%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO438^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 0.21s 0.32s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 20
% Syntax : Number of formulae : 163 ( 65 unt; 0 typ; 9 def)
% Number of atoms : 1190 ( 239 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 1735 ( 289 ~; 289 |; 13 &;1015 @)
% ( 8 <=>; 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 : 121 ( 121 >; 0 *; 0 +; 0 <<)
% Number of symbols : 71 ( 67 usr; 14 con; 0-4 aty)
% ( 109 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 386 ( 0 sgn 96 !; 0 ?; 386 :)
% 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,
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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_44,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_45,type,
vNOT: $o > $o ).
thf(func_def_46,type,
vIMP: $o > $o > $o ).
thf(func_def_47,type,
vAND: $o > $o > $o ).
thf(func_def_48,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vOR: $o > $o > $o ).
thf(func_def_51,type,
sF0: $o ).
thf(func_def_52,type,
sK1: $i > $i ).
thf(func_def_53,type,
sK2: $i > $i ).
thf(func_def_54,type,
sK3: $i > $i ).
thf(func_def_55,type,
sK4: $i > $i ).
thf(func_def_56,type,
sK5: $i > $i ).
thf(func_def_59,type,
sK8: $i > $i ).
thf(func_def_60,type,
sK9: $i > $i ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f18,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
thf(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X3: $i,X2: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( 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] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f33,axiom,
( mdia_s4
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',mdia_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 @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ p ) ) ) ) @ ( mbox_s4 @ ( mdia_s4 @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f37,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ p ) ) ) ) @ ( mbox_s4 @ ( mdia_s4 @ p ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f41,plain,
mtransitive @ rel_s4,
inference(rectify,[],[f35]) ).
thf(f42,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f41]) ).
thf(f45,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f46,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f45]) ).
thf(f67,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
inference(rectify,[],[f18]) ).
thf(f68,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f67]) ).
thf(f69,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f70,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f72,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f81,plain,
mreflexive @ rel_s4,
inference(rectify,[],[f34]) ).
thf(f82,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f81]) ).
thf(f83,plain,
~ ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ p ) ) ) ) @ ( mbox_s4 @ ( mdia_s4 @ p ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f84,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ p ) ) ) ) @ ( mbox_s4 @ ( mdia_s4 @ p ) ) ) )
!= $true ),
inference(fool_elimination,[],[f83]) ).
thf(f87,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f88,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f87]) ).
thf(f89,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X3 @ X2 ) )
=> ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f90,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f89]) ).
thf(f93,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f94,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f93]) ).
thf(f95,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f98,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ p ) ) ) ) @ ( mbox_s4 @ ( mdia_s4 @ p ) ) ) )
!= $true ),
inference(flattening,[],[f84]) ).
thf(f100,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f105,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f94]) ).
thf(f107,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f95]) ).
thf(f109,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f110,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ p ) ) ) ) @ ( mbox_s4 @ ( mdia_s4 @ p ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f116,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f82]) ).
thf(f118,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f119,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f120,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f128,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f134,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f42]) ).
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,[],[f107,f119,f105]) ).
thf(f146,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f109,f105,f128,f105]) ).
thf(f147,plain,
( ( ^ [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] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ p ) ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ p ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f110,f118,f138,f128,f146,f128,f146,f128,f146]) ).
thf(f148,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f116,f120]) ).
thf(f149,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y1 @ Y2 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f134,f100]) ).
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] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ p ) ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ p ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f151,plain,
sF0 != $true,
inference(definition_folding,[],[f147,f150]) ).
thf(f152,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y0 @ Y1 )
& ( rel_s4 @ Y2 @ Y0 ) )
=> ( rel_s4 @ Y2 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f153,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y0 @ Y1 )
& ( rel_s4 @ Y2 @ Y0 ) )
=> ( rel_s4 @ Y2 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ X1 @ Y0 )
& ( rel_s4 @ Y1 @ X1 ) )
=> ( rel_s4 @ Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f155,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ X1 @ Y0 )
& ( rel_s4 @ Y1 @ X1 ) )
=> ( rel_s4 @ Y1 @ Y0 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s4 @ X1 @ X2 )
& ( rel_s4 @ Y0 @ X1 ) )
=> ( rel_s4 @ Y0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f157,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s4 @ X1 @ X2 )
& ( rel_s4 @ Y0 @ X1 ) )
=> ( rel_s4 @ Y0 @ X2 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s4 @ X1 @ X2 )
& ( rel_s4 @ X3 @ X1 ) )
=> ( rel_s4 @ X3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f157]) ).
thf(f159,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( rel_s4 @ X1 @ X2 )
& ( rel_s4 @ X3 @ X1 ) )
= $false )
| ( $true
= ( rel_s4 @ X3 @ X2 ) ) ),
inference(imp_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_s4 @ X3 @ X2 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( rel_s4 @ X3 @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f159]) ).
thf(f161,plain,
( ( sF0 = $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] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ p ) ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ p ) ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f150]) ).
thf(f220,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( p @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) )
= $false )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f221,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( !! @ $i
@ ^ [Y4: $i] :
( ~ ( p @ Y4 )
| ~ ( rel_s4 @ Y3 @ Y4 ) ) )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) )
@ sK6 ) )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f220]) ).
thf(f222,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK6 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( p @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK6 @ Y0 ) ) ) )
= $false )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f221]) ).
thf(f223,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( p @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK6 @ Y0 ) ) ) )
= $false )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f222]) ).
thf(f224,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK6 @ Y0 ) ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f222]) ).
thf(f225,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK6 @ Y0 ) )
@ sK7 ) )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f224]) ).
thf(f226,plain,
( ( sF0 = $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) )
| ~ ( rel_s4 @ sK6 @ sK7 ) ) ) ),
inference(beta-eta_normalization,[],[f225]) ).
thf(f227,plain,
( ( $false
= ( ~ ( rel_s4 @ sK6 @ sK7 ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f226]) ).
thf(f228,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) ) )
= $false )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f226]) ).
thf(f229,plain,
( ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s4 @ sK7 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s4 @ sK7 @ Y0 ) )
@ X1 ) )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f229]) ).
thf(f231,plain,
! [X1: $i] :
( ( $true
= ( ~ ( p @ X1 )
| ~ ( rel_s4 @ sK7 @ X1 ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f230]) ).
thf(f232,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK7 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f231]) ).
thf(f233,plain,
! [X1: $i] :
( ( $true
= ( ~ ( p @ X1 ) ) )
| ( sF0 = $true )
| ( $false
= ( rel_s4 @ sK7 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( $false
= ( rel_s4 @ sK7 @ X1 ) )
| ( $false
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f233]) ).
thf(f235,plain,
( ( $true
= ( rel_s4 @ sK6 @ sK7 ) )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f227]) ).
thf(f236,plain,
( ( sF0 = $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( p @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK6 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f223]) ).
thf(f237,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( !! @ $i
@ ^ [Y3: $i] :
( ~ ( p @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK6 @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f236]) ).
thf(f238,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) ) )
| ~ ( rel_s4 @ sK6 @ X1 ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f237]) ).
thf(f239,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( rel_s4 @ sK6 @ X1 ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f238]) ).
thf(f240,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK6 @ X1 ) ) )
| ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f239]) ).
thf(f241,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) ) )
= $false )
| ( ( rel_s4 @ sK6 @ X1 )
= $false )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f240]) ).
thf(f242,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( rel_s4 @ sK6 @ X1 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) )
@ ( sK8 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f241]) ).
thf(f243,plain,
! [X1: $i] :
( ( ( rel_s4 @ sK6 @ X1 )
= $false )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ ( sK8 @ X1 ) @ Y0 ) ) )
| ~ ( rel_s4 @ X1 @ ( sK8 @ X1 ) ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f242]) ).
thf(f244,plain,
! [X1: $i] :
( ( ( rel_s4 @ sK6 @ X1 )
= $false )
| ( sF0 = $true )
| ( ( ~ ( rel_s4 @ X1 @ ( sK8 @ X1 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f243]) ).
thf(f245,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ ( sK8 @ X1 ) @ Y0 ) ) ) ) )
| ( ( rel_s4 @ sK6 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f243]) ).
thf(f246,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ ( sK8 @ X1 ) @ Y0 ) ) ) )
| ( ( rel_s4 @ sK6 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f245]) ).
thf(f247,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK6 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ ( sK8 @ X1 ) @ Y0 ) )
@ X2 ) )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f246]) ).
thf(f248,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK6 @ X1 )
= $false )
| ( sF0 = $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s4 @ X2 @ Y0 ) ) )
| ~ ( rel_s4 @ ( sK8 @ X1 ) @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f247]) ).
thf(f249,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s4 @ X2 @ Y0 ) ) ) ) )
| ( sF0 = $true )
| ( $true
= ( ~ ( rel_s4 @ ( sK8 @ X1 ) @ X2 ) ) )
| ( ( rel_s4 @ sK6 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f248]) ).
thf(f250,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ ( sK8 @ X1 ) @ X2 ) ) )
| ( sF0 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s4 @ X2 @ Y0 ) ) ) )
| ( ( rel_s4 @ sK6 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f249]) ).
thf(f251,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s4 @ X2 @ Y0 ) ) ) )
| ( $false
= ( rel_s4 @ ( sK8 @ X1 ) @ X2 ) )
| ( sF0 = $true )
| ( ( rel_s4 @ sK6 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f250]) ).
thf(f252,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s4 @ X2 @ Y0 ) )
@ ( sK9 @ X2 ) )
= $false )
| ( ( rel_s4 @ sK6 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ ( sK8 @ X1 ) @ X2 ) )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f251]) ).
thf(f253,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( p @ ( sK9 @ X2 ) )
| ~ ( rel_s4 @ X2 @ ( sK9 @ X2 ) ) )
= $false )
| ( $false
= ( rel_s4 @ ( sK8 @ X1 ) @ X2 ) )
| ( ( rel_s4 @ sK6 @ X1 )
= $false )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f252]) ).
thf(f254,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( rel_s4 @ X2 @ ( sK9 @ X2 ) ) ) )
| ( $false
= ( rel_s4 @ ( sK8 @ X1 ) @ X2 ) )
| ( sF0 = $true )
| ( ( rel_s4 @ sK6 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f253]) ).
thf(f255,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s4 @ ( sK8 @ X1 ) @ X2 ) )
| ( ( rel_s4 @ sK6 @ X1 )
= $false )
| ( ( ~ ( p @ ( sK9 @ X2 ) ) )
= $false )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f253]) ).
thf(f256,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s4 @ ( sK8 @ X1 ) @ X2 ) )
| ( sF0 = $true )
| ( ( rel_s4 @ sK6 @ X1 )
= $false )
| ( $true
= ( p @ ( sK9 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f255]) ).
thf(f257,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s4 @ ( sK8 @ X1 ) @ X2 ) )
| ( ( rel_s4 @ sK6 @ X1 )
= $false )
| ( $true
= ( rel_s4 @ X2 @ ( sK9 @ X2 ) ) )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f254]) ).
thf(f258,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( rel_s4 @ sK6 @ X1 )
= $false )
| ( $true
= ( rel_s4 @ X1 @ ( sK8 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f244]) ).
thf(f259,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f260,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f259]) ).
thf(f261,plain,
! [X1: $i] :
( $true
= ( rel_s4 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f260]) ).
thf(f291,definition,
( spl10_8
<=> ( sF0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl10_8])],[avatar_definition]) ).
thf(f295,definition,
( spl10_9
<=> ! [X1: $i] :
( ( $false
= ( rel_s4 @ sK7 @ X1 ) )
| ( $false
= ( p @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_9])],[avatar_definition]) ).
thf(f296,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s4 @ sK7 @ X1 ) )
| ( $false
= ( p @ X1 ) ) )
| ~ spl10_9 ),
inference(avatar_component_clause,[],[f295]) ).
thf(f297,plain,
( spl10_8
| spl10_9 ),
inference(avatar_split_clause,[],[f234,f295,f291]) ).
thf(f299,definition,
( spl10_10
<=> ( $true
= ( rel_s4 @ sK6 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_10])],[avatar_definition]) ).
thf(f301,plain,
( ( $true
= ( rel_s4 @ sK6 @ sK7 ) )
| ~ spl10_10 ),
inference(avatar_component_clause,[],[f299]) ).
thf(f302,plain,
( spl10_8
| spl10_10 ),
inference(avatar_split_clause,[],[f235,f299,f291]) ).
thf(f304,definition,
( spl10_11
<=> ! [X2: $i,X1: $i] :
( ( $false
= ( rel_s4 @ ( sK8 @ X1 ) @ X2 ) )
| ( $true
= ( p @ ( sK9 @ X2 ) ) )
| ( ( rel_s4 @ sK6 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl10_11])],[avatar_definition]) ).
thf(f305,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( rel_s4 @ ( sK8 @ X1 ) @ X2 ) )
| ( ( rel_s4 @ sK6 @ X1 )
= $false )
| ( $true
= ( p @ ( sK9 @ X2 ) ) ) )
| ~ spl10_11 ),
inference(avatar_component_clause,[],[f304]) ).
thf(f306,plain,
( spl10_11
| spl10_8 ),
inference(avatar_split_clause,[],[f256,f291,f304]) ).
thf(f308,definition,
( spl10_12
<=> ! [X2: $i,X1: $i] :
( ( $false
= ( rel_s4 @ ( sK8 @ X1 ) @ X2 ) )
| ( $true
= ( rel_s4 @ X2 @ ( sK9 @ X2 ) ) )
| ( ( rel_s4 @ sK6 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl10_12])],[avatar_definition]) ).
thf(f309,plain,
( ! [X2: $i,X1: $i] :
( ( $true
= ( rel_s4 @ X2 @ ( sK9 @ X2 ) ) )
| ( ( rel_s4 @ sK6 @ X1 )
= $false )
| ( $false
= ( rel_s4 @ ( sK8 @ X1 ) @ X2 ) ) )
| ~ spl10_12 ),
inference(avatar_component_clause,[],[f308]) ).
thf(f310,plain,
( spl10_12
| spl10_8 ),
inference(avatar_split_clause,[],[f257,f291,f308]) ).
thf(f312,definition,
( spl10_13
<=> ! [X1: $i] :
( ( ( rel_s4 @ sK6 @ X1 )
= $false )
| ( $true
= ( rel_s4 @ X1 @ ( sK8 @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_13])],[avatar_definition]) ).
thf(f313,plain,
( ! [X1: $i] :
( ( $true
= ( rel_s4 @ X1 @ ( sK8 @ X1 ) ) )
| ( ( rel_s4 @ sK6 @ X1 )
= $false ) )
| ~ spl10_13 ),
inference(avatar_component_clause,[],[f312]) ).
thf(f314,plain,
( spl10_13
| spl10_8 ),
inference(avatar_split_clause,[],[f258,f291,f312]) ).
thf(f315,plain,
~ spl10_8,
inference(avatar_split_clause,[],[f151,f291]) ).
thf(f338,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ sK7 @ X1 ) )
| ( $false
= ( rel_s4 @ X1 @ X0 ) )
| ( $true = $false )
| ( $false
= ( p @ X0 ) ) )
| ~ spl10_9 ),
inference(constrained_superposition,[],[f296,f160]) ).
thf(f341,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel_s4 @ sK7 @ X1 ) )
| ( $false
= ( rel_s4 @ X1 @ X0 ) )
| ( $false
= ( p @ X0 ) ) )
| ~ spl10_9 ),
inference(trivial_inequality_removal,[],[f338]) ).
thf(f359,plain,
( ! [X0: $i] :
( ( $false
= ( p @ X0 ) )
| ( $true = $false )
| ( $false
= ( rel_s4 @ sK6 @ sK7 ) )
| ( $false
= ( rel_s4 @ ( sK8 @ sK7 ) @ X0 ) ) )
| ~ spl10_9
| ~ spl10_13 ),
inference(constrained_superposition,[],[f313,f341]) ).
thf(f361,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s4 @ sK6 @ sK7 ) )
| ( $false
= ( p @ X0 ) )
| ( $false
= ( rel_s4 @ ( sK8 @ sK7 ) @ X0 ) ) )
| ~ spl10_9
| ~ spl10_13 ),
inference(trivial_inequality_removal,[],[f359]) ).
thf(f369,plain,
( ! [X0: $i] :
( ( $false
= ( p @ X0 ) )
| ( $true = $false )
| ( $false
= ( rel_s4 @ ( sK8 @ sK7 ) @ X0 ) ) )
| ~ spl10_9
| ~ spl10_10
| ~ spl10_13 ),
inference(forward_demodulation,[],[f361,f301]) ).
thf(f370,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s4 @ ( sK8 @ sK7 ) @ X0 ) )
| ( $false
= ( p @ X0 ) ) )
| ~ spl10_9
| ~ spl10_10
| ~ spl10_13 ),
inference(trivial_inequality_removal,[],[f369]) ).
thf(f570,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s4 @ sK6 @ X0 ) )
| ( $true = $false )
| ( $true
= ( p @ ( sK9 @ ( sK8 @ X0 ) ) ) ) )
| ~ spl10_11 ),
inference(constrained_superposition,[],[f261,f305]) ).
thf(f573,plain,
( ! [X0: $i] :
( ( $true
= ( p @ ( sK9 @ ( sK8 @ X0 ) ) ) )
| ( $false
= ( rel_s4 @ sK6 @ X0 ) ) )
| ~ spl10_11 ),
inference(trivial_inequality_removal,[],[f570]) ).
thf(f662,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s4 @ sK6 @ X0 ) )
| ( $true = $false )
| ( $false
= ( rel_s4 @ ( sK8 @ X0 ) @ ( sK8 @ sK7 ) ) )
| ( $false
= ( p @ ( sK9 @ ( sK8 @ sK7 ) ) ) ) )
| ~ spl10_9
| ~ spl10_10
| ~ spl10_12
| ~ spl10_13 ),
inference(constrained_superposition,[],[f370,f309]) ).
thf(f680,plain,
( ! [X0: $i] :
( ( $false
= ( p @ ( sK9 @ ( sK8 @ sK7 ) ) ) )
| ( $false
= ( rel_s4 @ ( sK8 @ X0 ) @ ( sK8 @ sK7 ) ) )
| ( $false
= ( rel_s4 @ sK6 @ X0 ) ) )
| ~ spl10_9
| ~ spl10_10
| ~ spl10_12
| ~ spl10_13 ),
inference(trivial_inequality_removal,[],[f662]) ).
thf(f709,definition,
( spl10_39
<=> ! [X1: $i] :
( ( ( rel_s4 @ sK6 @ X1 )
= $false )
| ( ( rel_s4 @ ( sK8 @ X1 ) @ ( sK8 @ sK7 ) )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl10_39])],[avatar_definition]) ).
thf(f710,plain,
( ! [X1: $i] :
( ( ( rel_s4 @ ( sK8 @ X1 ) @ ( sK8 @ sK7 ) )
= $false )
| ( ( rel_s4 @ sK6 @ X1 )
= $false ) )
| ~ spl10_39 ),
inference(avatar_component_clause,[],[f709]) ).
thf(f716,definition,
( spl10_41
<=> ( $false
= ( p @ ( sK9 @ ( sK8 @ sK7 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_41])],[avatar_definition]) ).
thf(f718,plain,
( ( $false
= ( p @ ( sK9 @ ( sK8 @ sK7 ) ) ) )
| ~ spl10_41 ),
inference(avatar_component_clause,[],[f716]) ).
thf(f729,plain,
( spl10_41
| spl10_39
| ~ spl10_9
| ~ spl10_10
| ~ spl10_12
| ~ spl10_13 ),
inference(avatar_split_clause,[],[f680,f312,f308,f299,f295,f709,f716]) ).
thf(f752,plain,
( ( $true = $false )
| ( $false
= ( rel_s4 @ sK6 @ sK7 ) )
| ~ spl10_39 ),
inference(constrained_superposition,[],[f261,f710]) ).
thf(f757,plain,
( ( $false
= ( rel_s4 @ sK6 @ sK7 ) )
| ~ spl10_39 ),
inference(trivial_inequality_removal,[],[f752]) ).
thf(f762,plain,
( ( $true = $false )
| ~ spl10_10
| ~ spl10_39 ),
inference(forward_demodulation,[],[f757,f301]) ).
thf(f763,plain,
( $false
| ~ spl10_10
| ~ spl10_39 ),
inference(trivial_inequality_removal,[],[f762]) ).
thf(f764,plain,
( ~ spl10_10
| ~ spl10_39 ),
inference(avatar_contradiction_clause,[],[f763]) ).
thf(f765,plain,
( ( $false
= ( rel_s4 @ sK6 @ sK7 ) )
| ( $true = $false )
| ~ spl10_11
| ~ spl10_41 ),
inference(constrained_superposition,[],[f718,f573]) ).
thf(f769,plain,
( ( $false
= ( rel_s4 @ sK6 @ sK7 ) )
| ~ spl10_11
| ~ spl10_41 ),
inference(trivial_inequality_removal,[],[f765]) ).
thf(f774,plain,
( ( $true = $false )
| ~ spl10_10
| ~ spl10_11
| ~ spl10_41 ),
inference(forward_demodulation,[],[f769,f301]) ).
thf(f775,plain,
( $false
| ~ spl10_10
| ~ spl10_11
| ~ spl10_41 ),
inference(trivial_inequality_removal,[],[f774]) ).
thf(f776,plain,
( ~ spl10_10
| ~ spl10_11
| ~ spl10_41 ),
inference(avatar_contradiction_clause,[],[f775]) ).
cnf(s7,plain,
( spl10_8
| spl10_9 ),
inference(sat_conversion,[],[f297]) ).
cnf(s8,plain,
( spl10_8
| spl10_10 ),
inference(sat_conversion,[],[f302]) ).
cnf(s9,plain,
( spl10_8
| spl10_11 ),
inference(sat_conversion,[],[f306]) ).
cnf(s10,plain,
( spl10_8
| spl10_12 ),
inference(sat_conversion,[],[f310]) ).
cnf(s11,plain,
( spl10_8
| spl10_13 ),
inference(sat_conversion,[],[f314]) ).
cnf(s12,plain,
~ spl10_8,
inference(sat_conversion,[],[f315]) ).
cnf(s51,plain,
( ~ spl10_9
| ~ spl10_10
| ~ spl10_12
| ~ spl10_13
| spl10_39
| spl10_41 ),
inference(sat_conversion,[],[f729]) ).
cnf(s57,plain,
( ~ spl10_10
| ~ spl10_39 ),
inference(sat_conversion,[],[f764]) ).
cnf(s59,plain,
( ~ spl10_10
| ~ spl10_11
| ~ spl10_41 ),
inference(sat_conversion,[],[f776]) ).
cnf(s61,plain,
spl10_13,
inference(rat,[],[s11,s12]) ).
cnf(s62,plain,
spl10_12,
inference(rat,[],[s10,s12]) ).
cnf(s63,plain,
spl10_11,
inference(rat,[],[s9,s12]) ).
cnf(s64,plain,
spl10_10,
inference(rat,[],[s8,s12]) ).
cnf(s65,plain,
~ spl10_41,
inference(rat,[],[s59,s63,s64]) ).
cnf(s66,plain,
~ spl10_39,
inference(rat,[],[s57,s64]) ).
cnf(s67,plain,
~ spl10_9,
inference(rat,[],[s51,s65,s66,s61,s62,s64]) ).
cnf(s70,plain,
$false,
inference(rat,[],[s7,s67,s12]) ).
thf(f777,plain,
$false,
inference(avatar_sat_refutation,[],[s70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO438^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n008.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 16:52:24 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.21/0.32 % (3419415)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.32 % (3419421)lrs+10_16_si=on:nwc=1.5:random_seed=1617258844:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.32 % (3419426)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.32 % (3419426)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.32 % (3419421)Instruction limit reached!
% 0.21/0.32 % (3419421)------------------------------
% 0.21/0.32 % (3419421)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3419421)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3419421)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3419421)Termination reason: Instruction limit
% 0.21/0.32 % (3419421)Termination phase: Saturation
% 0.21/0.32 % (3419421)Time elapsed: 0.006 s
% 0.21/0.32 % (3419421)Peak memory usage: 12 MB
% 0.21/0.32 % (3419421)Instructions burned: 20 (million)
% 0.21/0.32 % (3419422)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2127395273:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.32 % (3419420)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3245657360:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.32 % (3419425)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2761404911:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.32 % (3419423)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=3098163564:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.32 % (3419426)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=246744439:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.32 % (3419422)Instruction limit reached!
% 0.21/0.32 % (3419422)------------------------------
% 0.21/0.32 % (3419422)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3419422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3419422)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3419422)Termination reason: Instruction limit
% 0.21/0.32 % (3419422)Termination phase: Preprocessing 1
% 0.21/0.32 % (3419422)Time elapsed: 0.002 s
% 0.21/0.32 % (3419422)Peak memory usage: 10 MB
% 0.21/0.32 % (3419422)Instructions burned: 4 (million)
% 0.21/0.32 % (3419424)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3308942129:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.32 % (3419430)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3482588787:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.32 % (3419430)Instruction limit reached!
% 0.21/0.32 % (3419430)------------------------------
% 0.21/0.32 % (3419430)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3419430)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3419430)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3419430)Termination reason: Instruction limit
% 0.21/0.32 % (3419430)Termination phase: Preprocessing 1
% 0.21/0.32 % (3419430)Time elapsed: 0.001 s
% 0.21/0.32 % (3419430)Peak memory usage: 10 MB
% 0.21/0.32 % (3419430)Instructions burned: 4 (million)
% 0.21/0.32 % (3419426) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3419415-3419426"...
% 0.21/0.32 % (3419434)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3464308587:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.32 % (3419437)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.32 % (3419437)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2314949698:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.32 % (3419434)Instruction limit reached!
% 0.21/0.32 % (3419434)------------------------------
% 0.21/0.32 % (3419434)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3419434)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3419434)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3419434)Termination reason: Instruction limit
% 0.21/0.32 % (3419434)Termination phase: Function definition elimination
% 0.21/0.32 % (3419434)Time elapsed: 0.003 s
% 0.21/0.32 % (3419434)Peak memory usage: 10 MB
% 0.21/0.32 % (3419434)Instructions burned: 6 (million)
% 0.21/0.32 % (3419437)Instruction limit reached!
% 0.21/0.32 % (3419437)------------------------------
% 0.21/0.32 % (3419437)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3419437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3419437)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3419437)Termination reason: Instruction limit
% 0.21/0.32 % (3419437)Termination phase: Saturation
% 0.21/0.32 % (3419437)Time elapsed: 0.002 s
% 0.21/0.32 % (3419437)Peak memory usage: 11 MB
% 0.21/0.32 % (3419437)Instructions burned: 8 (million)
% 0.21/0.32 % (3419426)...printing done.
% 0.21/0.32 % (3419426)Refutation found. Thanks to Tanya!
% 0.21/0.32 % SZS status Theorem for theBenchmark
% 0.21/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.32 % (3419426)------------------------------
% 0.21/0.32 % (3419426)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3419426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3419426)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3419426)Termination reason: Refutation
% 0.21/0.32 % (3419426)Time elapsed: 0.025 s
% 0.21/0.32 % (3419426)Peak memory usage: 13 MB
% 0.21/0.32 % (3419426)Instructions burned: 46 (million)
% 0.21/0.32 % (3419415)Success in time 0.066 s
% 0.21/0.32 % Vampire exiting
%------------------------------------------------------------------------------