%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL601^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 08:14:26 AM UTC 2026
% Result : Theorem 0.49s 0.45s
% Output : Refutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 11
% Syntax : Number of formulae : 142 ( 36 unt; 0 typ; 4 def)
% Number of atoms : 915 ( 141 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 1840 ( 181 ~; 176 |; 32 &;1086 @)
% ( 7 <=>; 148 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 272 ( 272 >; 0 *; 0 +; 0 <<)
% Number of symbols : 73 ( 69 usr; 13 con; 0-4 aty)
% ( 210 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 383 ( 0 sgn 82 !; 0 ?; 383 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
individuals: $tType ).
thf(func_def_1,type,
prop_a: $i > $o ).
thf(func_def_2,type,
prop_b: $i > $o ).
thf(func_def_3,type,
prop_c: $i > $o ).
thf(func_def_4,type,
mfalse: $i > $o ).
thf(func_def_5,type,
mtrue: $i > $o ).
thf(func_def_6,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimpl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
miff: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mall: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_15,type,
mexists: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_16,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_17,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_18,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_19,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_20,type,
cartesian_product: ( $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(func_def_21,type,
pair_rel: $i > $i > $i > $i > $o ).
thf(func_def_22,type,
id_rel: ( $i > $o ) > $i > $i > $o ).
thf(func_def_23,type,
sub_rel: ( $i > $i > $o ) > ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
is_rel_on: ( $i > $i > $o ) > ( $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_25,type,
restrict_rel_domain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(func_def_26,type,
rel_diagonal: $i > $i > $o ).
thf(func_def_27,type,
rel_composition: ( $i > $i > $o ) > ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_28,type,
reflexive: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
irreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_30,type,
symmetric: ( $i > $i > $o ) > $o ).
thf(func_def_31,type,
transitive: ( $i > $i > $o ) > $o ).
thf(func_def_32,type,
equiv_rel: ( $i > $i > $o ) > $o ).
thf(func_def_33,type,
rel_codomain: ( $i > $i > $o ) > $i > $o ).
thf(func_def_34,type,
rel_domain: ( $i > $i > $o ) > $i > $o ).
thf(func_def_35,type,
rel_inverse: ( $i > $i > $o ) > $i > $i > $o ).
thf(func_def_36,type,
equiv_classes: ( $i > $i > $o ) > ( $i > $o ) > $o ).
thf(func_def_37,type,
restrict_rel_codomain: ( $i > $i > $o ) > ( $i > $o ) > $i > $i > $o ).
thf(func_def_38,type,
rel_field: ( $i > $i > $o ) > $i > $o ).
thf(func_def_39,type,
well_founded: ( $i > $i > $o ) > $o ).
thf(func_def_40,type,
upwards_well_founded: ( $i > $i > $o ) > $o ).
thf(func_def_41,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
vIMP: $o > $o > $o ).
thf(func_def_43,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_47,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vAND: $o > $o > $o ).
thf(func_def_49,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
vOR: $o > $o > $o ).
thf(func_def_53,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_54,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_55,type,
vNOT: $o > $o ).
thf(func_def_56,type,
vIFF: $o > $o > $o ).
thf(func_def_57,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_59,type,
sK1: $i > $i > $o ).
thf(func_def_63,type,
sK5: ( $i > $o ) > $i ).
thf(func_def_64,type,
sK6: $i > $o ).
thf(func_def_65,type,
sK7: $i > $i > $o ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimpl ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mimpl) ).
thf(f8,axiom,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f12,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f27,axiom,
( transitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X3: $i,X2: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET008^2.ax',transitive) ).
thf(f37,conjecture,
( ! [X0: $i > $i > $o,X1: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
<=> ! [X0: $i > $i > $o] : ( transitive @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
thf(f38,negated_conjecture,
~ ( ! [X0: $i > $i > $o,X1: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
<=> ! [X0: $i > $i > $o] : ( transitive @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f51,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f12]) ).
thf(f52,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f51]) ).
thf(f58,plain,
( transitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X2 )
& ( X0 @ X1 @ X3 ) )
=> ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f27]) ).
thf(f59,plain,
( transitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f58]) ).
thf(f65,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f66,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f65]) ).
thf(f68,plain,
~ ( ! [X0: $i > $i > $o,X1: $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ X0 @ X1 ) @ ( mbox @ X0 @ ( mbox @ X0 @ X1 ) ) ) )
<=> ! [X2: $i > $i > $o] : ( transitive @ X2 ) ),
inference(rectify,[],[f38]) ).
thf(f69,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ Y1 @ Y0 ) @ ( mbox @ Y1 @ ( mbox @ Y1 @ Y0 ) ) ) ) ) )
!= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] : ( transitive @ Y0 ) ) )
= $true ),
inference(fool_elimination,[],[f68]) ).
thf(f74,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f87,plain,
( ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f8]) ).
thf(f88,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f87]) ).
thf(f90,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f91,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f90]) ).
thf(f114,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f123,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f125,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f126,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] : ( mvalid @ ( mimpl @ ( mbox @ Y1 @ Y0 ) @ ( mbox @ Y1 @ ( mbox @ Y1 @ Y0 ) ) ) ) ) )
!= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] : ( transitive @ Y0 ) ) )
= $true ),
inference(cnf_transformation,[],[f69]) ).
thf(f130,plain,
( transitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f137,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f91]) ).
thf(f142,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f145,plain,
( mimpl
= ( ^ [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,[],[f125,f142,f137]) ).
thf(f149,plain,
( $true
= ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ^ [Y2: $i > $o] :
( !! @ $i
@ ^ [Y3: $i] : ( Y2 @ Y3 ) )
@ ( ^ [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 > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ Y1
@ Y0 )
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ Y1
@ ( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ Y1
@ Y0 ) ) ) ) ) )
!= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( ( Y1 @ Y4 @ Y2 )
& ( Y1 @ Y2 @ Y3 ) )
=> ( Y1 @ Y4 @ Y3 ) ) ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f126,f123,f145,f114,f114,f114,f130]) ).
thf(f150,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y0 @ Y4 ) ) ) ) ) ) ) ) )
!= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y0 @ Y4 ) ) ) ) ) ) ) ) )
= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y0 @ Y4 ) ) ) ) ) ) ) ) )
!= ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y0 @ Y4 ) ) ) ) ) ) ) ) )
= $true )
| ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
= $true ) ),
inference(xor_proxy_clausification,[],[f152]) ).
thf(f154,plain,
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
= $false )
| ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y0 @ Y4 ) ) ) ) ) ) ) ) )
= $false ) ),
inference(xor_proxy_clausification,[],[f152]) ).
thf(f156,definition,
( spl0_1
<=> ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f158,plain,
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f156]) ).
thf(f160,definition,
( spl0_2
<=> ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y0 @ Y4 ) ) ) ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f162,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y0 @ Y4 ) ) ) ) ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f160]) ).
thf(f163,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f153,f160,f156]) ).
thf(f165,definition,
( spl0_3
<=> ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f167,plain,
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f165]) ).
thf(f169,definition,
( spl0_4
<=> ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y0 @ Y4 ) ) ) ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
thf(f171,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y0 @ Y4 ) ) ) ) ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f169]) ).
thf(f172,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f154,f169,f165]) ).
thf(f173,plain,
( ( $false
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ sK1 ) )
| ~ spl0_3 ),
inference(sigma_proxy_clausification,[],[f167]) ).
thf(f174,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK1 @ Y2 @ Y0 )
& ( sK1 @ Y0 @ Y1 ) )
=> ( sK1 @ Y2 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f175,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( sK1 @ Y2 @ Y0 )
& ( sK1 @ Y0 @ Y1 ) )
=> ( sK1 @ Y2 @ Y1 ) ) ) )
@ sK2 )
= $false )
| ~ spl0_3 ),
inference(sigma_proxy_clausification,[],[f174]) ).
thf(f176,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK1 @ Y1 @ sK2 )
& ( sK1 @ sK2 @ Y0 ) )
=> ( sK1 @ Y1 @ Y0 ) ) ) )
= $false )
| ~ spl0_3 ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f177,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( sK1 @ Y1 @ sK2 )
& ( sK1 @ sK2 @ Y0 ) )
=> ( sK1 @ Y1 @ Y0 ) ) )
@ sK3 )
= $false )
| ~ spl0_3 ),
inference(sigma_proxy_clausification,[],[f176]) ).
thf(f178,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( sK1 @ Y0 @ sK2 )
& ( sK1 @ sK2 @ sK3 ) )
=> ( sK1 @ Y0 @ sK3 ) ) ) )
| ~ spl0_3 ),
inference(beta-eta_normalization,[],[f177]) ).
thf(f179,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( ( sK1 @ Y0 @ sK2 )
& ( sK1 @ sK2 @ sK3 ) )
=> ( sK1 @ Y0 @ sK3 ) )
@ sK4 ) )
| ~ spl0_3 ),
inference(sigma_proxy_clausification,[],[f178]) ).
thf(f180,plain,
( ( ( ( ( sK1 @ sK4 @ sK2 )
& ( sK1 @ sK2 @ sK3 ) )
=> ( sK1 @ sK4 @ sK3 ) )
= $false )
| ~ spl0_3 ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f181,plain,
( ( ( sK1 @ sK4 @ sK3 )
= $false )
| ~ spl0_3 ),
inference(imp_proxy_clausification,[],[f180]) ).
thf(f182,plain,
( ( $true
= ( ( sK1 @ sK4 @ sK2 )
& ( sK1 @ sK2 @ sK3 ) ) )
| ~ spl0_3 ),
inference(imp_proxy_clausification,[],[f180]) ).
thf(f187,plain,
( ( ( sK1 @ sK2 @ sK3 )
= $true )
| ~ spl0_3 ),
inference(and_proxy_clausification,[],[f182]) ).
thf(f188,plain,
( ( ( sK1 @ sK4 @ sK2 )
= $true )
| ~ spl0_3 ),
inference(and_proxy_clausification,[],[f182]) ).
thf(f203,plain,
( ! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y0 @ Y4 ) ) ) ) ) ) ) )
@ X1 )
= $true )
| ~ spl0_2 ),
inference(pi_proxy_clausification,[],[f162]) ).
thf(f204,plain,
( ! [X1: $i > $o] :
( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( X1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( X1 @ Y3 ) ) ) ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(beta-eta_normalization,[],[f203]) ).
thf(f205,plain,
( ! [X2: $i > $i > $o,X1: $i > $o] :
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( X1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( X1 @ Y3 ) ) ) ) ) ) )
@ X2 )
= $true )
| ~ spl0_2 ),
inference(pi_proxy_clausification,[],[f204]) ).
thf(f206,plain,
( ! [X2: $i > $i > $o,X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( X2 @ Y1 @ Y2 )
=> ( X1 @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(beta-eta_normalization,[],[f205]) ).
thf(f207,plain,
( ! [X2: $i > $i > $o,X3: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( X2 @ Y1 @ Y2 )
=> ( X1 @ Y2 ) ) ) ) ) )
@ X3 )
= $true )
| ~ spl0_2 ),
inference(pi_proxy_clausification,[],[f206]) ).
thf(f208,plain,
( ! [X2: $i > $i > $o,X3: $i,X1: $i > $o] :
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ X3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_2 ),
inference(beta-eta_normalization,[],[f207]) ).
thf(f209,plain,
( ! [X2: $i > $i > $o,X3: $i,X1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ X3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
= $true ) )
| ~ spl0_2 ),
inference(or_proxy_clausification,[],[f208]) ).
thf(f210,plain,
( ! [X2: $i > $i > $o,X3: $i,X1: $i > $o,X4: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
= $true )
| ( $true
= ( ^ [Y0: $i] :
( ( X2 @ X3 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( X2 @ Y0 @ Y1 )
=> ( X1 @ Y1 ) ) ) )
@ X4 ) ) )
| ~ spl0_2 ),
inference(pi_proxy_clausification,[],[f209]) ).
thf(f211,plain,
( ! [X2: $i > $i > $o,X3: $i,X1: $i > $o,X4: $i] :
( ( ( ( X2 @ X3 @ X4 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ X4 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( X2 @ X3 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
= $true ) )
| ~ spl0_2 ),
inference(beta-eta_normalization,[],[f210]) ).
thf(f215,plain,
( ! [X0: $i > $o] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ sK4 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) )
| ( ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ sK2 @ Y0 )
=> ( X0 @ Y0 ) ) ) )
= $true ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(constrained_superposition,[],[f211,f188]) ).
thf(f217,plain,
( ! [X0: $i > $o] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ sK4 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ sK2 @ Y0 )
=> ( X0 @ Y0 ) ) ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[],[f215]) ).
thf(f219,plain,
( ! [X0: $i > $o] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ sK2 @ Y0 )
=> ( X0 @ Y0 ) ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ sK4 @ Y0 )
=> ( X0 @ Y0 ) ) )
= $false ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(not_proxy_clausification,[],[f217]) ).
thf(f220,plain,
( ! [X0: $i > $o,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( sK1 @ sK2 @ Y0 )
=> ( X0 @ Y0 ) )
@ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ sK4 @ Y0 )
=> ( X0 @ Y0 ) ) )
= $false ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(pi_proxy_clausification,[],[f219]) ).
thf(f221,plain,
( ! [X0: $i > $o,X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ sK4 @ Y0 )
=> ( X0 @ Y0 ) ) )
= $false )
| ( ( ( sK1 @ sK2 @ X1 )
=> ( X0 @ X1 ) )
= $true ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(beta-eta_normalization,[],[f220]) ).
thf(f222,plain,
( ! [X0: $i > $o,X1: $i] :
( ( ( ( sK1 @ sK2 @ X1 )
=> ( X0 @ X1 ) )
= $true )
| ( ( ^ [Y0: $i] :
( ( sK1 @ sK4 @ Y0 )
=> ( X0 @ Y0 ) )
@ ( sK5 @ X0 ) )
= $false ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(sigma_proxy_clausification,[],[f221]) ).
thf(f223,plain,
( ! [X0: $i > $o,X1: $i] :
( ( ( ( sK1 @ sK4 @ ( sK5 @ X0 ) )
=> ( X0 @ ( sK5 @ X0 ) ) )
= $false )
| ( ( ( sK1 @ sK2 @ X1 )
=> ( X0 @ X1 ) )
= $true ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(beta-eta_normalization,[],[f222]) ).
thf(f224,plain,
( ! [X0: $i > $o,X1: $i] :
( ( ( ( sK1 @ sK2 @ X1 )
=> ( X0 @ X1 ) )
= $true )
| ( $false
= ( X0 @ ( sK5 @ X0 ) ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(imp_proxy_clausification,[],[f223]) ).
thf(f227,plain,
( ( ( ( sK1 @ sK2 @ sK3 )
=> $false )
= $true )
| ( $false
= ( sK1 @ sK4 @ ( sK5 @ ( sK1 @ sK4 ) ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(constrained_superposition,[],[f224,f181]) ).
thf(f234,plain,
( ( ( ~ ( sK1 @ sK2 @ sK3 ) )
= $true )
| ( $false
= ( sK1 @ sK4 @ ( sK5 @ ( sK1 @ sK4 ) ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[],[f227]) ).
thf(f235,plain,
( ( ( ~ $true ) = $true )
| ( $false
= ( sK1 @ sK4 @ ( sK5 @ ( sK1 @ sK4 ) ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f234,f187]) ).
thf(f236,plain,
( ( $false = $true )
| ( $false
= ( sK1 @ sK4 @ ( sK5 @ ( sK1 @ sK4 ) ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[],[f235]) ).
thf(f237,plain,
( ( $false
= ( sK1 @ sK4 @ ( sK5 @ ( sK1 @ sK4 ) ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f236]) ).
thf(f240,plain,
( ! [X0: $i] :
( ( $false
= ( $false
=> $false ) )
| ( $true
= ( ( sK1 @ sK2 @ X0 )
=> ( sK1 @ sK4 @ X0 ) ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(constrained_superposition,[],[f223,f237]) ).
thf(f241,plain,
( ! [X0: $i] :
( ( $true
= ( ( sK1 @ sK2 @ X0 )
=> ( sK1 @ sK4 @ X0 ) ) )
| ( $false = $true ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[],[f240]) ).
thf(f242,plain,
( ! [X0: $i] :
( $true
= ( ( sK1 @ sK2 @ X0 )
=> ( sK1 @ sK4 @ X0 ) ) )
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f241]) ).
thf(f247,plain,
( ( ( ( sK1 @ sK2 @ sK3 )
=> $false )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(constrained_superposition,[],[f242,f181]) ).
thf(f254,plain,
( ( ( ~ ( sK1 @ sK2 @ sK3 ) )
= $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[],[f247]) ).
thf(f258,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f254,f187]) ).
thf(f259,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(boolean_simplification,[],[f258]) ).
thf(f260,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f259]) ).
thf(f261,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f260]) ).
thf(f262,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_demodulation,[],[f158,f167]) ).
thf(f263,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f262]) ).
thf(f264,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f263]) ).
thf(f269,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_4 ),
inference(forward_demodulation,[],[f162,f171]) ).
thf(f270,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f269]) ).
thf(f271,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f270]) ).
thf(f273,plain,
( ! [X1: $i > $i > $o] :
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ X1 ) )
| ~ spl0_1 ),
inference(pi_proxy_clausification,[],[f158]) ).
thf(f274,plain,
( ! [X1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( X1 @ Y2 @ Y0 )
& ( X1 @ Y0 @ Y1 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_1 ),
inference(beta-eta_normalization,[],[f273]) ).
thf(f275,plain,
( ! [X2: $i,X1: $i > $i > $o] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( X1 @ Y2 @ Y0 )
& ( X1 @ Y0 @ Y1 ) )
=> ( X1 @ Y2 @ Y1 ) ) ) )
@ X2 )
= $true )
| ~ spl0_1 ),
inference(pi_proxy_clausification,[],[f274]) ).
thf(f276,plain,
( ! [X2: $i,X1: $i > $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( X1 @ Y1 @ X2 )
& ( X1 @ X2 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) ) ) )
| ~ spl0_1 ),
inference(beta-eta_normalization,[],[f275]) ).
thf(f277,plain,
( ! [X2: $i,X3: $i,X1: $i > $i > $o] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( X1 @ Y1 @ X2 )
& ( X1 @ X2 @ Y0 ) )
=> ( X1 @ Y1 @ Y0 ) ) )
@ X3 )
= $true )
| ~ spl0_1 ),
inference(pi_proxy_clausification,[],[f276]) ).
thf(f278,plain,
( ! [X2: $i,X3: $i,X1: $i > $i > $o] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( X1 @ Y0 @ X2 )
& ( X1 @ X2 @ X3 ) )
=> ( X1 @ Y0 @ X3 ) ) ) )
| ~ spl0_1 ),
inference(beta-eta_normalization,[],[f277]) ).
thf(f279,plain,
( ! [X2: $i,X3: $i,X1: $i > $i > $o,X4: $i] :
( ( ^ [Y0: $i] :
( ( ( X1 @ Y0 @ X2 )
& ( X1 @ X2 @ X3 ) )
=> ( X1 @ Y0 @ X3 ) )
@ X4 )
= $true )
| ~ spl0_1 ),
inference(pi_proxy_clausification,[],[f278]) ).
thf(f280,plain,
( ! [X2: $i,X3: $i,X1: $i > $i > $o,X4: $i] :
( ( ( ( X1 @ X4 @ X2 )
& ( X1 @ X2 @ X3 ) )
=> ( X1 @ X4 @ X3 ) )
= $true )
| ~ spl0_1 ),
inference(beta-eta_normalization,[],[f279]) ).
thf(f284,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
=> ( Y0 @ Y3 ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y3 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y0 @ Y4 ) ) ) ) ) ) ) )
@ sK6 ) )
| ~ spl0_4 ),
inference(sigma_proxy_clausification,[],[f171]) ).
thf(f285,plain,
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( sK6 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( sK6 @ Y3 ) ) ) ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta-eta_normalization,[],[f284]) ).
thf(f286,plain,
( ( $false
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( sK6 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( sK6 @ Y3 ) ) ) ) ) ) )
@ sK7 ) )
| ~ spl0_4 ),
inference(sigma_proxy_clausification,[],[f285]) ).
thf(f287,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK6 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK7 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK7 @ Y1 @ Y2 )
=> ( sK6 @ Y2 ) ) ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta-eta_normalization,[],[f286]) ).
thf(f288,plain,
( ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK6 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( sK7 @ Y0 @ Y1 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( sK7 @ Y1 @ Y2 )
=> ( sK6 @ Y2 ) ) ) ) ) )
@ sK8 )
= $false )
| ~ spl0_4 ),
inference(sigma_proxy_clausification,[],[f287]) ).
thf(f289,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK7 @ sK8 @ Y0 )
=> ( sK6 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( sK7 @ sK8 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK6 @ Y1 ) ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta-eta_normalization,[],[f288]) ).
thf(f290,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK7 @ sK8 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK6 @ Y1 ) ) ) ) )
= $false )
| ~ spl0_4 ),
inference(or_proxy_clausification,[],[f289]) ).
thf(f291,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( sK7 @ sK8 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(or_proxy_clausification,[],[f289]) ).
thf(f295,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK7 @ sK8 @ Y0 )
=> ( sK6 @ Y0 ) ) )
= $true )
| ~ spl0_4 ),
inference(not_proxy_clausification,[],[f291]) ).
thf(f298,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK7 @ sK8 @ Y0 )
=> ( sK6 @ Y0 ) )
@ X1 ) )
| ~ spl0_4 ),
inference(pi_proxy_clausification,[],[f295]) ).
thf(f299,plain,
( ! [X1: $i] :
( ( ( sK7 @ sK8 @ X1 )
=> ( sK6 @ X1 ) )
= $true )
| ~ spl0_4 ),
inference(beta-eta_normalization,[],[f298]) ).
thf(f301,plain,
( ( ( ^ [Y0: $i] :
( ( sK7 @ sK8 @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( sK7 @ Y0 @ Y1 )
=> ( sK6 @ Y1 ) ) ) )
@ sK9 )
= $false )
| ~ spl0_4 ),
inference(sigma_proxy_clausification,[],[f290]) ).
thf(f302,plain,
( ( ( ( sK7 @ sK8 @ sK9 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( sK7 @ sK9 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
= $false )
| ~ spl0_4 ),
inference(beta-eta_normalization,[],[f301]) ).
thf(f303,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK7 @ sK9 @ Y0 )
=> ( sK6 @ Y0 ) ) ) )
| ~ spl0_4 ),
inference(imp_proxy_clausification,[],[f302]) ).
thf(f304,plain,
( ( ( sK7 @ sK8 @ sK9 )
= $true )
| ~ spl0_4 ),
inference(imp_proxy_clausification,[],[f302]) ).
thf(f308,plain,
( ! [X0: $i] :
( $true
= ( ( $true
& ( sK7 @ sK9 @ X0 ) )
=> ( sK7 @ sK8 @ X0 ) ) )
| ~ spl0_1
| ~ spl0_4 ),
inference(constrained_superposition,[],[f280,f304]) ).
thf(f316,plain,
( ! [X0: $i] :
( ( ( sK7 @ sK9 @ X0 )
=> ( sK7 @ sK8 @ X0 ) )
= $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(boolean_simplification,[],[f308]) ).
thf(f327,plain,
( ( ( ^ [Y0: $i] :
( ( sK7 @ sK9 @ Y0 )
=> ( sK6 @ Y0 ) )
@ sK10 )
= $false )
| ~ spl0_4 ),
inference(sigma_proxy_clausification,[],[f303]) ).
thf(f328,plain,
( ( $false
= ( ( sK7 @ sK9 @ sK10 )
=> ( sK6 @ sK10 ) ) )
| ~ spl0_4 ),
inference(beta-eta_normalization,[],[f327]) ).
thf(f329,plain,
( ( ( sK6 @ sK10 )
= $false )
| ~ spl0_4 ),
inference(imp_proxy_clausification,[],[f328]) ).
thf(f330,plain,
( ( ( sK7 @ sK9 @ sK10 )
= $true )
| ~ spl0_4 ),
inference(imp_proxy_clausification,[],[f328]) ).
thf(f338,plain,
( ( ( $true
=> ( sK7 @ sK8 @ sK10 ) )
= $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(constrained_superposition,[],[f316,f330]) ).
thf(f344,plain,
( ( ( sK7 @ sK8 @ sK10 )
= $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(boolean_simplification,[],[f338]) ).
thf(f352,plain,
( ( $true
= ( $true
=> ( sK6 @ sK10 ) ) )
| ~ spl0_1
| ~ spl0_4 ),
inference(constrained_superposition,[],[f299,f344]) ).
thf(f358,plain,
( ( ( sK6 @ sK10 )
= $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(boolean_simplification,[],[f352]) ).
thf(f365,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[],[f358,f329]) ).
thf(f366,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f365]) ).
thf(f367,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f366]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f163]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f172]) ).
cnf(s4,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f261]) ).
cnf(s5,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(sat_conversion,[],[f264]) ).
cnf(s6,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f271]) ).
cnf(s7,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f367]) ).
cnf(s8,plain,
~ spl0_2,
inference(rat,[],[s2,s4,s6]) ).
cnf(s9,plain,
spl0_1,
inference(rat,[],[s1,s8]) ).
cnf(s10,plain,
~ spl0_4,
inference(rat,[],[s7,s9]) ).
cnf(s11,plain,
~ spl0_3,
inference(rat,[],[s5,s9]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s2,s10,s11]) ).
thf(f368,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL601^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 % Computer : n014.cluster.edu
% 0.10/0.24 % Model : x86_64 x86_64
% 0.10/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.24 % Memory : 8046.5625MB
% 0.10/0.24 % OS : Linux 6.8.0-71-generic
% 0.10/0.24 % CPULimit : 300
% 0.10/0.24 % WCLimit : 300
% 0.10/0.24 % DateTime : Tue Sep 29 09:17:00 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.24/0.30 Running higher-order theorem proving
% 0.24/0.31 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
% 0.49/0.45 % (2422249)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.49/0.45 % (2422255)lrs+10_16_si=on:nwc=1.5:random_seed=3493954435:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.49/0.45 % (2422260)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.49/0.45 % (2422260)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
% 0.49/0.45 % (2422255)Instruction limit reached!
% 0.49/0.45 % (2422255)------------------------------
% 0.49/0.45 % (2422255)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.45 % (2422255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.45 % (2422255)CaDiCaL version: 2.1.3
% 0.49/0.45 % (2422255)Termination reason: Instruction limit
% 0.49/0.45 % (2422255)Termination phase: Saturation
% 0.49/0.45 % (2422255)Time elapsed: 0.010 s
% 0.49/0.45 % (2422255)Peak memory usage: 12 MB
% 0.49/0.45 % (2422255)Instructions burned: 20 (million)
% 0.49/0.45 % (2422254)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=945300026:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.49/0.45 % (2422257)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=2058797425: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)
% 0.49/0.45 % (2422259)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1350744139:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.49/0.45 % (2422256)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3471852292:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.49/0.45 % (2422258)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=311652499:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.49/0.45 % (2422260)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=1290613929:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.49/0.45 % (2422256)Instruction limit reached!
% 0.49/0.45 % (2422256)------------------------------
% 0.49/0.45 % (2422256)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.45 % (2422256)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.45 % (2422256)CaDiCaL version: 2.1.3
% 0.49/0.45 % (2422256)Termination reason: Instruction limit
% 0.49/0.45 % (2422256)Termination phase: Property scanning
% 0.49/0.45 % (2422256)Time elapsed: 0.004 s
% 0.49/0.45 % (2422256)Peak memory usage: 10 MB
% 0.49/0.45 % (2422256)Instructions burned: 4 (million)
% 0.49/0.45 % (2422262)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3688827110:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.49/0.45 % (2422262)Instruction limit reached!
% 0.49/0.45 % (2422262)------------------------------
% 0.49/0.45 % (2422262)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.45 % (2422262)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.45 % (2422262)CaDiCaL version: 2.1.3
% 0.49/0.45 % (2422262)Termination reason: Instruction limit
% 0.49/0.45 % (2422262)Termination phase: Preprocessing 3
% 0.49/0.45 % (2422262)Time elapsed: 0.002 s
% 0.49/0.45 % (2422262)Peak memory usage: 10 MB
% 0.49/0.45 % (2422262)Instructions burned: 4 (million)
% 0.49/0.45 % (2422258)Instruction limit reached!
% 0.49/0.45 % (2422258)------------------------------
% 0.49/0.45 % (2422258)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.45 % (2422258)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.45 % (2422258)CaDiCaL version: 2.1.3
% 0.49/0.45 % (2422258)Termination reason: Instruction limit
% 0.49/0.45 % (2422258)Termination phase: Saturation
% 0.49/0.45 % (2422258)Time elapsed: 0.024 s
% 0.49/0.45 % (2422258)Peak memory usage: 12 MB
% 0.49/0.45 % (2422258)Instructions burned: 24 (million)
% 0.49/0.45 % (2422271)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.49/0.45 % (2422271)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2179864156:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.49/0.45 % (2422269)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2899390772:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.49/0.45 % (2422271)Instruction limit reached!
% 0.49/0.45 % (2422271)------------------------------
% 0.49/0.45 % (2422271)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.45 % (2422271)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.45 % (2422271)CaDiCaL version: 2.1.3
% 0.49/0.45 % (2422271)Termination reason: Instruction limit
% 0.49/0.45 % (2422271)Termination phase: Saturation
% 0.49/0.45 % (2422271)Time elapsed: 0.004 s
% 0.49/0.45 % (2422271)Peak memory usage: 12 MB
% 0.49/0.45 % (2422271)Instructions burned: 8 (million)
% 0.49/0.45 % (2422269)Instruction limit reached!
% 0.49/0.45 % (2422269)------------------------------
% 0.49/0.45 % (2422269)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.45 % (2422269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.45 % (2422269)CaDiCaL version: 2.1.3
% 0.49/0.45 % (2422269)Termination reason: Instruction limit
% 0.49/0.45 % (2422269)Termination phase: Property scanning
% 0.49/0.45 % (2422269)Time elapsed: 0.005 s
% 0.49/0.45 % (2422269)Peak memory usage: 10 MB
% 0.49/0.45 % (2422269)Instructions burned: 6 (million)
% 0.49/0.45 % (2422272)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4162769617:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.49/0.45 % (2422272)Instruction limit reached!
% 0.49/0.45 % (2422272)------------------------------
% 0.49/0.45 % (2422272)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.45 % (2422272)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.45 % (2422272)CaDiCaL version: 2.1.3
% 0.49/0.45 % (2422272)Termination reason: Instruction limit
% 0.49/0.45 % (2422272)Termination phase: Saturation
% 0.49/0.45 % (2422272)Time elapsed: 0.006 s
% 0.49/0.45 % (2422272)Peak memory usage: 12 MB
% 0.49/0.45 % (2422272)Instructions burned: 13 (million)
% 0.49/0.45 % (2422276)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=2827283973:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.49/0.45 % (2422259)Instruction limit reached!
% 0.49/0.45 % (2422259)------------------------------
% 0.49/0.45 % (2422259)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.45 % (2422259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.45 % (2422259)CaDiCaL version: 2.1.3
% 0.49/0.45 % (2422259)Termination reason: Instruction limit
% 0.49/0.45 % (2422259)Termination phase: Saturation
% 0.49/0.45 % (2422259)Time elapsed: 0.066 s
% 0.49/0.45 % (2422259)Peak memory usage: 12 MB
% 0.49/0.45 % (2422259)Instructions burned: 75 (million)
% 0.49/0.45 % (2422275)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
% 0.49/0.45 % (2422275)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.49/0.45 % (2422275)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3553192863:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.49/0.45 % (2422278)lrs+10_1_si=on:cs=on:random_seed=164556816:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.49/0.45 % (2422254)Instruction limit reached!
% 0.49/0.45 % (2422254)------------------------------
% 0.49/0.45 % (2422254)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.45 % (2422254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.45 % (2422254)CaDiCaL version: 2.1.3
% 0.49/0.45 % (2422254)Termination reason: Instruction limit
% 0.49/0.45 % (2422254)Termination phase: Saturation
% 0.49/0.45 % (2422254)Time elapsed: 0.079 s
% 0.49/0.45 % (2422254)Peak memory usage: 12 MB
% 0.49/0.45 % (2422254)Instructions burned: 88 (million)
% 0.49/0.45 % (2422276) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2422249-2422276"...
% 0.49/0.45 % (2422278)Instruction limit reached!
% 0.49/0.45 % (2422278)------------------------------
% 0.49/0.45 % (2422278)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.45 % (2422278)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.45 % (2422278)CaDiCaL version: 2.1.3
% 0.49/0.45 % (2422278)Termination reason: Instruction limit
% 0.49/0.45 % (2422278)Termination phase: Saturation
% 0.49/0.45 % (2422278)Time elapsed: 0.008 s
% 0.49/0.45 % (2422278)Peak memory usage: 11 MB
% 0.49/0.45 % (2422278)Instructions burned: 8 (million)
% 0.49/0.45 % (2422260) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2422249-2422260"...
% 0.49/0.45 % (2422276)...printing done.
% 0.49/0.45 % (2422276)Refutation found. Thanks to Tanya!
% 0.49/0.45 % SZS status Theorem for theBenchmark
% 0.49/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.49/0.46 % (2422276)------------------------------
% 0.49/0.46 % (2422276)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.49/0.46 % (2422276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.49/0.46 % (2422276)CaDiCaL version: 2.1.3
% 0.49/0.46 % (2422276)Termination reason: Refutation
% 0.49/0.46 % (2422276)Time elapsed: 0.022 s
% 0.49/0.46 % (2422276)Peak memory usage: 13 MB
% 0.49/0.46 % (2422276)Instructions burned: 42 (million)
% 0.49/0.46 % (2422249)Success in time 0.13 s
% 0.49/0.46 % Vampire exiting
%------------------------------------------------------------------------------