%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS276^7 : 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 : n018.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 08:11:54 AM UTC 2026
% Result : Theorem 0.21s 0.32s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 11
% Syntax : Number of formulae : 92 ( 57 unt; 0 typ; 2 def)
% Number of atoms : 527 ( 97 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 1028 ( 194 ~; 83 |; 0 &; 675 @)
% ( 2 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 92 ( 92 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 62 usr; 13 con; 0-4 aty)
% ( 42 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 238 ( 0 sgn 50 !; 0 ?; 238 :)
% 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,
teach: mu > mu > $i > $o ).
thf(func_def_37,type,
sue: mu ).
thf(func_def_38,type,
psych: mu ).
thf(func_def_39,type,
mary: mu ).
thf(func_def_40,type,
math: mu ).
thf(func_def_41,type,
john: mu ).
thf(func_def_42,type,
cs: mu ).
thf(func_def_43,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_48,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
vIMP: $o > $o > $o ).
thf(func_def_50,type,
vAND: $o > $o > $o ).
thf(func_def_51,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
vOR: $o > $o > $o ).
thf(func_def_54,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_55,type,
vNOT: $o > $o ).
thf(func_def_56,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_57,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_58,type,
sK0: $i > mu ).
thf(func_def_61,type,
sK3: $i > mu ).
thf(f2,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mnot) ).
thf(f3,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mor) ).
thf(f8,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mand) ).
thf(f15,axiom,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mforall_ind) ).
thf(f16,axiom,
( mexists_ind
= ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mexists_ind) ).
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] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f43,axiom,
( mvalid
@ ( mbox_s4
@ ( mand @ ( teach @ john @ math )
@ ( mand
@ ( mexists_ind
@ ^ [X0: mu] : ( teach @ X0 @ cs ) )
@ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',db) ).
thf(f44,conjecture,
( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [X0: mu] : ( teach @ X0 @ cs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',query) ).
thf(f45,negated_conjecture,
~ ( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [X0: mu] : ( teach @ X0 @ cs ) ) ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
thf(f47,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f48,plain,
~ ( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [X0: mu] : ( teach @ X0 @ cs ) ) ) ),
inference(rectify,[],[f45]) ).
thf(f49,plain,
( $true
!= ( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [Y0: mu] : ( teach @ Y0 @ cs ) ) ) ) ),
inference(fool_elimination,[],[f48]) ).
thf(f63,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f2]) ).
thf(f64,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f75,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f76,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f75]) ).
thf(f79,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f80,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f79]) ).
thf(f81,plain,
( mvalid
@ ( mbox_s4
@ ( mand @ ( teach @ john @ math )
@ ( mand
@ ( mexists_ind
@ ^ [X0: mu] : ( teach @ X0 @ cs ) )
@ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) ),
inference(rectify,[],[f43]) ).
thf(f82,plain,
( ( mvalid
@ ( mbox_s4
@ ( mand @ ( teach @ john @ math )
@ ( mand
@ ( mexists_ind
@ ^ [Y0: mu] : ( teach @ Y0 @ cs ) )
@ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f81]) ).
thf(f95,plain,
( mexists_ind
= ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f96,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f95]) ).
thf(f105,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f106,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f105]) ).
thf(f115,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f116,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f115]) ).
thf(f123,plain,
( $true
!= ( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [Y0: mu] : ( teach @ Y0 @ cs ) ) ) ) ),
inference(flattening,[],[f49]) ).
thf(f134,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f106]) ).
thf(f140,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f142,plain,
( ( mvalid
@ ( mbox_s4
@ ( mand @ ( teach @ john @ math )
@ ( mand
@ ( mexists_ind
@ ^ [Y0: mu] : ( teach @ Y0 @ cs ) )
@ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f82]) ).
thf(f145,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f116]) ).
thf(f148,plain,
( $true
!= ( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [Y0: mu] : ( teach @ Y0 @ cs ) ) ) ) ),
inference(cnf_transformation,[],[f123]) ).
thf(f152,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f80]) ).
thf(f161,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f169,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f76]) ).
thf(f171,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f96]) ).
thf(f175,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f140,f161,f145,f161,f161]) ).
thf(f181,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f171,f161,f169,f161]) ).
thf(f185,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( teach @ john @ math )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) )
@ ^ [Y0: mu] : ( teach @ Y0 @ cs ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( teach @ mary @ psych )
@ ( teach @ sue @ psych ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f142,f134,f152,f175,f175,f181,f175]) ).
thf(f186,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mu > $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( Y0 @ Y1 ) ) ) )
@ ^ [Y0: mu] : ( teach @ Y0 @ cs ) ) ) ) ),
inference(definition_unfolding,[],[f148,f134,f152,f181]) ).
thf(f200,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( teach @ Y2 @ cs @ Y1 ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f186]) ).
thf(f201,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( teach @ Y2 @ cs @ Y1 ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f200]) ).
thf(f202,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( teach @ Y1 @ cs @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f201]) ).
thf(f203,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( teach @ Y1 @ cs @ Y0 ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f202]) ).
thf(f204,plain,
( ( ~ ( rel_s4 @ sK1 @ sK2 )
| ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ~ ( teach @ Y0 @ cs @ sK2 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f203]) ).
thf(f205,plain,
( ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ~ ( teach @ Y0 @ cs @ sK2 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f204]) ).
thf(f206,plain,
( $false
= ( ~ ( rel_s4 @ sK1 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f204]) ).
thf(f207,plain,
( ( rel_s4 @ sK1 @ sK2 )
= $true ),
inference(not_proxy_clausification,[],[f206]) ).
thf(f208,plain,
( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ~ ( teach @ Y0 @ cs @ sK2 ) ) )
= $true ),
inference(not_proxy_clausification,[],[f205]) ).
thf(f209,plain,
! [X1: mu] :
( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ~ ( teach @ Y0 @ cs @ sK2 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f208]) ).
thf(f210,plain,
! [X1: mu] :
( $true
= ( ( exists_in_world @ X1 @ sK2 )
=> ~ ( teach @ X1 @ cs @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f209]) ).
thf(f211,plain,
! [X1: mu] :
( ( ( exists_in_world @ X1 @ sK2 )
= $false )
| ( $true
= ( ~ ( teach @ X1 @ cs @ sK2 ) ) ) ),
inference(imp_proxy_clausification,[],[f210]) ).
thf(f212,plain,
! [X1: mu] :
( ( ( teach @ X1 @ cs @ sK2 )
= $false )
| ( ( exists_in_world @ X1 @ sK2 )
= $false ) ),
inference(not_proxy_clausification,[],[f211]) ).
thf(f213,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( ~ ( teach @ john @ math @ Y1 )
| ~ ~ ( ~ ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( teach @ Y2 @ cs @ Y1 ) ) )
| ~ ~ ( ~ ( teach @ mary @ psych @ Y1 )
| ~ ( teach @ sue @ psych @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f214,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( ~ ( teach @ john @ math @ Y1 )
| ~ ~ ( ~ ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( teach @ Y2 @ cs @ Y1 ) ) )
| ~ ~ ( ~ ( teach @ mary @ psych @ Y1 )
| ~ ( teach @ sue @ psych @ Y1 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f213]) ).
thf(f215,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( ~ ( teach @ john @ math @ Y0 )
| ~ ~ ( ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( teach @ Y1 @ cs @ Y0 ) ) )
| ~ ~ ( ~ ( teach @ mary @ psych @ Y0 )
| ~ ( teach @ sue @ psych @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f214]) ).
thf(f216,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( ~ ( teach @ john @ math @ Y0 )
| ~ ~ ( ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( teach @ Y1 @ cs @ Y0 ) ) )
| ~ ~ ( ~ ( teach @ mary @ psych @ Y0 )
| ~ ( teach @ sue @ psych @ Y0 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f215]) ).
thf(f217,plain,
! [X2: $i,X1: $i] :
( $true
= ( ~ ( rel_s4 @ X1 @ X2 )
| ~ ( ~ ( teach @ john @ math @ X2 )
| ~ ~ ( ~ ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( teach @ Y0 @ cs @ X2 ) ) )
| ~ ~ ( ~ ( teach @ mary @ psych @ X2 )
| ~ ( teach @ sue @ psych @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f216]) ).
thf(f218,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( ~ ( teach @ john @ math @ X2 )
| ~ ~ ( ~ ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( teach @ Y0 @ cs @ X2 ) ) )
| ~ ~ ( ~ ( teach @ mary @ psych @ X2 )
| ~ ( teach @ sue @ psych @ X2 ) ) ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f217]) ).
thf(f219,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( teach @ john @ math @ X2 )
| ~ ~ ( ~ ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( teach @ Y0 @ cs @ X2 ) ) )
| ~ ~ ( ~ ( teach @ mary @ psych @ X2 )
| ~ ( teach @ sue @ psych @ X2 ) ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f218]) ).
thf(f220,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ~ ( ~ ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( teach @ Y0 @ cs @ X2 ) ) )
| ~ ~ ( ~ ( teach @ mary @ psych @ X2 )
| ~ ( teach @ sue @ psych @ X2 ) ) ) )
= $false )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f219]) ).
thf(f224,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( ( ~ ( ~ ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( teach @ Y0 @ cs @ X2 ) ) )
| ~ ~ ( ~ ( teach @ mary @ psych @ X2 )
| ~ ( teach @ sue @ psych @ X2 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f220]) ).
thf(f225,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( ~ ( ~ ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( teach @ Y0 @ cs @ X2 ) ) )
| ~ ~ ( ~ ( teach @ mary @ psych @ X2 )
| ~ ( teach @ sue @ psych @ X2 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f224]) ).
thf(f226,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( teach @ Y0 @ cs @ X2 ) ) )
| ~ ~ ( ~ ( teach @ mary @ psych @ X2 )
| ~ ( teach @ sue @ psych @ X2 ) ) )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f225]) ).
thf(f228,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( teach @ Y0 @ cs @ X2 ) ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f226]) ).
thf(f229,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( teach @ Y0 @ cs @ X2 ) ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( teach @ Y0 @ cs @ X2 ) ) )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f229]) ).
thf(f231,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( teach @ Y0 @ cs @ X2 ) )
@ ( sK3 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f230]) ).
thf(f232,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( ( exists_in_world @ ( sK3 @ X2 ) @ X2 )
=> ~ ( teach @ ( sK3 @ X2 ) @ cs @ X2 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f231]) ).
thf(f233,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( teach @ ( sK3 @ X2 ) @ cs @ X2 ) )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( exists_in_world @ ( sK3 @ X2 ) @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f232]) ).
thf(f235,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( teach @ ( sK3 @ X2 ) @ cs @ X2 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f233]) ).
thf(f255,plain,
! [X0: $i] :
( ( $false
= ( exists_in_world @ ( sK3 @ sK2 ) @ sK2 ) )
| ( $false
= ( rel_s4 @ X0 @ sK2 ) )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f212,f235]) ).
thf(f257,plain,
! [X0: $i] :
( ( $false
= ( rel_s4 @ X0 @ sK2 ) )
| ( $false
= ( exists_in_world @ ( sK3 @ sK2 ) @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f255]) ).
thf(f259,definition,
( spl4_1
<=> ! [X0: $i] :
( $false
= ( rel_s4 @ X0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f260,plain,
( ! [X0: $i] :
( $false
= ( rel_s4 @ X0 @ sK2 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f259]) ).
thf(f262,definition,
( spl4_2
<=> ( $false
= ( exists_in_world @ ( sK3 @ sK2 ) @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f264,plain,
( ( $false
= ( exists_in_world @ ( sK3 @ sK2 ) @ sK2 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f262]) ).
thf(f266,plain,
( spl4_2
| spl4_1 ),
inference(avatar_split_clause,[],[f257,f259,f262]) ).
thf(f267,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ X0 @ sK2 ) ) )
| ~ spl4_2 ),
inference(constrained_superposition,[],[f264,f234]) ).
thf(f269,plain,
( ! [X0: $i] :
( $false
= ( rel_s4 @ X0 @ sK2 ) )
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f267]) ).
thf(f271,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f269,f262,f259]) ).
thf(f272,plain,
( ( $true = $false )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f260,f207]) ).
thf(f282,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f272]) ).
thf(f283,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f282]) ).
cnf(s2,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f266]) ).
cnf(s3,plain,
( spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f271]) ).
cnf(s8,plain,
~ spl4_1,
inference(sat_conversion,[],[f283]) ).
cnf(s9,plain,
~ spl4_2,
inference(rat,[],[s3,s8]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s2,s9,s8]) ).
thf(f284,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KRS276^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 % Computer : n018.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Sep 29 08:44:27 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.25 Running higher-order theorem proving
% 0.21/0.27 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.32 % (4000002)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.32 % (4000007)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2071723808:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.32 % (4000013)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.32 % (4000013)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.32 % (4000007) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4000002-4000007"...
% 0.21/0.32 % (4000008)lrs+10_16_si=on:nwc=1.5:random_seed=2861313599:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.32 % (4000009)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2737459253:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.32 % (4000010)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=2344659579:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.32 % (4000011)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3442461559:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.32 % (4000012)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1120937816:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.32 % (4000013)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=3189373008:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.32 % (4000007)...printing done.
% 0.21/0.32 % (4000007)Refutation found. Thanks to Tanya!
% 0.21/0.32 % SZS status Theorem for theBenchmark
% 0.21/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.32 % (4000007)------------------------------
% 0.21/0.32 % (4000007)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (4000007)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (4000007)CaDiCaL version: 2.1.3
% 0.21/0.32 % (4000007)Termination reason: Refutation
% 0.21/0.32 % (4000007)Time elapsed: 0.007 s
% 0.21/0.32 % (4000007)Peak memory usage: 13 MB
% 0.21/0.32 % (4000007)Instructions burned: 24 (million)
% 0.21/0.32 % (4000002)Success in time 0.04 s
% 0.21/0.32 % Vampire exiting
%------------------------------------------------------------------------------