%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO460^2 : 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 : 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 08:47:52 AM UTC 2026
% Result : Theorem 0.06s 0.18s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 12
% Syntax : Number of formulae : 111 ( 47 unt; 0 typ; 4 def)
% Number of atoms : 768 ( 123 equ; 0 cnn)
% Maximal formula atoms : 13 ( 6 avg)
% Number of connectives : 1007 ( 288 ~; 165 |; 0 &; 518 @)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 85 ( 85 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 59 usr; 10 con; 0-4 aty)
% ( 32 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 172 ( 0 sgn 9 !; 0 ?; 172 :)
% 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_d: $i > $i > $o ).
thf(func_def_33,type,
mbox_d: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_d: ( $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,
r: $i > $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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_42,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_44,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_45,type,
vIMP: $o > $o > $o ).
thf(func_def_46,type,
vAND: $o > $o > $o ).
thf(func_def_47,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vOR: $o > $o > $o ).
thf(func_def_49,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vNOT: $o > $o ).
thf(func_def_53,type,
sK0: $i > $i ).
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,
( ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) )
= mand ),
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(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_d
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_d @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^2.ax',mbox_d) ).
thf(f33,axiom,
( mdia_d
= ( ^ [X0: $i > $o] : ( mnot @ ( mbox_d @ ( mnot @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^2.ax',mdia_d) ).
thf(f35,conjecture,
mvalid @ ( mimplies @ ( mor @ ( mdia_d @ ( mand @ p @ q ) ) @ ( mdia_d @ ( mand @ p @ r ) ) ) @ ( mdia_d @ p ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f36,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mor @ ( mdia_d @ ( mand @ p @ q ) ) @ ( mdia_d @ ( mand @ p @ r ) ) ) @ ( mdia_d @ p ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
thf(f39,plain,
( mdia_d
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_d @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f58,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f62,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f65,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f66,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f65]) ).
thf(f69,plain,
( mbox_d
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_d @ X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f70,plain,
( mbox_d
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f71,plain,
~ ( mvalid @ ( mimplies @ ( mor @ ( mdia_d @ ( mand @ p @ q ) ) @ ( mdia_d @ ( mand @ p @ r ) ) ) @ ( mdia_d @ p ) ) ),
inference(rectify,[],[f36]) ).
thf(f72,plain,
( ( mvalid @ ( mimplies @ ( mor @ ( mdia_d @ ( mand @ p @ q ) ) @ ( mdia_d @ ( mand @ p @ r ) ) ) @ ( mdia_d @ p ) ) )
!= $true ),
inference(fool_elimination,[],[f71]) ).
thf(f87,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f88,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f87]) ).
thf(f89,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f90,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f89]) ).
thf(f95,plain,
( ( mvalid @ ( mimplies @ ( mor @ ( mdia_d @ ( mand @ p @ q ) ) @ ( mdia_d @ ( mand @ p @ r ) ) ) @ ( mdia_d @ p ) ) )
!= $true ),
inference(flattening,[],[f72]) ).
thf(f96,plain,
( mdia_d
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_d @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f106,plain,
( ( mvalid @ ( mimplies @ ( mor @ ( mdia_d @ ( mand @ p @ q ) ) @ ( mdia_d @ ( mand @ p @ r ) ) ) @ ( mdia_d @ p ) ) )
!= $true ),
inference(cnf_transformation,[],[f95]) ).
thf(f107,plain,
( mbox_d
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_d @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f70]) ).
thf(f115,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f88]) ).
thf(f116,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f122,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f62]) ).
thf(f124,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f58]) ).
thf(f129,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f90]) ).
thf(f133,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,[],[f122,f115,f116,f115,f115]) ).
thf(f134,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,[],[f124,f116,f115]) ).
thf(f142,plain,
( mdia_d
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_d @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f96,f115,f107,f115]) ).
thf(f144,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 > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_d @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ p
@ q ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_d @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ p
@ r ) ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_d @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ p ) ) )
!= $true ),
inference(definition_unfolding,[],[f106,f129,f134,f116,f142,f133,f142,f133,f142]) ).
thf(f149,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_d @ Y0 @ Y1 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ~ ( ~ ( r @ Y1 )
| ~ ( p @ Y1 ) )
| ~ ( rel_d @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ~ ( ~ ( q @ Y1 )
| ~ ( p @ Y1 ) )
| ~ ( rel_d @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f150,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( p @ Y1 )
| ~ ( rel_d @ Y0 @ Y1 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ~ ( ~ ( r @ Y1 )
| ~ ( p @ Y1 ) )
| ~ ( rel_d @ Y0 @ Y1 ) ) )
| ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ~ ( ~ ( q @ Y1 )
| ~ ( p @ Y1 ) )
| ~ ( rel_d @ Y0 @ Y1 ) ) ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f149]) ).
thf(f151,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( r @ Y0 )
| ~ ( p @ Y0 ) )
| ~ ( rel_d @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( q @ Y0 )
| ~ ( p @ Y0 ) )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f150]) ).
thf(f152,plain,
( $false
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( r @ Y0 )
| ~ ( p @ Y0 ) )
| ~ ( rel_d @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( q @ Y0 )
| ~ ( p @ Y0 ) )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f151]) ).
thf(f153,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f151]) ).
thf(f154,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ),
inference(not_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( p @ Y0 )
| ~ ( rel_d @ sK1 @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X1: $i] :
( $true
= ( ~ ( p @ X1 )
| ~ ( rel_d @ sK1 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f155]) ).
thf(f157,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_d @ sK1 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X1: $i] :
( ( $true
= ( ~ ( p @ X1 ) ) )
| ( $false
= ( rel_d @ sK1 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( ( $false
= ( rel_d @ sK1 @ X1 ) )
| ( $false
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f158]) ).
thf(f160,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( r @ Y0 )
| ~ ( p @ Y0 ) )
| ~ ( rel_d @ sK1 @ Y0 ) ) )
| ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( q @ Y0 )
| ~ ( p @ Y0 ) )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f152]) ).
thf(f161,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( q @ Y0 )
| ~ ( p @ Y0 ) )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( r @ Y0 )
| ~ ( p @ Y0 ) )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f160]) ).
thf(f162,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( r @ Y0 )
| ~ ( p @ Y0 ) )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( q @ Y0 )
| ~ ( p @ Y0 ) )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f161]) ).
thf(f163,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( q @ Y0 )
| ~ ( p @ Y0 ) )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( r @ Y0 )
| ~ ( p @ Y0 ) )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f164,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ~ ( ~ ( q @ Y0 )
| ~ ( p @ Y0 ) )
| ~ ( rel_d @ sK1 @ Y0 ) )
@ sK2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ~ ( ~ ( r @ Y0 )
| ~ ( p @ Y0 ) )
| ~ ( rel_d @ sK1 @ Y0 ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ~ ( ~ ( q @ Y0 )
| ~ ( p @ Y0 ) )
| ~ ( rel_d @ sK1 @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ~ ( ~ ( r @ Y0 )
| ~ ( p @ Y0 ) )
| ~ ( rel_d @ sK1 @ Y0 ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f164]) ).
thf(f166,plain,
( ( $false
= ( ~ ~ ( ~ ( r @ sK3 )
| ~ ( p @ sK3 ) )
| ~ ( rel_d @ sK1 @ sK3 ) ) )
| ( $false
= ( ~ ~ ( ~ ( q @ sK2 )
| ~ ( p @ sK2 ) )
| ~ ( rel_d @ sK1 @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f165]) ).
thf(f167,plain,
( ( ( ~ ( rel_d @ sK1 @ sK3 ) )
= $false )
| ( $false
= ( ~ ~ ( ~ ( q @ sK2 )
| ~ ( p @ sK2 ) )
| ~ ( rel_d @ sK1 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( $false
= ( ~ ~ ( ~ ( r @ sK3 )
| ~ ( p @ sK3 ) ) ) )
| ( $false
= ( ~ ~ ( ~ ( q @ sK2 )
| ~ ( p @ sK2 ) )
| ~ ( rel_d @ sK1 @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f166]) ).
thf(f169,plain,
( ( $false
= ( ~ ~ ( ~ ( q @ sK2 )
| ~ ( p @ sK2 ) )
| ~ ( rel_d @ sK1 @ sK2 ) ) )
| ( ( ~ ( ~ ( r @ sK3 )
| ~ ( p @ sK3 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f168]) ).
thf(f170,plain,
( ( $false
= ( ~ ( rel_d @ sK1 @ sK2 ) ) )
| ( ( ~ ( ~ ( r @ sK3 )
| ~ ( p @ sK3 ) ) )
= $true ) ),
inference(or_proxy_clausification,[],[f169]) ).
thf(f171,plain,
( ( ( ~ ( ~ ( r @ sK3 )
| ~ ( p @ sK3 ) ) )
= $true )
| ( $false
= ( ~ ~ ( ~ ( q @ sK2 )
| ~ ( p @ sK2 ) ) ) ) ),
inference(or_proxy_clausification,[],[f169]) ).
thf(f172,plain,
( ( $false
= ( ~ ~ ( ~ ( q @ sK2 )
| ~ ( p @ sK2 ) ) ) )
| ( $false
= ( ~ ( r @ sK3 )
| ~ ( p @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f173,plain,
( ( $false
= ( ~ ( r @ sK3 )
| ~ ( p @ sK3 ) ) )
| ( $true
= ( ~ ( ~ ( q @ sK2 )
| ~ ( p @ sK2 ) ) ) ) ),
inference(not_proxy_clausification,[],[f172]) ).
thf(f174,plain,
( ( $true
= ( ~ ( ~ ( q @ sK2 )
| ~ ( p @ sK2 ) ) ) )
| ( $false
= ( ~ ( p @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f173]) ).
thf(f182,plain,
( ( $false
= ( ~ ( p @ sK3 ) ) )
| ( $false
= ( ~ ( q @ sK2 )
| ~ ( p @ sK2 ) ) ) ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f183,plain,
( ( $true
= ( p @ sK3 ) )
| ( $false
= ( ~ ( q @ sK2 )
| ~ ( p @ sK2 ) ) ) ),
inference(not_proxy_clausification,[],[f182]) ).
thf(f184,plain,
( ( $true
= ( p @ sK3 ) )
| ( $false
= ( ~ ( p @ sK2 ) ) ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f187,plain,
( ( $true
= ( p @ sK3 ) )
| ( ( p @ sK2 )
= $true ) ),
inference(not_proxy_clausification,[],[f184]) ).
thf(f188,plain,
( ( ( ~ ( ~ ( r @ sK3 )
| ~ ( p @ sK3 ) ) )
= $true )
| ( $true
= ( rel_d @ sK1 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f170]) ).
thf(f189,plain,
( ( $true
= ( rel_d @ sK1 @ sK2 ) )
| ( $false
= ( ~ ( r @ sK3 )
| ~ ( p @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f188]) ).
thf(f190,plain,
( ( $true
= ( rel_d @ sK1 @ sK2 ) )
| ( $false
= ( ~ ( p @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f189]) ).
thf(f193,plain,
( ( $true
= ( p @ sK3 ) )
| ( $true
= ( rel_d @ sK1 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f194,plain,
( ( $false
= ( ~ ~ ( ~ ( q @ sK2 )
| ~ ( p @ sK2 ) )
| ~ ( rel_d @ sK1 @ sK2 ) ) )
| ( $true
= ( rel_d @ sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f167]) ).
thf(f195,plain,
( ( $false
= ( ~ ( rel_d @ sK1 @ sK2 ) ) )
| ( $true
= ( rel_d @ sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f194]) ).
thf(f196,plain,
( ( $false
= ( ~ ~ ( ~ ( q @ sK2 )
| ~ ( p @ sK2 ) ) ) )
| ( $true
= ( rel_d @ sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f194]) ).
thf(f197,plain,
( ( $true
= ( ~ ( ~ ( q @ sK2 )
| ~ ( p @ sK2 ) ) ) )
| ( $true
= ( rel_d @ sK1 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f196]) ).
thf(f198,plain,
( ( $true
= ( rel_d @ sK1 @ sK3 ) )
| ( $false
= ( ~ ( q @ sK2 )
| ~ ( p @ sK2 ) ) ) ),
inference(not_proxy_clausification,[],[f197]) ).
thf(f199,plain,
( ( $false
= ( ~ ( p @ sK2 ) ) )
| ( $true
= ( rel_d @ sK1 @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f198]) ).
thf(f202,plain,
( ( $true
= ( rel_d @ sK1 @ sK3 ) )
| ( ( p @ sK2 )
= $true ) ),
inference(not_proxy_clausification,[],[f199]) ).
thf(f203,plain,
( ( $true
= ( rel_d @ sK1 @ sK3 ) )
| ( $true
= ( rel_d @ sK1 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f195]) ).
thf(f214,definition,
( spl4_3
<=> ( ( p @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f216,plain,
( ( ( p @ sK2 )
= $true )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f214]) ).
thf(f219,definition,
( spl4_4
<=> ( $true
= ( p @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f221,plain,
( ( $true
= ( p @ sK3 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f219]) ).
thf(f223,plain,
( spl4_3
| spl4_4 ),
inference(avatar_split_clause,[],[f187,f219,f214]) ).
thf(f225,definition,
( spl4_5
<=> ( $true
= ( rel_d @ sK1 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f227,plain,
( ( $true
= ( rel_d @ sK1 @ sK2 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f225]) ).
thf(f229,plain,
( spl4_5
| spl4_4 ),
inference(avatar_split_clause,[],[f193,f219,f225]) ).
thf(f231,definition,
( spl4_6
<=> ( $true
= ( rel_d @ sK1 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f233,plain,
( ( $true
= ( rel_d @ sK1 @ sK3 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f231]) ).
thf(f235,plain,
( spl4_3
| spl4_6 ),
inference(avatar_split_clause,[],[f202,f231,f214]) ).
thf(f236,plain,
( spl4_6
| spl4_5 ),
inference(avatar_split_clause,[],[f203,f225,f231]) ).
thf(f237,plain,
( ( $false
= ( p @ sK2 ) )
| ( $false = $true )
| ~ spl4_5 ),
inference(constrained_superposition,[],[f227,f159]) ).
thf(f240,plain,
( ( $false
= ( p @ sK2 ) )
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f237]) ).
thf(f244,plain,
( ( $false = $true )
| ~ spl4_3
| ~ spl4_5 ),
inference(forward_demodulation,[],[f240,f216]) ).
thf(f245,plain,
( $false
| ~ spl4_3
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f244]) ).
thf(f246,plain,
( ~ spl4_3
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f245]) ).
thf(f249,plain,
( ( $false
= ( p @ sK3 ) )
| ( $false = $true )
| ~ spl4_6 ),
inference(constrained_superposition,[],[f159,f233]) ).
thf(f250,plain,
( ( $false
= ( p @ sK3 ) )
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f249]) ).
thf(f252,plain,
( ( $false = $true )
| ~ spl4_4
| ~ spl4_6 ),
inference(forward_demodulation,[],[f250,f221]) ).
thf(f253,plain,
( $false
| ~ spl4_4
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f252]) ).
thf(f254,plain,
( ~ spl4_4
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f253]) ).
cnf(s4,plain,
( spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f223]) ).
cnf(s6,plain,
( spl4_4
| spl4_5 ),
inference(sat_conversion,[],[f229]) ).
cnf(s8,plain,
( spl4_3
| spl4_6 ),
inference(sat_conversion,[],[f235]) ).
cnf(s9,plain,
( spl4_5
| spl4_6 ),
inference(sat_conversion,[],[f236]) ).
cnf(s11,plain,
( ~ spl4_3
| ~ spl4_5 ),
inference(sat_conversion,[],[f246]) ).
cnf(s12,plain,
( ~ spl4_4
| ~ spl4_6 ),
inference(sat_conversion,[],[f254]) ).
cnf(s15,plain,
spl4_5,
inference(rat,[],[s12,s6,s9]) ).
cnf(s16,plain,
~ spl4_3,
inference(rat,[],[s11,s15]) ).
cnf(s17,plain,
spl4_6,
inference(rat,[],[s8,s16]) ).
cnf(s18,plain,
spl4_4,
inference(rat,[],[s4,s16]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s12,s17,s18]) ).
thf(f258,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SYO460^2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.11 % Computer : n012.cluster.edu
% 0.06/0.11 % Model : x86_64 x86_64
% 0.06/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.11 % Memory : 8046.5625MB
% 0.06/0.11 % OS : Linux 6.8.0-71-generic
% 0.06/0.11 % CPULimit : 300
% 0.06/0.11 % WCLimit : 300
% 0.06/0.11 % DateTime : Tue Sep 29 16:57:48 UTC 2026
% 0.06/0.12 % CPUTime :
% 0.06/0.12 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.06/0.13 Running higher-order theorem proving
% 0.06/0.14 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
% 0.06/0.18 % (382499)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.06/0.18 % (382524)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.06/0.18 % (382524)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
% 0.06/0.18 % (382517)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3215015599:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.06/0.18 % (382518)lrs+10_16_si=on:nwc=1.5:random_seed=3880458620:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.06/0.18 % (382520)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=4175345601: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)
% 0.06/0.18 % (382523)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=326081736:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.06/0.18 % (382519)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1273225415:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.06/0.18 % (382524)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=2090464357:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.06/0.18 % (382522)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2415693075:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.06/0.18 % (382519)Instruction limit reached!
% 0.06/0.18 % (382519)------------------------------
% 0.06/0.18 % (382519)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.18 % (382519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.18 % (382519)CaDiCaL version: 2.1.3
% 0.06/0.18 % (382519)Termination reason: Instruction limit
% 0.06/0.18 % (382519)Termination phase: Saturation
% 0.06/0.18 % (382519)Time elapsed: 0.002 s
% 0.06/0.18 % (382519)Peak memory usage: 10 MB
% 0.06/0.18 % (382519)Instructions burned: 7 (million)
% 0.06/0.18 % (382517) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-382499-382517"...
% 0.06/0.18 % (382518) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-382499-382518"...
% 0.06/0.18 % (382523) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-382499-382523"...
% 0.06/0.18 % (382524) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-382499-382524"...
% 0.06/0.18 % (382518)...printing done.
% 0.06/0.18 % (382517)...printing done.
% 0.06/0.18 % (382523)...printing done.
% 0.06/0.18 % (382517)Refutation found. Thanks to Tanya!
% 0.06/0.18 % SZS status Theorem for theBenchmark
% 0.06/0.18 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.18 % (382517)------------------------------
% 0.06/0.18 % (382517)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.18 % (382517)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.18 % (382517)CaDiCaL version: 2.1.3
% 0.06/0.18 % (382517)Termination reason: Refutation
% 0.06/0.18 % (382517)Time elapsed: 0.005 s
% 0.06/0.18 % (382517)Peak memory usage: 13 MB
% 0.06/0.18 % (382517)Instructions burned: 19 (million)
% 0.06/0.18 % (382499)Success in time 0.033 s
% 0.06/0.18 % Vampire exiting
%------------------------------------------------------------------------------