%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO455^5 : 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 : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:47:49 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 15
% Syntax : Number of formulae : 109 ( 51 unt; 0 typ; 5 def)
% Number of atoms : 705 ( 142 equ; 0 cnn)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 916 ( 160 ~; 159 |; 0 &; 550 @)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 127 ( 127 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 59 usr; 9 con; 0-4 aty)
% ( 43 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 259 ( 0 sgn 29 !; 0 ?; 259 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
rel_s4: $i > $i > $o ).
thf(func_def_33,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
q: $i > $o ).
thf(func_def_37,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_42,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_43,type,
vNOT: $o > $o ).
thf(func_def_46,type,
vOR: $o > $o > $o ).
thf(func_def_47,type,
vIMP: $o > $o > $o ).
thf(func_def_48,type,
vAND: $o > $o > $o ).
thf(func_def_49,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
sF0: $o ).
thf(func_def_53,type,
sK1: $i > $i ).
thf(func_def_54,type,
sK2: $i > $i ).
thf(func_def_55,type,
sK3: $i > $i ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) )
= mand ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f18,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f33,axiom,
( mdia_s4
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',mdia_s4) ).
thf(f34,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',a1) ).
thf(f36,conjecture,
mvalid @ ( mimplies @ ( mand @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( mor @ ( mnot @ p ) @ q ) ) ) @ ( mdia_s4 @ q ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f37,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mand @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( mor @ ( mnot @ p ) @ q ) ) ) @ ( mdia_s4 @ q ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f40,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f41,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f44,plain,
~ ( mvalid @ ( mimplies @ ( mand @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( mor @ ( mnot @ p ) @ q ) ) ) @ ( mdia_s4 @ q ) ) ),
inference(rectify,[],[f37]) ).
thf(f45,plain,
( ( mvalid @ ( mimplies @ ( mand @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( mor @ ( mnot @ p ) @ q ) ) ) @ ( mdia_s4 @ q ) ) )
!= $true ),
inference(fool_elimination,[],[f44]) ).
thf(f46,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f47,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f52,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f53,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f52]) ).
thf(f54,plain,
mreflexive @ rel_s4,
inference(rectify,[],[f34]) ).
thf(f55,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f54]) ).
thf(f56,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f69,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f70,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f71,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f82,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f87,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
inference(rectify,[],[f18]) ).
thf(f88,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f87]) ).
thf(f98,plain,
( ( mvalid @ ( mimplies @ ( mand @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( mor @ ( mnot @ p ) @ q ) ) ) @ ( mdia_s4 @ q ) ) )
!= $true ),
inference(flattening,[],[f45]) ).
thf(f106,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f55]) ).
thf(f107,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f108,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f71]) ).
thf(f110,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f114,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f117,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f119,plain,
( ( mvalid @ ( mimplies @ ( mand @ ( mbox_s4 @ p ) @ ( mbox_s4 @ ( mor @ ( mnot @ p ) @ q ) ) ) @ ( mdia_s4 @ q ) ) )
!= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f121,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f133,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f134,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f137,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f108,f117,f134,f117,f117]) ).
thf(f138,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f121,f134,f117]) ).
thf(f146,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f107,f117,f114,f117]) ).
thf(f147,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f106,f133]) ).
thf(f149,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ p )
@ q ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ q ) ) ) ),
inference(definition_unfolding,[],[f119,f110,f138,f137,f114,f114,f134,f117,f146]) ).
thf(f150,definition,
( sF0
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ p )
@ q ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ q ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f151,plain,
sF0 != $true,
inference(definition_folding,[],[f149,f150]) ).
thf(f152,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ p )
@ q ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ q ) ) ) )
| ( sF0 = $true ) ),
inference(iff_proxy_clausification,[],[f150]) ).
thf(f211,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f212,plain,
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( q @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f211]) ).
thf(f213,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ~ ( q @ Y0 ) ) )
| ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( q @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $false )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f212]) ).
thf(f214,plain,
( ( sF0 = $true )
| ( $false
= ( ~ ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( q @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f213]) ).
thf(f215,plain,
( ( sF0 = $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f213]) ).
thf(f216,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ~ ( q @ Y0 ) ) )
= $true )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f215]) ).
thf(f217,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ~ ( q @ Y0 ) )
@ X1 ) )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f216]) ).
thf(f218,plain,
! [X1: $i] :
( ( ( ~ ( rel_s4 @ sK4 @ X1 )
| ~ ( q @ X1 ) )
= $true )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f217]) ).
thf(f219,plain,
! [X1: $i] :
( ( ( ~ ( q @ X1 ) )
= $true )
| ( sF0 = $true )
| ( ( ~ ( rel_s4 @ sK4 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f218]) ).
thf(f220,plain,
! [X1: $i] :
( ( ( ~ ( rel_s4 @ sK4 @ X1 ) )
= $true )
| ( ( q @ X1 )
= $false )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f219]) ).
thf(f221,plain,
! [X1: $i] :
( ( ( rel_s4 @ sK4 @ X1 )
= $false )
| ( sF0 = $true )
| ( ( q @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f220]) ).
thf(f222,plain,
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( q @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( p @ Y0 ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f214]) ).
thf(f223,plain,
( ( sF0 = $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( q @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f222]) ).
thf(f224,plain,
( ( sF0 = $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f223]) ).
thf(f225,plain,
( ( sF0 = $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( q @ Y0 )
| ~ ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f223]) ).
thf(f226,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( q @ Y0 )
| ~ ( p @ Y0 ) ) )
= $true )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( q @ Y0 )
| ~ ( p @ Y0 ) )
@ X1 )
= $true )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f226]) ).
thf(f228,plain,
! [X1: $i] :
( ( ( ~ ( rel_s4 @ sK4 @ X1 )
| ( q @ X1 )
| ~ ( p @ X1 ) )
= $true )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f227]) ).
thf(f229,plain,
! [X1: $i] :
( ( $true
= ( ( q @ X1 )
| ~ ( p @ X1 ) ) )
| ( ( ~ ( rel_s4 @ sK4 @ X1 ) )
= $true )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X1: $i] :
( ( ( ~ ( rel_s4 @ sK4 @ X1 ) )
= $true )
| ( ( ~ ( p @ X1 ) )
= $true )
| ( sF0 = $true )
| ( ( q @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f229]) ).
thf(f231,plain,
! [X1: $i] :
( ( ( ~ ( p @ X1 ) )
= $true )
| ( sF0 = $true )
| ( ( q @ X1 )
= $true )
| ( ( rel_s4 @ sK4 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f230]) ).
thf(f232,plain,
! [X1: $i] :
( ( $false
= ( p @ X1 ) )
| ( ( q @ X1 )
= $true )
| ( sF0 = $true )
| ( ( rel_s4 @ sK4 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f231]) ).
thf(f233,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f224]) ).
thf(f234,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK4 @ Y0 )
| ( p @ Y0 ) )
@ X1 )
= $true )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f233]) ).
thf(f235,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK4 @ X1 )
| ( p @ X1 ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f234]) ).
thf(f236,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( $true
= ( p @ X1 ) )
| ( ( ~ ( rel_s4 @ sK4 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f235]) ).
thf(f237,plain,
! [X1: $i] :
( ( ( rel_s4 @ sK4 @ X1 )
= $false )
| ( sF0 = $true )
| ( $true
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f236]) ).
thf(f247,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f248,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f247]) ).
thf(f249,plain,
! [X1: $i] :
( $true
= ( rel_s4 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f248]) ).
thf(f303,definition,
( spl5_14
<=> ( sF0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl5_14])],[avatar_definition]) ).
thf(f307,definition,
( spl5_15
<=> ! [X1: $i] :
( ( ( rel_s4 @ sK4 @ X1 )
= $false )
| ( ( q @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl5_15])],[avatar_definition]) ).
thf(f308,plain,
( ! [X1: $i] :
( ( ( rel_s4 @ sK4 @ X1 )
= $false )
| ( ( q @ X1 )
= $false ) )
| ~ spl5_15 ),
inference(avatar_component_clause,[],[f307]) ).
thf(f309,plain,
( spl5_14
| spl5_15 ),
inference(avatar_split_clause,[],[f221,f307,f303]) ).
thf(f311,definition,
( spl5_16
<=> ! [X1: $i] :
( ( $false
= ( p @ X1 ) )
| ( ( rel_s4 @ sK4 @ X1 )
= $false )
| ( ( q @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl5_16])],[avatar_definition]) ).
thf(f312,plain,
( ! [X1: $i] :
( ( ( rel_s4 @ sK4 @ X1 )
= $false )
| ( ( q @ X1 )
= $true )
| ( $false
= ( p @ X1 ) ) )
| ~ spl5_16 ),
inference(avatar_component_clause,[],[f311]) ).
thf(f313,plain,
( spl5_14
| spl5_16 ),
inference(avatar_split_clause,[],[f232,f311,f303]) ).
thf(f315,definition,
( spl5_17
<=> ! [X1: $i] :
( ( ( rel_s4 @ sK4 @ X1 )
= $false )
| ( $true
= ( p @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_17])],[avatar_definition]) ).
thf(f316,plain,
( ! [X1: $i] :
( ( ( rel_s4 @ sK4 @ X1 )
= $false )
| ( $true
= ( p @ X1 ) ) )
| ~ spl5_17 ),
inference(avatar_component_clause,[],[f315]) ).
thf(f317,plain,
( spl5_14
| spl5_17 ),
inference(avatar_split_clause,[],[f237,f315,f303]) ).
thf(f318,plain,
~ spl5_14,
inference(avatar_split_clause,[],[f151,f303]) ).
thf(f333,plain,
( ( $false
= ( q @ sK4 ) )
| ( $false = $true )
| ~ spl5_15 ),
inference(constrained_superposition,[],[f249,f308]) ).
thf(f334,plain,
( ( $false
= ( q @ sK4 ) )
| ~ spl5_15 ),
inference(trivial_inequality_removal,[],[f333]) ).
thf(f339,plain,
( ( $true
= ( p @ sK4 ) )
| ( $false = $true )
| ~ spl5_17 ),
inference(constrained_superposition,[],[f316,f249]) ).
thf(f342,plain,
( ( $true
= ( p @ sK4 ) )
| ~ spl5_17 ),
inference(trivial_inequality_removal,[],[f339]) ).
thf(f358,plain,
( ( $false = $true )
| ( $false
= ( p @ sK4 ) )
| ( $true
= ( q @ sK4 ) )
| ~ spl5_16 ),
inference(constrained_superposition,[],[f249,f312]) ).
thf(f363,plain,
( ( $false
= ( p @ sK4 ) )
| ( $true
= ( q @ sK4 ) )
| ~ spl5_16 ),
inference(trivial_inequality_removal,[],[f358]) ).
thf(f367,plain,
( ( $true
= ( q @ sK4 ) )
| ( $false = $true )
| ~ spl5_16
| ~ spl5_17 ),
inference(forward_demodulation,[],[f363,f342]) ).
thf(f368,plain,
( ( $true
= ( q @ sK4 ) )
| ~ spl5_16
| ~ spl5_17 ),
inference(trivial_inequality_removal,[],[f367]) ).
thf(f372,plain,
( ( $false = $true )
| ~ spl5_15
| ~ spl5_16
| ~ spl5_17 ),
inference(forward_demodulation,[],[f368,f334]) ).
thf(f373,plain,
( $false
| ~ spl5_15
| ~ spl5_16
| ~ spl5_17 ),
inference(trivial_inequality_removal,[],[f372]) ).
thf(f374,plain,
( ~ spl5_15
| ~ spl5_16
| ~ spl5_17 ),
inference(avatar_contradiction_clause,[],[f373]) ).
cnf(s13,plain,
( spl5_14
| spl5_15 ),
inference(sat_conversion,[],[f309]) ).
cnf(s14,plain,
( spl5_14
| spl5_16 ),
inference(sat_conversion,[],[f313]) ).
cnf(s15,plain,
( spl5_14
| spl5_17 ),
inference(sat_conversion,[],[f317]) ).
cnf(s16,plain,
~ spl5_14,
inference(sat_conversion,[],[f318]) ).
cnf(s18,plain,
( ~ spl5_15
| ~ spl5_16
| ~ spl5_17 ),
inference(sat_conversion,[],[f374]) ).
cnf(s19,plain,
spl5_17,
inference(rat,[],[s15,s16]) ).
cnf(s20,plain,
spl5_16,
inference(rat,[],[s14,s16]) ).
cnf(s21,plain,
~ spl5_15,
inference(rat,[],[s18,s19,s20]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s13,s21,s16]) ).
thf(f375,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO455^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n009.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 16:57:16 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.23 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
% 0.21/0.28 % (73306)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (73328)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.28 % (73328)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
% 0.21/0.28 % (73328)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=3558014203:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.28 % (73328) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-73306-73328"...
% 0.21/0.28 % (73322)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2300814829:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.28 % (73326)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=516974451:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.28 % (73325)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=4255696969: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)
% 0.21/0.28 % (73323)lrs+10_16_si=on:nwc=1.5:random_seed=4207689173:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.28 % (73324)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3003653437:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.28 % (73328)...printing done.
% 0.21/0.28 % (73327)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1673928458:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.28 % (73328)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (73328)------------------------------
% 0.21/0.28 % (73328)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (73328)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (73328)CaDiCaL version: 2.1.3
% 0.21/0.28 % (73328)Termination reason: Refutation
% 0.21/0.28 % (73328)Time elapsed: 0.006 s
% 0.21/0.28 % (73328)Peak memory usage: 13 MB
% 0.21/0.28 % (73328)Instructions burned: 21 (million)
% 0.21/0.28 % (73306)Success in time 0.043 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------