119]) ).
thf(f190,plain,
( ( ( $true
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p2 @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) )
= $true )
| ~ spl2_2 ),
inference(boolean_simplification,[],[f189]) ).
thf(f191,plain,
( ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p2 @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) )
= $true )
| ~ spl2_2 ),
inference(boolean_simplification,[],[f190]) ).
thf(f192,plain,
( ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) )
| $false )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p1 @ Y0 ) ) )
| $false ) )
= $true )
| ~ spl2_2 ),
inference(forward_demodulation,[],[f191,f126]) ).
thf(f193,plain,
( ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) )
| $false )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p1 @ Y0 ) ) ) )
= $true )
| ~ spl2_2 ),
inference(boolean_simplification,[],[f192]) ).
thf(f194,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) )
| ~ spl2_2 ),
inference(boolean_simplification,[],[f193]) ).
thf(f195,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p1 @ Y0 ) ) ) )
| ~ spl2_2 ),
inference(and_proxy_clausification,[],[f194]) ).
thf(f196,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) ) ) )
| ~ spl2_2 ),
inference(and_proxy_clausification,[],[f194]) ).
thf(f197,plain,
( spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f196,f117,f113]) ).
thf(f209,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p1 @ Y1 ) ) ) )
@ X1 )
= $true )
| ~ spl2_1 ),
inference(pi_proxy_clausification,[],[f115]) ).
thf(f210,plain,
( ! [X1: $i] :
( $true
= ( ( irel @ sK1 @ X1 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ X1 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) )
| ~ spl2_1 ),
inference(beta-eta_normalization,[],[f209]) ).
thf(f212,plain,
( ( $true
= ( $true
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p1 @ Y0 ) ) ) ) )
| ~ spl2_1 ),
inference(constrained_superposition,[],[f210,f93]) ).
thf(f214,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p1 @ Y0 ) ) ) )
= $true )
| ~ spl2_1 ),
inference(boolean_simplification,[],[f212]) ).
thf(f216,plain,
( ( ( ~ $true ) = $true )
| ~ spl2_1
| ~ spl2_2 ),
inference(forward_demodulation,[],[f214,f195]) ).
thf(f217,plain,
( ( $true = $false )
| ~ spl2_1
| ~ spl2_2 ),
inference(boolean_simplification,[],[f216]) ).
thf(f218,plain,
( $false
| ~ spl2_1
| ~ spl2_2 ),
inference(trivial_inequality_removal,[],[f217]) ).
thf(f219,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_contradiction_clause,[],[f218]) ).
thf(f220,plain,
( ( $true
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) )
& ( $true
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p2 @ Y0 ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) ) )
| ~ spl2_1 ),
inference(forward_demodulation,[],[f187,f115]) ).
thf(f221,plain,
( ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) )
& $true
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) )
= $true )
| ~ spl2_1 ),
inference(boolean_simplification,[],[f220]) ).
thf(f222,plain,
( ( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) )
& ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p2 @ Y0 ) ) ) ) )
= $true )
| ~ spl2_1 ),
inference(boolean_simplification,[],[f221]) ).
thf(f223,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p1 @ Y0 ) ) ) )
| ~ spl2_1 ),
inference(not_proxy_clausification,[],[f214]) ).
thf(f480,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ( p1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) ) )
| ~ spl2_1 ),
inference(and_proxy_clausification,[],[f222]) ).
thf(f483,plain,
( ( ( $false
| ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl2_1 ),
inference(forward_demodulation,[],[f480,f223]) ).
thf(f484,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( irel @ sK1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( irel @ Y0 @ Y1 )
=> ( p2 @ Y1 ) ) ) ) ) )
| ~ spl2_1 ),
inference(boolean_simplification,[],[f483]) ).
thf(f485,plain,
( $false
| ~ spl2_1
| spl2_2 ),
inference(forward_subsumption_resolution,[],[f484,f118]) ).
thf(f486,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_contradiction_clause,[],[f485]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f120]) ).
cnf(s3,plain,
( spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f197]) ).
cnf(s4,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f219]) ).
cnf(s8,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f486]) ).
cnf(s9,plain,
spl2_1,
inference(rat,[],[s1,s3]) ).
cnf(s10,plain,
spl2_2,
inference(rat,[],[s8,s9]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s4,s10,s9]) ).
thf(f487,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN391^4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n010.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 16:16:04 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 Running higher-order theorem proving
% 0.10/0.22 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
% 0.21/0.32 % (3064706)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.32 % (3064711)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2861045744:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.32 % (3064717)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.32 % (3064717)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
% 0.21/0.32 % (3064712)lrs+10_16_si=on:nwc=1.5:random_seed=1627836397:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.32 % (3064713)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3564283111:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.32 % (3064714)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=2461014235:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.32 % (3064715)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1358876828:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.32 % (3064716)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1291934225:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.32 % (3064717)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=1039920763:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.32 % (3064713)Instruction limit reached!
% 0.21/0.32 % (3064713)------------------------------
% 0.21/0.32 % (3064713)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3064713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3064713)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3064713)Termination reason: Instruction limit
% 0.21/0.32 % (3064713)Termination phase: Property scanning
% 0.21/0.32 % (3064713)Time elapsed: 0.002 s
% 0.21/0.32 % (3064713)Peak memory usage: 10 MB
% 0.21/0.32 % (3064713)Instructions burned: 4 (million)
% 0.21/0.32 % (3064712)Instruction limit reached!
% 0.21/0.32 % (3064712)------------------------------
% 0.21/0.32 % (3064712)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3064712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3064712)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3064712)Termination reason: Instruction limit
% 0.21/0.32 % (3064712)Termination phase: Saturation
% 0.21/0.32 % (3064712)Time elapsed: 0.009 s
% 0.21/0.32 % (3064712)Peak memory usage: 12 MB
% 0.21/0.32 % (3064712)Instructions burned: 19 (million)
% 0.21/0.32 % (3064711)Instruction limit reached!
% 0.21/0.32 % (3064711)------------------------------
% 0.21/0.32 % (3064711)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3064711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3064711)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3064711)Termination reason: Instruction limit
% 0.21/0.32 % (3064711)Termination phase: Saturation
% 0.21/0.32 % (3064711)Time elapsed: 0.022 s
% 0.21/0.32 % (3064711)Peak memory usage: 12 MB
% 0.21/0.32 % (3064711)Instructions burned: 88 (million)
% 0.21/0.32 % (3064715)Instruction limit reached!
% 0.21/0.32 % (3064715)------------------------------
% 0.21/0.32 % (3064715)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3064715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3064715)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3064715)Termination reason: Instruction limit
% 0.21/0.32 % (3064715)Termination phase: Saturation
% 0.21/0.32 % (3064715)Time elapsed: 0.014 s
% 0.21/0.32 % (3064715)Peak memory usage: 11 MB
% 0.21/0.32 % (3064715)Instructions burned: 25 (million)
% 0.21/0.32 % (3064725)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2290911962:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.32 % (3064727)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.32 % (3064725)Instruction limit reached!
% 0.21/0.32 % (3064725)------------------------------
% 0.21/0.32 % (3064725)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3064725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3064725)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3064725)Termination reason: Instruction limit
% 0.21/0.32 % (3064725)Termination phase: Property scanning
% 0.21/0.32 % (3064725)Time elapsed: 0.002 s
% 0.21/0.32 % (3064725)Peak memory usage: 10 MB
% 0.21/0.32 % (3064725)Instructions burned: 4 (million)
% 0.21/0.32 % (3064727)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3168676938:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.32 % (3064727)Instruction limit reached!
% 0.21/0.32 % (3064727)------------------------------
% 0.21/0.32 % (3064727)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3064727)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3064727)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3064727)Termination reason: Instruction limit
% 0.21/0.32 % (3064727)Termination phase: Saturation
% 0.21/0.32 % (3064727)Time elapsed: 0.002 s
% 0.21/0.32 % (3064727)Peak memory usage: 11 MB
% 0.21/0.32 % (3064727)Instructions burned: 8 (million)
% 0.21/0.32 % (3064726)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2187954570:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.32 % (3064726)Instruction limit reached!
% 0.21/0.32 % (3064726)------------------------------
% 0.21/0.32 % (3064726)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3064726)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3064726)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3064726)Termination reason: Instruction limit
% 0.21/0.32 % (3064726)Termination phase: Saturation
% 0.21/0.32 % (3064726)Time elapsed: 0.003 s
% 0.21/0.32 % (3064726)Peak memory usage: 11 MB
% 0.21/0.32 % (3064726)Instructions burned: 6 (million)
% 0.21/0.32 % (3064728)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1124519004:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.21/0.32 % (3064732)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=2778403183:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.21/0.32 % (3064716)Instruction limit reached!
% 0.21/0.32 % (3064716)------------------------------
% 0.21/0.32 % (3064716)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3064716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3064716)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3064716)Termination reason: Instruction limit
% 0.21/0.32 % (3064716)Termination phase: Saturation
% 0.21/0.32 % (3064716)Time elapsed: 0.036 s
% 0.21/0.32 % (3064716)Peak memory usage: 12 MB
% 0.21/0.32 % (3064716)Instructions burned: 75 (million)
% 0.21/0.32 % (3064731)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
% 0.21/0.32 % (3064731)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.32 % (3064728)Instruction limit reached!
% 0.21/0.32 % (3064728)------------------------------
% 0.21/0.32 % (3064728)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3064728)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3064728)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3064728)Termination reason: Instruction limit
% 0.21/0.32 % (3064728)Termination phase: Saturation
% 0.21/0.32 % (3064728)Time elapsed: 0.006 s
% 0.21/0.32 % (3064728)Peak memory usage: 12 MB
% 0.21/0.32 % (3064728)Instructions burned: 13 (million)
% 0.21/0.32 % (3064731)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1401913108:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.21/0.32 % (3064732) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3064706-3064732"...
% 0.21/0.32 % (3064734)lrs+10_1_si=on:cs=on:random_seed=2221071450:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.21/0.32 % (3064737)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.21/0.32 % (3064732)...printing done.
% 0.21/0.32 % (3064732)Refutation found. Thanks to Tanya!
% 0.21/0.32 % SZS status Theorem for theBenchmark
% 0.21/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.32 % (3064732)------------------------------
% 0.21/0.32 % (3064732)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3064732)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3064732)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3064732)Termination reason: Refutation
% 0.21/0.32 % (3064732)Time elapsed: 0.017 s
% 0.21/0.32 % (3064732)Peak memory usage: 13 MB
% 0.21/0.32 % (3064732)Instructions burned: 64 (million)
% 0.21/0.32 % (3064706)Success in time 0.09 s
% 0.21/0.32 % Vampire exiting
%------------------------------------------------------------------------------