%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL724^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:14:34 AM UTC 2026
% Result : Theorem 0.23s 0.33s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 20
% Syntax : Number of formulae : 144 ( 54 unt; 0 typ; 10 def)
% Number of atoms : 858 ( 165 equ; 0 cnn)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 1078 ( 134 ~; 175 |; 17 &; 659 @)
% ( 8 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 115 ( 115 >; 0 *; 0 +; 0 <<)
% Number of symbols : 69 ( 65 usr; 17 con; 0-4 aty)
% ( 73 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 280 ( 0 sgn 46 !; 0 ?; 280 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: 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,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $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,
rel_s4: $i > $i > $o ).
thf(func_def_33,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
phi: $i > $o ).
thf(func_def_36,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_39,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_40,type,
vIMP: $o > $o > $o ).
thf(func_def_41,type,
vAND: $o > $o > $o ).
thf(func_def_42,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_45,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
vOR: $o > $o > $o ).
thf(func_def_47,type,
vNOT: $o > $o ).
thf(func_def_50,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
sF0: $o ).
thf(func_def_52,type,
sF1: $o ).
thf(func_def_56,type,
sK5: $i > $i ).
thf(func_def_58,type,
sK7: $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X2: $i,X3: $i,X1: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s4 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f34,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',a1) ).
thf(f35,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',a2) ).
thf(f36,conjecture,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ phi ) @ phi ) )
& ( mvalid @ ( mimplies @ ( mbox_s4 @ phi ) @ ( mbox_s4 @ ( mbox_s4 @ phi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f37,negated_conjecture,
~ ( ( mvalid @ ( mimplies @ ( mbox_s4 @ phi ) @ phi ) )
& ( mvalid @ ( mimplies @ ( mbox_s4 @ phi ) @ ( mbox_s4 @ ( mbox_s4 @ phi ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f47,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f48,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f47]) ).
thf(f51,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f52,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f51]) ).
thf(f53,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f54,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f55,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s4 ),
inference(rectify,[],[f32]) ).
thf(f56,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f57,plain,
mreflexive @ rel_s4,
inference(rectify,[],[f34]) ).
thf(f58,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f57]) ).
thf(f59,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f60,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f59]) ).
thf(f69,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f75,plain,
~ ( ( mvalid @ ( mimplies @ ( mbox_s4 @ phi ) @ phi ) )
& ( mvalid @ ( mimplies @ ( mbox_s4 @ phi ) @ ( mbox_s4 @ ( mbox_s4 @ phi ) ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f76,plain,
~ ( ( ( mvalid @ ( mimplies @ ( mbox_s4 @ phi ) @ ( mbox_s4 @ ( mbox_s4 @ phi ) ) ) )
= $true )
& ( ( mvalid @ ( mimplies @ ( mbox_s4 @ phi ) @ phi ) )
= $true ) ),
inference(fool_elimination,[],[f75]) ).
thf(f81,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X3 @ X1 ) )
=> ( X0 @ X3 @ X2 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f82,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f84,plain,
mtransitive @ rel_s4,
inference(rectify,[],[f35]) ).
thf(f85,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f84]) ).
thf(f98,plain,
( ( ( mvalid @ ( mimplies @ ( mbox_s4 @ phi ) @ phi ) )
!= $true )
| ( ( mvalid @ ( mimplies @ ( mbox_s4 @ phi ) @ ( mbox_s4 @ ( mbox_s4 @ phi ) ) ) )
!= $true ) ),
inference(ennf_transformation,[],[f76]) ).
thf(f103,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f106,plain,
( ( ( mvalid @ ( mimplies @ ( mbox_s4 @ phi ) @ phi ) )
!= $true )
| ( ( mvalid @ ( mimplies @ ( mbox_s4 @ phi ) @ ( mbox_s4 @ ( mbox_s4 @ phi ) ) ) )
!= $true ) ),
inference(cnf_transformation,[],[f98]) ).
thf(f107,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f108,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f69]) ).
thf(f109,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f116,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f58]) ).
thf(f117,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f85]) ).
thf(f120,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f126,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f133,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f138,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,[],[f108,f109,f107]) ).
thf(f147,plain,
( ( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ phi )
@ phi ) ) )
| ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ phi )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ phi ) ) ) )
!= $true ) ),
inference(definition_unfolding,[],[f106,f120,f138,f133,f120,f138,f133,f133,f133]) ).
thf(f148,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f116,f103]) ).
thf(f149,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y3 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f117,f126]) ).
thf(f150,definition,
( sF0
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ phi )
@ phi ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f151,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ phi )
@ phi ) )
= sF0 ),
inference(reorient_equations,[],[f150]) ).
thf(f152,definition,
( sF1
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ phi )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ phi ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f153,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ phi )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ phi ) ) ) )
= sF1 ),
inference(reorient_equations,[],[f152]) ).
thf(f154,plain,
( ( $true != sF0 )
| ( $true != sF1 ) ),
inference(definition_folding,[],[f147,f153,f151]) ).
thf(f155,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f156,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X1: $i] :
( $true
= ( rel_s4 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f156]) ).
thf(f159,plain,
( ( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ phi )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ phi ) ) ) )
= $false )
| ( $true = sF1 ) ),
inference(iff_proxy_clausification,[],[f153]) ).
thf(f160,plain,
( ( $true = sF1 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( phi @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( phi @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
( ( $true = sF1 )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( phi @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( phi @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) )
@ sK2 ) ) ),
inference(sigma_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( $true = sF1 )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( phi @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( phi @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) )
| ( $true = sF1 ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $true = sF1 )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f165,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) ) )
= $true )
| ( $true = sF1 ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_s4 @ sK2 @ Y0 ) )
@ X1 )
= $true )
| ( $true = sF1 ) ),
inference(pi_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X1: $i] :
( ( $true
= ( ( phi @ X1 )
| ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true = sF1 ) ),
inference(beta-eta_normalization,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( phi @ X1 ) )
| ( $true = sF1 ) ),
inference(or_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true = sF1 )
| ( $true
= ( phi @ X1 ) ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( phi @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK2 @ Y0 ) )
@ sK3 ) )
| ( $true = sF1 ) ),
inference(sigma_proxy_clausification,[],[f163]) ).
thf(f171,plain,
( ( $true = sF1 )
| ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_s4 @ sK3 @ Y0 ) ) )
| ~ ( rel_s4 @ sK2 @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f170]) ).
thf(f172,plain,
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK3 ) ) )
| ( $true = sF1 ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_s4 @ sK3 @ Y0 ) ) ) )
| ( $true = sF1 ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f174,plain,
( ( $true = sF1 )
| ( $false
= ( ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_s4 @ sK3 @ Y0 ) )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f173]) ).
thf(f175,plain,
( ( $true = sF1 )
| ( $false
= ( ( phi @ sK4 )
| ~ ( rel_s4 @ sK3 @ sK4 ) ) ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
( ( $false
= ( ~ ( rel_s4 @ sK3 @ sK4 ) ) )
| ( $true = sF1 ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f177,plain,
( ( $true = sF1 )
| ( $false
= ( phi @ sK4 ) ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f178,plain,
( ( $true = sF1 )
| ( $true
= ( rel_s4 @ sK3 @ sK4 ) ) ),
inference(not_proxy_clausification,[],[f176]) ).
thf(f179,plain,
( ( ( rel_s4 @ sK2 @ sK3 )
= $true )
| ( $true = sF1 ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f203,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y0 @ Y2 )
& ( rel_s4 @ Y2 @ Y1 ) )
=> ( rel_s4 @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f204,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y0 @ Y2 )
& ( rel_s4 @ Y2 @ Y1 ) )
=> ( rel_s4 @ Y0 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ X1 @ Y1 )
& ( rel_s4 @ Y1 @ Y0 ) )
=> ( rel_s4 @ X1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f204]) ).
thf(f206,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ X1 @ Y1 )
& ( rel_s4 @ Y1 @ Y0 ) )
=> ( rel_s4 @ X1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s4 @ X1 @ Y0 )
& ( rel_s4 @ Y0 @ X2 ) )
=> ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f206]) ).
thf(f208,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s4 @ X1 @ Y0 )
& ( rel_s4 @ Y0 @ X2 ) )
=> ( rel_s4 @ X1 @ X2 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s4 @ X1 @ X3 )
& ( rel_s4 @ X3 @ X2 ) )
=> ( rel_s4 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f208]) ).
thf(f210,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $true )
| ( $false
= ( ( rel_s4 @ X1 @ X3 )
& ( rel_s4 @ X3 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f209]) ).
thf(f211,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X3 @ X2 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $true )
| ( $false
= ( rel_s4 @ X1 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f210]) ).
thf(f213,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ phi )
@ phi ) ) )
| ( $true = sF0 ) ),
inference(iff_proxy_clausification,[],[f151]) ).
thf(f214,plain,
( ( $true = sF0 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( phi @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( phi @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f213]) ).
thf(f215,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( phi @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( phi @ Y0 ) )
@ sK6 ) )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f214]) ).
thf(f216,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_s4 @ sK6 @ Y0 ) ) )
| ( phi @ sK6 ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f215]) ).
thf(f217,plain,
( ( $false
= ( phi @ sK6 ) )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f216]) ).
thf(f218,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_s4 @ sK6 @ Y0 ) ) ) ) )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f216]) ).
thf(f219,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_s4 @ sK6 @ Y0 ) ) ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f218]) ).
thf(f220,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( ( ^ [Y0: $i] :
( ( phi @ Y0 )
| ~ ( rel_s4 @ sK6 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f219]) ).
thf(f221,plain,
! [X1: $i] :
( ( $true
= ( ( phi @ X1 )
| ~ ( rel_s4 @ sK6 @ X1 ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f220]) ).
thf(f222,plain,
! [X1: $i] :
( ( $true
= ( phi @ X1 ) )
| ( ( ~ ( rel_s4 @ sK6 @ X1 ) )
= $true )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f221]) ).
thf(f223,plain,
! [X1: $i] :
( ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s4 @ sK6 @ X1 ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f222]) ).
thf(f235,definition,
( spl8_1
<=> ( $true = sF1 ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
thf(f239,definition,
( spl8_2
<=> ! [X1: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( phi @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
thf(f240,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( phi @ X1 ) ) )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f239]) ).
thf(f241,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f169,f239,f235]) ).
thf(f243,definition,
( spl8_3
<=> ( $false
= ( phi @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
thf(f245,plain,
( ( $false
= ( phi @ sK4 ) )
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f243]) ).
thf(f246,plain,
( spl8_1
| spl8_3 ),
inference(avatar_split_clause,[],[f177,f243,f235]) ).
thf(f248,definition,
( spl8_4
<=> ( $true
= ( rel_s4 @ sK3 @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
thf(f250,plain,
( ( $true
= ( rel_s4 @ sK3 @ sK4 ) )
| ~ spl8_4 ),
inference(avatar_component_clause,[],[f248]) ).
thf(f251,plain,
( spl8_4
| spl8_1 ),
inference(avatar_split_clause,[],[f178,f235,f248]) ).
thf(f253,definition,
( spl8_5
<=> ( ( rel_s4 @ sK2 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition]) ).
thf(f255,plain,
( ( ( rel_s4 @ sK2 @ sK3 )
= $true )
| ~ spl8_5 ),
inference(avatar_component_clause,[],[f253]) ).
thf(f256,plain,
( spl8_1
| spl8_5 ),
inference(avatar_split_clause,[],[f179,f253,f235]) ).
thf(f270,definition,
( spl8_9
<=> ( $true = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition]) ).
thf(f274,definition,
( spl8_10
<=> ! [X1: $i] :
( ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s4 @ sK6 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_10])],[avatar_definition]) ).
thf(f275,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s4 @ sK6 @ X1 ) )
| ( $true
= ( phi @ X1 ) ) )
| ~ spl8_10 ),
inference(avatar_component_clause,[],[f274]) ).
thf(f276,plain,
( spl8_9
| spl8_10 ),
inference(avatar_split_clause,[],[f223,f274,f270]) ).
thf(f278,definition,
( spl8_11
<=> ( $false
= ( phi @ sK6 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_11])],[avatar_definition]) ).
thf(f280,plain,
( ( $false
= ( phi @ sK6 ) )
| ~ spl8_11 ),
inference(avatar_component_clause,[],[f278]) ).
thf(f281,plain,
( spl8_11
| spl8_9 ),
inference(avatar_split_clause,[],[f217,f270,f278]) ).
thf(f294,plain,
( ~ spl8_9
| ~ spl8_1 ),
inference(avatar_split_clause,[],[f154,f235,f270]) ).
thf(f333,plain,
( ( $true
= ( phi @ sK6 ) )
| ( $false = $true )
| ~ spl8_10 ),
inference(constrained_superposition,[],[f157,f275]) ).
thf(f334,plain,
( ( $true
= ( phi @ sK6 ) )
| ~ spl8_10 ),
inference(trivial_inequality_removal,[],[f333]) ).
thf(f337,plain,
( ( $false = $true )
| ~ spl8_10
| ~ spl8_11 ),
inference(forward_demodulation,[],[f334,f280]) ).
thf(f338,plain,
( $false
| ~ spl8_10
| ~ spl8_11 ),
inference(trivial_inequality_removal,[],[f337]) ).
thf(f339,plain,
( ~ spl8_10
| ~ spl8_11 ),
inference(avatar_contradiction_clause,[],[f338]) ).
thf(f349,plain,
( ! [X0: $i] :
( ( ( rel_s4 @ X0 @ sK4 )
= $true )
| ( $false = $true )
| ( $false
= ( rel_s4 @ X0 @ sK3 ) ) )
| ~ spl8_4 ),
inference(constrained_superposition,[],[f250,f211]) ).
thf(f354,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s4 @ X0 @ sK3 ) )
| ( ( rel_s4 @ X0 @ sK4 )
= $true ) )
| ~ spl8_4 ),
inference(trivial_inequality_removal,[],[f349]) ).
thf(f379,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK4 ) )
| ( $false = $true )
| ~ spl8_4
| ~ spl8_5 ),
inference(constrained_superposition,[],[f354,f255]) ).
thf(f386,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK4 ) )
| ~ spl8_4
| ~ spl8_5 ),
inference(trivial_inequality_removal,[],[f379]) ).
thf(f395,plain,
( ( $true
= ( phi @ sK4 ) )
| ( $false = $true )
| ~ spl8_2
| ~ spl8_4
| ~ spl8_5 ),
inference(constrained_superposition,[],[f240,f386]) ).
thf(f400,plain,
( ( $true
= ( phi @ sK4 ) )
| ~ spl8_2
| ~ spl8_4
| ~ spl8_5 ),
inference(trivial_inequality_removal,[],[f395]) ).
thf(f404,plain,
( ( $false = $true )
| ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5 ),
inference(forward_demodulation,[],[f400,f245]) ).
thf(f405,plain,
( $false
| ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5 ),
inference(trivial_inequality_removal,[],[f404]) ).
thf(f406,plain,
( ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5 ),
inference(avatar_contradiction_clause,[],[f405]) ).
cnf(s1,plain,
( spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f241]) ).
cnf(s2,plain,
( spl8_1
| spl8_3 ),
inference(sat_conversion,[],[f246]) ).
cnf(s3,plain,
( spl8_1
| spl8_4 ),
inference(sat_conversion,[],[f251]) ).
cnf(s4,plain,
( spl8_1
| spl8_5 ),
inference(sat_conversion,[],[f256]) ).
cnf(s7,plain,
( spl8_9
| spl8_10 ),
inference(sat_conversion,[],[f276]) ).
cnf(s8,plain,
( spl8_9
| spl8_11 ),
inference(sat_conversion,[],[f281]) ).
cnf(s11,plain,
( ~ spl8_1
| ~ spl8_9 ),
inference(sat_conversion,[],[f294]) ).
cnf(s15,plain,
( ~ spl8_10
| ~ spl8_11 ),
inference(sat_conversion,[],[f339]) ).
cnf(s18,plain,
( ~ spl8_2
| ~ spl8_3
| ~ spl8_4
| ~ spl8_5 ),
inference(sat_conversion,[],[f406]) ).
cnf(s19,plain,
spl8_1,
inference(rat,[],[s18,s1,s2,s3,s4]) ).
cnf(s20,plain,
~ spl8_9,
inference(rat,[],[s11,s19]) ).
cnf(s22,plain,
spl8_11,
inference(rat,[],[s8,s20]) ).
cnf(s23,plain,
spl8_10,
inference(rat,[],[s7,s20]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s15,s22,s23]) ).
thf(f407,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL724^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 % Computer : n004.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 10:00:52 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.10/0.26 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.33 % (1090397)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.33 % (1090404)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4080662586:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.33 % (1090404)Instruction limit reached!
% 0.23/0.33 % (1090404)------------------------------
% 0.23/0.33 % (1090404)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.33 % (1090404)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.33 % (1090404)CaDiCaL version: 2.1.3
% 0.23/0.33 % (1090404)Termination reason: Instruction limit
% 0.23/0.33 % (1090404)Termination phase: Saturation
% 0.23/0.33 % (1090404)Time elapsed: 0.002 s
% 0.23/0.33 % (1090404)Peak memory usage: 10 MB
% 0.23/0.33 % (1090404)Instructions burned: 7 (million)
% 0.23/0.33 % (1090408)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.33 % (1090408)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
% 0.23/0.33 % (1090402)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1269895093:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.33 % (1090403)lrs+10_16_si=on:nwc=1.5:random_seed=594498352:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.33 % (1090405)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=3694732601: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)
% 0.23/0.33 % (1090408)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=4027286961:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.33 % (1090406)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3098466514:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.33 % (1090410)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4182025829:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.23/0.33 % (1090407)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4053336876:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.33 % (1090410)Instruction limit reached!
% 0.23/0.33 % (1090410)------------------------------
% 0.23/0.33 % (1090410)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.33 % (1090410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.33 % (1090410)CaDiCaL version: 2.1.3
% 0.23/0.33 % (1090410)Termination reason: Instruction limit
% 0.23/0.33 % (1090410)Termination phase: Saturation
% 0.23/0.33 % (1090410)Time elapsed: 0.002 s
% 0.23/0.33 % (1090410)Peak memory usage: 11 MB
% 0.23/0.33 % (1090410)Instructions burned: 9 (million)
% 0.23/0.33 % (1090408) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1090397-1090408"...
% 0.23/0.33 % (1090403) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1090397-1090403"...
% 0.23/0.33 % (1090402) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1090397-1090402"...
% 0.23/0.33 % (1090408)...printing done.
% 0.23/0.33 % (1090403)...printing done.
% 0.23/0.33 % (1090408)Refutation found. Thanks to Tanya!
% 0.23/0.33 % SZS status Theorem for theBenchmark
% 0.23/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.33 % (1090408)------------------------------
% 0.23/0.33 % (1090408)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.33 % (1090408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.33 % (1090408)CaDiCaL version: 2.1.3
% 0.23/0.33 % (1090408)Termination reason: Refutation
% 0.23/0.33 % (1090408)Time elapsed: 0.013 s
% 0.23/0.33 % (1090408)Peak memory usage: 13 MB
% 0.23/0.33 % (1090408)Instructions burned: 23 (million)
% 0.23/0.33 % (1090397)Success in time 0.057 s
% 0.23/0.33 % Vampire exiting
%------------------------------------------------------------------------------