%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO444^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : 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 08:47:43 AM UTC 2026
% Result : Theorem 0.69s 0.38s
% Output : Refutation 0.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 18
% Syntax : Number of formulae : 177 ( 75 unt; 0 typ; 5 def)
% Number of atoms : 1231 ( 151 equ; 0 cnn)
% Maximal formula atoms : 14 ( 6 avg)
% Number of connectives : 2292 ( 552 ~; 350 |; 14 &;1185 @)
% ( 5 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 135 ( 135 >; 0 *; 0 +; 0 <<)
% Number of symbols : 64 ( 60 usr; 13 con; 0-4 aty)
% ( 157 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 391 ( 0 sgn 44 !; 0 ?; 391 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_40,type,
vNOT: $o > $o ).
thf(func_def_43,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_46,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_47,type,
vAND: $o > $o > $o ).
thf(func_def_48,type,
vIMP: $o > $o > $o ).
thf(func_def_49,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vOR: $o > $o > $o ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
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,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
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(f8,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) )
= mequiv ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mequiv) ).
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,X2: $i,X3: $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,
( mdia_s5
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mdia_s5) ).
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 @ ( mequiv @ ( mbox_s5 @ ( mor @ ( mnot @ p ) @ ( mdia_s5 @ q ) ) ) @ ( mor @ ( mnot @ ( mdia_s5 @ p ) ) @ ( mdia_s5 @ q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mbox_s5 @ ( mor @ ( mnot @ p ) @ ( mdia_s5 @ q ) ) ) @ ( mor @ ( mnot @ ( mdia_s5 @ p ) ) @ ( mdia_s5 @ q ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f40,plain,
~ ( mvalid @ ( mequiv @ ( mbox_s5 @ ( mor @ ( mnot @ p ) @ ( mdia_s5 @ q ) ) ) @ ( mor @ ( mnot @ ( mdia_s5 @ p ) ) @ ( mdia_s5 @ q ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f41,plain,
( ( ~ ( mvalid @ ( mequiv @ ( mbox_s5 @ ( mor @ ( mnot @ p ) @ ( mdia_s5 @ q ) ) ) @ ( mor @ ( mnot @ ( mdia_s5 @ p ) ) @ ( mdia_s5 @ q ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f40]) ).
thf(f46,plain,
msymmetric @ rel_s5,
inference(rectify,[],[f36]) ).
thf(f47,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f46]) ).
thf(f48,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f51,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f61,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f62,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f61]) ).
thf(f63,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f64,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f67,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) )
= mbox_s5 ),
inference(rectify,[],[f32]) ).
thf(f68,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f67]) ).
thf(f77,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f78,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
=> ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f79,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f78]) ).
thf(f80,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f85,plain,
mtransitive @ rel_s5,
inference(rectify,[],[f35]) ).
thf(f86,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f85]) ).
thf(f89,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f90,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f89]) ).
thf(f93,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f94,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f93]) ).
thf(f102,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f94]) ).
thf(f106,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f47]) ).
thf(f107,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f48]) ).
thf(f108,plain,
( ( ~ ( mvalid @ ( mequiv @ ( mbox_s5 @ ( mor @ ( mnot @ p ) @ ( mdia_s5 @ q ) ) ) @ ( mor @ ( mnot @ ( mdia_s5 @ p ) ) @ ( mdia_s5 @ q ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f41]) ).
thf(f109,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f116,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f122,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f124,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f86]) ).
thf(f127,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f80]) ).
thf(f128,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f129,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f79]) ).
thf(f132,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f77]) ).
thf(f138,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f62]) ).
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,[],[f107,f138,f109,f138,f138]) ).
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,[],[f132,f109,f138]) ).
thf(f144,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f127,f141,f142,f142]) ).
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,[],[f128,f138,f122,f138]) ).
thf(f151,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
@ rel_s5 )
= $true ),
inference(definition_unfolding,[],[f106,f129]) ).
thf(f152,plain,
( $true
= ( ~ ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 )
@ p )
@ ( ^ [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 ) ) )
@ q ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ 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 > $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 ) ) )
@ q ) ) ) ) ) ),
inference(definition_unfolding,[],[f108,f102,f144,f122,f109,f138,f150,f109,f138,f150,f150]) ).
thf(f153,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y2 )
& ( Y0 @ Y2 @ Y1 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f124,f116]) ).
thf(f156,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y2 @ Y1 )
& ( rel_s5 @ Y1 @ Y0 ) )
=> ( rel_s5 @ Y2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f157,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y0 @ Y1 )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f158,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( q @ Y2 ) ) ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
| ~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( q @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f159,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( q @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( q @ Y2 ) ) ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f158]) ).
thf(f162,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( q @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( q @ Y2 ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f159]) ).
thf(f163,plain,
( $false
= ( ^ [Y0: $i] :
~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( q @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( p @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( q @ Y2 ) ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( $false
= ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( ( ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) )
= $true )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f170,definition,
( spl1_1
<=> ( ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f172,plain,
( ( ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) )
= $true )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f170]) ).
thf(f174,definition,
( spl1_2
<=> ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f176,plain,
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f174]) ).
thf(f177,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f166,f174,f170]) ).
thf(f178,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
= $false )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f176]) ).
thf(f184,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f178]) ).
thf(f195,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
= $false )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f196,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
= $false )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f198,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) )
| $false ) )
= $true )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f176,f184]) ).
thf(f201,plain,
( ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f198]) ).
thf(f202,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f201]) ).
thf(f216,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ sK2 )
= $false )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f196]) ).
thf(f217,plain,
( ( ( ~ ( rel_s5 @ sK0 @ sK2 )
| ~ ( p @ sK2 ) )
= $false )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f216]) ).
thf(f218,plain,
( ( $false
= ( ~ ( p @ sK2 ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f217]) ).
thf(f219,plain,
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f217]) ).
thf(f228,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK2 ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f219]) ).
thf(f236,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f195]) ).
thf(f237,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ X1 )
= $true )
| ~ spl1_2 ),
inference(pi_proxy_clausification,[],[f236]) ).
thf(f238,plain,
( ! [X1: $i] :
( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( q @ X1 ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f237]) ).
thf(f264,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
@ X1 ) )
| ~ spl1_2 ),
inference(pi_proxy_clausification,[],[f202]) ).
thf(f265,plain,
( ! [X1: $i] :
( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( p @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f264]) ).
thf(f268,plain,
( ( $true
= ( ~ ( rel_s5 @ sK0 @ sK2 )
| $false
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f265,f218]) ).
thf(f272,plain,
( ( $true
= ( ~ ( rel_s5 @ sK0 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f268]) ).
thf(f280,plain,
( ( ( $false
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
= $true )
| ~ spl1_2 ),
inference(forward_demodulation,[],[f272,f219]) ).
thf(f281,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f280]) ).
thf(f300,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f281]) ).
thf(f301,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK3 )
= $false )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f300]) ).
thf(f302,plain,
( ( ( ~ ( rel_s5 @ sK2 @ sK3 )
| ~ ( q @ sK3 ) )
= $false )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f301]) ).
thf(f303,plain,
( ( ( ~ ( q @ sK3 ) )
= $false )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f302]) ).
thf(f304,plain,
( ( ( ~ ( rel_s5 @ sK2 @ sK3 ) )
= $false )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f302]) ).
thf(f307,plain,
( ( $true
= ( ~ ( rel_s5 @ sK0 @ sK3 )
| $false ) )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f238,f303]) ).
thf(f309,plain,
( ( $true
= ( ~ ( rel_s5 @ sK0 @ sK3 ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f307]) ).
thf(f318,plain,
( ( ( rel_s5 @ sK2 @ sK3 )
= $true )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f304]) ).
thf(f326,plain,
( ( ( rel_s5 @ sK0 @ sK3 )
= $false )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f309]) ).
thf(f360,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y0 @ Y1 )
=> ( rel_s5 @ Y1 @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f157]) ).
thf(f361,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ X1 @ Y0 )
=> ( rel_s5 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f360]) ).
thf(f362,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel_s5 @ X1 @ Y0 )
=> ( rel_s5 @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f361]) ).
thf(f363,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ X1 @ X2 )
=> ( rel_s5 @ X2 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f362]) ).
thf(f396,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y2 @ Y1 )
& ( rel_s5 @ Y1 @ Y0 ) )
=> ( rel_s5 @ Y2 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f156]) ).
thf(f397,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y1 @ Y0 )
& ( rel_s5 @ Y0 @ X1 ) )
=> ( rel_s5 @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f396]) ).
thf(f398,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y1 @ Y0 )
& ( rel_s5 @ Y0 @ X1 ) )
=> ( rel_s5 @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f397]) ).
thf(f399,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s5 @ Y0 @ X2 )
& ( rel_s5 @ X2 @ X1 ) )
=> ( rel_s5 @ Y0 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f398]) ).
thf(f400,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s5 @ Y0 @ X2 )
& ( rel_s5 @ X2 @ X1 ) )
=> ( rel_s5 @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f399]) ).
thf(f401,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s5 @ X3 @ X2 )
& ( rel_s5 @ X2 @ X1 ) )
=> ( rel_s5 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f400]) ).
thf(f420,plain,
( ! [X0: $i] :
( ( ( $true
& ( rel_s5 @ sK2 @ X0 ) )
=> ( rel_s5 @ sK0 @ X0 ) )
= $true )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f401,f228]) ).
thf(f438,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ sK2 @ X0 )
=> ( rel_s5 @ sK0 @ X0 ) )
= $true )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f420]) ).
thf(f457,plain,
( ( ( $true
=> ( rel_s5 @ sK0 @ sK3 ) )
= $true )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f438,f318]) ).
thf(f459,plain,
( ( ( rel_s5 @ sK0 @ sK3 )
= $true )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f457]) ).
thf(f467,plain,
( ( $true = $false )
| ~ spl1_2 ),
inference(forward_demodulation,[],[f459,f326]) ).
thf(f468,plain,
( $false
| ~ spl1_2 ),
inference(trivial_inequality_removal,[],[f467]) ).
thf(f469,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[],[f468]) ).
thf(f470,plain,
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
= $false )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f476,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) ) ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f470]) ).
thf(f477,plain,
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
= $false )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f470]) ).
thf(f487,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) ) )
@ sK4 )
= $false )
| ~ spl1_1 ),
inference(sigma_proxy_clausification,[],[f476]) ).
thf(f488,plain,
( ( ( ~ ( rel_s5 @ sK0 @ sK4 )
| ~ ( p @ sK4 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
= $false )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f487]) ).
thf(f489,plain,
( ( $false
= ( ~ ( p @ sK4 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f488]) ).
thf(f490,plain,
( ( ( ~ ( rel_s5 @ sK0 @ sK4 ) )
= $false )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f488]) ).
thf(f491,plain,
( ( ( rel_s5 @ sK0 @ sK4 )
= $true )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f490]) ).
thf(f499,plain,
( ( ( $true
=> ( rel_s5 @ sK4 @ sK0 ) )
= $true )
| ~ spl1_1 ),
inference(constrained_superposition,[],[f363,f491]) ).
thf(f503,plain,
( ( $true
= ( rel_s5 @ sK4 @ sK0 ) )
| ~ spl1_1 ),
inference(boolean_simplification,[],[f499]) ).
thf(f509,plain,
( ! [X0: $i] :
( ( ( $true
& ( rel_s5 @ sK0 @ X0 ) )
=> ( rel_s5 @ sK4 @ X0 ) )
= $true )
| ~ spl1_1 ),
inference(constrained_superposition,[],[f401,f503]) ).
thf(f516,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ sK0 @ X0 )
=> ( rel_s5 @ sK4 @ X0 ) )
= $true )
| ~ spl1_1 ),
inference(boolean_simplification,[],[f509]) ).
thf(f555,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
= $false )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f489]) ).
thf(f556,plain,
( ( $false
= ( ~ ( p @ sK4 ) ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f489]) ).
thf(f576,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f555]) ).
thf(f577,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( q @ Y0 ) )
@ X1 ) )
| ~ spl1_1 ),
inference(pi_proxy_clausification,[],[f576]) ).
thf(f578,plain,
( ! [X1: $i] :
( $true
= ( ~ ( rel_s5 @ sK4 @ X1 )
| ~ ( q @ X1 ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f577]) ).
thf(f641,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f477]) ).
thf(f659,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
= $true )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f641]) ).
thf(f685,definition,
( spl1_3
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
thf(f687,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) ) )
= $true )
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f685]) ).
thf(f689,definition,
( spl1_4
<=> ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
thf(f691,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
= $true )
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f689]) ).
thf(f692,plain,
( spl1_3
| spl1_4
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f659,f170,f689,f685]) ).
thf(f697,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ~ spl1_4 ),
inference(not_proxy_clausification,[],[f691]) ).
thf(f698,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK5 )
= $false )
| ~ spl1_4 ),
inference(sigma_proxy_clausification,[],[f697]) ).
thf(f699,plain,
( ( ( ~ ( rel_s5 @ sK0 @ sK5 )
| ~ ( q @ sK5 ) )
= $false )
| ~ spl1_4 ),
inference(beta-eta_normalization,[],[f698]) ).
thf(f700,plain,
( ( $false
= ( ~ ( q @ sK5 ) ) )
| ~ spl1_4 ),
inference(or_proxy_clausification,[],[f699]) ).
thf(f701,plain,
( ( ( ~ ( rel_s5 @ sK0 @ sK5 ) )
= $false )
| ~ spl1_4 ),
inference(or_proxy_clausification,[],[f699]) ).
thf(f710,definition,
( spl1_6
<=> ( $false
= ( ~ ( q @ sK5 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_6])],[avatar_definition]) ).
thf(f712,plain,
( ( $false
= ( ~ ( q @ sK5 ) ) )
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f710]) ).
thf(f714,plain,
( spl1_6
| ~ spl1_4 ),
inference(avatar_split_clause,[],[f700,f689,f710]) ).
thf(f728,plain,
( ( ( rel_s5 @ sK0 @ sK5 )
= $true )
| ~ spl1_4 ),
inference(not_proxy_clausification,[],[f701]) ).
thf(f735,plain,
( ( $true
= ( $true
=> ( rel_s5 @ sK4 @ sK5 ) ) )
| ~ spl1_1
| ~ spl1_4 ),
inference(constrained_superposition,[],[f516,f728]) ).
thf(f743,plain,
( ( $true
= ( rel_s5 @ sK4 @ sK5 ) )
| ~ spl1_1
| ~ spl1_4 ),
inference(boolean_simplification,[],[f735]) ).
thf(f780,plain,
( ( $true
= ( ~ $true
| ~ ( q @ sK5 ) ) )
| ~ spl1_1
| ~ spl1_4 ),
inference(constrained_superposition,[],[f578,f743]) ).
thf(f792,plain,
( ( ( $false
| ~ ( q @ sK5 ) )
= $true )
| ~ spl1_1
| ~ spl1_4 ),
inference(boolean_simplification,[],[f780]) ).
thf(f793,plain,
( ( $true
= ( ~ ( q @ sK5 ) ) )
| ~ spl1_1
| ~ spl1_4 ),
inference(boolean_simplification,[],[f792]) ).
thf(f797,plain,
( ( $true = $false )
| ~ spl1_1
| ~ spl1_4
| ~ spl1_6 ),
inference(forward_demodulation,[],[f793,f712]) ).
thf(f798,plain,
( $false
| ~ spl1_1
| ~ spl1_4
| ~ spl1_6 ),
inference(trivial_inequality_removal,[],[f797]) ).
thf(f799,plain,
( ~ spl1_1
| ~ spl1_4
| ~ spl1_6 ),
inference(avatar_contradiction_clause,[],[f798]) ).
thf(f800,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( p @ Y0 ) )
@ X1 )
= $true )
| ~ spl1_3 ),
inference(pi_proxy_clausification,[],[f687]) ).
thf(f801,plain,
( ! [X1: $i] :
( ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( p @ X1 ) )
= $true )
| ~ spl1_3 ),
inference(beta-eta_normalization,[],[f800]) ).
thf(f804,plain,
( ( ( ~ ( rel_s5 @ sK0 @ sK4 )
| $false )
= $true )
| ~ spl1_1
| ~ spl1_3 ),
inference(constrained_superposition,[],[f801,f556]) ).
thf(f814,plain,
( ( ( ~ ( rel_s5 @ sK0 @ sK4 ) )
= $true )
| ~ spl1_1
| ~ spl1_3 ),
inference(boolean_simplification,[],[f804]) ).
thf(f828,plain,
( ( $true = $false )
| ~ spl1_1
| ~ spl1_3 ),
inference(forward_demodulation,[],[f814,f490]) ).
thf(f829,plain,
( $false
| ~ spl1_1
| ~ spl1_3 ),
inference(trivial_inequality_removal,[],[f828]) ).
thf(f830,plain,
( ~ spl1_1
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[],[f829]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f177]) ).
cnf(s3,plain,
~ spl1_2,
inference(sat_conversion,[],[f469]) ).
cnf(s4,plain,
( ~ spl1_1
| spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f692]) ).
cnf(s6,plain,
( ~ spl1_4
| spl1_6 ),
inference(sat_conversion,[],[f714]) ).
cnf(s7,plain,
( ~ spl1_1
| ~ spl1_4
| ~ spl1_6 ),
inference(sat_conversion,[],[f799]) ).
cnf(s11,plain,
( ~ spl1_1
| ~ spl1_3 ),
inference(sat_conversion,[],[f830]) ).
cnf(s12,plain,
spl1_1,
inference(rat,[],[s1,s3]) ).
cnf(s13,plain,
~ spl1_3,
inference(rat,[],[s11,s12]) ).
cnf(s14,plain,
spl1_4,
inference(rat,[],[s4,s12,s13]) ).
cnf(s15,plain,
~ spl1_6,
inference(rat,[],[s7,s12,s14]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s6,s15,s14]) ).
thf(f831,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO444^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n013.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 16:51:21 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.69/0.38 % (2372799)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.69/0.38 % (2372806)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=412447354:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.69/0.38 % (2372806)Instruction limit reached!
% 0.69/0.38 % (2372806)------------------------------
% 0.69/0.38 % (2372806)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.38 % (2372806)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.38 % (2372806)CaDiCaL version: 2.1.3
% 0.69/0.38 % (2372806)Termination reason: Instruction limit
% 0.69/0.38 % (2372806)Termination phase: Property scanning
% 0.69/0.38 % (2372806)Time elapsed: 0.002 s
% 0.69/0.38 % (2372806)Peak memory usage: 10 MB
% 0.69/0.38 % (2372806)Instructions burned: 7 (million)
% 0.69/0.38 % (2372810)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.69/0.38 % (2372810)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
% 0.69/0.38 % (2372805)lrs+10_16_si=on:nwc=1.5:random_seed=3720644911:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.69/0.38 % (2372804)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1306922374:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.69/0.38 % (2372809)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3537519458:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.69/0.38 % (2372810)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=1012966851:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.69/0.38 % (2372808)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3273631341:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.69/0.38 % (2372807)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=3139740631: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)
% 0.69/0.38 % (2372812)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1229309284:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.69/0.38 % (2372812)Instruction limit reached!
% 0.69/0.38 % (2372812)------------------------------
% 0.69/0.38 % (2372812)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.38 % (2372812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.38 % (2372812)CaDiCaL version: 2.1.3
% 0.69/0.38 % (2372812)Termination reason: Instruction limit
% 0.69/0.38 % (2372812)Termination phase: Preprocessing 3
% 0.69/0.38 % (2372812)Time elapsed: 0.001 s
% 0.69/0.38 % (2372812)Peak memory usage: 10 MB
% 0.69/0.38 % (2372812)Instructions burned: 4 (million)
% 0.69/0.38 % (2372805)Instruction limit reached!
% 0.69/0.38 % (2372805)------------------------------
% 0.69/0.38 % (2372805)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.38 % (2372805)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.38 % (2372805)CaDiCaL version: 2.1.3
% 0.69/0.38 % (2372805)Termination reason: Instruction limit
% 0.69/0.38 % (2372805)Termination phase: Saturation
% 0.69/0.38 % (2372805)Time elapsed: 0.009 s
% 0.69/0.38 % (2372805)Peak memory usage: 12 MB
% 0.69/0.38 % (2372805)Instructions burned: 18 (million)
% 0.69/0.38 % (2372820)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=728298858:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.69/0.38 % (2372820)Instruction limit reached!
% 0.69/0.38 % (2372820)------------------------------
% 0.69/0.38 % (2372820)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.38 % (2372820)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.38 % (2372820)CaDiCaL version: 2.1.3
% 0.69/0.38 % (2372820)Termination reason: Instruction limit
% 0.69/0.38 % (2372820)Termination phase: Saturation
% 0.69/0.38 % (2372820)Time elapsed: 0.003 s
% 0.69/0.38 % (2372820)Peak memory usage: 11 MB
% 0.69/0.38 % (2372820)Instructions burned: 13 (million)
% 0.69/0.38 % (2372821)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.69/0.38 % (2372808)Instruction limit reached!
% 0.69/0.38 % (2372808)------------------------------
% 0.69/0.38 % (2372808)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.38 % (2372808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.38 % (2372808)CaDiCaL version: 2.1.3
% 0.69/0.38 % (2372808)Termination reason: Instruction limit
% 0.69/0.38 % (2372808)Termination phase: Saturation
% 0.69/0.38 % (2372808)Time elapsed: 0.022 s
% 0.69/0.38 % (2372808)Peak memory usage: 11 MB
% 0.69/0.38 % (2372808)Instructions burned: 24 (million)
% 0.69/0.38 % (2372821)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3470257765:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.69/0.38 % (2372823)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1083746236:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.69/0.38 % (2372823)Instruction limit reached!
% 0.69/0.38 % (2372823)------------------------------
% 0.69/0.38 % (2372823)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.38 % (2372823)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.38 % (2372823)CaDiCaL version: 2.1.3
% 0.69/0.38 % (2372823)Termination reason: Instruction limit
% 0.69/0.38 % (2372823)Termination phase: Saturation
% 0.69/0.38 % (2372823)Time elapsed: 0.003 s
% 0.69/0.38 % (2372823)Peak memory usage: 11 MB
% 0.69/0.38 % (2372823)Instructions burned: 12 (million)
% 0.69/0.38 % (2372809)Instruction limit reached!
% 0.69/0.38 % (2372809)------------------------------
% 0.69/0.38 % (2372809)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.38 % (2372809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.38 % (2372809)CaDiCaL version: 2.1.3
% 0.69/0.38 % (2372809)Termination reason: Instruction limit
% 0.69/0.38 % (2372809)Termination phase: Saturation
% 0.69/0.38 % (2372809)Time elapsed: 0.035 s
% 0.69/0.38 % (2372809)Peak memory usage: 12 MB
% 0.69/0.38 % (2372809)Instructions burned: 76 (million)
% 0.69/0.38 % (2372821)Instruction limit reached!
% 0.69/0.38 % (2372821)------------------------------
% 0.69/0.38 % (2372821)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.38 % (2372821)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.38 % (2372821)CaDiCaL version: 2.1.3
% 0.69/0.38 % (2372821)Termination reason: Instruction limit
% 0.69/0.38 % (2372821)Termination phase: Property scanning
% 0.69/0.38 % (2372821)Time elapsed: 0.007 s
% 0.69/0.38 % (2372821)Peak memory usage: 10 MB
% 0.69/0.38 % (2372821)Instructions burned: 7 (million)
% 0.69/0.38 % (2372804)Instruction limit reached!
% 0.69/0.38 % (2372804)------------------------------
% 0.69/0.38 % (2372804)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.38 % (2372804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.38 % (2372804)CaDiCaL version: 2.1.3
% 0.69/0.38 % (2372804)Termination reason: Instruction limit
% 0.69/0.38 % (2372804)Termination phase: Saturation
% 0.69/0.38 % (2372804)Time elapsed: 0.044 s
% 0.69/0.38 % (2372804)Peak memory usage: 12 MB
% 0.69/0.38 % (2372804)Instructions burned: 88 (million)
% 0.69/0.38 % (2372824)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
% 0.69/0.38 % (2372824)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.69/0.38 % (2372824)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=610609374:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.69/0.38 % (2372827)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=2029146184:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.69/0.38 % (2372828)lrs+10_1_si=on:cs=on:random_seed=1672814655:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.69/0.38 % (2372829)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.69/0.38 % (2372830)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=958247594:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.69/0.38 % (2372824)Instruction limit reached!
% 0.69/0.38 % (2372824)------------------------------
% 0.69/0.38 % (2372824)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.38 % (2372824)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.38 % (2372824)CaDiCaL version: 2.1.3
% 0.69/0.38 % (2372824)Termination reason: Instruction limit
% 0.69/0.38 % (2372824)Termination phase: Saturation
% 0.69/0.38 % (2372824)Time elapsed: 0.013 s
% 0.69/0.38 % (2372824)Peak memory usage: 12 MB
% 0.69/0.38 % (2372824)Instructions burned: 30 (million)
% 0.69/0.38 % (2372829)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=2748877547:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.69/0.38 % (2372828)Instruction limit reached!
% 0.69/0.38 % (2372828)------------------------------
% 0.69/0.38 % (2372828)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.38 % (2372828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.38 % (2372828)CaDiCaL version: 2.1.3
% 0.69/0.38 % (2372828)Termination reason: Instruction limit
% 0.69/0.38 % (2372828)Termination phase: Saturation
% 0.69/0.38 % (2372828)Time elapsed: 0.007 s
% 0.69/0.38 % (2372828)Peak memory usage: 10 MB
% 0.69/0.38 % (2372828)Instructions burned: 8 (million)
% 0.69/0.38 % (2372829)Instruction limit reached!
% 0.69/0.38 % (2372829)------------------------------
% 0.69/0.38 % (2372829)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.38 % (2372829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.38 % (2372829)CaDiCaL version: 2.1.3
% 0.69/0.38 % (2372829)Termination reason: Instruction limit
% 0.69/0.38 % (2372829)Termination phase: Property scanning
% 0.69/0.38 % (2372830)Refutation not found, incomplete strategy
% 0.69/0.38 % (2372830)------------------------------
% 0.69/0.38 % (2372830)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.38 % (2372829)Time elapsed: 0.001 s
% 0.69/0.38 % (2372829)Peak memory usage: 9 MB
% 0.69/0.38 % (2372830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.38 % (2372829)Instructions burned: 2 (million)
% 0.69/0.38 % (2372830)CaDiCaL version: 2.1.3
% 0.69/0.38 % (2372830)Termination reason: Refutation not found, incomplete strategy
% 0.69/0.38 % (2372830)Time elapsed: 0.004 s
% 0.69/0.38 % (2372830)Peak memory usage: 12 MB
% 0.69/0.38 % (2372830)Instructions burned: 7 (million)
% 0.69/0.38 % (2372830)------------------------------
% 0.69/0.38 % (2372830)------------------------------
% 0.69/0.38 % (2372827) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2372799-2372827"...
% 0.69/0.38 % (2372810) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2372799-2372810"...
% 0.69/0.38 % (2372837)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=1724096006:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.69/0.38 % (2372827)...printing done.
% 0.69/0.38 % (2372836)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=1516727760:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.69/0.38 % (2372827)Refutation found. Thanks to Tanya!
% 0.69/0.38 % SZS status Theorem for theBenchmark
% 0.69/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.69/0.38 % (2372827)------------------------------
% 0.69/0.38 % (2372827)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.69/0.38 % (2372827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.69/0.38 % (2372827)CaDiCaL version: 2.1.3
% 0.69/0.38 % (2372827)Termination reason: Refutation
% 0.69/0.38 % (2372827)Time elapsed: 0.030 s
% 0.69/0.38 % (2372827)Peak memory usage: 13 MB
% 0.69/0.38 % (2372827)Instructions burned: 71 (million)
% 0.69/0.38 % (2372799)Success in time 0.127 s
% 0.69/0.38 % Vampire exiting
%------------------------------------------------------------------------------