%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO440^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:47:42 AM UTC 2026
% Result : Theorem 0.22s 0.30s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 13
% Syntax : Number of formulae : 142 ( 76 unt; 0 typ; 2 def)
% Number of atoms : 1011 ( 202 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 1417 ( 199 ~; 192 |; 13 &; 899 @)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 79 ( 79 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 55 usr; 7 con; 0-4 aty)
% ( 100 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 296 ( 0 sgn 85 !; 0 ?; 296 :)
% 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,
p: $i > $o ).
thf(func_def_36,type,
vOR: $o > $o > $o ).
thf(func_def_37,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_41,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
vNOT: $o > $o ).
thf(func_def_43,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
vIMP: $o > $o > $o ).
thf(func_def_45,type,
vAND: $o > $o > $o ).
thf(func_def_46,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_52,type,
sK1: $i > $i ).
thf(func_def_54,type,
sK3: $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X3: $i,X1: $i,X2: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f33,axiom,
( ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ X0 ) ) ) )
= mdia_s4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',mdia_s4) ).
thf(f34,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',a1) ).
thf(f35,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',a2) ).
thf(f36,conjecture,
mvalid @ ( mimplies @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) ) @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f37,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) ) @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f38,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f39,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f48,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f55,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f56,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f61,plain,
~ ( mvalid @ ( mimplies @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) ) @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f62,plain,
( ( mvalid @ ( mimplies @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) ) @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) )
!= $true ),
inference(fool_elimination,[],[f61]) ).
thf(f63,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X1 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f64,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f66,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f67,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f66]) ).
thf(f85,plain,
mtransitive @ rel_s4,
inference(rectify,[],[f35]) ).
thf(f86,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f85]) ).
thf(f87,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f90,plain,
mreflexive @ rel_s4,
inference(rectify,[],[f34]) ).
thf(f91,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f90]) ).
thf(f92,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f93,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f92]) ).
thf(f94,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f95,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f94]) ).
thf(f98,plain,
( ( mvalid @ ( mimplies @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) ) @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) )
!= $true ),
inference(flattening,[],[f62]) ).
thf(f100,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f105,plain,
( ( mvalid @ ( mimplies @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) ) @ ( mdia_s4 @ ( mbox_s4 @ p ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f106,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f87]) ).
thf(f107,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f108,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f91]) ).
thf(f114,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f118,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f93]) ).
thf(f122,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f125,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f128,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f86]) ).
thf(f130,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f95]) ).
thf(f138,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f100,f107,f118]) ).
thf(f146,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f106,f118,f114,f118]) ).
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] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p ) ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p ) ) ) ) ),
inference(definition_unfolding,[],[f105,f130,f138,f146,f114,f146,f114,f146,f114]) ).
thf(f148,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s4 )
= $true ),
inference(definition_unfolding,[],[f108,f125]) ).
thf(f149,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y1 @ Y3 ) )
=> ( Y0 @ Y2 @ Y3 ) ) ) ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f128,f122]) ).
thf(f150,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y1 @ Y0 )
& ( rel_s4 @ Y0 @ Y2 ) )
=> ( rel_s4 @ Y1 @ Y2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f151,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y1 @ Y0 )
& ( rel_s4 @ Y0 @ Y2 ) )
=> ( rel_s4 @ Y1 @ Y2 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y0 @ X1 )
& ( rel_s4 @ X1 @ Y1 ) )
=> ( rel_s4 @ Y0 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y0 @ X1 )
& ( rel_s4 @ X1 @ Y1 ) )
=> ( rel_s4 @ Y0 @ Y1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s4 @ X2 @ X1 )
& ( rel_s4 @ X1 @ Y0 ) )
=> ( rel_s4 @ X2 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f155,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s4 @ X2 @ X1 )
& ( rel_s4 @ X1 @ Y0 ) )
=> ( rel_s4 @ X2 @ Y0 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s4 @ X2 @ X1 )
& ( rel_s4 @ X1 @ X3 ) )
=> ( rel_s4 @ X2 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f157,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( rel_s4 @ X2 @ X1 )
& ( rel_s4 @ X1 @ X3 ) )
= $false )
| ( $true
= ( rel_s4 @ X2 @ X3 ) ) ),
inference(imp_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_s4 @ X2 @ X3 ) )
| ( ( rel_s4 @ X2 @ X1 )
= $false )
| ( ( rel_s4 @ X1 @ X3 )
= $false ) ),
inference(and_proxy_clausification,[],[f157]) ).
thf(f159,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f160,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X1: $i] :
( $true
= ( rel_s4 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f162,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f163,plain,
( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( rel_s4 @ Y3 @ Y4 )
| ( p @ Y4 ) ) ) ) ) ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f167,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f166]) ).
thf(f168,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X1: $i] :
( ( ~ ( rel_s4 @ sK0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( p @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f168]) ).
thf(f170,plain,
! [X1: $i] :
( ( ( ~ ( rel_s4 @ sK0 @ X1 ) )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( ( rel_s4 @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( p @ Y0 ) ) )
= $false )
| ( ( rel_s4 @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( p @ Y0 ) )
@ ( sK1 @ X1 ) )
= $false )
| ( ( rel_s4 @ sK0 @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X1: $i] :
( ( ( ~ ( rel_s4 @ X1 @ ( sK1 @ X1 ) )
| ( p @ ( sK1 @ X1 ) ) )
= $false )
| ( ( rel_s4 @ sK0 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f175,plain,
! [X1: $i] :
( ( ( rel_s4 @ sK0 @ X1 )
= $false )
| ( ( p @ ( sK1 @ X1 ) )
= $false ) ),
inference(or_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X1: $i] :
( ( ( rel_s4 @ sK0 @ X1 )
= $false )
| ( ( ~ ( rel_s4 @ X1 @ ( sK1 @ X1 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f174]) ).
thf(f177,plain,
! [X1: $i] :
( ( $true
= ( rel_s4 @ X1 @ ( sK1 @ X1 ) ) )
| ( ( rel_s4 @ sK0 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f176]) ).
thf(f178,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f165]) ).
thf(f179,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f180,plain,
( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s4 @ Y2 @ Y3 )
| ( p @ Y3 ) ) ) ) ) ) ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( ~ ( rel_s4 @ sK0 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f180]) ).
thf(f182,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f183,plain,
( ( ~ ( rel_s4 @ sK0 @ sK2 ) )
= $false ),
inference(or_proxy_clausification,[],[f181]) ).
thf(f184,plain,
( ( rel_s4 @ sK0 @ sK2 )
= $true ),
inference(not_proxy_clausification,[],[f183]) ).
thf(f185,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f186,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK2 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X1: $i] :
( $true
= ( ~ ( rel_s4 @ sK2 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f186]) ).
thf(f188,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK2 @ X1 ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
= $false )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ ( sK3 @ X1 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X1: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( ( ~ ( rel_s4 @ X1 @ ( sK3 @ X1 ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ ( sK3 @ X1 ) @ Y0 )
| ( p @ Y0 ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f191]) ).
thf(f193,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ ( sK3 @ X1 ) @ Y0 )
| ( p @ Y0 ) ) ) )
= $false )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X1: $i] :
( ( ( ~ ( rel_s4 @ X1 @ ( sK3 @ X1 ) ) )
= $false )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f192]) ).
thf(f195,plain,
! [X1: $i] :
( ( $true
= ( rel_s4 @ X1 @ ( sK3 @ X1 ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ ( sK3 @ X1 ) @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f193]) ).
thf(f197,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ ( sK3 @ X1 ) @ Y0 )
| ( p @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( ( ~ ( rel_s4 @ ( sK3 @ X1 ) @ X2 )
| ( p @ X2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f197]) ).
thf(f199,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ ( sK3 @ X1 ) @ X2 ) ) )
| ( ( p @ X2 )
= $true )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ ( sK3 @ X1 ) @ X2 )
= $false )
| ( ( p @ X2 )
= $true )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f199]) ).
thf(f227,plain,
! [X0: $i] :
( ( ( rel_s4 @ sK0 @ ( sK3 @ X0 ) )
= $false )
| ( $true = $false )
| ( $true
= ( p @ ( sK1 @ ( sK3 @ X0 ) ) ) )
| ( ( rel_s4 @ sK2 @ X0 )
= $false ) ),
inference(constrained_superposition,[],[f200,f177]) ).
thf(f232,plain,
! [X0: $i] :
( ( ( rel_s4 @ sK0 @ ( sK3 @ X0 ) )
= $false )
| ( $true
= ( p @ ( sK1 @ ( sK3 @ X0 ) ) ) )
| ( ( rel_s4 @ sK2 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f227]) ).
thf(f278,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( rel_s4 @ X1 @ X0 )
= $false )
| ( $false
= ( p @ ( sK1 @ X0 ) ) )
| ( ( rel_s4 @ sK0 @ X1 )
= $false ) ),
inference(constrained_superposition,[],[f158,f175]) ).
thf(f291,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( rel_s4 @ X0 @ sK2 ) )
| ( ( rel_s4 @ X0 @ sK0 )
= $false ) ),
inference(constrained_superposition,[],[f158,f184]) ).
thf(f308,plain,
! [X0: $i] :
( ( $true
= ( rel_s4 @ X0 @ sK2 ) )
| ( ( rel_s4 @ X0 @ sK0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f291]) ).
thf(f316,plain,
! [X0: $i,X1: $i] :
( ( ( rel_s4 @ sK0 @ X1 )
= $false )
| ( ( rel_s4 @ X1 @ X0 )
= $false )
| ( $false
= ( p @ ( sK1 @ X0 ) ) ) ),
inference(trivial_inequality_removal,[],[f278]) ).
thf(f334,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( rel_s4 @ X0 @ X1 ) )
| ( $true = $false )
| ( ( rel_s4 @ X0 @ sK0 )
= $false )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(constrained_superposition,[],[f308,f158]) ).
thf(f349,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( ( rel_s4 @ X0 @ sK0 )
= $false )
| ( $true
= ( rel_s4 @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[],[f334]) ).
thf(f532,plain,
! [X0: $i,X1: $i] :
( ( ( rel_s4 @ X0 @ sK0 )
= $false )
| ( ( rel_s4 @ sK0 @ X0 )
= $false )
| ( ( p @ ( sK1 @ X1 ) )
= $false )
| ( $true = $false )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) ) ),
inference(constrained_superposition,[],[f349,f316]) ).
thf(f539,plain,
! [X0: $i] :
( ( $true = $false )
| ( ( rel_s4 @ sK2 @ sK2 )
= $false )
| ( $true
= ( rel_s4 @ X0 @ ( sK3 @ sK2 ) ) )
| ( ( rel_s4 @ X0 @ sK0 )
= $false ) ),
inference(constrained_superposition,[],[f195,f349]) ).
thf(f562,plain,
! [X0: $i] :
( ( ( rel_s4 @ sK2 @ sK2 )
= $false )
| ( ( rel_s4 @ X0 @ sK0 )
= $false )
| ( $true
= ( rel_s4 @ X0 @ ( sK3 @ sK2 ) ) ) ),
inference(trivial_inequality_removal,[],[f539]) ).
thf(f590,plain,
! [X0: $i,X1: $i] :
( ( ( p @ ( sK1 @ X1 ) )
= $false )
| ( ( rel_s4 @ X0 @ sK0 )
= $false )
| ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( ( rel_s4 @ sK0 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f532]) ).
thf(f597,definition,
( spl4_5
<=> ! [X0: $i] :
( ( ( rel_s4 @ X0 @ sK0 )
= $false )
| ( ( rel_s4 @ sK0 @ X0 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f598,plain,
( ! [X0: $i] :
( ( ( rel_s4 @ sK0 @ X0 )
= $false )
| ( ( rel_s4 @ X0 @ sK0 )
= $false ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f597]) ).
thf(f600,definition,
( spl4_6
<=> ! [X1: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( ( p @ ( sK1 @ X1 ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f601,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s4 @ sK2 @ X1 ) )
| ( ( p @ ( sK1 @ X1 ) )
= $false ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f600]) ).
thf(f603,plain,
! [X0: $i] :
( ( ( rel_s4 @ X0 @ sK0 )
= $false )
| ( $true
= ( rel_s4 @ X0 @ ( sK3 @ sK2 ) ) )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f562,f161]) ).
thf(f604,plain,
! [X0: $i] :
( ( $true
= ( rel_s4 @ X0 @ ( sK3 @ sK2 ) ) )
| ( ( rel_s4 @ X0 @ sK0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f603]) ).
thf(f609,plain,
( spl4_5
| spl4_6 ),
inference(avatar_split_clause,[],[f590,f600,f597]) ).
thf(f619,plain,
( ( ( rel_s4 @ sK0 @ sK0 )
= $false )
| ( $false != $false )
| ~ spl4_5 ),
inference(equality_factoring,[],[f598]) ).
thf(f624,plain,
( ( ( rel_s4 @ sK0 @ sK0 )
= $false )
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f619]) ).
thf(f637,plain,
( ( $true = $false )
| ~ spl4_5 ),
inference(forward_demodulation,[],[f624,f161]) ).
thf(f638,plain,
( $false
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f637]) ).
thf(f639,plain,
~ spl4_5,
inference(avatar_contradiction_clause,[],[f638]) ).
thf(f644,plain,
( ( ( rel_s4 @ sK2 @ sK2 )
= $false )
| ( ( p @ ( sK1 @ ( sK3 @ sK2 ) ) )
= $false )
| ( $true = $false )
| ~ spl4_6 ),
inference(constrained_superposition,[],[f601,f195]) ).
thf(f664,plain,
( ( ( rel_s4 @ sK2 @ sK2 )
= $false )
| ( ( p @ ( sK1 @ ( sK3 @ sK2 ) ) )
= $false )
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f644]) ).
thf(f666,plain,
( ( $true = $false )
| ( ( p @ ( sK1 @ ( sK3 @ sK2 ) ) )
= $false )
| ~ spl4_6 ),
inference(forward_demodulation,[],[f664,f161]) ).
thf(f667,plain,
( ( ( p @ ( sK1 @ ( sK3 @ sK2 ) ) )
= $false )
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f666]) ).
thf(f677,plain,
( ( $true
= ( p @ ( sK1 @ ( sK3 @ sK2 ) ) ) )
| ( $true = $false )
| ( ( rel_s4 @ sK0 @ sK0 )
= $false )
| ( ( rel_s4 @ sK2 @ sK2 )
= $false ) ),
inference(constrained_superposition,[],[f604,f232]) ).
thf(f717,plain,
( ( $true
= ( p @ ( sK1 @ ( sK3 @ sK2 ) ) ) )
| ( ( rel_s4 @ sK0 @ sK0 )
= $false )
| ( ( rel_s4 @ sK2 @ sK2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f677]) ).
thf(f720,plain,
( ( ( rel_s4 @ sK0 @ sK0 )
= $false )
| ( ( rel_s4 @ sK2 @ sK2 )
= $false )
| ( $true = $false )
| ~ spl4_6 ),
inference(forward_demodulation,[],[f717,f667]) ).
thf(f721,plain,
( ( ( rel_s4 @ sK0 @ sK0 )
= $false )
| ( ( rel_s4 @ sK2 @ sK2 )
= $false )
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f720]) ).
thf(f724,plain,
( ( $true = $false )
| ( ( rel_s4 @ sK2 @ sK2 )
= $false )
| ~ spl4_6 ),
inference(forward_demodulation,[],[f721,f161]) ).
thf(f725,plain,
( ( ( rel_s4 @ sK2 @ sK2 )
= $false )
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f724]) ).
thf(f729,plain,
( ( $true = $false )
| ~ spl4_6 ),
inference(forward_demodulation,[],[f725,f161]) ).
thf(f730,plain,
( $false
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f729]) ).
thf(f731,plain,
~ spl4_6,
inference(avatar_contradiction_clause,[],[f730]) ).
cnf(s6,plain,
( spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f609]) ).
cnf(s10,plain,
~ spl4_5,
inference(sat_conversion,[],[f639]) ).
cnf(s12,plain,
~ spl4_6,
inference(sat_conversion,[],[f731]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s6,s12,s10]) ).
thf(f732,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO440^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n016.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 16:56:50 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 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
% 0.22/0.30 % (613041)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.30 % (613047)lrs+10_16_si=on:nwc=1.5:random_seed=3709175681:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.30 % (613047)Instruction limit reached!
% 0.22/0.30 % (613047)------------------------------
% 0.22/0.30 % (613047)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (613047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (613047)CaDiCaL version: 2.1.3
% 0.22/0.30 % (613047)Termination reason: Instruction limit
% 0.22/0.30 % (613047)Termination phase: Saturation
% 0.22/0.30 % (613047)Time elapsed: 0.006 s
% 0.22/0.30 % (613047)Peak memory usage: 12 MB
% 0.22/0.30 % (613047)Instructions burned: 21 (million)
% 0.22/0.30 % (613046)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3798350921:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.30 % (613048)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1144699553:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.30 % (613050)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1705530792:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.30 % (613049)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=3283674937: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)
% 0.22/0.30 % (613048)Instruction limit reached!
% 0.22/0.30 % (613048)------------------------------
% 0.22/0.30 % (613048)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (613048)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (613048)CaDiCaL version: 2.1.3
% 0.22/0.30 % (613048)Termination reason: Instruction limit
% 0.22/0.30 % (613048)Termination phase: Property scanning
% 0.22/0.30 % (613048)Time elapsed: 0.003 s
% 0.22/0.30 % (613048)Peak memory usage: 10 MB
% 0.22/0.30 % (613048)Instructions burned: 7 (million)
% 0.22/0.30 % (613051)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3327254664:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.30 % (613052)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.30 % (613052)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
% 0.22/0.30 % (613052)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=296568250:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.30 % (613050)Instruction limit reached!
% 0.22/0.30 % (613050)------------------------------
% 0.22/0.30 % (613050)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (613050)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (613050)CaDiCaL version: 2.1.3
% 0.22/0.30 % (613050)Termination reason: Instruction limit
% 0.22/0.30 % (613050)Termination phase: Saturation
% 0.22/0.30 % (613050)Time elapsed: 0.015 s
% 0.22/0.30 % (613050)Peak memory usage: 12 MB
% 0.22/0.30 % (613050)Instructions burned: 24 (million)
% 0.22/0.30 % (613054)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2741293840:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.30 % (613054)Instruction limit reached!
% 0.22/0.30 % (613054)------------------------------
% 0.22/0.30 % (613054)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (613054)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (613054)CaDiCaL version: 2.1.3
% 0.22/0.30 % (613054)Termination reason: Instruction limit
% 0.22/0.30 % (613054)Termination phase: Property scanning
% 0.22/0.30 % (613054)Time elapsed: 0.002 s
% 0.22/0.30 % (613054)Peak memory usage: 10 MB
% 0.22/0.30 % (613054)Instructions burned: 3 (million)
% 0.22/0.30 % (613059)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2252091141:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.30 % (613046) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-613041-613046"...
% 0.22/0.30 % (613059)Instruction limit reached!
% 0.22/0.30 % (613059)------------------------------
% 0.22/0.30 % (613059)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (613059)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (613059)CaDiCaL version: 2.1.3
% 0.22/0.30 % (613059)Termination reason: Instruction limit
% 0.22/0.30 % (613059)Termination phase: Property scanning
% 0.22/0.30 % (613059)Time elapsed: 0.003 s
% 0.22/0.30 % (613059)Peak memory usage: 10 MB
% 0.22/0.30 % (613059)Instructions burned: 5 (million)
% 0.22/0.30 % (613046)...printing done.
% 0.22/0.30 % (613046)Refutation found. Thanks to Tanya!
% 0.22/0.30 % SZS status Theorem for theBenchmark
% 0.22/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.31 % (613046)------------------------------
% 0.22/0.31 % (613046)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (613046)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (613046)CaDiCaL version: 2.1.3
% 0.22/0.31 % (613046)Termination reason: Refutation
% 0.22/0.31 % (613046)Time elapsed: 0.028 s
% 0.22/0.31 % (613046)Peak memory usage: 13 MB
% 0.22/0.31 % (613046)Instructions burned: 53 (million)
% 0.22/0.31 % (613041)Success in time 0.068 s
% 0.22/0.31 % Vampire exiting
%------------------------------------------------------------------------------