%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NLP265^18 : 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 : 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 08:16:31 AM UTC 2026
% Result : ContradictoryAxioms 0.25s 0.34s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 242 ( 54 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 302 ( 12 ~; 13 |; 0 &; 247 @)
% ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 92 ( 50 ^; 42 !; 0 ?; 92 :)
% 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_17,type,
vOR: $o > $o > $o ).
thf(func_def_18,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_19,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_20,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_21,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_24,type,
vNOT: $o > $o ).
thf(func_def_25,type,
vAND: $o > $o > $o ).
thf(func_def_26,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_27,type,
vIMP: $o > $o > $o ).
thf(func_def_28,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_29,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $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 ).
thf(func_def_34,type,
sK3: mworld ).
thf(func_def_35,type,
sK4: mworld > mworld ).
thf(func_def_36,type,
sK5: mworld > mworld ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mlocal_def) ).
thf(f2,axiom,
( ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) )
= mnot ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot_def) ).
thf(f7,axiom,
( ( ^ [X0: mindex,X1: mworld > $o,X2: mworld] :
! [X3: mworld] :
( ( mrel @ X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_def) ).
thf(f11,axiom,
! [X0: mworld,X1: mworld] : ( mrel @ '#b_alice' @ X0 @ X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_#b_alice_universal') ).
thf(f12,axiom,
! [X1: mworld,X0: mworld] : ( mrel @ '#b_bob' @ X0 @ X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mrel_#b_bob_universal') ).
thf(f15,axiom,
mlocal @ ( mbox @ '#b_alice' @ ( bigcity @ portland ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
thf(f16,axiom,
mlocal @ ( mbox @ '#b_alice' @ ( mbox @ '#b_bob' @ ( mnot @ ( bigcity @ portland ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(f21,plain,
mlocal @ ( mbox @ '#b_alice' @ ( bigcity @ portland ) ),
inference(rectify,[],[f15]) ).
thf(f22,plain,
( ( mlocal @ ( mbox @ '#b_alice' @ ( bigcity @ portland ) ) )
= $true ),
inference(fool_elimination,[],[f21]) ).
thf(f25,plain,
! [X0: mworld,X1: mworld] : ( mrel @ '#b_bob' @ X1 @ X0 ),
inference(rectify,[],[f12]) ).
thf(f26,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ '#b_bob' @ X1 @ X0 )
= $true ),
inference(fool_elimination,[],[f25]) ).
thf(f27,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) )
= mnot ),
inference(rectify,[],[f2]) ).
thf(f28,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f27]) ).
thf(f35,plain,
( ( ^ [X0: mindex,X1: mworld > $o,X2: mworld] :
! [X3: mworld] :
( ( mrel @ X0 @ X2 @ X3 )
=> ( X1 @ X3 ) ) )
= mbox ),
inference(rectify,[],[f7]) ).
thf(f36,plain,
( mbox
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(fool_elimination,[],[f35]) ).
thf(f39,plain,
mlocal @ ( mbox @ '#b_alice' @ ( mbox @ '#b_bob' @ ( mnot @ ( bigcity @ portland ) ) ) ),
inference(rectify,[],[f16]) ).
thf(f40,plain,
( ( mlocal @ ( mbox @ '#b_alice' @ ( mbox @ '#b_bob' @ ( mnot @ ( bigcity @ portland ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f39]) ).
thf(f49,plain,
! [X0: mworld,X1: mworld] : ( mrel @ '#b_alice' @ X0 @ X1 ),
inference(rectify,[],[f11]) ).
thf(f50,plain,
! [X1: mworld,X0: mworld] :
( ( mrel @ '#b_alice' @ X0 @ X1 )
= $true ),
inference(fool_elimination,[],[f49]) ).
thf(f51,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f53,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ '#b_alice' @ X1 @ X0 )
= $true ),
inference(rectify,[],[f50]) ).
thf(f55,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[],[f51]) ).
thf(f58,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ '#b_alice' @ X1 @ X0 )
= $true ),
inference(cnf_transformation,[],[f53]) ).
thf(f64,plain,
( mbox
= ( ^ [Y0: mindex,Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y0 @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) ) ) ),
inference(cnf_transformation,[],[f36]) ).
thf(f65,plain,
( ( mlocal @ ( mbox @ '#b_alice' @ ( bigcity @ portland ) ) )
= $true ),
inference(cnf_transformation,[],[f22]) ).
thf(f66,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f67,plain,
( ( mlocal @ ( mbox @ '#b_alice' @ ( mbox @ '#b_bob' @ ( mnot @ ( bigcity @ portland ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f40]) ).
thf(f70,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ '#b_bob' @ X1 @ X0 )
= $true ),
inference(cnf_transformation,[],[f26]) ).
thf(f75,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,[],[f65,f55,f64]) ).
thf(f76,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,[],[f67,f55,f64,f64,f66]) ).
thf(f79,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b_alice' @ mactual @ Y0 )
=> ( bigcity @ portland @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f75]) ).
thf(f80,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ '#b_alice' @ mactual @ Y0 )
=> ( bigcity @ portland @ Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f79]) ).
thf(f81,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ '#b_alice' @ mactual @ X1 )
=> ( bigcity @ portland @ X1 ) ) ),
inference(beta-eta_normalization,[],[f80]) ).
thf(f82,plain,
! [X1: mworld] :
( ( ( mrel @ '#b_alice' @ mactual @ X1 )
= $false )
| ( $true
= ( bigcity @ portland @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f81]) ).
thf(f135,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b_alice' @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#b_bob' @ Y0 @ Y1 )
=> ~ ( bigcity @ portland @ Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f76]) ).
thf(f136,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#b_alice' @ mactual @ Y0 )
=> ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ '#b_bob' @ Y0 @ Y1 )
=> ~ ( bigcity @ portland @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f135]) ).
thf(f137,plain,
! [X1: mworld] :
( ( ( mrel @ '#b_alice' @ mactual @ X1 )
=> ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ '#b_bob' @ X1 @ Y0 )
=> ~ ( bigcity @ portland @ Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f136]) ).
thf(f138,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,[],[f137]) ).
thf(f139,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ '#b_bob' @ X1 @ Y0 )
=> ~ ( bigcity @ portland @ Y0 ) )
@ X2 ) )
| ( ( mrel @ '#b_alice' @ mactual @ X1 )
= $false ) ),
inference(pi_proxy_clausification,[],[f138]) ).
thf(f140,plain,
! [X2: mworld,X1: mworld] :
( ( $true
= ( ( mrel @ '#b_bob' @ X1 @ X2 )
=> ~ ( bigcity @ portland @ X2 ) ) )
| ( ( mrel @ '#b_alice' @ mactual @ X1 )
= $false ) ),
inference(beta-eta_normalization,[],[f139]) ).
thf(f141,plain,
! [X2: mworld,X1: mworld] :
( ( ( ~ ( bigcity @ portland @ X2 ) )
= $true )
| ( ( mrel @ '#b_bob' @ X1 @ X2 )
= $false )
| ( ( mrel @ '#b_alice' @ mactual @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f140]) ).
thf(f142,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ '#b_alice' @ mactual @ X1 )
= $false )
| ( ( bigcity @ portland @ X2 )
= $false )
| ( ( mrel @ '#b_bob' @ X1 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[],[f141]) ).
thf(f147,plain,
! [X2: mworld,X1: mworld] :
( ( ( bigcity @ portland @ X2 )
= $false )
| ( ( mrel @ '#b_bob' @ X1 @ X2 )
= $false )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f142,f58]) ).
thf(f148,plain,
! [X2: mworld,X1: mworld] :
( ( ( mrel @ '#b_bob' @ X1 @ X2 )
= $false )
| ( ( bigcity @ portland @ X2 )
= $false ) ),
inference(trivial_inequality_removal,[],[f147]) ).
thf(f151,plain,
! [X2: mworld] :
( ( $true = $false )
| ( ( bigcity @ portland @ X2 )
= $false ) ),
inference(forward_demodulation,[],[f148,f70]) ).
thf(f152,plain,
! [X2: mworld] :
( ( bigcity @ portland @ X2 )
= $false ),
inference(trivial_inequality_removal,[],[f151]) ).
thf(f156,plain,
! [X0: mworld] :
( ( $true = $false )
| ( ( bigcity @ portland @ X0 )
= $true ) ),
inference(constrained_superposition,[],[f58,f82]) ).
thf(f157,plain,
! [X0: mworld] :
( ( bigcity @ portland @ X0 )
= $true ),
inference(trivial_inequality_removal,[],[f156]) ).
thf(f159,plain,
$true = $false,
inference(forward_demodulation,[],[f157,f152]) ).
thf(f160,plain,
$false,
inference(trivial_inequality_removal,[],[f159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NLP265^18 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n002.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 11:46:07 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.27 Running higher-order theorem proving
% 0.25/0.29 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
% 0.25/0.34 % (1173942)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.25/0.34 % (1173948)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2783617089:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.25/0.34 % (1173954)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.25/0.34 % (1173954)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.25/0.34 % (1173948) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1173942-1173948"...
% 0.25/0.34 % (1173953)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3098378023:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.25/0.34 % (1173952)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2881702298:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.25/0.34 % (1173951)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=3098294355: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)
% 0.25/0.34 % (1173950)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1345904141:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.25/0.34 % (1173954)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3085329754:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.25/0.34 % (1173948)...printing done.
% 0.25/0.34 % (1173948)Refutation found. Thanks to Tanya!
% 0.25/0.34 % SZS status ContradictoryAxioms for theBenchmark
% 0.25/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.34 % (1173948)------------------------------
% 0.25/0.34 % (1173948)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.34 % (1173948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.34 % (1173948)CaDiCaL version: 2.1.3
% 0.25/0.34 % (1173948)Termination reason: Refutation
% 0.25/0.34 % (1173948)Time elapsed: 0.009 s
% 0.25/0.34 % (1173948)Peak memory usage: 13 MB
% 0.25/0.34 % (1173948)Instructions burned: 13 (million)
% 0.25/0.34 % (1173942)Success in time 0.037 s
% 0.25/0.34 % Vampire exiting
%------------------------------------------------------------------------------