%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO435^1 : 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 : n013.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 08:47:41 AM UTC 2026
% Result : Theorem 0.25s 0.29s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 18
% Syntax : Number of formulae : 151 ( 63 unt; 0 typ; 7 def)
% Number of atoms : 1155 ( 233 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 1687 ( 282 ~; 286 |; 13 &; 982 @)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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 : 69 ( 65 usr; 12 con; 0-4 aty)
% ( 106 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 375 ( 0 sgn 88 !; 0 ?; 375 :)
% 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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_37,type,
vIMP: $o > $o > $o ).
thf(func_def_38,type,
vAND: $o > $o > $o ).
thf(func_def_39,type,
db3:
!>[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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_44,type,
vOR: $o > $o > $o ).
thf(func_def_45,type,
vNOT: $o > $o ).
thf(func_def_46,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_47,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_50,type,
db4:
!>[X0: $tType] : X0 ).
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_58,type,
sK7: $i > $i ).
thf(func_def_60,type,
sK9: $i > $i ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( ( ^ [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] :
! [X2: $i,X1: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s4 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f33,axiom,
( ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ X0 ) ) ) )
= mdia_s4 ),
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 @ p ) ) @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ p ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f37,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mdia_s4 @ p ) ) @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ p ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f42,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f52,plain,
mreflexive @ rel_s4,
inference(rectify,[],[f34]) ).
thf(f53,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f52]) ).
thf(f56,plain,
~ ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mdia_s4 @ p ) ) @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ p ) ) ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f57,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mdia_s4 @ p ) ) @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ p ) ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f56]) ).
thf(f60,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) )
= mreflexive ),
inference(rectify,[],[f18]) ).
thf(f61,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f60]) ).
thf(f62,plain,
mtransitive @ rel_s4,
inference(rectify,[],[f35]) ).
thf(f63,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f62]) ).
thf(f66,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s4 ),
inference(rectify,[],[f32]) ).
thf(f67,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f66]) ).
thf(f71,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X2 @ X1 ) )
=> ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f72,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f73,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f74,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f73]) ).
thf(f81,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f82,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f87,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f88,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f87]) ).
thf(f93,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f98,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mdia_s4 @ p ) ) @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ p ) ) ) ) ) )
!= $true ),
inference(flattening,[],[f57]) ).
thf(f101,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f109,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f93]) ).
thf(f113,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f114,plain,
( ( mvalid @ ( mimplies @ ( mbox_s4 @ ( mdia_s4 @ p ) ) @ ( mbox_s4 @ ( mdia_s4 @ ( mbox_s4 @ ( mdia_s4 @ p ) ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f120,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f53]) ).
thf(f121,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f123,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f129,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f130,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f63]) ).
thf(f133,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f134,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f74]) ).
thf(f138,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f123,f121,f101]) ).
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,f101,f113,f101]) ).
thf(f147,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [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 ) ) )
@ ( ^ [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 ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f114,f134,f138,f113,f146,f113,f146,f113,f146]) ).
thf(f148,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f120,f133]) ).
thf(f149,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ rel_s4 )
= $true ),
inference(definition_unfolding,[],[f130,f129]) ).
thf(f150,definition,
( sF0
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [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 ) ) )
@ ( ^ [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,
( ( $false
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [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 ) ) )
@ ( ^ [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 ) ) ) ) ) ) )
| ( sF0 = $true ) ),
inference(iff_proxy_clausification,[],[f150]) ).
thf(f209,plain,
( ( sF0 = $true )
| ( ( !! @ $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 ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f210,plain,
( ( sF0 = $true )
| ( ( ^ [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 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f209]) ).
thf(f211,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,[],[f210]) ).
thf(f212,plain,
( ( sF0 = $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 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f211]) ).
thf(f213,plain,
( ( sF0 = $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK6 @ Y0 ) ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f211]) ).
thf(f214,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK6 @ Y0 ) ) )
= $true )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f213]) ).
thf(f215,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK6 @ Y0 ) )
@ X1 )
= $true )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f214]) ).
thf(f216,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) ) )
| ~ ( rel_s4 @ sK6 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f215]) ).
thf(f217,plain,
! [X1: $i] :
( ( ( ~ ( rel_s4 @ sK6 @ X1 ) )
= $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) )
= $true )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f216]) ).
thf(f218,plain,
! [X1: $i] :
( ( ( rel_s4 @ sK6 @ X1 )
= $false )
| ( sF0 = $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f217]) ).
thf(f219,plain,
! [X1: $i] :
( ( ( rel_s4 @ sK6 @ X1 )
= $false )
| ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) ) )
= $false ) ),
inference(not_proxy_clausification,[],[f218]) ).
thf(f220,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) )
@ ( sK7 @ X1 ) )
= $false )
| ( sF0 = $true )
| ( ( rel_s4 @ sK6 @ X1 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f219]) ).
thf(f221,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( rel_s4 @ sK6 @ X1 )
= $false )
| ( $false
= ( ~ ( p @ ( sK7 @ X1 ) )
| ~ ( rel_s4 @ X1 @ ( sK7 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f220]) ).
thf(f222,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( rel_s4 @ sK6 @ X1 )
= $false )
| ( ( ~ ( rel_s4 @ X1 @ ( sK7 @ X1 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f221]) ).
thf(f223,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( rel_s4 @ sK6 @ X1 )
= $false )
| ( ( ~ ( p @ ( sK7 @ X1 ) ) )
= $false ) ),
inference(or_proxy_clausification,[],[f221]) ).
thf(f224,plain,
! [X1: $i] :
( ( ( rel_s4 @ sK6 @ X1 )
= $false )
| ( ( p @ ( sK7 @ X1 ) )
= $true )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f223]) ).
thf(f225,plain,
! [X1: $i] :
( ( ( rel_s4 @ X1 @ ( sK7 @ X1 ) )
= $true )
| ( ( rel_s4 @ sK6 @ X1 )
= $false )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f222]) ).
thf(f226,plain,
( ( sF0 = $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 ) )
@ sK8 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f212]) ).
thf(f227,plain,
( ( sF0 = $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK8 @ Y0 ) ) )
| ~ ( rel_s4 @ sK6 @ sK8 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f226]) ).
thf(f228,plain,
( ( ( ~ ( rel_s4 @ sK6 @ sK8 ) )
= $false )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f227]) ).
thf(f229,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK8 @ Y0 ) ) ) )
= $false )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f227]) ).
thf(f230,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK8 @ Y0 ) ) )
= $true )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f229]) ).
thf(f231,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK8 @ Y0 ) )
@ X1 ) )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f230]) ).
thf(f232,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) ) )
| ~ ( rel_s4 @ sK8 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f231]) ).
thf(f233,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( ~ ( rel_s4 @ sK8 @ X1 ) )
= $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f232]) ).
thf(f234,plain,
! [X1: $i] :
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) ) )
| ( sF0 = $true )
| ( ( rel_s4 @ sK8 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f233]) ).
thf(f235,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( rel_s4 @ sK8 @ X1 )
= $false )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f234]) ).
thf(f236,plain,
! [X1: $i] :
( ( ( rel_s4 @ sK8 @ X1 )
= $false )
| ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ X1 @ Y0 ) )
@ ( sK9 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f235]) ).
thf(f237,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( rel_s4 @ sK8 @ X1 )
= $false )
| ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s4 @ ( sK9 @ X1 ) @ Y0 ) ) )
| ~ ( rel_s4 @ X1 @ ( sK9 @ X1 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f236]) ).
thf(f238,plain,
! [X1: $i] :
( ( ( ~ ( rel_s4 @ X1 @ ( sK9 @ X1 ) ) )
= $false )
| ( sF0 = $true )
| ( ( rel_s4 @ sK8 @ X1 )
= $false ) ),
inference(or_proxy_clausification,[],[f237]) ).
thf(f239,plain,
! [X1: $i] :
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s4 @ ( sK9 @ X1 ) @ Y0 ) ) ) )
= $false )
| ( ( rel_s4 @ sK8 @ X1 )
= $false )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f237]) ).
thf(f240,plain,
! [X1: $i] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s4 @ ( sK9 @ X1 ) @ Y0 ) ) )
= $true )
| ( sF0 = $true )
| ( ( rel_s4 @ sK8 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f239]) ).
thf(f241,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK8 @ X1 )
= $false )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s4 @ ( sK9 @ X1 ) @ Y0 ) )
@ X2 ) )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f240]) ).
thf(f242,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( p @ X2 )
| ~ ( rel_s4 @ ( sK9 @ X1 ) @ X2 ) ) )
| ( sF0 = $true )
| ( ( rel_s4 @ sK8 @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f241]) ).
thf(f243,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( rel_s4 @ ( sK9 @ X1 ) @ X2 ) )
= $true )
| ( sF0 = $true )
| ( ( rel_s4 @ sK8 @ X1 )
= $false )
| ( $true
= ( ~ ( p @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f242]) ).
thf(f244,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( p @ X2 ) ) )
| ( ( rel_s4 @ sK8 @ X1 )
= $false )
| ( sF0 = $true )
| ( ( rel_s4 @ ( sK9 @ X1 ) @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f243]) ).
thf(f245,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK8 @ X1 )
= $false )
| ( ( rel_s4 @ ( sK9 @ X1 ) @ X2 )
= $false )
| ( ( p @ X2 )
= $false )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f244]) ).
thf(f246,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( rel_s4 @ X1 @ ( sK9 @ X1 ) )
= $true )
| ( ( rel_s4 @ sK8 @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f238]) ).
thf(f247,plain,
( ( $true
= ( rel_s4 @ sK6 @ sK8 ) )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f228]) ).
thf(f248,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y1 @ Y2 )
& ( rel_s4 @ Y2 @ Y0 ) )
=> ( rel_s4 @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f249,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y1 @ Y2 )
& ( rel_s4 @ Y2 @ Y0 ) )
=> ( rel_s4 @ Y1 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f248]) ).
thf(f250,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y0 @ Y1 )
& ( rel_s4 @ Y1 @ X1 ) )
=> ( rel_s4 @ Y0 @ X1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f249]) ).
thf(f251,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y0 @ Y1 )
& ( rel_s4 @ Y1 @ X1 ) )
=> ( rel_s4 @ Y0 @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f250]) ).
thf(f252,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s4 @ X2 @ Y0 )
& ( rel_s4 @ Y0 @ X1 ) )
=> ( rel_s4 @ X2 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f251]) ).
thf(f253,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( rel_s4 @ X2 @ Y0 )
& ( rel_s4 @ Y0 @ X1 ) )
=> ( rel_s4 @ X2 @ X1 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f252]) ).
thf(f254,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( rel_s4 @ X2 @ X3 )
& ( rel_s4 @ X3 @ X1 ) )
=> ( rel_s4 @ X2 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f253]) ).
thf(f255,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s4 @ X2 @ X1 )
= $true )
| ( ( ( rel_s4 @ X2 @ X3 )
& ( rel_s4 @ X3 @ X1 ) )
= $false ) ),
inference(imp_proxy_clausification,[],[f254]) ).
thf(f256,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X3 @ X1 ) )
| ( ( rel_s4 @ X2 @ X3 )
= $false )
| ( ( rel_s4 @ X2 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f255]) ).
thf(f257,plain,
( ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) )
= $true ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f258,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f257]) ).
thf(f259,plain,
! [X1: $i] :
( ( rel_s4 @ X1 @ X1 )
= $true ),
inference(beta-eta_normalization,[],[f258]) ).
thf(f289,definition,
( spl10_8
<=> ! [X1: $i] :
( ( ( rel_s4 @ sK6 @ X1 )
= $false )
| ( ( p @ ( sK7 @ X1 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl10_8])],[avatar_definition]) ).
thf(f290,plain,
( ! [X1: $i] :
( ( ( rel_s4 @ sK6 @ X1 )
= $false )
| ( ( p @ ( sK7 @ X1 ) )
= $true ) )
| ~ spl10_8 ),
inference(avatar_component_clause,[],[f289]) ).
thf(f292,definition,
( spl10_9
<=> ( sF0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl10_9])],[avatar_definition]) ).
thf(f295,plain,
( spl10_8
| spl10_9 ),
inference(avatar_split_clause,[],[f224,f292,f289]) ).
thf(f297,definition,
( spl10_10
<=> ! [X1: $i] :
( ( ( rel_s4 @ X1 @ ( sK7 @ X1 ) )
= $true )
| ( ( rel_s4 @ sK6 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl10_10])],[avatar_definition]) ).
thf(f298,plain,
( ! [X1: $i] :
( ( ( rel_s4 @ X1 @ ( sK7 @ X1 ) )
= $true )
| ( ( rel_s4 @ sK6 @ X1 )
= $false ) )
| ~ spl10_10 ),
inference(avatar_component_clause,[],[f297]) ).
thf(f299,plain,
( spl10_10
| spl10_9 ),
inference(avatar_split_clause,[],[f225,f292,f297]) ).
thf(f301,definition,
( spl10_11
<=> ! [X2: $i,X1: $i] :
( ( ( rel_s4 @ sK8 @ X1 )
= $false )
| ( ( p @ X2 )
= $false )
| ( ( rel_s4 @ ( sK9 @ X1 ) @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl10_11])],[avatar_definition]) ).
thf(f302,plain,
( ! [X2: $i,X1: $i] :
( ( ( rel_s4 @ ( sK9 @ X1 ) @ X2 )
= $false )
| ( ( rel_s4 @ sK8 @ X1 )
= $false )
| ( ( p @ X2 )
= $false ) )
| ~ spl10_11 ),
inference(avatar_component_clause,[],[f301]) ).
thf(f303,plain,
( spl10_9
| spl10_11 ),
inference(avatar_split_clause,[],[f245,f301,f292]) ).
thf(f305,definition,
( spl10_12
<=> ! [X1: $i] :
( ( ( rel_s4 @ X1 @ ( sK9 @ X1 ) )
= $true )
| ( ( rel_s4 @ sK8 @ X1 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl10_12])],[avatar_definition]) ).
thf(f306,plain,
( ! [X1: $i] :
( ( ( rel_s4 @ X1 @ ( sK9 @ X1 ) )
= $true )
| ( ( rel_s4 @ sK8 @ X1 )
= $false ) )
| ~ spl10_12 ),
inference(avatar_component_clause,[],[f305]) ).
thf(f307,plain,
( spl10_12
| spl10_9 ),
inference(avatar_split_clause,[],[f246,f292,f305]) ).
thf(f309,definition,
( spl10_13
<=> ( $true
= ( rel_s4 @ sK6 @ sK8 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_13])],[avatar_definition]) ).
thf(f311,plain,
( ( $true
= ( rel_s4 @ sK6 @ sK8 ) )
| ~ spl10_13 ),
inference(avatar_component_clause,[],[f309]) ).
thf(f312,plain,
( spl10_13
| spl10_9 ),
inference(avatar_split_clause,[],[f247,f292,f309]) ).
thf(f313,plain,
~ spl10_9,
inference(avatar_split_clause,[],[f151,f292]) ).
thf(f370,plain,
( ! [X0: $i,X1: $i] :
( ( $true = $false )
| ( ( rel_s4 @ X1 @ X0 )
= $false )
| ( ( rel_s4 @ X1 @ ( sK9 @ X0 ) )
= $true )
| ( ( rel_s4 @ sK8 @ X0 )
= $false ) )
| ~ spl10_12 ),
inference(constrained_superposition,[],[f306,f256]) ).
thf(f374,plain,
( ! [X0: $i,X1: $i] :
( ( ( rel_s4 @ X1 @ ( sK9 @ X0 ) )
= $true )
| ( ( rel_s4 @ sK8 @ X0 )
= $false )
| ( ( rel_s4 @ X1 @ X0 )
= $false ) )
| ~ spl10_12 ),
inference(trivial_inequality_removal,[],[f370]) ).
thf(f409,plain,
( ! [X0: $i] :
( ( ( p @ ( sK7 @ ( sK9 @ X0 ) ) )
= $false )
| ( $true = $false )
| ( ( rel_s4 @ sK6 @ ( sK9 @ X0 ) )
= $false )
| ( ( rel_s4 @ sK8 @ X0 )
= $false ) )
| ~ spl10_10
| ~ spl10_11 ),
inference(constrained_superposition,[],[f302,f298]) ).
thf(f417,plain,
( ! [X0: $i] :
( ( ( rel_s4 @ sK6 @ ( sK9 @ X0 ) )
= $false )
| ( ( p @ ( sK7 @ ( sK9 @ X0 ) ) )
= $false )
| ( ( rel_s4 @ sK8 @ X0 )
= $false ) )
| ~ spl10_10
| ~ spl10_11 ),
inference(trivial_inequality_removal,[],[f409]) ).
thf(f554,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( rel_s4 @ sK6 @ X0 )
= $false )
| ( ( p @ ( sK7 @ ( sK9 @ X0 ) ) )
= $true )
| ( ( rel_s4 @ sK8 @ X0 )
= $false ) )
| ~ spl10_8
| ~ spl10_12 ),
inference(constrained_superposition,[],[f290,f374]) ).
thf(f561,plain,
( ! [X0: $i] :
( ( ( p @ ( sK7 @ ( sK9 @ X0 ) ) )
= $true )
| ( ( rel_s4 @ sK8 @ X0 )
= $false )
| ( ( rel_s4 @ sK6 @ X0 )
= $false ) )
| ~ spl10_8
| ~ spl10_12 ),
inference(trivial_inequality_removal,[],[f554]) ).
thf(f604,plain,
( ! [X0: $i] :
( ( ( rel_s4 @ sK6 @ X0 )
= $false )
| ( ( rel_s4 @ sK8 @ X0 )
= $false )
| ( ( rel_s4 @ sK8 @ X0 )
= $false )
| ( ( p @ ( sK7 @ ( sK9 @ X0 ) ) )
= $false )
| ( $true = $false ) )
| ~ spl10_10
| ~ spl10_11
| ~ spl10_12 ),
inference(constrained_superposition,[],[f374,f417]) ).
thf(f605,plain,
( ! [X0: $i] :
( ( ( rel_s4 @ sK6 @ X0 )
= $false )
| ( ( p @ ( sK7 @ ( sK9 @ X0 ) ) )
= $false )
| ( ( rel_s4 @ sK8 @ X0 )
= $false )
| ( $true = $false ) )
| ~ spl10_10
| ~ spl10_11
| ~ spl10_12 ),
inference(duplicate_literal_removal,[],[f604]) ).
thf(f606,plain,
( ! [X0: $i] :
( ( ( p @ ( sK7 @ ( sK9 @ X0 ) ) )
= $false )
| ( ( rel_s4 @ sK8 @ X0 )
= $false )
| ( ( rel_s4 @ sK6 @ X0 )
= $false ) )
| ~ spl10_10
| ~ spl10_11
| ~ spl10_12 ),
inference(trivial_inequality_removal,[],[f605]) ).
thf(f614,plain,
( ! [X0: $i] :
( ( ( rel_s4 @ sK6 @ X0 )
= $false )
| ( ( rel_s4 @ sK8 @ X0 )
= $false )
| ( ( rel_s4 @ sK8 @ X0 )
= $false )
| ( $true = $false )
| ( ( rel_s4 @ sK6 @ X0 )
= $false ) )
| ~ spl10_8
| ~ spl10_10
| ~ spl10_11
| ~ spl10_12 ),
inference(constrained_superposition,[],[f606,f561]) ).
thf(f617,plain,
( ! [X0: $i] :
( ( ( rel_s4 @ sK6 @ X0 )
= $false )
| ( $true = $false )
| ( ( rel_s4 @ sK8 @ X0 )
= $false ) )
| ~ spl10_8
| ~ spl10_10
| ~ spl10_11
| ~ spl10_12 ),
inference(duplicate_literal_removal,[],[f614]) ).
thf(f618,plain,
( ! [X0: $i] :
( ( ( rel_s4 @ sK8 @ X0 )
= $false )
| ( ( rel_s4 @ sK6 @ X0 )
= $false ) )
| ~ spl10_8
| ~ spl10_10
| ~ spl10_11
| ~ spl10_12 ),
inference(trivial_inequality_removal,[],[f617]) ).
thf(f630,plain,
( ( ( rel_s4 @ sK6 @ sK8 )
= $false )
| ( $true = $false )
| ~ spl10_8
| ~ spl10_10
| ~ spl10_11
| ~ spl10_12 ),
inference(constrained_superposition,[],[f259,f618]) ).
thf(f652,plain,
( ( ( rel_s4 @ sK6 @ sK8 )
= $false )
| ~ spl10_8
| ~ spl10_10
| ~ spl10_11
| ~ spl10_12 ),
inference(trivial_inequality_removal,[],[f630]) ).
thf(f667,plain,
( ( $true = $false )
| ~ spl10_8
| ~ spl10_10
| ~ spl10_11
| ~ spl10_12
| ~ spl10_13 ),
inference(forward_demodulation,[],[f652,f311]) ).
thf(f668,plain,
( $false
| ~ spl10_8
| ~ spl10_10
| ~ spl10_11
| ~ spl10_12
| ~ spl10_13 ),
inference(trivial_inequality_removal,[],[f667]) ).
thf(f669,plain,
( ~ spl10_8
| ~ spl10_10
| ~ spl10_11
| ~ spl10_12
| ~ spl10_13 ),
inference(avatar_contradiction_clause,[],[f668]) ).
cnf(s7,plain,
( spl10_8
| spl10_9 ),
inference(sat_conversion,[],[f295]) ).
cnf(s8,plain,
( spl10_9
| spl10_10 ),
inference(sat_conversion,[],[f299]) ).
cnf(s9,plain,
( spl10_9
| spl10_11 ),
inference(sat_conversion,[],[f303]) ).
cnf(s10,plain,
( spl10_9
| spl10_12 ),
inference(sat_conversion,[],[f307]) ).
cnf(s11,plain,
( spl10_9
| spl10_13 ),
inference(sat_conversion,[],[f312]) ).
cnf(s12,plain,
~ spl10_9,
inference(sat_conversion,[],[f313]) ).
cnf(s31,plain,
( ~ spl10_8
| ~ spl10_10
| ~ spl10_11
| ~ spl10_12
| ~ spl10_13 ),
inference(sat_conversion,[],[f669]) ).
cnf(s33,plain,
spl10_13,
inference(rat,[],[s11,s12]) ).
cnf(s34,plain,
spl10_12,
inference(rat,[],[s10,s12]) ).
cnf(s35,plain,
spl10_11,
inference(rat,[],[s9,s12]) ).
cnf(s36,plain,
spl10_10,
inference(rat,[],[s8,s12]) ).
cnf(s37,plain,
~ spl10_8,
inference(rat,[],[s31,s33,s34,s35,s36]) ).
cnf(s38,plain,
$false,
inference(rat,[],[s7,s12,s37]) ).
thf(f672,plain,
$false,
inference(avatar_sat_refutation,[],[s38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO435^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n013.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 16:51:06 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.22 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
% 0.25/0.29 % (2371911)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.29 % (2371919)lrs+10_16_si=on:nwc=1.5:random_seed=3358966381:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.25/0.29 % (2371918)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=913191432:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.25/0.29 % (2371920)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4216143906:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.25/0.29 % (2371924)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.25/0.29 % (2371924)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
% 0.25/0.29 % (2371920)Instruction limit reached!
% 0.25/0.29 % (2371920)------------------------------
% 0.25/0.29 % (2371920)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.29 % (2371920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.29 % (2371920)CaDiCaL version: 2.1.3
% 0.25/0.29 % (2371920)Termination reason: Instruction limit
% 0.25/0.29 % (2371920)Termination phase: Property scanning
% 0.25/0.29 % (2371920)Time elapsed: 0.004 s
% 0.25/0.29 % (2371920)Peak memory usage: 9 MB
% 0.25/0.29 % (2371920)Instructions burned: 4 (million)
% 0.25/0.29 % (2371922)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=609477468:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.25/0.29 % (2371924)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=4185784375:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.25/0.29 % (2371919)Instruction limit reached!
% 0.25/0.29 % (2371919)------------------------------
% 0.25/0.29 % (2371919)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.29 % (2371919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.29 % (2371919)CaDiCaL version: 2.1.3
% 0.25/0.29 % (2371919)Termination reason: Instruction limit
% 0.25/0.29 % (2371919)Termination phase: Saturation
% 0.25/0.29 % (2371919)Time elapsed: 0.010 s
% 0.25/0.29 % (2371919)Peak memory usage: 12 MB
% 0.25/0.29 % (2371919)Instructions burned: 19 (million)
% 0.25/0.29 % (2371922)Instruction limit reached!
% 0.25/0.29 % (2371922)------------------------------
% 0.25/0.29 % (2371922)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.29 % (2371922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.29 % (2371922)CaDiCaL version: 2.1.3
% 0.25/0.29 % (2371922)Termination reason: Instruction limit
% 0.25/0.29 % (2371922)Termination phase: Saturation
% 0.25/0.29 % (2371922)Time elapsed: 0.007 s
% 0.25/0.29 % (2371922)Peak memory usage: 12 MB
% 0.25/0.29 % (2371922)Instructions burned: 24 (million)
% 0.25/0.29 % (2371921)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=3048658891: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)
% 0.25/0.29 % (2371923)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1582028338:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.25/0.29 % (2371933)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.25/0.29 % (2371933)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2751921718:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.25/0.29 % (2371933)Instruction limit reached!
% 0.25/0.29 % (2371933)------------------------------
% 0.25/0.29 % (2371933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.29 % (2371933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.29 % (2371933)CaDiCaL version: 2.1.3
% 0.25/0.29 % (2371933)Termination reason: Instruction limit
% 0.25/0.29 % (2371933)Termination phase: Saturation
% 0.25/0.29 % (2371933)Time elapsed: 0.002 s
% 0.25/0.29 % (2371933)Peak memory usage: 11 MB
% 0.25/0.29 % (2371933)Instructions burned: 8 (million)
% 0.25/0.29 % (2371924) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2371911-2371924"...
% 0.25/0.29 % (2371932)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3164459171:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.25/0.29 % (2371932)Instruction limit reached!
% 0.25/0.29 % (2371932)------------------------------
% 0.25/0.29 % (2371932)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.29 % (2371932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.29 % (2371932)CaDiCaL version: 2.1.3
% 0.25/0.29 % (2371932)Termination reason: Instruction limit
% 0.25/0.29 % (2371932)Termination phase: Function definition elimination
% 0.25/0.29 % (2371932)Time elapsed: 0.003 s
% 0.25/0.29 % (2371932)Peak memory usage: 10 MB
% 0.25/0.29 % (2371932)Instructions burned: 6 (million)
% 0.25/0.29 % (2371924)...printing done.
% 0.25/0.29 % (2371924)Refutation found. Thanks to Tanya!
% 0.25/0.29 % SZS status Theorem for theBenchmark
% 0.25/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.30 % (2371924)------------------------------
% 0.25/0.30 % (2371924)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.30 % (2371924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.30 % (2371924)CaDiCaL version: 2.1.3
% 0.25/0.30 % (2371924)Termination reason: Refutation
% 0.25/0.30 % (2371924)Time elapsed: 0.027 s
% 0.25/0.30 % (2371924)Peak memory usage: 13 MB
% 0.25/0.30 % (2371924)Instructions burned: 44 (million)
% 0.25/0.30 % (2371911)Success in time 0.072 s
% 0.25/0.30 % Vampire exiting
%------------------------------------------------------------------------------