%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET576^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:23:17 AM UTC 2026
% Result : Theorem 0.35s 0.46s
% Output : Refutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 20
% Syntax : Number of formulae : 199 ( 73 unt; 0 typ; 8 def)
% Number of atoms : 1831 ( 339 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 3268 ( 472 ~; 433 |; 0 &;2140 @)
% ( 7 <=>; 113 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 213 ( 213 >; 0 *; 0 +; 0 <<)
% Number of symbols : 71 ( 67 usr; 14 con; 0-4 aty)
% ( 103 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 595 ( 0 sgn 139 !; 0 ?; 595 :)
% 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,
intersect: mu > mu > $i > $o ).
thf(func_def_37,type,
disjoint: mu > mu > $i > $o ).
thf(func_def_38,type,
member: mu > mu > $i > $o ).
thf(func_def_39,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_40,type,
vNOT: $o > $o ).
thf(func_def_41,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_44,type,
vIMP: $o > $o > $o ).
thf(func_def_45,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
vOR: $o > $o > $o ).
thf(func_def_50,type,
vAND: $o > $o > $o ).
thf(func_def_51,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_54,type,
sK0: $i > mu ).
thf(func_def_55,type,
sF1: $o ).
thf(func_def_56,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_57,type,
sK2: mu > $i > mu > mu ).
thf(func_def_58,type,
sK3: mu > $i > mu > mu ).
thf(func_def_60,type,
sK5: mu ).
thf(func_def_61,type,
sK6: mu ).
thf(f2,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL015^0.ax',mor) ).
thf(f8,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) )
= mand ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mand) ).
thf(f9,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mimplies) ).
thf(f11,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) )
= mequiv ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mequiv) ).
thf(f15,axiom,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_ind ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mforall_ind) ).
thf(f16,axiom,
( ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) )
= mexists_ind ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mexists_ind) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mvalid) ).
thf(f37,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] :
( mequiv @ ( intersect @ X0 @ X1 )
@ ( mexists_ind
@ ^ [X2: mu] : ( mand @ ( member @ X2 @ X0 ) @ ( member @ X2 @ X1 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
thf(f38,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mequiv @ ( disjoint @ X0 @ X1 ) @ ( mnot @ ( intersect @ X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).
thf(f39,axiom,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( intersect @ X0 @ X1 ) @ ( intersect @ X1 @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_intersect) ).
thf(f40,conjecture,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] :
( mimplies
@ ( mforall_ind
@ ^ [X2: mu] : ( mimplies @ ( member @ X2 @ X0 ) @ ( mnot @ ( member @ X2 @ X1 ) ) ) )
@ ( disjoint @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th17) ).
thf(f41,negated_conjecture,
~ ( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] :
( mimplies
@ ( mforall_ind
@ ^ [X2: mu] : ( mimplies @ ( member @ X2 @ X0 ) @ ( mnot @ ( member @ X2 @ X1 ) ) ) )
@ ( disjoint @ X0 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
thf(f44,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f45,plain,
( ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_ind ),
inference(rectify,[],[f15]) ).
thf(f46,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f45]) ).
thf(f47,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mequiv @ ( disjoint @ X0 @ X1 ) @ ( mnot @ ( intersect @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f48,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mequiv @ ( disjoint @ Y0 @ Y1 ) @ ( mnot @ ( intersect @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f47]) ).
thf(f54,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f3]) ).
thf(f55,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f56,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f59,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mimplies @ ( intersect @ X0 @ X1 ) @ ( intersect @ X1 @ X0 ) ) ) ) ),
inference(rectify,[],[f39]) ).
thf(f60,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mimplies @ ( intersect @ Y0 @ Y1 ) @ ( intersect @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f59]) ).
thf(f65,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f66,plain,
~ ( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] :
( mimplies
@ ( mforall_ind
@ ^ [X2: mu] : ( mimplies @ ( member @ X2 @ X0 ) @ ( mnot @ ( member @ X2 @ X1 ) ) ) )
@ ( disjoint @ X0 @ X1 ) ) ) ) ),
inference(rectify,[],[f41]) ).
thf(f67,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] :
( mimplies
@ ( mforall_ind
@ ^ [Y2: mu] : ( mimplies @ ( member @ Y2 @ Y0 ) @ ( mnot @ ( member @ Y2 @ Y1 ) ) ) )
@ ( disjoint @ Y0 @ Y1 ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f66]) ).
thf(f81,plain,
( ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) )
= mexists_ind ),
inference(rectify,[],[f16]) ).
thf(f82,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f83,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f84,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f94,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f2]) ).
thf(f95,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f94]) ).
thf(f96,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] :
( mequiv @ ( intersect @ X0 @ X1 )
@ ( mexists_ind
@ ^ [X2: mu] : ( mand @ ( member @ X2 @ X0 ) @ ( member @ X2 @ X1 ) ) ) ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f97,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] :
( mequiv @ ( intersect @ Y0 @ Y1 )
@ ( mexists_ind
@ ^ [Y2: mu] : ( mand @ ( member @ Y2 @ Y0 ) @ ( member @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f96]) ).
thf(f111,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] :
( mimplies
@ ( mforall_ind
@ ^ [Y2: mu] : ( mimplies @ ( member @ Y2 @ Y0 ) @ ( mnot @ ( member @ Y2 @ Y1 ) ) ) )
@ ( disjoint @ Y0 @ Y1 ) ) ) ) )
!= $true ),
inference(flattening,[],[f67]) ).
thf(f117,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f95]) ).
thf(f118,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f120,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] :
( mequiv @ ( intersect @ Y0 @ Y1 )
@ ( mexists_ind
@ ^ [Y2: mu] : ( mand @ ( member @ Y2 @ Y0 ) @ ( member @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f97]) ).
thf(f121,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mequiv @ ( disjoint @ Y0 @ Y1 ) @ ( mnot @ ( intersect @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f48]) ).
thf(f129,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f132,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f134,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mimplies @ ( intersect @ Y0 @ Y1 ) @ ( intersect @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f60]) ).
thf(f135,plain,
( ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] :
( mimplies
@ ( mforall_ind
@ ^ [Y2: mu] : ( mimplies @ ( member @ Y2 @ Y0 ) @ ( mnot @ ( member @ Y2 @ Y1 ) ) ) )
@ ( disjoint @ Y0 @ Y1 ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f111]) ).
thf(f145,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f65]) ).
thf(f147,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f152,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f154,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f82]) ).
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] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f129,f117,f152,f117,f117]) ).
thf(f160,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f145,f152,f117]) ).
thf(f162,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f147,f159,f160,f160]) ).
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,[],[f154,f117,f132,f117]) ).
thf(f168,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ ( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y5 ) ) )
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ Y2
@ Y3 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ Y3
@ Y2 ) )
@ ( intersect @ Y0 @ Y1 )
@ ( ^ [Y2: mu > $i > $o] :
( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( ^ [Y3: mu > $i > $o,Y4: $i] :
( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y4 )
=> ( Y3 @ Y5 @ Y4 ) ) )
@ ^ [Y3: mu] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( Y2 @ Y3 ) ) ) )
@ ^ [Y2: mu] :
( ^ [Y3: $i > $o,Y4: $i > $o] :
( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ ( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y4 ) ) )
@ ( member @ Y2 @ Y0 )
@ ( member @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f120,f118,f132,f132,f162,f165,f159]) ).
thf(f169,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ ( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y5 ) ) )
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ Y2
@ Y3 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o] :
( ^ [Y6: $i > $o,Y7: $i > $o,Y8: $i] :
( ( Y6 @ Y8 )
| ( Y7 @ Y8 ) )
@ ( ^ [Y6: $i > $o,Y7: $i] :
~ ( Y6 @ Y7 )
@ Y4 )
@ Y5 )
@ Y3
@ Y2 ) )
@ ( disjoint @ Y0 @ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( intersect @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f121,f118,f132,f132,f162,f117]) ).
thf(f170,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ ( intersect @ Y0 @ Y1 )
@ ( intersect @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f134,f118,f132,f132,f160]) ).
thf(f171,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ 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 > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ Y4 )
@ ( member @ Y2 @ Y0 )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( member @ Y2 @ Y1 ) ) ) )
@ ( disjoint @ Y0 @ Y1 ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f135,f118,f132,f132,f160,f132,f160,f117]) ).
thf(f174,definition,
( sF1
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ 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 > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ Y4 )
@ ( member @ Y2 @ Y0 )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( member @ Y2 @ Y1 ) ) ) )
@ ( disjoint @ Y0 @ Y1 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f175,plain,
sF1 != $true,
inference(definition_folding,[],[f171,f174]) ).
thf(f179,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( ~ ( intersect @ Y1 @ Y2 @ Y0 )
| ( intersect @ Y2 @ Y1 @ Y0 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f180,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( ~ ( intersect @ Y1 @ Y2 @ Y0 )
| ( intersect @ Y2 @ Y1 @ Y0 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X1: $i] :
( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ( ~ ( intersect @ Y0 @ Y1 @ X1 )
| ( intersect @ Y1 @ Y0 @ X1 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f182,plain,
! [X2: mu,X1: $i] :
( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ( ~ ( intersect @ Y0 @ Y1 @ X1 )
| ( intersect @ Y1 @ Y0 @ X1 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X2: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( intersect @ X2 @ Y0 @ X1 )
| ( intersect @ Y0 @ X2 @ X1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f184,plain,
! [X2: mu,X1: $i] :
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( intersect @ X2 @ Y0 @ X1 )
| ( intersect @ Y0 @ X2 @ X1 ) ) ) )
= $true )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( ~ ( intersect @ X2 @ Y0 @ X1 )
| ( intersect @ Y0 @ X2 @ X1 ) ) )
@ X3 )
= $true )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( ( exists_in_world @ X3 @ X1 )
=> ( ~ ( intersect @ X2 @ X3 @ X1 )
| ( intersect @ X3 @ X2 @ X1 ) ) )
= $true )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f187,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( ~ ( intersect @ X2 @ X3 @ X1 )
| ( intersect @ X3 @ X2 @ X1 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( ~ ( intersect @ X2 @ X3 @ X1 ) )
= $true )
| ( ( intersect @ X3 @ X2 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( intersect @ X3 @ X2 @ X1 )
= $true )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( intersect @ X2 @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f188]) ).
thf(f199,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ~ ( ~ ( ~ ( intersect @ Y1 @ Y2 @ Y0 )
| ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ~ ~ ( ~ ( member @ Y3 @ Y1 @ Y0 )
| ~ ( member @ Y3 @ Y2 @ Y0 ) ) ) ) )
| ~ ( ~ ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ~ ~ ( ~ ( member @ Y3 @ Y1 @ Y0 )
| ~ ( member @ Y3 @ Y2 @ Y0 ) ) ) )
| ( intersect @ Y1 @ Y2 @ Y0 ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f168]) ).
thf(f200,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ~ ( ~ ( ~ ( intersect @ Y1 @ Y2 @ Y0 )
| ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ~ ~ ( ~ ( member @ Y3 @ Y1 @ Y0 )
| ~ ( member @ Y3 @ Y2 @ Y0 ) ) ) ) )
| ~ ( ~ ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ~ ~ ( ~ ( member @ Y3 @ Y1 @ Y0 )
| ~ ( member @ Y3 @ Y2 @ Y0 ) ) ) )
| ( intersect @ Y1 @ Y2 @ Y0 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X1: $i] :
( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ( ~ ( ~ ( intersect @ Y0 @ Y1 @ X1 )
| ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X1 )
=> ~ ~ ( ~ ( member @ Y2 @ Y0 @ X1 )
| ~ ( member @ Y2 @ Y1 @ X1 ) ) ) ) )
| ~ ( ~ ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X1 )
=> ~ ~ ( ~ ( member @ Y2 @ Y0 @ X1 )
| ~ ( member @ Y2 @ Y1 @ X1 ) ) ) )
| ( intersect @ Y0 @ Y1 @ X1 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f200]) ).
thf(f202,plain,
! [X2: mu,X1: $i] :
( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ( ~ ( ~ ( intersect @ Y0 @ Y1 @ X1 )
| ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X1 )
=> ~ ~ ( ~ ( member @ Y2 @ Y0 @ X1 )
| ~ ( member @ Y2 @ Y1 @ X1 ) ) ) ) )
| ~ ( ~ ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ X1 )
=> ~ ~ ( ~ ( member @ Y2 @ Y0 @ X1 )
| ~ ( member @ Y2 @ Y1 @ X1 ) ) ) )
| ( intersect @ Y0 @ Y1 @ X1 ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f201]) ).
thf(f203,plain,
! [X2: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ~ ( intersect @ X2 @ Y0 @ X1 )
| ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ~ ( ~ ( member @ Y1 @ X2 @ X1 )
| ~ ( member @ Y1 @ Y0 @ X1 ) ) ) ) )
| ~ ( ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ~ ( ~ ( member @ Y1 @ X2 @ X1 )
| ~ ( member @ Y1 @ Y0 @ X1 ) ) ) )
| ( intersect @ X2 @ Y0 @ X1 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f202]) ).
thf(f204,plain,
! [X2: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ~ ( intersect @ X2 @ Y0 @ X1 )
| ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ~ ( ~ ( member @ Y1 @ X2 @ X1 )
| ~ ( member @ Y1 @ Y0 @ X1 ) ) ) ) )
| ~ ( ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ~ ( ~ ( member @ Y1 @ X2 @ X1 )
| ~ ( member @ Y1 @ Y0 @ X1 ) ) ) )
| ( intersect @ X2 @ Y0 @ X1 ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ~ ( intersect @ X2 @ Y0 @ X1 )
| ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ~ ( ~ ( member @ Y1 @ X2 @ X1 )
| ~ ( member @ Y1 @ Y0 @ X1 ) ) ) ) )
| ~ ( ~ ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ~ ( ~ ( member @ Y1 @ X2 @ X1 )
| ~ ( member @ Y1 @ Y0 @ X1 ) ) ) )
| ( intersect @ X2 @ Y0 @ X1 ) ) ) )
@ X3 )
= $true )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( ( exists_in_world @ X3 @ X1 )
=> ~ ( ~ ( ~ ( intersect @ X2 @ X3 @ X1 )
| ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ~ ( ~ ( member @ Y0 @ X2 @ X1 )
| ~ ( member @ Y0 @ X3 @ X1 ) ) ) ) )
| ~ ( ~ ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ~ ( ~ ( member @ Y0 @ X2 @ X1 )
| ~ ( member @ Y0 @ X3 @ X1 ) ) ) )
| ( intersect @ X2 @ X3 @ X1 ) ) ) )
= $true )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f205]) ).
thf(f207,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( ~ ( ~ ( ~ ( intersect @ X2 @ X3 @ X1 )
| ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ~ ( ~ ( member @ Y0 @ X2 @ X1 )
| ~ ( member @ Y0 @ X3 @ X1 ) ) ) ) )
| ~ ( ~ ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ~ ( ~ ( member @ Y0 @ X2 @ X1 )
| ~ ( member @ Y0 @ X3 @ X1 ) ) ) )
| ( intersect @ X2 @ X3 @ X1 ) ) ) )
= $true )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( ~ ( ~ ( intersect @ X2 @ X3 @ X1 )
| ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ~ ( ~ ( member @ Y0 @ X2 @ X1 )
| ~ ( member @ Y0 @ X3 @ X1 ) ) ) ) )
| ~ ( ~ ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ~ ( ~ ( member @ Y0 @ X2 @ X1 )
| ~ ( member @ Y0 @ X3 @ X1 ) ) ) )
| ( intersect @ X2 @ X3 @ X1 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f207]) ).
thf(f210,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( ~ ( ~ ( intersect @ X2 @ X3 @ X1 )
| ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ~ ( ~ ( member @ Y0 @ X2 @ X1 )
| ~ ( member @ Y0 @ X3 @ X1 ) ) ) ) ) )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f208]) ).
thf(f211,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( ~ ( intersect @ X2 @ X3 @ X1 )
| ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ~ ( ~ ( member @ Y0 @ X2 @ X1 )
| ~ ( member @ Y0 @ X3 @ X1 ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f210]) ).
thf(f212,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( ~ ( intersect @ X2 @ X3 @ X1 ) )
= $true )
| ( ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ~ ( ~ ( member @ Y0 @ X2 @ X1 )
| ~ ( member @ Y0 @ X3 @ X1 ) ) ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f211]) ).
thf(f213,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( intersect @ X2 @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ~ ( ~ ( member @ Y0 @ X2 @ X1 )
| ~ ( member @ Y0 @ X3 @ X1 ) ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f212]) ).
thf(f214,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( intersect @ X2 @ X3 @ X1 )
= $false )
| ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ~ ( ~ ( member @ Y0 @ X2 @ X1 )
| ~ ( member @ Y0 @ X3 @ X1 ) ) ) )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f213]) ).
thf(f215,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ~ ( ~ ( member @ Y0 @ X2 @ X1 )
| ~ ( member @ Y0 @ X3 @ X1 ) ) )
@ ( sK2 @ X3 @ X1 @ X2 ) )
= $false )
| ( ( intersect @ X2 @ X3 @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f214]) ).
thf(f216,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( ( exists_in_world @ ( sK2 @ X3 @ X1 @ X2 ) @ X1 )
=> ~ ~ ( ~ ( member @ ( sK2 @ X3 @ X1 @ X2 ) @ X2 @ X1 )
| ~ ( member @ ( sK2 @ X3 @ X1 @ X2 ) @ X3 @ X1 ) ) )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( intersect @ X2 @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f215]) ).
thf(f217,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( intersect @ X2 @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( ~ ~ ( ~ ( member @ ( sK2 @ X3 @ X1 @ X2 ) @ X2 @ X1 )
| ~ ( member @ ( sK2 @ X3 @ X1 @ X2 ) @ X3 @ X1 ) ) )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f216]) ).
thf(f218,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( exists_in_world @ ( sK2 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( intersect @ X2 @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f216]) ).
thf(f219,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( ~ ( ~ ( member @ ( sK2 @ X3 @ X1 @ X2 ) @ X2 @ X1 )
| ~ ( member @ ( sK2 @ X3 @ X1 @ X2 ) @ X3 @ X1 ) ) )
= $true )
| ( ( intersect @ X2 @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f217]) ).
thf(f220,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( ~ ( member @ ( sK2 @ X3 @ X1 @ X2 ) @ X2 @ X1 )
| ~ ( member @ ( sK2 @ X3 @ X1 @ X2 ) @ X3 @ X1 ) )
= $false )
| ( ( intersect @ X2 @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f219]) ).
thf(f221,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( ~ ( member @ ( sK2 @ X3 @ X1 @ X2 ) @ X3 @ X1 ) )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( intersect @ X2 @ X3 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f220]) ).
thf(f222,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( intersect @ X2 @ X3 @ X1 )
= $false )
| ( ( ~ ( member @ ( sK2 @ X3 @ X1 @ X2 ) @ X2 @ X1 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f220]) ).
thf(f223,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( member @ ( sK2 @ X3 @ X1 @ X2 ) @ X2 @ X1 )
= $true )
| ( ( intersect @ X2 @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f222]) ).
thf(f224,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( member @ ( sK2 @ X3 @ X1 @ X2 ) @ X3 @ X1 )
= $true )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( intersect @ X2 @ X3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f221]) ).
thf(f237,plain,
( ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ 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 > $o] :
( ^ [Y5: $i > $o,Y6: $i > $o,Y7: $i] :
( ( Y5 @ Y7 )
| ( Y6 @ Y7 ) )
@ ( ^ [Y5: $i > $o,Y6: $i] :
~ ( Y5 @ Y6 )
@ Y3 )
@ Y4 )
@ ( member @ Y2 @ Y0 )
@ ( ^ [Y3: $i > $o,Y4: $i] :
~ ( Y3 @ Y4 )
@ ( member @ Y2 @ Y1 ) ) ) )
@ ( disjoint @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( sF1 = $true ) ),
inference(iff_proxy_clausification,[],[f174]) ).
thf(f258,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( ~ ( member @ Y3 @ Y1 @ Y0 )
| ~ ( member @ Y3 @ Y2 @ Y0 ) ) ) )
| ( disjoint @ Y1 @ Y2 @ Y0 ) ) ) ) ) ) ) )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f237]) ).
thf(f259,plain,
( ( ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ( ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y0 )
=> ( ~ ( member @ Y3 @ Y1 @ Y0 )
| ~ ( member @ Y3 @ Y2 @ Y0 ) ) ) )
| ( disjoint @ Y1 @ Y2 @ Y0 ) ) ) ) ) )
@ sK4 )
= $false )
| ( sF1 = $true ) ),
inference(sigma_proxy_clausification,[],[f258]) ).
thf(f260,plain,
( ( sF1 = $true )
| ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK4 )
=> ( ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ sK4 )
=> ( ~ ( member @ Y2 @ Y0 @ sK4 )
| ~ ( member @ Y2 @ Y1 @ sK4 ) ) ) )
| ( disjoint @ Y0 @ Y1 @ sK4 ) ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f259]) ).
thf(f261,plain,
( ( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK4 )
=> ( ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ sK4 )
=> ( ~ ( member @ Y2 @ Y0 @ sK4 )
| ~ ( member @ Y2 @ Y1 @ sK4 ) ) ) )
| ( disjoint @ Y0 @ Y1 @ sK4 ) ) ) ) )
@ sK5 )
= $false )
| ( sF1 = $true ) ),
inference(sigma_proxy_clausification,[],[f260]) ).
thf(f262,plain,
( ( ( ( exists_in_world @ sK5 @ sK4 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ( ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK4 )
=> ( ~ ( member @ Y1 @ sK5 @ sK4 )
| ~ ( member @ Y1 @ Y0 @ sK4 ) ) ) )
| ( disjoint @ sK5 @ Y0 @ sK4 ) ) ) ) )
= $false )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f261]) ).
thf(f263,plain,
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ( ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK4 )
=> ( ~ ( member @ Y1 @ sK5 @ sK4 )
| ~ ( member @ Y1 @ Y0 @ sK4 ) ) ) )
| ( disjoint @ sK5 @ Y0 @ sK4 ) ) ) )
= $false )
| ( sF1 = $true ) ),
inference(imp_proxy_clausification,[],[f262]) ).
thf(f264,plain,
( ( sF1 = $true )
| ( ( exists_in_world @ sK5 @ sK4 )
= $true ) ),
inference(imp_proxy_clausification,[],[f262]) ).
thf(f265,plain,
( ( sF1 = $true )
| ( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ( ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK4 )
=> ( ~ ( member @ Y1 @ sK5 @ sK4 )
| ~ ( member @ Y1 @ Y0 @ sK4 ) ) ) )
| ( disjoint @ sK5 @ Y0 @ sK4 ) ) )
@ sK6 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f263]) ).
thf(f266,plain,
( ( ( ( exists_in_world @ sK6 @ sK4 )
=> ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ( ~ ( member @ Y0 @ sK5 @ sK4 )
| ~ ( member @ Y0 @ sK6 @ sK4 ) ) ) )
| ( disjoint @ sK5 @ sK6 @ sK4 ) ) )
= $false )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f265]) ).
thf(f267,plain,
( ( ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ( ~ ( member @ Y0 @ sK5 @ sK4 )
| ~ ( member @ Y0 @ sK6 @ sK4 ) ) ) )
| ( disjoint @ sK5 @ sK6 @ sK4 ) )
= $false )
| ( sF1 = $true ) ),
inference(imp_proxy_clausification,[],[f266]) ).
thf(f268,plain,
( ( ( exists_in_world @ sK6 @ sK4 )
= $true )
| ( sF1 = $true ) ),
inference(imp_proxy_clausification,[],[f266]) ).
thf(f269,plain,
( ( ( disjoint @ sK5 @ sK6 @ sK4 )
= $false )
| ( sF1 = $true ) ),
inference(or_proxy_clausification,[],[f267]) ).
thf(f270,plain,
( ( sF1 = $true )
| ( ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ( ~ ( member @ Y0 @ sK5 @ sK4 )
| ~ ( member @ Y0 @ sK6 @ sK4 ) ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f267]) ).
thf(f271,plain,
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ( ~ ( member @ Y0 @ sK5 @ sK4 )
| ~ ( member @ Y0 @ sK6 @ sK4 ) ) ) )
= $true )
| ( sF1 = $true ) ),
inference(not_proxy_clausification,[],[f270]) ).
thf(f272,plain,
! [X1: mu] :
( ( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ( ~ ( member @ Y0 @ sK5 @ sK4 )
| ~ ( member @ Y0 @ sK6 @ sK4 ) ) )
@ X1 )
= $true )
| ( sF1 = $true ) ),
inference(pi_proxy_clausification,[],[f271]) ).
thf(f273,plain,
! [X1: mu] :
( ( ( ( exists_in_world @ X1 @ sK4 )
=> ( ~ ( member @ X1 @ sK5 @ sK4 )
| ~ ( member @ X1 @ sK6 @ sK4 ) ) )
= $true )
| ( sF1 = $true ) ),
inference(beta-eta_normalization,[],[f272]) ).
thf(f274,plain,
! [X1: mu] :
( ( ( ~ ( member @ X1 @ sK5 @ sK4 )
| ~ ( member @ X1 @ sK6 @ sK4 ) )
= $true )
| ( sF1 = $true )
| ( ( exists_in_world @ X1 @ sK4 )
= $false ) ),
inference(imp_proxy_clausification,[],[f273]) ).
thf(f275,plain,
! [X1: mu] :
( ( sF1 = $true )
| ( ( ~ ( member @ X1 @ sK5 @ sK4 ) )
= $true )
| ( ( exists_in_world @ X1 @ sK4 )
= $false )
| ( ( ~ ( member @ X1 @ sK6 @ sK4 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f274]) ).
thf(f276,plain,
! [X1: mu] :
( ( ( member @ X1 @ sK5 @ sK4 )
= $false )
| ( sF1 = $true )
| ( ( ~ ( member @ X1 @ sK6 @ sK4 ) )
= $true )
| ( ( exists_in_world @ X1 @ sK4 )
= $false ) ),
inference(not_proxy_clausification,[],[f275]) ).
thf(f277,plain,
! [X1: mu] :
( ( ( member @ X1 @ sK6 @ sK4 )
= $false )
| ( ( exists_in_world @ X1 @ sK4 )
= $false )
| ( ( member @ X1 @ sK5 @ sK4 )
= $false )
| ( sF1 = $true ) ),
inference(not_proxy_clausification,[],[f276]) ).
thf(f278,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ~ ( ~ ( ~ ( disjoint @ Y1 @ Y2 @ Y0 )
| ~ ( intersect @ Y1 @ Y2 @ Y0 ) )
| ~ ( ~ ~ ( intersect @ Y1 @ Y2 @ Y0 )
| ( disjoint @ Y1 @ Y2 @ Y0 ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f279,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y0 )
=> ~ ( ~ ( ~ ( disjoint @ Y1 @ Y2 @ Y0 )
| ~ ( intersect @ Y1 @ Y2 @ Y0 ) )
| ~ ( ~ ~ ( intersect @ Y1 @ Y2 @ Y0 )
| ( disjoint @ Y1 @ Y2 @ Y0 ) ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f278]) ).
thf(f280,plain,
! [X1: $i] :
( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ( ~ ( ~ ( disjoint @ Y0 @ Y1 @ X1 )
| ~ ( intersect @ Y0 @ Y1 @ X1 ) )
| ~ ( ~ ~ ( intersect @ Y0 @ Y1 @ X1 )
| ( disjoint @ Y0 @ Y1 @ X1 ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f279]) ).
thf(f281,plain,
! [X2: mu,X1: $i] :
( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ X1 )
=> ~ ( ~ ( ~ ( disjoint @ Y0 @ Y1 @ X1 )
| ~ ( intersect @ Y0 @ Y1 @ X1 ) )
| ~ ( ~ ~ ( intersect @ Y0 @ Y1 @ X1 )
| ( disjoint @ Y0 @ Y1 @ X1 ) ) ) ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f280]) ).
thf(f282,plain,
! [X2: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ~ ( disjoint @ X2 @ Y0 @ X1 )
| ~ ( intersect @ X2 @ Y0 @ X1 ) )
| ~ ( ~ ~ ( intersect @ X2 @ Y0 @ X1 )
| ( disjoint @ X2 @ Y0 @ X1 ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f281]) ).
thf(f283,plain,
! [X2: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ~ ( disjoint @ X2 @ Y0 @ X1 )
| ~ ( intersect @ X2 @ Y0 @ X1 ) )
| ~ ( ~ ~ ( intersect @ X2 @ Y0 @ X1 )
| ( disjoint @ X2 @ Y0 @ X1 ) ) ) ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f282]) ).
thf(f284,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ~ ( disjoint @ X2 @ Y0 @ X1 )
| ~ ( intersect @ X2 @ Y0 @ X1 ) )
| ~ ( ~ ~ ( intersect @ X2 @ Y0 @ X1 )
| ( disjoint @ X2 @ Y0 @ X1 ) ) ) )
@ X3 )
= $true )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f283]) ).
thf(f285,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( ( exists_in_world @ X3 @ X1 )
=> ~ ( ~ ( ~ ( disjoint @ X2 @ X3 @ X1 )
| ~ ( intersect @ X2 @ X3 @ X1 ) )
| ~ ( ~ ~ ( intersect @ X2 @ X3 @ X1 )
| ( disjoint @ X2 @ X3 @ X1 ) ) ) )
= $true ) ),
inference(beta-eta_normalization,[],[f284]) ).
thf(f286,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( ~ ( ~ ( ~ ( disjoint @ X2 @ X3 @ X1 )
| ~ ( intersect @ X2 @ X3 @ X1 ) )
| ~ ( ~ ~ ( intersect @ X2 @ X3 @ X1 )
| ( disjoint @ X2 @ X3 @ X1 ) ) ) )
= $true )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f285]) ).
thf(f287,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( ~ ( ~ ( disjoint @ X2 @ X3 @ X1 )
| ~ ( intersect @ X2 @ X3 @ X1 ) )
| ~ ( ~ ~ ( intersect @ X2 @ X3 @ X1 )
| ( disjoint @ X2 @ X3 @ X1 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f286]) ).
thf(f288,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( ~ ( ~ ~ ( intersect @ X2 @ X3 @ X1 )
| ( disjoint @ X2 @ X3 @ X1 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f287]) ).
thf(f294,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( ~ ~ ( intersect @ X2 @ X3 @ X1 )
| ( disjoint @ X2 @ X3 @ X1 ) )
= $true )
| ( ( exists_in_world @ X3 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f288]) ).
thf(f295,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( ~ ~ ( intersect @ X2 @ X3 @ X1 ) )
= $true )
| ( ( disjoint @ X2 @ X3 @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f294]) ).
thf(f296,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( disjoint @ X2 @ X3 @ X1 )
= $true )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( ~ ( intersect @ X2 @ X3 @ X1 ) )
= $false ) ),
inference(not_proxy_clausification,[],[f295]) ).
thf(f297,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( disjoint @ X2 @ X3 @ X1 )
= $true )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( ( exists_in_world @ X3 @ X1 )
= $false )
| ( ( intersect @ X2 @ X3 @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f296]) ).
thf(f315,definition,
( spl7_5
<=> ( ( exists_in_world @ sK5 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
thf(f317,plain,
( ( ( exists_in_world @ sK5 @ sK4 )
= $true )
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f315]) ).
thf(f319,definition,
( spl7_6
<=> ( sF1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
thf(f322,plain,
( spl7_5
| spl7_6 ),
inference(avatar_split_clause,[],[f264,f319,f315]) ).
thf(f324,definition,
( spl7_7
<=> ( ( exists_in_world @ sK6 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
thf(f326,plain,
( ( ( exists_in_world @ sK6 @ sK4 )
= $true )
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f324]) ).
thf(f327,plain,
( spl7_6
| spl7_7 ),
inference(avatar_split_clause,[],[f268,f324,f319]) ).
thf(f329,definition,
( spl7_8
<=> ! [X1: mu] :
( ( ( member @ X1 @ sK6 @ sK4 )
= $false )
| ( ( member @ X1 @ sK5 @ sK4 )
= $false )
| ( ( exists_in_world @ X1 @ sK4 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
thf(f330,plain,
( ! [X1: mu] :
( ( ( member @ X1 @ sK6 @ sK4 )
= $false )
| ( ( exists_in_world @ X1 @ sK4 )
= $false )
| ( ( member @ X1 @ sK5 @ sK4 )
= $false ) )
| ~ spl7_8 ),
inference(avatar_component_clause,[],[f329]) ).
thf(f331,plain,
( spl7_8
| spl7_6 ),
inference(avatar_split_clause,[],[f277,f319,f329]) ).
thf(f333,definition,
( spl7_9
<=> ( ( disjoint @ sK5 @ sK6 @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl7_9])],[avatar_definition]) ).
thf(f335,plain,
( ( ( disjoint @ sK5 @ sK6 @ sK4 )
= $false )
| ~ spl7_9 ),
inference(avatar_component_clause,[],[f333]) ).
thf(f336,plain,
( spl7_6
| spl7_9 ),
inference(avatar_split_clause,[],[f269,f333,f319]) ).
thf(f337,plain,
~ spl7_6,
inference(avatar_split_clause,[],[f175,f319]) ).
thf(f365,plain,
( ( ( exists_in_world @ sK5 @ sK4 )
= $false )
| ( ( intersect @ sK5 @ sK6 @ sK4 )
= $true )
| ( ( exists_in_world @ sK6 @ sK4 )
= $false )
| ( $false = $true )
| ~ spl7_9 ),
inference(constrained_superposition,[],[f297,f335]) ).
thf(f371,plain,
( ( ( exists_in_world @ sK5 @ sK4 )
= $false )
| ( ( intersect @ sK5 @ sK6 @ sK4 )
= $true )
| ( ( exists_in_world @ sK6 @ sK4 )
= $false )
| ~ spl7_9 ),
inference(trivial_inequality_removal,[],[f365]) ).
thf(f375,plain,
( ( ( exists_in_world @ sK6 @ sK4 )
= $false )
| ( $false = $true )
| ( ( intersect @ sK5 @ sK6 @ sK4 )
= $true )
| ~ spl7_5
| ~ spl7_9 ),
inference(forward_demodulation,[],[f371,f317]) ).
thf(f376,plain,
( ( ( intersect @ sK5 @ sK6 @ sK4 )
= $true )
| ( ( exists_in_world @ sK6 @ sK4 )
= $false )
| ~ spl7_5
| ~ spl7_9 ),
inference(trivial_inequality_removal,[],[f375]) ).
thf(f379,plain,
( ( $false = $true )
| ( ( intersect @ sK5 @ sK6 @ sK4 )
= $true )
| ~ spl7_5
| ~ spl7_7
| ~ spl7_9 ),
inference(forward_demodulation,[],[f376,f326]) ).
thf(f380,plain,
( ( ( intersect @ sK5 @ sK6 @ sK4 )
= $true )
| ~ spl7_5
| ~ spl7_7
| ~ spl7_9 ),
inference(trivial_inequality_removal,[],[f379]) ).
thf(f390,plain,
( ! [X0: mu] :
( ( ( exists_in_world @ ( sK2 @ X0 @ sK4 @ sK6 ) @ sK4 )
= $false )
| ( ( member @ ( sK2 @ X0 @ sK4 @ sK6 ) @ sK5 @ sK4 )
= $false )
| ( ( exists_in_world @ sK6 @ sK4 )
= $false )
| ( ( exists_in_world @ X0 @ sK4 )
= $false )
| ( $false = $true )
| ( ( intersect @ sK6 @ X0 @ sK4 )
= $false ) )
| ~ spl7_8 ),
inference(constrained_superposition,[],[f223,f330]) ).
thf(f400,plain,
( ! [X0: mu] :
( ( ( intersect @ sK6 @ X0 @ sK4 )
= $false )
| ( ( member @ ( sK2 @ X0 @ sK4 @ sK6 ) @ sK5 @ sK4 )
= $false )
| ( ( exists_in_world @ X0 @ sK4 )
= $false )
| ( ( exists_in_world @ sK6 @ sK4 )
= $false )
| ( ( exists_in_world @ ( sK2 @ X0 @ sK4 @ sK6 ) @ sK4 )
= $false ) )
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f390]) ).
thf(f406,plain,
( ! [X0: mu] :
( ( ( exists_in_world @ ( sK2 @ X0 @ sK4 @ sK6 ) @ sK4 )
= $false )
| ( ( exists_in_world @ X0 @ sK4 )
= $false )
| ( $false = $true )
| ( ( member @ ( sK2 @ X0 @ sK4 @ sK6 ) @ sK5 @ sK4 )
= $false )
| ( ( intersect @ sK6 @ X0 @ sK4 )
= $false ) )
| ~ spl7_7
| ~ spl7_8 ),
inference(forward_demodulation,[],[f400,f326]) ).
thf(f407,plain,
( ! [X0: mu] :
( ( ( member @ ( sK2 @ X0 @ sK4 @ sK6 ) @ sK5 @ sK4 )
= $false )
| ( ( exists_in_world @ ( sK2 @ X0 @ sK4 @ sK6 ) @ sK4 )
= $false )
| ( ( exists_in_world @ X0 @ sK4 )
= $false )
| ( ( intersect @ sK6 @ X0 @ sK4 )
= $false ) )
| ~ spl7_7
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f406]) ).
thf(f484,plain,
( ( ( exists_in_world @ sK5 @ sK4 )
= $false )
| ( ( exists_in_world @ sK6 @ sK4 )
= $false )
| ( $false = $true )
| ( ( exists_in_world @ sK5 @ sK4 )
= $false )
| ( ( intersect @ sK6 @ sK5 @ sK4 )
= $false )
| ( ( intersect @ sK6 @ sK5 @ sK4 )
= $false )
| ( ( exists_in_world @ ( sK2 @ sK5 @ sK4 @ sK6 ) @ sK4 )
= $false )
| ~ spl7_7
| ~ spl7_8 ),
inference(constrained_superposition,[],[f407,f224]) ).
thf(f490,plain,
( ( ( exists_in_world @ sK5 @ sK4 )
= $false )
| ( ( exists_in_world @ ( sK2 @ sK5 @ sK4 @ sK6 ) @ sK4 )
= $false )
| ( ( exists_in_world @ sK6 @ sK4 )
= $false )
| ( $false = $true )
| ( ( intersect @ sK6 @ sK5 @ sK4 )
= $false )
| ~ spl7_7
| ~ spl7_8 ),
inference(duplicate_literal_removal,[],[f484]) ).
thf(f491,plain,
( ( ( intersect @ sK6 @ sK5 @ sK4 )
= $false )
| ( ( exists_in_world @ sK6 @ sK4 )
= $false )
| ( ( exists_in_world @ ( sK2 @ sK5 @ sK4 @ sK6 ) @ sK4 )
= $false )
| ( ( exists_in_world @ sK5 @ sK4 )
= $false )
| ~ spl7_7
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f490]) ).
thf(f494,plain,
( ( ( exists_in_world @ sK5 @ sK4 )
= $false )
| ( ( exists_in_world @ ( sK2 @ sK5 @ sK4 @ sK6 ) @ sK4 )
= $false )
| ( ( intersect @ sK6 @ sK5 @ sK4 )
= $false )
| ( $false = $true )
| ~ spl7_7
| ~ spl7_8 ),
inference(forward_demodulation,[],[f491,f326]) ).
thf(f495,plain,
( ( ( intersect @ sK6 @ sK5 @ sK4 )
= $false )
| ( ( exists_in_world @ ( sK2 @ sK5 @ sK4 @ sK6 ) @ sK4 )
= $false )
| ( ( exists_in_world @ sK5 @ sK4 )
= $false )
| ~ spl7_7
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f494]) ).
thf(f498,plain,
( ( ( exists_in_world @ ( sK2 @ sK5 @ sK4 @ sK6 ) @ sK4 )
= $false )
| ( ( intersect @ sK6 @ sK5 @ sK4 )
= $false )
| ( $false = $true )
| ~ spl7_5
| ~ spl7_7
| ~ spl7_8 ),
inference(forward_demodulation,[],[f495,f317]) ).
thf(f499,plain,
( ( ( exists_in_world @ ( sK2 @ sK5 @ sK4 @ sK6 ) @ sK4 )
= $false )
| ( ( intersect @ sK6 @ sK5 @ sK4 )
= $false )
| ~ spl7_5
| ~ spl7_7
| ~ spl7_8 ),
inference(trivial_inequality_removal,[],[f498]) ).
thf(f501,definition,
( spl7_10
<=> ( ( intersect @ sK6 @ sK5 @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl7_10])],[avatar_definition]) ).
thf(f502,plain,
( ( ( intersect @ sK6 @ sK5 @ sK4 )
!= $false )
| spl7_10 ),
inference(avatar_component_clause,[],[f501]) ).
thf(f503,plain,
( ( ( intersect @ sK6 @ sK5 @ sK4 )
= $false )
| ~ spl7_10 ),
inference(avatar_component_clause,[],[f501]) ).
thf(f505,definition,
( spl7_11
<=> ( ( exists_in_world @ ( sK2 @ sK5 @ sK4 @ sK6 ) @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl7_11])],[avatar_definition]) ).
thf(f507,plain,
( ( ( exists_in_world @ ( sK2 @ sK5 @ sK4 @ sK6 ) @ sK4 )
= $false )
| ~ spl7_11 ),
inference(avatar_component_clause,[],[f505]) ).
thf(f509,plain,
( spl7_10
| spl7_11
| ~ spl7_5
| ~ spl7_7
| ~ spl7_8 ),
inference(avatar_split_clause,[],[f499,f329,f324,f315,f505,f501]) ).
thf(f512,plain,
( ( ( exists_in_world @ sK5 @ sK4 )
= $false )
| ( $false = $true )
| ( ( intersect @ sK5 @ sK6 @ sK4 )
= $false )
| ( ( exists_in_world @ sK6 @ sK4 )
= $false )
| ~ spl7_10 ),
inference(constrained_superposition,[],[f189,f503]) ).
thf(f515,plain,
( ( ( exists_in_world @ sK6 @ sK4 )
= $false )
| ( ( exists_in_world @ sK5 @ sK4 )
= $false )
| ( ( intersect @ sK5 @ sK6 @ sK4 )
= $false )
| ~ spl7_10 ),
inference(trivial_inequality_removal,[],[f512]) ).
thf(f518,plain,
( ( ( exists_in_world @ sK5 @ sK4 )
= $false )
| ( ( intersect @ sK5 @ sK6 @ sK4 )
= $false )
| ( $false = $true )
| ~ spl7_7
| ~ spl7_10 ),
inference(forward_demodulation,[],[f515,f326]) ).
thf(f519,plain,
( ( ( intersect @ sK5 @ sK6 @ sK4 )
= $false )
| ( ( exists_in_world @ sK5 @ sK4 )
= $false )
| ~ spl7_7
| ~ spl7_10 ),
inference(trivial_inequality_removal,[],[f518]) ).
thf(f522,plain,
( ( ( exists_in_world @ sK5 @ sK4 )
= $false )
| ( $false = $true )
| ~ spl7_5
| ~ spl7_7
| ~ spl7_9
| ~ spl7_10 ),
inference(forward_demodulation,[],[f519,f380]) ).
thf(f523,plain,
( ( ( exists_in_world @ sK5 @ sK4 )
= $false )
| ~ spl7_5
| ~ spl7_7
| ~ spl7_9
| ~ spl7_10 ),
inference(trivial_inequality_removal,[],[f522]) ).
thf(f527,plain,
( ( $false = $true )
| ~ spl7_5
| ~ spl7_7
| ~ spl7_9
| ~ spl7_10 ),
inference(forward_demodulation,[],[f523,f317]) ).
thf(f528,plain,
( $false
| ~ spl7_5
| ~ spl7_7
| ~ spl7_9
| ~ spl7_10 ),
inference(trivial_inequality_removal,[],[f527]) ).
thf(f529,plain,
( ~ spl7_5
| ~ spl7_7
| ~ spl7_9
| ~ spl7_10 ),
inference(avatar_contradiction_clause,[],[f528]) ).
thf(f558,plain,
( ( $false = $true )
| ( ( intersect @ sK6 @ sK5 @ sK4 )
= $false )
| ( ( exists_in_world @ sK6 @ sK4 )
= $false )
| ( ( exists_in_world @ sK5 @ sK4 )
= $false )
| ~ spl7_11 ),
inference(constrained_superposition,[],[f218,f507]) ).
thf(f562,plain,
( ( ( intersect @ sK6 @ sK5 @ sK4 )
= $false )
| ( ( exists_in_world @ sK6 @ sK4 )
= $false )
| ( ( exists_in_world @ sK5 @ sK4 )
= $false )
| ~ spl7_11 ),
inference(trivial_inequality_removal,[],[f558]) ).
thf(f566,plain,
( ( ( exists_in_world @ sK5 @ sK4 )
= $false )
| ( ( exists_in_world @ sK6 @ sK4 )
= $false )
| spl7_10
| ~ spl7_11 ),
inference(forward_subsumption_resolution,[],[f562,f502]) ).
thf(f569,plain,
( ( $false = $true )
| ( ( exists_in_world @ sK6 @ sK4 )
= $false )
| ~ spl7_5
| spl7_10
| ~ spl7_11 ),
inference(forward_demodulation,[],[f566,f317]) ).
thf(f570,plain,
( ( ( exists_in_world @ sK6 @ sK4 )
= $false )
| ~ spl7_5
| spl7_10
| ~ spl7_11 ),
inference(trivial_inequality_removal,[],[f569]) ).
thf(f574,plain,
( ( $false = $true )
| ~ spl7_5
| ~ spl7_7
| spl7_10
| ~ spl7_11 ),
inference(forward_demodulation,[],[f570,f326]) ).
thf(f575,plain,
( $false
| ~ spl7_5
| ~ spl7_7
| spl7_10
| ~ spl7_11 ),
inference(trivial_inequality_removal,[],[f574]) ).
thf(f576,plain,
( ~ spl7_5
| ~ spl7_7
| spl7_10
| ~ spl7_11 ),
inference(avatar_contradiction_clause,[],[f575]) ).
cnf(s4,plain,
( spl7_5
| spl7_6 ),
inference(sat_conversion,[],[f322]) ).
cnf(s5,plain,
( spl7_6
| spl7_7 ),
inference(sat_conversion,[],[f327]) ).
cnf(s6,plain,
( spl7_6
| spl7_8 ),
inference(sat_conversion,[],[f331]) ).
cnf(s7,plain,
( spl7_6
| spl7_9 ),
inference(sat_conversion,[],[f336]) ).
cnf(s8,plain,
~ spl7_6,
inference(sat_conversion,[],[f337]) ).
cnf(s10,plain,
( ~ spl7_5
| ~ spl7_7
| ~ spl7_8
| spl7_10
| spl7_11 ),
inference(sat_conversion,[],[f509]) ).
cnf(s12,plain,
( ~ spl7_5
| ~ spl7_7
| ~ spl7_9
| ~ spl7_10 ),
inference(sat_conversion,[],[f529]) ).
cnf(s14,plain,
( ~ spl7_5
| ~ spl7_7
| spl7_10
| ~ spl7_11 ),
inference(sat_conversion,[],[f576]) ).
cnf(s15,plain,
spl7_9,
inference(rat,[],[s7,s8]) ).
cnf(s16,plain,
spl7_8,
inference(rat,[],[s6,s8]) ).
cnf(s17,plain,
spl7_7,
inference(rat,[],[s5,s8]) ).
cnf(s18,plain,
spl7_5,
inference(rat,[],[s4,s8]) ).
cnf(s19,plain,
~ spl7_10,
inference(rat,[],[s12,s17,s15,s18]) ).
cnf(s20,plain,
~ spl7_11,
inference(rat,[],[s14,s18,s17,s19]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s10,s18,s17,s16,s20,s19]) ).
thf(f577,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET576^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.27 % Computer : n018.cluster.edu
% 0.12/0.27 % Model : x86_64 x86_64
% 0.12/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.27 % Memory : 8046.5625MB
% 0.12/0.27 % OS : Linux 6.8.0-71-generic
% 0.12/0.27 % CPULimit : 300
% 0.12/0.27 % WCLimit : 300
% 0.12/0.27 % DateTime : Tue Sep 29 13:39:56 UTC 2026
% 0.12/0.27 % CPUTime :
% 0.12/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.28/0.33 Running higher-order theorem proving
% 0.28/0.35 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.35/0.46 % (75872)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.35/0.46 % (75879)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3914911731:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.35/0.46 % (75879)Instruction limit reached!
% 0.35/0.46 % (75879)------------------------------
% 0.35/0.46 % (75879)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.46 % (75879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.46 % (75879)CaDiCaL version: 2.1.3
% 0.35/0.46 % (75879)Termination reason: Instruction limit
% 0.35/0.46 % (75879)Termination phase: Property scanning
% 0.35/0.46 % (75879)Time elapsed: 0.002 s
% 0.35/0.46 % (75879)Peak memory usage: 10 MB
% 0.35/0.46 % (75879)Instructions burned: 4 (million)
% 0.35/0.46 % (75877)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3482587407:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.35/0.46 % (75878)lrs+10_16_si=on:nwc=1.5:random_seed=1856604335:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.35/0.46 % (75880)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=794886298: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)
% 0.35/0.46 % (75881)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1504980952:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.35/0.46 % (75883)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.35/0.46 % (75883)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
% 0.35/0.46 % (75883)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=953964656:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.35/0.46 % (75878)Instruction limit reached!
% 0.35/0.46 % (75878)------------------------------
% 0.35/0.46 % (75878)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.46 % (75878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.46 % (75878)CaDiCaL version: 2.1.3
% 0.35/0.46 % (75878)Termination reason: Instruction limit
% 0.35/0.46 % (75878)Termination phase: Saturation
% 0.35/0.46 % (75878)Time elapsed: 0.015 s
% 0.35/0.46 % (75878)Peak memory usage: 11 MB
% 0.35/0.46 % (75878)Instructions burned: 18 (million)
% 0.35/0.46 % (75882)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=688246463:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.35/0.46 % (75885)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3808938103:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.35/0.46 % (75885)Instruction limit reached!
% 0.35/0.46 % (75885)------------------------------
% 0.35/0.46 % (75885)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.46 % (75885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.46 % (75885)CaDiCaL version: 2.1.3
% 0.35/0.46 % (75885)Termination reason: Instruction limit
% 0.35/0.46 % (75885)Termination phase: shuffling
% 0.35/0.46 % (75885)Time elapsed: 0.002 s
% 0.35/0.46 % (75885)Peak memory usage: 9 MB
% 0.35/0.46 % (75885)Instructions burned: 2 (million)
% 0.35/0.46 % (75881)Instruction limit reached!
% 0.35/0.46 % (75881)------------------------------
% 0.35/0.46 % (75881)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.46 % (75881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.46 % (75881)CaDiCaL version: 2.1.3
% 0.35/0.46 % (75881)Termination reason: Instruction limit
% 0.35/0.46 % (75881)Termination phase: Saturation
% 0.35/0.46 % (75881)Time elapsed: 0.023 s
% 0.35/0.46 % (75881)Peak memory usage: 12 MB
% 0.35/0.46 % (75881)Instructions burned: 24 (million)
% 0.35/0.46 % (75883) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-75872-75883"...
% 0.35/0.46 % (75883)...printing done.
% 0.35/0.46 % (75883)Refutation found. Thanks to Tanya!
% 0.35/0.46 % SZS status Theorem for theBenchmark
% 0.35/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.35/0.46 % (75883)------------------------------
% 0.35/0.46 % (75883)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.46 % (75883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.46 % (75883)CaDiCaL version: 2.1.3
% 0.35/0.46 % (75883)Termination reason: Refutation
% 0.35/0.46 % (75883)Time elapsed: 0.028 s
% 0.35/0.46 % (75883)Peak memory usage: 13 MB
% 0.35/0.46 % (75883)Instructions burned: 62 (million)
% 0.35/0.46 % (75872)Success in time 0.092 s
% 0.35/0.46 % Vampire exiting
%------------------------------------------------------------------------------