%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NLP264^7 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:16:31 AM UTC 2026
% Result : Theorem 0.20s 0.34s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 10
% Syntax : Number of formulae : 93 ( 65 unt; 0 typ; 0 def)
% Number of atoms : 504 ( 115 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 682 ( 91 ~; 85 |; 0 &; 478 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% Number of symbols : 64 ( 60 usr; 10 con; 0-4 aty)
% ( 28 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 174 ( 128 ^; 46 !; 0 ?; 174 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
qmltpeq: 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,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_7,type,
mtrue: $i > $o ).
thf(func_def_8,type,
mfalse: $i > $o ).
thf(func_def_9,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_11,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_12,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_13,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_14,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_15,type,
exists_in_world: mu > $i > $o ).
thf(func_def_16,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_17,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_18,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_19,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_29,type,
mvalid: ( $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,
minvalid: ( $i > $o ) > $o ).
thf(func_def_33,type,
rel_s4: $i > $i > $o ).
thf(func_def_34,type,
mbox_s4: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
mdia_s4: ( $i > $o ) > $i > $o ).
thf(func_def_36,type,
dest: mu > $i > $o ).
thf(func_def_37,type,
class: mu > $i > $o ).
thf(func_def_38,type,
price: mu > $i > $o ).
thf(func_def_39,type,
first: mu ).
thf(func_def_40,type,
ninetyfive: mu ).
thf(func_def_41,type,
paris: mu ).
thf(func_def_42,type,
second: mu ).
thf(func_def_43,type,
seventy: mu ).
thf(func_def_46,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
vIMP: $o > $o > $o ).
thf(func_def_48,type,
vAND: $o > $o > $o ).
thf(func_def_49,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_51,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_52,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_54,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_55,type,
vOR: $o > $o > $o ).
thf(func_def_56,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_57,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_58,type,
vNOT: $o > $o ).
thf(func_def_59,type,
sK0: $i > mu ).
thf(f2,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mnot) ).
thf(f3,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mor) ).
thf(f8,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mand) ).
thf(f9,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mimplies) ).
thf(f28,axiom,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mvalid) ).
thf(f32,axiom,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s4 ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f43,axiom,
mvalid @ ( mbox_s4 @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',law2) ).
thf(f46,axiom,
mvalid @ ( mbox_s4 @ ( dest @ paris ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',belief1) ).
thf(f47,axiom,
mvalid @ ( mbox_s4 @ ( class @ second ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',belief2) ).
thf(f48,conjecture,
mvalid @ ( mbox_s4 @ ( price @ seventy ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f49,negated_conjecture,
~ ( mvalid @ ( mbox_s4 @ ( price @ seventy ) ) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
thf(f50,plain,
~ ( mvalid @ ( mbox_s4 @ ( price @ seventy ) ) ),
inference(rectify,[],[f49]) ).
thf(f51,plain,
( ( mvalid @ ( mbox_s4 @ ( price @ seventy ) ) )
!= $true ),
inference(fool_elimination,[],[f50]) ).
thf(f60,plain,
mvalid @ ( mbox_s4 @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ),
inference(rectify,[],[f43]) ).
thf(f61,plain,
( ( mvalid @ ( mbox_s4 @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) )
= $true ),
inference(fool_elimination,[],[f60]) ).
thf(f66,plain,
mvalid @ ( mbox_s4 @ ( class @ second ) ),
inference(rectify,[],[f47]) ).
thf(f67,plain,
( ( mvalid @ ( mbox_s4 @ ( class @ second ) ) )
= $true ),
inference(fool_elimination,[],[f66]) ).
thf(f91,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f95,plain,
mvalid @ ( mbox_s4 @ ( dest @ paris ) ),
inference(rectify,[],[f46]) ).
thf(f96,plain,
( ( mvalid @ ( mbox_s4 @ ( dest @ paris ) ) )
= $true ),
inference(fool_elimination,[],[f95]) ).
thf(f99,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f100,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f99]) ).
thf(f106,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f107,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f106]) ).
thf(f108,plain,
( ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ~ ( rel_s4 @ X1 @ X2 )
| ( X0 @ X2 ) ) )
= mbox_s4 ),
inference(rectify,[],[f32]) ).
thf(f109,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f108]) ).
thf(f130,plain,
( ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) )
= mvalid ),
inference(rectify,[],[f28]) ).
thf(f131,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f130]) ).
thf(f132,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f135,plain,
( ( mvalid @ ( mbox_s4 @ ( price @ seventy ) ) )
!= $true ),
inference(flattening,[],[f51]) ).
thf(f147,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f109]) ).
thf(f149,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f107]) ).
thf(f152,plain,
( ( mvalid @ ( mbox_s4 @ ( price @ seventy ) ) )
!= $true ),
inference(cnf_transformation,[],[f135]) ).
thf(f154,plain,
( ( mvalid @ ( mbox_s4 @ ( dest @ paris ) ) )
= $true ),
inference(cnf_transformation,[],[f96]) ).
thf(f156,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f100]) ).
thf(f163,plain,
( ( mvalid @ ( mbox_s4 @ ( class @ second ) ) )
= $true ),
inference(cnf_transformation,[],[f67]) ).
thf(f171,plain,
( ( mvalid @ ( mbox_s4 @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) )
= $true ),
inference(cnf_transformation,[],[f61]) ).
thf(f175,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f91]) ).
thf(f178,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f132]) ).
thf(f184,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f131]) ).
thf(f191,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,[],[f175,f149,f156,f149,f149]) ).
thf(f192,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,[],[f178,f156,f149]) ).
thf(f200,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( price @ seventy ) ) ) ),
inference(definition_unfolding,[],[f152,f184,f147]) ).
thf(f202,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( dest @ paris ) ) ) ),
inference(definition_unfolding,[],[f154,f184,f147]) ).
thf(f204,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( class @ second ) ) ) ),
inference(definition_unfolding,[],[f163,f184,f147]) ).
thf(f207,plain,
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
| ~ ( rel_s4 @ Y1 @ Y2 ) ) )
@ ( ^ [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 > $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 ) ) )
@ ( dest @ paris )
@ ( class @ second ) )
@ ( price @ seventy ) ) ) )
= $true ),
inference(definition_unfolding,[],[f171,f184,f147,f192,f191]) ).
thf(f246,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( price @ seventy @ Y1 )
| ~ ~ ( ~ ( class @ second @ Y1 )
| ~ ( dest @ paris @ Y1 ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f207]) ).
thf(f247,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( price @ seventy @ Y1 )
| ~ ~ ( ~ ( class @ second @ Y1 )
| ~ ( dest @ paris @ Y1 ) )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f246]) ).
thf(f248,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( price @ seventy @ Y0 )
| ~ ~ ( ~ ( class @ second @ Y0 )
| ~ ( dest @ paris @ Y0 ) )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f247]) ).
thf(f249,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( price @ seventy @ Y0 )
| ~ ~ ( ~ ( class @ second @ Y0 )
| ~ ( dest @ paris @ Y0 ) )
| ~ ( rel_s4 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f248]) ).
thf(f250,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( price @ seventy @ X2 )
| ~ ~ ( ~ ( class @ second @ X2 )
| ~ ( dest @ paris @ X2 ) )
| ~ ( rel_s4 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f249]) ).
thf(f251,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( ( price @ seventy @ X2 )
| ~ ~ ( ~ ( class @ second @ X2 )
| ~ ( dest @ paris @ X2 ) ) ) ) ),
inference(or_proxy_clausification,[],[f250]) ).
thf(f252,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( price @ seventy @ X2 )
| ~ ~ ( ~ ( class @ second @ X2 )
| ~ ( dest @ paris @ X2 ) ) ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f251]) ).
thf(f253,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ~ ( ~ ( class @ second @ X2 )
| ~ ( dest @ paris @ X2 ) ) ) )
| ( ( price @ seventy @ X2 )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(or_proxy_clausification,[],[f252]) ).
thf(f254,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( ~ ( class @ second @ X2 )
| ~ ( dest @ paris @ X2 ) ) )
= $false )
| ( ( price @ seventy @ X2 )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f253]) ).
thf(f255,plain,
! [X2: $i,X1: $i] :
( ( ( price @ seventy @ X2 )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( ~ ( class @ second @ X2 )
| ~ ( dest @ paris @ X2 ) )
= $true ) ),
inference(not_proxy_clausification,[],[f254]) ).
thf(f256,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( dest @ paris @ X2 ) ) )
| ( ( price @ seventy @ X2 )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( class @ second @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f255]) ).
thf(f257,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( class @ second @ X2 ) ) )
| ( ( price @ seventy @ X2 )
= $true )
| ( ( dest @ paris @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f256]) ).
thf(f258,plain,
! [X2: $i,X1: $i] :
( ( ( dest @ paris @ X2 )
= $false )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( ( price @ seventy @ X2 )
= $true )
| ( ( class @ second @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f257]) ).
thf(f271,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( class @ second @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f204]) ).
thf(f272,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( class @ second @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f271]) ).
thf(f273,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( class @ second @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f272]) ).
thf(f274,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( class @ second @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f273]) ).
thf(f275,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( class @ second @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f274]) ).
thf(f276,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( ( class @ second @ X2 )
= $true ) ),
inference(or_proxy_clausification,[],[f275]) ).
thf(f277,plain,
! [X2: $i,X1: $i] :
( ( ( class @ second @ X2 )
= $true )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f276]) ).
thf(f278,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( dest @ paris @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f202]) ).
thf(f279,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( dest @ paris @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f278]) ).
thf(f280,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( dest @ paris @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f279]) ).
thf(f281,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( dest @ paris @ Y0 )
| ~ ( rel_s4 @ X1 @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f280]) ).
thf(f282,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( dest @ paris @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) ),
inference(beta-eta_normalization,[],[f281]) ).
thf(f283,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( dest @ paris @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f282]) ).
thf(f284,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( dest @ paris @ X2 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f283]) ).
thf(f285,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( price @ seventy @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f200]) ).
thf(f286,plain,
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( price @ seventy @ Y1 )
| ~ ( rel_s4 @ Y0 @ Y1 ) ) )
@ sK1 )
= $false ),
inference(sigma_proxy_clausification,[],[f285]) ).
thf(f287,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( price @ seventy @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) ) )
= $false ),
inference(beta-eta_normalization,[],[f286]) ).
thf(f288,plain,
( $false
= ( ^ [Y0: $i] :
( ( price @ seventy @ Y0 )
| ~ ( rel_s4 @ sK1 @ Y0 ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f287]) ).
thf(f289,plain,
( ( ( price @ seventy @ sK2 )
| ~ ( rel_s4 @ sK1 @ sK2 ) )
= $false ),
inference(beta-eta_normalization,[],[f288]) ).
thf(f290,plain,
( $false
= ( ~ ( rel_s4 @ sK1 @ sK2 ) ) ),
inference(or_proxy_clausification,[],[f289]) ).
thf(f291,plain,
( ( price @ seventy @ sK2 )
= $false ),
inference(or_proxy_clausification,[],[f289]) ).
thf(f292,plain,
( $true
= ( rel_s4 @ sK1 @ sK2 ) ),
inference(not_proxy_clausification,[],[f290]) ).
thf(f304,plain,
( ( $true = $false )
| ( $true
= ( class @ second @ sK2 ) ) ),
inference(constrained_superposition,[],[f292,f277]) ).
thf(f306,plain,
( $true
= ( class @ second @ sK2 ) ),
inference(trivial_inequality_removal,[],[f304]) ).
thf(f310,plain,
( ( $true
= ( dest @ paris @ sK2 ) )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f292,f284]) ).
thf(f312,plain,
( $true
= ( dest @ paris @ sK2 ) ),
inference(trivial_inequality_removal,[],[f310]) ).
thf(f353,plain,
( ( ( dest @ paris @ sK2 )
= $false )
| ( $true
= ( price @ seventy @ sK2 ) )
| ( ( class @ second @ sK2 )
= $false )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f292,f258]) ).
thf(f354,plain,
( ( $true
= ( price @ seventy @ sK2 ) )
| ( ( dest @ paris @ sK2 )
= $false )
| ( ( class @ second @ sK2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f353]) ).
thf(f362,plain,
( ( ( class @ second @ sK2 )
= $false )
| ( ( dest @ paris @ sK2 )
= $false )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f354,f291]) ).
thf(f363,plain,
( ( ( class @ second @ sK2 )
= $false )
| ( ( dest @ paris @ sK2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f362]) ).
thf(f370,plain,
( ( $true = $false )
| ( ( dest @ paris @ sK2 )
= $false ) ),
inference(forward_demodulation,[],[f363,f306]) ).
thf(f371,plain,
( ( dest @ paris @ sK2 )
= $false ),
inference(trivial_inequality_removal,[],[f370]) ).
thf(f378,plain,
$true = $false,
inference(backward_demodulation,[],[f312,f371]) ).
thf(f379,plain,
$false,
inference(trivial_inequality_removal,[],[f378]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NLP264^7 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 % Computer : n015.cluster.edu
% 0.08/0.21 % Model : x86_64 x86_64
% 0.08/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.21 % Memory : 8046.5625MB
% 0.08/0.21 % OS : Linux 6.8.0-71-generic
% 0.08/0.21 % CPULimit : 300
% 0.08/0.21 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Sep 29 11:45:03 UTC 2026
% 0.08/0.22 % CPUTime :
% 0.08/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.25 Running higher-order theorem proving
% 0.20/0.27 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.34 % (3421670)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.34 % (3421677)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=331427994:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.34 % (3421675)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=21479015:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.34 % (3421676)lrs+10_16_si=on:nwc=1.5:random_seed=2215897752:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.34 % (3421680)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2372738110:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.34 % (3421678)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=2136915308:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.34 % (3421679)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=158929857:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.34 % (3421677)Instruction limit reached!
% 0.20/0.34 % (3421677)------------------------------
% 0.20/0.34 % (3421677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (3421677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (3421677)CaDiCaL version: 2.1.3
% 0.20/0.34 % (3421677)Termination reason: Instruction limit
% 0.20/0.34 % (3421677)Termination phase: Property scanning
% 0.20/0.34 % (3421677)Time elapsed: 0.003 s
% 0.20/0.34 % (3421677)Peak memory usage: 10 MB
% 0.20/0.34 % (3421677)Instructions burned: 6 (million)
% 0.20/0.34 % (3421681)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.34 % (3421681)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.34 % (3421676)Instruction limit reached!
% 0.20/0.34 % (3421676)------------------------------
% 0.20/0.34 % (3421676)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (3421676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (3421676)CaDiCaL version: 2.1.3
% 0.20/0.34 % (3421676)Termination reason: Instruction limit
% 0.20/0.34 % (3421676)Termination phase: Saturation
% 0.20/0.34 % (3421676)Time elapsed: 0.009 s
% 0.20/0.34 % (3421676)Peak memory usage: 12 MB
% 0.20/0.34 % (3421676)Instructions burned: 18 (million)
% 0.20/0.34 % (3421680) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3421670-3421680"...
% 0.20/0.34 % (3421681)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=2364842493:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.34 % (3421680)...printing done.
% 0.20/0.34 % (3421680)Refutation found. Thanks to Tanya!
% 0.20/0.34 % SZS status Theorem for theBenchmark
% 0.20/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.34 % (3421680)------------------------------
% 0.20/0.34 % (3421680)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (3421680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (3421680)CaDiCaL version: 2.1.3
% 0.20/0.34 % (3421680)Termination reason: Refutation
% 0.20/0.34 % (3421680)Time elapsed: 0.015 s
% 0.20/0.34 % (3421680)Peak memory usage: 13 MB
% 0.20/0.34 % (3421680)Instructions burned: 29 (million)
% 0.20/0.34 % (3421670)Success in time 0.058 s
% 0.20/0.34 % Vampire exiting
%------------------------------------------------------------------------------