%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NLP267^4 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 0.36s 0.44s
% Output : Refutation 0.36s
% 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,
vNOT: $o > $o ).
thf(func_def_20,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_22,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_25,type,
vIMP: $o > $o > $o ).
thf(func_def_26,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_27,type,
vAND: $o > $o > $o ).
thf(func_def_28,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_29,type,
vIFF: $o > $o > $o ).
thf(func_def_30,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_31,type,
vOR: $o > $o > $o ).
thf(func_def_32,type,
sK0: mworld ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f3,axiom,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand_def) ).
thf(f5,axiom,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies_def) ).
thf(f7,axiom,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(f12,axiom,
mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',law2) ).
thf(f15,axiom,
mlocal @ ( mbox @ ( dest @ paris ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',belief1) ).
thf(f16,axiom,
mlocal @ ( mbox @ ( class @ second ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',belief2) ).
thf(f17,conjecture,
mlocal @ ( mbox @ ( price @ seventy ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
thf(f18,negated_conjecture,
~ ( mlocal @ ( mbox @ ( price @ seventy ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
thf(f23,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f24,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f23]) ).
thf(f25,plain,
mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ),
inference(rectify,[],[f12]) ).
thf(f26,plain,
( ( mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) )
= $true ),
inference(fool_elimination,[],[f25]) ).
thf(f27,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f28,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f27]) ).
thf(f31,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[],[f7]) ).
thf(f32,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f31]) ).
thf(f37,plain,
mlocal @ ( mbox @ ( class @ second ) ),
inference(rectify,[],[f16]) ).
thf(f38,plain,
( ( mlocal @ ( mbox @ ( class @ second ) ) )
= $true ),
inference(fool_elimination,[],[f37]) ).
thf(f39,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f42,plain,
~ ( mlocal @ ( mbox @ ( price @ seventy ) ) ),
inference(rectify,[],[f18]) ).
thf(f43,plain,
( ( mlocal @ ( mbox @ ( price @ seventy ) ) )
!= $true ),
inference(fool_elimination,[],[f42]) ).
thf(f44,plain,
mlocal @ ( mbox @ ( dest @ paris ) ),
inference(rectify,[],[f15]) ).
thf(f45,plain,
( ( mlocal @ ( mbox @ ( dest @ paris ) ) )
= $true ),
inference(fool_elimination,[],[f44]) ).
thf(f52,plain,
( ( mlocal @ ( mbox @ ( price @ seventy ) ) )
!= $true ),
inference(flattening,[],[f43]) ).
thf(f56,plain,
( ( mlocal @ ( mbox @ ( dest @ paris ) ) )
= $true ),
inference(cnf_transformation,[],[f45]) ).
thf(f57,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f60,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f39]) ).
thf(f61,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f32]) ).
thf(f62,plain,
( ( mlocal @ ( mbox @ ( class @ second ) ) )
= $true ),
inference(cnf_transformation,[],[f38]) ).
thf(f63,plain,
( ( mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) )
= $true ),
inference(cnf_transformation,[],[f26]) ).
thf(f65,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f70,plain,
( ( mlocal @ ( mbox @ ( price @ seventy ) ) )
!= $true ),
inference(cnf_transformation,[],[f52]) ).
thf(f75,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( dest @ paris ) ) )
= $true ),
inference(definition_unfolding,[],[f56,f60,f61]) ).
thf(f77,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( class @ second ) ) )
= $true ),
inference(definition_unfolding,[],[f62,f60,f61]) ).
thf(f78,plain,
( ( ^ [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] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( dest @ paris )
@ ( class @ second ) )
@ ( price @ seventy ) ) ) )
= $true ),
inference(definition_unfolding,[],[f63,f60,f61,f57,f65]) ).
thf(f80,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,[],[f70,f60,f61]) ).
thf(f82,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( dest @ paris @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f75]) ).
thf(f83,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( dest @ paris @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f82]) ).
thf(f84,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( dest @ paris @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f83]) ).
thf(f85,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( dest @ paris @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f84]) ).
thf(f98,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ( dest @ paris @ Y0 )
& ( class @ second @ Y0 ) )
=> ( price @ seventy @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f78]) ).
thf(f99,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ( dest @ paris @ Y0 )
& ( class @ second @ Y0 ) )
=> ( price @ seventy @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f98]) ).
thf(f100,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( ( ( dest @ paris @ X1 )
& ( class @ second @ X1 ) )
=> ( price @ seventy @ X1 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f99]) ).
thf(f101,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( ( ( dest @ paris @ X1 )
& ( class @ second @ X1 ) )
=> ( price @ seventy @ X1 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f100]) ).
thf(f102,plain,
! [X1: mworld] :
( ( ( ( dest @ paris @ X1 )
& ( class @ second @ X1 ) )
= $false )
| ( ( mrel @ mactual @ X1 )
= $false )
| ( ( price @ seventy @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f101]) ).
thf(f103,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $false
= ( dest @ paris @ X1 ) )
| ( ( price @ seventy @ X1 )
= $true )
| ( ( class @ second @ X1 )
= $false ) ),
inference(and_proxy_clausification,[],[f102]) ).
thf(f104,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( price @ seventy @ Y0 ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f80]) ).
thf(f105,plain,
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( price @ seventy @ Y0 ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f104]) ).
thf(f106,plain,
( ( ( mrel @ mactual @ sK0 )
=> ( price @ seventy @ sK0 ) )
= $false ),
inference(beta-eta_normalization,[],[f105]) ).
thf(f107,plain,
( ( price @ seventy @ sK0 )
= $false ),
inference(imp_proxy_clausification,[],[f106]) ).
thf(f108,plain,
( ( mrel @ mactual @ sK0 )
= $true ),
inference(imp_proxy_clausification,[],[f106]) ).
thf(f109,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( class @ second @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f77]) ).
thf(f110,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( class @ second @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f109]) ).
thf(f111,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( class @ second @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f110]) ).
thf(f112,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( class @ second @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f111]) ).
thf(f121,plain,
( ( $true
= ( dest @ paris @ sK0 ) )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f108,f85]) ).
thf(f123,plain,
( $true
= ( dest @ paris @ sK0 ) ),
inference(trivial_inequality_removal,[],[f121]) ).
thf(f127,plain,
( ( ( class @ second @ sK0 )
= $true )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f112,f108]) ).
thf(f131,plain,
( ( class @ second @ sK0 )
= $true ),
inference(trivial_inequality_removal,[],[f127]) ).
thf(f187,plain,
( ( ( price @ seventy @ sK0 )
= $true )
| ( ( class @ second @ sK0 )
= $false )
| ( $false
= ( dest @ paris @ sK0 ) )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f108,f103]) ).
thf(f188,plain,
( ( ( class @ second @ sK0 )
= $false )
| ( ( price @ seventy @ sK0 )
= $true )
| ( $false
= ( dest @ paris @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f187]) ).
thf(f192,plain,
( ( $false = $true )
| ( ( price @ seventy @ sK0 )
= $true )
| ( $false
= ( dest @ paris @ sK0 ) ) ),
inference(forward_demodulation,[],[f188,f131]) ).
thf(f193,plain,
( ( $false
= ( dest @ paris @ sK0 ) )
| ( ( price @ seventy @ sK0 )
= $true ) ),
inference(trivial_inequality_removal,[],[f192]) ).
thf(f200,plain,
( ( ( price @ seventy @ sK0 )
= $true )
| ( $false = $true ) ),
inference(forward_demodulation,[],[f193,f123]) ).
thf(f201,plain,
( ( price @ seventy @ sK0 )
= $true ),
inference(trivial_inequality_removal,[],[f200]) ).
thf(f208,plain,
$false = $true,
inference(forward_demodulation,[],[f201,f107]) ).
thf(f209,plain,
$false,
inference(trivial_inequality_removal,[],[f208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NLP267^4 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.09 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.30 % Computer : n005.cluster.edu
% 0.12/0.30 % Model : x86_64 x86_64
% 0.12/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.30 % Memory : 8046.5625MB
% 0.12/0.30 % OS : Linux 6.8.0-71-generic
% 0.12/0.30 % CPULimit : 300
% 0.12/0.30 % WCLimit : 300
% 0.12/0.30 % DateTime : Tue Sep 29 11:50:31 UTC 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.31 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.30/0.36 Running higher-order theorem proving
% 0.30/0.38 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
% 0.36/0.44 % (1574514)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.36/0.44 % (1574519)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3076459848:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.36/0.44 % (1574519) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1574514-1574519"...
% 0.36/0.44 % (1574519)...printing done.
% 0.36/0.44 % (1574519)Refutation found. Thanks to Tanya!
% 0.36/0.44 % SZS status Theorem for theBenchmark
% 0.36/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.36/0.44 % (1574519)------------------------------
% 0.36/0.44 % (1574519)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.36/0.44 % (1574519)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.36/0.44 % (1574519)CaDiCaL version: 2.1.3
% 0.36/0.44 % (1574519)Termination reason: Refutation
% 0.36/0.44 % (1574519)Time elapsed: 0.007 s
% 0.36/0.44 % (1574519)Peak memory usage: 12 MB
% 0.36/0.44 % (1574519)Instructions burned: 13 (million)
% 0.36/0.44 % (1574514)Success in time 0.043 s
% 0.36/0.44 % Vampire exiting
%------------------------------------------------------------------------------