%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : KRS275^7 : 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 : n013.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 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 12
% Syntax : Number of formulae : 84 ( 64 unt; 0 typ; 0 def)
% Number of atoms : 454 ( 88 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 904 ( 149 ~; 67 |; 0 &; 625 @)
% ( 0 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 102 ( 102 >; 0 *; 0 +; 0 <<)
% Number of symbols : 64 ( 60 usr; 10 con; 0-4 aty)
% ( 42 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 234 ( 193 ^; 41 !; 0 ?; 234 :)
% 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,
cs: mu ).
thf(func_def_41,type,
math: mu ).
thf(func_def_42,type,
john: mu ).
thf(func_def_43,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
vIMP: $o > $o > $o ).
thf(func_def_45,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_51,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_52,type,
vNOT: $o > $o ).
thf(func_def_53,type,
vOR: $o > $o > $o ).
thf(func_def_54,type,
vAND: $o > $o > $o ).
thf(func_def_55,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_56,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_57,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_58,type,
sK0: $i > mu ).
thf(func_def_60,type,
sK2: mu > $i ).
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,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
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,
( ( ^ [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(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(f18,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
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,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s4 ),
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(f41,axiom,
! [X0: $i] : ( exists_in_world @ math @ X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_of_math_ax) ).
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
@ ( mexists_ind
@ ^ [X0: mu] : ( mbox_s4 @ ( teach @ john @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',query) ).
thf(f45,negated_conjecture,
~ ( mvalid
@ ( mexists_ind
@ ^ [X0: mu] : ( mbox_s4 @ ( teach @ john @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
thf(f53,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f3]) ).
thf(f54,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f57,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(f58,plain,
( $true
= ( mvalid
@ ( mbox_s4
@ ( mand @ ( teach @ john @ math )
@ ( mand
@ ( mexists_ind
@ ^ [Y0: mu] : ( teach @ Y0 @ cs ) )
@ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f61,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f64,plain,
~ ( mvalid
@ ( mexists_ind
@ ^ [X0: mu] : ( mbox_s4 @ ( teach @ john @ X0 ) ) ) ),
inference(rectify,[],[f45]) ).
thf(f65,plain,
( $true
!= ( mvalid
@ ( mexists_ind
@ ^ [Y0: mu] : ( mbox_s4 @ ( teach @ john @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f64]) ).
thf(f66,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s4 ),
inference(rectify,[],[f32]) ).
thf(f67,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f66]) ).
thf(f78,plain,
mreflexive @ rel_s4,
inference(rectify,[],[f34]) ).
thf(f79,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f78]) ).
thf(f80,plain,
( mexists_ind
= ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f81,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f80]) ).
thf(f87,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f2]) ).
thf(f88,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f87]) ).
thf(f91,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f92,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f91]) ).
thf(f106,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
inference(rectify,[],[f18]) ).
thf(f107,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f106]) ).
thf(f112,plain,
! [X0: $i] : ( exists_in_world @ math @ X0 ),
inference(rectify,[],[f41]) ).
thf(f113,plain,
! [X0: $i] :
( ( exists_in_world @ math @ X0 )
= $true ),
inference(fool_elimination,[],[f112]) ).
thf(f118,plain,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_ind ),
inference(rectify,[],[f15]) ).
thf(f119,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f118]) ).
thf(f123,plain,
( $true
!= ( mvalid
@ ( mexists_ind
@ ^ [Y0: mu] : ( mbox_s4 @ ( teach @ john @ Y0 ) ) ) ) ),
inference(flattening,[],[f65]) ).
thf(f132,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f135,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f92]) ).
thf(f136,plain,
( $true
= ( mvalid
@ ( mbox_s4
@ ( mand @ ( teach @ john @ math )
@ ( mand
@ ( mexists_ind
@ ^ [Y0: mu] : ( teach @ Y0 @ cs ) )
@ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f144,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f145,plain,
( $true
!= ( mvalid
@ ( mexists_ind
@ ^ [Y0: mu] : ( mbox_s4 @ ( teach @ john @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f123]) ).
thf(f148,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f151,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f119]) ).
thf(f155,plain,
! [X0: $i] :
( ( exists_in_world @ math @ X0 )
= $true ),
inference(cnf_transformation,[],[f113]) ).
thf(f156,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f157,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f167,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f79]) ).
thf(f168,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f107]) ).
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,[],[f144,f156,f157,f156,f156]) ).
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,[],[f132,f156,f151,f156]) ).
thf(f184,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ 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 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f136,f135,f148,f175,f175,f181,f175]) ).
thf(f185,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ 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] :
( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( teach @ john @ Y0 ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f145,f135,f181,f148]) ).
thf(f187,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s4 )
= $true ),
inference(definition_unfolding,[],[f167,f168]) ).
thf(f188,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( teach @ john @ Y1 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f189,plain,
( $false
= ( ^ [Y0: $i] :
~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( teach @ john @ Y1 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f188]) ).
thf(f190,plain,
( ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( teach @ john @ Y0 @ Y1 )
| ~ ( rel_s4 @ sK1 @ Y1 ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f189]) ).
thf(f191,plain,
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( teach @ john @ Y0 @ Y1 )
| ~ ( rel_s4 @ sK1 @ Y1 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X1: mu] :
( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( teach @ john @ Y0 @ Y1 )
| ~ ( rel_s4 @ sK1 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f191]) ).
thf(f193,plain,
! [X1: mu] :
( ( ( exists_in_world @ X1 @ sK1 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( teach @ john @ X1 @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f192]) ).
thf(f194,plain,
! [X1: mu] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( teach @ john @ X1 @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) )
= $true )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X1: mu] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( teach @ john @ X1 @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X1: mu] :
( ( ( ^ [Y0: $i] :
( ( teach @ john @ X1 @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ ( sK2 @ X1 ) )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X1: mu] :
( ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( ( ( teach @ john @ X1 @ ( sK2 @ X1 ) )
| ~ ( rel_s4 @ sK1 @ ( sK2 @ X1 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f196]) ).
thf(f199,plain,
! [X1: mu] :
( ( ( teach @ john @ X1 @ ( sK2 @ X1 ) )
= $false )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f197]) ).
thf(f210,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f211,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f210]) ).
thf(f212,plain,
! [X1: $i] :
( ( rel_s4 @ X1 @ X1 )
= $true ),
inference(beta-eta_normalization,[],[f211]) ).
thf(f213,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( teach @ john @ math @ Y1 )
| ~ ~ ( ~ ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( teach @ Y2 @ cs @ Y1 ) ) )
| ~ ~ ( ~ ( teach @ mary @ psych @ Y1 )
| ~ ( teach @ sue @ psych @ Y1 ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f184]) ).
thf(f214,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ~ ( teach @ john @ math @ Y1 )
| ~ ~ ( ~ ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( teach @ Y2 @ cs @ Y1 ) ) )
| ~ ~ ( ~ ( teach @ mary @ psych @ Y1 )
| ~ ( teach @ sue @ psych @ Y1 ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f213]) ).
thf(f215,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ~ ( teach @ john @ math @ Y0 )
| ~ ~ ( ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( teach @ Y1 @ cs @ Y0 ) ) )
| ~ ~ ( ~ ( teach @ mary @ psych @ Y0 )
| ~ ( teach @ sue @ psych @ Y0 ) ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f214]) ).
thf(f216,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( ~ ( teach @ john @ math @ Y0 )
| ~ ~ ( ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( teach @ Y1 @ cs @ Y0 ) ) )
| ~ ~ ( ~ ( teach @ mary @ psych @ Y0 )
| ~ ( teach @ sue @ psych @ Y0 ) ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f215]) ).
thf(f217,plain,
! [X2: $i,X1: $i] :
( ( ~ ( ~ ( teach @ john @ math @ X2 )
| ~ ~ ( ~ ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( teach @ Y0 @ cs @ X2 ) ) )
| ~ ~ ( ~ ( teach @ mary @ psych @ X2 )
| ~ ( teach @ sue @ psych @ X2 ) ) ) )
| ~ ( rel_s4 @ X1 @ X2 ) )
= $true ),
inference(beta-eta_normalization,[],[f216]) ).
thf(f218,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( ~ ( 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 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f217]) ).
thf(f219,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ X1 @ X2 ) )
= $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 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f218]) ).
thf(f220,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $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 ) ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f219]) ).
thf(f222,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( teach @ john @ math @ X2 ) )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f220]) ).
thf(f223,plain,
! [X2: $i,X1: $i] :
( ( ( teach @ john @ math @ X2 )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f222]) ).
thf(f243,plain,
! [X0: $i] :
( ( $false
= ( rel_s4 @ X0 @ ( sK2 @ math ) ) )
| ( ( exists_in_world @ math @ sK1 )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f199,f223]) ).
thf(f245,plain,
! [X0: $i] :
( ( ( exists_in_world @ math @ sK1 )
= $false )
| ( $false
= ( rel_s4 @ X0 @ ( sK2 @ math ) ) ) ),
inference(trivial_inequality_removal,[],[f243]) ).
thf(f249,plain,
! [X0: $i] :
( ( $false
= ( rel_s4 @ X0 @ ( sK2 @ math ) ) )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f245,f155]) ).
thf(f250,plain,
! [X0: $i] :
( $false
= ( rel_s4 @ X0 @ ( sK2 @ math ) ) ),
inference(trivial_inequality_removal,[],[f249]) ).
thf(f254,plain,
$true = $false,
inference(constrained_superposition,[],[f250,f212]) ).
thf(f258,plain,
$false,
inference(trivial_inequality_removal,[],[f254]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS275^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.17 % Computer : n013.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Sep 29 08:40:21 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.20 Running higher-order theorem proving
% 0.11/0.22 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
% 0.20/0.28 % (1806093)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.28 % (1806098)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2451904354:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.28 % (1806098) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1806093-1806098"...
% 0.20/0.28 % (1806099)lrs+10_16_si=on:nwc=1.5:random_seed=2454576781:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.28 % (1806098)...printing done.
% 0.20/0.28 % (1806098)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (1806098)------------------------------
% 0.20/0.28 % (1806098)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1806098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1806098)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1806098)Termination reason: Refutation
% 0.20/0.28 % (1806098)Time elapsed: 0.012 s
% 0.20/0.28 % (1806098)Peak memory usage: 12 MB
% 0.20/0.28 % (1806098)Instructions burned: 22 (million)
% 0.20/0.28 % (1806093)Success in time 0.052 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------