%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PLA032^7 : 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 : n016.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 08:20:25 AM UTC 2026
% Result : Theorem 0.22s 0.36s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 21
% Syntax : Number of formulae : 171 ( 69 unt; 0 typ; 9 def)
% Number of atoms : 1396 ( 269 equ; 0 cnn)
% Maximal formula atoms : 10 ( 8 avg)
% Number of connectives : 2105 ( 340 ~; 328 |; 0 &;1289 @)
% ( 8 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 165 ( 165 >; 0 *; 0 +; 0 <<)
% Number of symbols : 73 ( 69 usr; 15 con; 0-4 aty)
% ( 85 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 468 ( 0 sgn 128 !; 0 ?; 468 :)
% 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,
defused: mu > $i > $o ).
thf(func_def_37,type,
h: mu > $i > $o ).
thf(func_def_38,type,
bomb: mu > $i > $o ).
thf(func_def_39,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_41,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
vIMP: $o > $o > $o ).
thf(func_def_43,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vAND: $o > $o > $o ).
thf(func_def_48,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vOR: $o > $o > $o ).
thf(func_def_50,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_51,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_52,type,
vNOT: $o > $o ).
thf(func_def_53,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_54,type,
sK0: $i > mu ).
thf(func_def_55,type,
sF1: $o ).
thf(func_def_56,type,
sK2: $i > mu ).
thf(func_def_57,type,
sK3: mu > $i > mu ).
thf(func_def_58,type,
sK4: $i > mu ).
thf(func_def_59,type,
sK5: mu > $i > mu ).
thf(func_def_62,type,
sK8: 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(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(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,
( 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(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,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL015^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ 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(f39,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] :
( mexists_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( bomb @ X0 ) @ ( h @ X1 ) ) @ ( defused @ X0 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).
thf(f40,conjecture,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] :
( mexists_ind
@ ^ [X1: mu] : ( mimplies @ ( mand @ ( bomb @ X0 ) @ ( h @ X1 ) ) @ ( defused @ X0 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f41,negated_conjecture,
~ ( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] :
( mexists_ind
@ ^ [X1: mu] : ( mimplies @ ( mand @ ( bomb @ X0 ) @ ( h @ X1 ) ) @ ( defused @ X0 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
thf(f43,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f44,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f43]) ).
thf(f51,plain,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] :
( mexists_ind
@ ^ [X1: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( bomb @ X0 ) @ ( h @ X1 ) ) @ ( defused @ X0 ) ) ) ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f52,plain,
( $true
= ( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] :
( mexists_ind
@ ^ [Y1: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( bomb @ Y0 ) @ ( h @ Y1 ) ) @ ( defused @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f51]) ).
thf(f53,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f54,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f58,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f59,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f58]) ).
thf(f66,plain,
mreflexive @ rel_s4,
inference(rectify,[],[f34]) ).
thf(f67,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f66]) ).
thf(f69,plain,
( mexists_ind
= ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f70,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f75,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f76,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f75]) ).
thf(f77,plain,
~ ( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] :
( mexists_ind
@ ^ [X1: mu] : ( mimplies @ ( mand @ ( bomb @ X0 ) @ ( h @ X1 ) ) @ ( defused @ X0 ) ) ) ) ) ),
inference(rectify,[],[f41]) ).
thf(f78,plain,
( $true
!= ( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] :
( mexists_ind
@ ^ [Y1: mu] : ( mimplies @ ( mand @ ( bomb @ Y0 ) @ ( h @ Y1 ) ) @ ( defused @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f77]) ).
thf(f83,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f97,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) )
= mbox_s4 ),
inference(rectify,[],[f32]) ).
thf(f98,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f97]) ).
thf(f106,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f107,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f106]) ).
thf(f110,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f111,plain,
( $true
!= ( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] :
( mexists_ind
@ ^ [Y1: mu] : ( mimplies @ ( mand @ ( bomb @ Y0 ) @ ( h @ Y1 ) ) @ ( defused @ Y0 ) ) ) ) ) ) ),
inference(flattening,[],[f78]) ).
thf(f116,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f110]) ).
thf(f118,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f123,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f67]) ).
thf(f127,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f129,plain,
( $true
= ( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] :
( mexists_ind
@ ^ [Y1: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( bomb @ Y0 ) @ ( h @ Y1 ) ) @ ( defused @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f130,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f133,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f98]) ).
thf(f134,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f76]) ).
thf(f135,plain,
( $true
!= ( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] :
( mexists_ind
@ ^ [Y1: mu] : ( mimplies @ ( mand @ ( bomb @ Y0 ) @ ( h @ Y1 ) ) @ ( defused @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f111]) ).
thf(f141,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f107]) ).
thf(f149,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f83]) ).
thf(f154,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f159,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f116,f134,f127,f134,f134]) ).
thf(f160,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,[],[f149,f127,f134]) ).
thf(f165,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,[],[f130,f134,f154,f134]) ).
thf(f169,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f123,f141]) ).
thf(f170,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] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: mu > $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: mu > $i > $o,Y3: $i] :
( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) )
@ ^ [Y2: mu] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( Y1 @ Y2 ) ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y3 @ Y4 )
| ( Y2 @ Y4 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( bomb @ Y0 )
@ ( h @ Y1 ) )
@ ( defused @ Y0 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f129,f118,f133,f154,f165,f133,f160,f159]) ).
thf(f171,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] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: mu > $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: mu > $i > $o,Y3: $i] :
( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) )
@ ^ [Y2: mu] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( Y1 @ Y2 ) ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( bomb @ Y0 )
@ ( h @ Y1 ) )
@ ( defused @ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f135,f118,f133,f154,f165,f160,f159]) ).
thf(f174,definition,
( sF1
= ( ^ [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] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: mu > $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: mu > $i > $o,Y3: $i] :
( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) )
@ ^ [Y2: mu] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( Y1 @ Y2 ) ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( bomb @ Y0 )
@ ( h @ Y1 ) )
@ ( defused @ Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f175,plain,
$true != sF1,
inference(definition_folding,[],[f171,f174]) ).
thf(f202,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y1 @ Y4 )
| ( defused @ Y2 @ Y4 )
| ~ ~ ( ~ ( h @ Y3 @ Y4 )
| ~ ( bomb @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f203,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y1 )
=> ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y1 @ Y4 )
| ( defused @ Y2 @ Y4 )
| ~ ~ ( ~ ( h @ Y3 @ Y4 )
| ~ ( bomb @ Y2 @ Y4 ) ) ) ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y0 @ Y3 )
| ( defused @ Y1 @ Y3 )
| ~ ~ ( ~ ( h @ Y2 @ Y3 )
| ~ ( bomb @ Y1 @ Y3 ) ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f203]) ).
thf(f205,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y0 @ Y3 )
| ( defused @ Y1 @ Y3 )
| ~ ~ ( ~ ( h @ Y2 @ Y3 )
| ~ ( bomb @ Y1 @ Y3 ) ) ) ) ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X2: $i,X1: $i] :
( ( ~ ( rel_s4 @ X1 @ X2 )
| ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ X2 @ Y2 )
| ( defused @ Y0 @ Y2 )
| ~ ~ ( ~ ( h @ Y1 @ Y2 )
| ~ ( bomb @ Y0 @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f205]) ).
thf(f207,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ X1 @ X2 ) )
= $true )
| ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ X2 @ Y2 )
| ( defused @ Y0 @ Y2 )
| ~ ~ ( ~ ( h @ Y1 @ Y2 )
| ~ ( bomb @ Y0 @ Y2 ) ) ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ X2 @ Y2 )
| ( defused @ Y0 @ Y2 )
| ~ ~ ( ~ ( h @ Y1 @ Y2 )
| ~ ( bomb @ Y0 @ Y2 ) ) ) ) ) ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X2: $i,X3: mu,X1: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ X2 @ Y2 )
| ( defused @ Y0 @ Y2 )
| ~ ~ ( ~ ( h @ Y1 @ Y2 )
| ~ ( bomb @ Y0 @ Y2 ) ) ) ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f208]) ).
thf(f210,plain,
! [X2: $i,X3: mu,X1: $i] :
( ( ( ( exists_in_world @ X3 @ X2 )
=> ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ X2 @ Y1 )
| ( defused @ X3 @ Y1 )
| ~ ~ ( ~ ( h @ Y0 @ Y1 )
| ~ ( bomb @ X3 @ Y1 ) ) ) ) ) ) )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(beta-eta_normalization,[],[f209]) ).
thf(f211,plain,
! [X2: $i,X3: mu,X1: $i] :
( ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( $true
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ X2 @ Y1 )
| ( defused @ X3 @ Y1 )
| ~ ~ ( ~ ( h @ Y0 @ Y1 )
| ~ ( bomb @ X3 @ Y1 ) ) ) ) ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f210]) ).
thf(f212,plain,
! [X2: $i,X3: mu,X1: $i] :
( ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ X2 @ Y1 )
| ( defused @ X3 @ Y1 )
| ~ ~ ( ~ ( h @ Y0 @ Y1 )
| ~ ( bomb @ X3 @ Y1 ) ) ) ) ) )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f211]) ).
thf(f213,plain,
! [X2: $i,X3: mu,X1: $i] :
( ( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ X2 @ Y1 )
| ( defused @ X3 @ Y1 )
| ~ ~ ( ~ ( h @ Y0 @ Y1 )
| ~ ( bomb @ X3 @ Y1 ) ) ) ) )
@ ( sK3 @ X3 @ X2 ) )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f212]) ).
thf(f214,plain,
! [X2: $i,X3: mu,X1: $i] :
( ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( ( exists_in_world @ ( sK3 @ X3 @ X2 ) @ X2 )
=> ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ( defused @ X3 @ Y0 )
| ~ ~ ( ~ ( h @ ( sK3 @ X3 @ X2 ) @ Y0 )
| ~ ( bomb @ X3 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f213]) ).
thf(f215,plain,
! [X2: $i,X3: mu,X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ( defused @ X3 @ Y0 )
| ~ ~ ( ~ ( h @ ( sK3 @ X3 @ X2 ) @ Y0 )
| ~ ( bomb @ X3 @ Y0 ) ) ) ) )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f214]) ).
thf(f216,plain,
! [X2: $i,X3: mu,X1: $i] :
( ( $true
= ( exists_in_world @ ( sK3 @ X3 @ X2 ) @ X2 ) )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f214]) ).
thf(f217,plain,
! [X2: $i,X3: mu,X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ( defused @ X3 @ Y0 )
| ~ ~ ( ~ ( h @ ( sK3 @ X3 @ X2 ) @ Y0 )
| ~ ( bomb @ X3 @ Y0 ) ) ) ) )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f215]) ).
thf(f218,plain,
! [X2: $i,X3: mu,X1: $i,X4: $i] :
( ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X2 @ Y0 )
| ( defused @ X3 @ Y0 )
| ~ ~ ( ~ ( h @ ( sK3 @ X3 @ X2 ) @ Y0 )
| ~ ( bomb @ X3 @ Y0 ) ) )
@ X4 ) ) ),
inference(pi_proxy_clausification,[],[f217]) ).
thf(f219,plain,
! [X2: $i,X3: mu,X1: $i,X4: $i] :
( ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X4 )
| ( defused @ X3 @ X4 )
| ~ ~ ( ~ ( h @ ( sK3 @ X3 @ X2 ) @ X4 )
| ~ ( bomb @ X3 @ X4 ) ) ) ) ),
inference(beta-eta_normalization,[],[f218]) ).
thf(f220,plain,
! [X2: $i,X3: mu,X1: $i,X4: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( ( defused @ X3 @ X4 )
| ~ ~ ( ~ ( h @ ( sK3 @ X3 @ X2 ) @ X4 )
| ~ ( bomb @ X3 @ X4 ) ) )
= $true )
| ( $true
= ( ~ ( rel_s4 @ X2 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f219]) ).
thf(f221,plain,
! [X2: $i,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( ~ ( rel_s4 @ X2 @ X4 ) ) )
| ( $true
= ( defused @ X3 @ X4 ) )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ~ ( ~ ( h @ ( sK3 @ X3 @ X2 ) @ X4 )
| ~ ( bomb @ X3 @ X4 ) ) ) ) ),
inference(or_proxy_clausification,[],[f220]) ).
thf(f222,plain,
! [X2: $i,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( defused @ X3 @ X4 ) )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $true
= ( ~ ~ ( ~ ( h @ ( sK3 @ X3 @ X2 ) @ X4 )
| ~ ( bomb @ X3 @ X4 ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f221]) ).
thf(f223,plain,
! [X2: $i,X3: mu,X1: $i,X4: $i] :
( ( $true
= ( defused @ X3 @ X4 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( ( ~ ( ~ ( h @ ( sK3 @ X3 @ X2 ) @ X4 )
| ~ ( bomb @ X3 @ X4 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f222]) ).
thf(f224,plain,
! [X2: $i,X3: mu,X1: $i,X4: $i] :
( ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( h @ ( sK3 @ X3 @ X2 ) @ X4 )
| ~ ( bomb @ X3 @ X4 ) ) )
| ( $true
= ( defused @ X3 @ X4 ) )
| ( ( exists_in_world @ X3 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f223]) ).
thf(f225,plain,
! [X2: $i,X3: mu,X1: $i,X4: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( defused @ X3 @ X4 ) )
| ( $true
= ( ~ ( h @ ( sK3 @ X3 @ X2 ) @ X4 ) ) )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( $true
= ( ~ ( bomb @ X3 @ X4 ) ) ) ),
inference(or_proxy_clausification,[],[f224]) ).
thf(f226,plain,
! [X2: $i,X3: mu,X1: $i,X4: $i] :
( ( ( h @ ( sK3 @ X3 @ X2 ) @ X4 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( defused @ X3 @ X4 ) )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( $true
= ( ~ ( bomb @ X3 @ X4 ) ) )
| ( $false
= ( rel_s4 @ X2 @ X4 ) ) ),
inference(not_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X2: $i,X3: mu,X1: $i,X4: $i] :
( ( ( h @ ( sK3 @ X3 @ X2 ) @ X4 )
= $false )
| ( ( exists_in_world @ X3 @ X2 )
= $false )
| ( $true
= ( defused @ X3 @ X4 ) )
| ( $false
= ( rel_s4 @ X2 @ X4 ) )
| ( $false
= ( bomb @ X3 @ X4 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f226]) ).
thf(f228,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f229,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X1: $i] :
( $true
= ( rel_s4 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f229]) ).
thf(f253,plain,
( ( $false
= ( ^ [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] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: mu > $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: mu > $i > $o,Y3: $i] :
( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( Y2 @ Y4 @ Y3 ) ) )
@ ^ [Y2: mu] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( Y1 @ Y2 ) ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( bomb @ Y0 )
@ ( h @ Y1 ) )
@ ( defused @ Y0 ) ) ) ) ) ) )
| ( $true = sF1 ) ),
inference(iff_proxy_clausification,[],[f174]) ).
thf(f277,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y1 )
=> ~ ( ( defused @ Y2 @ Y1 )
| ~ ~ ( ~ ( h @ Y3 @ Y1 )
| ~ ( bomb @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) )
= $false )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f253]) ).
thf(f278,plain,
( ( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y1 )
=> ~ ( ( defused @ Y2 @ Y1 )
| ~ ~ ( ~ ( h @ Y3 @ Y1 )
| ~ ( bomb @ Y2 @ Y1 ) ) ) ) ) ) ) ) )
@ sK6 )
= $false )
| ( $true = sF1 ) ),
inference(sigma_proxy_clausification,[],[f277]) ).
thf(f279,plain,
( ( $true = sF1 )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK6 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ~ ( ( defused @ Y1 @ Y0 )
| ~ ~ ( ~ ( h @ Y2 @ Y0 )
| ~ ( bomb @ Y1 @ Y0 ) ) ) ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f278]) ).
thf(f280,plain,
( ( $true = sF1 )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK6 @ Y0 )
| ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ~ ( ( defused @ Y1 @ Y0 )
| ~ ~ ( ~ ( h @ Y2 @ Y0 )
| ~ ( bomb @ Y1 @ Y0 ) ) ) ) ) ) ) )
@ sK7 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f279]) ).
thf(f281,plain,
( ( $true = sF1 )
| ( $false
= ( ~ ( rel_s4 @ sK6 @ sK7 )
| ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK7 )
=> ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK7 )
=> ~ ( ( defused @ Y0 @ sK7 )
| ~ ~ ( ~ ( h @ Y1 @ sK7 )
| ~ ( bomb @ Y0 @ sK7 ) ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f280]) ).
thf(f282,plain,
( ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK7 )
=> ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK7 )
=> ~ ( ( defused @ Y0 @ sK7 )
| ~ ~ ( ~ ( h @ Y1 @ sK7 )
| ~ ( bomb @ Y0 @ sK7 ) ) ) ) ) ) ) )
| ( $true = sF1 ) ),
inference(or_proxy_clausification,[],[f281]) ).
thf(f285,plain,
( ( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK7 )
=> ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK7 )
=> ~ ( ( defused @ Y0 @ sK7 )
| ~ ~ ( ~ ( h @ Y1 @ sK7 )
| ~ ( bomb @ Y0 @ sK7 ) ) ) ) ) )
@ sK8 ) )
| ( $true = sF1 ) ),
inference(sigma_proxy_clausification,[],[f282]) ).
thf(f286,plain,
( ( $false
= ( ( exists_in_world @ sK8 @ sK7 )
=> ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK7 )
=> ~ ( ( defused @ sK8 @ sK7 )
| ~ ~ ( ~ ( h @ Y0 @ sK7 )
| ~ ( bomb @ sK8 @ sK7 ) ) ) ) ) ) )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f285]) ).
thf(f287,plain,
( ( $true = sF1 )
| ( ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK7 )
=> ~ ( ( defused @ sK8 @ sK7 )
| ~ ~ ( ~ ( h @ Y0 @ sK7 )
| ~ ( bomb @ sK8 @ sK7 ) ) ) ) ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f286]) ).
thf(f288,plain,
( ( $true = sF1 )
| ( $true
= ( exists_in_world @ sK8 @ sK7 ) ) ),
inference(imp_proxy_clausification,[],[f286]) ).
thf(f289,plain,
( ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK7 )
=> ~ ( ( defused @ sK8 @ sK7 )
| ~ ~ ( ~ ( h @ Y0 @ sK7 )
| ~ ( bomb @ sK8 @ sK7 ) ) ) ) ) )
| ( $true = sF1 ) ),
inference(not_proxy_clausification,[],[f287]) ).
thf(f290,plain,
! [X1: mu] :
( ( $true = sF1 )
| ( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK7 )
=> ~ ( ( defused @ sK8 @ sK7 )
| ~ ~ ( ~ ( h @ Y0 @ sK7 )
| ~ ( bomb @ sK8 @ sK7 ) ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f289]) ).
thf(f291,plain,
! [X1: mu] :
( ( $true = sF1 )
| ( $true
= ( ( exists_in_world @ X1 @ sK7 )
=> ~ ( ( defused @ sK8 @ sK7 )
| ~ ~ ( ~ ( h @ X1 @ sK7 )
| ~ ( bomb @ sK8 @ sK7 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f290]) ).
thf(f292,plain,
! [X1: mu] :
( ( $true = sF1 )
| ( $true
= ( ~ ( ( defused @ sK8 @ sK7 )
| ~ ~ ( ~ ( h @ X1 @ sK7 )
| ~ ( bomb @ sK8 @ sK7 ) ) ) ) )
| ( ( exists_in_world @ X1 @ sK7 )
= $false ) ),
inference(imp_proxy_clausification,[],[f291]) ).
thf(f293,plain,
! [X1: mu] :
( ( ( exists_in_world @ X1 @ sK7 )
= $false )
| ( $true = sF1 )
| ( ( ( defused @ sK8 @ sK7 )
| ~ ~ ( ~ ( h @ X1 @ sK7 )
| ~ ( bomb @ sK8 @ sK7 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f292]) ).
thf(f294,plain,
! [X1: mu] :
( ( $true = sF1 )
| ( ( ~ ~ ( ~ ( h @ X1 @ sK7 )
| ~ ( bomb @ sK8 @ sK7 ) ) )
= $false )
| ( ( exists_in_world @ X1 @ sK7 )
= $false ) ),
inference(or_proxy_clausification,[],[f293]) ).
thf(f295,plain,
! [X1: mu] :
( ( ( exists_in_world @ X1 @ sK7 )
= $false )
| ( ( defused @ sK8 @ sK7 )
= $false )
| ( $true = sF1 ) ),
inference(or_proxy_clausification,[],[f293]) ).
thf(f296,plain,
! [X1: mu] :
( ( $true
= ( ~ ( ~ ( h @ X1 @ sK7 )
| ~ ( bomb @ sK8 @ sK7 ) ) ) )
| ( $true = sF1 )
| ( ( exists_in_world @ X1 @ sK7 )
= $false ) ),
inference(not_proxy_clausification,[],[f294]) ).
thf(f297,plain,
! [X1: mu] :
( ( $false
= ( ~ ( h @ X1 @ sK7 )
| ~ ( bomb @ sK8 @ sK7 ) ) )
| ( ( exists_in_world @ X1 @ sK7 )
= $false )
| ( $true = sF1 ) ),
inference(not_proxy_clausification,[],[f296]) ).
thf(f298,plain,
! [X1: mu] :
( ( $true = sF1 )
| ( ( exists_in_world @ X1 @ sK7 )
= $false )
| ( ( ~ ( bomb @ sK8 @ sK7 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f297]) ).
thf(f299,plain,
! [X1: mu] :
( ( $false
= ( ~ ( h @ X1 @ sK7 ) ) )
| ( ( exists_in_world @ X1 @ sK7 )
= $false )
| ( $true = sF1 ) ),
inference(or_proxy_clausification,[],[f297]) ).
thf(f300,plain,
! [X1: mu] :
( ( $true = sF1 )
| ( ( exists_in_world @ X1 @ sK7 )
= $false )
| ( $true
= ( h @ X1 @ sK7 ) ) ),
inference(not_proxy_clausification,[],[f299]) ).
thf(f301,plain,
! [X1: mu] :
( ( ( exists_in_world @ X1 @ sK7 )
= $false )
| ( $true = sF1 )
| ( ( bomb @ sK8 @ sK7 )
= $true ) ),
inference(not_proxy_clausification,[],[f298]) ).
thf(f315,definition,
( spl9_4
<=> ( $true = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl9_4])],[avatar_definition]) ).
thf(f324,definition,
( spl9_6
<=> ( $true
= ( exists_in_world @ sK8 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_6])],[avatar_definition]) ).
thf(f326,plain,
( ( $true
= ( exists_in_world @ sK8 @ sK7 ) )
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f324]) ).
thf(f327,plain,
( spl9_4
| spl9_6 ),
inference(avatar_split_clause,[],[f288,f324,f315]) ).
thf(f329,definition,
( spl9_7
<=> ( ( defused @ sK8 @ sK7 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl9_7])],[avatar_definition]) ).
thf(f331,plain,
( ( ( defused @ sK8 @ sK7 )
= $false )
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f329]) ).
thf(f333,definition,
( spl9_8
<=> ! [X1: mu] :
( ( exists_in_world @ X1 @ sK7 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl9_8])],[avatar_definition]) ).
thf(f334,plain,
( ! [X1: mu] :
( ( exists_in_world @ X1 @ sK7 )
= $false )
| ~ spl9_8 ),
inference(avatar_component_clause,[],[f333]) ).
thf(f335,plain,
( spl9_4
| spl9_7
| spl9_8 ),
inference(avatar_split_clause,[],[f295,f333,f329,f315]) ).
thf(f337,definition,
( spl9_9
<=> ! [X1: mu] :
( ( ( exists_in_world @ X1 @ sK7 )
= $false )
| ( $true
= ( h @ X1 @ sK7 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl9_9])],[avatar_definition]) ).
thf(f338,plain,
( ! [X1: mu] :
( ( $true
= ( h @ X1 @ sK7 ) )
| ( ( exists_in_world @ X1 @ sK7 )
= $false ) )
| ~ spl9_9 ),
inference(avatar_component_clause,[],[f337]) ).
thf(f339,plain,
( spl9_9
| spl9_4 ),
inference(avatar_split_clause,[],[f300,f315,f337]) ).
thf(f341,definition,
( spl9_10
<=> ( ( bomb @ sK8 @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl9_10])],[avatar_definition]) ).
thf(f343,plain,
( ( ( bomb @ sK8 @ sK7 )
= $true )
| ~ spl9_10 ),
inference(avatar_component_clause,[],[f341]) ).
thf(f344,plain,
( spl9_8
| spl9_10
| spl9_4 ),
inference(avatar_split_clause,[],[f301,f315,f341,f333]) ).
thf(f345,plain,
~ spl9_4,
inference(avatar_split_clause,[],[f175,f315]) ).
thf(f361,plain,
( ( $true = $false )
| ~ spl9_6
| ~ spl9_8 ),
inference(constrained_superposition,[],[f326,f334]) ).
thf(f365,plain,
( $false
| ~ spl9_6
| ~ spl9_8 ),
inference(trivial_inequality_removal,[],[f361]) ).
thf(f366,plain,
( ~ spl9_6
| ~ spl9_8 ),
inference(avatar_contradiction_clause,[],[f365]) ).
thf(f426,definition,
( spl9_13
<=> ! [X1: $i] :
( $false
= ( rel_s4 @ X1 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl9_13])],[avatar_definition]) ).
thf(f427,plain,
( ! [X1: $i] :
( $false
= ( rel_s4 @ X1 @ sK7 ) )
| ~ spl9_13 ),
inference(avatar_component_clause,[],[f426]) ).
thf(f443,plain,
( ! [X2: $i,X0: mu,X1: $i] :
( ( ( rel_s4 @ X2 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ X1 @ sK7 ) )
| ( ( exists_in_world @ ( sK3 @ X0 @ X1 ) @ sK7 )
= $false )
| ( $true = $false )
| ( $true
= ( defused @ X0 @ sK7 ) )
| ( $false
= ( bomb @ X0 @ sK7 ) )
| ( ( exists_in_world @ X0 @ X1 )
= $false ) )
| ~ spl9_9 ),
inference(constrained_superposition,[],[f338,f227]) ).
thf(f445,plain,
( ! [X2: $i,X0: mu,X1: $i] :
( ( ( exists_in_world @ ( sK3 @ X0 @ X1 ) @ sK7 )
= $false )
| ( $false
= ( bomb @ X0 @ sK7 ) )
| ( ( rel_s4 @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X0 @ X1 )
= $false )
| ( $true
= ( defused @ X0 @ sK7 ) )
| ( $false
= ( rel_s4 @ X1 @ sK7 ) ) )
| ~ spl9_9 ),
inference(trivial_inequality_removal,[],[f443]) ).
thf(f447,plain,
( ! [X2: $i,X0: mu,X1: $i] :
( ( $true
= ( defused @ X0 @ sK7 ) )
| ( $false
= ( bomb @ X0 @ sK7 ) )
| ( ( rel_s4 @ X2 @ sK7 )
= $false )
| ( $false
= ( rel_s4 @ sK7 @ sK7 ) )
| ( $true = $false )
| ( $false
= ( exists_in_world @ X0 @ sK7 ) )
| ( $false
= ( exists_in_world @ X0 @ sK7 ) )
| ( $false
= ( rel_s4 @ X1 @ sK7 ) ) )
| ~ spl9_9 ),
inference(constrained_superposition,[],[f445,f216]) ).
thf(f454,plain,
( ! [X2: $i,X0: mu,X1: $i] :
( ( $false
= ( rel_s4 @ X1 @ sK7 ) )
| ( $false
= ( bomb @ X0 @ sK7 ) )
| ( $false
= ( rel_s4 @ sK7 @ sK7 ) )
| ( $false
= ( exists_in_world @ X0 @ sK7 ) )
| ( $true
= ( defused @ X0 @ sK7 ) )
| ( $true = $false )
| ( ( rel_s4 @ X2 @ sK7 )
= $false ) )
| ~ spl9_9 ),
inference(duplicate_literal_removal,[],[f447]) ).
thf(f455,plain,
( ! [X2: $i,X0: mu,X1: $i] :
( ( $false
= ( exists_in_world @ X0 @ sK7 ) )
| ( ( rel_s4 @ X2 @ sK7 )
= $false )
| ( $false
= ( rel_s4 @ sK7 @ sK7 ) )
| ( $false
= ( bomb @ X0 @ sK7 ) )
| ( $false
= ( rel_s4 @ X1 @ sK7 ) )
| ( $true
= ( defused @ X0 @ sK7 ) ) )
| ~ spl9_9 ),
inference(trivial_inequality_removal,[],[f454]) ).
thf(f461,plain,
( ! [X2: $i,X0: mu,X1: $i] :
( ( $false
= ( rel_s4 @ X1 @ sK7 ) )
| ( $true
= ( defused @ X0 @ sK7 ) )
| ( ( rel_s4 @ X2 @ sK7 )
= $false )
| ( $true = $false )
| ( $false
= ( exists_in_world @ X0 @ sK7 ) )
| ( $false
= ( bomb @ X0 @ sK7 ) ) )
| ~ spl9_9 ),
inference(forward_demodulation,[],[f455,f230]) ).
thf(f462,plain,
( ! [X2: $i,X0: mu,X1: $i] :
( ( $false
= ( bomb @ X0 @ sK7 ) )
| ( $true
= ( defused @ X0 @ sK7 ) )
| ( ( rel_s4 @ X2 @ sK7 )
= $false )
| ( $false
= ( exists_in_world @ X0 @ sK7 ) )
| ( $false
= ( rel_s4 @ X1 @ sK7 ) ) )
| ~ spl9_9 ),
inference(trivial_inequality_removal,[],[f461]) ).
thf(f464,definition,
( spl9_15
<=> ! [X0: mu] :
( ( $false
= ( exists_in_world @ X0 @ sK7 ) )
| ( $false
= ( bomb @ X0 @ sK7 ) )
| ( $true
= ( defused @ X0 @ sK7 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl9_15])],[avatar_definition]) ).
thf(f465,plain,
( ! [X0: mu] :
( ( $true
= ( defused @ X0 @ sK7 ) )
| ( $false
= ( bomb @ X0 @ sK7 ) )
| ( $false
= ( exists_in_world @ X0 @ sK7 ) ) )
| ~ spl9_15 ),
inference(avatar_component_clause,[],[f464]) ).
thf(f467,plain,
( spl9_15
| spl9_13
| spl9_13
| ~ spl9_9 ),
inference(avatar_split_clause,[],[f462,f337,f426,f426,f464]) ).
thf(f481,plain,
( ( $true = $false )
| ~ spl9_13 ),
inference(constrained_superposition,[],[f230,f427]) ).
thf(f489,plain,
( $false
| ~ spl9_13 ),
inference(trivial_inequality_removal,[],[f481]) ).
thf(f490,plain,
~ spl9_13,
inference(avatar_contradiction_clause,[],[f489]) ).
thf(f503,plain,
( ( ( bomb @ sK8 @ sK7 )
= $false )
| ( $false
= ( exists_in_world @ sK8 @ sK7 ) )
| ( $true = $false )
| ~ spl9_7
| ~ spl9_15 ),
inference(constrained_superposition,[],[f331,f465]) ).
thf(f505,plain,
( ( $false
= ( exists_in_world @ sK8 @ sK7 ) )
| ( ( bomb @ sK8 @ sK7 )
= $false )
| ~ spl9_7
| ~ spl9_15 ),
inference(trivial_inequality_removal,[],[f503]) ).
thf(f508,plain,
( ( $true = $false )
| ( ( bomb @ sK8 @ sK7 )
= $false )
| ~ spl9_6
| ~ spl9_7
| ~ spl9_15 ),
inference(forward_demodulation,[],[f505,f326]) ).
thf(f509,plain,
( ( ( bomb @ sK8 @ sK7 )
= $false )
| ~ spl9_6
| ~ spl9_7
| ~ spl9_15 ),
inference(trivial_inequality_removal,[],[f508]) ).
thf(f513,plain,
( ( $true = $false )
| ~ spl9_6
| ~ spl9_7
| ~ spl9_10
| ~ spl9_15 ),
inference(forward_demodulation,[],[f509,f343]) ).
thf(f514,plain,
( $false
| ~ spl9_6
| ~ spl9_7
| ~ spl9_10
| ~ spl9_15 ),
inference(trivial_inequality_removal,[],[f513]) ).
thf(f515,plain,
( ~ spl9_6
| ~ spl9_7
| ~ spl9_10
| ~ spl9_15 ),
inference(avatar_contradiction_clause,[],[f514]) ).
cnf(s4,plain,
( spl9_4
| spl9_6 ),
inference(sat_conversion,[],[f327]) ).
cnf(s5,plain,
( spl9_4
| spl9_7
| spl9_8 ),
inference(sat_conversion,[],[f335]) ).
cnf(s6,plain,
( spl9_4
| spl9_9 ),
inference(sat_conversion,[],[f339]) ).
cnf(s7,plain,
( spl9_4
| spl9_8
| spl9_10 ),
inference(sat_conversion,[],[f344]) ).
cnf(s8,plain,
~ spl9_4,
inference(sat_conversion,[],[f345]) ).
cnf(s11,plain,
( ~ spl9_6
| ~ spl9_8 ),
inference(sat_conversion,[],[f366]) ).
cnf(s18,plain,
( spl9_13
| ~ spl9_9
| spl9_13
| spl9_15 ),
inference(sat_conversion,[],[f467]) ).
cnf(s19,plain,
( ~ spl9_9
| spl9_13
| spl9_15 ),
inference(rat,[],[s18]) ).
cnf(s21,plain,
~ spl9_13,
inference(sat_conversion,[],[f490]) ).
cnf(s25,plain,
( ~ spl9_6
| ~ spl9_7
| ~ spl9_10
| ~ spl9_15 ),
inference(sat_conversion,[],[f515]) ).
cnf(s26,plain,
( ~ spl9_9
| spl9_15 ),
inference(rat,[],[s19,s21]) ).
cnf(s31,plain,
( spl9_8
| spl9_10 ),
inference(rat,[],[s7,s8]) ).
cnf(s32,plain,
spl9_9,
inference(rat,[],[s6,s8]) ).
cnf(s33,plain,
spl9_15,
inference(rat,[],[s26,s32]) ).
cnf(s34,plain,
( spl9_7
| spl9_8 ),
inference(rat,[],[s5,s8]) ).
cnf(s35,plain,
spl9_6,
inference(rat,[],[s4,s8]) ).
cnf(s36,plain,
~ spl9_8,
inference(rat,[],[s11,s35]) ).
cnf(s37,plain,
spl9_10,
inference(rat,[],[s31,s36]) ).
cnf(s38,plain,
spl9_7,
inference(rat,[],[s34,s36]) ).
cnf(s39,plain,
$false,
inference(rat,[],[s25,s33,s35,s37,s38]) ).
thf(f516,plain,
$false,
inference(avatar_sat_refutation,[],[s39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PLA032^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n016.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 13:25:19 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 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
% 0.22/0.36 % (332380)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.36 % (332391)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.36 % (332391)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
% 0.22/0.36 % (332388)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=3180265380: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)
% 0.22/0.36 % (332385)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2240384084:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.36 % (332389)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2314685873:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.36 % (332391)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=3539999279:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.36 % (332390)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3245318162:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.36 % (332389)Instruction limit reached!
% 0.22/0.36 % (332389)------------------------------
% 0.22/0.36 % (332389)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (332389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (332389)CaDiCaL version: 2.1.3
% 0.22/0.36 % (332389)Termination reason: Instruction limit
% 0.22/0.36 % (332389)Termination phase: Saturation
% 0.22/0.36 % (332389)Time elapsed: 0.014 s
% 0.22/0.36 % (332389)Peak memory usage: 12 MB
% 0.22/0.36 % (332389)Instructions burned: 24 (million)
% 0.22/0.36 % (332387)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1167473158:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.36 % (332387)Instruction limit reached!
% 0.22/0.36 % (332387)------------------------------
% 0.22/0.36 % (332387)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (332387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (332387)CaDiCaL version: 2.1.3
% 0.22/0.36 % (332387)Termination reason: Instruction limit
% 0.22/0.36 % (332387)Termination phase: Property scanning
% 0.22/0.36 % (332387)Time elapsed: 0.002 s
% 0.22/0.36 % (332387)Peak memory usage: 10 MB
% 0.22/0.36 % (332387)Instructions burned: 4 (million)
% 0.22/0.36 % (332386)lrs+10_16_si=on:nwc=1.5:random_seed=1757114604:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.36 % (332391) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-332380-332391"...
% 0.22/0.36 % (332386)Instruction limit reached!
% 0.22/0.36 % (332386)------------------------------
% 0.22/0.36 % (332386)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (332386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (332386)CaDiCaL version: 2.1.3
% 0.22/0.36 % (332386)Termination reason: Instruction limit
% 0.22/0.36 % (332386)Termination phase: Saturation
% 0.22/0.36 % (332386)Time elapsed: 0.015 s
% 0.22/0.36 % (332386)Peak memory usage: 11 MB
% 0.22/0.36 % (332386)Instructions burned: 18 (million)
% 0.22/0.36 % (332400)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1304993319:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.36 % (332391)...printing done.
% 0.22/0.36 % (332400)Instruction limit reached!
% 0.22/0.36 % (332400)------------------------------
% 0.22/0.36 % (332400)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (332400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (332400)CaDiCaL version: 2.1.3
% 0.22/0.36 % (332400)Termination reason: Instruction limit
% 0.22/0.36 % (332400)Termination phase: Property scanning
% 0.22/0.36 % (332400)Time elapsed: 0.006 s
% 0.22/0.36 % (332400)Peak memory usage: 10 MB
% 0.22/0.36 % (332400)Instructions burned: 6 (million)
% 0.22/0.36 % (332391)Refutation found. Thanks to Tanya!
% 0.22/0.36 % SZS status Theorem for theBenchmark
% 0.22/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.36 % (332391)------------------------------
% 0.22/0.36 % (332391)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.36 % (332391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.36 % (332391)CaDiCaL version: 2.1.3
% 0.22/0.36 % (332391)Termination reason: Refutation
% 0.22/0.36 % (332391)Time elapsed: 0.045 s
% 0.22/0.36 % (332391)Peak memory usage: 13 MB
% 0.22/0.36 % (332391)Instructions burned: 49 (million)
% 0.22/0.36 % (332380)Success in time 0.108 s
% 0.22/0.36 % Vampire exiting
%------------------------------------------------------------------------------