%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n002.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 08:16:35 AM UTC 2026
% Result : Theorem 0.20s 0.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 12
% Syntax : Number of formulae : 103 ( 73 unt; 0 typ; 0 def)
% Number of atoms : 516 ( 124 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 712 ( 91 ~; 85 |; 0 &; 504 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 74 ( 74 >; 0 *; 0 +; 0 <<)
% Number of symbols : 64 ( 60 usr; 10 con; 0-4 aty)
% ( 32 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 198 ( 138 ^; 60 !; 0 ?; 198 :)
% 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_44,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_45,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_46,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_47,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_48,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_49,type,
vNOT: $o > $o ).
thf(func_def_50,type,
vOR: $o > $o > $o ).
thf(func_def_51,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_52,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_55,type,
vIMP: $o > $o > $o ).
thf(func_def_56,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_57,type,
vAND: $o > $o > $o ).
thf(func_def_58,type,
db4:
!>[X0: $tType] : X0 ).
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] :
( ( X1 @ X2 )
| ( X0 @ 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(f18,axiom,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mreflexive) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL015^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',mbox_s4) ).
thf(f34,axiom,
mreflexive @ rel_s4,
file('/export/starexec/sandbox2/benchmark/Axioms/LCL013^5.ax',a1) ).
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(f51,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f52,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f51]) ).
thf(f53,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f54,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f53]) ).
thf(f60,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f61,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f9]) ).
thf(f74,plain,
( mreflexive
= ( ^ [X0: $i > $i > $o] :
! [X1: $i] : ( X0 @ X1 @ X1 ) ) ),
inference(rectify,[],[f18]) ).
thf(f75,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f74]) ).
thf(f94,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f95,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f94]) ).
thf(f102,plain,
( mbox_s4
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f103,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f102]) ).
thf(f105,plain,
mreflexive @ rel_s4,
inference(rectify,[],[f34]) ).
thf(f106,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(fool_elimination,[],[f105]) ).
thf(f123,plain,
mvalid @ ( mbox_s4 @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ),
inference(rectify,[],[f43]) ).
thf(f124,plain,
( ( mvalid @ ( mbox_s4 @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) )
= $true ),
inference(fool_elimination,[],[f123]) ).
thf(f129,plain,
mvalid @ ( mbox_s4 @ ( dest @ paris ) ),
inference(rectify,[],[f46]) ).
thf(f130,plain,
( ( mvalid @ ( mbox_s4 @ ( dest @ paris ) ) )
= $true ),
inference(fool_elimination,[],[f129]) ).
thf(f131,plain,
mvalid @ ( mbox_s4 @ ( class @ second ) ),
inference(rectify,[],[f47]) ).
thf(f132,plain,
( ( mvalid @ ( mbox_s4 @ ( class @ second ) ) )
= $true ),
inference(fool_elimination,[],[f131]) ).
thf(f133,plain,
~ ( mvalid @ ( mbox_s4 @ ( price @ seventy ) ) ),
inference(rectify,[],[f49]) ).
thf(f134,plain,
( ( mvalid @ ( mbox_s4 @ ( price @ seventy ) ) )
!= $true ),
inference(fool_elimination,[],[f133]) ).
thf(f135,plain,
( ( mvalid @ ( mbox_s4 @ ( price @ seventy ) ) )
!= $true ),
inference(flattening,[],[f134]) ).
thf(f140,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f52]) ).
thf(f141,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f54]) ).
thf(f146,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f60]) ).
thf(f147,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f61]) ).
thf(f156,plain,
( mreflexive
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f75]) ).
thf(f166,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f95]) ).
thf(f170,plain,
( mbox_s4
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f103]) ).
thf(f172,plain,
( ( mreflexive @ rel_s4 )
= $true ),
inference(cnf_transformation,[],[f106]) ).
thf(f181,plain,
( ( mvalid @ ( mbox_s4 @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) )
= $true ),
inference(cnf_transformation,[],[f124]) ).
thf(f184,plain,
( ( mvalid @ ( mbox_s4 @ ( dest @ paris ) ) )
= $true ),
inference(cnf_transformation,[],[f130]) ).
thf(f185,plain,
( ( mvalid @ ( mbox_s4 @ ( class @ second ) ) )
= $true ),
inference(cnf_transformation,[],[f132]) ).
thf(f186,plain,
( ( mvalid @ ( mbox_s4 @ ( price @ seventy ) ) )
!= $true ),
inference(cnf_transformation,[],[f135]) ).
thf(f190,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f146,f140,f141,f140,f140]) ).
thf(f191,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,[],[f147,f141,f140]) ).
thf(f199,plain,
( $true
= ( ^ [Y0: $i > $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
@ rel_s4 ) ),
inference(definition_unfolding,[],[f172,f156]) ).
thf(f202,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ 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 > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) )
@ ( dest @ paris )
@ ( class @ second ) )
@ ( price @ seventy ) ) ) ) ),
inference(definition_unfolding,[],[f181,f166,f170,f191,f190]) ).
thf(f205,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( dest @ paris ) ) ) ),
inference(definition_unfolding,[],[f184,f166,f170]) ).
thf(f206,plain,
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( class @ second ) ) ) ),
inference(definition_unfolding,[],[f185,f166,f170]) ).
thf(f207,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_s4 @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( price @ seventy ) ) ) ),
inference(definition_unfolding,[],[f186,f166,f170]) ).
thf(f208,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( price @ seventy @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f207]) ).
thf(f209,plain,
( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( price @ seventy @ Y1 ) ) )
@ sK1 ) ),
inference(sigma_proxy_clausification,[],[f208]) ).
thf(f210,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( price @ seventy @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f209]) ).
thf(f211,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ sK1 @ Y0 )
| ( price @ seventy @ Y0 ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f210]) ).
thf(f212,plain,
( $false
= ( ~ ( rel_s4 @ sK1 @ sK2 )
| ( price @ seventy @ sK2 ) ) ),
inference(beta-eta_normalization,[],[f211]) ).
thf(f213,plain,
( $false
= ( price @ seventy @ sK2 ) ),
inference(or_proxy_clausification,[],[f212]) ).
thf(f216,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( class @ second @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f206]) ).
thf(f217,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( class @ second @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f216]) ).
thf(f218,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( class @ second @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f217]) ).
thf(f219,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( class @ second @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f218]) ).
thf(f220,plain,
! [X2: $i,X1: $i] :
( $true
= ( ~ ( rel_s4 @ X1 @ X2 )
| ( class @ second @ X2 ) ) ),
inference(beta-eta_normalization,[],[f219]) ).
thf(f221,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( class @ second @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f220]) ).
thf(f222,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( class @ second @ X2 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f221]) ).
thf(f223,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( dest @ paris @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f205]) ).
thf(f224,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ( dest @ paris @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f223]) ).
thf(f225,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( dest @ paris @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f224]) ).
thf(f226,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ( dest @ paris @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f225]) ).
thf(f227,plain,
! [X2: $i,X1: $i] :
( $true
= ( ~ ( rel_s4 @ X1 @ X2 )
| ( dest @ paris @ X2 ) ) ),
inference(beta-eta_normalization,[],[f226]) ).
thf(f228,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( dest @ paris @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f227]) ).
thf(f229,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( dest @ paris @ X2 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f228]) ).
thf(f254,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ~ ( ~ ( dest @ paris @ Y1 )
| ~ ( class @ second @ Y1 ) )
| ( price @ seventy @ Y1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f202]) ).
thf(f255,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_s4 @ Y0 @ Y1 )
| ~ ~ ( ~ ( dest @ paris @ Y1 )
| ~ ( class @ second @ Y1 ) )
| ( price @ seventy @ Y1 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f254]) ).
thf(f256,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ~ ( ~ ( dest @ paris @ Y0 )
| ~ ( class @ second @ Y0 ) )
| ( price @ seventy @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f255]) ).
thf(f257,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_s4 @ X1 @ Y0 )
| ~ ~ ( ~ ( dest @ paris @ Y0 )
| ~ ( class @ second @ Y0 ) )
| ( price @ seventy @ Y0 ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f256]) ).
thf(f258,plain,
! [X2: $i,X1: $i] :
( $true
= ( ~ ( rel_s4 @ X1 @ X2 )
| ~ ~ ( ~ ( dest @ paris @ X2 )
| ~ ( class @ second @ X2 ) )
| ( price @ seventy @ X2 ) ) ),
inference(beta-eta_normalization,[],[f257]) ).
thf(f259,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ~ ( ~ ( dest @ paris @ X2 )
| ~ ( class @ second @ X2 ) )
| ( price @ seventy @ X2 ) ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f258]) ).
thf(f260,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( price @ seventy @ X2 ) )
| ( $true
= ( ~ ( rel_s4 @ X1 @ X2 ) ) )
| ( $true
= ( ~ ~ ( ~ ( dest @ paris @ X2 )
| ~ ( class @ second @ X2 ) ) ) ) ),
inference(or_proxy_clausification,[],[f259]) ).
thf(f261,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( price @ seventy @ X2 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ~ ( ~ ( dest @ paris @ X2 )
| ~ ( class @ second @ X2 ) ) ) ) ),
inference(not_proxy_clausification,[],[f260]) ).
thf(f262,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( price @ seventy @ X2 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( ~ ( ~ ( dest @ paris @ X2 )
| ~ ( class @ second @ X2 ) ) ) ) ),
inference(not_proxy_clausification,[],[f261]) ).
thf(f263,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( price @ seventy @ X2 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( dest @ paris @ X2 )
| ~ ( class @ second @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f262]) ).
thf(f264,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( price @ seventy @ X2 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $true
= ( ~ ( class @ second @ X2 ) ) )
| ( $true
= ( ~ ( dest @ paris @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f263]) ).
thf(f265,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( price @ seventy @ X2 ) )
| ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( class @ second @ X2 ) )
| ( $true
= ( ~ ( dest @ paris @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f264]) ).
thf(f266,plain,
! [X2: $i,X1: $i] :
( ( ( rel_s4 @ X1 @ X2 )
= $false )
| ( $false
= ( dest @ paris @ X2 ) )
| ( $false
= ( class @ second @ X2 ) )
| ( $true
= ( price @ seventy @ X2 ) ) ),
inference(not_proxy_clausification,[],[f265]) ).
thf(f289,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 ) ) ),
inference(beta-eta_normalization,[],[f199]) ).
thf(f290,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( rel_s4 @ Y0 @ Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f289]) ).
thf(f291,plain,
! [X1: $i] :
( $true
= ( rel_s4 @ X1 @ X1 ) ),
inference(beta-eta_normalization,[],[f290]) ).
thf(f303,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( class @ second @ X0 ) ) ),
inference(constrained_superposition,[],[f291,f222]) ).
thf(f304,plain,
! [X0: $i] :
( $true
= ( class @ second @ X0 ) ),
inference(trivial_inequality_removal,[],[f303]) ).
thf(f309,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( dest @ paris @ X0 ) ) ),
inference(constrained_superposition,[],[f291,f229]) ).
thf(f310,plain,
! [X0: $i] :
( $true
= ( dest @ paris @ X0 ) ),
inference(trivial_inequality_removal,[],[f309]) ).
thf(f442,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( dest @ paris @ X0 ) )
| ( $false
= ( class @ second @ X0 ) )
| ( $true
= ( price @ seventy @ X0 ) ) ),
inference(constrained_superposition,[],[f291,f266]) ).
thf(f450,plain,
! [X0: $i] :
( ( $false
= ( dest @ paris @ X0 ) )
| ( $false
= ( class @ second @ X0 ) )
| ( $true
= ( price @ seventy @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f442]) ).
thf(f463,plain,
! [X0: $i] :
( ( $true = $false )
| ( $false
= ( class @ second @ X0 ) )
| ( $true
= ( price @ seventy @ X0 ) ) ),
inference(forward_demodulation,[],[f450,f310]) ).
thf(f464,plain,
! [X0: $i] :
( ( $false
= ( class @ second @ X0 ) )
| ( $true
= ( price @ seventy @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f463]) ).
thf(f475,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( price @ seventy @ X0 ) ) ),
inference(forward_demodulation,[],[f464,f304]) ).
thf(f476,plain,
! [X0: $i] :
( $true
= ( price @ seventy @ X0 ) ),
inference(trivial_inequality_removal,[],[f475]) ).
thf(f637,plain,
$true = $false,
inference(constrained_superposition,[],[f213,f476]) ).
thf(f638,plain,
$false,
inference(trivial_inequality_removal,[],[f637]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.09/0.20 % Computer : n002.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 11:44:37 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.30 % (1171245)Will run a generic schedule for satisfiability detection.
% 0.20/0.30 % (1171251)% WARNING: option uhcvi not known.
% 0.20/0.30 % (1171254)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=869330573:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.30 % (1171250)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2848565726_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.30 % (1171251)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3092281612:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.30 % (1171252)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1432379828:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.30 % (1171254)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.30 % (1171251)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.30 % (1171251)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.30 % Exception at run slice level
% 0.20/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.30 % (1171251) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1171245-1171251"...
% 0.20/0.30 % (1171254) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1171245-1171254"...
% 0.20/0.30 % (1171254)...printing done.
% 0.20/0.30 % (1171254)Refutation found. Thanks to Tanya!
% 0.20/0.30 % SZS status Theorem for theBenchmark
% 0.20/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.30 % (1171254)------------------------------
% 0.20/0.30 % (1171254)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (1171254)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (1171254)CaDiCaL version: 2.1.3
% 0.20/0.30 % (1171254)Termination reason: Refutation
% 0.20/0.30 % (1171254)Time elapsed: 0.020 s
% 0.20/0.30 % (1171254)Peak memory usage: 12 MB
% 0.20/0.30 % (1171254)Instructions burned: 46 (million)
% 0.20/0.30 % (1171245)Success in time 0.058 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------