%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO445^1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 0.20s 0.36s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 17
% Syntax : Number of formulae : 180 ( 73 unt; 0 typ; 4 def)
% Number of atoms : 1281 ( 161 equ; 0 cnn)
% Maximal formula atoms : 12 ( 7 avg)
% Number of connectives : 2271 ( 497 ~; 370 |; 14 &;1196 @)
% ( 4 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 130 ( 130 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 59 usr; 12 con; 0-4 aty)
% ( 160 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 387 ( 0 sgn 46 !; 0 ?; 387 :)
% 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,
vNOT: $o > $o ).
thf(func_def_38,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_41,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
vIMP: $o > $o > $o ).
thf(func_def_43,type,
vAND: $o > $o > $o ).
thf(func_def_44,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_47,type,
vOR: $o > $o > $o ).
thf(func_def_50,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) )
= mimplies ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) )
= mequiv ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f21,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X3: $i,X2: $i,X1: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) )
= mtransitive ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mtransitive) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_s5
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',mbox_s5) ).
thf(f33,axiom,
( ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ X0 ) ) ) )
= mdia_s5 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',mdia_s5) ).
thf(f35,axiom,
mtransitive @ rel_s5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a2) ).
thf(f36,axiom,
msymmetric @ rel_s5,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',a3) ).
thf(f37,conjecture,
mvalid @ ( mequiv @ ( mor @ ( mbox_s5 @ p ) @ ( mdia_s5 @ q ) ) @ ( mbox_s5 @ ( mor @ p @ ( mdia_s5 @ q ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mequiv @ ( mor @ ( mbox_s5 @ p ) @ ( mdia_s5 @ q ) ) @ ( mbox_s5 @ ( mor @ p @ ( mdia_s5 @ q ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f39,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f40,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f46,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f47,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f50,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f58,plain,
~ ( mvalid @ ( mequiv @ ( mor @ ( mbox_s5 @ p ) @ ( mdia_s5 @ q ) ) @ ( mbox_s5 @ ( mor @ p @ ( mdia_s5 @ q ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f59,plain,
( $true
= ( ~ ( mvalid @ ( mequiv @ ( mor @ ( mbox_s5 @ p ) @ ( mdia_s5 @ q ) ) @ ( mbox_s5 @ ( mor @ p @ ( mdia_s5 @ q ) ) ) ) ) ) ),
inference(fool_elimination,[],[f58]) ).
thf(f62,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f63,plain,
( mbox_s5
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f64,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f63]) ).
thf(f67,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X3 @ X2 )
& ( X0 @ X2 @ X1 ) )
=> ( X0 @ X3 @ X1 ) ) )
= mtransitive ),
inference(rectify,[],[f21]) ).
thf(f68,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f67]) ).
thf(f81,plain,
msymmetric @ rel_s5,
inference(rectify,[],[f36]) ).
thf(f82,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f81]) ).
thf(f85,plain,
mtransitive @ rel_s5,
inference(rectify,[],[f35]) ).
thf(f86,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f85]) ).
thf(f91,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f92,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f93,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f92]) ).
thf(f98,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f99,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f100,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f99]) ).
thf(f103,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f93]) ).
thf(f109,plain,
( mdia_s5
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s5 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f111,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f115,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f116,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f118,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f98]) ).
thf(f121,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f91]) ).
thf(f122,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f64]) ).
thf(f125,plain,
( $true
= ( ~ ( mvalid @ ( mequiv @ ( mor @ ( mbox_s5 @ p ) @ ( mdia_s5 @ q ) ) @ ( mbox_s5 @ ( mor @ p @ ( mdia_s5 @ q ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f59]) ).
thf(f127,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f100]) ).
thf(f128,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f68]) ).
thf(f130,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f82]) ).
thf(f134,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f86]) ).
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] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f121,f115,f127,f115,f115]) ).
thf(f142,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f118,f127,f115]) ).
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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f111,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,[],[f109,f115,f122,f115]) ).
thf(f151,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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ 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] :
( ( Y5 @ Y6 )
| ( Y4 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ 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] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ 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,[],[f125,f116,f144,f127,f122,f150,f122,f127,f150]) ).
thf(f153,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f130,f103]) ).
thf(f154,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y1 @ Y2 ) )
=> ( Y0 @ Y1 @ Y3 ) ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f134,f128]) ).
thf(f156,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ( !! @ $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 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( q @ Y2 ) ) )
| ( p @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( q @ Y2 ) ) )
| ( p @ Y1 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f157,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f158,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y1 @ Y2 )
& ( rel_s5 @ Y0 @ Y1 ) )
=> ( rel_s5 @ Y0 @ Y2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f161,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
~ ( ~ ( ~ ( !! @ $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 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( q @ Y2 ) ) )
| ( p @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( q @ Y2 ) ) )
| ( p @ Y1 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f156]) ).
thf(f162,plain,
( ( ^ [Y0: $i] :
~ ( ~ ( ~ ( !! @ $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 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( q @ Y2 ) ) )
| ( p @ Y1 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ~ ( q @ Y2 ) ) )
| ( p @ Y1 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( ( ~ ( ~ ( ~ ( !! @ $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 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( p @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
( $true
= ( ~ ( ~ ( !! @ $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 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( p @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( ( $true
= ( ~ ( ~ ( !! @ $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 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( p @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f169,definition,
( spl1_1
<=> ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f171,plain,
( ( $true
= ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f169]) ).
thf(f173,definition,
( spl1_2
<=> ( $true
= ( ~ ( ~ ( !! @ $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 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( p @ Y0 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f175,plain,
( ( $true
= ( ~ ( ~ ( !! @ $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 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( p @ Y0 ) ) ) ) ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f173]) ).
thf(f176,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f165,f173,f169]) ).
thf(f177,plain,
( ( ( ~ ( !! @ $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 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( p @ Y0 ) ) ) )
= $false )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f175]) ).
thf(f184,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f194,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
= $false )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f195,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
= $false )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f198,plain,
( ( $true
= ( ~ ( $false
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( p @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( p @ Y0 ) ) )
| ~ $false ) ) )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f164,f184]) ).
thf(f200,plain,
( ( ( ~ ( $false
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( p @ Y0 ) ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( p @ Y0 ) ) )
| $true ) )
= $true )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f198]) ).
thf(f201,plain,
( ( $true
= ( ~ ( $false
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( p @ Y0 ) ) ) )
| ~ $true ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f200]) ).
thf(f202,plain,
( ( $true
= ( ~ ( $false
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( p @ Y0 ) ) ) )
| $false ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f201]) ).
thf(f203,plain,
( ( $true
= ( ~ ( $false
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( p @ Y0 ) ) ) ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f202]) ).
thf(f204,plain,
( ( $true
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( p @ Y0 ) ) ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f203]) ).
thf(f205,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( p @ Y0 ) ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f204]) ).
thf(f215,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK2 )
= $false )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f194]) ).
thf(f216,plain,
( ( ( ~ ( rel_s5 @ sK0 @ sK2 )
| ( p @ sK2 ) )
= $false )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f215]) ).
thf(f217,plain,
( ( ( p @ sK2 )
= $false )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f216]) ).
thf(f218,plain,
( ( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 ) ) )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f216]) ).
thf(f221,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK2 ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f218]) ).
thf(f229,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f195]) ).
thf(f230,plain,
( ! [X1: $i] :
( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ X1 )
= $true )
| ~ spl1_2 ),
inference(pi_proxy_clausification,[],[f229]) ).
thf(f231,plain,
( ! [X1: $i] :
( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( q @ X1 ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f230]) ).
thf(f257,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( p @ Y0 ) )
@ X1 ) )
| ~ spl1_2 ),
inference(pi_proxy_clausification,[],[f205]) ).
thf(f258,plain,
( ! [X1: $i] :
( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ X1 @ Y0 )
| ~ ( q @ Y0 ) ) )
| ( p @ X1 ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f257]) ).
thf(f260,plain,
( ( $true
= ( ~ ( rel_s5 @ sK0 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( q @ Y0 ) ) )
| $false ) )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f258,f217]) ).
thf(f264,plain,
( ( $true
= ( ~ ( rel_s5 @ sK0 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f260]) ).
thf(f270,plain,
( ( $true
= ( $false
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ~ spl1_2 ),
inference(forward_demodulation,[],[f264,f218]) ).
thf(f271,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f270]) ).
thf(f281,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( q @ Y0 ) ) )
= $false )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f271]) ).
thf(f282,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK3 )
= $false )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f281]) ).
thf(f283,plain,
( ( ( ~ ( rel_s5 @ sK2 @ sK3 )
| ~ ( q @ sK3 ) )
= $false )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f282]) ).
thf(f284,plain,
( ( ( ~ ( q @ sK3 ) )
= $false )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f283]) ).
thf(f285,plain,
( ( ( ~ ( rel_s5 @ sK2 @ sK3 ) )
= $false )
| ~ spl1_2 ),
inference(or_proxy_clausification,[],[f283]) ).
thf(f288,plain,
( ( $true
= ( ~ ( rel_s5 @ sK0 @ sK3 )
| $false ) )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f231,f284]) ).
thf(f289,plain,
( ( $true
= ( ~ ( rel_s5 @ sK0 @ sK3 ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f288]) ).
thf(f299,plain,
( ( $true
= ( rel_s5 @ sK2 @ sK3 ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f285]) ).
thf(f307,plain,
( ( ( rel_s5 @ sK0 @ sK3 )
= $false )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f289]) ).
thf(f341,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f157]) ).
thf(f342,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f341]) ).
thf(f343,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f342]) ).
thf(f344,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel_s5 @ X2 @ X1 )
=> ( rel_s5 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f343]) ).
thf(f345,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ X2 @ X1 )
= $false )
| ( ( rel_s5 @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f344]) ).
thf(f377,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y1 @ Y2 )
& ( rel_s5 @ Y0 @ Y1 ) )
=> ( rel_s5 @ Y0 @ Y2 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f158]) ).
thf(f378,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y0 @ Y1 )
& ( rel_s5 @ X1 @ Y0 ) )
=> ( rel_s5 @ X1 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f377]) ).
thf(f379,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y0 @ Y1 )
& ( rel_s5 @ X1 @ Y0 ) )
=> ( rel_s5 @ X1 @ Y1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f378]) ).
thf(f380,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s5 @ X2 @ Y0 )
& ( rel_s5 @ X1 @ X2 ) )
=> ( rel_s5 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f379]) ).
thf(f381,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s5 @ X2 @ Y0 )
& ( rel_s5 @ X1 @ X2 ) )
=> ( rel_s5 @ X1 @ Y0 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f380]) ).
thf(f382,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s5 @ X2 @ X3 )
& ( rel_s5 @ X1 @ X2 ) )
=> ( rel_s5 @ X1 @ X3 ) ) ),
inference(beta-eta_normalization,[],[f381]) ).
thf(f394,plain,
( ! [X0: $i] :
( $true
= ( ( ( rel_s5 @ sK2 @ X0 )
& $true )
=> ( rel_s5 @ sK0 @ X0 ) ) )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f382,f221]) ).
thf(f418,plain,
( ! [X0: $i] :
( $true
= ( ( rel_s5 @ sK2 @ X0 )
=> ( rel_s5 @ sK0 @ X0 ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f394]) ).
thf(f438,plain,
( ( $true
= ( $true
=> ( rel_s5 @ sK0 @ sK3 ) ) )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f418,f299]) ).
thf(f443,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK3 ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f438]) ).
thf(f448,plain,
( ( $true = $false )
| ~ spl1_2 ),
inference(forward_demodulation,[],[f443,f307]) ).
thf(f449,plain,
( $false
| ~ spl1_2 ),
inference(trivial_inequality_removal,[],[f448]) ).
thf(f450,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[],[f449]) ).
thf(f451,plain,
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( p @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $false )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f457,plain,
( ( ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) )
= $false )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f451]) ).
thf(f458,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( p @ Y0 ) ) ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f451]) ).
thf(f468,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( q @ Y1 ) ) )
| ( p @ Y0 ) )
@ sK4 )
= $false )
| ~ spl1_1 ),
inference(sigma_proxy_clausification,[],[f458]) ).
thf(f469,plain,
( ( ( ~ ( rel_s5 @ sK0 @ sK4 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( q @ Y0 ) ) )
| ( p @ sK4 ) )
= $false )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f468]) ).
thf(f470,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( q @ Y0 ) ) )
| ( p @ sK4 ) )
= $false )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f469]) ).
thf(f471,plain,
( ( ( ~ ( rel_s5 @ sK0 @ sK4 ) )
= $false )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f469]) ).
thf(f472,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK4 ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f471]) ).
thf(f480,plain,
( ( $true
= ( $true
=> ( rel_s5 @ sK4 @ sK0 ) ) )
| ~ spl1_1 ),
inference(constrained_superposition,[],[f344,f472]) ).
thf(f485,plain,
( ( $true
= ( rel_s5 @ sK4 @ sK0 ) )
| ~ spl1_1 ),
inference(boolean_simplification,[],[f480]) ).
thf(f491,plain,
( ! [X0: $i] :
( $true
= ( ( ( rel_s5 @ sK0 @ X0 )
& $true )
=> ( rel_s5 @ sK4 @ X0 ) ) )
| ~ spl1_1 ),
inference(constrained_superposition,[],[f382,f485]) ).
thf(f497,plain,
( ! [X0: $i] :
( $true
= ( ( rel_s5 @ sK0 @ X0 )
=> ( rel_s5 @ sK4 @ X0 ) ) )
| ~ spl1_1 ),
inference(boolean_simplification,[],[f491]) ).
thf(f536,plain,
( ( ( p @ sK4 )
= $false )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f470]) ).
thf(f537,plain,
( ( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
= $false )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f470]) ).
thf(f546,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( q @ Y0 ) ) ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f537]) ).
thf(f547,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK4 @ Y0 )
| ~ ( q @ Y0 ) )
@ X1 ) )
| ~ spl1_1 ),
inference(pi_proxy_clausification,[],[f546]) ).
thf(f548,plain,
( ! [X1: $i] :
( $true
= ( ~ ( rel_s5 @ sK4 @ X1 )
| ~ ( q @ X1 ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f547]) ).
thf(f625,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ~ spl1_1 ),
inference(not_proxy_clausification,[],[f457]) ).
thf(f647,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
| ~ spl1_1 ),
inference(or_proxy_clausification,[],[f625]) ).
thf(f673,definition,
( spl1_3
<=> ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
thf(f675,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
| ~ spl1_3 ),
inference(avatar_component_clause,[],[f673]) ).
thf(f677,definition,
( spl1_4
<=> ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition]) ).
thf(f679,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) ) ) )
| ~ spl1_4 ),
inference(avatar_component_clause,[],[f677]) ).
thf(f680,plain,
( spl1_3
| spl1_4
| ~ spl1_1 ),
inference(avatar_split_clause,[],[f647,f169,f677,f673]) ).
thf(f685,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) ) )
= $false )
| ~ spl1_4 ),
inference(not_proxy_clausification,[],[f679]) ).
thf(f686,plain,
( ( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( q @ Y0 ) )
@ sK5 )
= $false )
| ~ spl1_4 ),
inference(sigma_proxy_clausification,[],[f685]) ).
thf(f687,plain,
( ( ( ~ ( rel_s5 @ sK0 @ sK5 )
| ~ ( q @ sK5 ) )
= $false )
| ~ spl1_4 ),
inference(beta-eta_normalization,[],[f686]) ).
thf(f688,plain,
( ( ( ~ ( q @ sK5 ) )
= $false )
| ~ spl1_4 ),
inference(or_proxy_clausification,[],[f687]) ).
thf(f690,plain,
( ( ( ~ $false
| ~ ( q @ sK5 ) )
= $false )
| ( $true
= ( rel_s5 @ sK5 @ sK0 ) )
| ~ spl1_4 ),
inference(constrained_superposition,[],[f687,f345]) ).
thf(f691,plain,
( ( ( $true
| ~ ( q @ sK5 ) )
= $false )
| ( $true
= ( rel_s5 @ sK5 @ sK0 ) )
| ~ spl1_4 ),
inference(boolean_simplification,[],[f690]) ).
thf(f692,plain,
( ( $true = $false )
| ( $true
= ( rel_s5 @ sK5 @ sK0 ) )
| ~ spl1_4 ),
inference(boolean_simplification,[],[f691]) ).
thf(f693,plain,
( ( $true
= ( rel_s5 @ sK5 @ sK0 ) )
| ~ spl1_4 ),
inference(trivial_inequality_removal,[],[f692]) ).
thf(f714,plain,
( ( $true
= ( $true
=> ( rel_s5 @ sK0 @ sK5 ) ) )
| ~ spl1_4 ),
inference(constrained_superposition,[],[f344,f693]) ).
thf(f716,plain,
( ( $true
= ( rel_s5 @ sK0 @ sK5 ) )
| ~ spl1_4 ),
inference(boolean_simplification,[],[f714]) ).
thf(f727,plain,
( ( $true
= ( $true
=> ( rel_s5 @ sK4 @ sK5 ) ) )
| ~ spl1_1
| ~ spl1_4 ),
inference(constrained_superposition,[],[f497,f716]) ).
thf(f745,plain,
( ( $true
= ( rel_s5 @ sK4 @ sK5 ) )
| ~ spl1_1
| ~ spl1_4 ),
inference(boolean_simplification,[],[f727]) ).
thf(f765,plain,
( ( $true
= ( ~ $true
| ~ ( q @ sK5 ) ) )
| ~ spl1_1
| ~ spl1_4 ),
inference(constrained_superposition,[],[f548,f745]) ).
thf(f777,plain,
( ( $true
= ( $false
| ~ ( q @ sK5 ) ) )
| ~ spl1_1
| ~ spl1_4 ),
inference(boolean_simplification,[],[f765]) ).
thf(f778,plain,
( ( $true
= ( ~ ( q @ sK5 ) ) )
| ~ spl1_1
| ~ spl1_4 ),
inference(boolean_simplification,[],[f777]) ).
thf(f785,plain,
( ( $true = $false )
| ~ spl1_1
| ~ spl1_4 ),
inference(forward_demodulation,[],[f778,f688]) ).
thf(f786,plain,
( $false
| ~ spl1_1
| ~ spl1_4 ),
inference(trivial_inequality_removal,[],[f785]) ).
thf(f787,plain,
( ~ spl1_1
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[],[f786]) ).
thf(f788,plain,
( ! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) )
| ~ spl1_3 ),
inference(pi_proxy_clausification,[],[f675]) ).
thf(f789,plain,
( ! [X1: $i] :
( $true
= ( ~ ( rel_s5 @ sK0 @ X1 )
| ( p @ X1 ) ) )
| ~ spl1_3 ),
inference(beta-eta_normalization,[],[f788]) ).
thf(f791,plain,
( ( $true
= ( ~ ( rel_s5 @ sK0 @ sK4 )
| $false ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(constrained_superposition,[],[f789,f536]) ).
thf(f803,plain,
( ( $true
= ( ~ ( rel_s5 @ sK0 @ sK4 ) ) )
| ~ spl1_1
| ~ spl1_3 ),
inference(boolean_simplification,[],[f791]) ).
thf(f810,plain,
( ( $true = $false )
| ~ spl1_1
| ~ spl1_3 ),
inference(forward_demodulation,[],[f803,f471]) ).
thf(f811,plain,
( $false
| ~ spl1_1
| ~ spl1_3 ),
inference(trivial_inequality_removal,[],[f810]) ).
thf(f812,plain,
( ~ spl1_1
| ~ spl1_3 ),
inference(avatar_contradiction_clause,[],[f811]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f176]) ).
cnf(s3,plain,
~ spl1_2,
inference(sat_conversion,[],[f450]) ).
cnf(s4,plain,
( ~ spl1_1
| spl1_3
| spl1_4 ),
inference(sat_conversion,[],[f680]) ).
cnf(s5,plain,
( ~ spl1_1
| ~ spl1_4 ),
inference(sat_conversion,[],[f787]) ).
cnf(s8,plain,
( ~ spl1_1
| ~ spl1_3 ),
inference(sat_conversion,[],[f812]) ).
cnf(s9,plain,
spl1_1,
inference(rat,[],[s1,s3]) ).
cnf(s10,plain,
~ spl1_3,
inference(rat,[],[s8,s9]) ).
cnf(s11,plain,
~ spl1_4,
inference(rat,[],[s5,s9]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s4,s11,s10,s9]) ).
thf(f813,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO445^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.16 % Computer : n002.cluster.edu
% 0.10/0.16 % Model : x86_64 x86_64
% 0.10/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.16 % Memory : 8046.5625MB
% 0.10/0.16 % OS : Linux 6.8.0-71-generic
% 0.10/0.16 % CPULimit : 300
% 0.10/0.16 % WCLimit : 300
% 0.10/0.16 % DateTime : Tue Sep 29 16:54:37 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 Running higher-order theorem proving
% 0.10/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.35 % (1554459)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.35 % (1554475)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3495148958:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.35 % (1554482)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.35 % (1554482)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.35 % (1554476)lrs+10_16_si=on:nwc=1.5:random_seed=3640278526:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.35 % (1554477)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3711616598:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.35 % (1554478)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=2372538862:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.35 % (1554479)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=704594979:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.35 % (1554481)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3318867452:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.35 % (1554482)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=648708439:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.35 % (1554477)Instruction limit reached!
% 0.20/0.35 % (1554477)------------------------------
% 0.20/0.35 % (1554477)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (1554477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (1554477)CaDiCaL version: 2.1.3
% 0.20/0.35 % (1554477)Termination reason: Instruction limit
% 0.20/0.35 % (1554477)Termination phase: Property scanning
% 0.20/0.35 % (1554477)Time elapsed: 0.002 s
% 0.20/0.35 % (1554477)Peak memory usage: 10 MB
% 0.20/0.35 % (1554477)Instructions burned: 4 (million)
% 0.20/0.35 % (1554476)Instruction limit reached!
% 0.20/0.35 % (1554476)------------------------------
% 0.20/0.35 % (1554476)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (1554476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (1554476)CaDiCaL version: 2.1.3
% 0.20/0.35 % (1554476)Termination reason: Instruction limit
% 0.20/0.35 % (1554476)Termination phase: Saturation
% 0.20/0.35 % (1554476)Time elapsed: 0.010 s
% 0.20/0.35 % (1554476)Peak memory usage: 12 MB
% 0.20/0.35 % (1554476)Instructions burned: 19 (million)
% 0.20/0.35 % (1554479)Instruction limit reached!
% 0.20/0.35 % (1554479)------------------------------
% 0.20/0.35 % (1554479)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (1554479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (1554479)CaDiCaL version: 2.1.3
% 0.20/0.35 % (1554479)Termination reason: Instruction limit
% 0.20/0.35 % (1554479)Termination phase: Saturation
% 0.20/0.35 % (1554479)Time elapsed: 0.014 s
% 0.20/0.35 % (1554479)Peak memory usage: 11 MB
% 0.20/0.35 % (1554479)Instructions burned: 25 (million)
% 0.20/0.35 % (1554475)Instruction limit reached!
% 0.20/0.35 % (1554475)------------------------------
% 0.20/0.35 % (1554475)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (1554475)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (1554475)CaDiCaL version: 2.1.3
% 0.20/0.35 % (1554475)Termination reason: Instruction limit
% 0.20/0.35 % (1554475)Termination phase: Saturation
% 0.20/0.35 % (1554475)Time elapsed: 0.024 s
% 0.20/0.35 % (1554475)Peak memory usage: 12 MB
% 0.20/0.35 % (1554475)Instructions burned: 88 (million)
% 0.20/0.35 % (1554500)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1932840500:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.35 % (1554500)Instruction limit reached!
% 0.20/0.35 % (1554500)------------------------------
% 0.20/0.35 % (1554500)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (1554500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (1554500)CaDiCaL version: 2.1.3
% 0.20/0.36 % (1554500)Termination reason: Instruction limit
% 0.20/0.36 % (1554500)Termination phase: Property scanning
% 0.20/0.36 % (1554500)Time elapsed: 0.002 s
% 0.20/0.36 % (1554500)Peak memory usage: 10 MB
% 0.20/0.36 % (1554500)Instructions burned: 4 (million)
% 0.20/0.36 % (1554506)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=227770134:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.36 % (1554508)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.36 % (1554506)Instruction limit reached!
% 0.20/0.36 % (1554506)------------------------------
% 0.20/0.36 % (1554506)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (1554506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (1554506)CaDiCaL version: 2.1.3
% 0.20/0.36 % (1554506)Termination reason: Instruction limit
% 0.20/0.36 % (1554506)Termination phase: Function definition elimination
% 0.20/0.36 % (1554506)Time elapsed: 0.003 s
% 0.20/0.36 % (1554506)Peak memory usage: 10 MB
% 0.20/0.36 % (1554506)Instructions burned: 6 (million)
% 0.20/0.36 % (1554508)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1880137683:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.36 % (1554509)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4157442424:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/0.36 % (1554481)Instruction limit reached!
% 0.20/0.36 % (1554481)------------------------------
% 0.20/0.36 % (1554481)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (1554481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (1554481)CaDiCaL version: 2.1.3
% 0.20/0.36 % (1554481)Termination reason: Instruction limit
% 0.20/0.36 % (1554481)Termination phase: Saturation
% 0.20/0.36 % (1554481)Time elapsed: 0.035 s
% 0.20/0.36 % (1554481)Peak memory usage: 12 MB
% 0.20/0.36 % (1554481)Instructions burned: 75 (million)
% 0.20/0.36 % (1554508)Instruction limit reached!
% 0.20/0.36 % (1554508)------------------------------
% 0.20/0.36 % (1554508)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (1554508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (1554508)CaDiCaL version: 2.1.3
% 0.20/0.36 % (1554508)Termination reason: Instruction limit
% 0.20/0.36 % (1554508)Termination phase: Saturation
% 0.20/0.36 % (1554508)Time elapsed: 0.004 s
% 0.20/0.36 % (1554508)Peak memory usage: 11 MB
% 0.20/0.36 % (1554508)Instructions burned: 8 (million)
% 0.20/0.36 % (1554514)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.36 % (1554514)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.36 % (1554509)Instruction limit reached!
% 0.20/0.36 % (1554509)------------------------------
% 0.20/0.36 % (1554509)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (1554509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (1554509)CaDiCaL version: 2.1.3
% 0.20/0.36 % (1554509)Termination reason: Instruction limit
% 0.20/0.36 % (1554509)Termination phase: Saturation
% 0.20/0.36 % (1554509)Time elapsed: 0.006 s
% 0.20/0.36 % (1554509)Peak memory usage: 12 MB
% 0.20/0.36 % (1554509)Instructions burned: 13 (million)
% 0.20/0.36 % (1554514)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3826382947:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.20/0.36 % (1554523)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.20/0.36 % (1554523)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=906299303:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.36 % (1554523)Instruction limit reached!
% 0.20/0.36 % (1554523)------------------------------
% 0.20/0.36 % (1554523)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (1554523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (1554523)CaDiCaL version: 2.1.3
% 0.20/0.36 % (1554523)Termination reason: Instruction limit
% 0.20/0.36 % (1554523)Termination phase: Property scanning
% 0.20/0.36 % (1554523)Time elapsed: 0.001 s
% 0.20/0.36 % (1554523)Peak memory usage: 10 MB
% 0.20/0.36 % (1554523)Instructions burned: 5 (million)
% 0.20/0.36 % (1554519)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=1945095824:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.20/0.36 % (1554522)lrs+10_1_si=on:cs=on:random_seed=3651243959:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.20/0.36 % (1554514)Instruction limit reached!
% 0.20/0.36 % (1554514)------------------------------
% 0.20/0.36 % (1554514)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (1554514)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (1554514)CaDiCaL version: 2.1.3
% 0.20/0.36 % (1554514)Termination reason: Instruction limit
% 0.20/0.36 % (1554514)Termination phase: Saturation
% 0.20/0.36 % (1554514)Time elapsed: 0.013 s
% 0.20/0.36 % (1554514)Peak memory usage: 11 MB
% 0.20/0.36 % (1554514)Instructions burned: 28 (million)
% 0.20/0.36 % (1554522)Instruction limit reached!
% 0.20/0.36 % (1554522)------------------------------
% 0.20/0.36 % (1554522)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (1554522)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (1554522)CaDiCaL version: 2.1.3
% 0.20/0.36 % (1554522)Termination reason: Instruction limit
% 0.20/0.36 % (1554522)Termination phase: Saturation
% 0.20/0.36 % (1554522)Time elapsed: 0.004 s
% 0.20/0.36 % (1554522)Peak memory usage: 11 MB
% 0.20/0.36 % (1554522)Instructions burned: 8 (million)
% 0.20/0.36 % (1554526)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1417757509:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.20/0.36 % (1554533)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2133995783:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.20/0.36 % (1554533)Refutation not found, incomplete strategy
% 0.20/0.36 % (1554533)------------------------------
% 0.20/0.36 % (1554533)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (1554533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (1554533)CaDiCaL version: 2.1.3
% 0.20/0.36 % (1554533)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.36 % (1554533)Time elapsed: 0.002 s
% 0.20/0.36 % (1554533)Peak memory usage: 12 MB
% 0.20/0.36 % (1554533)Instructions burned: 8 (million)
% 0.20/0.36 % (1554533)------------------------------
% 0.20/0.36 % (1554533)------------------------------
% 0.20/0.36 % (1554526)Refutation not found, incomplete strategy
% 0.20/0.36 % (1554526)------------------------------
% 0.20/0.36 % (1554526)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (1554526)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (1554526)CaDiCaL version: 2.1.3
% 0.20/0.36 % (1554526)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.36 % (1554526)Time elapsed: 0.004 s
% 0.20/0.36 % (1554526)Peak memory usage: 12 MB
% 0.20/0.36 % (1554526)Instructions burned: 6 (million)
% 0.20/0.36 % (1554526)------------------------------
% 0.20/0.36 % (1554526)------------------------------
% 0.20/0.36 % (1554546)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=651280071:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/327Mi)
% 0.20/0.36 % (1554538)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2006966304:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 0.20/0.36 % (1554482)Instruction limit reached!
% 0.20/0.36 % (1554482)------------------------------
% 0.20/0.36 % (1554482)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.36 % (1554482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.36 % (1554482)CaDiCaL version: 2.1.3
% 0.20/0.36 % (1554482)Termination reason: Instruction limit
% 0.20/0.36 % (1554482)Termination phase: Saturation
% 0.20/0.36 % (1554482)Time elapsed: 0.078 s
% 0.20/0.36 % (1554482)Peak memory usage: 13 MB
% 0.20/0.36 % (1554482)Instructions burned: 158 (million)
% 0.20/0.36 % (1554519) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1554459-1554519"...
% 0.20/0.36 % (1554541)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1649504552:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 0.20/0.36 % (1554519)...printing done.
% 0.20/0.36 % (1554519)Refutation found. Thanks to Tanya!
% 0.20/0.36 % SZS status Theorem for theBenchmark
% 0.20/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.36 % (1554519)------------------------------
% 0.96/0.36 % (1554519)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.96/0.36 % (1554519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.96/0.36 % (1554519)CaDiCaL version: 2.1.3
% 0.96/0.36 % (1554519)Termination reason: Refutation
% 0.96/0.36 % (1554519)Time elapsed: 0.035 s
% 0.96/0.36 % (1554519)Peak memory usage: 13 MB
% 0.96/0.36 % (1554519)Instructions burned: 68 (million)
% 0.96/0.36 % (1554459)Success in time 0.13 s
% 0.96/0.36 % Vampire exiting
%------------------------------------------------------------------------------