%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO454^6 : 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 : 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 08:47:48 AM UTC 2026
% Result : Theorem 0.20s 0.35s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 23
% Syntax : Number of formulae : 186 ( 82 unt; 0 typ; 9 def)
% Number of atoms : 1297 ( 260 equ; 0 cnn)
% Maximal formula atoms : 13 ( 6 avg)
% Number of connectives : 1703 ( 306 ~; 303 |; 13 &; 967 @)
% ( 8 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 159 ( 159 >; 0 *; 0 +; 0 <<)
% Number of symbols : 68 ( 64 usr; 15 con; 0-4 aty)
% ( 84 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 407 ( 0 sgn 97 !; 0 ?; 407 :)
% 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_s5: $i > $i > $o ).
thf(func_def_33,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
q: $i > $o ).
thf(func_def_37,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
vIMP: $o > $o > $o ).
thf(func_def_39,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_43,type,
vAND: $o > $o > $o ).
thf(func_def_44,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_46,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_47,type,
vNOT: $o > $o ).
thf(func_def_48,type,
vOR: $o > $o > $o ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
sF0: $o ).
thf(func_def_53,type,
sK1: $i > $i ).
thf(func_def_54,type,
sK2: $i > $i ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) )
= mand ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mand) ).
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(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f21,axiom,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X3: $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,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) )
= mbox_s5 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(f33,axiom,
( ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ X0 ) ) ) )
= mdia_s5 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mdia_s5) ).
thf(f34,axiom,
mreflexive @ rel_s5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',a1) ).
thf(f35,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',a2) ).
thf(f36,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',a3) ).
thf(f37,conjecture,
mvalid @ ( mor @ ( mdia_s5 @ ( mand @ ( mdia_s5 @ p ) @ ( mnot @ q ) ) ) @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ q ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mor @ ( mdia_s5 @ ( mand @ ( mdia_s5 @ p ) @ ( mnot @ q ) ) ) @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ q ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f53,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f54,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f55,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f56,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f57,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f58,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f57]) ).
thf(f59,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f67,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X2 )
& ( X0 @ X1 @ X3 ) )
=> ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f68,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f67]) ).
thf(f70,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f71,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f75,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f76,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f75]) ).
thf(f77,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
=> ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f78,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f77]) ).
thf(f79,plain,
mtransitive @ rel_s5,
inference(rectify,[],[f35]) ).
thf(f80,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f79]) ).
thf(f81,plain,
mreflexive @ rel_s5,
inference(rectify,[],[f34]) ).
thf(f82,plain,
( ( mreflexive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f81]) ).
thf(f87,plain,
~ ( mvalid @ ( mor @ ( mdia_s5 @ ( mand @ ( mdia_s5 @ p ) @ ( mnot @ q ) ) ) @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ q ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f88,plain,
( ( mvalid @ ( mor @ ( mdia_s5 @ ( mand @ ( mdia_s5 @ p ) @ ( mnot @ q ) ) ) @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ q ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f87]) ).
thf(f93,plain,
msymmetric @ rel_s5,
inference(rectify,[],[f36]) ).
thf(f94,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f93]) ).
thf(f97,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) )
= mbox_s5 ),
inference(rectify,[],[f32]) ).
thf(f98,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f97]) ).
thf(f101,plain,
( ( mvalid @ ( mor @ ( mdia_s5 @ ( mand @ ( mdia_s5 @ p ) @ ( mnot @ q ) ) ) @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ q ) ) ) ) )
!= $true ),
inference(flattening,[],[f88]) ).
thf(f103,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f80]) ).
thf(f106,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f107,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f78]) ).
thf(f109,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f110,plain,
( ( mreflexive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f82]) ).
thf(f113,plain,
( ( mvalid @ ( mor @ ( mdia_s5 @ ( mand @ ( mdia_s5 @ p ) @ ( mnot @ q ) ) ) @ ( mbox_s5 @ ( mimplies @ p @ ( mbox_s5 @ q ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f101]) ).
thf(f123,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f98]) ).
thf(f125,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f71]) ).
thf(f126,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f130,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f132,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f133,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f76]) ).
thf(f136,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f137,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f94]) ).
thf(f141,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f130,f126,f133,f126,f126]) ).
thf(f142,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,[],[f125,f133,f126]) ).
thf(f150,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f109,f126,f123,f126]) ).
thf(f151,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y3 @ Y2 ) ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f103,f106]) ).
thf(f152,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f110,f132]) ).
thf(f153,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ q ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [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 )
@ p
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) ) ) ) ) ),
inference(definition_unfolding,[],[f113,f136,f133,f150,f141,f150,f126,f123,f142,f123]) ).
thf(f154,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f137,f107]) ).
thf(f155,definition,
( sF0
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ q ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [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 )
@ p
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f156,plain,
$true != sF0,
inference(definition_folding,[],[f153,f155]) ).
thf(f157,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y0 @ Y1 )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f158,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y0 @ Y1 )
=> ( rel_s5 @ Y1 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ X1 @ Y0 )
=> ( rel_s5 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f158]) ).
thf(f160,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel_s5 @ X1 @ Y0 )
=> ( rel_s5 @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel_s5 @ X1 @ X2 )
=> ( rel_s5 @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f160]) ).
thf(f162,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ X2 @ X1 )
= $true )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y2 @ Y0 )
& ( rel_s5 @ Y0 @ Y1 ) )
=> ( rel_s5 @ Y2 @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f164,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y2 @ Y0 )
& ( rel_s5 @ Y0 @ Y1 ) )
=> ( rel_s5 @ Y2 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f163]) ).
thf(f165,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y1 @ X1 )
& ( rel_s5 @ X1 @ Y0 ) )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f164]) ).
thf(f166,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y1 @ X1 )
& ( rel_s5 @ X1 @ Y0 ) )
=> ( rel_s5 @ Y1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f165]) ).
thf(f167,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s5 @ Y0 @ X1 )
& ( rel_s5 @ X1 @ X2 ) )
=> ( rel_s5 @ Y0 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f166]) ).
thf(f168,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s5 @ Y0 @ X1 )
& ( rel_s5 @ X1 @ X2 ) )
=> ( rel_s5 @ Y0 @ X2 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f167]) ).
thf(f169,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s5 @ X3 @ X1 )
& ( rel_s5 @ X1 @ X2 ) )
=> ( rel_s5 @ X3 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f168]) ).
thf(f170,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s5 @ X3 @ X2 )
= $true )
| ( $false
= ( ( rel_s5 @ X3 @ X1 )
& ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X3 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( ( rel_s5 @ X3 @ X2 )
= $true ) ),
inference(and_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f173,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s5 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X1: $i] :
( $true
= ( rel_s5 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f175,plain,
( ( $false
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ~ ( rel_s5 @ Y2 @ Y3 )
| ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ q ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [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 )
@ p
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(iff_proxy_clausification,[],[f155]) ).
thf(f221,plain,
( ( $true = sF0 )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) )
| ~ ~ ( q @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f222,plain,
( ( $true = sF0 )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( p @ Y2 ) ) )
| ~ ~ ( q @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) ) ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f221]) ).
thf(f223,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ~ ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f222]) ).
thf(f224,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) ) )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f223]) ).
thf(f225,plain,
( ( $true = sF0 )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f223]) ).
thf(f226,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ~ ( q @ Y0 ) ) ) ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ~ ( q @ Y0 ) ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f226]) ).
thf(f228,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s5 @ sK3 @ X1 )
| ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( q @ X1 ) ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f227]) ).
thf(f229,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $true
= ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( q @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_s5 @ sK3 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f228]) ).
thf(f230,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $true
= ( ~ ( rel_s5 @ sK3 @ X1 ) ) )
| ( $false
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( q @ X1 ) ) ) ) ),
inference(not_proxy_clausification,[],[f229]) ).
thf(f231,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $false
= ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( q @ X1 ) ) ) )
| ( $false
= ( rel_s5 @ sK3 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f230]) ).
thf(f232,plain,
! [X1: $i] :
( ( $true = sF0 )
| ( $false
= ( rel_s5 @ sK3 @ X1 ) )
| ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ~ ( q @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f231]) ).
thf(f233,plain,
! [X1: $i] :
( ( ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( p @ Y0 ) ) ) )
= $true )
| ( $false
= ( rel_s5 @ sK3 @ X1 ) )
| ( $true = sF0 )
| ( $true
= ( ~ ~ ( q @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X1: $i] :
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( p @ Y0 ) ) ) ) )
| ( $true = sF0 )
| ( $true
= ( ~ ~ ( q @ X1 ) ) )
| ( $false
= ( rel_s5 @ sK3 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f233]) ).
thf(f235,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( p @ Y0 ) ) ) )
| ( $false
= ( rel_s5 @ sK3 @ X1 ) )
| ( $true
= ( ~ ~ ( q @ X1 ) ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f234]) ).
thf(f236,plain,
! [X2: $i,X1: $i] :
( ( $true = sF0 )
| ( $true
= ( ~ ~ ( q @ X1 ) ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( p @ Y0 ) )
@ X2 ) )
| ( $false
= ( rel_s5 @ sK3 @ X1 ) ) ),
inference(pi_proxy_clausification,[],[f235]) ).
thf(f237,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( q @ X1 ) ) )
| ( $false
= ( rel_s5 @ sK3 @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( p @ Y0 ) )
@ X2 ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f236]) ).
thf(f238,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( p @ Y0 ) )
@ X2 ) )
| ( $true = sF0 )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_s5 @ sK3 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f237]) ).
thf(f239,plain,
! [X2: $i,X1: $i] :
( ( $true = sF0 )
| ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 )
| ~ ( p @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f238]) ).
thf(f240,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_s5 @ X1 @ X2 ) ) )
| ( $true = sF0 )
| ( $true
= ( ~ ( p @ X2 ) ) )
| ( $false
= ( rel_s5 @ sK3 @ X1 ) ) ),
inference(or_proxy_clausification,[],[f239]) ).
thf(f241,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( p @ X2 ) ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $true = sF0 )
| ( $false
= ( rel_s5 @ sK3 @ X1 ) )
| ( $true
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f240]) ).
thf(f242,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( p @ X2 ) )
| ( $false
= ( rel_s5 @ sK3 @ X1 ) )
| ( $true = sF0 )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $true
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f241]) ).
thf(f243,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ sK4 ) )
| ( $true = sF0 ) ),
inference(sigma_proxy_clausification,[],[f224]) ).
thf(f244,plain,
( ( $true = sF0 )
| ( $false
= ( ~ ( rel_s5 @ sK3 @ sK4 )
| ~ ( p @ sK4 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f243]) ).
thf(f245,plain,
( ( $true = sF0 )
| ( $false
= ( ~ ( p @ sK4 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f244]) ).
thf(f246,plain,
( ( $true = sF0 )
| ( $false
= ( ~ ( rel_s5 @ sK3 @ sK4 ) ) ) ),
inference(or_proxy_clausification,[],[f244]) ).
thf(f247,plain,
( ( ( rel_s5 @ sK3 @ sK4 )
= $true )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f246]) ).
thf(f248,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f245]) ).
thf(f249,plain,
( ( $true = sF0 )
| ( $false
= ( ~ ( p @ sK4 ) ) ) ),
inference(or_proxy_clausification,[],[f245]) ).
thf(f250,plain,
( ( $true
= ( p @ sK4 ) )
| ( $true = sF0 ) ),
inference(not_proxy_clausification,[],[f249]) ).
thf(f251,plain,
( ( $true = sF0 )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ( q @ Y0 ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f248]) ).
thf(f252,plain,
( ( $false
= ( ~ ( rel_s5 @ sK4 @ sK5 )
| ( q @ sK5 ) ) )
| ( $true = sF0 ) ),
inference(beta-eta_normalization,[],[f251]) ).
thf(f253,plain,
( ( $false
= ( q @ sK5 ) )
| ( $true = sF0 ) ),
inference(or_proxy_clausification,[],[f252]) ).
thf(f254,plain,
( ( $true = sF0 )
| ( $false
= ( ~ ( rel_s5 @ sK4 @ sK5 ) ) ) ),
inference(or_proxy_clausification,[],[f252]) ).
thf(f255,plain,
( ( $true = sF0 )
| ( $true
= ( rel_s5 @ sK4 @ sK5 ) ) ),
inference(not_proxy_clausification,[],[f254]) ).
thf(f277,definition,
( spl6_6
<=> ! [X2: $i,X1: $i] :
( ( $false
= ( p @ X2 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_s5 @ sK3 @ X1 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
thf(f278,plain,
( ! [X2: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK3 @ X1 ) )
| ( $false
= ( p @ X2 ) )
| ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( $true
= ( q @ X1 ) ) )
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f277]) ).
thf(f280,definition,
( spl6_7
<=> ( $true = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
thf(f283,plain,
( spl6_6
| spl6_7 ),
inference(avatar_split_clause,[],[f242,f280,f277]) ).
thf(f285,definition,
( spl6_8
<=> ( ( rel_s5 @ sK3 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
thf(f287,plain,
( ( ( rel_s5 @ sK3 @ sK4 )
= $true )
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f285]) ).
thf(f288,plain,
( spl6_7
| spl6_8 ),
inference(avatar_split_clause,[],[f247,f285,f280]) ).
thf(f290,definition,
( spl6_9
<=> ( $true
= ( p @ sK4 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition]) ).
thf(f292,plain,
( ( $true
= ( p @ sK4 ) )
| ~ spl6_9 ),
inference(avatar_component_clause,[],[f290]) ).
thf(f293,plain,
( spl6_9
| spl6_7 ),
inference(avatar_split_clause,[],[f250,f280,f290]) ).
thf(f295,definition,
( spl6_10
<=> ( $true
= ( rel_s5 @ sK4 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition]) ).
thf(f297,plain,
( ( $true
= ( rel_s5 @ sK4 @ sK5 ) )
| ~ spl6_10 ),
inference(avatar_component_clause,[],[f295]) ).
thf(f298,plain,
( spl6_10
| spl6_7 ),
inference(avatar_split_clause,[],[f255,f280,f295]) ).
thf(f300,definition,
( spl6_11
<=> ( $false
= ( q @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_11])],[avatar_definition]) ).
thf(f302,plain,
( ( $false
= ( q @ sK5 ) )
| ~ spl6_11 ),
inference(avatar_component_clause,[],[f300]) ).
thf(f303,plain,
( spl6_7
| spl6_11 ),
inference(avatar_split_clause,[],[f253,f300,f280]) ).
thf(f304,plain,
~ spl6_7,
inference(avatar_split_clause,[],[f156,f280]) ).
thf(f323,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( rel_s5 @ sK4 @ X0 ) )
| ( $true
= ( rel_s5 @ sK3 @ X0 ) ) )
| ~ spl6_8 ),
inference(constrained_superposition,[],[f171,f287]) ).
thf(f329,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ sK4 @ X0 ) )
| ( $false = $true )
| ( $false
= ( rel_s5 @ sK5 @ X0 ) ) )
| ~ spl6_10 ),
inference(constrained_superposition,[],[f297,f171]) ).
thf(f334,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ sK3 @ X0 ) )
| ( $false
= ( rel_s5 @ sK4 @ X0 ) ) )
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f323]) ).
thf(f336,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ sK4 @ X0 ) )
| ( $false
= ( rel_s5 @ sK5 @ X0 ) ) )
| ~ spl6_10 ),
inference(trivial_inequality_removal,[],[f329]) ).
thf(f342,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK4 @ X0 ) )
| ( ( rel_s5 @ sK3 @ X1 )
= $true )
| ( $false = $true )
| ( $false
= ( rel_s5 @ X0 @ X1 ) ) )
| ~ spl6_8 ),
inference(constrained_superposition,[],[f334,f171]) ).
thf(f344,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK4 @ X0 ) )
| ( ( rel_s5 @ sK3 @ X1 )
= $true )
| ( $false
= ( rel_s5 @ X0 @ X1 ) ) )
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f342]) ).
thf(f357,plain,
( ! [X0: $i,X1: $i] :
( ( ( rel_s5 @ sK3 @ X1 )
= $true )
| ( $false
= ( rel_s5 @ X0 @ X1 ) )
| ( $false
= ( rel_s5 @ sK5 @ X0 ) )
| ( $false = $true ) )
| ~ spl6_8
| ~ spl6_10 ),
inference(constrained_superposition,[],[f344,f336]) ).
thf(f369,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ sK5 @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ X1 ) )
| ( ( rel_s5 @ sK3 @ X1 )
= $true ) )
| ~ spl6_8
| ~ spl6_10 ),
inference(trivial_inequality_removal,[],[f357]) ).
thf(f535,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X0 @ X1 ) )
| ( $false = $true )
| ( $false
= ( rel_s5 @ X0 @ sK5 ) )
| ( ( rel_s5 @ sK3 @ X1 )
= $true ) )
| ~ spl6_8
| ~ spl6_10 ),
inference(constrained_superposition,[],[f369,f162]) ).
thf(f547,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK5 ) )
| ( $false
= ( rel_s5 @ X0 @ X1 ) )
| ( ( rel_s5 @ sK3 @ X1 )
= $true ) )
| ~ spl6_8
| ~ spl6_10 ),
inference(trivial_inequality_removal,[],[f535]) ).
thf(f571,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ sK3 @ sK5 ) )
| ( $false
= ( rel_s5 @ X0 @ sK5 ) )
| ( $false != $false ) )
| ~ spl6_8
| ~ spl6_10 ),
inference(equality_factoring,[],[f547]) ).
thf(f573,plain,
( ! [X0: $i] :
( ( $true
= ( rel_s5 @ sK3 @ sK5 ) )
| ( $false
= ( rel_s5 @ X0 @ sK5 ) ) )
| ~ spl6_8
| ~ spl6_10 ),
inference(trivial_inequality_removal,[],[f571]) ).
thf(f594,definition,
( spl6_17
<=> ! [X0: $i] :
( $false
= ( rel_s5 @ X0 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_17])],[avatar_definition]) ).
thf(f595,plain,
( ! [X0: $i] :
( $false
= ( rel_s5 @ X0 @ sK5 ) )
| ~ spl6_17 ),
inference(avatar_component_clause,[],[f594]) ).
thf(f597,definition,
( spl6_18
<=> ( $true
= ( rel_s5 @ sK3 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_18])],[avatar_definition]) ).
thf(f599,plain,
( ( $true
= ( rel_s5 @ sK3 @ sK5 ) )
| ~ spl6_18 ),
inference(avatar_component_clause,[],[f597]) ).
thf(f600,plain,
( spl6_17
| spl6_18
| ~ spl6_8
| ~ spl6_10 ),
inference(avatar_split_clause,[],[f573,f295,f285,f597,f594]) ).
thf(f602,plain,
( ( $false = $true )
| ~ spl6_17 ),
inference(constrained_superposition,[],[f595,f174]) ).
thf(f637,plain,
( $false
| ~ spl6_17 ),
inference(trivial_inequality_removal,[],[f602]) ).
thf(f638,plain,
~ spl6_17,
inference(avatar_contradiction_clause,[],[f637]) ).
thf(f647,plain,
( ! [X0: $i] :
( ( $false = $true )
| ( $false
= ( rel_s5 @ sK5 @ X0 ) )
| ( $true
= ( q @ sK5 ) )
| ( $false
= ( p @ X0 ) ) )
| ~ spl6_6
| ~ spl6_18 ),
inference(constrained_superposition,[],[f278,f599]) ).
thf(f650,plain,
( ! [X0: $i] :
( ( $false
= ( p @ X0 ) )
| ( $true
= ( q @ sK5 ) )
| ( $false
= ( rel_s5 @ sK5 @ X0 ) ) )
| ~ spl6_6
| ~ spl6_18 ),
inference(trivial_inequality_removal,[],[f647]) ).
thf(f655,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK5 @ X0 ) )
| ( $false = $true )
| ( $false
= ( p @ X0 ) ) )
| ~ spl6_6
| ~ spl6_11
| ~ spl6_18 ),
inference(forward_demodulation,[],[f650,f302]) ).
thf(f656,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ sK5 @ X0 ) )
| ( $false
= ( p @ X0 ) ) )
| ~ spl6_6
| ~ spl6_11
| ~ spl6_18 ),
inference(trivial_inequality_removal,[],[f655]) ).
thf(f667,plain,
( ! [X0: $i] :
( ( $false
= ( p @ X0 ) )
| ( $false
= ( rel_s5 @ X0 @ sK5 ) )
| ( $false = $true ) )
| ~ spl6_6
| ~ spl6_11
| ~ spl6_18 ),
inference(constrained_superposition,[],[f162,f656]) ).
thf(f669,plain,
( ! [X0: $i] :
( ( $false
= ( rel_s5 @ X0 @ sK5 ) )
| ( $false
= ( p @ X0 ) ) )
| ~ spl6_6
| ~ spl6_11
| ~ spl6_18 ),
inference(trivial_inequality_removal,[],[f667]) ).
thf(f696,plain,
( ( $false = $true )
| ( $false
= ( rel_s5 @ sK5 @ sK5 ) )
| ( $false
= ( p @ sK4 ) )
| ~ spl6_6
| ~ spl6_10
| ~ spl6_11
| ~ spl6_18 ),
inference(constrained_superposition,[],[f336,f669]) ).
thf(f717,plain,
( ( $false
= ( p @ sK4 ) )
| ( $false
= ( rel_s5 @ sK5 @ sK5 ) )
| ~ spl6_6
| ~ spl6_10
| ~ spl6_11
| ~ spl6_18 ),
inference(trivial_inequality_removal,[],[f696]) ).
thf(f740,plain,
( ( $false = $true )
| ( $false
= ( rel_s5 @ sK5 @ sK5 ) )
| ~ spl6_6
| ~ spl6_9
| ~ spl6_10
| ~ spl6_11
| ~ spl6_18 ),
inference(forward_demodulation,[],[f717,f292]) ).
thf(f741,plain,
( ( $false
= ( rel_s5 @ sK5 @ sK5 ) )
| ~ spl6_6
| ~ spl6_9
| ~ spl6_10
| ~ spl6_11
| ~ spl6_18 ),
inference(trivial_inequality_removal,[],[f740]) ).
thf(f748,plain,
( ( $false = $true )
| ~ spl6_6
| ~ spl6_9
| ~ spl6_10
| ~ spl6_11
| ~ spl6_18 ),
inference(forward_demodulation,[],[f741,f174]) ).
thf(f749,plain,
( $false
| ~ spl6_6
| ~ spl6_9
| ~ spl6_10
| ~ spl6_11
| ~ spl6_18 ),
inference(trivial_inequality_removal,[],[f748]) ).
thf(f750,plain,
( ~ spl6_6
| ~ spl6_9
| ~ spl6_10
| ~ spl6_11
| ~ spl6_18 ),
inference(avatar_contradiction_clause,[],[f749]) ).
cnf(s5,plain,
( spl6_6
| spl6_7 ),
inference(sat_conversion,[],[f283]) ).
cnf(s6,plain,
( spl6_7
| spl6_8 ),
inference(sat_conversion,[],[f288]) ).
cnf(s7,plain,
( spl6_7
| spl6_9 ),
inference(sat_conversion,[],[f293]) ).
cnf(s8,plain,
( spl6_7
| spl6_10 ),
inference(sat_conversion,[],[f298]) ).
cnf(s9,plain,
( spl6_7
| spl6_11 ),
inference(sat_conversion,[],[f303]) ).
cnf(s10,plain,
~ spl6_7,
inference(sat_conversion,[],[f304]) ).
cnf(s19,plain,
( ~ spl6_8
| ~ spl6_10
| spl6_17
| spl6_18 ),
inference(sat_conversion,[],[f600]) ).
cnf(s23,plain,
~ spl6_17,
inference(sat_conversion,[],[f638]) ).
cnf(s32,plain,
( ~ spl6_6
| ~ spl6_9
| ~ spl6_10
| ~ spl6_11
| ~ spl6_18 ),
inference(sat_conversion,[],[f750]) ).
cnf(s34,plain,
( ~ spl6_8
| ~ spl6_10
| spl6_18 ),
inference(rat,[],[s19,s23]) ).
cnf(s36,plain,
spl6_11,
inference(rat,[],[s9,s10]) ).
cnf(s37,plain,
spl6_10,
inference(rat,[],[s8,s10]) ).
cnf(s38,plain,
spl6_9,
inference(rat,[],[s7,s10]) ).
cnf(s40,plain,
spl6_8,
inference(rat,[],[s6,s10]) ).
cnf(s41,plain,
spl6_18,
inference(rat,[],[s34,s37,s40]) ).
cnf(s42,plain,
~ spl6_6,
inference(rat,[],[s32,s38,s36,s37,s41]) ).
cnf(s43,plain,
$false,
inference(rat,[],[s5,s10,s42]) ).
thf(f751,plain,
$false,
inference(avatar_sat_refutation,[],[s43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO454^6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n008.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 16:55:54 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 Running higher-order theorem proving
% 0.20/0.27 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
% 0.20/0.35 % (3424384)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.35 % (3424394)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=163987117:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.35 % (3424395)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.35 % (3424395)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
% 0.20/0.35 % (3424390)lrs+10_16_si=on:nwc=1.5:random_seed=484178403:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.35 % (3424389)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1156994566:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.35 % (3424391)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1692438475:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.35 % (3424395)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=2198001388:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.35 % (3424392)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=28641185: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)
% 0.20/0.35 % (3424393)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3631906423:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.35 % (3424391)Instruction limit reached!
% 0.20/0.35 % (3424391)------------------------------
% 0.20/0.35 % (3424391)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (3424391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (3424391)CaDiCaL version: 2.1.3
% 0.20/0.35 % (3424391)Termination reason: Instruction limit
% 0.20/0.35 % (3424391)Termination phase: Property scanning
% 0.20/0.35 % (3424391)Time elapsed: 0.002 s
% 0.20/0.35 % (3424391)Peak memory usage: 10 MB
% 0.20/0.35 % (3424391)Instructions burned: 4 (million)
% 0.20/0.35 % (3424390)Instruction limit reached!
% 0.20/0.35 % (3424390)------------------------------
% 0.20/0.35 % (3424390)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (3424390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (3424390)CaDiCaL version: 2.1.3
% 0.20/0.35 % (3424390)Termination reason: Instruction limit
% 0.20/0.35 % (3424390)Termination phase: Saturation
% 0.20/0.35 % (3424390)Time elapsed: 0.010 s
% 0.20/0.35 % (3424390)Peak memory usage: 12 MB
% 0.20/0.35 % (3424390)Instructions burned: 19 (million)
% 0.20/0.35 % (3424394)Instruction limit reached!
% 0.20/0.35 % (3424394)------------------------------
% 0.20/0.35 % (3424394)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (3424394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (3424394)CaDiCaL version: 2.1.3
% 0.20/0.35 % (3424394)Termination reason: Instruction limit
% 0.20/0.35 % (3424394)Termination phase: Saturation
% 0.20/0.35 % (3424394)Time elapsed: 0.020 s
% 0.20/0.35 % (3424394)Peak memory usage: 12 MB
% 0.20/0.35 % (3424394)Instructions burned: 77 (million)
% 0.20/0.35 % (3424393)Instruction limit reached!
% 0.20/0.35 % (3424393)------------------------------
% 0.20/0.35 % (3424393)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (3424393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (3424393)CaDiCaL version: 2.1.3
% 0.20/0.35 % (3424393)Termination reason: Instruction limit
% 0.20/0.35 % (3424393)Termination phase: Saturation
% 0.20/0.35 % (3424393)Time elapsed: 0.014 s
% 0.20/0.35 % (3424393)Peak memory usage: 11 MB
% 0.20/0.35 % (3424393)Instructions burned: 25 (million)
% 0.20/0.35 % (3424395) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3424384-3424395"...
% 0.20/0.35 % (3424405)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.35 % (3424405)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3367849684:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.35 % (3424389) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3424384-3424389"...
% 0.20/0.35 % (3424395)...printing done.
% 0.20/0.35 % (3424403)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3892297878:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.35 % (3424395)Refutation found. Thanks to Tanya!
% 0.20/0.35 % SZS status Theorem for theBenchmark
% 0.20/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.35 % (3424395)------------------------------
% 0.20/0.35 % (3424395)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (3424395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (3424395)CaDiCaL version: 2.1.3
% 0.20/0.35 % (3424395)Termination reason: Refutation
% 0.20/0.35 % (3424395)Time elapsed: 0.024 s
% 0.20/0.35 % (3424395)Peak memory usage: 13 MB
% 0.20/0.35 % (3424395)Instructions burned: 46 (million)
% 0.20/0.35 % (3424384)Success in time 0.069 s
% 0.20/0.35 % Vampire exiting
%------------------------------------------------------------------------------