%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO436^1 : 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 : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:47:41 AM UTC 2026
% Result : Theorem 0.20s 0.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 10
% Syntax : Number of formulae : 104 ( 67 unt; 0 typ; 2 def)
% Number of atoms : 702 ( 125 equ; 0 cnn)
% Maximal formula atoms : 13 ( 6 avg)
% Number of connectives : 898 ( 96 ~; 129 |; 13 &; 584 @)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 56 ( 56 >; 0 *; 0 +; 0 <<)
% Number of symbols : 60 ( 56 usr; 9 con; 0-4 aty)
% ( 62 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 195 ( 0 sgn 49 !; 0 ?; 195 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
rel_s4: $i > $i > $o ).
thf(func_def_33,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
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,
vOR: $o > $o > $o ).
thf(func_def_45,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_46,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_49,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_50,type,
vNOT: $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/sandbox2/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',mor) ).
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(f21,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i,X3: $i] :
( ( ( X0 @ X2 @ X3 )
& ( X0 @ X1 @ X2 ) )
=> ( X0 @ X1 @ X3 ) ) )
= mtransitive ),
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_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f35,axiom,
mtransitive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',a2) ).
thf(f36,conjecture,
mvalid @ ( mimplies @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mbox_s4 @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f37,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mbox_s4 @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f41,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f42,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f46,plain,
mtransitive @ rel_s4,
inference(rectify,[],[f35]) ).
thf(f47,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f46]) ).
thf(f49,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f50,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f49]) ).
thf(f71,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X3 )
& ( X0 @ X2 @ X1 ) )
=> ( X0 @ X2 @ X3 ) ) )
= mtransitive ),
inference(rectify,[],[f21]) ).
thf(f72,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f73,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f81,plain,
~ ( mvalid @ ( mimplies @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mbox_s4 @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f82,plain,
( ( mvalid @ ( mimplies @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mbox_s4 @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f81]) ).
thf(f83,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f84,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f83]) ).
thf(f96,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s4 ),
inference(rectify,[],[f32]) ).
thf(f97,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f96]) ).
thf(f98,plain,
( ( mvalid @ ( mimplies @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mbox_s4 @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ) )
!= $true ),
inference(flattening,[],[f82]) ).
thf(f100,plain,
( ( mtransitive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f47]) ).
thf(f102,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f108,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f84]) ).
thf(f113,plain,
( ( mvalid @ ( mimplies @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) @ ( mbox_s4 @ ( mor @ ( mbox_s4 @ p ) @ ( mbox_s4 @ q ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f120,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f72]) ).
thf(f121,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f97]) ).
thf(f129,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f73]) ).
thf(f131,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f50]) ).
thf(f138,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,[],[f129,f131,f108]) ).
thf(f147,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f100,f120]) ).
thf(f148,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [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 )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ q ) ) ) ) )
!= $true ),
inference(definition_unfolding,[],[f113,f102,f138,f131,f121,f121,f121,f131,f121,f121]) ).
thf(f150,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y1 @ Y2 )
& ( rel_s4 @ Y2 @ Y0 ) )
=> ( rel_s4 @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f147]) ).
thf(f151,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s4 @ Y1 @ Y2 )
& ( rel_s4 @ Y2 @ Y0 ) )
=> ( rel_s4 @ Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y0 @ Y1 )
& ( rel_s4 @ Y1 @ X1 ) )
=> ( rel_s4 @ Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s4 @ Y0 @ Y1 )
& ( rel_s4 @ Y1 @ X1 ) )
=> ( rel_s4 @ Y0 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s4 @ X2 @ Y0 )
& ( rel_s4 @ Y0 @ X1 ) )
=> ( rel_s4 @ X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f155,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s4 @ X2 @ Y0 )
& ( rel_s4 @ Y0 @ X1 ) )
=> ( rel_s4 @ X2 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( rel_s4 @ X2 @ X3 )
& ( rel_s4 @ X3 @ X1 ) )
=> ( rel_s4 @ X2 @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f157,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( rel_s4 @ X2 @ X3 )
& ( rel_s4 @ X3 @ X1 ) )
= $false )
| ( ( rel_s4 @ X2 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( rel_s4 @ X3 @ X1 ) )
| ( ( rel_s4 @ X2 @ X1 )
= $true )
| ( ( rel_s4 @ X2 @ X3 )
= $false ) ),
inference(and_proxy_clausification,[],[f157]) ).
thf(f162,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( q @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f148]) ).
thf(f163,plain,
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( q @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) )
= $false ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
( ( ~ ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f167,plain,
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( q @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ~ ( rel_s4 @ sK0 @ sK1 ) )
= $false ),
inference(beta-eta_normalization,[],[f167]) ).
thf(f169,plain,
( $false
= ( ~ ( rel_s4 @ sK0 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f168]) ).
thf(f171,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
= $false ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
= $false ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f173,plain,
( $false
= ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( ( q @ sK2 )
| ~ ( rel_s4 @ sK1 @ sK2 ) )
= $false ),
inference(beta-eta_normalization,[],[f173]) ).
thf(f175,plain,
( ( ~ ( rel_s4 @ sK1 @ sK2 ) )
= $false ),
inference(or_proxy_clausification,[],[f174]) ).
thf(f176,plain,
( ( q @ sK2 )
= $false ),
inference(or_proxy_clausification,[],[f174]) ).
thf(f177,plain,
( $true
= ( rel_s4 @ sK1 @ sK2 ) ),
inference(not_proxy_clausification,[],[f175]) ).
thf(f178,plain,
( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ sK3 )
= $false ),
inference(sigma_proxy_clausification,[],[f171]) ).
thf(f179,plain,
( ( ( p @ sK3 )
| ~ ( rel_s4 @ sK1 @ sK3 ) )
= $false ),
inference(beta-eta_normalization,[],[f178]) ).
thf(f180,plain,
( ( ~ ( rel_s4 @ sK1 @ sK3 ) )
= $false ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f181,plain,
( ( p @ sK3 )
= $false ),
inference(or_proxy_clausification,[],[f179]) ).
thf(f182,plain,
( ( rel_s4 @ sK1 @ sK3 )
= $true ),
inference(not_proxy_clausification,[],[f180]) ).
thf(f183,plain,
( $true
= ( rel_s4 @ sK0 @ sK1 ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f184,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) ) )
= $true ),
inference(not_proxy_clausification,[],[f165]) ).
thf(f185,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ X1 )
= $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) ) )
= $true ) ),
inference(pi_proxy_clausification,[],[f185]) ).
thf(f187,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( q @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ X1 )
= $true )
| ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK0 @ Y0 ) )
@ X2 )
= $true ) ),
inference(pi_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( p @ X2 )
| ~ ( rel_s4 @ sK0 @ X2 ) ) )
| ( ( ( q @ X1 )
| ~ ( rel_s4 @ sK0 @ X1 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f187]) ).
thf(f189,plain,
! [X2: $i,X1: $i] :
( ( ( ( q @ X1 )
| ~ ( rel_s4 @ sK0 @ X1 ) )
= $true )
| ( ( p @ X2 )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK0 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f188]) ).
thf(f190,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK0 @ X1 ) ) )
| ( ( p @ X2 )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK0 @ X2 ) ) )
| ( ( q @ X1 )
= $true ) ),
inference(or_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X2: $i,X1: $i] :
( ( ( q @ X1 )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK0 @ X2 ) ) )
| ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( ( p @ X2 )
= $true ) ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f192,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( ( q @ X1 )
= $true )
| ( ( p @ X2 )
= $true )
| ( ( rel_s4 @ sK0 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f191]) ).
thf(f194,definition,
( spl4_1
<=> ! [X2: $i] :
( ( ( p @ X2 )
= $true )
| ( ( rel_s4 @ sK0 @ X2 )
= $false ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f195,plain,
( ! [X2: $i] :
( ( ( rel_s4 @ sK0 @ X2 )
= $false )
| ( ( p @ X2 )
= $true ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f194]) ).
thf(f197,definition,
( spl4_2
<=> ! [X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( ( q @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f198,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s4 @ sK0 @ X1 ) )
| ( ( q @ X1 )
= $true ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f197]) ).
thf(f199,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f192,f197,f194]) ).
thf(f219,plain,
! [X0: $i] :
( ( $true
= ( rel_s4 @ X0 @ sK2 ) )
| ( ( rel_s4 @ X0 @ sK1 )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f177,f158]) ).
thf(f220,plain,
! [X0: $i] :
( ( ( rel_s4 @ X0 @ sK3 )
= $true )
| ( $true = $false )
| ( ( rel_s4 @ X0 @ sK1 )
= $false ) ),
inference(constrained_superposition,[],[f182,f158]) ).
thf(f227,plain,
! [X0: $i] :
( ( $true
= ( rel_s4 @ X0 @ sK2 ) )
| ( ( rel_s4 @ X0 @ sK1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f219]) ).
thf(f233,plain,
! [X0: $i] :
( ( ( rel_s4 @ X0 @ sK3 )
= $true )
| ( ( rel_s4 @ X0 @ sK1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f220]) ).
thf(f253,plain,
( ( ( rel_s4 @ sK0 @ sK1 )
= $false )
| ( $true = $false )
| ( ( q @ sK2 )
= $true )
| ~ spl4_2 ),
inference(constrained_superposition,[],[f198,f227]) ).
thf(f257,plain,
( ( ( rel_s4 @ sK0 @ sK1 )
= $false )
| ( ( q @ sK2 )
= $true )
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f253]) ).
thf(f264,plain,
( ( $true = $false )
| ( ( q @ sK2 )
= $true )
| ~ spl4_2 ),
inference(forward_demodulation,[],[f257,f183]) ).
thf(f265,plain,
( ( ( q @ sK2 )
= $true )
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f264]) ).
thf(f269,plain,
( ( $true = $false )
| ~ spl4_2 ),
inference(forward_demodulation,[],[f265,f176]) ).
thf(f270,plain,
( $false
| ~ spl4_2 ),
inference(trivial_inequality_removal,[],[f269]) ).
thf(f271,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f270]) ).
thf(f301,plain,
( ( ( rel_s4 @ sK0 @ sK1 )
= $false )
| ( $true = $false )
| ( $true
= ( p @ sK3 ) )
| ~ spl4_1 ),
inference(constrained_superposition,[],[f195,f233]) ).
thf(f308,plain,
( ( ( rel_s4 @ sK0 @ sK1 )
= $false )
| ( $true
= ( p @ sK3 ) )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f301]) ).
thf(f312,plain,
( ( $true
= ( p @ sK3 ) )
| ( $true = $false )
| ~ spl4_1 ),
inference(forward_demodulation,[],[f308,f183]) ).
thf(f313,plain,
( ( $true
= ( p @ sK3 ) )
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f312]) ).
thf(f317,plain,
( ( $true = $false )
| ~ spl4_1 ),
inference(forward_demodulation,[],[f313,f181]) ).
thf(f318,plain,
( $false
| ~ spl4_1 ),
inference(trivial_inequality_removal,[],[f317]) ).
thf(f319,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f318]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f199]) ).
cnf(s3,plain,
~ spl4_2,
inference(sat_conversion,[],[f271]) ).
cnf(s5,plain,
~ spl4_1,
inference(sat_conversion,[],[f319]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s3,s5]) ).
thf(f320,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO436^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.18 % Computer : n015.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Tue Sep 29 16:55:03 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.06/0.22 Running higher-order theorem proving
% 0.06/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.30 % (3792874)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.30 % (3792888)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3916883744:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.30 % (3792890)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.30 % (3792890)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
% 0.20/0.30 % (3792886)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2090910981:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.30 % (3792884)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2886229404:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.30 % (3792885)lrs+10_16_si=on:nwc=1.5:random_seed=310033353:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.30 % (3792888)Instruction limit reached!
% 0.20/0.30 % (3792888)------------------------------
% 0.20/0.30 % (3792888)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3792888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3792888)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3792888)Termination reason: Instruction limit
% 0.20/0.30 % (3792888)Termination phase: Saturation
% 0.20/0.30 % (3792888)Time elapsed: 0.007 s
% 0.20/0.30 % (3792888)Peak memory usage: 11 MB
% 0.20/0.30 % (3792888)Instructions burned: 25 (million)
% 0.20/0.30 % (3792887)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=2158094515: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)
% 0.20/0.30 % (3792890)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=1740733858:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.30 % (3792889)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=915907686:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.30 % (3792886)Instruction limit reached!
% 0.20/0.30 % (3792886)------------------------------
% 0.20/0.30 % (3792886)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3792886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3792886)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3792886)Termination reason: Instruction limit
% 0.20/0.30 % (3792886)Termination phase: Preprocessing 2
% 0.20/0.30 % (3792886)Time elapsed: 0.002 s
% 0.20/0.30 % (3792886)Peak memory usage: 10 MB
% 0.20/0.30 % (3792886)Instructions burned: 4 (million)
% 0.20/0.30 % (3792884) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3792874-3792884"...
% 0.20/0.30 % (3792885)Instruction limit reached!
% 0.20/0.30 % (3792885)------------------------------
% 0.20/0.30 % (3792885)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3792885)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3792885)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3792885)Termination reason: Instruction limit
% 0.20/0.30 % (3792885)Termination phase: Saturation
% 0.20/0.30 % (3792885)Time elapsed: 0.009 s
% 0.20/0.30 % (3792885)Peak memory usage: 12 MB
% 0.20/0.30 % (3792885)Instructions burned: 18 (million)
% 0.20/0.30 % (3792890) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3792874-3792890"...
% 0.20/0.30 % (3792901)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2684244847:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.30 % (3792901)Instruction limit reached!
% 0.20/0.30 % (3792901)------------------------------
% 0.20/0.30 % (3792901)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (3792901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (3792901)CaDiCaL version: 2.1.3
% 0.20/0.30 % (3792901)Termination reason: Instruction limit
% 0.20/0.30 % (3792901)Termination phase: Property scanning
% 0.20/0.30 % (3792901)Time elapsed: 0.001 s
% 0.20/0.30 % (3792901)Peak memory usage: 10 MB
% 0.20/0.30 % (3792901)Instructions burned: 4 (million)
% 0.20/0.30 % (3792884)...printing done.
% 0.20/0.30 % (3792884)Refutation found. Thanks to Tanya!
% 0.20/0.30 % SZS status Theorem for theBenchmark
% 0.20/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.31 % (3792884)------------------------------
% 0.20/0.31 % (3792884)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (3792884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (3792884)CaDiCaL version: 2.1.3
% 0.20/0.31 % (3792884)Termination reason: Refutation
% 0.20/0.31 % (3792884)Time elapsed: 0.012 s
% 0.20/0.31 % (3792884)Peak memory usage: 13 MB
% 0.20/0.31 % (3792884)Instructions burned: 22 (million)
% 0.20/0.31 % (3792874)Success in time 0.055 s
% 0.20/0.31 % Vampire exiting
%------------------------------------------------------------------------------