%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NLP267^1 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 08:16:32 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 68 ( 47 unt; 0 typ; 0 def)
% Number of atoms : 397 ( 77 equ; 0 cnn)
% Maximal formula atoms : 10 ( 5 avg)
% Number of connectives : 374 ( 7 ~; 19 |; 10 &; 299 @)
% ( 0 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 33 ( 29 usr; 8 con; 0-4 aty)
% ( 10 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 80 ( 67 ^; 13 !; 0 ?; 80 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
mrel: mworld > mworld > $o ).
thf(func_def_1,type,
mactual: mworld ).
thf(func_def_2,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_4,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_5,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_16,type,
price: $i > mworld > $o ).
thf(func_def_17,type,
dest: $i > mworld > $o ).
thf(func_def_18,type,
class: $i > mworld > $o ).
thf(func_def_19,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_20,type,
vAND: $o > $o > $o ).
thf(func_def_21,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_24,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_27,type,
vNOT: $o > $o ).
thf(func_def_28,type,
vOR: $o > $o > $o ).
thf(func_def_29,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_30,type,
vIMP: $o > $o > $o ).
thf(func_def_31,type,
vIFF: $o > $o > $o ).
thf(func_def_32,type,
sK0: mworld ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).
thf(f3,axiom,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand_def) ).
thf(f5,axiom,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies_def) ).
thf(f7,axiom,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def) ).
thf(f10,axiom,
mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',law2) ).
thf(f13,axiom,
mlocal @ ( mbox @ ( dest @ paris ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',belief1) ).
thf(f14,axiom,
mlocal @ ( mbox @ ( class @ second ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',belief2) ).
thf(f15,conjecture,
mlocal @ ( mbox @ ( price @ seventy ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).
thf(f16,negated_conjecture,
~ ( mlocal @ ( mbox @ ( price @ seventy ) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f19,plain,
mlocal @ ( mbox @ ( dest @ paris ) ),
inference(rectify,[],[f13]) ).
thf(f20,plain,
( ( mlocal @ ( mbox @ ( dest @ paris ) ) )
= $true ),
inference(fool_elimination,[],[f19]) ).
thf(f25,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f30,plain,
mlocal @ ( mbox @ ( class @ second ) ),
inference(rectify,[],[f14]) ).
thf(f31,plain,
( ( mlocal @ ( mbox @ ( class @ second ) ) )
= $true ),
inference(fool_elimination,[],[f30]) ).
thf(f32,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[],[f7]) ).
thf(f33,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f32]) ).
thf(f34,plain,
mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ),
inference(rectify,[],[f10]) ).
thf(f35,plain,
( ( mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) )
= $true ),
inference(fool_elimination,[],[f34]) ).
thf(f36,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f37,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f36]) ).
thf(f38,plain,
~ ( mlocal @ ( mbox @ ( price @ seventy ) ) ),
inference(rectify,[],[f16]) ).
thf(f39,plain,
( ( mlocal @ ( mbox @ ( price @ seventy ) ) )
!= $true ),
inference(fool_elimination,[],[f38]) ).
thf(f44,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f45,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f44]) ).
thf(f46,plain,
( ( mlocal @ ( mbox @ ( price @ seventy ) ) )
!= $true ),
inference(flattening,[],[f39]) ).
thf(f47,plain,
( ( mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) )
= $true ),
inference(cnf_transformation,[],[f35]) ).
thf(f48,plain,
( ( mlocal @ ( mbox @ ( dest @ paris ) ) )
= $true ),
inference(cnf_transformation,[],[f20]) ).
thf(f52,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f37]) ).
thf(f53,plain,
( ( mlocal @ ( mbox @ ( price @ seventy ) ) )
!= $true ),
inference(cnf_transformation,[],[f46]) ).
thf(f58,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f45]) ).
thf(f59,plain,
( ( mlocal @ ( mbox @ ( class @ second ) ) )
= $true ),
inference(cnf_transformation,[],[f31]) ).
thf(f60,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f25]) ).
thf(f61,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f33]) ).
thf(f64,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( dest @ paris )
@ ( class @ second ) )
@ ( price @ seventy ) ) ) ) ),
inference(definition_unfolding,[],[f47,f60,f61,f52,f58]) ).
thf(f65,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( dest @ paris ) ) ) ),
inference(definition_unfolding,[],[f48,f60,f61]) ).
thf(f66,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( price @ seventy ) ) )
!= $true ),
inference(definition_unfolding,[],[f53,f60,f61]) ).
thf(f70,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( class @ second ) ) ) ),
inference(definition_unfolding,[],[f59,f60,f61]) ).
thf(f77,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( dest @ paris @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f65]) ).
thf(f78,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( dest @ paris @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f77]) ).
thf(f79,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( dest @ paris @ X1 ) ) ),
inference(beta-eta_normalization,[],[f78]) ).
thf(f80,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( dest @ paris @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f79]) ).
thf(f81,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( class @ second @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f70]) ).
thf(f82,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( class @ second @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f81]) ).
thf(f83,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( class @ second @ X1 ) ) ),
inference(beta-eta_normalization,[],[f82]) ).
thf(f84,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( class @ second @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f83]) ).
thf(f91,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ( class @ second @ Y0 )
& ( dest @ paris @ Y0 ) )
=> ( price @ seventy @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f64]) ).
thf(f92,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ( class @ second @ Y0 )
& ( dest @ paris @ Y0 ) )
=> ( price @ seventy @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f91]) ).
thf(f93,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( ( ( class @ second @ X1 )
& ( dest @ paris @ X1 ) )
=> ( price @ seventy @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f92]) ).
thf(f94,plain,
! [X1: mworld] :
( ( $true
= ( ( ( class @ second @ X1 )
& ( dest @ paris @ X1 ) )
=> ( price @ seventy @ X1 ) ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f93]) ).
thf(f95,plain,
! [X1: mworld] :
( ( $false
= ( ( class @ second @ X1 )
& ( dest @ paris @ X1 ) ) )
| ( ( price @ seventy @ X1 )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f94]) ).
thf(f96,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( class @ second @ X1 )
= $false )
| ( ( price @ seventy @ X1 )
= $true )
| ( $false
= ( dest @ paris @ X1 ) ) ),
inference(and_proxy_clausification,[],[f95]) ).
thf(f97,plain,
( $true
!= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( price @ seventy @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f66]) ).
thf(f98,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( price @ seventy @ Y0 ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f97]) ).
thf(f99,plain,
( ( ( mrel @ mactual @ sK0 )
=> ( price @ seventy @ sK0 ) )
= $false ),
inference(beta-eta_normalization,[],[f98]) ).
thf(f100,plain,
( ( price @ seventy @ sK0 )
= $false ),
inference(imp_proxy_clausification,[],[f99]) ).
thf(f101,plain,
( $true
= ( mrel @ mactual @ sK0 ) ),
inference(imp_proxy_clausification,[],[f99]) ).
thf(f108,plain,
( ( $true
= ( dest @ paris @ sK0 ) )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f101,f80]) ).
thf(f110,plain,
( $true
= ( dest @ paris @ sK0 ) ),
inference(trivial_inequality_removal,[],[f108]) ).
thf(f112,plain,
( ( $true
= ( class @ second @ sK0 ) )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f84,f101]) ).
thf(f114,plain,
( $true
= ( class @ second @ sK0 ) ),
inference(trivial_inequality_removal,[],[f112]) ).
thf(f133,plain,
( ( ( dest @ paris @ sK0 )
= $false )
| ( $true
= ( price @ seventy @ sK0 ) )
| ( $false
= ( class @ second @ sK0 ) )
| ( $true = $false ) ),
inference(constrained_superposition,[],[f101,f96]) ).
thf(f134,plain,
( ( $true
= ( price @ seventy @ sK0 ) )
| ( $false
= ( class @ second @ sK0 ) )
| ( ( dest @ paris @ sK0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f133]) ).
thf(f136,plain,
( ( $false
= ( class @ second @ sK0 ) )
| ( ( dest @ paris @ sK0 )
= $false )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f134,f100]) ).
thf(f137,plain,
( ( $false
= ( class @ second @ sK0 ) )
| ( ( dest @ paris @ sK0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f136]) ).
thf(f140,plain,
( ( $true = $false )
| ( ( dest @ paris @ sK0 )
= $false ) ),
inference(forward_demodulation,[],[f137,f114]) ).
thf(f141,plain,
( ( dest @ paris @ sK0 )
= $false ),
inference(trivial_inequality_removal,[],[f140]) ).
thf(f144,plain,
$true = $false,
inference(constrained_superposition,[],[f141,f110]) ).
thf(f146,plain,
$false,
inference(trivial_inequality_removal,[],[f144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NLP267^1 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n019.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 11:51:48 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.20/0.29 % (658485)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.29 % (658491)lrs+10_16_si=on:nwc=1.5:random_seed=575767665:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.29 % (658491) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-658485-658491"...
% 0.20/0.29 % (658491)...printing done.
% 0.20/0.29 % (658491)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.29 % (658491)------------------------------
% 0.20/0.29 % (658491)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (658491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (658491)CaDiCaL version: 2.1.3
% 0.20/0.29 % (658491)Termination reason: Refutation
% 0.20/0.29 % (658491)Time elapsed: 0.007 s
% 0.20/0.29 % (658491)Peak memory usage: 12 MB
% 0.20/0.29 % (658491)Instructions burned: 11 (million)
% 0.20/0.29 % (658485)Success in time 0.043 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------