%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ081^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 08:20:51 AM UTC 2026
% Result : Theorem 0.09s 0.29s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 94 ( 11 unt; 0 typ; 5 def)
% Number of atoms : 661 ( 148 equ; 0 cnn)
% Maximal formula atoms : 10 ( 7 avg)
% Number of connectives : 489 ( 96 ~; 110 |; 17 &; 234 @)
% ( 7 <=>; 17 =>; 0 <=; 8 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 12 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 39 !; 8 ?; 47 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
says: $i > $o > $o ).
thf(func_def_6,type,
is_a: $i > $i > $o ).
thf(func_def_8,type,
vNOT: $o > $o ).
thf(func_def_9,type,
vOR: $o > $o > $o ).
thf(f1,axiom,
! [X0: $i] :
( ( is_a @ X0 @ islander )
=> ( ( is_a @ X0 @ knave )
| ( is_a @ X0 @ knight ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kk_6_1) ).
thf(f2,axiom,
! [X0: $i] :
( ( is_a @ X0 @ knight )
=> ! [X1: $o] :
( ( says @ X0 @ X1 )
=> X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kk_6_2) ).
thf(f3,axiom,
! [X0: $i] :
( ( is_a @ X0 @ knave )
=> ! [X1: $o] :
( ( says @ X0 @ X1 )
=> ~ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kk_6_3) ).
thf(f4,axiom,
( ( is_a @ mel @ islander )
& ( is_a @ zoey @ islander ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kk_6_4) ).
thf(f5,axiom,
says @ zoey @ ( is_a @ mel @ knave ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kk_6_5) ).
thf(f7,conjecture,
? [X1: $i,X0: $i] :
( ( ( X0 = knight )
<~> ( X0 = knave ) )
& ( is_a @ zoey @ X1 )
& ( ( X1 = knight )
<~> ( X1 = knave ) )
& ( is_a @ mel @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',query) ).
thf(f8,negated_conjecture,
~ ? [X1: $i,X0: $i] :
( ( ( X0 = knight )
<~> ( X0 = knave ) )
& ( is_a @ zoey @ X1 )
& ( ( X1 = knight )
<~> ( X1 = knave ) )
& ( is_a @ mel @ X0 ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f11,plain,
( ( is_a @ mel @ islander )
& ( is_a @ zoey @ islander ) ),
inference(rectify,[],[f4]) ).
thf(f12,plain,
( ( ( is_a @ zoey @ islander )
= $true )
& ( ( is_a @ mel @ islander )
= $true ) ),
inference(fool_elimination,[],[f11]) ).
thf(f13,plain,
! [X0: $i] :
( ( is_a @ X0 @ islander )
=> ( ( is_a @ X0 @ knave )
| ( is_a @ X0 @ knight ) ) ),
inference(rectify,[],[f1]) ).
thf(f14,plain,
! [X0: $i] :
( ( ( is_a @ X0 @ islander )
= $true )
=> ( ( ( is_a @ X0 @ knight )
= $true )
| ( ( is_a @ X0 @ knave )
= $true ) ) ),
inference(fool_elimination,[],[f13]) ).
thf(f15,plain,
! [X0: $i] :
( ( is_a @ X0 @ knave )
=> ! [X1: $o] :
( ( says @ X0 @ X1 )
=> ~ X1 ) ),
inference(rectify,[],[f3]) ).
thf(f16,plain,
! [X0: $i] :
( ( ( is_a @ X0 @ knave )
= $true )
=> ! [X1: $o] :
( ( ( says @ X0 @ X1 )
= $true )
=> ( $true != X1 ) ) ),
inference(fool_elimination,[],[f15]) ).
thf(f17,plain,
! [X0: $i] :
( ( is_a @ X0 @ knight )
=> ! [X1: $o] :
( ( says @ X0 @ X1 )
=> X1 ) ),
inference(rectify,[],[f2]) ).
thf(f18,plain,
! [X0: $i] :
( ( ( is_a @ X0 @ knight )
= $true )
=> ! [X1: $o] :
( ( ( says @ X0 @ X1 )
= $true )
=> ( $true = X1 ) ) ),
inference(fool_elimination,[],[f17]) ).
thf(f19,plain,
says @ zoey @ ( is_a @ mel @ knave ),
inference(rectify,[],[f5]) ).
thf(f20,plain,
( ( says @ zoey @ ( is_a @ mel @ knave ) )
= $true ),
inference(fool_elimination,[],[f19]) ).
thf(f21,plain,
~ ? [X0: $i,X1: $i] :
( ( ( knight = X1 )
<~> ( knave = X1 ) )
& ( is_a @ zoey @ X0 )
& ( ( knight = X0 )
<~> ( knave = X0 ) )
& ( is_a @ mel @ X1 ) ),
inference(rectify,[],[f8]) ).
thf(f22,plain,
~ ? [X0: $i,X1: $i] :
( ( $true
= ( is_a @ mel @ X1 ) )
& ( ( knave = X1 )
<~> ( knight = X1 ) )
& ( ( is_a @ zoey @ X0 )
= $true )
& ( ( knave = X0 )
<~> ( knight = X0 ) ) ),
inference(fool_elimination,[],[f21]) ).
thf(f23,plain,
! [X0: $i] :
( ( ( is_a @ X0 @ knave )
= $true )
=> ! [X1: $o] :
( ( ( says @ X0 @ X1 )
= $true )
=> ( $true != X1 ) ) ),
inference(flattening,[],[f16]) ).
thf(f24,plain,
! [X0: $i] :
( ! [X1: $o] :
( ( $true != X1 )
| ( ( says @ X0 @ X1 )
!= $true ) )
| ( ( is_a @ X0 @ knave )
!= $true ) ),
inference(ennf_transformation,[],[f23]) ).
thf(f25,plain,
! [X0: $i,X1: $i] :
( ( ( is_a @ zoey @ X0 )
!= $true )
| ( $true
!= ( is_a @ mel @ X1 ) )
| ( ( knave = X1 )
<=> ( knight = X1 ) )
| ( ( knave = X0 )
<=> ( knight = X0 ) ) ),
inference(ennf_transformation,[],[f22]) ).
thf(f26,plain,
! [X0: $i] :
( ( ( is_a @ X0 @ knight )
= $true )
| ( ( is_a @ X0 @ knave )
= $true )
| ( ( is_a @ X0 @ islander )
!= $true ) ),
inference(ennf_transformation,[],[f14]) ).
thf(f27,plain,
! [X0: $i] :
( ( ( is_a @ X0 @ knave )
= $true )
| ( ( is_a @ X0 @ knight )
= $true )
| ( ( is_a @ X0 @ islander )
!= $true ) ),
inference(flattening,[],[f26]) ).
thf(f28,plain,
! [X0: $i] :
( ! [X1: $o] :
( ( $true = X1 )
| ( ( says @ X0 @ X1 )
!= $true ) )
| ( ( is_a @ X0 @ knight )
!= $true ) ),
inference(ennf_transformation,[],[f18]) ).
thf(f29,plain,
! [X0: $i,X1: $i] :
( ( ( is_a @ zoey @ X0 )
!= $true )
| ( $true
!= ( is_a @ mel @ X1 ) )
| ( ( ( knave = X1 )
| ( knight != X1 ) )
& ( ( knight = X1 )
| ( knave != X1 ) ) )
| ( ( ( knave = X0 )
| ( knight != X0 ) )
& ( ( knight = X0 )
| ( knave != X0 ) ) ) ),
inference(nnf_transformation,[],[f25]) ).
thf(f30,plain,
( ( is_a @ mel @ islander )
= $true ),
inference(cnf_transformation,[],[f12]) ).
thf(f31,plain,
( ( is_a @ zoey @ islander )
= $true ),
inference(cnf_transformation,[],[f12]) ).
thf(f33,plain,
! [X0: $i,X1: $i] :
( ( ( is_a @ zoey @ X0 )
!= $true )
| ( $true
!= ( is_a @ mel @ X1 ) )
| ( knight = X1 )
| ( knave != X1 )
| ( knave = X0 )
| ( knight != X0 ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f34,plain,
! [X0: $i,X1: $i] :
( ( ( is_a @ zoey @ X0 )
!= $true )
| ( $true
!= ( is_a @ mel @ X1 ) )
| ( knave = X1 )
| ( knight != X1 )
| ( knight = X0 )
| ( knave != X0 ) ),
inference(cnf_transformation,[],[f29]) ).
thf(f36,plain,
! [X0: $i,X1: $o] :
( ( $true != X1 )
| ( ( says @ X0 @ X1 )
!= $true )
| ( ( is_a @ X0 @ knave )
!= $true ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f37,plain,
! [X0: $i,X1: $o] :
( ( ( says @ X0 @ X1 )
!= $true )
| ( ( is_a @ X0 @ knight )
!= $true )
| ( $true = X1 ) ),
inference(cnf_transformation,[],[f28]) ).
thf(f39,plain,
( ( says @ zoey @ ( is_a @ mel @ knave ) )
= $true ),
inference(cnf_transformation,[],[f20]) ).
thf(f40,plain,
! [X0: $i] :
( ( ( is_a @ X0 @ islander )
!= $true )
| ( ( is_a @ X0 @ knave )
= $true )
| ( ( is_a @ X0 @ knight )
= $true ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f45,plain,
! [X0: $i] :
( ( ( is_a @ zoey @ X0 )
!= $true )
| ( ( is_a @ mel @ knight )
!= $true )
| ( knight = knave )
| ( knight = X0 )
| ( knave != X0 ) ),
inference(equality_resolution,[],[f34]) ).
thf(f46,plain,
( ( ( is_a @ mel @ knight )
!= $true )
| ( knight = knave )
| ( ( is_a @ zoey @ knave )
!= $true )
| ( knight = knave ) ),
inference(equality_resolution,[],[f45]) ).
thf(f47,plain,
! [X0: $i] :
( ( ( is_a @ zoey @ X0 )
!= $true )
| ( ( is_a @ mel @ knave )
!= $true )
| ( knight = knave )
| ( knave = X0 )
| ( knight != X0 ) ),
inference(equality_resolution,[],[f33]) ).
thf(f48,plain,
( ( knight = knave )
| ( ( is_a @ zoey @ knight )
!= $true )
| ( ( is_a @ mel @ knave )
!= $true )
| ( knight = knave ) ),
inference(equality_resolution,[],[f47]) ).
thf(f51,plain,
! [X0: $i] :
( ( ( says @ X0 @ $true )
!= $true )
| ( ( is_a @ X0 @ knave )
!= $true ) ),
inference(equality_resolution,[],[f36]) ).
thf(f52,plain,
( ( ( is_a @ zoey @ knave )
!= $true )
| ( knight = knave )
| ( ( is_a @ mel @ knight )
!= $true ) ),
inference(duplicate_literal_removal,[],[f46]) ).
thf(f53,plain,
( ( ( is_a @ zoey @ knight )
!= $true )
| ( ( is_a @ mel @ knave )
!= $true )
| ( knight = knave ) ),
inference(duplicate_literal_removal,[],[f48]) ).
thf(f57,definition,
( spl0_1
<=> ( ( is_a @ mel @ knight )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f59,plain,
( ( ( is_a @ mel @ knight )
!= $true )
| spl0_1 ),
inference(avatar_component_clause,[],[f57]) ).
thf(f61,definition,
( spl0_2
<=> ( ( is_a @ zoey @ knave )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f63,plain,
( ( ( is_a @ zoey @ knave )
!= $true )
| spl0_2 ),
inference(avatar_component_clause,[],[f61]) ).
thf(f65,definition,
( spl0_3
<=> ( knight = knave ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f67,plain,
( ( knight = knave )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f65]) ).
thf(f68,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f52,f65,f61,f57]) ).
thf(f70,definition,
( spl0_4
<=> ( ( is_a @ mel @ knave )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
thf(f71,plain,
( ( ( is_a @ mel @ knave )
= $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f70]) ).
thf(f72,plain,
( ( ( is_a @ mel @ knave )
!= $true )
| spl0_4 ),
inference(avatar_component_clause,[],[f70]) ).
thf(f74,definition,
( spl0_5
<=> ( ( is_a @ zoey @ knight )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
thf(f76,plain,
( ( ( is_a @ zoey @ knight )
!= $true )
| spl0_5 ),
inference(avatar_component_clause,[],[f74]) ).
thf(f77,plain,
( ~ spl0_4
| spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f53,f74,f65,f70]) ).
thf(f80,plain,
( ( ( is_a @ zoey @ knight )
!= $true )
| ( ( is_a @ mel @ knave )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f37,f39]) ).
thf(f81,plain,
( ( ( is_a @ zoey @ knight )
!= $true )
| ( ( is_a @ mel @ knave )
= $true ) ),
inference(trivial_inequality_removal,[],[f80]) ).
thf(f82,plain,
( ( ( is_a @ zoey @ knight )
!= $true )
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f81,f72]) ).
thf(f83,plain,
( ~ spl0_5
| spl0_4 ),
inference(avatar_split_clause,[],[f82,f70,f74]) ).
thf(f84,plain,
( ( ( is_a @ mel @ knave )
= $true )
| ( ( is_a @ mel @ knight )
= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f40,f30]) ).
thf(f85,plain,
( ( ( is_a @ zoey @ knave )
= $true )
| ( $true != $true )
| ( ( is_a @ zoey @ knight )
= $true ) ),
inference(constrained_superposition,[],[f40,f31]) ).
thf(f86,plain,
( ( ( is_a @ zoey @ knight )
= $true )
| ( ( is_a @ zoey @ knave )
= $true ) ),
inference(trivial_inequality_removal,[],[f85]) ).
thf(f87,plain,
( ( ( is_a @ mel @ knave )
= $true )
| ( ( is_a @ mel @ knight )
= $true ) ),
inference(trivial_inequality_removal,[],[f84]) ).
thf(f88,plain,
( ( ( is_a @ zoey @ knave )
= $true )
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f86,f76]) ).
thf(f89,plain,
( ( ( is_a @ mel @ knave )
= $true )
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f87,f59]) ).
thf(f90,plain,
( spl0_2
| spl0_5 ),
inference(avatar_split_clause,[],[f88,f74,f61]) ).
thf(f91,plain,
( $false
| spl0_1
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f89,f72]) ).
thf(f92,plain,
( spl0_1
| spl0_4 ),
inference(avatar_contradiction_clause,[],[f91]) ).
thf(f93,plain,
( ( ( is_a @ mel @ knight )
= $true )
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f87,f72]) ).
thf(f95,plain,
( ( ( is_a @ mel @ knave )
= $true )
| ~ spl0_3
| spl0_4 ),
inference(forward_demodulation,[],[f93,f67]) ).
thf(f98,plain,
( $false
| ~ spl0_3
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f95,f72]) ).
thf(f99,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_contradiction_clause,[],[f98]) ).
thf(f105,plain,
( ( ( says @ zoey @ $true )
= $true )
| ~ spl0_4 ),
inference(constrained_superposition,[],[f39,f71]) ).
thf(f106,plain,
( ( $true != $true )
| ( ( is_a @ zoey @ knave )
!= $true )
| ~ spl0_4 ),
inference(constrained_superposition,[],[f51,f105]) ).
thf(f107,plain,
( ( ( is_a @ zoey @ knave )
!= $true )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f106]) ).
thf(f110,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f107,f70,f61]) ).
thf(f111,plain,
( ( ( is_a @ zoey @ knight )
= $true )
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f86,f63]) ).
thf(f114,plain,
( ( ( is_a @ zoey @ knave )
= $true )
| spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f111,f67]) ).
thf(f115,plain,
( $false
| spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f114,f63]) ).
thf(f116,plain,
( spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f115]) ).
cnf(s1,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f68]) ).
cnf(s2,plain,
( spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f77]) ).
cnf(s5,plain,
( spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f83]) ).
cnf(s6,plain,
( spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f90]) ).
cnf(s7,plain,
( spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f92]) ).
cnf(s9,plain,
( ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f99]) ).
cnf(s13,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f110]) ).
cnf(s15,plain,
( spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f116]) ).
cnf(s16,plain,
~ spl0_4,
inference(rat,[],[s2,s6,s15,s13]) ).
cnf(s17,plain,
~ spl0_3,
inference(rat,[],[s9,s16]) ).
cnf(s18,plain,
spl0_1,
inference(rat,[],[s7,s16]) ).
cnf(s19,plain,
~ spl0_5,
inference(rat,[],[s5,s16]) ).
cnf(s20,plain,
~ spl0_2,
inference(rat,[],[s1,s17,s18]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s6,s19,s20]) ).
thf(f117,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ081^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n015.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % 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 13:25:03 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running higher-order theorem proving
% 0.09/0.26 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
% 0.09/0.29 % (3503346)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.09/0.29 % (3503351)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=638191367:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.09/0.29 % (3503351) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3503346-3503351"...
% 0.09/0.29 % (3503351)...printing done.
% 0.09/0.29 % (3503357)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.09/0.29 % (3503357)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
% 0.09/0.29 % (3503351)Refutation found. Thanks to Tanya!
% 0.09/0.29 % SZS status Theorem for theBenchmark
% 0.09/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.29 % (3503351)------------------------------
% 0.09/0.29 % (3503351)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.29 % (3503351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.29 % (3503351)CaDiCaL version: 2.1.3
% 0.09/0.29 % (3503351)Termination reason: Refutation
% 0.09/0.29 % (3503351)Time elapsed: 0.003 s
% 0.09/0.29 % (3503351)Peak memory usage: 13 MB
% 0.09/0.29 % (3503351)Instructions burned: 7 (million)
% 0.09/0.29 % (3503346)Success in time 0.021 s
% 0.09/0.29 % Vampire exiting
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