%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO448^1 : 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 : n009.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 0.22s 0.32s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 10
% Syntax : Number of formulae : 101 ( 80 unt; 0 typ; 0 def)
% Number of atoms : 653 ( 111 equ; 0 cnn)
% Maximal formula atoms : 14 ( 6 avg)
% Number of connectives : 959 ( 90 ~; 100 |; 13 &; 655 @)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 70 ( 70 >; 0 *; 0 +; 0 <<)
% Number of symbols : 58 ( 54 usr; 7 con; 0-4 aty)
% ( 79 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 222 ( 174 ^; 48 !; 0 ?; 222 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
rel_s5: $i > $i > $o ).
thf(func_def_33,type,
mbox_s5: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_s5: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
q: $i > $o ).
thf(func_def_37,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_38,type,
vIMP: $o > $o > $o ).
thf(func_def_39,type,
vAND: $o > $o > $o ).
thf(func_def_40,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_44,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_45,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_48,type,
vOR: $o > $o > $o ).
thf(func_def_49,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $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/sandbox/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/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
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(f19,axiom,
( ( ^ [X0: $i > $i > $o] :
! [X2: $i,X1: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ X2 @ X1 ) ) )
= msymmetric ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',msymmetric) ).
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/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,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) )
= mbox_s5 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^6.ax',mbox_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 @ ( mor @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ q ) @ ( mbox_s5 @ p ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f38,negated_conjecture,
~ ( mvalid @ ( mor @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ q ) @ ( mbox_s5 @ p ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
thf(f41,plain,
( ( ^ [X0: $i > $i > $o] :
! [X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
=> ( X0 @ X1 @ X2 ) ) )
= msymmetric ),
inference(rectify,[],[f19]) ).
thf(f42,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f41]) ).
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(f48,plain,
~ ( mvalid @ ( mor @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ q ) @ ( mbox_s5 @ p ) ) ) ) ),
inference(rectify,[],[f38]) ).
thf(f49,plain,
( ( mvalid @ ( mor @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ q ) @ ( mbox_s5 @ p ) ) ) ) )
!= $true ),
inference(fool_elimination,[],[f48]) ).
thf(f59,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f60,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f59]) ).
thf(f65,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f66,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f67,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f66]) ).
thf(f77,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s5 @ X1 @ X2 ) ) )
= mbox_s5 ),
inference(rectify,[],[f32]) ).
thf(f78,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f77]) ).
thf(f79,plain,
mtransitive @ rel_s5,
inference(rectify,[],[f35]) ).
thf(f80,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f79]) ).
thf(f81,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(f82,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,[],[f81]) ).
thf(f83,plain,
msymmetric @ rel_s5,
inference(rectify,[],[f36]) ).
thf(f84,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(fool_elimination,[],[f83]) ).
thf(f101,plain,
( ( mvalid @ ( mor @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ q ) @ ( mbox_s5 @ p ) ) ) ) )
!= $true ),
inference(flattening,[],[f49]) ).
thf(f107,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f111,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f47]) ).
thf(f115,plain,
( msymmetric
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f118,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,[],[f82]) ).
thf(f120,plain,
( ( msymmetric @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f84]) ).
thf(f121,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f65]) ).
thf(f123,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f125,plain,
( mbox_s5
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f78]) ).
thf(f131,plain,
( ( mtransitive @ rel_s5 )
= $true ),
inference(cnf_transformation,[],[f80]) ).
thf(f135,plain,
( ( mvalid @ ( mor @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ p ) @ ( mbox_s5 @ q ) ) ) @ ( mbox_s5 @ ( mimplies @ ( mbox_s5 @ q ) @ ( mbox_s5 @ p ) ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f101]) ).
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,[],[f121,f123,f107]) ).
thf(f151,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y1 @ Y2 )
=> ( Y0 @ Y2 @ Y1 ) ) ) )
@ rel_s5 )
= $true ),
inference(definition_unfolding,[],[f120,f115]) ).
thf(f152,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( ( Y0 @ Y2 @ Y3 )
& ( Y0 @ Y3 @ Y1 ) )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) )
@ rel_s5 )
= $true ),
inference(definition_unfolding,[],[f131,f118]) ).
thf(f153,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 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ 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 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p ) ) ) ) ) ),
inference(definition_unfolding,[],[f135,f111,f123,f125,f142,f125,f125,f125,f142,f125,f125]) ).
thf(f158,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y0 @ Y1 )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f159,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( rel_s5 @ Y0 @ Y1 )
=> ( rel_s5 @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( rel_s5 @ X1 @ Y0 )
=> ( rel_s5 @ Y0 @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f159]) ).
thf(f161,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( rel_s5 @ X1 @ Y0 )
=> ( rel_s5 @ Y0 @ X1 ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f160]) ).
thf(f162,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( rel_s5 @ X1 @ X2 )
=> ( rel_s5 @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f161]) ).
thf(f163,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s5 @ X1 @ X2 )
= $false )
| ( ( rel_s5 @ X2 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f153]) ).
thf(f165,plain,
( $false
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ~ ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( q @ Y2 ) ) )
| ( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s5 @ Y1 @ Y2 )
| ( p @ Y2 ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f169,plain,
( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( $false
= ( ~ ( rel_s5 @ sK0 @ sK1 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f169]) ).
thf(f171,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f172,plain,
( ( ~ ( rel_s5 @ sK0 @ sK1 ) )
= $false ),
inference(or_proxy_clausification,[],[f170]) ).
thf(f173,plain,
( $true
= ( rel_s5 @ sK0 @ sK1 ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) ) ) ),
inference(or_proxy_clausification,[],[f171]) ).
thf(f181,plain,
( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK1 @ Y0 )
| ( q @ Y0 ) )
@ sK2 )
= $false ),
inference(sigma_proxy_clausification,[],[f174]) ).
thf(f182,plain,
( $false
= ( ~ ( rel_s5 @ sK1 @ sK2 )
| ( q @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f181]) ).
thf(f183,plain,
( $false
= ( q @ sK2 ) ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f184,plain,
( ( ~ ( rel_s5 @ sK1 @ sK2 ) )
= $false ),
inference(or_proxy_clausification,[],[f182]) ).
thf(f185,plain,
( ( rel_s5 @ sK1 @ sK2 )
= $true ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f186,plain,
( ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK0 @ Y0 )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s5 @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) )
@ sK3 )
= $false ),
inference(sigma_proxy_clausification,[],[f167]) ).
thf(f187,plain,
( $false
= ( ~ ( rel_s5 @ sK0 @ sK3 )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f186]) ).
thf(f188,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( p @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f187]) ).
thf(f189,plain,
( ( ~ ( rel_s5 @ sK0 @ sK3 ) )
= $false ),
inference(or_proxy_clausification,[],[f187]) ).
thf(f190,plain,
( ( rel_s5 @ sK0 @ sK3 )
= $true ),
inference(not_proxy_clausification,[],[f189]) ).
thf(f192,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) ) ) )
= $false ),
inference(or_proxy_clausification,[],[f188]) ).
thf(f193,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) ) )
= $true ),
inference(not_proxy_clausification,[],[f192]) ).
thf(f194,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s5 @ sK3 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X1: $i] :
( $true
= ( ~ ( rel_s5 @ sK3 @ X1 )
| ( q @ X1 ) ) ),
inference(beta-eta_normalization,[],[f194]) ).
thf(f196,plain,
! [X1: $i] :
( ( ( q @ X1 )
= $true )
| ( ( ~ ( rel_s5 @ sK3 @ X1 ) )
= $true ) ),
inference(or_proxy_clausification,[],[f195]) ).
thf(f197,plain,
! [X1: $i] :
( ( $false
= ( rel_s5 @ sK3 @ X1 ) )
| ( ( q @ X1 )
= $true ) ),
inference(not_proxy_clausification,[],[f196]) ).
thf(f203,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y1 @ Y2 )
& ( rel_s5 @ Y2 @ Y0 ) )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f152]) ).
thf(f204,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( ( rel_s5 @ Y1 @ Y2 )
& ( rel_s5 @ Y2 @ Y0 ) )
=> ( rel_s5 @ Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y0 @ Y1 )
& ( rel_s5 @ Y1 @ X1 ) )
=> ( rel_s5 @ Y0 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f204]) ).
thf(f206,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ( rel_s5 @ Y0 @ Y1 )
& ( rel_s5 @ Y1 @ X1 ) )
=> ( rel_s5 @ Y0 @ X1 ) ) )
@ X2 )
= $true ),
inference(pi_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ( rel_s5 @ X2 @ Y0 )
& ( rel_s5 @ Y0 @ X1 ) )
=> ( rel_s5 @ X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f206]) ).
thf(f208,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ( rel_s5 @ X2 @ Y0 )
& ( rel_s5 @ Y0 @ X1 ) )
=> ( rel_s5 @ X2 @ X1 ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f207]) ).
thf(f209,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( ( rel_s5 @ X2 @ X3 )
& ( rel_s5 @ X3 @ X1 ) )
=> ( rel_s5 @ X2 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f208]) ).
thf(f210,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( ( rel_s5 @ X2 @ X3 )
& ( rel_s5 @ X3 @ X1 ) ) )
| ( ( rel_s5 @ X2 @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f209]) ).
thf(f211,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( rel_s5 @ X2 @ X3 )
= $false )
| ( ( rel_s5 @ X3 @ X1 )
= $false )
| ( ( rel_s5 @ X2 @ X1 )
= $true ) ),
inference(and_proxy_clausification,[],[f210]) ).
thf(f269,plain,
! [X0: $i] :
( ( ( rel_s5 @ X0 @ sK1 )
= $true )
| ( ( rel_s5 @ X0 @ sK0 )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f211,f173]) ).
thf(f271,plain,
! [X0: $i] :
( ( ( rel_s5 @ X0 @ sK2 )
= $true )
| ( ( rel_s5 @ X0 @ sK1 )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f211,f185]) ).
thf(f304,plain,
! [X0: $i] :
( ( ( rel_s5 @ X0 @ sK2 )
= $true )
| ( ( rel_s5 @ X0 @ sK1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f271]) ).
thf(f306,plain,
! [X0: $i] :
( ( ( rel_s5 @ X0 @ sK1 )
= $true )
| ( ( rel_s5 @ X0 @ sK0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f269]) ).
thf(f358,plain,
( ( $true = $false )
| ( ( rel_s5 @ sK3 @ sK1 )
= $false )
| ( $true
= ( q @ sK2 ) ) ),
inference(constrained_superposition,[],[f197,f304]) ).
thf(f365,plain,
( ( $true
= ( q @ sK2 ) )
| ( ( rel_s5 @ sK3 @ sK1 )
= $false ) ),
inference(trivial_inequality_removal,[],[f358]) ).
thf(f369,plain,
( ( ( rel_s5 @ sK3 @ sK1 )
= $false )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f365,f183]) ).
thf(f370,plain,
( ( rel_s5 @ sK3 @ sK1 )
= $false ),
inference(trivial_inequality_removal,[],[f369]) ).
thf(f394,plain,
( ( ( rel_s5 @ sK3 @ sK0 )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f370,f306]) ).
thf(f395,plain,
( ( rel_s5 @ sK3 @ sK0 )
= $false ),
inference(trivial_inequality_removal,[],[f394]) ).
thf(f412,plain,
( ( $true = $false )
| ( ( rel_s5 @ sK0 @ sK3 )
= $false ) ),
inference(constrained_superposition,[],[f163,f395]) ).
thf(f413,plain,
( ( rel_s5 @ sK0 @ sK3 )
= $false ),
inference(trivial_inequality_removal,[],[f412]) ).
thf(f417,plain,
$true = $false,
inference(forward_demodulation,[],[f413,f190]) ).
thf(f418,plain,
$false,
inference(trivial_inequality_removal,[],[f417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO448^1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n009.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 16:52:15 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.22/0.32 % (66156)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.32 % (66167)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.32 % (66167)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
% 0.22/0.32 % (66161)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3023332206:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.32 % (66165)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2458750201:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.32 % (66163)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3137467614:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.32 % (66162)lrs+10_16_si=on:nwc=1.5:random_seed=4151449216:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.32 % (66164)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=4150115216: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)
% 0.22/0.32 % (66166)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=552809092:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.32 % (66167)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=1077907718:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.32 % (66163)Instruction limit reached!
% 0.22/0.32 % (66163)------------------------------
% 0.22/0.32 % (66163)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (66163)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (66163)CaDiCaL version: 2.1.3
% 0.22/0.32 % (66163)Termination reason: Instruction limit
% 0.22/0.32 % (66163)Termination phase: Property scanning
% 0.22/0.32 % (66163)Time elapsed: 0.002 s
% 0.22/0.32 % (66163)Peak memory usage: 10 MB
% 0.22/0.32 % (66163)Instructions burned: 4 (million)
% 0.22/0.32 % (66162)Instruction limit reached!
% 0.22/0.32 % (66162)------------------------------
% 0.22/0.32 % (66162)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (66162)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (66162)CaDiCaL version: 2.1.3
% 0.22/0.32 % (66162)Termination reason: Instruction limit
% 0.22/0.32 % (66162)Termination phase: Saturation
% 0.22/0.32 % (66162)Time elapsed: 0.010 s
% 0.22/0.32 % (66162)Peak memory usage: 12 MB
% 0.22/0.32 % (66162)Instructions burned: 19 (million)
% 0.22/0.32 % (66161) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-66156-66161"...
% 0.22/0.32 % (66165)Instruction limit reached!
% 0.22/0.32 % (66165)------------------------------
% 0.22/0.32 % (66165)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (66165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (66165)CaDiCaL version: 2.1.3
% 0.22/0.32 % (66165)Termination reason: Instruction limit
% 0.22/0.32 % (66165)Termination phase: Saturation
% 0.22/0.32 % (66165)Time elapsed: 0.014 s
% 0.22/0.32 % (66165)Peak memory usage: 12 MB
% 0.22/0.32 % (66165)Instructions burned: 25 (million)
% 0.22/0.32 % (66161)...printing done.
% 0.22/0.32 % (66161)Refutation found. Thanks to Tanya!
% 0.22/0.32 % SZS status Theorem for theBenchmark
% 0.22/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.32 % (66161)------------------------------
% 0.22/0.32 % (66161)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (66161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (66161)CaDiCaL version: 2.1.3
% 0.22/0.32 % (66161)Termination reason: Refutation
% 0.22/0.32 % (66161)Time elapsed: 0.015 s
% 0.22/0.32 % (66161)Peak memory usage: 12 MB
% 0.22/0.32 % (66161)Instructions burned: 29 (million)
% 0.22/0.32 % (66156)Success in time 0.065 s
% 0.22/0.32 % Vampire exiting
%------------------------------------------------------------------------------