%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% 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 08:11:55 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% 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 : 524 ( 97 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 1017 ( 192 ~; 81 |; 0 &; 669 @)
% ( 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)
% ( 41 !!; 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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_47,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_48,type,
vNOT: $o > $o ).
thf(func_def_49,type,
vOR: $o > $o > $o ).
thf(func_def_50,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_51,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_54,type,
vIMP: $o > $o > $o ).
thf(func_def_55,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_56,type,
vAND: $o > $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,
( 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] :
( ( 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,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f48,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f49,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f50,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f56,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f64,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f65,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f64]) ).
thf(f66,plain,
( mexists_ind
= ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f67,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f66]) ).
thf(f90,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f91,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f90]) ).
thf(f98,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f99,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f98]) ).
thf(f119,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(f120,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,[],[f119]) ).
thf(f121,plain,
~ ( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [X0: mu] : ( teach @ X0 @ cs ) ) ) ),
inference(rectify,[],[f45]) ).
thf(f122,plain,
( $true
!= ( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [Y0: mu] : ( teach @ Y0 @ cs ) ) ) ) ),
inference(fool_elimination,[],[f121]) ).
thf(f123,plain,
( $true
!= ( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [Y0: mu] : ( teach @ Y0 @ cs ) ) ) ) ),
inference(flattening,[],[f122]) ).
thf(f128,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f129,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f134,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
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,[],[f65]) ).
thf(f142,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f154,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f91]) ).
thf(f158,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f99]) ).
thf(f169,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,[],[f120]) ).
thf(f170,plain,
( $true
!= ( mvalid
@ ( mbox_s4
@ ( mexists_ind
@ ^ [Y0: mu] : ( teach @ Y0 @ cs ) ) ) ) ),
inference(cnf_transformation,[],[f123]) ).
thf(f174,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,[],[f134,f128,f129,f128,f128]) ).
thf(f180,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,[],[f142,f128,f141,f128]) ).
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,[],[f169,f154,f158,f174,f174,f180,f174]) ).
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,[],[f170,f154,f158,f180]) ).
thf(f187,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( teach @ Y2 @ cs @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f186]) ).
thf(f188,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,[],[f187]) ).
thf(f189,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,[],[f188]) ).
thf(f190,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,[],[f189]) ).
thf(f191,plain,
( $false
= ( ~ ( rel_s4 @ sK1 @ sK2 )
| ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ~ ( teach @ Y0 @ cs @ sK2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f190]) ).
thf(f192,plain,
( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ~ ( teach @ Y0 @ cs @ sK2 ) ) ) ) ),
inference(or_proxy_clausification,[],[f191]) ).
thf(f193,plain,
( $false
= ( ~ ( rel_s4 @ sK1 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f191]) ).
thf(f194,plain,
( $true
= ( rel_s4 @ sK1 @ sK2 ) ),
inference(not_proxy_clausification,[],[f193]) ).
thf(f195,plain,
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ~ ( teach @ Y0 @ cs @ sK2 ) ) ) ),
inference(not_proxy_clausification,[],[f192]) ).
thf(f196,plain,
! [X1: mu] :
( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK2 )
=> ~ ( teach @ Y0 @ cs @ sK2 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X1: mu] :
( $true
= ( ( exists_in_world @ X1 @ sK2 )
=> ~ ( teach @ X1 @ cs @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f196]) ).
thf(f198,plain,
! [X1: mu] :
( ( $false
= ( exists_in_world @ X1 @ sK2 ) )
| ( $true
= ( ~ ( teach @ X1 @ cs @ sK2 ) ) ) ),
inference(imp_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X1: mu] :
( ( $false
= ( teach @ X1 @ cs @ sK2 ) )
| ( $false
= ( exists_in_world @ X1 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f198]) ).
thf(f200,plain,
( $true
= ( !! @ $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 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f201,plain,
! [X1: $i] :
( $true
= ( ^ [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 ) ),
inference(pi_proxy_clausification,[],[f200]) ).
thf(f202,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,[],[f201]) ).
thf(f203,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,[],[f202]) ).
thf(f204,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,[],[f203]) ).
thf(f205,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,[],[f204]) ).
thf(f206,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,[],[f205]) ).
thf(f207,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ~ ( ~ ~ ( !! @ 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,[],[f206]) ).
thf(f211,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( ~ ~ ( !! @ 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,[],[f207]) ).
thf(f212,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ~ ( !! @ 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,[],[f211]) ).
thf(f214,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( teach @ Y0 @ cs @ X2 ) ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f212]) ).
thf(f215,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( teach @ Y0 @ cs @ X2 ) ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f214]) ).
thf(f216,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( teach @ Y0 @ cs @ X2 ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f215]) ).
thf(f217,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( teach @ Y0 @ cs @ X2 ) )
@ ( sK3 @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(sigma_proxy_clausification,[],[f216]) ).
thf(f218,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( teach @ Y0 @ cs @ X2 ) )
@ ( sK3 @ X2 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f217]) ).
thf(f219,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ( exists_in_world @ ( sK3 @ X2 ) @ X2 )
=> ~ ( teach @ ( sK3 @ X2 ) @ cs @ X2 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f218]) ).
thf(f220,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( teach @ ( sK3 @ X2 ) @ cs @ X2 ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f219]) ).
thf(f221,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( exists_in_world @ ( sK3 @ X2 ) @ X2 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f219]) ).
thf(f222,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( teach @ ( sK3 @ X2 ) @ cs @ X2 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f220]) ).
thf(f326,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ X0 @ sK2 ) )
| ( $false
= ( exists_in_world @ ( sK3 @ sK2 ) @ sK2 ) ) ),
inference(constrained_superposition,[],[f222,f199]) ).
thf(f332,plain,
! [X0: $i] :
( ( $false
= ( rel_s4 @ X0 @ sK2 ) )
| ( $false
= ( exists_in_world @ ( sK3 @ sK2 ) @ sK2 ) ) ),
inference(trivial_inequality_removal,[],[f326]) ).
thf(f334,definition,
( spl4_1
<=> ! [X0: $i] :
( $false
= ( rel_s4 @ X0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f335,plain,
( ! [X0: $i] :
( $false
= ( rel_s4 @ X0 @ sK2 ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f334]) ).
thf(f337,definition,
( spl4_2
<=> ( $false
= ( exists_in_world @ ( sK3 @ sK2 ) @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f339,plain,
( ( $false
= ( exists_in_world @ ( sK3 @ sK2 ) @ sK2 ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f337]) ).
thf(f341,plain,
( spl4_2
| spl4_1 ),
inference(avatar_split_clause,[],[f332,f334,f337]) ).
thf(f344,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $false
= ( rel_s4 @ X0 @ sK2 ) ) )
| ~ spl4_2 ),
inference(constrained_superposition,[],[f221,f339]) ).
thf(f346,plain,
( ! [X0: $i] :
( $false
= ( rel_s4 @ X0 @ sK2 ) )
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f344]) ).
thf(f349,plain,
( spl4_1
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f346,f337,f334]) ).
thf(f350,plain,
( ( $true = $false )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f335,f194]) ).
thf(f364,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f350]) ).
thf(f365,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f364]) ).
cnf(s2,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f341]) ).
cnf(s3,plain,
( spl4_1
| ~ spl4_2 ),
inference(sat_conversion,[],[f349]) ).
cnf(s8,plain,
~ spl4_1,
inference(sat_conversion,[],[f365]) ).
cnf(s9,plain,
~ spl4_2,
inference(rat,[],[s3,s8]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s2,s9,s8]) ).
thf(f366,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KRS276^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 08:44:56 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.20 Running first-order model finding
% 0.08/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.27 % (785138)Will run a generic schedule for satisfiability detection.
% 0.19/0.27 % (785144)% WARNING: option uhcvi not known.
% 0.19/0.27 % (785144)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2918365747:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.27 % (785144)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.27 % (785144)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.27 % (785143)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3609110468_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.27 % (785145)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2988235170:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.27 % (785146)dis+10_1_sil=32000:sp=arity:random_seed=3555052827:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.27 % (785147)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3057783427:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.27 % (785148)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2844993730:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.27 % (785149)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3223914560:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.27 % (785147)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.27 % Exception at run slice level
% 0.19/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.27 % (785149) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-785138-785149"...
% 0.19/0.27 % (785145) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-785138-785145"...
% 0.19/0.27 % (785149)...printing done.
% 0.19/0.27 % (785149)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (785149)------------------------------
% 0.19/0.27 % (785149)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (785149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (785149)CaDiCaL version: 2.1.3
% 0.19/0.27 % (785149)Termination reason: Refutation
% 0.19/0.27 % (785149)Time elapsed: 0.016 s
% 0.19/0.27 % (785149)Peak memory usage: 13 MB
% 0.19/0.27 % (785149)Instructions burned: 29 (million)
% 0.19/0.27 % (785138)Success in time 0.059 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------