%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO446^1 : 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 : n017.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 0.79s 0.42s
% Output : Refutation 0.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 17
% Syntax : Number of formulae : 188 ( 77 unt; 0 typ; 4 def)
% Number of atoms : 1384 ( 158 equ; 0 cnn)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 2695 ( 637 ~; 450 |; 14 &;1367 @)
% ( 4 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 146 ( 146 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 59 usr; 12 con; 0-4 aty)
% ( 194 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 445 ( 0 sgn 44 !; 0 ?; 445 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
rel_s5: $i > $i > $o ).
thf(func_def_33,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
q: $i > $o ).
thf(func_def_37,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
vIMP: $o > $o > $o ).
thf(func_def_39,type,
vAND: $o > $o > $o ).
thf(func_def_40,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_45,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_49,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_50,type,
vNOT: $o > $o ).
thf(func_def_51,type,
vOR: $o > $o > $o ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
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,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) ) ),
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] :
! [X2: $i,X1: $i,X3: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( 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] :
( ~ ( rel_s5 @ X1 @ X2 )
| ( X0 @ 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 @ ( mdia_s5 @ ( mand @ p @ ( mdia_s5 @ q ) ) ) @ ( mand @ ( mdia_s5 @ p ) @ ( mdia_s5 @ q ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mand @ p @ ( mdia_s5 @ q ) ) ) @ ( mand @ ( mdia_s5 @ p ) @ ( mdia_s5 @ q ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f45,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f46,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f45]) ).
thf(f55,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s5 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s5 ),
inference(rectify,[],[f32]) ).
thf(f56,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f59,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f60,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f61,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f60]) ).
thf(f63,plain,
( mtransitive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X2 @ X1 )
& ( X0 @ X1 @ X3 ) )
=> ( X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[],[f21]) ).
thf(f64,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f65,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f66,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f69,plain,
~ ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mand @ p @ ( mdia_s5 @ q ) ) ) @ ( mand @ ( mdia_s5 @ p ) @ ( mdia_s5 @ q ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f70,plain,
( ( ~ ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mand @ p @ ( mdia_s5 @ q ) ) ) @ ( mand @ ( mdia_s5 @ p ) @ ( mdia_s5 @ q ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f69]) ).
thf(f71,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f72,plain,
mtransitive @ rel_s5,
inference(rectify,[],[f35]) ).
thf(f73,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f72]) ).
thf(f82,plain,
msymmetric @ rel_s5,
inference(rectify,[],[f36]) ).
thf(f83,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f82]) ).
thf(f92,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f93,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f92]) ).
thf(f94,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
=> ( X0 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f95,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f94]) ).
thf(f103,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f95]) ).
thf(f104,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f56]) ).
thf(f107,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f73]) ).
thf(f108,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f71]) ).
thf(f113,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f114,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f65]) ).
thf(f117,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f122,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f128,plain,
( ( ~ ( mvalid @ ( mequiv @ ( mdia_s5 @ ( mand @ p @ ( mdia_s5 @ q ) ) ) @ ( mand @ ( mdia_s5 @ p ) @ ( mdia_s5 @ q ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f70]) ).
thf(f129,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f83]) ).
thf(f130,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f133,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f93]) ).
thf(f135,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f66]) ).
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,[],[f113,f130,f133,f130,f130]) ).
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,[],[f114,f133,f130]) ).
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,[],[f135,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] :
( ( Y1 @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f108,f130,f104,f130]) ).
thf(f151,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y3 @ Y1 )
& ( Y0 @ Y2 @ Y3 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ rel_s5 )
= $true ),
inference(definition_unfolding,[],[f107,f122]) ).
thf(f153,plain,
( ( ~ ( ^ [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 > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ p
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ q ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s5 @ Y2 @ 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] :
( ( Y1 @ Y3 )
| ~ ( rel_s5 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ q ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f128,f117,f144,f150,f141,f150,f141,f150,f150]) ).
thf(f154,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f129,f103]) ).
thf(f155,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y2 @ Y0 )
& ( rel_s5 @ Y1 @ Y2 ) )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f156,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ~ ( ~ ( p @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( q @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ~ ( ~ ( p @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( q @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f157,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( q @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( q @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f156]) ).
thf(f158,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( q @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) )
| ~ ( ~ ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( q @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f157]) ).
thf(f159,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( q @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) )
| ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( q @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f158]) ).
thf(f160,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( q @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( q @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f159]) ).
thf(f161,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( q @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( q @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(boolean_simplification,[],[f160]) ).
thf(f163,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y0 @ Y1 )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f166,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( q @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( q @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f167,plain,
( $false
= ( ^ [Y0: $i] :
~ ( ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( q @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( q @ Y2 )
| ~ ( rel_s5 @ Y1 @ Y2 ) ) )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( $false
= ( ~ ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ) )
= $true )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f169]) ).
thf(f174,definition,
( spl1_1
<=> ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f176,plain,
( ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f174]) ).
thf(f178,definition,
( spl1_2
<=> ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f180,plain,
( ( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ) )
= $true )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f178]) ).
thf(f181,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f170,f178,f174]) ).
thf(f182,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f180]) ).
thf(f188,plain,
( ( $false
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f189,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f199,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) )
@ sK2 ) )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f189]) ).
thf(f200,plain,
( ( $false
= ( ~ ( p @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK2 @ Y0 ) ) )
| ~ ( rel_s5 @ sK0 @ sK2 ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f199]) ).
thf(f201,plain,
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f200]) ).
thf(f202,plain,
( ( $false
= ( ~ ( p @ sK2 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK2 @ Y0 ) ) ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f200]) ).
thf(f203,plain,
( ( ( rel_s5 @ sK0 @ sK2 )
= $true )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f201]) ).
thf(f211,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK2 @ Y0 ) ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f202]) ).
thf(f212,plain,
( ( $false
= ( ~ ( p @ sK2 ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f202]) ).
thf(f230,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK2 @ Y0 ) )
@ sK3 ) )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f211]) ).
thf(f231,plain,
( ( $false
= ( ~ ( q @ sK3 )
| ~ ( rel_s5 @ sK2 @ sK3 ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f230]) ).
thf(f232,plain,
( ( $false
= ( ~ ( rel_s5 @ sK2 @ sK3 ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f231]) ).
thf(f233,plain,
( ( $false
= ( ~ ( q @ sK3 ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f231]) ).
thf(f234,plain,
( ( ( q @ sK3 )
= $true )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f233]) ).
thf(f242,plain,
( ( ( rel_s5 @ sK2 @ sK3 )
= $true )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f232]) ).
thf(f250,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) )
= $true )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f188]) ).
thf(f268,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
= $true )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f250]) ).
thf(f270,definition,
( spl1_3
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
thf(f271,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
!= $true )
| spl1_3 ),
inference(avatar_component_clause,[],[f270]) ).
thf(f272,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
= $true )
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f270]) ).
thf(f274,definition,
( spl1_4
<=> ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
thf(f275,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
!= $true )
| spl1_4 ),
inference(avatar_component_clause,[],[f274]) ).
thf(f276,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
= $true )
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f274]) ).
thf(f277,plain,
( spl1_3
| spl1_4
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f268,f178,f274,f270]) ).
thf(f278,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) )
@ X1 )
= $true )
| ~ spl1_3 ),
inference(pi_proxy_clausification,[],[f272]) ).
thf(f279,plain,
( ! [X1: $i] :
( ( ~ ( q @ X1 )
| ~ ( rel_s5 @ sK0 @ X1 ) )
= $true )
| ~ spl1_3 ),
inference(beta-eta_normalization,[],[f278]) ).
thf(f284,plain,
( ( ( ~ $true
| ~ ( rel_s5 @ sK0 @ sK3 ) )
= $true )
| ~ spl1_2
| ~ spl1_3 ),
inference(constrained_superposition,[],[f279,f234]) ).
thf(f286,plain,
( ( $true
= ( $false
| ~ ( rel_s5 @ sK0 @ sK3 ) ) )
| ~ spl1_2
| ~ spl1_3 ),
inference(boolean_simplification,[],[f284]) ).
thf(f287,plain,
( ( ( ~ ( rel_s5 @ sK0 @ sK3 ) )
= $true )
| ~ spl1_2
| ~ spl1_3 ),
inference(boolean_simplification,[],[f286]) ).
thf(f310,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK3 ) )
| ~ spl1_2
| ~ spl1_3 ),
inference(not_proxy_clausification,[],[f287]) ).
thf(f318,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y0 @ Y1 )
=> ( rel_s5 @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f163]) ).
thf(f319,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ X1 @ Y0 )
=> ( rel_s5 @ Y0 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f318]) ).
thf(f320,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel_s5 @ X1 @ Y0 )
=> ( rel_s5 @ Y0 @ X1 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f319]) ).
thf(f321,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ X1 @ X2 )
=> ( rel_s5 @ X2 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f320]) ).
thf(f372,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y2 @ Y0 )
& ( rel_s5 @ Y1 @ Y2 ) )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f155]) ).
thf(f373,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y1 @ X1 )
& ( rel_s5 @ Y0 @ Y1 ) )
=> ( rel_s5 @ Y0 @ X1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f372]) ).
thf(f374,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y1 @ X1 )
& ( rel_s5 @ Y0 @ Y1 ) )
=> ( rel_s5 @ Y0 @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f373]) ).
thf(f375,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s5 @ Y0 @ X1 )
& ( rel_s5 @ X2 @ Y0 ) )
=> ( rel_s5 @ X2 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f374]) ).
thf(f376,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( ( rel_s5 @ Y0 @ X1 )
& ( rel_s5 @ X2 @ Y0 ) )
=> ( rel_s5 @ X2 @ X1 ) )
@ X3 )
= $true ),
inference(pi_proxy_clausification,[],[f375]) ).
thf(f377,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( rel_s5 @ X3 @ X1 )
& ( rel_s5 @ X2 @ X3 ) )
=> ( rel_s5 @ X2 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f376]) ).
thf(f389,plain,
( ! [X0: $i] :
( $true
= ( ( ( rel_s5 @ sK2 @ X0 )
& $true )
=> ( rel_s5 @ sK0 @ X0 ) ) )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f377,f203]) ).
thf(f405,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ sK2 @ X0 )
=> ( rel_s5 @ sK0 @ X0 ) )
= $true )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f389]) ).
thf(f433,plain,
( ( ( $true
=> ( rel_s5 @ sK0 @ sK3 ) )
= $true )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f405,f242]) ).
thf(f438,plain,
( ( ( rel_s5 @ sK0 @ sK3 )
= $true )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f433]) ).
thf(f443,plain,
( ( $false = $true )
| ~ spl1_2
| ~ spl1_3 ),
inference(forward_demodulation,[],[f438,f310]) ).
thf(f444,plain,
( $false
| ~ spl1_2
| ~ spl1_3 ),
inference(trivial_inequality_removal,[],[f443]) ).
thf(f445,plain,
( ~ spl1_2
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[],[f444]) ).
thf(f611,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) )
@ sK4 ) )
| spl1_3 ),
inference(sigma_proxy_clausification,[],[f271]) ).
thf(f612,plain,
( ( $false
= ( ~ ( q @ sK4 )
| ~ ( rel_s5 @ sK0 @ sK4 ) ) )
| spl1_3 ),
inference(beta-eta_normalization,[],[f611]) ).
thf(f613,plain,
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK4 ) ) )
| spl1_3 ),
inference(or_proxy_clausification,[],[f612]) ).
thf(f614,plain,
( ( ( ~ ( q @ sK4 ) )
= $false )
| spl1_3 ),
inference(or_proxy_clausification,[],[f612]) ).
thf(f623,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK4 ) )
| spl1_3 ),
inference(not_proxy_clausification,[],[f613]) ).
thf(f632,plain,
( ! [X0: $i] :
( ( ( $true
& ( rel_s5 @ X0 @ sK0 ) )
=> ( rel_s5 @ X0 @ sK4 ) )
= $true )
| spl1_3 ),
inference(constrained_superposition,[],[f377,f623]) ).
thf(f641,plain,
( ! [X0: $i] :
( ( ( rel_s5 @ X0 @ sK0 )
=> ( rel_s5 @ X0 @ sK4 ) )
= $true )
| spl1_3 ),
inference(boolean_simplification,[],[f632]) ).
thf(f795,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) )
@ X1 )
= $true )
| ~ spl1_4 ),
inference(pi_proxy_clausification,[],[f276]) ).
thf(f796,plain,
( ! [X1: $i] :
( ( ~ ( p @ X1 )
| ~ ( rel_s5 @ sK0 @ X1 ) )
= $true )
| ~ spl1_4 ),
inference(beta-eta_normalization,[],[f795]) ).
thf(f1073,plain,
( ( ( ~ ( p @ sK2 )
| $false )
= $true )
| ~ spl1_2
| ~ spl1_4 ),
inference(constrained_superposition,[],[f796,f201]) ).
thf(f1087,plain,
( ( $true
= ( ~ ( p @ sK2 ) ) )
| ~ spl1_2
| ~ spl1_4 ),
inference(boolean_simplification,[],[f1073]) ).
thf(f1101,plain,
( ( $false = $true )
| ~ spl1_2
| ~ spl1_4 ),
inference(forward_demodulation,[],[f1087,f212]) ).
thf(f1102,plain,
( $false
| ~ spl1_2
| ~ spl1_4 ),
inference(trivial_inequality_removal,[],[f1101]) ).
thf(f1103,plain,
( ~ spl1_2
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f1102]) ).
thf(f1108,plain,
( ( $true
= ( ~ ( $true
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) ) )
| ~ spl1_1
| ~ spl1_4 ),
inference(forward_demodulation,[],[f176,f276]) ).
thf(f1109,plain,
( ( ( ~ ( $true
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) )
= $true )
| ~ spl1_1
| ~ spl1_4 ),
inference(boolean_simplification,[],[f1108]) ).
thf(f1110,plain,
( ( $true = ( ~ $true ) )
| ~ spl1_1
| ~ spl1_4 ),
inference(boolean_simplification,[],[f1109]) ).
thf(f1111,plain,
( ( $false = $true )
| ~ spl1_1
| ~ spl1_4 ),
inference(boolean_simplification,[],[f1110]) ).
thf(f1112,plain,
( $false
| ~ spl1_1
| ~ spl1_4 ),
inference(trivial_inequality_removal,[],[f1111]) ).
thf(f1113,plain,
( ~ spl1_1
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f1112]) ).
thf(f1114,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) )
@ sK5 ) )
| spl1_4 ),
inference(sigma_proxy_clausification,[],[f275]) ).
thf(f1115,plain,
( ( $false
= ( ~ ( p @ sK5 )
| ~ ( rel_s5 @ sK0 @ sK5 ) ) )
| spl1_4 ),
inference(beta-eta_normalization,[],[f1114]) ).
thf(f1116,plain,
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK5 ) ) )
| spl1_4 ),
inference(or_proxy_clausification,[],[f1115]) ).
thf(f1117,plain,
( ( $false
= ( ~ ( p @ sK5 ) ) )
| spl1_4 ),
inference(or_proxy_clausification,[],[f1115]) ).
thf(f1121,plain,
( ( ( p @ sK5 )
= $true )
| spl1_4 ),
inference(not_proxy_clausification,[],[f1117]) ).
thf(f1129,plain,
( ( ( rel_s5 @ sK0 @ sK5 )
= $true )
| spl1_4 ),
inference(not_proxy_clausification,[],[f1116]) ).
thf(f1141,plain,
( ( ( $true
=> ( rel_s5 @ sK5 @ sK0 ) )
= $true )
| spl1_4 ),
inference(constrained_superposition,[],[f321,f1129]) ).
thf(f1148,plain,
( ( ( rel_s5 @ sK5 @ sK0 )
= $true )
| spl1_4 ),
inference(boolean_simplification,[],[f1141]) ).
thf(f1154,plain,
( ( ( $true
=> ( rel_s5 @ sK5 @ sK4 ) )
= $true )
| spl1_3
| spl1_4 ),
inference(constrained_superposition,[],[f641,f1148]) ).
thf(f1164,plain,
( ( $true
= ( rel_s5 @ sK5 @ sK4 ) )
| spl1_3
| spl1_4 ),
inference(boolean_simplification,[],[f1154]) ).
thf(f1391,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f176]) ).
thf(f1397,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f1391]) ).
thf(f1398,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f1391]) ).
thf(f1408,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f1398]) ).
thf(f1414,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) ) )
= $true )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f1397]) ).
thf(f1415,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( q @ Y1 )
| ~ ( rel_s5 @ Y0 @ Y1 ) ) )
| ~ ( rel_s5 @ sK0 @ Y0 ) )
@ X1 ) )
| ~ spl1_1 ),
inference(pi_proxy_clausification,[],[f1414]) ).
thf(f1416,plain,
( ! [X1: $i] :
( ( ~ ( p @ X1 )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ X1 @ Y0 ) ) )
| ~ ( rel_s5 @ sK0 @ X1 ) )
= $true )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f1415]) ).
thf(f1425,plain,
( ( ( ~ $true
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK5 @ Y0 ) ) )
| ~ ( rel_s5 @ sK0 @ sK5 ) )
= $true )
| ~ spl1_1
| spl1_4 ),
inference(constrained_superposition,[],[f1416,f1121]) ).
thf(f1429,plain,
( ( ( $false
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK5 @ Y0 ) ) )
| ~ ( rel_s5 @ sK0 @ sK5 ) )
= $true )
| ~ spl1_1
| spl1_4 ),
inference(boolean_simplification,[],[f1425]) ).
thf(f1430,plain,
( ( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK5 @ Y0 ) ) )
| ~ ( rel_s5 @ sK0 @ sK5 ) ) )
| ~ spl1_1
| spl1_4 ),
inference(boolean_simplification,[],[f1429]) ).
thf(f1442,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK5 @ Y0 ) ) )
| $false )
= $true )
| ~ spl1_1
| spl1_4 ),
inference(forward_demodulation,[],[f1430,f1116]) ).
thf(f1443,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK5 @ Y0 ) ) ) )
| ~ spl1_1
| spl1_4 ),
inference(boolean_simplification,[],[f1442]) ).
thf(f1462,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( q @ Y0 )
| ~ ( rel_s5 @ sK5 @ Y0 ) )
@ X1 )
= $true )
| ~ spl1_1
| spl1_4 ),
inference(pi_proxy_clausification,[],[f1443]) ).
thf(f1463,plain,
( ! [X1: $i] :
( ( ~ ( q @ X1 )
| ~ ( rel_s5 @ sK5 @ X1 ) )
= $true )
| ~ spl1_1
| spl1_4 ),
inference(beta-eta_normalization,[],[f1462]) ).
thf(f1469,plain,
( ( ( ~ ( q @ sK4 )
| ~ $true )
= $true )
| ~ spl1_1
| spl1_3
| spl1_4 ),
inference(constrained_superposition,[],[f1463,f1164]) ).
thf(f1477,plain,
( ( ( ~ ( q @ sK4 )
| $false )
= $true )
| ~ spl1_1
| spl1_3
| spl1_4 ),
inference(boolean_simplification,[],[f1469]) ).
thf(f1478,plain,
( ( ( ~ ( q @ sK4 ) )
= $true )
| ~ spl1_1
| spl1_3
| spl1_4 ),
inference(boolean_simplification,[],[f1477]) ).
thf(f1493,plain,
( ( $false = $true )
| ~ spl1_1
| spl1_3
| spl1_4 ),
inference(forward_demodulation,[],[f1478,f614]) ).
thf(f1494,plain,
( $false
| ~ spl1_1
| spl1_3
| spl1_4 ),
inference(trivial_inequality_removal,[],[f1493]) ).
thf(f1495,plain,
( ~ spl1_1
| spl1_3
| spl1_4 ),
inference(avatar_contradiction_clause,[],[f1494]) ).
thf(f1509,plain,
( ( $false = $true )
| ~ spl1_1
| ~ spl1_3 ),
inference(forward_demodulation,[],[f272,f1408]) ).
thf(f1510,plain,
( $false
| ~ spl1_1
| ~ spl1_3 ),
inference(trivial_inequality_removal,[],[f1509]) ).
thf(f1511,plain,
( ~ spl1_1
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[],[f1510]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f181]) ).
cnf(s2,plain,
( ~ spl1_2
| spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f277]) ).
cnf(s4,plain,
( ~ spl1_2
| ~ spl1_3 ),
inference(sat_conversion,[],[f445]) ).
cnf(s8,plain,
( ~ spl1_2
| ~ spl1_4 ),
inference(sat_conversion,[],[f1103]) ).
cnf(s9,plain,
( ~ spl1_1
| ~ spl1_4 ),
inference(sat_conversion,[],[f1113]) ).
cnf(s12,plain,
( ~ spl1_1
| spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f1495]) ).
cnf(s13,plain,
( ~ spl1_1
| ~ spl1_3 ),
inference(sat_conversion,[],[f1511]) ).
cnf(s14,plain,
~ spl1_2,
inference(rat,[],[s2,s4,s8]) ).
cnf(s15,plain,
spl1_1,
inference(rat,[],[s1,s14]) ).
cnf(s16,plain,
~ spl1_3,
inference(rat,[],[s13,s15]) ).
cnf(s17,plain,
~ spl1_4,
inference(rat,[],[s9,s15]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s12,s17,s15,s16]) ).
thf(f1512,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO446^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n017.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 16:47:23 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.10/0.26 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
% 0.79/0.42 % (595614)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.79/0.42 % (595625)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3781289844:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.79/0.42 % (595626)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.79/0.42 % (595626)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
% 0.79/0.42 % (595621)lrs+10_16_si=on:nwc=1.5:random_seed=811051500:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.79/0.42 % (595620)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=97933432:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.79/0.42 % (595622)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=536672196:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.79/0.42 % (595624)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1975755281:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.79/0.42 % (595623)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=3366555927: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)
% 0.79/0.42 % (595626)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=3293500556:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.79/0.42 % (595622)Instruction limit reached!
% 0.79/0.42 % (595622)------------------------------
% 0.79/0.42 % (595622)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.42 % (595622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.42 % (595622)CaDiCaL version: 2.1.3
% 0.79/0.42 % (595622)Termination reason: Instruction limit
% 0.79/0.42 % (595622)Termination phase: Property scanning
% 0.79/0.42 % (595622)Time elapsed: 0.003 s
% 0.79/0.42 % (595622)Peak memory usage: 10 MB
% 0.79/0.42 % (595622)Instructions burned: 3 (million)
% 0.79/0.42 % (595621)Instruction limit reached!
% 0.79/0.42 % (595621)------------------------------
% 0.79/0.42 % (595621)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.42 % (595621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.42 % (595621)CaDiCaL version: 2.1.3
% 0.79/0.42 % (595621)Termination reason: Instruction limit
% 0.79/0.42 % (595621)Termination phase: Saturation
% 0.79/0.42 % (595621)Time elapsed: 0.016 s
% 0.79/0.42 % (595621)Peak memory usage: 12 MB
% 0.79/0.42 % (595621)Instructions burned: 18 (million)
% 0.79/0.42 % (595625)Instruction limit reached!
% 0.79/0.42 % (595625)------------------------------
% 0.79/0.42 % (595625)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.42 % (595625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.42 % (595625)CaDiCaL version: 2.1.3
% 0.79/0.42 % (595625)Termination reason: Instruction limit
% 0.79/0.42 % (595625)Termination phase: Saturation
% 0.79/0.42 % (595625)Time elapsed: 0.034 s
% 0.79/0.42 % (595625)Peak memory usage: 12 MB
% 0.79/0.42 % (595625)Instructions burned: 75 (million)
% 0.79/0.42 % (595624)Instruction limit reached!
% 0.79/0.42 % (595624)------------------------------
% 0.79/0.42 % (595624)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.42 % (595624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.42 % (595624)CaDiCaL version: 2.1.3
% 0.79/0.42 % (595624)Termination reason: Instruction limit
% 0.79/0.42 % (595624)Termination phase: Saturation
% 0.79/0.42 % (595624)Time elapsed: 0.023 s
% 0.79/0.42 % (595624)Peak memory usage: 11 MB
% 0.79/0.42 % (595624)Instructions burned: 24 (million)
% 0.79/0.42 % (595634)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2939793165:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.79/0.42 % (595636)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.79/0.42 % (595634)Instruction limit reached!
% 0.79/0.42 % (595634)------------------------------
% 0.79/0.42 % (595634)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.42 % (595634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.42 % (595634)CaDiCaL version: 2.1.3
% 0.79/0.42 % (595634)Termination reason: Instruction limit
% 0.79/0.42 % (595634)Termination phase: Preprocessing 3
% 0.79/0.42 % (595634)Time elapsed: 0.004 s
% 0.79/0.42 % (595634)Peak memory usage: 10 MB
% 0.79/0.42 % (595634)Instructions burned: 4 (million)
% 0.79/0.42 % (595635)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1548653281:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.79/0.42 % (595636)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2857056798:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.79/0.42 % (595636)Instruction limit reached!
% 0.79/0.42 % (595636)------------------------------
% 0.79/0.42 % (595636)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.42 % (595636)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.42 % (595636)CaDiCaL version: 2.1.3
% 0.79/0.42 % (595636)Termination reason: Instruction limit
% 0.79/0.42 % (595636)Termination phase: Saturation
% 0.79/0.42 % (595636)Time elapsed: 0.003 s
% 0.79/0.42 % (595636)Peak memory usage: 10 MB
% 0.79/0.42 % (595636)Instructions burned: 8 (million)
% 0.79/0.42 % (595635)Instruction limit reached!
% 0.79/0.42 % (595635)------------------------------
% 0.79/0.42 % (595635)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.42 % (595635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.42 % (595635)CaDiCaL version: 2.1.3
% 0.79/0.42 % (595635)Termination reason: Instruction limit
% 0.79/0.42 % (595635)Termination phase: Property scanning
% 0.79/0.42 % (595635)Time elapsed: 0.005 s
% 0.79/0.42 % (595635)Peak memory usage: 10 MB
% 0.79/0.42 % (595635)Instructions burned: 5 (million)
% 0.79/0.42 % (595637)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2146695112:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.79/0.42 % (595642)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=1349995886:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.79/0.42 % (595637)Instruction limit reached!
% 0.79/0.42 % (595637)------------------------------
% 0.79/0.42 % (595637)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.42 % (595637)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.42 % (595637)CaDiCaL version: 2.1.3
% 0.79/0.42 % (595637)Termination reason: Instruction limit
% 0.79/0.42 % (595637)Termination phase: Saturation
% 0.79/0.42 % (595637)Time elapsed: 0.010 s
% 0.79/0.42 % (595637)Peak memory usage: 11 MB
% 0.79/0.42 % (595637)Instructions burned: 12 (million)
% 0.79/0.42 % (595640)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
% 0.79/0.42 % (595640)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.79/0.42 % (595640)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1246884511:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.79/0.42 % (595643)lrs+10_1_si=on:cs=on:random_seed=3811070418:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.79/0.42 % (595620)Instruction limit reached!
% 0.79/0.42 % (595620)------------------------------
% 0.79/0.42 % (595620)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.42 % (595620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.42 % (595620)CaDiCaL version: 2.1.3
% 0.79/0.42 % (595620)Termination reason: Instruction limit
% 0.79/0.42 % (595620)Termination phase: Saturation
% 0.79/0.42 % (595620)Time elapsed: 0.078 s
% 0.79/0.42 % (595620)Peak memory usage: 12 MB
% 0.79/0.42 % (595620)Instructions burned: 87 (million)
% 0.79/0.42 % (595643)Instruction limit reached!
% 0.79/0.42 % (595643)------------------------------
% 0.79/0.42 % (595643)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.42 % (595643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.42 % (595643)CaDiCaL version: 2.1.3
% 0.79/0.42 % (595643)Termination reason: Instruction limit
% 0.79/0.42 % (595643)Termination phase: Saturation
% 0.79/0.42 % (595643)Time elapsed: 0.008 s
% 0.79/0.42 % (595643)Peak memory usage: 12 MB
% 0.79/0.42 % (595643)Instructions burned: 8 (million)
% 0.79/0.42 % (595646)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.79/0.42 % (595646)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=228686298:i=2:add=on:rtra=on_2998 on theBenchmark for (2998ds/2Mi)
% 0.79/0.42 % (595646)Instruction limit reached!
% 0.79/0.42 % (595646)------------------------------
% 0.79/0.42 % (595646)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.42 % (595646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.42 % (595646)CaDiCaL version: 2.1.3
% 0.79/0.42 % (595646)Termination reason: Instruction limit
% 0.79/0.42 % (595646)Termination phase: shuffling
% 0.79/0.42 % (595646)Time elapsed: 0.001 s
% 0.79/0.42 % (595646)Peak memory usage: 9 MB
% 0.79/0.42 % (595646)Instructions burned: 2 (million)
% 0.79/0.42 % (595640)Instruction limit reached!
% 0.79/0.42 % (595640)------------------------------
% 0.79/0.42 % (595640)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.42 % (595640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.42 % (595640)CaDiCaL version: 2.1.3
% 0.79/0.42 % (595640)Termination reason: Instruction limit
% 0.79/0.42 % (595640)Termination phase: Saturation
% 0.79/0.42 % (595640)Time elapsed: 0.023 s
% 0.79/0.42 % (595640)Peak memory usage: 11 MB
% 0.79/0.42 % (595640)Instructions burned: 28 (million)
% 0.79/0.42 % (595642) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-595614-595642"...
% 0.79/0.42 % (595642)...printing done.
% 0.79/0.42 % (595649)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2234376840:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/38Mi)
% 0.79/0.42 % (595642)Refutation found. Thanks to Tanya!
% 0.79/0.42 % SZS status Theorem for theBenchmark
% 0.79/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.79/0.43 % (595642)------------------------------
% 0.79/0.43 % (595642)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.79/0.43 % (595642)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.79/0.43 % (595642)CaDiCaL version: 2.1.3
% 0.79/0.43 % (595642)Termination reason: Refutation
% 0.79/0.43 % (595642)Time elapsed: 0.048 s
% 0.79/0.43 % (595642)Peak memory usage: 13 MB
% 0.79/0.43 % (595642)Instructions burned: 101 (million)
% 0.79/0.43 % (595614)Success in time 0.151 s
% 0.79/0.43 % Vampire exiting
%------------------------------------------------------------------------------