%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV442^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 08:40:00 AM UTC 2026
% Result : Theorem 0.25s 0.36s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 92 ( 53 unt; 0 typ; 5 def)
% Number of atoms : 463 ( 94 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 607 ( 47 ~; 60 |; 0 &; 415 @)
% ( 4 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 163 ( 163 >; 0 *; 0 +; 0 <<)
% Number of symbols : 73 ( 69 usr; 12 con; 0-4 aty)
% ( 40 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 236 ( 0 sgn 13 !; 1 ?; 236 :)
% 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,
reli: $i > $i > $o ).
thf(func_def_21,type,
relr: $i > $i > $o ).
thf(func_def_22,type,
cs4_atom: ( $i > $o ) > $i > $o ).
thf(func_def_23,type,
cs4_and: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_24,type,
cs4_or: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_25,type,
cs4_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_26,type,
cs4_true: $i > $o ).
thf(func_def_27,type,
cs4_false: $i > $o ).
thf(func_def_28,type,
cs4_all: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_29,type,
cs4_box: ( $i > $o ) > $i > $o ).
thf(func_def_30,type,
cs4_valid: ( $i > $o ) > $o ).
thf(func_def_31,type,
princ_inj: individuals > $i > $o ).
thf(func_def_32,type,
bl_atom: ( $i > $o ) > $i > $o ).
thf(func_def_33,type,
bl_princ: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
bl_and: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
bl_or: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_36,type,
bl_impl: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_37,type,
bl_all: ( individuals > $i > $o ) > $i > $o ).
thf(func_def_38,type,
bl_true: $i > $o ).
thf(func_def_39,type,
bl_false: $i > $o ).
thf(func_def_40,type,
bl_says: individuals > ( $i > $o ) > $i > $o ).
thf(func_def_41,type,
bl_valid: ( $i > $o ) > $o ).
thf(func_def_42,type,
loca: individuals ).
thf(func_def_43,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_45,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
vAND: $o > $o > $o ).
thf(func_def_47,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vOR: $o > $o > $o ).
thf(func_def_53,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_54,type,
vNOT: $o > $o ).
thf(func_def_55,type,
vIMP: $o > $o > $o ).
thf(func_def_56,type,
sK0: $i > $o ).
thf(func_def_57,type,
sF1: $o ).
thf(func_def_58,type,
sK2: $i > ( $i > $o ) > $i ).
thf(func_def_59,type,
sK3: $i > ( $i > $o ) > $i ).
thf(func_def_60,type,
sK4: $i > ( $i > $o ) > $i ).
thf(func_def_61,type,
sK5: $i > $i ).
thf(func_def_65,type,
sK9: $i > ( $i > $o ) > $i ).
thf(func_def_66,type,
sK10: $i > ( $i > $o ) > $i ).
thf(func_def_67,type,
sK11: $i > ( $i > $o ) > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL008^0.ax',mor) ).
thf(f6,axiom,
( mimpl
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mimpl) ).
thf(f8,axiom,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mbox) ).
thf(f12,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL008^0.ax',mvalid) ).
thf(f16,axiom,
( ( ^ [X0: $i > $o] : ( mbox @ reli @ X0 ) )
= cs4_atom ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL009^0.ax',cs4_atom) ).
thf(f19,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mbox @ reli @ ( mimpl @ X0 @ X1 ) ) )
= cs4_impl ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL009^0.ax',cs4_impl) ).
thf(f30,axiom,
( bl_atom
= ( ^ [X0: $i > $o] : ( cs4_atom @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV010^0.ax',bl_atom) ).
thf(f34,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( cs4_impl @ X0 @ X1 ) )
= bl_impl ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV010^0.ax',bl_impl) ).
thf(f39,axiom,
bl_valid = mvalid,
file('/export/starexec/sandbox2/benchmark/Axioms/SWV010^0.ax',bl_valid_def) ).
thf(f41,conjecture,
! [X0: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_atom @ X0 ) @ ( bl_atom @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bl_id) ).
thf(f42,negated_conjecture,
~ ! [X0: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_atom @ X0 ) @ ( bl_atom @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
thf(f46,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f47,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f49,plain,
~ ! [X0: $i > $o] : ( bl_valid @ ( bl_impl @ ( bl_atom @ X0 ) @ ( bl_atom @ X0 ) ) ),
inference(rectify,[],[f42]) ).
thf(f50,plain,
~ ! [X0: $i > $o] :
( ( bl_valid @ ( bl_impl @ ( bl_atom @ X0 ) @ ( bl_atom @ X0 ) ) )
= $true ),
inference(fool_elimination,[],[f49]) ).
thf(f51,plain,
( cs4_atom
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ Y0 ) ) ),
inference(fool_elimination,[],[f16]) ).
thf(f52,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f12]) ).
thf(f53,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f52]) ).
thf(f56,plain,
( bl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( cs4_impl @ Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f34]) ).
thf(f59,plain,
( mbox
= ( ^ [X0: $i > $i > $o,X1: $i > $o,X2: $i] :
! [X3: $i] :
( ( X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f8]) ).
thf(f60,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f59]) ).
thf(f62,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f63,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f64,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f81,plain,
( bl_atom
= ( ^ [Y0: $i > $o] : ( cs4_atom @ Y0 ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f94,plain,
( cs4_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ reli @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f97,plain,
? [X0: $i > $o] :
( ( bl_valid @ ( bl_impl @ ( bl_atom @ X0 ) @ ( bl_atom @ X0 ) ) )
!= $true ),
inference(ennf_transformation,[],[f50]) ).
thf(f98,plain,
( ( bl_valid @ ( bl_impl @ ( bl_atom @ sK0 ) @ ( bl_atom @ sK0 ) ) )
!= $true ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f97]) ).
thf(f100,plain,
mvalid = bl_valid,
inference(cnf_transformation,[],[f39]) ).
thf(f101,plain,
( mbox
= ( ^ [Y0: $i > $i > $o,Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f104,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f105,plain,
( bl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( cs4_impl @ Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f107,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f110,plain,
( cs4_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mbox @ reli @ ( mimpl @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f94]) ).
thf(f119,plain,
( mimpl
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f125,plain,
( bl_atom
= ( ^ [Y0: $i > $o] : ( cs4_atom @ Y0 ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f128,plain,
( ( bl_valid @ ( bl_impl @ ( bl_atom @ sK0 ) @ ( bl_atom @ sK0 ) ) )
!= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f136,plain,
( cs4_atom
= ( ^ [Y0: $i > $o] : ( mbox @ reli @ Y0 ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f138,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f143,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,[],[f119,f104,f138]) ).
thf(f145,plain,
( cs4_atom
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $i > $o,Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y1 @ Y3 @ Y4 )
=> ( Y2 @ Y4 ) ) )
@ reli
@ Y0 ) ) ),
inference(definition_unfolding,[],[f136,f101]) ).
thf(f148,plain,
( cs4_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ ( ^ [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 )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f110,f101,f143]) ).
thf(f153,plain,
( bl_atom
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ Y1 )
@ Y0 ) ) ),
inference(definition_unfolding,[],[f125,f145]) ).
thf(f157,plain,
( bl_impl
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $i > $o,Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y6 @ Y7 )
=> ( Y5 @ Y7 ) ) )
@ reli
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ Y2
@ Y3 ) )
@ Y0
@ Y1 ) ) ),
inference(definition_unfolding,[],[f105,f148]) ).
thf(f160,plain,
( bl_valid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(definition_unfolding,[],[f100,f107]) ).
thf(f165,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $i > $o,Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y6 @ Y7 )
=> ( Y5 @ Y7 ) ) )
@ reli
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ Y2
@ Y3 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ Y1 )
@ Y0 )
@ sK0 )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ Y1 )
@ Y0 )
@ sK0 ) ) )
!= $true ),
inference(definition_unfolding,[],[f128,f160,f157,f153,f153]) ).
thf(f170,definition,
( sF1
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $i > $o,Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y6 @ Y7 )
=> ( Y5 @ Y7 ) ) )
@ reli
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ Y2
@ Y3 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ Y1 )
@ Y0 )
@ sK0 )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ Y1 )
@ Y0 )
@ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f171,plain,
sF1 != $true,
inference(definition_folding,[],[f165,f170]) ).
thf(f224,plain,
( ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $i > $o,Y5: $i > $o,Y6: $i] :
( !! @ $i
@ ^ [Y7: $i] :
( ( Y4 @ Y6 @ Y7 )
=> ( Y5 @ Y7 ) ) )
@ reli
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ Y2
@ Y3 ) )
@ Y0
@ Y1 )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ Y1 )
@ Y0 )
@ sK0 )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o] :
( ^ [Y2: $i > $i > $o,Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y2 @ Y4 @ Y5 )
=> ( Y3 @ Y5 ) ) )
@ reli
@ Y1 )
@ Y0 )
@ sK0 ) ) )
= $false )
| ( sF1 = $true ) ),
inference(iff_proxy_clausification,[],[f170]) ).
thf(f240,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( sK0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( sK0 @ Y2 ) ) ) ) ) ) )
= $false )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f224]) ).
thf(f241,plain,
( ( sF1 = $true )
| ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( sK0 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( reli @ Y1 @ Y2 )
=> ( sK0 @ Y2 ) ) ) ) ) )
@ sK6 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f240]) ).
thf(f242,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK6 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK0 @ Y1 ) ) ) ) ) ) )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f241]) ).
thf(f243,plain,
( ( ( ^ [Y0: $i] :
( ( reli @ sK6 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( reli @ Y0 @ Y1 )
=> ( sK0 @ Y1 ) ) ) ) )
@ sK7 )
= $false )
| ( sF1 = $true ) ),
inference(sigma_proxy_clausification,[],[f242]) ).
thf(f244,plain,
( ( $false
= ( ( reli @ sK6 @ sK7 )
=> ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( sK0 @ Y0 ) ) ) ) ) )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f243]) ).
thf(f245,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( sK0 @ Y0 ) ) ) ) )
| ( sF1 = $true ) ),
inference(imp_proxy_clausification,[],[f244]) ).
thf(f247,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( sK0 @ Y0 ) ) )
= $false )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f245]) ).
thf(f248,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( sK0 @ Y0 ) ) ) ) )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f245]) ).
thf(f249,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( sK0 @ Y0 ) ) )
= $true )
| ( sF1 = $true ) ),
inference(not_proxy_clausification,[],[f248]) ).
thf(f250,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( sK0 @ Y0 ) )
@ X1 )
= $true )
| ( sF1 = $true ) ),
inference(pi_proxy_clausification,[],[f249]) ).
thf(f251,plain,
! [X1: $i] :
( ( ( ( reli @ sK7 @ X1 )
=> ( sK0 @ X1 ) )
= $true )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f250]) ).
thf(f252,plain,
! [X1: $i] :
( ( sF1 = $true )
| ( ( reli @ sK7 @ X1 )
= $false )
| ( $true
= ( sK0 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f251]) ).
thf(f253,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( reli @ sK7 @ Y0 )
=> ( sK0 @ Y0 ) )
@ sK8 ) )
| ( sF1 = $true ) ),
inference(sigma_proxy_clausification,[],[f247]) ).
thf(f254,plain,
( ( $false
= ( ( reli @ sK7 @ sK8 )
=> ( sK0 @ sK8 ) ) )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f253]) ).
thf(f255,plain,
( ( ( sK0 @ sK8 )
= $false )
| ( sF1 = $true ) ),
inference(imp_proxy_clausification,[],[f254]) ).
thf(f256,plain,
( ( sF1 = $true )
| ( ( reli @ sK7 @ sK8 )
= $true ) ),
inference(imp_proxy_clausification,[],[f254]) ).
thf(f306,definition,
( spl12_4
<=> ( sF1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
thf(f315,definition,
( spl12_6
<=> ! [X1: $i] :
( ( ( reli @ sK7 @ X1 )
= $false )
| ( $true
= ( sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl12_6])],[avatar_definition]) ).
thf(f316,plain,
( ! [X1: $i] :
( ( ( reli @ sK7 @ X1 )
= $false )
| ( $true
= ( sK0 @ X1 ) ) )
| ~ spl12_6 ),
inference(avatar_component_clause,[],[f315]) ).
thf(f317,plain,
( spl12_6
| spl12_4 ),
inference(avatar_split_clause,[],[f252,f306,f315]) ).
thf(f319,definition,
( spl12_7
<=> ( ( reli @ sK7 @ sK8 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl12_7])],[avatar_definition]) ).
thf(f321,plain,
( ( ( reli @ sK7 @ sK8 )
= $true )
| ~ spl12_7 ),
inference(avatar_component_clause,[],[f319]) ).
thf(f322,plain,
( spl12_4
| spl12_7 ),
inference(avatar_split_clause,[],[f256,f319,f306]) ).
thf(f324,definition,
( spl12_8
<=> ( ( sK0 @ sK8 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl12_8])],[avatar_definition]) ).
thf(f326,plain,
( ( ( sK0 @ sK8 )
= $false )
| ~ spl12_8 ),
inference(avatar_component_clause,[],[f324]) ).
thf(f327,plain,
( spl12_8
| spl12_4 ),
inference(avatar_split_clause,[],[f255,f306,f324]) ).
thf(f328,plain,
~ spl12_4,
inference(avatar_split_clause,[],[f171,f306]) ).
thf(f358,plain,
( ( ( sK0 @ sK8 )
= $true )
| ( $false = $true )
| ~ spl12_6
| ~ spl12_7 ),
inference(constrained_superposition,[],[f321,f316]) ).
thf(f361,plain,
( ( ( sK0 @ sK8 )
= $true )
| ~ spl12_6
| ~ spl12_7 ),
inference(trivial_inequality_removal,[],[f358]) ).
thf(f365,plain,
( ( $false = $true )
| ~ spl12_6
| ~ spl12_7
| ~ spl12_8 ),
inference(forward_demodulation,[],[f361,f326]) ).
thf(f366,plain,
( $false
| ~ spl12_6
| ~ spl12_7
| ~ spl12_8 ),
inference(trivial_inequality_removal,[],[f365]) ).
thf(f367,plain,
( ~ spl12_6
| ~ spl12_7
| ~ spl12_8 ),
inference(avatar_contradiction_clause,[],[f366]) ).
cnf(s4,plain,
( spl12_4
| spl12_6 ),
inference(sat_conversion,[],[f317]) ).
cnf(s5,plain,
( spl12_4
| spl12_7 ),
inference(sat_conversion,[],[f322]) ).
cnf(s6,plain,
( spl12_4
| spl12_8 ),
inference(sat_conversion,[],[f327]) ).
cnf(s7,plain,
~ spl12_4,
inference(sat_conversion,[],[f328]) ).
cnf(s9,plain,
( ~ spl12_6
| ~ spl12_7
| ~ spl12_8 ),
inference(sat_conversion,[],[f367]) ).
cnf(s10,plain,
spl12_8,
inference(rat,[],[s6,s7]) ).
cnf(s11,plain,
spl12_7,
inference(rat,[],[s5,s7]) ).
cnf(s12,plain,
~ spl12_6,
inference(rat,[],[s9,s10,s11]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s4,s12,s7]) ).
thf(f368,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV442^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 % Computer : n026.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 16:06:57 UTC 2026
% 0.10/0.25 % CPUTime :
% 0.10/0.25 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.29 Running higher-order theorem proving
% 0.25/0.31 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.25/0.36 % (787921)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.36 % (787932)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.25/0.36 % (787932)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
% 0.25/0.36 % (787932)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=2891089284:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.25/0.36 % (787932) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-787921-787932"...
% 0.25/0.36 % (787932)...printing done.
% 0.25/0.36 % (787927)lrs+10_16_si=on:nwc=1.5:random_seed=1605338189:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.25/0.36 % (787932)Refutation found. Thanks to Tanya!
% 0.25/0.36 % SZS status Theorem for theBenchmark
% 0.25/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.36 % (787932)------------------------------
% 0.25/0.36 % (787932)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.36 % (787932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.36 % (787932)CaDiCaL version: 2.1.3
% 0.25/0.36 % (787932)Termination reason: Refutation
% 0.25/0.36 % (787932)Time elapsed: 0.011 s
% 0.25/0.36 % (787932)Peak memory usage: 13 MB
% 0.25/0.36 % (787932)Instructions burned: 21 (million)
% 0.25/0.36 % (787921)Success in time 0.038 s
% 0.25/0.36 % Vampire exiting
%------------------------------------------------------------------------------