%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n002.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 08:15:09 AM UTC 2026
% Result : Theorem 0.32s 0.47s
% Output : Refutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 17
% Syntax : Number of formulae : 172 ( 52 unt; 0 typ; 7 def)
% Number of atoms : 1210 ( 224 equ; 0 cnn)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 1342 ( 187 ~; 273 |; 17 &; 773 @)
% ( 7 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 67 ( 67 >; 0 *; 0 +; 0 <<)
% Number of symbols : 65 ( 61 usr; 15 con; 0-4 aty)
% ( 73 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 249 ( 0 sgn 74 !; 0 ?; 249 :)
% 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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_37,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_39,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
vNOT: $o > $o ).
thf(func_def_42,type,
vOR: $o > $o > $o ).
thf(func_def_43,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vIMP: $o > $o > $o ).
thf(func_def_48,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_49,type,
vAND: $o > $o > $o ).
thf(func_def_50,type,
db4:
!>[X0: $tType] : X0 ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
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] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
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 ) @ ( mbox_s4 @ ( mbox_s4 @ phi ) ) ) )
& ( mvalid @ ( mimplies @ ( mbox_s4 @ phi ) @ phi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
thf(f37,negated_conjecture,
~ ( ( mvalid @ ( mimplies @ ( mbox_s4 @ phi ) @ ( mbox_s4 @ ( mbox_s4 @ phi ) ) ) )
& ( mvalid @ ( mimplies @ ( mbox_s4 @ phi ) @ phi ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f40,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f41,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f40]) ).
thf(f42,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f43,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f42]) ).
thf(f45,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f61,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f62,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f61]) ).
thf(f67,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f68,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f67]) ).
thf(f81,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f82,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f89,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f90,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f89]) ).
thf(f92,plain,
mreflexive @ rel_s4,
inference(rectify,[],[f34]) ).
thf(f93,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f92]) ).
thf(f94,plain,
mtransitive @ rel_s4,
inference(rectify,[],[f35]) ).
thf(f95,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f94]) ).
thf(f96,plain,
~ ( ( mvalid @ ( mimplies @ ( mbox_s4 @ phi ) @ ( mbox_s4 @ ( mbox_s4 @ phi ) ) ) )
& ( mvalid @ ( mimplies @ ( mbox_s4 @ phi ) @ phi ) ) ),
inference(rectify,[],[f37]) ).
thf(f97,plain,
~ ( ( ( mvalid @ ( mimplies @ ( mbox_s4 @ phi ) @ ( mbox_s4 @ ( mbox_s4 @ phi ) ) ) )
= $true )
& ( ( mvalid @ ( mimplies @ ( mbox_s4 @ phi ) @ phi ) )
= $true ) ),
inference(fool_elimination,[],[f96]) ).
thf(f98,plain,
( ( ( mvalid @ ( mimplies @ ( mbox_s4 @ phi ) @ ( mbox_s4 @ ( mbox_s4 @ phi ) ) ) )
!= $true )
| ( ( mvalid @ ( mimplies @ ( mbox_s4 @ phi ) @ phi ) )
!= $true ) ),
inference(ennf_transformation,[],[f97]) ).
thf(f101,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f41]) ).
thf(f102,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f104,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f116,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f119,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f126,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f130,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f132,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f93]) ).
thf(f133,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f95]) ).
thf(f134,plain,
( ( ( mvalid @ ( mimplies @ ( mbox_s4 @ phi ) @ ( mbox_s4 @ ( mbox_s4 @ phi ) ) ) )
!= $true )
| ( ( mvalid @ ( mimplies @ ( mbox_s4 @ phi ) @ phi ) )
!= $true ) ),
inference(cnf_transformation,[],[f98]) ).
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,[],[f104,f102,f101]) ).
thf(f147,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f132,f116]) ).
thf(f148,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f133,f119]) ).
thf(f149,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] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ phi )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ phi ) ) ) ) )
| ( $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] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ phi )
@ phi ) ) ) ),
inference(definition_unfolding,[],[f134,f126,f138,f130,f130,f130,f126,f138,f130]) ).
thf(f150,plain,
( ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( phi @ Y2 ) ) ) ) ) ) ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) )
| ( phi @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( phi @ Y2 ) ) ) ) ) )
@ sK0 ) )
| ( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) )
| ( phi @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f150]) ).
thf(f152,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( phi @ Y2 ) ) ) ) ) )
@ sK0 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) )
| ( phi @ Y0 ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ( phi @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( phi @ Y0 ) ) )
| ( phi @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f154,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( phi @ Y0 ) ) )
| ( phi @ sK1 ) ) ) ),
inference(or_proxy_clausification,[],[f153]) ).
thf(f155,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ( phi @ Y0 ) ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( phi @ Y0 ) ) )
| ( phi @ sK1 ) ) ) ),
inference(or_proxy_clausification,[],[f153]) ).
thf(f156,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ( phi @ Y0 ) ) ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( phi @ Y0 ) ) )
| ( phi @ sK1 ) ) ) ),
inference(not_proxy_clausification,[],[f155]) ).
thf(f157,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ( phi @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( phi @ Y0 ) ) )
| ( phi @ sK1 ) ) ) ),
inference(pi_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ( phi @ Y0 ) )
@ X1 ) )
| ( $false
= ( phi @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ( phi @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( phi @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f160,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ( phi @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( phi @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ( phi @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( phi @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK0 @ X1 )
| ( phi @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X2 )
| ( phi @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( phi @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X2 )
| ( phi @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( phi @ X1 ) )
| ( $true
= ( phi @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( phi @ X1 ) )
| ( $true
= ( phi @ X2 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( phi @ X1 ) )
| ( $true
= ( phi @ X2 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $false
= ( rel_s4 @ sK1 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK0 @ X1 )
| ( phi @ X1 ) ) )
| ( $false
= ( phi @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f168,plain,
! [X1: $i] :
( ( $true
= ( phi @ X1 ) )
| ( $false
= ( phi @ sK1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X1: $i] :
( ( $true
= ( phi @ X1 ) )
| ( $false
= ( phi @ sK1 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) ) )
@ sK2 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( phi @ Y0 ) ) )
| ( phi @ sK1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f154]) ).
thf(f171,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) ) )
@ sK2 ) )
| ( $false
= ( phi @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) ) )
@ sK2 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( phi @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f173,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) ) )
@ sK2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( phi @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( phi @ Y1 ) ) ) )
@ sK2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( phi @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f173]) ).
thf(f175,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ sK0 @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 )
| ( phi @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f174]) ).
thf(f176,plain,
! [X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 )
| ( phi @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ sK0 @ sK2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 )
| ( phi @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f175]) ).
thf(f178,plain,
! [X1: $i] :
( ( $true
= ( rel_s4 @ sK0 @ sK2 ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 )
| ( phi @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X1: $i] :
( ( $true
= ( rel_s4 @ sK0 @ sK2 ) )
| ( $true
= ( phi @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X1: $i] :
( ( $true
= ( rel_s4 @ sK0 @ sK2 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s4 @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( phi @ Y0 ) )
@ sK3 ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 )
| ( phi @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f176]) ).
thf(f182,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( phi @ Y0 ) )
@ sK3 ) )
| ( $true
= ( phi @ X1 ) )
| ( $true
= ( ~ ( rel_s4 @ sK1 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( phi @ Y0 ) )
@ sK3 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s4 @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK3 )
| ( phi @ sK3 ) ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s4 @ sK1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f183]) ).
thf(f185,plain,
! [X1: $i] :
( ( $false
= ( phi @ sK3 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s4 @ sK1 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK3 ) ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s4 @ sK1 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f187,plain,
! [X1: $i] :
( ( $true
= ( rel_s4 @ sK2 @ sK3 ) )
| ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s4 @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f186]) ).
thf(f188,plain,
( ( $false
= ( ~ ( rel_s4 @ sK0 @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) ) ) )
| ( $false
= ( phi @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f171]) ).
thf(f189,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( phi @ Y0 ) ) ) )
| ( $false
= ( phi @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f188]) ).
thf(f190,plain,
( ( $false
= ( ~ ( rel_s4 @ sK0 @ sK2 ) ) )
| ( $false
= ( phi @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f188]) ).
thf(f191,plain,
( ( $true
= ( rel_s4 @ sK0 @ sK2 ) )
| ( $false
= ( phi @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f192,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ( phi @ Y0 ) )
@ sK4 ) )
| ( $false
= ( phi @ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f189]) ).
thf(f193,plain,
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK4 )
| ( phi @ sK4 ) ) )
| ( $false
= ( phi @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f192]) ).
thf(f194,plain,
( ( $false
= ( phi @ sK4 ) )
| ( $false
= ( phi @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f195,plain,
( ( $false
= ( ~ ( rel_s4 @ sK2 @ sK4 ) ) )
| ( $false
= ( phi @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f193]) ).
thf(f196,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK4 ) )
| ( $false
= ( phi @ sK1 ) ) ),
inference(not_proxy_clausification,[],[f195]) ).
thf(f197,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y2 @ Y1 )
& ( rel_s4 @ Y1 @ Y0 ) )
=> ( rel_s4 @ Y2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f198,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y2 @ Y1 )
& ( rel_s4 @ Y1 @ Y0 ) )
=> ( rel_s4 @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f197]) ).
thf(f199,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y1 @ Y0 )
& ( rel_s4 @ Y0 @ X1 ) )
=> ( rel_s4 @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f198]) ).
thf(f200,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y1 @ Y0 )
& ( rel_s4 @ Y0 @ X1 ) )
=> ( rel_s4 @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s4 @ Y0 @ X2 )
& ( rel_s4 @ X2 @ X1 ) )
=> ( rel_s4 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f200]) ).
thf(f202,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s4 @ Y0 @ X2 )
& ( rel_s4 @ X2 @ X1 ) )
=> ( rel_s4 @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f201]) ).
thf(f203,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s4 @ X3 @ X2 )
& ( rel_s4 @ X2 @ X1 ) )
=> ( rel_s4 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f202]) ).
thf(f204,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( rel_s4 @ X3 @ X2 )
& ( rel_s4 @ X2 @ X1 ) ) )
| ( $true
= ( rel_s4 @ X3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X2 @ X1 ) )
| ( $true
= ( rel_s4 @ X3 @ X1 ) )
| ( $false
= ( rel_s4 @ X3 @ X2 ) ) ),
inference(and_proxy_clausification,[],[f204]) ).
thf(f206,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f207,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X1: $i] :
( $true
= ( rel_s4 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f207]) ).
thf(f210,definition,
( spl5_1
<=> ( $false
= ( phi @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f211,plain,
( ( $false
!= ( phi @ sK1 ) )
| spl5_1 ),
inference(avatar_component_clause,[],[f210]) ).
thf(f212,plain,
( ( $false
= ( phi @ sK1 ) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f210]) ).
thf(f214,definition,
( spl5_2
<=> ( $false
= ( phi @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f216,plain,
( ( $false
= ( phi @ sK4 ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f214]) ).
thf(f217,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f194,f214,f210]) ).
thf(f225,definition,
( spl5_5
<=> ! [X1: $i] :
( ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s4 @ sK1 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_5])],[avatar_definition]) ).
thf(f226,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s4 @ sK1 @ X1 ) )
| ( $true
= ( phi @ X1 ) ) )
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f225]) ).
thf(f228,definition,
( spl5_6
<=> ( $false
= ( phi @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_6])],[avatar_definition]) ).
thf(f230,plain,
( ( $false
= ( phi @ sK3 ) )
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f228]) ).
thf(f231,plain,
( spl5_5
| spl5_6 ),
inference(avatar_split_clause,[],[f185,f228,f225]) ).
thf(f288,plain,
( ( $true = $false )
| ( $true
= ( phi @ sK1 ) )
| ~ spl5_5 ),
inference(constrained_superposition,[],[f226,f208]) ).
thf(f291,plain,
( ( $true
= ( phi @ sK1 ) )
| ~ spl5_5 ),
inference(trivial_inequality_removal,[],[f288]) ).
thf(f296,plain,
( ( $true = $false )
| ~ spl5_1
| ~ spl5_5 ),
inference(forward_demodulation,[],[f291,f212]) ).
thf(f297,plain,
( $false
| ~ spl5_1
| ~ spl5_5 ),
inference(trivial_inequality_removal,[],[f296]) ).
thf(f298,plain,
( ~ spl5_1
| ~ spl5_5 ),
inference(avatar_contradiction_clause,[],[f297]) ).
thf(f302,definition,
( spl5_9
<=> ( $true
= ( rel_s4 @ sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition]) ).
thf(f303,plain,
( ( $true
!= ( rel_s4 @ sK0 @ sK2 ) )
| spl5_9 ),
inference(avatar_component_clause,[],[f302]) ).
thf(f304,plain,
( ( $true
= ( rel_s4 @ sK0 @ sK2 ) )
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f302]) ).
thf(f305,plain,
( spl5_5
| spl5_9 ),
inference(avatar_split_clause,[],[f180,f302,f225]) ).
thf(f307,definition,
( spl5_10
<=> ( $true
= ( rel_s4 @ sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_10])],[avatar_definition]) ).
thf(f309,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK3 ) )
| ~ spl5_10 ),
inference(avatar_component_clause,[],[f307]) ).
thf(f310,plain,
( spl5_5
| spl5_10 ),
inference(avatar_split_clause,[],[f187,f307,f225]) ).
thf(f315,definition,
( spl5_12
<=> ! [X1: $i] :
( ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_12])],[avatar_definition]) ).
thf(f316,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( $true
= ( phi @ X1 ) ) )
| ~ spl5_12 ),
inference(avatar_component_clause,[],[f315]) ).
thf(f317,plain,
( spl5_5
| spl5_12 ),
inference(avatar_split_clause,[],[f166,f315,f225]) ).
thf(f361,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s4 @ X0 @ sK3 ) )
| ( $false
= ( rel_s4 @ X0 @ sK2 ) ) )
| ~ spl5_10 ),
inference(constrained_superposition,[],[f309,f205]) ).
thf(f368,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s4 @ X0 @ sK3 ) )
| ( $false
= ( rel_s4 @ X0 @ sK2 ) ) )
| ~ spl5_10 ),
inference(trivial_inequality_removal,[],[f361]) ).
thf(f450,plain,
( ( $true = $false )
| ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ( $true
= ( phi @ sK3 ) )
| ~ spl5_10
| ~ spl5_12 ),
inference(constrained_superposition,[],[f368,f316]) ).
thf(f461,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ( $true
= ( phi @ sK3 ) )
| ~ spl5_10
| ~ spl5_12 ),
inference(trivial_inequality_removal,[],[f450]) ).
thf(f464,plain,
( ( $true = $false )
| ( $true
= ( phi @ sK3 ) )
| ~ spl5_9
| ~ spl5_10
| ~ spl5_12 ),
inference(forward_demodulation,[],[f461,f304]) ).
thf(f465,plain,
( ( $true
= ( phi @ sK3 ) )
| ~ spl5_9
| ~ spl5_10
| ~ spl5_12 ),
inference(trivial_inequality_removal,[],[f464]) ).
thf(f466,plain,
( ( $true = $false )
| ~ spl5_6
| ~ spl5_9
| ~ spl5_10
| ~ spl5_12 ),
inference(forward_demodulation,[],[f465,f230]) ).
thf(f467,plain,
( $false
| ~ spl5_6
| ~ spl5_9
| ~ spl5_10
| ~ spl5_12 ),
inference(trivial_inequality_removal,[],[f466]) ).
thf(f468,plain,
( ~ spl5_6
| ~ spl5_9
| ~ spl5_10
| ~ spl5_12 ),
inference(avatar_contradiction_clause,[],[f467]) ).
thf(f502,plain,
( ( $true
= ( rel_s4 @ sK2 @ sK4 ) )
| spl5_1 ),
inference(forward_subsumption_resolution,[],[f196,f211]) ).
thf(f504,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s4 @ X0 @ sK4 ) )
| ( $false
= ( rel_s4 @ X0 @ sK2 ) ) )
| spl5_1 ),
inference(constrained_superposition,[],[f205,f502]) ).
thf(f505,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s4 @ X0 @ sK4 ) )
| ( $false
= ( rel_s4 @ X0 @ sK2 ) ) )
| spl5_1 ),
inference(trivial_inequality_removal,[],[f504]) ).
thf(f625,plain,
( ! [X1: $i] :
( ( $true
= ( phi @ X1 ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) ) )
| spl5_1 ),
inference(forward_subsumption_resolution,[],[f169,f211]) ).
thf(f626,plain,
( spl5_12
| spl5_1 ),
inference(avatar_split_clause,[],[f625,f210,f315]) ).
thf(f682,plain,
( ( $true = $false )
| ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ( $true
= ( phi @ sK4 ) )
| spl5_1
| ~ spl5_12 ),
inference(constrained_superposition,[],[f505,f316]) ).
thf(f683,plain,
( ( $false
= ( rel_s4 @ sK0 @ sK2 ) )
| ( $true
= ( phi @ sK4 ) )
| spl5_1
| ~ spl5_12 ),
inference(trivial_inequality_removal,[],[f682]) ).
thf(f694,plain,
( ( $true = $false )
| ( $true
= ( phi @ sK4 ) )
| spl5_1
| ~ spl5_9
| ~ spl5_12 ),
inference(forward_demodulation,[],[f683,f304]) ).
thf(f695,plain,
( ( $true
= ( phi @ sK4 ) )
| spl5_1
| ~ spl5_9
| ~ spl5_12 ),
inference(trivial_inequality_removal,[],[f694]) ).
thf(f702,plain,
( ( $true = $false )
| spl5_1
| ~ spl5_2
| ~ spl5_9
| ~ spl5_12 ),
inference(forward_demodulation,[],[f695,f216]) ).
thf(f703,plain,
( $false
| spl5_1
| ~ spl5_2
| ~ spl5_9
| ~ spl5_12 ),
inference(trivial_inequality_removal,[],[f702]) ).
thf(f704,plain,
( spl5_1
| ~ spl5_2
| ~ spl5_9
| ~ spl5_12 ),
inference(avatar_contradiction_clause,[],[f703]) ).
thf(f705,plain,
( ( $true
= ( rel_s4 @ sK0 @ sK2 ) )
| spl5_1 ),
inference(forward_subsumption_resolution,[],[f191,f211]) ).
thf(f714,plain,
( $false
| spl5_1
| spl5_9 ),
inference(forward_subsumption_resolution,[],[f705,f303]) ).
thf(f715,plain,
( spl5_1
| spl5_9 ),
inference(avatar_contradiction_clause,[],[f714]) ).
cnf(s15,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f217]) ).
cnf(s19,plain,
( spl5_5
| spl5_6 ),
inference(sat_conversion,[],[f231]) ).
cnf(s45,plain,
( ~ spl5_1
| ~ spl5_5 ),
inference(sat_conversion,[],[f298]) ).
cnf(s49,plain,
( spl5_5
| spl5_9 ),
inference(sat_conversion,[],[f305]) ).
cnf(s53,plain,
( spl5_5
| spl5_10 ),
inference(sat_conversion,[],[f310]) ).
cnf(s57,plain,
( spl5_5
| spl5_12 ),
inference(sat_conversion,[],[f317]) ).
cnf(s111,plain,
( ~ spl5_6
| ~ spl5_9
| ~ spl5_10
| ~ spl5_12 ),
inference(sat_conversion,[],[f468]) ).
cnf(s180,plain,
( spl5_1
| spl5_12 ),
inference(sat_conversion,[],[f626]) ).
cnf(s214,plain,
( spl5_1
| ~ spl5_2
| ~ spl5_9
| ~ spl5_12 ),
inference(sat_conversion,[],[f704]) ).
cnf(s225,plain,
( spl5_1
| spl5_9 ),
inference(sat_conversion,[],[f715]) ).
cnf(s226,plain,
spl5_1,
inference(rat,[],[s214,s15,s180,s225]) ).
cnf(s227,plain,
~ spl5_5,
inference(rat,[],[s45,s226]) ).
cnf(s230,plain,
spl5_12,
inference(rat,[],[s57,s227]) ).
cnf(s231,plain,
spl5_10,
inference(rat,[],[s53,s227]) ).
cnf(s232,plain,
spl5_9,
inference(rat,[],[s49,s227]) ).
cnf(s233,plain,
spl5_6,
inference(rat,[],[s19,s227]) ).
cnf(s234,plain,
$false,
inference(rat,[],[s111,s230,s231,s232,s233]) ).
thf(f716,plain,
$false,
inference(avatar_sat_refutation,[],[s234]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL724^1 : TPTP v9.3.1. Bugfixed v5.0.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.30 % Computer : n002.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8046.5625MB
% 0.11/0.30 % OS : Linux 6.8.0-71-generic
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Sep 29 10:03:53 UTC 2026
% 0.28/0.31 % CPUTime :
% 0.28/0.31 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.28/0.36 Running first-order model finding
% 0.28/0.36 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.32/0.47 % (1077016)Will run a generic schedule for satisfiability detection.
% 0.32/0.47 % (1077025)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=421351697:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.32/0.47 % (1077025)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.32/0.47 % (1077022)% WARNING: option uhcvi not known.
% 0.32/0.47 % (1077021)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2540404216_2999 on theBenchmark for (2999ds/0Mi)
% 0.32/0.47 % (1077022)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=781920510:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.32/0.47 % (1077023)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3772494273:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.32/0.47 % (1077024)dis+10_1_sil=32000:sp=arity:random_seed=1233356252:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.32/0.47 % (1077026)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=323633841:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.32/0.47 % (1077022)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.32/0.47 % Exception at run slice level
% 0.32/0.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.32/0.47 % (1077022)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.32/0.47 % (1077027)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2752034599:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.32/0.47 % (1077025)Instruction limit reached!
% 0.32/0.47 % (1077025)------------------------------
% 0.32/0.47 % (1077025)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.47 % (1077025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.47 % (1077025)CaDiCaL version: 2.1.3
% 0.32/0.47 % (1077025)Termination reason: Instruction limit
% 0.32/0.47 % (1077025)Termination phase: Saturation
% 0.32/0.47 % (1077025)Time elapsed: 0.048 s
% 0.32/0.47 % (1077025)Peak memory usage: 12 MB
% 0.32/0.47 % (1077025)Instructions burned: 118 (million)
% 0.32/0.47 % (1077023) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1077016-1077023"...
% 0.32/0.47 % (1077034)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2961318937:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.32/0.47 % Exception at run slice level
% 0.32/0.47 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.32/0.47 % (1077023)...printing done.
% 0.32/0.47 % (1077023)Refutation found. Thanks to Tanya!
% 0.32/0.47 % SZS status Theorem for theBenchmark
% 0.32/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.32/0.48 % (1077023)------------------------------
% 0.32/0.48 % (1077023)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.32/0.48 % (1077023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.32/0.48 % (1077023)CaDiCaL version: 2.1.3
% 0.32/0.48 % (1077023)Termination reason: Refutation
% 0.32/0.48 % (1077023)Time elapsed: 0.043 s
% 0.32/0.48 % (1077023)Peak memory usage: 13 MB
% 0.32/0.48 % (1077023)Instructions burned: 44 (million)
% 0.32/0.48 % (1077016)Success in time 0.101 s
% 0.32/0.48 % Vampire exiting
%------------------------------------------------------------------------------