%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NLP265^17 : 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 : n007.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 : ContradictoryAxioms 0.21s 0.32s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 239 ( 53 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 299 ( 12 ~; 13 |; 0 &; 244 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Number of types : 4 ( 2 usr)
% Number of type conns : 17 ( 17 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 35 usr; 11 con; 0-4 aty)
% ( 11 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 76 ( 50 ^; 26 !; 0 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(type_def_6,type,
mindex: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
mrel: mindex > mworld > mworld > $o ).
thf(func_def_1,type,
'#i_alice': mindex ).
thf(func_def_2,type,
'#i_bob': mindex ).
thf(func_def_3,type,
'#b_alice': mindex ).
thf(func_def_4,type,
'#b_bob': mindex ).
thf(func_def_5,type,
mactual: mworld ).
thf(func_def_6,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_8,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
mbox: mindex > ( mworld > $o ) > mworld > $o ).
thf(func_def_14,type,
mdia: mindex > ( mworld > $o ) > mworld > $o ).
thf(func_def_16,type,
bigcity: $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_23,type,
vOR: $o > $o > $o ).
thf(func_def_24,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_25,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_26,type,
vAND: $o > $o > $o ).
thf(func_def_27,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_28,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_29,type,
vIMP: $o > $o > $o ).
thf(func_def_30,type,
vIFF: $o > $o > $o ).
thf(func_def_31,type,
sK0: mworld > mworld ).
thf(func_def_32,type,
sK1: mworld > mworld ).
thf(func_def_33,type,
sK2: mworld > mworld ).
thf(func_def_34,type,
sK3: mworld > mworld ).
thf(func_def_35,type,
sK4: mworld ).
thf(func_def_36,type,
sK5: mworld ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mlocal_def) ).
thf(f2,axiom,
( ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot_def) ).
thf(f7,axiom,
( mbox
= ( ^ [X0: mindex,X1: mworld > $o,X2: mworld] :
! [X3: mworld] :
( ( mrel @ X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_def) ).
thf(f13,axiom,
! [X0: mworld] : ( mrel @ '#b_alice' @ X0 @ X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','mrel_#b_alice_reflexive') ).
thf(f15,axiom,
! [X0: mworld] : ( mrel @ '#b_bob' @ X0 @ X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','mrel_#b_bob_reflexive') ).
thf(f19,axiom,
mlocal @ ( mbox @ '#b_alice' @ ( bigcity @ portland ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
thf(f20,axiom,
mlocal @ ( mbox @ '#b_alice' @ ( mbox @ '#b_bob' @ ( mnot @ ( bigcity @ portland ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
thf(f25,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f2]) ).
thf(f26,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f25]) ).
thf(f27,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f28,plain,
mlocal @ ( mbox @ '#b_alice' @ ( mbox @ '#b_bob' @ ( mnot @ ( bigcity @ portland ) ) ) ),
inference(rectify,[],[f20]) ).
thf(f29,plain,
( ( mlocal @ ( mbox @ '#b_alice' @ ( mbox @ '#b_bob' @ ( mnot @ ( bigcity @ portland ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f28]) ).
thf(f40,plain,
mlocal @ ( mbox @ '#b_alice' @ ( bigcity @ portland ) ),
inference(rectify,[],[f19]) ).
thf(f41,plain,
( ( mlocal @ ( mbox @ '#b_alice' @ ( bigcity @ portland ) ) )
= $true ),
inference(fool_elimination,[],[f40]) ).
thf(f44,plain,
! [X0: mworld] : ( mrel @ '#b_bob' @ X0 @ X0 ),
inference(rectify,[],[f15]) ).
thf(f45,plain,
! [X0: mworld] :
( ( mrel @ '#b_bob' @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f44]) ).
thf(f50,plain,
( mbox
= ( ^ [X0: mindex,X1: mworld > $o,X2: mworld] :
! [X3: mworld] :
( ( mrel @ X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) ) ),
inference(rectify,[],[f7]) ).
thf(f51,plain,
( mbox
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f50]) ).
thf(f60,plain,
! [X0: mworld] : ( mrel @ '#b_alice' @ X0 @ X0 ),
inference(rectify,[],[f13]) ).
thf(f61,plain,
! [X0: mworld] :
( ( mrel @ '#b_alice' @ X0 @ X0 )
= $true ),
inference(fool_elimination,[],[f60]) ).
thf(f77,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f82,plain,
( mbox
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f86,plain,
! [X0: mworld] :
( ( mrel @ '#b_alice' @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f61]) ).
thf(f89,plain,
( ( mlocal @ ( mbox @ '#b_alice' @ ( bigcity @ portland ) ) )
= $true ),
inference(cnf_transformation,[],[f41]) ).
thf(f90,plain,
( ( mlocal @ ( mbox @ '#b_alice' @ ( mbox @ '#b_bob' @ ( mnot @ ( bigcity @ portland ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f29]) ).
thf(f91,plain,
! [X0: mworld] :
( ( mrel @ '#b_bob' @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[],[f45]) ).
thf(f96,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f102,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#b_alice'
@ ( bigcity @ portland ) ) )
= $true ),
inference(definition_unfolding,[],[f89,f77,f82]) ).
thf(f103,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#b_alice'
@ ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ '#b_bob'
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 )
@ ( bigcity @ portland ) ) ) ) ) ),
inference(definition_unfolding,[],[f90,f77,f82,f82,f96]) ).
thf(f105,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b_alice' @ mactual @ Y0 )
=> ( bigcity @ portland @ Y0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f102]) ).
thf(f106,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ '#b_alice' @ mactual @ Y0 )
=> ( bigcity @ portland @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f105]) ).
thf(f107,plain,
! [X1: mworld] :
( ( ( mrel @ '#b_alice' @ mactual @ X1 )
=> ( bigcity @ portland @ X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f106]) ).
thf(f108,plain,
! [X1: mworld] :
( ( ( mrel @ '#b_alice' @ mactual @ X1 )
= $false )
| ( ( bigcity @ portland @ X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f107]) ).
thf(f109,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b_alice' @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#b_bob' @ Y0 @ Y1 )
=> ~ ( bigcity @ portland @ Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f103]) ).
thf(f110,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ '#b_alice' @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#b_bob' @ Y0 @ Y1 )
=> ~ ( bigcity @ portland @ Y1 ) ) ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f109]) ).
thf(f111,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ '#b_alice' @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b_bob' @ X1 @ Y0 )
=> ~ ( bigcity @ portland @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f110]) ).
thf(f112,plain,
! [X1: mworld] :
( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b_bob' @ X1 @ Y0 )
=> ~ ( bigcity @ portland @ Y0 ) ) )
= $true )
| ( ( mrel @ '#b_alice' @ mactual @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f111]) ).
thf(f113,plain,
! [X2: mworld,X1: mworld] :
( ( ( ^ [Y0: mworld] :
( ( mrel @ '#b_bob' @ X1 @ Y0 )
=> ~ ( bigcity @ portland @ Y0 ) )
@ X2 )
= $true )
| ( ( mrel @ '#b_alice' @ mactual @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f112]) ).
thf(f114,plain,
! [X2: mworld,X1: mworld] :
( ( ( ( mrel @ '#b_bob' @ X1 @ X2 )
=> ~ ( bigcity @ portland @ X2 ) )
= $true )
| ( ( mrel @ '#b_alice' @ mactual @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f113]) ).
thf(f115,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ '#b_alice' @ mactual @ X1 )
= $false )
| ( $false
= ( mrel @ '#b_bob' @ X1 @ X2 ) )
| ( ( ~ ( bigcity @ portland @ X2 ) )
= $true ) ),
inference(imp_proxy_clausification,[],[f114]) ).
thf(f116,plain,
! [X2: mworld,X1: mworld] :
( ( $false
= ( mrel @ '#b_bob' @ X1 @ X2 ) )
| ( $false
= ( bigcity @ portland @ X2 ) )
| ( ( mrel @ '#b_alice' @ mactual @ X1 )
= $false ) ),
inference(not_proxy_clausification,[],[f115]) ).
thf(f174,plain,
( ( ( bigcity @ portland @ mactual )
= $true )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f86,f108]) ).
thf(f175,plain,
( ( bigcity @ portland @ mactual )
= $true ),
inference(trivial_inequality_removal,[],[f174]) ).
thf(f180,plain,
! [X0: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ '#b_alice' @ mactual @ X0 ) )
| ( ( bigcity @ portland @ X0 )
= $false ) ),
inference(constrained_superposition,[],[f91,f116]) ).
thf(f181,plain,
! [X0: mworld] :
( ( $false
= ( mrel @ '#b_alice' @ mactual @ X0 ) )
| ( ( bigcity @ portland @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f180]) ).
thf(f185,plain,
( ( $false = $true )
| ( $false
= ( bigcity @ portland @ mactual ) ) ),
inference(constrained_superposition,[],[f181,f86]) ).
thf(f187,plain,
( $false
= ( bigcity @ portland @ mactual ) ),
inference(trivial_inequality_removal,[],[f185]) ).
thf(f189,plain,
$false = $true,
inference(forward_demodulation,[],[f187,f175]) ).
thf(f190,plain,
$false,
inference(trivial_inequality_removal,[],[f189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NLP265^17 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n007.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.21 % DateTime : Tue Sep 29 11:40:26 UTC 2026
% 0.08/0.21 % CPUTime :
% 0.08/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.25 Running higher-order theorem proving
% 0.21/0.27 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
% 0.21/0.32 % (3251338)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.32 % (3251347)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1577237385:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.32 % (3251343)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1299278062:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.32 % (3251345)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2290269855:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.32 % (3251348)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3856549763:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.32 % (3251346)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=3996392032: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)
% 0.21/0.32 % (3251345)Instruction limit reached!
% 0.21/0.32 % (3251345)------------------------------
% 0.21/0.32 % (3251345)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (3251345)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (3251345)CaDiCaL version: 2.1.3
% 0.21/0.32 % (3251345)Termination reason: Instruction limit
% 0.21/0.32 % (3251345)Termination phase: Property scanning
% 0.21/0.32 % (3251345)Time elapsed: 0.002 s
% 0.21/0.32 % (3251345)Peak memory usage: 10 MB
% 0.21/0.32 % (3251345)Instructions burned: 3 (million)
% 0.21/0.32 % (3251344)lrs+10_16_si=on:nwc=1.5:random_seed=1905178449:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.32 % (3251343) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3251338-3251343"...
% 0.21/0.32 % (3251348) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3251338-3251348"...
% 0.21/0.32 % (3251343)...printing done.
% 0.21/0.32 % (3251343)Refutation found. Thanks to Tanya!
% 0.21/0.32 % SZS status ContradictoryAxioms for theBenchmark
% 0.21/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.33 % (3251343)------------------------------
% 0.21/0.33 % (3251343)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.33 % (3251343)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.33 % (3251343)CaDiCaL version: 2.1.3
% 0.21/0.33 % (3251343)Termination reason: Refutation
% 0.21/0.33 % (3251343)Time elapsed: 0.008 s
% 0.21/0.33 % (3251343)Peak memory usage: 12 MB
% 0.21/0.33 % (3251343)Instructions burned: 15 (million)
% 0.21/0.33 % (3251338)Success in time 0.046 s
% 0.21/0.33 % Vampire exiting
%------------------------------------------------------------------------------