%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO566^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.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 08:48:25 AM UTC 2026
% Result : Theorem 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 9
% Syntax : Number of formulae : 77 ( 58 unt; 0 typ; 0 def)
% Number of atoms : 510 ( 97 equ; 0 cnn)
% Maximal formula atoms : 12 ( 6 avg)
% Number of connectives : 707 ( 51 ~; 65 |; 0 &; 518 @)
% ( 0 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 72 ( 72 >; 0 *; 0 +; 0 <<)
% Number of symbols : 58 ( 54 usr; 5 con; 0-4 aty)
% ( 40 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 189 ( 156 ^; 33 !; 0 ?; 189 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
qmltpeq: 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,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_7,type,
mtrue: $i > $o ).
thf(func_def_8,type,
mfalse: $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
exists_in_world: mu > $i > $o ).
thf(func_def_16,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_17,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_18,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_19,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
mvalid: ( $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,
minvalid: ( $i > $o ) > $o ).
thf(func_def_33,type,
rel_s4: $i > $i > $o ).
thf(func_def_34,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(func_def_36,type,
g: mu > $i > $o ).
thf(func_def_37,type,
f: mu > $i > $o ).
thf(func_def_38,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_39,type,
vNOT: $o > $o ).
thf(func_def_40,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_43,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
vOR: $o > $o > $o ).
thf(func_def_45,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
vIMP: $o > $o > $o ).
thf(func_def_47,type,
vAND: $o > $o > $o ).
thf(func_def_48,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_52,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
sK0: $i > mu ).
thf(func_def_55,type,
sK2: mu ).
thf(f2,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mnot) ).
thf(f3,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mor) ).
thf(f9,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mimplies) ).
thf(f15,axiom,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_ind ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mforall_ind) ).
thf(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mreflexive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f34,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',a1) ).
thf(f37,conjecture,
( mvalid
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] : ( mimplies @ ( f @ X0 ) @ ( g @ X0 ) ) ) )
@ ( mimplies
@ ( mforall_ind
@ ^ [X0: mu] : ( f @ X0 ) )
@ ( mforall_ind
@ ^ [X0: mu] : ( g @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f38,negated_conjecture,
~ ( mvalid
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] : ( mimplies @ ( f @ X0 ) @ ( g @ X0 ) ) ) )
@ ( mimplies
@ ( mforall_ind
@ ^ [X0: mu] : ( f @ X0 ) )
@ ( mforall_ind
@ ^ [X0: mu] : ( g @ X0 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f42,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f43,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f51,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f52,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f51]) ).
thf(f54,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f55,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f57,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f58,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f69,plain,
~ ( mvalid
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] : ( mimplies @ ( f @ X0 ) @ ( g @ X0 ) ) ) )
@ ( mimplies
@ ( mforall_ind
@ ^ [X1: mu] : ( f @ X1 ) )
@ ( mforall_ind
@ ^ [X2: mu] : ( g @ X2 ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f70,plain,
( ( mvalid
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] : ( mimplies @ ( f @ Y0 ) @ ( g @ Y0 ) ) ) )
@ ( mimplies
@ ( mforall_ind
@ ^ [Y0: mu] : ( f @ Y0 ) )
@ ( mforall_ind
@ ^ [Y0: mu] : ( g @ Y0 ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f69]) ).
thf(f77,plain,
mreflexive @ rel_s4,
inference(rectify,[],[f34]) ).
thf(f78,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f77]) ).
thf(f83,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f84,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f91,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f96,plain,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_ind ),
inference(rectify,[],[f15]) ).
thf(f97,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f96]) ).
thf(f102,plain,
( ( mvalid
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] : ( mimplies @ ( f @ Y0 ) @ ( g @ Y0 ) ) ) )
@ ( mimplies
@ ( mforall_ind
@ ^ [Y0: mu] : ( f @ Y0 ) )
@ ( mforall_ind
@ ^ [Y0: mu] : ( g @ Y0 ) ) ) ) )
!= $true ),
inference(flattening,[],[f70]) ).
thf(f110,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f118,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f121,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f78]) ).
thf(f124,plain,
( ( mvalid
@ ( mimplies
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] : ( mimplies @ ( f @ Y0 ) @ ( g @ Y0 ) ) ) )
@ ( mimplies
@ ( mforall_ind
@ ^ [Y0: mu] : ( f @ Y0 ) )
@ ( mforall_ind
@ ^ [Y0: mu] : ( g @ Y0 ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f102]) ).
thf(f128,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f133,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f134,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f137,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f91]) ).
thf(f141,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f97]) ).
thf(f148,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,[],[f137,f134,f118]) ).
thf(f157,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s4 )
= $true ),
inference(definition_unfolding,[],[f121,f110]) ).
thf(f158,plain,
( ( ^ [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] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i > $o] :
( ^ [Y3: $i > $o,Y4: $i > $o,Y5: $i] :
( ( Y4 @ Y5 )
| ( Y3 @ Y5 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ Y1 )
@ Y2 )
@ ( f @ Y0 )
@ ( g @ Y0 ) ) ) )
@ ( ^ [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: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] : ( f @ Y0 ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] : ( g @ Y0 ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f124,f128,f148,f133,f141,f148,f148,f141,f141]) ).
thf(f159,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( g @ Y1 @ Y0 ) ) )
| ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( f @ Y1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ( g @ Y2 @ Y1 )
| ~ ( f @ Y2 @ Y1 ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
( ( ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( g @ Y1 @ Y0 ) ) )
| ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( f @ Y1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ( g @ Y2 @ Y1 )
| ~ ( f @ Y2 @ Y1 ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( g @ Y0 @ sK1 ) ) )
| ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( f @ Y0 @ sK1 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ( g @ Y1 @ Y0 )
| ~ ( f @ Y1 @ Y0 ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f162,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ( g @ Y1 @ Y0 )
| ~ ( f @ Y1 @ Y0 ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( g @ Y0 @ sK1 ) ) )
| ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( f @ Y0 @ sK1 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f164,plain,
( ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( f @ Y0 @ sK1 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( g @ Y0 @ sK1 ) ) )
= $false ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f166,plain,
( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( g @ Y0 @ sK1 ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f165]) ).
thf(f167,plain,
( ( ( exists_in_world @ sK2 @ sK1 )
=> ( g @ sK2 @ sK1 ) )
= $false ),
inference(beta-eta_normalization,[],[f166]) ).
thf(f168,plain,
( ( g @ sK2 @ sK1 )
= $false ),
inference(imp_proxy_clausification,[],[f167]) ).
thf(f169,plain,
( ( exists_in_world @ sK2 @ sK1 )
= $true ),
inference(imp_proxy_clausification,[],[f167]) ).
thf(f170,plain,
( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( f @ Y0 @ sK1 ) ) )
= $true ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f171,plain,
! [X1: mu] :
( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( f @ Y0 @ sK1 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X1: mu] :
( ( ( exists_in_world @ X1 @ sK1 )
=> ( f @ X1 @ sK1 ) )
= $true ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f173,plain,
! [X1: mu] :
( ( ( f @ X1 @ sK1 )
= $true )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ( g @ Y1 @ Y0 )
| ~ ( f @ Y1 @ Y0 ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
= $true ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f175,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ( g @ Y1 @ Y0 )
| ~ ( f @ Y1 @ Y0 ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X1: $i] :
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ( g @ Y0 @ X1 )
| ~ ( f @ Y0 @ X1 ) ) ) )
| ~ ( rel_s4 @ sK1 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ( g @ Y0 @ X1 )
| ~ ( f @ Y0 @ X1 ) ) ) )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f178,plain,
! [X2: mu,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 ) ) )
| ( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ( g @ Y0 @ X1 )
| ~ ( f @ Y0 @ X1 ) ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X2: mu,X1: $i] :
( ( ( rel_s4 @ sK1 @ X1 )
= $false )
| ( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ( g @ Y0 @ X1 )
| ~ ( f @ Y0 @ X1 ) ) )
@ X2 )
= $true ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X2: mu,X1: $i] :
( ( ( rel_s4 @ sK1 @ X1 )
= $false )
| ( $true
= ( ( exists_in_world @ X2 @ X1 )
=> ( ( g @ X2 @ X1 )
| ~ ( f @ X2 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f179]) ).
thf(f181,plain,
! [X2: mu,X1: $i] :
( ( ( ( g @ X2 @ X1 )
| ~ ( f @ X2 @ X1 ) )
= $true )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( rel_s4 @ sK1 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X2: mu,X1: $i] :
( ( ( g @ X2 @ X1 )
= $true )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( rel_s4 @ sK1 @ X1 )
= $false )
| ( ( ~ ( f @ X2 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X2: mu,X1: $i] :
( ( ( f @ X2 @ X1 )
= $false )
| ( ( rel_s4 @ sK1 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( g @ X2 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f184,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f185,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X1: $i] :
( ( rel_s4 @ X1 @ X1 )
= $true ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f196,plain,
! [X0: mu] :
( ( $true = $false )
| ( ( g @ X0 @ sK1 )
= $true )
| ( ( rel_s4 @ sK1 @ sK1 )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false ) ),
inference(constrained_superposition,[],[f173,f183]) ).
thf(f198,plain,
! [X0: mu] :
( ( ( g @ X0 @ sK1 )
= $true )
| ( ( rel_s4 @ sK1 @ sK1 )
= $false )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( $true = $false ) ),
inference(duplicate_literal_removal,[],[f196]) ).
thf(f199,plain,
! [X0: mu] :
( ( ( rel_s4 @ sK1 @ sK1 )
= $false )
| ( ( g @ X0 @ sK1 )
= $true )
| ( ( exists_in_world @ X0 @ sK1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f198]) ).
thf(f202,plain,
! [X0: mu] :
( ( ( g @ X0 @ sK1 )
= $true )
| ( ( exists_in_world @ X0 @ sK1 )
= $false )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f199,f186]) ).
thf(f203,plain,
! [X0: mu] :
( ( ( g @ X0 @ sK1 )
= $true )
| ( ( exists_in_world @ X0 @ sK1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f202]) ).
thf(f207,plain,
( ( ( exists_in_world @ sK2 @ sK1 )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f168,f203]) ).
thf(f208,plain,
( ( exists_in_world @ sK2 @ sK1 )
= $false ),
inference(trivial_inequality_removal,[],[f207]) ).
thf(f210,plain,
$true = $false,
inference(forward_demodulation,[],[f208,f169]) ).
thf(f211,plain,
$false,
inference(trivial_inequality_removal,[],[f210]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO566^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.17 % Computer : n020.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 17:15:50 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.28 % (1343204)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.19/0.28 % (1343209)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3576958188:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.19/0.28 % (1343209) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1343204-1343209"...
% 0.19/0.28 % (1343215)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.19/0.28 % (1343215)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
% 0.19/0.28 % (1343209)...printing done.
% 0.19/0.28 % (1343209)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.28 % (1343209)------------------------------
% 0.19/0.28 % (1343209)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (1343209)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (1343209)CaDiCaL version: 2.1.3
% 0.19/0.28 % (1343209)Termination reason: Refutation
% 0.19/0.28 % (1343209)Time elapsed: 0.005 s
% 0.19/0.28 % (1343209)Peak memory usage: 12 MB
% 0.19/0.28 % (1343209)Instructions burned: 17 (million)
% 0.19/0.28 % (1343204)Success in time 0.043 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------