%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET575^7 : 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 : n019.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 08:23:16 AM UTC 2026
% Result : Theorem 2.59s 0.68s
% Output : Refutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 12
% Syntax : Number of formulae : 105 ( 98 unt; 0 typ; 0 def)
% Number of atoms : 1605 ( 97 equ; 0 cnn)
% Maximal formula atoms : 26 ( 15 avg)
% Number of connectives : 4701 ( 661 ~; 495 |; 0 &;2954 @)
% ( 0 <=>; 138 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 163 ( 163 >; 0 *; 0 +; 0 <<)
% Number of symbols : 64 ( 60 usr; 8 con; 0-4 aty)
% ( 453 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 751 ( 724 ^; 27 !; 0 ?; 751 :)
% 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,
member: mu > mu > $i > $o ).
thf(func_def_37,type,
intersect: mu > mu > $i > $o ).
thf(func_def_38,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_39,type,
vIMP: $o > $o > $o ).
thf(func_def_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_44,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_45,type,
vNOT: $o > $o ).
thf(func_def_46,type,
vAND: $o > $o > $o ).
thf(func_def_47,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_51,type,
vOR: $o > $o > $o ).
thf(func_def_52,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_54,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_55,type,
db7:
!>[X0: $tType] : X0 ).
thf(func_def_58,type,
sK2: mu ).
thf(func_def_59,type,
sK3: $i > mu ).
thf(func_def_61,type,
sK5: 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,
( ( ^ [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,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mimplies) ).
thf(f15,axiom,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/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(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mreflexive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f34,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',a1) ).
thf(f37,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] :
( mand
@ ( mbox_s4
@ ( mimplies @ ( mbox_s4 @ ( intersect @ X0 @ X1 ) )
@ ( mexists_ind
@ ^ [X2: mu] : ( mand @ ( mbox_s4 @ ( member @ X2 @ X0 ) ) @ ( mbox_s4 @ ( member @ X2 @ X1 ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mexists_ind
@ ^ [X2: mu] : ( mand @ ( mbox_s4 @ ( member @ X2 @ X0 ) ) @ ( mbox_s4 @ ( member @ X2 @ X1 ) ) ) )
@ ( mbox_s4 @ ( intersect @ X0 @ X1 ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).
thf(f39,conjecture,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] :
( mbox_s4
@ ( mimplies @ ( mbox_s4 @ ( intersect @ X0 @ X1 ) )
@ ( mexists_ind
@ ^ [X2: mu] : ( mand @ ( mbox_s4 @ ( member @ X2 @ X0 ) ) @ ( mbox_s4 @ ( member @ X2 @ X1 ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th15) ).
thf(f40,negated_conjecture,
~ ( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] :
( mbox_s4
@ ( mimplies @ ( mbox_s4 @ ( intersect @ X0 @ X1 ) )
@ ( mexists_ind
@ ^ [X2: mu] : ( mand @ ( mbox_s4 @ ( member @ X2 @ X0 ) ) @ ( mbox_s4 @ ( member @ X2 @ X1 ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f39]) ).
thf(f41,plain,
( mforall_ind
= ( ^ [X0: mu > $i > $o,X1: $i] :
! [X2: mu] :
( ( exists_in_world @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f15]) ).
thf(f42,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f51,plain,
mreflexive @ rel_s4,
inference(rectify,[],[f34]) ).
thf(f52,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f51]) ).
thf(f65,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f66,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f67,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f66]) ).
thf(f76,plain,
~ ( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] :
( mbox_s4
@ ( mimplies @ ( mbox_s4 @ ( intersect @ X0 @ X1 ) )
@ ( mexists_ind
@ ^ [X2: mu] : ( mand @ ( mbox_s4 @ ( member @ X2 @ X0 ) ) @ ( mbox_s4 @ ( member @ X2 @ X1 ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f40]) ).
thf(f77,plain,
( $true
= ( ~ ( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Y1: mu] :
( mbox_s4
@ ( mimplies @ ( mbox_s4 @ ( intersect @ Y0 @ Y1 ) )
@ ( mexists_ind
@ ^ [Y2: mu] : ( mand @ ( mbox_s4 @ ( member @ Y2 @ Y0 ) ) @ ( mbox_s4 @ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f76]) ).
thf(f78,plain,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X0: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [X1: mu] :
( mand
@ ( mbox_s4
@ ( mimplies @ ( mbox_s4 @ ( intersect @ X0 @ X1 ) )
@ ( mexists_ind
@ ^ [X2: mu] : ( mand @ ( mbox_s4 @ ( member @ X2 @ X0 ) ) @ ( mbox_s4 @ ( member @ X2 @ X1 ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mexists_ind
@ ^ [X3: mu] : ( mand @ ( mbox_s4 @ ( member @ X3 @ X0 ) ) @ ( mbox_s4 @ ( member @ X3 @ X1 ) ) ) )
@ ( mbox_s4 @ ( intersect @ X0 @ X1 ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f79,plain,
( $true
= ( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Y1: mu] :
( mand
@ ( mbox_s4
@ ( mimplies @ ( mbox_s4 @ ( intersect @ Y0 @ Y1 ) )
@ ( mexists_ind
@ ^ [Y2: mu] : ( mand @ ( mbox_s4 @ ( member @ Y2 @ Y0 ) ) @ ( mbox_s4 @ ( member @ Y2 @ Y1 ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mexists_ind
@ ^ [Y2: mu] : ( mand @ ( mbox_s4 @ ( member @ Y2 @ Y0 ) ) @ ( mbox_s4 @ ( member @ Y2 @ Y1 ) ) ) )
@ ( mbox_s4 @ ( intersect @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f78]) ).
thf(f83,plain,
( mexists_ind
= ( ^ [X0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [X1: mu] : ( mnot @ ( X0 @ X1 ) ) ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f84,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f88,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f89,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f88]) ).
thf(f95,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f96,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f95]) ).
thf(f100,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f101,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f100]) ).
thf(f104,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f107,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f108,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f107]) ).
thf(f114,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f108]) ).
thf(f118,plain,
( mforall_ind
= ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f119,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f96]) ).
thf(f120,plain,
( $true
= ( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Y1: mu] :
( mand
@ ( mbox_s4
@ ( mimplies @ ( mbox_s4 @ ( intersect @ Y0 @ Y1 ) )
@ ( mexists_ind
@ ^ [Y2: mu] : ( mand @ ( mbox_s4 @ ( member @ Y2 @ Y0 ) ) @ ( mbox_s4 @ ( member @ Y2 @ Y1 ) ) ) ) ) )
@ ( mbox_s4
@ ( mimplies
@ ( mexists_ind
@ ^ [Y2: mu] : ( mand @ ( mbox_s4 @ ( member @ Y2 @ Y0 ) ) @ ( mbox_s4 @ ( member @ Y2 @ Y1 ) ) ) )
@ ( mbox_s4 @ ( intersect @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f79]) ).
thf(f121,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f89]) ).
thf(f122,plain,
( $true
= ( ~ ( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [Y0: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Y1: mu] :
( mbox_s4
@ ( mimplies @ ( mbox_s4 @ ( intersect @ Y0 @ Y1 ) )
@ ( mexists_ind
@ ^ [Y2: mu] : ( mand @ ( mbox_s4 @ ( member @ Y2 @ Y0 ) ) @ ( mbox_s4 @ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f77]) ).
thf(f131,plain,
( mexists_ind
= ( ^ [Y0: mu > $i > $o] :
( mnot
@ ( mforall_ind
@ ^ [Y1: mu] : ( mnot @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f132,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f104]) ).
thf(f135,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f101]) ).
thf(f144,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f52]) ).
thf(f146,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f65]) ).
thf(f147,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f151,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,[],[f146,f114,f147,f114,f114]) ).
thf(f152,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,[],[f132,f147,f114]) ).
thf(f157,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,[],[f131,f114,f118,f114]) ).
thf(f161,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( ^ [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] :
~ ( 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] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
@ ( ^ [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: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
@ ( 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 ) ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
@ ( member @ Y2 @ Y0 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
@ ( member @ Y2 @ Y1 ) ) ) ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
@ ( ^ [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 > $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 ) ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
@ ( member @ Y2 @ Y0 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
@ ( member @ Y2 @ Y1 ) ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
@ ( intersect @ Y0 @ Y1 ) ) ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f120,f135,f121,f118,f121,f118,f151,f121,f152,f121,f157,f151,f121,f121,f121,f152,f157,f151,f121,f121,f121]) ).
thf(f162,plain,
( ( ~ ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: mu > $i > $o,Y1: $i] :
( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: mu] :
( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: mu > $i > $o,Y2: $i] :
( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: mu] :
( ^ [Y2: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
@ ( ^ [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: $i > $o,Y3: $i] :
( !! @ $i
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
@ ( 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 ) ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
@ ( member @ Y2 @ Y0 ) )
@ ( ^ [Y3: $i > $o,Y4: $i] :
( !! @ $i
@ ^ [Y5: $i] :
( ( Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
@ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f122,f135,f121,f118,f121,f118,f121,f152,f121,f157,f151,f121,f121]) ).
thf(f164,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s4 )
= $true ),
inference(definition_unfolding,[],[f144,f119]) ).
thf(f167,plain,
( ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) )
= $true ),
inference(beta-eta_normalization,[],[f164]) ).
thf(f168,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( intersect @ Y2 @ Y4 @ Y6 )
| ~ ( rel_s4 @ Y5 @ Y6 ) ) )
| ~ ( !! @ mu
@ ^ [Y6: mu] :
( ( exists_in_world @ Y6 @ Y5 )
=> ~ ~ ( ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( member @ Y6 @ Y2 @ Y7 )
| ~ ( rel_s4 @ Y5 @ Y7 ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( member @ Y6 @ Y4 @ Y7 )
| ~ ( rel_s4 @ Y5 @ Y7 ) ) ) ) ) )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f169,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( intersect @ Y2 @ Y4 @ Y6 )
| ~ ( rel_s4 @ Y5 @ Y6 ) ) )
| ~ ( !! @ mu
@ ^ [Y6: mu] :
( ( exists_in_world @ Y6 @ Y5 )
=> ( ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( member @ Y6 @ Y2 @ Y7 )
| ~ ( rel_s4 @ Y5 @ Y7 ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( member @ Y6 @ Y4 @ Y7 )
| ~ ( rel_s4 @ Y5 @ Y7 ) ) ) ) ) )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f168]) ).
thf(f170,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( intersect @ Y2 @ Y4 @ Y6 )
| ~ ( rel_s4 @ Y5 @ Y6 ) ) )
| ~ ( !! @ mu
@ ^ [Y6: mu] :
( ( exists_in_world @ Y6 @ Y5 )
=> ~ ~ ( ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( member @ Y6 @ Y2 @ Y7 )
| ~ ( rel_s4 @ Y5 @ Y7 ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( member @ Y6 @ Y4 @ Y7 )
| ~ ( rel_s4 @ Y5 @ Y7 ) ) ) ) ) )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ~ ( !! @ mu
@ ^ [Y6: mu] :
( ( exists_in_world @ Y6 @ Y5 )
=> ~ ~ ( ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( member @ Y6 @ Y2 @ Y7 )
| ~ ( rel_s4 @ Y5 @ Y7 ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( member @ Y6 @ Y4 @ Y7 )
| ~ ( rel_s4 @ Y5 @ Y7 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y6: $i] :
( ( intersect @ Y2 @ Y4 @ Y6 )
| ~ ( rel_s4 @ Y5 @ Y6 ) ) )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f171,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( intersect @ Y2 @ Y4 @ Y6 )
| ~ ( rel_s4 @ Y5 @ Y6 ) ) )
| ~ ( !! @ mu
@ ^ [Y6: mu] :
( ( exists_in_world @ Y6 @ Y5 )
=> ~ ~ ( ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( member @ Y6 @ Y2 @ Y7 )
| ~ ( rel_s4 @ Y5 @ Y7 ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( member @ Y6 @ Y4 @ Y7 )
| ~ ( rel_s4 @ Y5 @ Y7 ) ) ) ) ) )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( !! @ mu
@ ^ [Y6: mu] :
( ( exists_in_world @ Y6 @ Y5 )
=> ~ ~ ( ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( member @ Y6 @ Y2 @ Y7 )
| ~ ( rel_s4 @ Y5 @ Y7 ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( member @ Y6 @ Y4 @ Y7 )
| ~ ( rel_s4 @ Y5 @ Y7 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y6: $i] :
( ( intersect @ Y2 @ Y4 @ Y6 )
| ~ ( rel_s4 @ Y5 @ Y6 ) ) )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) )
= $true ),
inference(boolean_simplification,[],[f170]) ).
thf(f172,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( intersect @ Y2 @ Y4 @ Y6 )
| ~ ( rel_s4 @ Y5 @ Y6 ) ) )
| ~ ( !! @ mu
@ ^ [Y6: mu] :
( ( exists_in_world @ Y6 @ Y5 )
=> ( ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( member @ Y6 @ Y2 @ Y7 )
| ~ ( rel_s4 @ Y5 @ Y7 ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( member @ Y6 @ Y4 @ Y7 )
| ~ ( rel_s4 @ Y5 @ Y7 ) ) ) ) ) )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( !! @ mu
@ ^ [Y6: mu] :
( ( exists_in_world @ Y6 @ Y5 )
=> ( ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( member @ Y6 @ Y2 @ Y7 )
| ~ ( rel_s4 @ Y5 @ Y7 ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( member @ Y6 @ Y4 @ Y7 )
| ~ ( rel_s4 @ Y5 @ Y7 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y6: $i] :
( ( intersect @ Y2 @ Y4 @ Y6 )
| ~ ( rel_s4 @ Y5 @ Y6 ) ) )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) )
= $true ),
inference(boolean_simplification,[],[f171]) ).
thf(f173,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( intersect @ Y2 @ Y4 @ Y6 )
| ~ ( rel_s4 @ Y5 @ Y6 ) ) )
| ~ ( !! @ mu
@ ^ [Y6: mu] :
( ( exists_in_world @ Y6 @ Y5 )
=> ( ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( member @ Y6 @ Y2 @ Y7 )
| ~ ( rel_s4 @ Y5 @ Y7 ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( member @ Y6 @ Y4 @ Y7 )
| ~ ( rel_s4 @ Y5 @ Y7 ) ) ) ) ) )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f174,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( intersect @ Y2 @ Y4 @ Y6 )
| ~ ( rel_s4 @ Y5 @ Y6 ) ) )
| ~ ( !! @ mu
@ ^ [Y6: mu] :
( ( exists_in_world @ Y6 @ Y5 )
=> ( ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( member @ Y6 @ Y2 @ Y7 )
| ~ ( rel_s4 @ Y5 @ Y7 ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( member @ Y6 @ Y4 @ Y7 )
| ~ ( rel_s4 @ Y5 @ Y7 ) ) ) ) ) )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f173]) ).
thf(f176,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( intersect @ Y1 @ Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ~ ( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y4 )
=> ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( member @ Y5 @ Y1 @ Y6 )
| ~ ( rel_s4 @ Y4 @ Y6 ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( member @ Y5 @ Y3 @ Y6 )
| ~ ( rel_s4 @ Y4 @ Y6 ) ) ) ) ) )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f178,plain,
( ( ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( intersect @ Y1 @ Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ~ ( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y4 )
=> ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( member @ Y5 @ Y1 @ Y6 )
| ~ ( rel_s4 @ Y4 @ Y6 ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( member @ Y5 @ Y3 @ Y6 )
| ~ ( rel_s4 @ Y4 @ Y6 ) ) ) ) ) )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f176]) ).
thf(f179,plain,
( $false
= ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( intersect @ Y0 @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( member @ Y4 @ Y0 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( member @ Y4 @ Y2 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y1 ) ) ) ) )
| ~ ( rel_s4 @ sK0 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f178]) ).
thf(f181,plain,
( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( intersect @ Y0 @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( member @ Y4 @ Y0 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( member @ Y4 @ Y2 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y1 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f185,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f167]) ).
thf(f186,plain,
! [X1: $i] :
( ( rel_s4 @ X1 @ X1 )
= $true ),
inference(beta-eta_normalization,[],[f185]) ).
thf(f192,plain,
( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK1 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( intersect @ Y0 @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( member @ Y4 @ Y0 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( member @ Y4 @ Y2 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y1 ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f181]) ).
thf(f193,plain,
( ( ( exists_in_world @ sK2 @ sK1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( intersect @ sK2 @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( member @ Y3 @ sK2 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( member @ Y3 @ Y1 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f192]) ).
thf(f196,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( intersect @ sK2 @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( member @ Y3 @ sK2 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( member @ Y3 @ Y1 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f193]) ).
thf(f197,plain,
( $true
= ( exists_in_world @ sK2 @ sK1 ) ),
inference(imp_proxy_clausification,[],[f193]) ).
thf(f202,plain,
( ( ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( intersect @ sK2 @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( member @ Y3 @ sK2 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( member @ Y3 @ Y1 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ sK4 )
= $false ),
inference(sigma_proxy_clausification,[],[f196]) ).
thf(f203,plain,
( $false
= ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( intersect @ sK2 @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( member @ Y2 @ sK2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( member @ Y2 @ Y0 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) ) )
| ~ ( rel_s4 @ sK4 @ Y1 ) ) ) ) )
| ~ ( rel_s4 @ sK1 @ sK4 ) ) ),
inference(beta-eta_normalization,[],[f202]) ).
thf(f206,plain,
( ( ~ ( rel_s4 @ sK1 @ sK4 ) )
= $false ),
inference(or_proxy_clausification,[],[f203]) ).
thf(f207,plain,
( $false
= ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( intersect @ sK2 @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( member @ Y2 @ sK2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( member @ Y2 @ Y0 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) ) )
| ~ ( rel_s4 @ sK4 @ Y1 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f203]) ).
thf(f210,plain,
( $true
= ( rel_s4 @ sK1 @ sK4 ) ),
inference(not_proxy_clausification,[],[f206]) ).
thf(f347,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( intersect @ Y2 @ Y4 @ Y6 )
| ~ ( rel_s4 @ Y5 @ Y6 ) ) )
| ~ ( !! @ mu
@ ^ [Y6: mu] :
( ( exists_in_world @ Y6 @ Y5 )
=> ( ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( member @ Y6 @ Y2 @ Y7 )
| ~ ( rel_s4 @ Y5 @ Y7 ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( member @ Y6 @ Y4 @ Y7 )
| ~ ( rel_s4 @ Y5 @ Y7 ) ) ) ) ) )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( !! @ mu
@ ^ [Y6: mu] :
( ( exists_in_world @ Y6 @ Y5 )
=> ( ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( member @ Y6 @ Y2 @ Y7 )
| ~ ( rel_s4 @ Y5 @ Y7 ) ) )
| ~ ( !! @ $i
@ ^ [Y7: $i] :
( ( member @ Y6 @ Y4 @ Y7 )
| ~ ( rel_s4 @ Y5 @ Y7 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y6: $i] :
( ( intersect @ Y2 @ Y4 @ Y6 )
| ~ ( rel_s4 @ Y5 @ Y6 ) ) )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f172]) ).
thf(f348,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( intersect @ Y1 @ Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ~ ( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y4 )
=> ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( member @ Y5 @ Y1 @ Y6 )
| ~ ( rel_s4 @ Y4 @ Y6 ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( member @ Y5 @ Y3 @ Y6 )
| ~ ( rel_s4 @ Y4 @ Y6 ) ) ) ) ) )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y4 )
=> ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( member @ Y5 @ Y1 @ Y6 )
| ~ ( rel_s4 @ Y4 @ Y6 ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( member @ Y5 @ Y3 @ Y6 )
| ~ ( rel_s4 @ Y4 @ Y6 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y5: $i] :
( ( intersect @ Y1 @ Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f347]) ).
thf(f355,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( intersect @ Y1 @ Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ~ ( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y4 )
=> ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( member @ Y5 @ Y1 @ Y6 )
| ~ ( rel_s4 @ Y4 @ Y6 ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( member @ Y5 @ Y3 @ Y6 )
| ~ ( rel_s4 @ Y4 @ Y6 ) ) ) ) ) )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( !! @ mu
@ ^ [Y5: mu] :
( ( exists_in_world @ Y5 @ Y4 )
=> ( ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( member @ Y5 @ Y1 @ Y6 )
| ~ ( rel_s4 @ Y4 @ Y6 ) ) )
| ~ ( !! @ $i
@ ^ [Y6: $i] :
( ( member @ Y5 @ Y3 @ Y6 )
| ~ ( rel_s4 @ Y4 @ Y6 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y5: $i] :
( ( intersect @ Y1 @ Y3 @ Y5 )
| ~ ( rel_s4 @ Y4 @ Y5 ) ) )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f348]) ).
thf(f356,plain,
! [X2: $i,X1: $i] :
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X2 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( intersect @ Y0 @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( member @ Y4 @ Y0 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( member @ Y4 @ Y2 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( member @ Y4 @ Y0 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( member @ Y4 @ Y2 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( intersect @ Y0 @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) ) )
| ~ ( rel_s4 @ X2 @ Y1 ) ) ) ) )
| ~ ( rel_s4 @ X1 @ X2 ) )
= $true ),
inference(beta-eta_normalization,[],[f355]) ).
thf(f365,plain,
! [X0: $i] :
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( intersect @ Y0 @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( member @ Y4 @ Y0 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( member @ Y4 @ Y2 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( member @ Y4 @ Y0 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( member @ Y4 @ Y2 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( intersect @ Y0 @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) ) )
| ~ ( rel_s4 @ X0 @ Y1 ) ) ) ) )
| ~ $true )
= $true ),
inference(superposition,[],[f356,f186]) ).
thf(f372,plain,
! [X0: $i] :
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( intersect @ Y0 @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( member @ Y4 @ Y0 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( member @ Y4 @ Y2 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( member @ Y4 @ Y0 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( member @ Y4 @ Y2 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( intersect @ Y0 @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) ) )
| ~ ( rel_s4 @ X0 @ Y1 ) ) ) ) )
| $false )
= $true ),
inference(boolean_simplification,[],[f365]) ).
thf(f373,plain,
! [X0: $i] :
( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( intersect @ Y0 @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( member @ Y4 @ Y0 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( member @ Y4 @ Y2 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( member @ Y4 @ Y0 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( member @ Y4 @ Y2 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( intersect @ Y0 @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) ) )
| ~ ( rel_s4 @ X0 @ Y1 ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f372]) ).
thf(f448,plain,
! [X0: $i,X1: mu] :
( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( intersect @ Y0 @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( member @ Y4 @ Y0 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( member @ Y4 @ Y2 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( !! @ mu
@ ^ [Y4: mu] :
( ( exists_in_world @ Y4 @ Y3 )
=> ( ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( member @ Y4 @ Y0 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) )
| ~ ( !! @ $i
@ ^ [Y5: $i] :
( ( member @ Y4 @ Y2 @ Y5 )
| ~ ( rel_s4 @ Y3 @ Y5 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y4: $i] :
( ( intersect @ Y0 @ Y2 @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) ) )
| ~ ( rel_s4 @ X0 @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f373]) ).
thf(f449,plain,
! [X0: $i,X1: mu] :
( ( ( exists_in_world @ X1 @ X0 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( intersect @ X1 @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( member @ Y3 @ X1 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( member @ Y3 @ Y1 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( member @ Y3 @ X1 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( member @ Y3 @ Y1 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( intersect @ X1 @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) ) )
| ~ ( rel_s4 @ X0 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f448]) ).
thf(f460,plain,
( ( $true
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( intersect @ sK2 @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( member @ Y3 @ sK2 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( member @ Y3 @ Y1 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( member @ Y3 @ sK2 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( member @ Y3 @ Y1 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( intersect @ sK2 @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) )
= $true ),
inference(superposition,[],[f449,f197]) ).
thf(f466,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( intersect @ sK2 @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( member @ Y3 @ sK2 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( member @ Y3 @ Y1 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( member @ Y3 @ sK2 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( member @ Y3 @ Y1 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( intersect @ sK2 @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
= $true ),
inference(boolean_simplification,[],[f460]) ).
thf(f581,plain,
( $false
= ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( intersect @ sK2 @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( member @ Y2 @ sK2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( member @ Y2 @ Y0 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) ) )
| ~ ( rel_s4 @ sK4 @ Y1 ) ) ) )
@ sK5 ) ),
inference(sigma_proxy_clausification,[],[f207]) ).
thf(f582,plain,
( $false
= ( ( exists_in_world @ sK5 @ sK4 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( intersect @ sK2 @ sK5 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y1 @ sK2 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y1 @ sK5 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) ) )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f581]) ).
thf(f593,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( intersect @ sK2 @ sK5 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y1 @ sK2 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y1 @ sK5 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) ) )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) ) ),
inference(imp_proxy_clausification,[],[f582]) ).
thf(f594,plain,
( $true
= ( exists_in_world @ sK5 @ sK4 ) ),
inference(imp_proxy_clausification,[],[f582]) ).
thf(f626,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( intersect @ sK2 @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( member @ Y3 @ sK2 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( member @ Y3 @ Y1 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( !! @ mu
@ ^ [Y3: mu] :
( ( exists_in_world @ Y3 @ Y2 )
=> ( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( member @ Y3 @ sK2 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ( member @ Y3 @ Y1 @ Y4 )
| ~ ( rel_s4 @ Y2 @ Y4 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y3: $i] :
( ( intersect @ sK2 @ Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) ) )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f466]) ).
thf(f627,plain,
! [X1: $i] :
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ X1 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( intersect @ sK2 @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( member @ Y2 @ sK2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( member @ Y2 @ Y0 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) ) )
| ~ ( rel_s4 @ X1 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( member @ Y2 @ sK2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( member @ Y2 @ Y0 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( intersect @ sK2 @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ X1 @ Y1 ) ) ) ) ) )
| ~ ( rel_s4 @ sK1 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f626]) ).
thf(f634,plain,
( $true
= ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( intersect @ sK2 @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( member @ Y2 @ sK2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( member @ Y2 @ Y0 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) ) )
| ~ ( rel_s4 @ sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( member @ Y2 @ sK2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( member @ Y2 @ Y0 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( intersect @ sK2 @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ sK4 @ Y1 ) ) ) ) ) )
| ~ $true ) ),
inference(superposition,[],[f627,f210]) ).
thf(f636,plain,
( ( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( intersect @ sK2 @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( member @ Y2 @ sK2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( member @ Y2 @ Y0 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) ) )
| ~ ( rel_s4 @ sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( member @ Y2 @ sK2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( member @ Y2 @ Y0 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( intersect @ sK2 @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ sK4 @ Y1 ) ) ) ) ) )
| $false )
= $true ),
inference(boolean_simplification,[],[f634]) ).
thf(f637,plain,
( ( !! @ mu
@ ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( intersect @ sK2 @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( member @ Y2 @ sK2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( member @ Y2 @ Y0 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) ) )
| ~ ( rel_s4 @ sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( member @ Y2 @ sK2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( member @ Y2 @ Y0 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( intersect @ sK2 @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ sK4 @ Y1 ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f636]) ).
thf(f1271,plain,
! [X1: mu] :
( ( ^ [Y0: mu] :
( ( exists_in_world @ Y0 @ sK4 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( intersect @ sK2 @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( member @ Y2 @ sK2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( member @ Y2 @ Y0 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) ) )
| ~ ( rel_s4 @ sK4 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ mu
@ ^ [Y2: mu] :
( ( exists_in_world @ Y2 @ Y1 )
=> ( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( member @ Y2 @ sK2 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ( member @ Y2 @ Y0 @ Y3 )
| ~ ( rel_s4 @ Y1 @ Y3 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( intersect @ sK2 @ Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ sK4 @ Y1 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f637]) ).
thf(f1272,plain,
! [X1: mu] :
( ( ( exists_in_world @ X1 @ sK4 )
=> ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( intersect @ sK2 @ X1 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y1 @ sK2 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y1 @ X1 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) ) )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y1 @ sK2 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y1 @ X1 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( intersect @ sK2 @ X1 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f1271]) ).
thf(f1293,plain,
( ( $true
=> ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( intersect @ sK2 @ sK5 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y1 @ sK2 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y1 @ sK5 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) ) )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y1 @ sK2 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y1 @ sK5 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( intersect @ sK2 @ sK5 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) ) ) )
= $true ),
inference(superposition,[],[f1272,f594]) ).
thf(f1298,plain,
( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( intersect @ sK2 @ sK5 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y1 @ sK2 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y1 @ sK5 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) ) )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y1 @ sK2 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y1 @ sK5 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( intersect @ sK2 @ sK5 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f1293]) ).
thf(f1301,plain,
( $true
= ( ~ ( ~ $false
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y1 @ sK2 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y1 @ sK5 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( intersect @ sK2 @ sK5 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) ) ) ) ),
inference(forward_demodulation,[],[f1298,f593]) ).
thf(f1302,plain,
( ( ~ ( $true
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ mu
@ ^ [Y1: mu] :
( ( exists_in_world @ Y1 @ Y0 )
=> ( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y1 @ sK2 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y1 @ sK5 @ Y2 )
| ~ ( rel_s4 @ Y0 @ Y2 ) ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( intersect @ sK2 @ sK5 @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f1301]) ).
thf(f1303,plain,
( ( ~ $true ) = $true ),
inference(boolean_simplification,[],[f1302]) ).
thf(f1304,plain,
$false = $true,
inference(boolean_simplification,[],[f1303]) ).
thf(f1305,plain,
$false,
inference(trivial_inequality_removal,[],[f1304]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET575^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n019.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:37:48 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.23 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
% 0.21/0.37 % (772063)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.37 % (772074)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=598980012:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.37 % (772080)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.37 % (772080)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
% 0.21/0.37 % (772076)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=490382159:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.37 % (772078)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1266234390:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.37 % (772075)lrs+10_16_si=on:nwc=1.5:random_seed=2497579207:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.37 % (772079)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2285129298:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.37 % (772077)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=599543823: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)
% 0.21/0.37 % (772080)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=138805389:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.37 % (772076)Instruction limit reached!
% 0.21/0.37 % (772076)------------------------------
% 0.21/0.37 % (772076)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (772076)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (772076)CaDiCaL version: 2.1.3
% 0.21/0.37 % (772076)Termination reason: Instruction limit
% 0.21/0.37 % (772076)Termination phase: Property scanning
% 0.21/0.37 % (772076)Time elapsed: 0.002 s
% 0.21/0.37 % (772076)Peak memory usage: 10 MB
% 0.21/0.37 % (772076)Instructions burned: 4 (million)
% 0.21/0.37 % (772075)Instruction limit reached!
% 0.21/0.37 % (772075)------------------------------
% 0.21/0.37 % (772075)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (772075)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (772075)CaDiCaL version: 2.1.3
% 0.21/0.37 % (772075)Termination reason: Instruction limit
% 0.21/0.37 % (772075)Termination phase: Saturation
% 0.21/0.37 % (772075)Time elapsed: 0.008 s
% 0.21/0.37 % (772075)Peak memory usage: 11 MB
% 0.21/0.37 % (772075)Instructions burned: 18 (million)
% 0.21/0.37 % (772078)Instruction limit reached!
% 0.21/0.37 % (772078)------------------------------
% 0.21/0.37 % (772078)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (772078)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (772078)CaDiCaL version: 2.1.3
% 0.21/0.37 % (772078)Termination reason: Instruction limit
% 0.21/0.37 % (772078)Termination phase: Saturation
% 0.21/0.37 % (772078)Time elapsed: 0.014 s
% 0.21/0.37 % (772078)Peak memory usage: 12 MB
% 0.21/0.37 % (772078)Instructions burned: 24 (million)
% 0.21/0.37 % (772074)Instruction limit reached!
% 0.21/0.37 % (772074)------------------------------
% 0.21/0.37 % (772074)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (772074)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.37 % (772074)CaDiCaL version: 2.1.3
% 0.21/0.37 % (772074)Termination reason: Instruction limit
% 0.21/0.37 % (772074)Termination phase: Saturation
% 0.21/0.37 % (772074)Time elapsed: 0.023 s
% 0.21/0.37 % (772074)Peak memory usage: 12 MB
% 0.21/0.37 % (772074)Instructions burned: 88 (million)
% 0.21/0.37 % (772096)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3113764523:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.37 % (772096)Instruction limit reached!
% 0.21/0.37 % (772096)------------------------------
% 0.21/0.37 % (772096)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.37 % (772096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.40 % (772096)CaDiCaL version: 2.1.3
% 0.83/0.40 % (772096)Termination reason: Instruction limit
% 0.83/0.40 % (772096)Termination phase: Property scanning
% 0.83/0.40 % (772096)Time elapsed: 0.002 s
% 0.83/0.40 % (772096)Peak memory usage: 10 MB
% 0.83/0.40 % (772096)Instructions burned: 4 (million)
% 0.83/0.40 % (772101)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=578977112:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.83/0.40 % (772104)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.83/0.40 % (772101)Instruction limit reached!
% 0.83/0.40 % (772101)------------------------------
% 0.83/0.40 % (772101)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.40 % (772101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.40 % (772101)CaDiCaL version: 2.1.3
% 0.83/0.40 % (772101)Termination reason: Instruction limit
% 0.83/0.40 % (772101)Termination phase: Property scanning
% 0.83/0.40 % (772101)Time elapsed: 0.003 s
% 0.83/0.40 % (772101)Peak memory usage: 10 MB
% 0.83/0.40 % (772101)Instructions burned: 6 (million)
% 0.83/0.40 % (772104)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3678516353:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.83/0.40 % (772106)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3024971132:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.83/0.40 % (772079)Instruction limit reached!
% 0.83/0.40 % (772079)------------------------------
% 0.83/0.40 % (772079)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.40 % (772079)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.40 % (772079)CaDiCaL version: 2.1.3
% 0.83/0.40 % (772079)Termination reason: Instruction limit
% 0.83/0.40 % (772079)Termination phase: Saturation
% 0.83/0.40 % (772079)Time elapsed: 0.036 s
% 0.83/0.40 % (772079)Peak memory usage: 12 MB
% 0.83/0.40 % (772079)Instructions burned: 77 (million)
% 0.83/0.40 % (772104)Instruction limit reached!
% 0.83/0.40 % (772104)------------------------------
% 0.83/0.40 % (772104)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.40 % (772104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.40 % (772104)CaDiCaL version: 2.1.3
% 0.83/0.40 % (772104)Termination reason: Instruction limit
% 0.83/0.40 % (772104)Termination phase: Property scanning
% 0.83/0.40 % (772104)Time elapsed: 0.004 s
% 0.83/0.40 % (772104)Peak memory usage: 10 MB
% 0.83/0.40 % (772104)Instructions burned: 9 (million)
% 0.83/0.40 % (772111)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
% 0.83/0.40 % (772111)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.83/0.40 % (772106)Instruction limit reached!
% 0.83/0.40 % (772106)------------------------------
% 0.83/0.40 % (772106)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.40 % (772106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.40 % (772106)CaDiCaL version: 2.1.3
% 0.83/0.40 % (772106)Termination reason: Instruction limit
% 0.83/0.40 % (772106)Termination phase: Saturation
% 0.83/0.40 % (772106)Time elapsed: 0.006 s
% 0.83/0.40 % (772106)Peak memory usage: 11 MB
% 0.83/0.40 % (772106)Instructions burned: 13 (million)
% 0.83/0.40 % (772111)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=4232942238:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.83/0.40 % (772117)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=322476140:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.83/0.40 % (772124)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.83/0.40 % (772111)Instruction limit reached!
% 0.83/0.40 % (772111)------------------------------
% 0.83/0.43 % (772111)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.43 % (772111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.43 % (772111)CaDiCaL version: 2.1.3
% 0.83/0.43 % (772111)Termination reason: Instruction limit
% 0.83/0.43 % (772111)Termination phase: Saturation
% 0.83/0.43 % (772111)Time elapsed: 0.011 s
% 0.83/0.43 % (772111)Peak memory usage: 12 MB
% 0.83/0.43 % (772111)Instructions burned: 31 (million)
% 0.83/0.43 % (772123)lrs+10_1_si=on:cs=on:random_seed=1487868021:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.83/0.43 % (772124)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=4092782341:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.83/0.43 % (772124)Instruction limit reached!
% 0.83/0.43 % (772124)------------------------------
% 0.83/0.43 % (772124)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.43 % (772124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.43 % (772124)CaDiCaL version: 2.1.3
% 0.83/0.43 % (772124)Termination reason: Instruction limit
% 0.83/0.43 % (772124)Termination phase: Property scanning
% 0.83/0.43 % (772124)Time elapsed: 0.002 s
% 0.83/0.43 % (772124)Peak memory usage: 9 MB
% 0.83/0.43 % (772124)Instructions burned: 4 (million)
% 0.83/0.43 % (772123)Instruction limit reached!
% 0.83/0.43 % (772123)------------------------------
% 0.83/0.43 % (772123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.43 % (772123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.43 % (772123)CaDiCaL version: 2.1.3
% 0.83/0.43 % (772123)Termination reason: Instruction limit
% 0.83/0.43 % (772123)Termination phase: Property scanning
% 0.83/0.43 % (772123)Time elapsed: 0.004 s
% 0.83/0.43 % (772123)Peak memory usage: 10 MB
% 0.83/0.43 % (772123)Instructions burned: 9 (million)
% 0.83/0.43 % (772127)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=416085452:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.83/0.43 % (772127)Refutation not found, incomplete strategy
% 0.83/0.43 % (772127)------------------------------
% 0.83/0.43 % (772127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.43 % (772127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.43 % (772127)CaDiCaL version: 2.1.3
% 0.83/0.43 % (772127)Termination reason: Refutation not found, incomplete strategy
% 0.83/0.43 % (772127)Time elapsed: 0.010 s
% 0.83/0.43 % (772127)Peak memory usage: 12 MB
% 0.83/0.43 % (772127)Instructions burned: 21 (million)
% 0.83/0.43 % (772146)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3689854990:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.83/0.43 % (772127)------------------------------
% 0.83/0.43 % (772127)------------------------------
% 0.83/0.43 % (772146)Instruction limit reached!
% 0.83/0.43 % (772146)------------------------------
% 0.83/0.43 % (772146)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.43 % (772146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.43 % (772146)CaDiCaL version: 2.1.3
% 0.83/0.43 % (772146)Termination reason: Instruction limit
% 0.83/0.43 % (772146)Termination phase: Saturation
% 0.83/0.43 % (772146)Time elapsed: 0.004 s
% 0.83/0.43 % (772146)Peak memory usage: 12 MB
% 0.83/0.43 % (772146)Instructions burned: 16 (million)
% 0.83/0.43 % (772144)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=3135897932:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.83/0.43 % (772080)Instruction limit reached!
% 0.83/0.43 % (772080)------------------------------
% 0.83/0.43 % (772080)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.43 % (772080)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.43 % (772080)CaDiCaL version: 2.1.3
% 0.83/0.43 % (772080)Termination reason: Instruction limit
% 0.83/0.43 % (772080)Termination phase: Saturation
% 0.83/0.43 % (772080)Time elapsed: 0.077 s
% 0.83/0.43 % (772080)Peak memory usage: 12 MB
% 0.83/0.43 % (772080)Instructions burned: 164 (million)
% 0.83/0.43 % (772136)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=4006950256:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 1.62/0.48 % (772154)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2413971841:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.62/0.48 % (772154)Instruction limit reached!
% 1.62/0.48 % (772154)------------------------------
% 1.62/0.48 % (772154)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.48 % (772154)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.48 % (772154)CaDiCaL version: 2.1.3
% 1.62/0.48 % (772154)Termination reason: Instruction limit
% 1.62/0.48 % (772154)Termination phase: Saturation
% 1.62/0.48 % (772154)Time elapsed: 0.004 s
% 1.62/0.48 % (772154)Peak memory usage: 12 MB
% 1.62/0.48 % (772154)Instructions burned: 18 (million)
% 1.62/0.48 % (772144)Instruction limit reached!
% 1.62/0.48 % (772144)------------------------------
% 1.62/0.48 % (772144)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.48 % (772144)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.48 % (772144)CaDiCaL version: 2.1.3
% 1.62/0.48 % (772144)Termination reason: Instruction limit
% 1.62/0.48 % (772144)Termination phase: Saturation
% 1.62/0.48 % (772144)Time elapsed: 0.015 s
% 1.62/0.48 % (772153)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=90279615:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 1.62/0.48 % (772144)Peak memory usage: 12 MB
% 1.62/0.48 % (772144)Instructions burned: 26 (million)
% 1.62/0.48 % (772117)Instruction limit reached!
% 1.62/0.48 % (772117)------------------------------
% 1.62/0.48 % (772117)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.48 % (772117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.48 % (772117)CaDiCaL version: 2.1.3
% 1.62/0.48 % (772117)Termination reason: Instruction limit
% 1.62/0.48 % (772117)Termination phase: Saturation
% 1.62/0.48 % (772117)Time elapsed: 0.044 s
% 1.62/0.48 % (772117)Peak memory usage: 12 MB
% 1.62/0.48 % (772117)Instructions burned: 86 (million)
% 1.62/0.48 % (772136)Refutation not found, incomplete strategy
% 1.62/0.48 % (772136)------------------------------
% 1.62/0.48 % (772136)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.48 % (772136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.48 % (772136)CaDiCaL version: 2.1.3
% 1.62/0.48 % (772136)Termination reason: Refutation not found, incomplete strategy
% 1.62/0.48 % (772136)Time elapsed: 0.015 s
% 1.62/0.48 % (772136)Peak memory usage: 12 MB
% 1.62/0.48 % (772136)Instructions burned: 20 (million)
% 1.62/0.48 % (772157)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=588037868:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.62/0.48 % (772136)------------------------------
% 1.62/0.48 % (772136)------------------------------
% 1.62/0.48 % (772157)Instruction limit reached!
% 1.62/0.48 % (772157)------------------------------
% 1.62/0.48 % (772157)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.48 % (772157)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.48 % (772157)CaDiCaL version: 2.1.3
% 1.62/0.48 % (772157)Termination reason: Instruction limit
% 1.62/0.48 % (772157)Termination phase: Property scanning
% 1.62/0.48 % (772157)Time elapsed: 0.002 s
% 1.62/0.48 % (772157)Peak memory usage: 10 MB
% 1.62/0.48 % (772157)Instructions burned: 3 (million)
% 1.62/0.48 % (772165)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=378146493:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.62/0.48 % (772165)Instruction limit reached!
% 1.62/0.48 % (772165)------------------------------
% 1.62/0.48 % (772165)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.48 % (772165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.48 % (772165)CaDiCaL version: 2.1.3
% 1.62/0.48 % (772165)Termination reason: Instruction limit
% 1.62/0.48 % (772165)Termination phase: Saturation
% 1.62/0.48 % (772165)Time elapsed: 0.007 s
% 1.62/0.48 % (772165)Peak memory usage: 11 MB
% 1.62/0.48 % (772165)Instructions burned: 29 (million)
% 1.62/0.48 % (772167)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=1650816952:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.62/0.48 % (772168)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=3845203271:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.62/0.52 % (772170)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) 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
% 1.62/0.52 % (772170)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.62/0.52 % (772170)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=3719678959:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.62/0.52 % (772171)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.62/0.52 % (772167)Instruction limit reached!
% 1.62/0.52 % (772167)------------------------------
% 1.62/0.52 % (772167)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.52 % (772167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.52 % (772167)CaDiCaL version: 2.1.3
% 1.62/0.52 % (772167)Termination reason: Instruction limit
% 1.62/0.52 % (772167)Termination phase: Saturation
% 1.62/0.52 % (772167)Time elapsed: 0.010 s
% 1.62/0.52 % (772167)Peak memory usage: 11 MB
% 1.62/0.52 % (772167)Instructions burned: 24 (million)
% 1.62/0.52 % (772171)lrs+1010_4:1_slsqr=8,1:to=kbo:cha=on:drc=off:si=on:sp=arity:lcm=predicate:uwa=off:fd=preordered:gs=on:nwc=5:s2agt=32:slsqc=1:kmz=on:updr=off:chr=on:pe=on:slsq=on:random_seed=3895155181:i=8:nm=2:rtra=on:fe=abstraction:inj=on_2998 on theBenchmark for (2998ds/8Mi)
% 1.62/0.52 % (772174)dis+1004_50_to=lpo:drc=off:fde=unused:cnfonf=lazy_not_gen_be_off:si=on:sp=reverse_arity:spb=units:cbe=off:foolp=on:random_seed=2159395667:uwa_fpi=on:i=31:doe=on:bd=preordered:rtra=on:fsd=on_2998 on theBenchmark for (2998ds/31Mi)
% 1.62/0.52 % (772170)Instruction limit reached!
% 1.62/0.52 % (772170)------------------------------
% 1.62/0.52 % (772170)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.52 % (772170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.52 % (772170)CaDiCaL version: 2.1.3
% 1.62/0.52 % (772170)Termination reason: Instruction limit
% 1.62/0.52 % (772170)Termination phase: Saturation
% 1.62/0.52 % (772170)Time elapsed: 0.007 s
% 1.62/0.52 % (772170)Peak memory usage: 12 MB
% 1.62/0.52 % (772170)Instructions burned: 16 (million)
% 1.62/0.52 % (772171)Instruction limit reached!
% 1.62/0.52 % (772171)------------------------------
% 1.62/0.52 % (772171)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.52 % (772171)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.52 % (772171)CaDiCaL version: 2.1.3
% 1.62/0.52 % (772171)Termination reason: Instruction limit
% 1.62/0.52 % (772171)Termination phase: Function definition elimination
% 1.62/0.52 % (772171)Time elapsed: 0.004 s
% 1.62/0.52 % (772171)Peak memory usage: 10 MB
% 1.62/0.52 % (772171)Instructions burned: 9 (million)
% 1.62/0.52 % (772174)Instruction limit reached!
% 1.62/0.52 % (772174)------------------------------
% 1.62/0.52 % (772174)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.52 % (772174)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/0.52 % (772174)CaDiCaL version: 2.1.3
% 1.62/0.52 % (772174)Termination reason: Instruction limit
% 1.62/0.52 % (772174)Termination phase: Saturation
% 1.62/0.52 % (772174)Time elapsed: 0.009 s
% 1.62/0.52 % (772174)Peak memory usage: 12 MB
% 1.62/0.52 % (772174)Instructions burned: 33 (million)
% 1.62/0.52 % (772184)dis+10_1024_sil=128000:cnfonf=off:si=on:fd=off:random_seed=3284337739:i=7:hud=5:bd=preordered:rtra=on:bet=on_2998 on theBenchmark for (2998ds/7Mi)
% 1.62/0.52 % (772186)lrs+10_1_plsq=on:drc=ordering:cnfonf=lazy_not_gen_be_off:bsd=on:si=on:plsqr=32,1:cs=on:random_seed=2668635745:i=23:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.62/0.52 % (772191)dis+1010_2:1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:uwa=off:slsq=on:random_seed=3305427227:i=1240:rtra=on:ixr=off_2998 on theBenchmark for (2998ds/1240Mi)
% 1.62/0.52 % (772184)Instruction limit reached!
% 1.62/0.52 % (772184)------------------------------
% 1.62/0.52 % (772184)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.62/0.52 % (772184)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.59 % (772184)CaDiCaL version: 2.1.3
% 2.24/0.59 % (772184)Termination reason: Instruction limit
% 2.24/0.59 % (772184)Termination phase: Function definition elimination
% 2.24/0.59 % (772184)Time elapsed: 0.004 s
% 2.24/0.59 % (772184)Peak memory usage: 11 MB
% 2.24/0.59 % (772184)Instructions burned: 9 (million)
% 2.24/0.59 % (772168)Instruction limit reached!
% 2.24/0.59 % (772168)------------------------------
% 2.24/0.59 % (772168)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.59 % (772168)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.59 % (772168)CaDiCaL version: 2.1.3
% 2.24/0.59 % (772168)Termination reason: Instruction limit
% 2.24/0.59 % (772168)Termination phase: Saturation
% 2.24/0.59 % (772168)Time elapsed: 0.032 s
% 2.24/0.59 % (772168)Peak memory usage: 12 MB
% 2.24/0.59 % (772168)Instructions burned: 60 (million)
% 2.24/0.59 % (772188)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=436808292:s2a=on:i=20:kws=inv_frequency:bd=all:rtra=on_2998 on theBenchmark for (2998ds/20Mi)
% 2.24/0.59 % (772186)Instruction limit reached!
% 2.24/0.59 % (772186)------------------------------
% 2.24/0.59 % (772186)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.59 % (772186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.59 % (772186)CaDiCaL version: 2.1.3
% 2.24/0.59 % (772186)Termination reason: Instruction limit
% 2.24/0.59 % (772186)Termination phase: Saturation
% 2.24/0.59 % (772186)Time elapsed: 0.011 s
% 2.24/0.59 % (772186)Peak memory usage: 11 MB
% 2.24/0.59 % (772186)Instructions burned: 25 (million)
% 2.24/0.59 % (772188)Instruction limit reached!
% 2.24/0.59 % (772188)------------------------------
% 2.24/0.59 % (772188)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.59 % (772188)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.59 % (772188)CaDiCaL version: 2.1.3
% 2.24/0.59 % (772188)Termination reason: Instruction limit
% 2.24/0.59 % (772188)Termination phase: Saturation
% 2.24/0.59 % (772188)Time elapsed: 0.012 s
% 2.24/0.59 % (772188)Peak memory usage: 12 MB
% 2.24/0.59 % (772188)Instructions burned: 22 (million)
% 2.24/0.59 % (772199)ott+1002_32_tgt=ground:si=on:sp=const_max:acc=on:nwc=0.5:random_seed=3131933882:i=143:fgj=on:piset=pi_sigma:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/143Mi)
% 2.24/0.59 % (772200)lrs+1002_1_sil=128000:si=on:acc=on:uwa=off:random_seed=348717274:st=5:s2a=on:i=193:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/193Mi)
% 2.24/0.59 % (772207)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 2.24/0.59 % (772205)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2322789992:i=42:hud=10:rtra=on_2998 on theBenchmark for (2998ds/42Mi)
% 2.24/0.59 % (772207)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2020174849:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2998 on theBenchmark for (2998ds/7Mi)
% 2.24/0.59 % (772207)Instruction limit reached!
% 2.24/0.59 % (772207)------------------------------
% 2.24/0.59 % (772207)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.59 % (772207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.59 % (772207)CaDiCaL version: 2.1.3
% 2.24/0.59 % (772207)Termination reason: Instruction limit
% 2.24/0.59 % (772207)Termination phase: Property scanning
% 2.24/0.59 % (772207)Time elapsed: 0.003 s
% 2.24/0.59 % (772207)Peak memory usage: 10 MB
% 2.24/0.59 % (772207)Instructions burned: 7 (million)
% 2.24/0.59 % (772200)Refutation not found, incomplete strategy
% 2.24/0.59 % (772200)------------------------------
% 2.24/0.59 % (772200)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.24/0.59 % (772200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.24/0.59 % (772200)CaDiCaL version: 2.1.3
% 2.24/0.59 % (772200)Termination reason: Refutation not found, incomplete strategy
% 2.24/0.59 % (772200)Time elapsed: 0.017 s
% 2.24/0.59 % (772200)Peak memory usage: 12 MB
% 2.24/0.59 % (772200)Instructions burned: 32 (million)
% 2.24/0.59 % (772200)------------------------------
% 2.24/0.59 % (772200)------------------------------
% 2.24/0.59 % (772205)Instruction limit reached!
% 2.24/0.59 % (772205)------------------------------
% 2.24/0.59 % (772205)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.68 % (772205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.68 % (772205)CaDiCaL version: 2.1.3
% 2.59/0.68 % (772205)Termination reason: Instruction limit
% 2.59/0.68 % (772205)Termination phase: Saturation
% 2.59/0.68 % (772205)Time elapsed: 0.021 s
% 2.59/0.68 % (772205)Peak memory usage: 12 MB
% 2.59/0.68 % (772205)Instructions burned: 44 (million)
% 2.59/0.68 % (772212)lrs+10_1_to=lpo:sil=128000:si=on:sp=arity:urr=on:random_seed=4024645640:i=181:sd=2:bd=preordered:rtra=on:ss=axioms_2997 on theBenchmark for (2997ds/181Mi)
% 2.59/0.68 % (772213)dis+10_8_sil=128000:plsq=on:plsqc=1:si=on:sp=unary_first:sos=on:lma=off:plsqr=64,1:uwa=interpreted_only:foolp=on:random_seed=2454368614:st=3:avsq=on:i=169:avsqr=8,1:sd=2:kws=precedence:bd=preordered:rtra=on:ss=axioms:ntd=on_2997 on theBenchmark for (2997ds/169Mi)
% 2.59/0.68 % (772212)Refutation not found, incomplete strategy
% 2.59/0.68 % (772212)------------------------------
% 2.59/0.68 % (772212)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.68 % (772212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.68 % (772212)CaDiCaL version: 2.1.3
% 2.59/0.68 % (772212)Termination reason: Refutation not found, incomplete strategy
% 2.59/0.68 % (772212)Time elapsed: 0.007 s
% 2.59/0.68 % (772212)Peak memory usage: 12 MB
% 2.59/0.68 % (772212)Instructions burned: 13 (million)
% 2.59/0.68 % (772212)------------------------------
% 2.59/0.68 % (772212)------------------------------
% 2.59/0.68 % (772214)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(5) has been set then sine_level_split_queue(off) is equal to on
% 2.59/0.68 % (772214)lrs+1002_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=arity:cbe=off:uwa=all:slsqc=5:random_seed=444307646:st=4:s2a=on:i=6:add=on:doe=on:hud=10:rtra=on:bet=on:ss=axioms_2997 on theBenchmark for (2997ds/6Mi)
% 2.59/0.68 % (772213)Refutation not found, incomplete strategy
% 2.59/0.68 % (772213)------------------------------
% 2.59/0.68 % (772213)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.68 % (772213)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.68 % (772213)CaDiCaL version: 2.1.3
% 2.59/0.68 % (772213)Termination reason: Refutation not found, incomplete strategy
% 2.59/0.68 % (772213)Time elapsed: 0.015 s
% 2.59/0.68 % (772213)Peak memory usage: 13 MB
% 2.59/0.68 % (772213)Instructions burned: 32 (million)
% 2.59/0.68 % (772213)------------------------------
% 2.59/0.68 % (772213)------------------------------
% 2.59/0.68 % (772214)Instruction limit reached!
% 2.59/0.68 % (772214)------------------------------
% 2.59/0.68 % (772214)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.68 % (772214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.68 % (772214)CaDiCaL version: 2.1.3
% 2.59/0.68 % (772214)Termination reason: Instruction limit
% 2.59/0.68 % (772214)Termination phase: SInE selection
% 2.59/0.68 % (772214)Time elapsed: 0.003 s
% 2.59/0.68 % (772214)Peak memory usage: 10 MB
% 2.59/0.68 % (772214)Instructions burned: 6 (million)
% 2.59/0.68 % (772222)ott+2_5:4_anc=none:to=lpo:si=on:lma=off:cbe=off:uwa=ground:nwc=3:random_seed=2053890771:uwa_fpi=on:i=22:add=on:doe=on:ins=1:rtra=on_2997 on theBenchmark for (2997ds/22Mi)
% 2.59/0.68 % (772199)Instruction limit reached!
% 2.59/0.68 % (772199)------------------------------
% 2.59/0.68 % (772199)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.68 % (772199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.68 % (772199)CaDiCaL version: 2.1.3
% 2.59/0.68 % (772199)Termination reason: Instruction limit
% 2.59/0.68 % (772199)Termination phase: Saturation
% 2.59/0.68 % (772199)Time elapsed: 0.073 s
% 2.59/0.68 % (772199)Peak memory usage: 13 MB
% 2.59/0.68 % (772199)Instructions burned: 145 (million)
% 2.59/0.68 % (772222)Instruction limit reached!
% 2.59/0.68 % (772222)------------------------------
% 2.59/0.68 % (772222)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.68 % (772222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.68 % (772222)CaDiCaL version: 2.1.3
% 2.59/0.68 % (772222)Termination reason: Instruction limit
% 2.59/0.68 % (772222)Termination phase: Saturation
% 2.59/0.68 % (772222)Time elapsed: 0.011 s
% 2.59/0.68 % (772222)Peak memory usage: 11 MB
% 2.59/0.68 % (772222)Instructions burned: 22 (million)
% 2.59/0.68 % (772230)dis+1010_1_to=lpo:sil=128000:cnfonf=lazy_pi_sigma_gen:sas=cadical:si=on:sos=all:uwa=off:sac=on:random_seed=3022138250:i=19:add=on:rtra=on_2997 on theBenchmark for (2997ds/19Mi)
% 2.59/0.68 % (772232)ott+10_1_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:lma=off:plsqr=128,1:urr=ec_only:uwa=off:rp=on:nwc=20:br=off:random_seed=1258448008:i=316:bs=unit_only:ins=25:rtra=on:ntd=on_2997 on theBenchmark for (2997ds/316Mi)
% 2.59/0.68 % (772230)Instruction limit reached!
% 2.59/0.68 % (772230)------------------------------
% 2.59/0.68 % (772230)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.68 % (772230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.68 % (772230)CaDiCaL version: 2.1.3
% 2.59/0.68 % (772230)Termination reason: Instruction limit
% 2.59/0.68 % (772230)Termination phase: Saturation
% 2.59/0.68 % (772230)Time elapsed: 0.009 s
% 2.59/0.68 % (772230)Peak memory usage: 12 MB
% 2.59/0.68 % (772230)Instructions burned: 21 (million)
% 2.59/0.68 % (772238)dis+1004_4:1_slsqr=1,2:to=lpo:plsq=on:fde=unused:e2e=on:si=on:spb=goal_then_units:acc=on:urr=on:uwa=off:fd=preordered:s2agt=16:slsqc=1:slsq=on:random_seed=2373466052:hsq=on:hsqr=16,1:s2a=on:i=853:add=off:bd=all:nm=64:rtra=on:gtg=position:c=on:ntd=on_2997 on theBenchmark for (2997ds/853Mi)
% 2.59/0.68 % (772240)dis+1003_3:4_to=kbo:plsq=on:prc=on:sims=off:e2e=on:si=on:spb=intro:acc=on:urr=on:uwa=off:foolp=on:s2agt=32:slsqc=3:slsq=on:random_seed=1699725963:hsq=on:hsqr=16,1:s2a=on:i=45:erml=3:slsql=off:rtra=on:gtg=exists_top:er=filter:ntd=on_2997 on theBenchmark for (2997ds/45Mi)
% 2.59/0.68 % (772153)Instruction limit reached!
% 2.59/0.68 % (772153)------------------------------
% 2.59/0.68 % (772153)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.68 % (772153)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.68 % (772153)CaDiCaL version: 2.1.3
% 2.59/0.68 % (772153)Termination reason: Instruction limit
% 2.59/0.68 % (772153)Termination phase: Saturation
% 2.59/0.68 % (772153)Time elapsed: 0.172 s
% 2.59/0.68 % (772153)Peak memory usage: 13 MB
% 2.59/0.68 % (772153)Instructions burned: 328 (million)
% 2.59/0.68 % (772242)lrs+1002_1_sil=128000:fde=unused:e2e=on:si=on:sos=on:uwa=interpreted_only:random_seed=4256187011:i=480:rtra=on_2997 on theBenchmark for (2997ds/480Mi)
% 2.59/0.68 % (772242)Refutation not found, incomplete strategy
% 2.59/0.68 % (772242)------------------------------
% 2.59/0.68 % (772242)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.68 % (772242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.68 % (772242)CaDiCaL version: 2.1.3
% 2.59/0.68 % (772242)Termination reason: Refutation not found, incomplete strategy
% 2.59/0.68 % (772242)Time elapsed: 0.008 s
% 2.59/0.68 % (772242)Peak memory usage: 12 MB
% 2.59/0.68 % (772242)Instructions burned: 11 (million)
% 2.59/0.68 % (772242)------------------------------
% 2.59/0.68 % (772242)------------------------------
% 2.59/0.68 % (772240)Instruction limit reached!
% 2.59/0.68 % (772240)------------------------------
% 2.59/0.68 % (772240)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.68 % (772240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.68 % (772240)CaDiCaL version: 2.1.3
% 2.59/0.68 % (772240)Termination reason: Instruction limit
% 2.59/0.68 % (772240)Termination phase: Saturation
% 2.59/0.68 % (772240)Time elapsed: 0.024 s
% 2.59/0.68 % (772240)Peak memory usage: 13 MB
% 2.59/0.68 % (772240)Instructions burned: 46 (million)
% 2.59/0.68 % (772249)dis+1010_40_sil=128000:si=on:uwa=off:nwc=1:sac=on:chr=on:avsqc=3:random_seed=87894765:avsq=on:i=21:avsqr=8,1:kws=frequency:fgj=on:bd=all:rtra=on:fe=axiom:ntd=on_2996 on theBenchmark for (2996ds/21Mi)
% 2.59/0.68 % (772249)Instruction limit reached!
% 2.59/0.68 % (772249)------------------------------
% 2.59/0.68 % (772249)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.68 % (772249)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.68 % (772249)CaDiCaL version: 2.1.3
% 2.59/0.68 % (772249)Termination reason: Instruction limit
% 2.59/0.68 % (772249)Termination phase: Saturation
% 2.59/0.68 % (772249)Time elapsed: 0.011 s
% 2.59/0.68 % (772249)Peak memory usage: 11 MB
% 2.59/0.68 % (772249)Instructions burned: 21 (million)
% 2.59/0.68 % (772253)WARNING Broken Constraint: if sine_level_split_queue_cutoffs(2) has been set then sine_level_split_queue(off) is equal to on
% 2.59/0.68 % (772253)ott+1002_3_si=on:sp=weighted_frequency:spb=goal:cbe=off:slsqc=2:random_seed=2007694730:cts=off:uwa_fpi=on:i=200:av=off:fsr=off:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/200Mi)
% 2.59/0.68 % (772255)lrs+10_1_sil=128000:fde=unused:si=on:random_seed=197582245:s2a=on:i=13:kws=inv_frequency:bd=all:rtra=on_2996 on theBenchmark for (2996ds/13Mi)
% 2.59/0.68 % (772255)Instruction limit reached!
% 2.59/0.68 % (772255)------------------------------
% 2.59/0.68 % (772255)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.68 % (772255)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.68 % (772255)CaDiCaL version: 2.1.3
% 2.59/0.68 % (772255)Termination reason: Instruction limit
% 2.59/0.68 % (772255)Termination phase: Saturation
% 2.59/0.68 % (772255)Time elapsed: 0.008 s
% 2.59/0.68 % (772255)Peak memory usage: 12 MB
% 2.59/0.68 % (772255)Instructions burned: 14 (million)
% 2.59/0.68 % (772259)lrs+1010_1_anc=none:slsqr=1,2:sil=128000:cnfonf=conj_eager:sas=cadical:si=on:hi=on:uwa=one_side_interpreted:rp=on:nwc=2:slsqc=3:slsq=on:random_seed=4210621556:i=66:s2at=3:nm=2:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/66Mi)
% 2.59/0.68 % (772077)Instruction limit reached!
% 2.59/0.68 % (772077)------------------------------
% 2.59/0.68 % (772077)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.68 % (772077)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.68 % (772077)CaDiCaL version: 2.1.3
% 2.59/0.68 % (772077)Termination reason: Instruction limit
% 2.59/0.68 % (772077)Termination phase: Saturation
% 2.59/0.68 % (772077)Time elapsed: 0.321 s
% 2.59/0.68 % (772077)Peak memory usage: 15 MB
% 2.59/0.68 % (772077)Instructions burned: 634 (million)
% 2.59/0.68 % (772265)lrs+1004_128_si=on:sos=all:uwa=off:random_seed=2159653634:i=51:fsr=off:rtra=on_2996 on theBenchmark for (2996ds/51Mi)
% 2.59/0.68 % (772259)Instruction limit reached!
% 2.59/0.68 % (772259)------------------------------
% 2.59/0.68 % (772259)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.68 % (772259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.68 % (772259)CaDiCaL version: 2.1.3
% 2.59/0.68 % (772259)Termination reason: Instruction limit
% 2.59/0.68 % (772259)Termination phase: Saturation
% 2.59/0.68 % (772259)Time elapsed: 0.034 s
% 2.59/0.68 % (772259)Peak memory usage: 12 MB
% 2.59/0.68 % (772259)Instructions burned: 66 (million)
% 2.59/0.68 % (772269)dis+1002_64_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:cbe=off:uwa=off:nwc=0.5:random_seed=3811211943:i=31:kws=inv_frequency:bd=all:rtra=on:ntd=on_2996 on theBenchmark for (2996ds/31Mi)
% 2.59/0.68 % (772279)dis+1010_40_to=kbo:tgt=full:fde=unused:si=on:sp=const_frequency:lma=off:cbe=off:uwa=interpreted_only:random_seed=2357321493:i=137:kws=precedence:bd=all:rtra=on:c=on:ntd=on_2996 on theBenchmark for (2996ds/137Mi)
% 2.59/0.68 % (772269)Instruction limit reached!
% 2.59/0.68 % (772269)------------------------------
% 2.59/0.68 % (772269)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.68 % (772269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.68 % (772269)CaDiCaL version: 2.1.3
% 2.59/0.68 % (772269)Termination reason: Instruction limit
% 2.59/0.68 % (772269)Termination phase: Saturation
% 2.59/0.68 % (772269)Time elapsed: 0.016 s
% 2.59/0.68 % (772269)Peak memory usage: 11 MB
% 2.59/0.68 % (772269)Instructions burned: 33 (million)
% 2.59/0.68 % (772232) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-772063-772232"...
% 2.59/0.68 % (772265)Instruction limit reached!
% 2.59/0.68 % (772265)------------------------------
% 2.59/0.68 % (772265)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.68 % (772265)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.68 % (772265)CaDiCaL version: 2.1.3
% 2.59/0.68 % (772265)Termination reason: Instruction limit
% 2.59/0.68 % (772265)Termination phase: Saturation
% 2.59/0.68 % (772265)Time elapsed: 0.035 s
% 2.59/0.68 % (772265)Peak memory usage: 12 MB
% 2.59/0.68 % (772265)Instructions burned: 53 (million)
% 2.59/0.68 % (772232)...printing done.
% 2.59/0.68 % (772232)Refutation found. Thanks to Tanya!
% 2.59/0.68 % SZS status Theorem for theBenchmark
% 2.59/0.68 % SZS output start Proof for theBenchmark
% See solution above
% 2.59/0.68 % (772232)------------------------------
% 2.59/0.68 % (772232)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 2.59/0.68 % (772232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.59/0.68 % (772232)CaDiCaL version: 2.1.3
% 2.59/0.68 % (772232)Termination reason: Refutation
% 2.59/0.68 % (772232)Time elapsed: 0.146 s
% 2.59/0.68 % (772232)Peak memory usage: 16 MB
% 2.59/0.68 % (772232)Instructions burned: 286 (million)
% 2.59/0.68 % (772063)Success in time 0.437 s
% 2.59/0.68 % Vampire exiting
%------------------------------------------------------------------------------