%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NLP267^5 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n018.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 08:16:36 AM UTC 2026
% Result : Theorem 0.08s 0.25s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 66 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 399 ( 80 equ; 0 cnn)
% Maximal formula atoms : 10 ( 6 avg)
% Number of connectives : 385 ( 7 ~; 24 |; 10 &; 305 @)
% ( 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 : 86 ( 67 ^; 19 !; 0 ?; 86 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_21,type,
vNOT: $o > $o ).
thf(func_def_22,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_23,type,
vAND: $o > $o > $o ).
thf(func_def_24,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
vOR: $o > $o > $o ).
thf(func_def_26,type,
vIMP: $o > $o > $o ).
thf(func_def_27,type,
vIFF: $o > $o > $o ).
thf(func_def_28,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_29,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_32,type,
sK0: mworld ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
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,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
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(f19,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f22,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f3]) ).
thf(f23,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f22]) ).
thf(f26,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f27,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f26]) ).
thf(f30,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f31,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f30]) ).
thf(f40,plain,
mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ),
inference(rectify,[],[f12]) ).
thf(f41,plain,
( ( mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) )
= $true ),
inference(fool_elimination,[],[f40]) ).
thf(f46,plain,
mlocal @ ( mbox @ ( dest @ paris ) ),
inference(rectify,[],[f15]) ).
thf(f47,plain,
( ( mlocal @ ( mbox @ ( dest @ paris ) ) )
= $true ),
inference(fool_elimination,[],[f46]) ).
thf(f48,plain,
mlocal @ ( mbox @ ( class @ second ) ),
inference(rectify,[],[f16]) ).
thf(f49,plain,
( ( mlocal @ ( mbox @ ( class @ second ) ) )
= $true ),
inference(fool_elimination,[],[f48]) ).
thf(f50,plain,
~ ( mlocal @ ( mbox @ ( price @ seventy ) ) ),
inference(rectify,[],[f18]) ).
thf(f51,plain,
( ( mlocal @ ( mbox @ ( price @ seventy ) ) )
!= $true ),
inference(fool_elimination,[],[f50]) ).
thf(f52,plain,
( ( mlocal @ ( mbox @ ( price @ seventy ) ) )
!= $true ),
inference(flattening,[],[f51]) ).
thf(f55,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f19]) ).
thf(f57,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f23]) ).
thf(f59,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f61,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f66,plain,
( ( mlocal @ ( mbox @ ( mimplies @ ( mand @ ( dest @ paris ) @ ( class @ second ) ) @ ( price @ seventy ) ) ) )
= $true ),
inference(cnf_transformation,[],[f41]) ).
thf(f69,plain,
( ( mlocal @ ( mbox @ ( dest @ paris ) ) )
= $true ),
inference(cnf_transformation,[],[f47]) ).
thf(f70,plain,
( ( mlocal @ ( mbox @ ( class @ second ) ) )
= $true ),
inference(cnf_transformation,[],[f49]) ).
thf(f71,plain,
( ( mlocal @ ( mbox @ ( price @ seventy ) ) )
!= $true ),
inference(cnf_transformation,[],[f52]) ).
thf(f75,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] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( dest @ paris )
@ ( class @ second ) )
@ ( price @ seventy ) ) ) ) ),
inference(definition_unfolding,[],[f66,f55,f61,f59,f57]) ).
thf(f78,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,[],[f69,f55,f61]) ).
thf(f79,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,[],[f70,f55,f61]) ).
thf(f80,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( price @ seventy ) ) ) ),
inference(definition_unfolding,[],[f71,f55,f61]) ).
thf(f81,plain,
( $true
!= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( price @ seventy @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f80]) ).
thf(f82,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( price @ seventy @ Y0 ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f81]) ).
thf(f83,plain,
( $false
= ( ( mrel @ mactual @ sK0 )
=> ( price @ seventy @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f82]) ).
thf(f84,plain,
( $false
= ( price @ seventy @ sK0 ) ),
inference(imp_proxy_clausification,[],[f83]) ).
thf(f85,plain,
( $true
= ( mrel @ mactual @ sK0 ) ),
inference(imp_proxy_clausification,[],[f83]) ).
thf(f86,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( class @ second @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f79]) ).
thf(f87,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( class @ second @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f86]) ).
thf(f88,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( class @ second @ X1 ) ) ),
inference(beta-eta_normalization,[],[f87]) ).
thf(f89,plain,
! [X1: mworld] :
( ( $true
= ( class @ second @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f88]) ).
thf(f90,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( dest @ paris @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f78]) ).
thf(f91,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( dest @ paris @ Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f90]) ).
thf(f92,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( dest @ paris @ X1 ) ) ),
inference(beta-eta_normalization,[],[f91]) ).
thf(f93,plain,
! [X1: mworld] :
( ( $true
= ( dest @ paris @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f92]) ).
thf(f106,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ( dest @ paris @ Y0 )
& ( class @ second @ Y0 ) )
=> ( price @ seventy @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f75]) ).
thf(f107,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( ( dest @ paris @ Y0 )
& ( class @ second @ Y0 ) )
=> ( price @ seventy @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f106]) ).
thf(f108,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( ( ( dest @ paris @ X1 )
& ( class @ second @ X1 ) )
=> ( price @ seventy @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f107]) ).
thf(f109,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ( ( dest @ paris @ X1 )
& ( class @ second @ X1 ) )
=> ( price @ seventy @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f108]) ).
thf(f110,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ( dest @ paris @ X1 )
& ( class @ second @ X1 ) ) )
| ( $true
= ( price @ seventy @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f109]) ).
thf(f111,plain,
! [X1: mworld] :
( ( $false
= ( class @ second @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( price @ seventy @ X1 ) )
| ( $false
= ( dest @ paris @ X1 ) ) ),
inference(and_proxy_clausification,[],[f110]) ).
thf(f165,plain,
! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true
= ( price @ seventy @ X0 ) )
| ( $false
= ( dest @ paris @ X0 ) ) ),
inference(constrained_superposition,[],[f89,f111]) ).
thf(f166,plain,
! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true
= ( price @ seventy @ X0 ) )
| ( $false
= ( dest @ paris @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f165]) ).
thf(f167,plain,
! [X0: mworld] :
( ( $false
= ( dest @ paris @ X0 ) )
| ( $true
= ( price @ seventy @ X0 ) )
| ( $false
= ( mrel @ mactual @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f166]) ).
thf(f272,plain,
! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true
= ( price @ seventy @ X0 ) )
| ( $false
= ( mrel @ mactual @ X0 ) ) ),
inference(constrained_superposition,[],[f93,f167]) ).
thf(f273,plain,
! [X0: mworld] :
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ X0 ) )
| ( $true
= ( price @ seventy @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f272]) ).
thf(f274,plain,
! [X0: mworld] :
( ( $true
= ( price @ seventy @ X0 ) )
| ( $false
= ( mrel @ mactual @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f273]) ).
thf(f386,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ sK0 ) ) ),
inference(constrained_superposition,[],[f84,f274]) ).
thf(f387,plain,
( $false
= ( mrel @ mactual @ sK0 ) ),
inference(trivial_inequality_removal,[],[f386]) ).
thf(f400,plain,
$true = $false,
inference(constrained_superposition,[],[f85,f387]) ).
thf(f407,plain,
$false,
inference(trivial_inequality_removal,[],[f400]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NLP267^5 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n018.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 11:53:41 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.08/0.25 % (4181346)Will run a generic schedule for satisfiability detection.
% 0.08/0.25 % (4181356)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=868595782:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.08/0.25 % (4181352)% WARNING: option uhcvi not known.
% 0.08/0.25 % (4181352)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1047285178:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.08/0.25 % (4181352)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.08/0.25 % (4181352)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.08/0.25 % (4181356) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4181346-4181356"...
% 0.08/0.25 % (4181356)...printing done.
% 0.08/0.25 % (4181351)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1406401427_2999 on theBenchmark for (2999ds/0Mi)
% 0.08/0.25 % (4181356)Refutation found. Thanks to Tanya!
% 0.08/0.25 % SZS status Theorem for theBenchmark
% 0.08/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.25 % (4181356)------------------------------
% 0.08/0.25 % (4181356)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.25 % (4181356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.25 % (4181356)CaDiCaL version: 2.1.3
% 0.08/0.25 % (4181356)Termination reason: Refutation
% 0.08/0.25 % (4181356)Time elapsed: 0.008 s
% 0.08/0.25 % (4181356)Peak memory usage: 12 MB
% 0.08/0.25 % (4181356)Instructions burned: 26 (million)
% 0.08/0.25 % (4181346)Success in time 0.035 s
% 0.08/0.25 % Vampire exiting
%------------------------------------------------------------------------------