%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO457^5 : 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 : n007.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 08:47:50 AM UTC 2026
% Result : Theorem 0.10s 0.26s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 14
% Syntax : Number of formulae : 98 ( 47 unt; 0 typ; 5 def)
% Number of atoms : 575 ( 114 equ; 0 cnn)
% Maximal formula atoms : 9 ( 5 avg)
% Number of connectives : 780 ( 141 ~; 127 |; 0 &; 465 @)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 108 ( 108 >; 0 *; 0 +; 0 <<)
% Number of symbols : 64 ( 60 usr; 10 con; 0-4 aty)
% ( 43 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 223 ( 0 sgn 22 !; 0 ?; 223 :)
% 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,
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,
vIMP: $o > $o > $o ).
thf(func_def_42,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_44,type,
vAND: $o > $o > $o ).
thf(func_def_45,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_50,type,
vNOT: $o > $o ).
thf(func_def_51,type,
vOR: $o > $o > $o ).
thf(func_def_52,type,
sF0: $o ).
thf(func_def_53,type,
sK1: $i > $i ).
thf(func_def_54,type,
sK2: $i > $i ).
thf(func_def_55,type,
sK3: $i > $i ).
thf(f3,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mreflexive) ).
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] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s4 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f33,axiom,
( ( ^ [X0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ X0 ) ) ) )
= mdia_s4 ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',mdia_s4) ).
thf(f34,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^5.ax',a1) ).
thf(f36,conjecture,
mvalid @ ( mimplies @ ( mdia_s4 @ ( mbox_s4 @ p ) ) @ ( mdia_s4 @ ( mimplies @ q @ p ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f37,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mdia_s4 @ ( mbox_s4 @ p ) ) @ ( mdia_s4 @ ( mimplies @ q @ p ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f38,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f39,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f38]) ).
thf(f52,plain,
~ ( mvalid @ ( mimplies @ ( mdia_s4 @ ( mbox_s4 @ p ) ) @ ( mdia_s4 @ ( mimplies @ q @ p ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f53,plain,
( ( mvalid @ ( mimplies @ ( mdia_s4 @ ( mbox_s4 @ p ) ) @ ( mdia_s4 @ ( mimplies @ q @ p ) ) ) )
!= $true ),
inference(fool_elimination,[],[f52]) ).
thf(f60,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f33]) ).
thf(f63,plain,
mreflexive @ rel_s4,
inference(rectify,[],[f34]) ).
thf(f64,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f63]) ).
thf(f70,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f71,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f70]) ).
thf(f81,plain,
( ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[],[f4]) ).
thf(f82,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f81]) ).
thf(f89,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s4 ),
inference(rectify,[],[f32]) ).
thf(f90,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f89]) ).
thf(f93,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f94,plain,
( ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f3]) ).
thf(f95,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f94]) ).
thf(f98,plain,
( ( mvalid @ ( mimplies @ ( mdia_s4 @ ( mbox_s4 @ p ) ) @ ( mdia_s4 @ ( mimplies @ q @ p ) ) ) )
!= $true ),
inference(flattening,[],[f53]) ).
thf(f100,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f93]) ).
thf(f103,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] : ( mnot @ ( mbox_s4 @ ( mnot @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f115,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f95]) ).
thf(f123,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f71]) ).
thf(f124,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f82]) ).
thf(f127,plain,
( ( mvalid @ ( mimplies @ ( mdia_s4 @ ( mbox_s4 @ p ) ) @ ( mdia_s4 @ ( mimplies @ q @ p ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f98]) ).
thf(f129,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f130,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f64]) ).
thf(f133,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f90]) ).
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,[],[f100,f124,f115]) ).
thf(f146,plain,
( mdia_s4
= ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f103,f115,f133,f115]) ).
thf(f148,plain,
( $true
!= ( ^ [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 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ p ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [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 )
@ q
@ p ) ) ) ) ),
inference(definition_unfolding,[],[f127,f123,f138,f146,f133,f146,f138]) ).
thf(f149,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f130,f129]) ).
thf(f150,definition,
( sF0
= ( ^ [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 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ p ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [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 )
@ q
@ p ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f151,plain,
sF0 != $true,
inference(definition_folding,[],[f148,f150]) ).
thf(f161,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f149]) ).
thf(f162,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X1: $i] :
( $true
= ( rel_s4 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f162]) ).
thf(f164,plain,
( ( $false
= ( ^ [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 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ p ) )
@ ( ^ [Y0: $i > $o] :
( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ ( ^ [Y1: $i > $o,Y2: $i] :
( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
| ~ ( rel_s4 @ Y2 @ Y3 ) ) )
@ ( ^ [Y1: $i > $o,Y2: $i] :
~ ( Y1 @ Y2 )
@ Y0 ) ) )
@ ( ^ [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 )
@ q
@ p ) ) ) ) )
| ( sF0 = $true ) ),
inference(iff_proxy_clausification,[],[f150]) ).
thf(f198,plain,
( ( sF0 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ( p @ Y1 )
| ~ ( q @ Y1 ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f164]) ).
thf(f199,plain,
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( ( p @ Y1 )
| ~ ( q @ Y1 ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( !! @ $i
@ ^ [Y2: $i] :
( ( p @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) )
@ sK4 ) ) ),
inference(sigma_proxy_clausification,[],[f198]) ).
thf(f200,plain,
( ( sF0 = $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) )
| ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f199]) ).
thf(f201,plain,
( ( $false
= ( ~ ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f200]) ).
thf(f202,plain,
( ( sF0 = $true )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f200]) ).
thf(f203,plain,
( ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[],[f202]) ).
thf(f204,plain,
! [X1: $i] :
( ( ( ^ [Y0: $i] :
( ~ ( ( p @ Y0 )
| ~ ( q @ Y0 ) )
| ~ ( rel_s4 @ sK4 @ Y0 ) )
@ X1 )
= $true )
| ( sF0 = $true ) ),
inference(pi_proxy_clausification,[],[f203]) ).
thf(f205,plain,
! [X1: $i] :
( ( $true
= ( ~ ( ( p @ X1 )
| ~ ( q @ X1 ) )
| ~ ( rel_s4 @ sK4 @ X1 ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f204]) ).
thf(f206,plain,
! [X1: $i] :
( ( ( ~ ( ( p @ X1 )
| ~ ( q @ X1 ) ) )
= $true )
| ( $true
= ( ~ ( rel_s4 @ sK4 @ X1 ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f205]) ).
thf(f207,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ sK4 @ X1 ) ) )
| ( $false
= ( ( p @ X1 )
| ~ ( q @ X1 ) ) )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f206]) ).
thf(f208,plain,
! [X1: $i] :
( ( $false
= ( ( p @ X1 )
| ~ ( q @ X1 ) ) )
| ( sF0 = $true )
| ( $false
= ( rel_s4 @ sK4 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f207]) ).
thf(f210,plain,
! [X1: $i] :
( ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s4 @ sK4 @ X1 ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f208]) ).
thf(f212,plain,
( ( sF0 = $true )
| ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f201]) ).
thf(f213,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK4 @ Y0 ) ) ) )
| ( sF0 = $true ) ),
inference(not_proxy_clausification,[],[f212]) ).
thf(f214,plain,
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ( p @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
| ~ ( rel_s4 @ sK4 @ Y0 ) )
@ sK5 ) ) ),
inference(sigma_proxy_clausification,[],[f213]) ).
thf(f215,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK5 @ Y0 ) ) )
| ~ ( rel_s4 @ sK4 @ sK5 ) ) )
| ( sF0 = $true ) ),
inference(beta-eta_normalization,[],[f214]) ).
thf(f216,plain,
( ( $false
= ( ~ ( rel_s4 @ sK4 @ sK5 ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f215]) ).
thf(f217,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK5 @ Y0 ) ) ) ) )
| ( sF0 = $true ) ),
inference(or_proxy_clausification,[],[f215]) ).
thf(f218,plain,
( ( sF0 = $true )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK5 @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f217]) ).
thf(f219,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( ^ [Y0: $i] :
( ( p @ Y0 )
| ~ ( rel_s4 @ sK5 @ Y0 ) )
@ X1 )
= $true ) ),
inference(pi_proxy_clausification,[],[f218]) ).
thf(f220,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( $true
= ( ( p @ X1 )
| ~ ( rel_s4 @ sK5 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f219]) ).
thf(f221,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( ( ~ ( rel_s4 @ sK5 @ X1 ) )
= $true )
| ( $true
= ( p @ X1 ) ) ),
inference(or_proxy_clausification,[],[f220]) ).
thf(f222,plain,
! [X1: $i] :
( ( sF0 = $true )
| ( $false
= ( rel_s4 @ sK5 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f221]) ).
thf(f223,plain,
( ( sF0 = $true )
| ( $true
= ( rel_s4 @ sK4 @ sK5 ) ) ),
inference(not_proxy_clausification,[],[f216]) ).
thf(f245,definition,
( spl6_6
<=> ! [X1: $i] :
( ( $false
= ( p @ X1 ) )
| ( $false
= ( rel_s4 @ sK4 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_6])],[avatar_definition]) ).
thf(f246,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s4 @ sK4 @ X1 ) )
| ( $false
= ( p @ X1 ) ) )
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f245]) ).
thf(f248,definition,
( spl6_7
<=> ( sF0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl6_7])],[avatar_definition]) ).
thf(f251,plain,
( spl6_6
| spl6_7 ),
inference(avatar_split_clause,[],[f210,f248,f245]) ).
thf(f257,definition,
( spl6_9
<=> ! [X1: $i] :
( ( $false
= ( rel_s4 @ sK5 @ X1 ) )
| ( $true
= ( p @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition]) ).
thf(f258,plain,
( ! [X1: $i] :
( ( $false
= ( rel_s4 @ sK5 @ X1 ) )
| ( $true
= ( p @ X1 ) ) )
| ~ spl6_9 ),
inference(avatar_component_clause,[],[f257]) ).
thf(f259,plain,
( spl6_7
| spl6_9 ),
inference(avatar_split_clause,[],[f222,f257,f248]) ).
thf(f261,definition,
( spl6_10
<=> ( $true
= ( rel_s4 @ sK4 @ sK5 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition]) ).
thf(f263,plain,
( ( $true
= ( rel_s4 @ sK4 @ sK5 ) )
| ~ spl6_10 ),
inference(avatar_component_clause,[],[f261]) ).
thf(f264,plain,
( spl6_10
| spl6_7 ),
inference(avatar_split_clause,[],[f223,f248,f261]) ).
thf(f265,plain,
~ spl6_7,
inference(avatar_split_clause,[],[f151,f248]) ).
thf(f282,plain,
( ( $false
= ( p @ sK5 ) )
| ( $false = $true )
| ~ spl6_6
| ~ spl6_10 ),
inference(constrained_superposition,[],[f263,f246]) ).
thf(f284,plain,
( ( $false
= ( p @ sK5 ) )
| ~ spl6_6
| ~ spl6_10 ),
inference(trivial_inequality_removal,[],[f282]) ).
thf(f316,plain,
( ( $true
= ( p @ sK5 ) )
| ( $false = $true )
| ~ spl6_9 ),
inference(constrained_superposition,[],[f258,f163]) ).
thf(f321,plain,
( ( $true
= ( p @ sK5 ) )
| ~ spl6_9 ),
inference(trivial_inequality_removal,[],[f316]) ).
thf(f325,plain,
( ( $false = $true )
| ~ spl6_6
| ~ spl6_9
| ~ spl6_10 ),
inference(forward_demodulation,[],[f321,f284]) ).
thf(f326,plain,
( $false
| ~ spl6_6
| ~ spl6_9
| ~ spl6_10 ),
inference(trivial_inequality_removal,[],[f325]) ).
thf(f327,plain,
( ~ spl6_6
| ~ spl6_9
| ~ spl6_10 ),
inference(avatar_contradiction_clause,[],[f326]) ).
cnf(s5,plain,
( spl6_6
| spl6_7 ),
inference(sat_conversion,[],[f251]) ).
cnf(s7,plain,
( spl6_7
| spl6_9 ),
inference(sat_conversion,[],[f259]) ).
cnf(s8,plain,
( spl6_7
| spl6_10 ),
inference(sat_conversion,[],[f264]) ).
cnf(s9,plain,
~ spl6_7,
inference(sat_conversion,[],[f265]) ).
cnf(s12,plain,
( ~ spl6_6
| ~ spl6_9
| ~ spl6_10 ),
inference(sat_conversion,[],[f327]) ).
cnf(s14,plain,
spl6_10,
inference(rat,[],[s8,s9]) ).
cnf(s15,plain,
spl6_9,
inference(rat,[],[s7,s9]) ).
cnf(s16,plain,
~ spl6_6,
inference(rat,[],[s12,s14,s15]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s5,s9,s16]) ).
thf(f328,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO457^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.17 % Computer : n007.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Sep 29 16:55:26 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 Running higher-order theorem proving
% 0.10/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.26 % (3642821)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.10/0.26 % (3642832)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.10/0.26 % (3642832)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
% 0.10/0.26 % (3642832)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=2360293748:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.10/0.26 % (3642832) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3642821-3642832"...
% 0.10/0.26 % (3642832)...printing done.
% 0.10/0.26 % (3642832)Refutation found. Thanks to Tanya!
% 0.10/0.26 % SZS status Theorem for theBenchmark
% 0.10/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.26 % (3642832)------------------------------
% 0.10/0.26 % (3642832)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.26 % (3642832)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.26 % (3642832)CaDiCaL version: 2.1.3
% 0.10/0.26 % (3642832)Termination reason: Refutation
% 0.10/0.26 % (3642832)Time elapsed: 0.006 s
% 0.10/0.26 % (3642832)Peak memory usage: 13 MB
% 0.10/0.26 % (3642832)Instructions burned: 20 (million)
% 0.10/0.26 % (3642821)Success in time 0.032 s
% 0.10/0.26 % Vampire exiting
%------------------------------------------------------------------------------