%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO468^6 : 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 : n012.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 08:47:59 AM UTC 2026
% Result : Theorem 0.08s 0.18s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 10
% Syntax : Number of formulae : 92 ( 74 unt; 0 typ; 0 def)
% Number of atoms : 548 ( 98 equ; 0 cnn)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 791 ( 70 ~; 77 |; 13 &; 547 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 68 ( 68 >; 0 *; 0 +; 0 <<)
% Number of symbols : 57 ( 53 usr; 6 con; 0-4 aty)
% ( 62 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 198 ( 152 ^; 46 !; 0 ?; 198 :)
% 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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_40,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_45,type,
vNOT: $o > $o ).
thf(func_def_46,type,
vOR: $o > $o > $o ).
thf(func_def_47,type,
vAND: $o > $o > $o ).
thf(func_def_48,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_50,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $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,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
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(f19,axiom,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
thf(f21,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( 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] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) )
= mbox_s5 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^6.ax',mbox_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 @ ( mor @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ p ) @ q ) ) @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ q ) @ p ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mor @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ p ) @ q ) ) @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ q ) @ p ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f39,plain,
( msymmetric
= ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f19]) ).
thf(f40,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f46,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f47,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f50,plain,
msymmetric @ rel_s5,
inference(rectify,[],[f36]) ).
thf(f51,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f50]) ).
thf(f52,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i,X3: $i] :
( ( ( X0 @ X1 @ X2 )
& ( X0 @ X2 @ X3 ) )
=> ( X0 @ X1 @ X3 ) ) )
= mtransitive ),
inference(rectify,[],[f21]) ).
thf(f53,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f52]) ).
thf(f65,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) )
= mbox_s5 ),
inference(rectify,[],[f32]) ).
thf(f66,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f65]) ).
thf(f69,plain,
mtransitive @ rel_s5,
inference(rectify,[],[f35]) ).
thf(f70,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f69]) ).
thf(f71,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f72,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f71]) ).
thf(f82,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f92,plain,
~ ( mvalid @ ( mor @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ p ) @ q ) ) @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ q ) @ p ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f93,plain,
( ( mvalid @ ( mor @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ p ) @ q ) ) @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ q ) @ p ) ) ) )
!= $true ),
inference(fool_elimination,[],[f92]) ).
thf(f96,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f97,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f96]) ).
thf(f101,plain,
( ( mvalid @ ( mor @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ p ) @ q ) ) @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ q ) @ p ) ) ) )
!= $true ),
inference(flattening,[],[f93]) ).
thf(f103,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f97]) ).
thf(f104,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f111,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f112,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f120,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f51]) ).
thf(f121,plain,
( mtransitive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f53]) ).
thf(f130,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f70]) ).
thf(f133,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f134,plain,
( ( mvalid @ ( mor @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ p ) @ q ) ) @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ q ) @ p ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f101]) ).
thf(f138,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f72]) ).
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,[],[f111,f112,f138]) ).
thf(f152,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
=> ( Y0 @ Y1 @ Y2 ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f120,f104]) ).
thf(f153,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y1 )
& ( Y0 @ Y3 @ Y2 ) )
=> ( Y0 @ Y3 @ Y1 ) ) ) ) )
@ rel_s5 ) ),
inference(definition_unfolding,[],[f130,f121]) ).
thf(f154,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p )
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q )
@ p ) ) ) ) ),
inference(definition_unfolding,[],[f134,f103,f112,f133,f142,f133,f133,f142,f133]) ).
thf(f158,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) )
| ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) )
| ( p @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f154]) ).
thf(f159,plain,
( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) )
| ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) )
| ( p @ Y1 ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ( p @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ( p @ Y0 ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( q @ Y0 ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f163,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( q @ Y0 ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( ~ ( rel_s5 @ sK0 @ sK1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( q @ sK1 ) )
= $false ),
inference(beta-eta_normalization,[],[f163]) ).
thf(f165,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( q @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 ) ) ),
inference(or_proxy_clausification,[],[f164]) ).
thf(f167,plain,
( ( rel_s5 @ sK0 @ sK1 )
= $true ),
inference(not_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( $false
= ( q @ sK1 ) ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f175,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ( p @ Y0 ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f161]) ).
thf(f176,plain,
( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( q @ Y0 ) ) )
| ( p @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f175]) ).
thf(f177,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( q @ Y0 ) ) )
| ( p @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f178,plain,
( $false
= ( ~ ( rel_s5 @ sK0 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f176]) ).
thf(f179,plain,
( $true
= ( rel_s5 @ sK0 @ sK2 ) ),
inference(not_proxy_clausification,[],[f178]) ).
thf(f181,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f182,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( q @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f181]) ).
thf(f183,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK2 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f182]) ).
thf(f184,plain,
! [X1: $i] :
( $true
= ( ~ ( rel_s5 @ sK2 @ X1 )
| ( q @ X1 ) ) ),
inference(beta-eta_normalization,[],[f183]) ).
thf(f185,plain,
! [X1: $i] :
( ( ( ~ ( rel_s5 @ sK2 @ X1 ) )
= $true )
| ( $true
= ( q @ X1 ) ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X1: $i] :
( ( $false
= ( rel_s5 @ sK2 @ X1 ) )
| ( $true
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f185]) ).
thf(f187,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y1 @ Y0 )
& ( rel_s5 @ Y2 @ Y1 ) )
=> ( rel_s5 @ Y2 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f188,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y1 @ Y0 )
& ( rel_s5 @ Y2 @ Y1 ) )
=> ( rel_s5 @ Y2 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y0 @ X1 )
& ( rel_s5 @ Y1 @ Y0 ) )
=> ( rel_s5 @ Y1 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f188]) ).
thf(f190,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y0 @ X1 )
& ( rel_s5 @ Y1 @ Y0 ) )
=> ( rel_s5 @ Y1 @ X1 ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f189]) ).
thf(f191,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s5 @ X2 @ X1 )
& ( rel_s5 @ Y0 @ X2 ) )
=> ( rel_s5 @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f190]) ).
thf(f192,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s5 @ X2 @ X1 )
& ( rel_s5 @ Y0 @ X2 ) )
=> ( rel_s5 @ Y0 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f191]) ).
thf(f193,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s5 @ X2 @ X1 )
& ( rel_s5 @ X3 @ X2 ) )
=> ( rel_s5 @ X3 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f192]) ).
thf(f194,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( rel_s5 @ X3 @ X1 ) )
| ( $false
= ( ( rel_s5 @ X2 @ X1 )
& ( rel_s5 @ X3 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s5 @ X2 @ X1 )
= $false )
| ( $false
= ( rel_s5 @ X3 @ X2 ) )
| ( $true
= ( rel_s5 @ X3 @ X1 ) ) ),
inference(and_proxy_clausification,[],[f194]) ).
thf(f196,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f197,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y1 @ Y0 )
=> ( rel_s5 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f197]) ).
thf(f199,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( rel_s5 @ Y0 @ X1 )
=> ( rel_s5 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel_s5 @ X2 @ X1 )
=> ( rel_s5 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f199]) ).
thf(f201,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ X2 @ X1 )
= $false )
| ( ( rel_s5 @ X1 @ X2 )
= $true ) ),
inference(imp_proxy_clausification,[],[f200]) ).
thf(f248,plain,
! [X0: $i] :
( ( ( rel_s5 @ X0 @ sK0 )
= $false )
| ( $true = $false )
| ( $true
= ( rel_s5 @ X0 @ sK1 ) ) ),
inference(constrained_superposition,[],[f195,f167]) ).
thf(f282,plain,
! [X0: $i] :
( ( $true
= ( rel_s5 @ X0 @ sK1 ) )
| ( ( rel_s5 @ X0 @ sK0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f248]) ).
thf(f296,plain,
( ( $true
= ( q @ sK1 ) )
| ( $true = $false )
| ( $false
= ( rel_s5 @ sK2 @ sK0 ) ) ),
inference(constrained_superposition,[],[f282,f186]) ).
thf(f309,plain,
( ( $false
= ( rel_s5 @ sK2 @ sK0 ) )
| ( $true
= ( q @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f296]) ).
thf(f319,plain,
( ( $false
= ( rel_s5 @ sK2 @ sK0 ) )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f309,f168]) ).
thf(f320,plain,
( $false
= ( rel_s5 @ sK2 @ sK0 ) ),
inference(trivial_inequality_removal,[],[f319]) ).
thf(f324,plain,
( ( $false
= ( rel_s5 @ sK0 @ sK2 ) )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f320,f201]) ).
thf(f327,plain,
( $false
= ( rel_s5 @ sK0 @ sK2 ) ),
inference(trivial_inequality_removal,[],[f324]) ).
thf(f331,plain,
$true = $false,
inference(forward_demodulation,[],[f327,f179]) ).
thf(f332,plain,
$false,
inference(trivial_inequality_removal,[],[f331]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYO468^6 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.10 % Computer : n012.cluster.edu
% 0.00/0.10 % Model : x86_64 x86_64
% 0.00/0.10 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.10 % Memory : 8046.5625MB
% 0.00/0.10 % OS : Linux 6.8.0-71-generic
% 0.00/0.10 % CPULimit : 300
% 0.00/0.10 % WCLimit : 300
% 0.00/0.10 % DateTime : Tue Sep 29 17:01:48 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 0.08/0.13 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
% 0.08/0.18 % (393462)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.08/0.18 % (393473)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.08/0.18 % (393473)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
% 0.08/0.18 % (393469)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1905804261:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.08/0.18 % (393468)lrs+10_16_si=on:nwc=1.5:random_seed=4202171858:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.08/0.18 % (393473)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=654241684:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.08/0.18 % (393467)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4283600819:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.08/0.18 % (393471)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4107995150:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.08/0.18 % (393472)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3896331066:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.08/0.18 % (393470)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=1809012391: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)
% 0.08/0.18 % (393469)Instruction limit reached!
% 0.08/0.18 % (393469)------------------------------
% 0.08/0.18 % (393469)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.18 % (393469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.18 % (393469)CaDiCaL version: 2.1.3
% 0.08/0.18 % (393469)Termination reason: Instruction limit
% 0.08/0.18 % (393469)Termination phase: Clausification
% 0.08/0.18 % (393469)Time elapsed: 0.002 s
% 0.08/0.18 % (393469)Peak memory usage: 10 MB
% 0.08/0.18 % (393469)Instructions burned: 4 (million)
% 0.08/0.18 % (393467) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-393462-393467"...
% 0.08/0.18 % (393468) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-393462-393468"...
% 0.08/0.18 % (393473) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-393462-393473"...
% 0.08/0.18 % (393467)...printing done.
% 0.08/0.18 % (393468)...printing done.
% 0.08/0.18 % (393471)Instruction limit reached!
% 0.08/0.18 % (393471)------------------------------
% 0.08/0.18 % (393471)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.18 % (393471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.18 % (393471)CaDiCaL version: 2.1.3
% 0.08/0.18 % (393471)Termination reason: Instruction limit
% 0.08/0.18 % (393471)Termination phase: Saturation
% 0.08/0.18 % (393471)Time elapsed: 0.008 s
% 0.08/0.18 % (393471)Peak memory usage: 11 MB
% 0.08/0.18 % (393471)Instructions burned: 26 (million)
% 0.08/0.18 % (393467)Refutation found. Thanks to Tanya!
% 0.08/0.18 % SZS status Theorem for theBenchmark
% 0.08/0.18 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.18 % (393467)------------------------------
% 0.08/0.18 % (393467)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.18 % (393467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.18 % (393467)CaDiCaL version: 2.1.3
% 0.08/0.18 % (393467)Termination reason: Refutation
% 0.08/0.18 % (393467)Time elapsed: 0.007 s
% 0.08/0.18 % (393467)Peak memory usage: 12 MB
% 0.08/0.18 % (393467)Instructions burned: 24 (million)
% 0.08/0.18 % (393462)Success in time 0.041 s
% 0.08/0.18 % Vampire exiting
%------------------------------------------------------------------------------