%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:23:37 AM UTC 2026
% Result : Theorem 3.54s 0.96s
% Output : Refutation 3.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 13
% Syntax : Number of formulae : 152 ( 75 unt; 0 typ; 2 def)
% Number of atoms : 1442 ( 280 equ; 0 cnn)
% Maximal formula atoms : 10 ( 9 avg)
% Number of connectives : 2679 ( 378 ~; 300 |; 0 &;1826 @)
% ( 2 <=>; 92 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 167 ( 167 >; 0 *; 0 +; 0 <<)
% Number of symbols : 64 ( 60 usr; 8 con; 0-4 aty)
% ( 81 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 481 ( 0 sgn 123 !; 0 ?; 481 :)
% 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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_43,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_44,type,
vNOT: $o > $o ).
thf(func_def_45,type,
vOR: $o > $o > $o ).
thf(func_def_46,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vIMP: $o > $o > $o ).
thf(func_def_51,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_52,type,
vAND: $o > $o > $o ).
thf(func_def_53,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_54,type,
sK0: $i > mu ).
thf(func_def_56,type,
sK2: mu ).
thf(func_def_57,type,
sK3: mu ).
thf(func_def_58,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_59,type,
sK4: mu > $i > mu > mu ).
thf(f2,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mnot) ).
thf(f3,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/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/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,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mequiv) ).
thf(f15,axiom,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL015^0.ax',mexists_ind) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
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(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(f43,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f44,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f43]) ).
thf(f45,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f46,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f45]) ).
thf(f52,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f53,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f55,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f11]) ).
thf(f60,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f61,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f60]) ).
thf(f62,plain,
( mexists_ind
= ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f63,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f62]) ).
thf(f86,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f87,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f86]) ).
thf(f103,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(f104,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] :
( mequiv @ ( intersect @ Y0 @ Y1 )
@ ( mexists_ind
@ ^ [Y2: mu] : ( mand @ ( member @ Y2 @ Y0 ) @ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f103]) ).
thf(f105,plain,
( mvalid
@ ( mforall_ind
@ ^ [X0: mu] :
( mforall_ind
@ ^ [X1: mu] : ( mequiv @ ( disjoint @ X0 @ X1 ) @ ( mnot @ ( intersect @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f106,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mequiv @ ( disjoint @ Y0 @ Y1 ) @ ( mnot @ ( intersect @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f105]) ).
thf(f109,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(f110,plain,
( $true
!= ( 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 ) ) ) ) ) ),
inference(fool_elimination,[],[f109]) ).
thf(f111,plain,
( $true
!= ( 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 ) ) ) ) ) ),
inference(flattening,[],[f110]) ).
thf(f116,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f117,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f122,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f123,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f125,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f129,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f130,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f63]) ).
thf(f142,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f87]) ).
thf(f151,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] :
( mequiv @ ( intersect @ Y0 @ Y1 )
@ ( mexists_ind
@ ^ [Y2: mu] : ( mand @ ( member @ Y2 @ Y0 ) @ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f104]) ).
thf(f152,plain,
( $true
= ( mvalid
@ ( mforall_ind
@ ^ [Y0: mu] :
( mforall_ind
@ ^ [Y1: mu] : ( mequiv @ ( disjoint @ Y0 @ Y1 ) @ ( mnot @ ( intersect @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f106]) ).
thf(f154,plain,
( $true
!= ( 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 ) ) ) ) ) ),
inference(cnf_transformation,[],[f111]) ).
thf(f158,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,[],[f122,f116,f117,f116,f116]) ).
thf(f159,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,[],[f123,f117,f116]) ).
thf(f161,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,[],[f125,f158,f159,f159]) ).
thf(f164,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,f116,f129,f116]) ).
thf(f169,plain,
( $true
= ( ^ [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 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f151,f142,f129,f129,f161,f164,f158]) ).
thf(f170,plain,
( $true
= ( ^ [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 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f152,f142,f129,f129,f161,f116]) ).
thf(f172,plain,
( $true
!= ( ^ [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 ) ) ) ) ) ),
inference(definition_unfolding,[],[f154,f142,f129,f129,f159,f129,f159,f116]) ).
thf(f173,plain,
( $true
!= ( !! @ $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 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f172]) ).
thf(f174,plain,
( $false
= ( ^ [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 ) ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK1 )
=> ( ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ sK1 )
=> ( ~ ( member @ Y2 @ Y0 @ sK1 )
| ~ ( member @ Y2 @ Y1 @ sK1 ) ) ) )
| ( disjoint @ Y0 @ Y1 @ sK1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK1 )
=> ( ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ sK1 )
=> ( ~ ( member @ Y2 @ Y0 @ sK1 )
| ~ ( member @ Y2 @ Y1 @ sK1 ) ) ) )
| ( disjoint @ Y0 @ Y1 @ sK1 ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( $false
= ( ( exists_in_world @ sK2 @ sK1 )
=> ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK1 )
=> ( ~ ( member @ Y1 @ sK2 @ sK1 )
| ~ ( member @ Y1 @ Y0 @ sK1 ) ) ) )
| ( disjoint @ sK2 @ Y0 @ sK1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f176]) ).
thf(f178,plain,
( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK1 )
=> ( ~ ( member @ Y1 @ sK2 @ sK1 )
| ~ ( member @ Y1 @ Y0 @ sK1 ) ) ) )
| ( disjoint @ sK2 @ Y0 @ sK1 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f177]) ).
thf(f179,plain,
( $true
= ( exists_in_world @ sK2 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f177]) ).
thf(f180,plain,
( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ sK1 )
=> ( ~ ( member @ Y1 @ sK2 @ sK1 )
| ~ ( member @ Y1 @ Y0 @ sK1 ) ) ) )
| ( disjoint @ sK2 @ Y0 @ sK1 ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f178]) ).
thf(f181,plain,
( $false
= ( ( exists_in_world @ sK3 @ sK1 )
=> ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( ~ ( member @ Y0 @ sK2 @ sK1 )
| ~ ( member @ Y0 @ sK3 @ sK1 ) ) ) )
| ( disjoint @ sK2 @ sK3 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f182,plain,
( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( ~ ( member @ Y0 @ sK2 @ sK1 )
| ~ ( member @ Y0 @ sK3 @ sK1 ) ) ) )
| ( disjoint @ sK2 @ sK3 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f181]) ).
thf(f183,plain,
( $true
= ( exists_in_world @ sK3 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f181]) ).
thf(f184,plain,
( $false
= ( disjoint @ sK2 @ sK3 @ sK1 ) ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f185,plain,
( $false
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( ~ ( member @ Y0 @ sK2 @ sK1 )
| ~ ( member @ Y0 @ sK3 @ sK1 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f186,plain,
( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( ~ ( member @ Y0 @ sK2 @ sK1 )
| ~ ( member @ Y0 @ sK3 @ sK1 ) ) ) ) ),
inference(not_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X1: mu] :
( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( ~ ( member @ Y0 @ sK2 @ sK1 )
| ~ ( member @ Y0 @ sK3 @ sK1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X1: mu] :
( $true
= ( ( exists_in_world @ X1 @ sK1 )
=> ( ~ ( member @ X1 @ sK2 @ sK1 )
| ~ ( member @ X1 @ sK3 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f189,plain,
! [X1: mu] :
( ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $true
= ( ~ ( member @ X1 @ sK2 @ sK1 )
| ~ ( member @ X1 @ sK3 @ sK1 ) ) ) ),
inference(imp_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X1: mu] :
( ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $true
= ( ~ ( member @ X1 @ sK3 @ sK1 ) ) )
| ( $true
= ( ~ ( member @ X1 @ sK2 @ sK1 ) ) ) ),
inference(or_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X1: mu] :
( ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( member @ X1 @ sK3 @ sK1 ) )
| ( $true
= ( ~ ( member @ X1 @ sK2 @ sK1 ) ) ) ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X1: mu] :
( ( $false
= ( member @ X1 @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ X1 @ sK1 ) )
| ( $false
= ( member @ X1 @ sK2 @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f191]) ).
thf(f204,plain,
( $true
= ( !! @ $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 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f205,plain,
! [X1: $i] :
( $true
= ( ^ [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 ) ),
inference(pi_proxy_clausification,[],[f204]) ).
thf(f206,plain,
! [X1: $i] :
( $true
= ( !! @ 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 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f205]) ).
thf(f207,plain,
! [X2: mu,X1: $i] :
( $true
= ( ^ [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 ) ),
inference(pi_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X2: mu,X1: $i] :
( $true
= ( ( 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 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f207]) ).
thf(f209,plain,
! [X2: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ~ ( disjoint @ X2 @ Y0 @ X1 )
| ~ ( intersect @ X2 @ Y0 @ X1 ) )
| ~ ( ~ ~ ( intersect @ X2 @ Y0 @ X1 )
| ( disjoint @ X2 @ Y0 @ X1 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f208]) ).
thf(f210,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( ~ ( disjoint @ X2 @ Y0 @ X1 )
| ~ ( intersect @ X2 @ Y0 @ X1 ) )
| ~ ( ~ ~ ( intersect @ X2 @ Y0 @ X1 )
| ( disjoint @ X2 @ Y0 @ X1 ) ) ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f209]) ).
thf(f211,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ( exists_in_world @ X3 @ X1 )
=> ~ ( ~ ( ~ ( disjoint @ X2 @ X3 @ X1 )
| ~ ( intersect @ X2 @ X3 @ X1 ) )
| ~ ( ~ ~ ( intersect @ X2 @ X3 @ X1 )
| ( disjoint @ X2 @ X3 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f210]) ).
thf(f212,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( ~ ( ~ ( ~ ( disjoint @ X2 @ X3 @ X1 )
| ~ ( intersect @ X2 @ X3 @ X1 ) )
| ~ ( ~ ~ ( intersect @ X2 @ X3 @ X1 )
| ( disjoint @ X2 @ X3 @ X1 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f211]) ).
thf(f213,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( ~ ( ~ ( disjoint @ X2 @ X3 @ X1 )
| ~ ( intersect @ X2 @ X3 @ X1 ) )
| ~ ( ~ ~ ( intersect @ X2 @ X3 @ X1 )
| ( disjoint @ X2 @ X3 @ X1 ) ) ) ) ),
inference(not_proxy_clausification,[],[f212]) ).
thf(f214,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( ~ ( ~ ~ ( intersect @ X2 @ X3 @ X1 )
| ( disjoint @ X2 @ X3 @ X1 ) ) ) ) ),
inference(or_proxy_clausification,[],[f213]) ).
thf(f220,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( ~ ~ ( intersect @ X2 @ X3 @ X1 )
| ( disjoint @ X2 @ X3 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f214]) ).
thf(f221,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( disjoint @ X2 @ X3 @ X1 ) )
| ( $true
= ( ~ ~ ( intersect @ X2 @ X3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f220]) ).
thf(f222,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( disjoint @ X2 @ X3 @ X1 ) )
| ( $false
= ( ~ ( intersect @ X2 @ X3 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f221]) ).
thf(f223,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( intersect @ X2 @ X3 @ X1 ) )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( disjoint @ X2 @ X3 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f222]) ).
thf(f224,plain,
( $true
= ( !! @ $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 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f225,plain,
! [X1: $i] :
( $true
= ( ^ [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 ) ),
inference(pi_proxy_clausification,[],[f224]) ).
thf(f226,plain,
! [X1: $i] :
( $true
= ( !! @ 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 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f225]) ).
thf(f227,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 )
| ~ ( !! @ 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 ) ),
inference(pi_proxy_clausification,[],[f226]) ).
thf(f228,plain,
! [X2: mu,X1: $i] :
( $true
= ( ( 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 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f227]) ).
thf(f229,plain,
! [X2: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( !! @ 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 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ^ [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 ) ) ),
inference(pi_proxy_clausification,[],[f229]) ).
thf(f231,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $true
= ( ( 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 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f230]) ).
thf(f232,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( ~ ( ~ ( ~ ( 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 ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f231]) ).
thf(f233,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ 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 ) ) ) ) ),
inference(not_proxy_clausification,[],[f232]) ).
thf(f235,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( ~ ( ~ ( intersect @ X2 @ X3 @ X1 )
| ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ~ ( ~ ( member @ Y0 @ X2 @ X1 )
| ~ ( member @ Y0 @ X3 @ X1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f233]) ).
thf(f236,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( ~ ( intersect @ X2 @ X3 @ X1 )
| ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ~ ( ~ ( member @ Y0 @ X2 @ X1 )
| ~ ( member @ Y0 @ X3 @ X1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f235]) ).
thf(f237,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( ~ ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ~ ( ~ ( member @ Y0 @ X2 @ X1 )
| ~ ( member @ Y0 @ X3 @ X1 ) ) ) ) ) )
| ( $true
= ( ~ ( intersect @ X2 @ X3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f236]) ).
thf(f238,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ~ ( ~ ( member @ Y0 @ X2 @ X1 )
| ~ ( member @ Y0 @ X3 @ X1 ) ) ) ) )
| ( $true
= ( ~ ( intersect @ X2 @ X3 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f237]) ).
thf(f239,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ~ ( ~ ( member @ Y0 @ X2 @ X1 )
| ~ ( member @ Y0 @ X3 @ X1 ) ) )
@ ( sK4 @ X3 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ( intersect @ X2 @ X3 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f238]) ).
thf(f240,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ~ ( ~ ( member @ Y0 @ X2 @ X1 )
| ~ ( member @ Y0 @ X3 @ X1 ) ) )
@ ( sK4 @ X3 @ X1 @ X2 ) ) )
| ( $false
= ( intersect @ X2 @ X3 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f239]) ).
thf(f241,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( ( exists_in_world @ ( sK4 @ X3 @ X1 @ X2 ) @ X1 )
=> ~ ~ ( ~ ( member @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 @ X1 )
| ~ ( member @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 @ X1 ) ) ) )
| ( $false
= ( intersect @ X2 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f240]) ).
thf(f242,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( ~ ~ ( ~ ( member @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 @ X1 )
| ~ ( member @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 @ X1 ) ) ) )
| ( $false
= ( intersect @ X2 @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f241]) ).
thf(f243,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( exists_in_world @ ( sK4 @ X3 @ X1 @ X2 ) @ X1 ) )
| ( $false
= ( intersect @ X2 @ X3 @ X1 ) )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f241]) ).
thf(f244,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $true
= ( ~ ( ~ ( member @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 @ X1 )
| ~ ( member @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 @ X1 ) ) ) )
| ( $false
= ( intersect @ X2 @ X3 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f242]) ).
thf(f245,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( ~ ( member @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 @ X1 )
| ~ ( member @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 @ X1 ) ) )
| ( $false
= ( intersect @ X2 @ X3 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f244]) ).
thf(f246,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( ~ ( member @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 @ X1 ) ) )
| ( $false
= ( intersect @ X2 @ X3 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f245]) ).
thf(f247,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( $false
= ( ~ ( member @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 @ X1 ) ) )
| ( $false
= ( intersect @ X2 @ X3 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f245]) ).
thf(f248,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( member @ ( sK4 @ X3 @ X1 @ X2 ) @ X2 @ X1 ) )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( intersect @ X2 @ X3 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f247]) ).
thf(f249,plain,
! [X2: mu,X3: mu,X1: $i] :
( ( $true
= ( member @ ( sK4 @ X3 @ X1 @ X2 ) @ X3 @ X1 ) )
| ( $false
= ( exists_in_world @ X3 @ X1 ) )
| ( ( exists_in_world @ X2 @ X1 )
= $false )
| ( $false
= ( intersect @ X2 @ X3 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f246]) ).
thf(f1018,plain,
! [X0: mu] :
( ( $true = $false )
| ( $false
= ( exists_in_world @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ X0 @ sK1 ) )
| ( $false
= ( intersect @ X0 @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ ( sK4 @ sK3 @ sK1 @ X0 ) @ sK1 ) )
| ( $false
= ( member @ ( sK4 @ sK3 @ sK1 @ X0 ) @ sK2 @ sK1 ) ) ),
inference(constrained_superposition,[],[f249,f192]) ).
thf(f1025,plain,
! [X0: mu] :
( ( $false
= ( exists_in_world @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ X0 @ sK1 ) )
| ( $false
= ( intersect @ X0 @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ ( sK4 @ sK3 @ sK1 @ X0 ) @ sK1 ) )
| ( $false
= ( member @ ( sK4 @ sK3 @ sK1 @ X0 ) @ sK2 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f1018]) ).
thf(f1032,plain,
! [X0: mu] :
( ( $true = $false )
| ( $false
= ( exists_in_world @ X0 @ sK1 ) )
| ( $false
= ( intersect @ X0 @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ ( sK4 @ sK3 @ sK1 @ X0 ) @ sK1 ) )
| ( $false
= ( member @ ( sK4 @ sK3 @ sK1 @ X0 ) @ sK2 @ sK1 ) ) ),
inference(forward_demodulation,[],[f1025,f183]) ).
thf(f1033,plain,
! [X0: mu] :
( ( $false
= ( member @ ( sK4 @ sK3 @ sK1 @ X0 ) @ sK2 @ sK1 ) )
| ( $false
= ( intersect @ X0 @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ ( sK4 @ sK3 @ sK1 @ X0 ) @ sK1 ) )
| ( $false
= ( exists_in_world @ X0 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f1032]) ).
thf(f2689,plain,
! [X2: $i,X0: mu,X1: mu] :
( ( $true = $false )
| ( $false
= ( exists_in_world @ X1 @ X2 ) )
| ( $true
= ( disjoint @ X0 @ X1 @ X2 ) )
| ( ( exists_in_world @ X0 @ X2 )
= $false )
| ( $true
= ( exists_in_world @ ( sK4 @ X1 @ X2 @ X0 ) @ X2 ) )
| ( $false
= ( exists_in_world @ X1 @ X2 ) )
| ( ( exists_in_world @ X0 @ X2 )
= $false ) ),
inference(constrained_superposition,[],[f223,f243]) ).
thf(f2696,plain,
! [X2: $i,X0: mu,X1: mu] :
( ( $true = $false )
| ( $false
= ( exists_in_world @ X1 @ X2 ) )
| ( $true
= ( disjoint @ X0 @ X1 @ X2 ) )
| ( ( exists_in_world @ X0 @ X2 )
= $false )
| ( $true
= ( exists_in_world @ ( sK4 @ X1 @ X2 @ X0 ) @ X2 ) ) ),
inference(duplicate_literal_removal,[],[f2689]) ).
thf(f2697,plain,
! [X2: $i,X0: mu,X1: mu] :
( ( $true
= ( exists_in_world @ ( sK4 @ X1 @ X2 @ X0 ) @ X2 ) )
| ( $true
= ( disjoint @ X0 @ X1 @ X2 ) )
| ( ( exists_in_world @ X0 @ X2 )
= $false )
| ( $false
= ( exists_in_world @ X1 @ X2 ) ) ),
inference(trivial_inequality_removal,[],[f2696]) ).
thf(f3807,plain,
( ( $true = $false )
| ( $false
= ( intersect @ sK2 @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ ( sK4 @ sK3 @ sK1 @ sK2 ) @ sK1 ) )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( $false
= ( exists_in_world @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( $false
= ( intersect @ sK2 @ sK3 @ sK1 ) ) ),
inference(constrained_superposition,[],[f1033,f248]) ).
thf(f3813,plain,
( ( $true = $false )
| ( $false
= ( intersect @ sK2 @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ ( sK4 @ sK3 @ sK1 @ sK2 ) @ sK1 ) )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( $false
= ( exists_in_world @ sK3 @ sK1 ) ) ),
inference(duplicate_literal_removal,[],[f3807]) ).
thf(f3814,plain,
( ( $false
= ( intersect @ sK2 @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ ( sK4 @ sK3 @ sK1 @ sK2 ) @ sK1 ) )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( $false
= ( exists_in_world @ sK3 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f3813]) ).
thf(f3817,plain,
( ( $true = $false )
| ( $false
= ( intersect @ sK2 @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ ( sK4 @ sK3 @ sK1 @ sK2 ) @ sK1 ) )
| ( $false
= ( exists_in_world @ sK3 @ sK1 ) ) ),
inference(forward_demodulation,[],[f3814,f179]) ).
thf(f3818,plain,
( ( $false
= ( intersect @ sK2 @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ ( sK4 @ sK3 @ sK1 @ sK2 ) @ sK1 ) )
| ( $false
= ( exists_in_world @ sK3 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f3817]) ).
thf(f3821,plain,
( ( $true = $false )
| ( $false
= ( intersect @ sK2 @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ ( sK4 @ sK3 @ sK1 @ sK2 ) @ sK1 ) ) ),
inference(forward_demodulation,[],[f3818,f183]) ).
thf(f3822,plain,
( ( $false
= ( intersect @ sK2 @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ ( sK4 @ sK3 @ sK1 @ sK2 ) @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f3821]) ).
thf(f3824,definition,
( spl5_41
<=> ( $false
= ( exists_in_world @ ( sK4 @ sK3 @ sK1 @ sK2 ) @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_41])],[avatar_definition]) ).
thf(f3826,plain,
( ( $false
= ( exists_in_world @ ( sK4 @ sK3 @ sK1 @ sK2 ) @ sK1 ) )
| ~ spl5_41 ),
inference(avatar_component_clause,[],[f3824]) ).
thf(f3828,definition,
( spl5_42
<=> ( $false
= ( intersect @ sK2 @ sK3 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_42])],[avatar_definition]) ).
thf(f3830,plain,
( ( $false
= ( intersect @ sK2 @ sK3 @ sK1 ) )
| ~ spl5_42 ),
inference(avatar_component_clause,[],[f3828]) ).
thf(f3832,plain,
( spl5_41
| spl5_42 ),
inference(avatar_split_clause,[],[f3822,f3828,f3824]) ).
thf(f4347,plain,
( ( $true = $false )
| ( $true
= ( disjoint @ sK2 @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( $false
= ( exists_in_world @ sK3 @ sK1 ) )
| ~ spl5_41 ),
inference(constrained_superposition,[],[f3826,f2697]) ).
thf(f4350,plain,
( ( $true
= ( disjoint @ sK2 @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( $false
= ( exists_in_world @ sK3 @ sK1 ) )
| ~ spl5_41 ),
inference(trivial_inequality_removal,[],[f4347]) ).
thf(f4364,plain,
( ( $true = $false )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( $false
= ( exists_in_world @ sK3 @ sK1 ) )
| ~ spl5_41 ),
inference(forward_demodulation,[],[f4350,f184]) ).
thf(f4365,plain,
( ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ( $false
= ( exists_in_world @ sK3 @ sK1 ) )
| ~ spl5_41 ),
inference(trivial_inequality_removal,[],[f4364]) ).
thf(f4386,plain,
( ( $true = $false )
| ( $false
= ( exists_in_world @ sK3 @ sK1 ) )
| ~ spl5_41 ),
inference(forward_demodulation,[],[f4365,f179]) ).
thf(f4387,plain,
( ( $false
= ( exists_in_world @ sK3 @ sK1 ) )
| ~ spl5_41 ),
inference(trivial_inequality_removal,[],[f4386]) ).
thf(f4542,plain,
( ( $true = $false )
| ~ spl5_41 ),
inference(constrained_superposition,[],[f4387,f183]) ).
thf(f4549,plain,
( $false
| ~ spl5_41 ),
inference(trivial_inequality_removal,[],[f4542]) ).
thf(f4550,plain,
~ spl5_41,
inference(avatar_contradiction_clause,[],[f4549]) ).
thf(f4924,plain,
( ( $true = $false )
| ( $false
= ( exists_in_world @ sK3 @ sK1 ) )
| ( $true
= ( disjoint @ sK2 @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ~ spl5_42 ),
inference(constrained_superposition,[],[f223,f3830]) ).
thf(f4929,plain,
( ( $false
= ( exists_in_world @ sK3 @ sK1 ) )
| ( $true
= ( disjoint @ sK2 @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ~ spl5_42 ),
inference(trivial_inequality_removal,[],[f4924]) ).
thf(f4936,plain,
( ( $true = $false )
| ( $true
= ( disjoint @ sK2 @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ~ spl5_42 ),
inference(forward_demodulation,[],[f4929,f183]) ).
thf(f4937,plain,
( ( $true
= ( disjoint @ sK2 @ sK3 @ sK1 ) )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ~ spl5_42 ),
inference(trivial_inequality_removal,[],[f4936]) ).
thf(f4944,plain,
( ( $true = $false )
| ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ~ spl5_42 ),
inference(forward_demodulation,[],[f4937,f184]) ).
thf(f4945,plain,
( ( $false
= ( exists_in_world @ sK2 @ sK1 ) )
| ~ spl5_42 ),
inference(trivial_inequality_removal,[],[f4944]) ).
thf(f5155,plain,
( ( $true = $false )
| ~ spl5_42 ),
inference(constrained_superposition,[],[f4945,f179]) ).
thf(f5162,plain,
( $false
| ~ spl5_42 ),
inference(trivial_inequality_removal,[],[f5155]) ).
thf(f5163,plain,
~ spl5_42,
inference(avatar_contradiction_clause,[],[f5162]) ).
cnf(s291,plain,
( spl5_41
| spl5_42 ),
inference(sat_conversion,[],[f3832]) ).
cnf(s350,plain,
~ spl5_41,
inference(sat_conversion,[],[f4550]) ).
cnf(s357,plain,
~ spl5_42,
inference(sat_conversion,[],[f5163]) ).
cnf(s358,plain,
$false,
inference(rat,[],[s291,s357,s350]) ).
thf(f5164,plain,
$false,
inference(avatar_sat_refutation,[],[s358]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.11/0.27 % Computer : n020.cluster.edu
% 0.11/0.27 % Model : x86_64 x86_64
% 0.11/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.27 % Memory : 8046.5625MB
% 0.11/0.27 % OS : Linux 6.8.0-71-generic
% 0.11/0.27 % CPULimit : 300
% 0.11/0.27 % WCLimit : 300
% 0.11/0.27 % DateTime : Tue Sep 29 13:38:34 UTC 2026
% 0.23/0.28 % CPUTime :
% 0.23/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.23/0.32 Running first-order model finding
% 0.23/0.32 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.54/0.96 % (1059149)Will run a generic schedule for satisfiability detection.
% 3.54/0.96 % (1059154)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3873684019_2999 on theBenchmark for (2999ds/0Mi)
% 3.54/0.96 % Exception at run slice level
% 3.54/0.96 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.54/0.96 % (1059155)% WARNING: option uhcvi not known.
% 3.54/0.96 % (1059155)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=210289018:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 3.54/0.96 % (1059160)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=345680505:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 3.54/0.96 % (1059156)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=535227532:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 3.54/0.96 % (1059157)dis+10_1_sil=32000:sp=arity:random_seed=3470759630:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 3.54/0.96 % (1059159)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=614812442:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 3.54/0.96 % (1059155)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.54/0.96 % (1059158)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2505367291:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 3.54/0.96 % (1059155)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.54/0.96 % (1059158)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.54/0.96 % (1059162)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=95771543:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 3.54/0.96 % Exception at run slice level
% 3.54/0.96 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.54/0.96 % (1059170)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3761520067:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 3.54/0.96 % (1059157)Instruction limit reached!
% 3.54/0.96 % (1059157)------------------------------
% 3.54/0.96 % (1059157)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.54/0.96 % (1059157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/0.96 % (1059157)CaDiCaL version: 2.1.3
% 3.54/0.96 % (1059157)Termination reason: Instruction limit
% 3.54/0.96 % (1059157)Termination phase: Saturation
% 3.54/0.96 % (1059157)Time elapsed: 0.086 s
% 3.54/0.96 % (1059157)Peak memory usage: 12 MB
% 3.54/0.96 % (1059157)Instructions burned: 104 (million)
% 3.54/0.96 % (1059159)Instruction limit reached!
% 3.54/0.96 % (1059159)------------------------------
% 3.54/0.96 % (1059159)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.54/0.96 % (1059159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/0.96 % (1059159)CaDiCaL version: 2.1.3
% 3.54/0.96 % (1059159)Termination reason: Instruction limit
% 3.54/0.96 % (1059159)Termination phase: Saturation
% 3.54/0.96 % (1059159)Time elapsed: 0.106 s
% 3.54/0.96 % (1059159)Peak memory usage: 12 MB
% 3.54/0.96 % (1059159)Instructions burned: 132 (million)
% 3.54/0.96 % (1059158)Instruction limit reached!
% 3.54/0.96 % (1059158)------------------------------
% 3.54/0.96 % (1059158)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.54/0.96 % (1059158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/0.96 % (1059158)CaDiCaL version: 2.1.3
% 3.54/0.96 % (1059158)Termination reason: Instruction limit
% 3.54/0.96 % (1059158)Termination phase: Saturation
% 3.54/0.96 % (1059158)Time elapsed: 0.106 s
% 3.54/0.96 % (1059158)Peak memory usage: 12 MB
% 3.54/0.96 % (1059158)Instructions burned: 117 (million)
% 3.54/0.96 % (1059172)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3578260202:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 3.54/0.96 % (1059160)Instruction limit reached!
% 3.54/0.96 % (1059160)------------------------------
% 3.54/0.96 % (1059160)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.54/0.96 % (1059160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/0.96 % (1059160)CaDiCaL version: 2.1.3
% 3.54/0.96 % (1059160)Termination reason: Instruction limit
% 3.54/0.96 % (1059160)Termination phase: Saturation
% 3.54/0.96 % (1059160)Time elapsed: 0.126 s
% 3.54/0.96 % (1059160)Peak memory usage: 12 MB
% 3.54/0.96 % (1059160)Instructions burned: 160 (million)
% 3.54/0.96 % (1059170)Instruction limit reached!
% 3.54/0.96 % (1059170)------------------------------
% 3.54/0.96 % (1059170)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.54/0.96 % (1059170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/0.96 % (1059170)CaDiCaL version: 2.1.3
% 3.54/0.96 % (1059170)Termination reason: Instruction limit
% 3.54/0.96 % (1059170)Termination phase: Saturation
% 3.54/0.96 % (1059170)Time elapsed: 0.061 s
% 3.54/0.96 % (1059170)Peak memory usage: 12 MB
% 3.54/0.96 % (1059170)Instructions burned: 131 (million)
% 3.54/0.96 % (1059172)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.54/0.96 % (1059172)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.54/0.96 % (1059174)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1666517798:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 3.54/0.96 % (1059173)ott-21_1_sil=16000:fs=off:random_seed=313560197:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 3.54/0.96 % (1059176)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1169084247:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 3.54/0.96 % Exception at run slice level
% 3.54/0.96 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.54/0.96 % (1059177)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=3897448938:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 3.54/0.96 % (1059181)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=3296304472:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 3.54/0.96 % Exception at run slice level
% 3.54/0.96 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.54/0.96 % (1059184)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=859136543:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2997 on theBenchmark for (2997ds/692Mi)
% 3.54/0.96 % (1059184)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.54/0.96 % (1059173)Instruction limit reached!
% 3.54/0.96 % (1059173)------------------------------
% 3.54/0.96 % (1059173)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.54/0.96 % (1059173)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/0.96 % (1059173)CaDiCaL version: 2.1.3
% 3.54/0.96 % (1059173)Termination reason: Instruction limit
% 3.54/0.96 % (1059173)Termination phase: Saturation
% 3.54/0.96 % (1059173)Time elapsed: 0.147 s
% 3.54/0.96 % (1059173)Peak memory usage: 12 MB
% 3.54/0.96 % (1059173)Instructions burned: 180 (million)
% 3.54/0.96 % (1059186)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=427978327:i=879:kws=inv_precedence:fsr=off_2996 on theBenchmark for (2996ds/879Mi)
% 3.54/0.96 % (1059186)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.54/0.96 % (1059184)Instruction limit reached!
% 3.54/0.96 % (1059184)------------------------------
% 3.54/0.96 % (1059184)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.54/0.96 % (1059184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/0.96 % (1059184)CaDiCaL version: 2.1.3
% 3.54/0.96 % (1059184)Termination reason: Instruction limit
% 3.54/0.96 % (1059184)Termination phase: Saturation
% 3.54/0.96 % (1059184)Time elapsed: 0.264 s
% 3.54/0.96 % (1059184)Peak memory usage: 13 MB
% 3.54/0.96 % (1059184)Instructions burned: 694 (million)
% 3.54/0.96 % (1059188)fmb+10_1_sil=64000:random_seed=2942370679:i=22061:nm=2:gsp=on_2995 on theBenchmark for (2995ds/22061Mi)
% 3.54/0.96 % (1059188)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.54/0.96 % Exception at run slice level
% 3.54/0.96 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.54/0.96 % (1059190)fmb+10_1_sil=16000:sas=cadical:fmbss=20:random_seed=936378807:i=9515:nm=5_2994 on theBenchmark for (2994ds/9515Mi)
% 3.54/0.96 % Exception at run slice level
% 3.54/0.96 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.54/0.96 % (1059174)Instruction limit reached!
% 3.54/0.96 % (1059174)------------------------------
% 3.54/0.96 % (1059174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.54/0.96 % (1059174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/0.96 % (1059174)CaDiCaL version: 2.1.3
% 3.54/0.96 % (1059174)Termination reason: Instruction limit
% 3.54/0.96 % (1059174)Termination phase: Saturation
% 3.54/0.96 % (1059174)Time elapsed: 0.398 s
% 3.54/0.96 % (1059174)Peak memory usage: 12 MB
% 3.54/0.96 % (1059174)Instructions burned: 479 (million)
% 3.54/0.96 % (1059192)fmb+10_1_sil=64000:sas=cadical:fmbss=8:random_seed=1421346931:fmbsr=1.7:i=920_2994 on theBenchmark for (2994ds/920Mi)
% 3.54/0.96 % Exception at run slice level
% 3.54/0.96 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 3.54/0.96 % (1059193)dis-4_1_sil=16000:drc=ordering:sp=const_frequency:sac=on:newcnf=on:random_seed=2850513634:i=5131_2994 on theBenchmark for (2994ds/5131Mi)
% 3.54/0.96 % (1059193)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 3.54/0.96 % (1059195)ott+11_16_sil=32000:fde=unused:bsd=on:sas=cadical:sp=arity:spb=units:lsd=10:nwc=3:random_seed=260275502:i=1472:ins=7:fdi=8:gsp=on_2994 on theBenchmark for (2994ds/1472Mi)
% 3.54/0.96 % (1059186) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1059149-1059186"...
% 3.54/0.96 % (1059195)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.54/0.96 % (1059195)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 3.54/0.96 % (1059186)...printing done.
% 3.54/0.96 % (1059186)Refutation found. Thanks to Tanya!
% 3.54/0.96 % SZS status Theorem for theBenchmark
% 3.54/0.96 % SZS output start Proof for theBenchmark
% See solution above
% 3.54/0.96 % (1059186)------------------------------
% 3.54/0.96 % (1059186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 3.54/0.96 % (1059186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.54/0.96 % (1059186)CaDiCaL version: 2.1.3
% 3.54/0.96 % (1059186)Termination reason: Refutation
% 3.54/0.96 % (1059186)Time elapsed: 0.277 s
% 3.54/0.96 % (1059186)Peak memory usage: 14 MB
% 3.54/0.96 % (1059186)Instructions burned: 362 (million)
% 3.54/0.96 % (1059149)Success in time 0.629 s
% 3.54/0.96 % Vampire exiting
%------------------------------------------------------------------------------