%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ081^2 : TPTP v9.3.1. Bugfixed v7.1.0.
% 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 08:20:51 AM UTC 2026
% Result : Theorem 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 55 ( 8 unt; 0 typ; 4 def)
% Number of atoms : 298 ( 84 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 223 ( 78 ~; 65 |; 16 &; 58 @)
% ( 4 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 21 !; 8 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_2,type,
knight: $i > $o ).
thf(func_def_3,type,
knave: $i > $o ).
thf(func_def_4,type,
says: $i > $o > $o ).
thf(func_def_8,type,
vAND: $o > $o > $o ).
thf(func_def_9,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X0: $i] :
( ( knave @ X0 )
<~> ( knight @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knights_xor_knaves) ).
thf(f6,conjecture,
? [X1: $i > $o,X0: $i > $o] :
( ( ( X0 = knave )
| ( X0 = knight ) )
& ( X1 @ mel )
& ( ( X1 = knight )
| ( X1 = knave ) )
& ( X0 @ zoey ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',what_are_zoey_and_mel) ).
thf(f7,negated_conjecture,
~ ? [X1: $i > $o,X0: $i > $o] :
( ( ( X0 = knave )
| ( X0 = knight ) )
& ( X1 @ mel )
& ( ( X1 = knight )
| ( X1 = knave ) )
& ( X0 @ zoey ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
! [X0: $i] :
( ( knave @ X0 )
<~> ( knight @ X0 ) ),
inference(rectify,[],[f1]) ).
thf(f9,plain,
! [X0: $i] :
( ( knight @ X0 )
!= ( knave @ X0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f14,plain,
~ ? [X0: $i > $o,X1: $i > $o] :
( ( ( knave = X1 )
| ( knight = X1 ) )
& ( X0 @ mel )
& ( ( knight = X0 )
| ( knave = X0 ) )
& ( X1 @ zoey ) ),
inference(rectify,[],[f7]) ).
thf(f15,plain,
~ ? [X1: $i > $o,X0: $i > $o] :
( ( $true
= ( X1 @ zoey ) )
& ( ( knave = X0 )
| ( knight = X0 ) )
& ( $true
= ( X0 @ mel ) )
& ( ( knight = X1 )
| ( knave = X1 ) ) ),
inference(fool_elimination,[],[f14]) ).
thf(f25,plain,
! [X1: $i > $o,X0: $i > $o] :
( ( $true
!= ( X0 @ mel ) )
| ( ( knight != X1 )
& ( knave != X1 ) )
| ( ( knave != X0 )
& ( knight != X0 ) )
| ( $true
!= ( X1 @ zoey ) ) ),
inference(ennf_transformation,[],[f15]) ).
thf(f26,plain,
! [X0: $i > $o,X1: $i > $o] :
( ( ( X1 @ mel )
!= $true )
| ( ( knight != X0 )
& ( knave != X0 ) )
| ( ( knave != X1 )
& ( knight != X1 ) )
| ( ( X0 @ zoey )
!= $true ) ),
inference(rectify,[],[f25]) ).
thf(f28,plain,
! [X0: $i] :
( ( knight @ X0 )
!= ( knave @ X0 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f30,plain,
! [X0: $i > $o,X1: $i > $o] :
( ( ( X1 @ mel )
!= $true )
| ( knave != X0 )
| ( knight != X1 )
| ( ( X0 @ zoey )
!= $true ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f31,plain,
! [X0: $i > $o,X1: $i > $o] :
( ( ( X1 @ mel )
!= $true )
| ( knave != X0 )
| ( knave != X1 )
| ( ( X0 @ zoey )
!= $true ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f32,plain,
! [X0: $i > $o,X1: $i > $o] :
( ( ( X1 @ mel )
!= $true )
| ( knight != X0 )
| ( knight != X1 )
| ( ( X0 @ zoey )
!= $true ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f33,plain,
! [X0: $i > $o,X1: $i > $o] :
( ( ( X1 @ mel )
!= $true )
| ( knight != X0 )
| ( knave != X1 )
| ( ( X0 @ zoey )
!= $true ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f37,plain,
! [X1: $i > $o] :
( ( ( X1 @ mel )
!= $true )
| ( knave != X1 )
| ( ( knight @ zoey )
!= $true ) ),
inference(equality_resolution,[],[f33]) ).
thf(f38,plain,
( ( ( knight @ zoey )
!= $true )
| ( ( knave @ mel )
!= $true ) ),
inference(equality_resolution,[],[f37]) ).
thf(f39,plain,
! [X1: $i > $o] :
( ( ( X1 @ mel )
!= $true )
| ( knight != X1 )
| ( ( knight @ zoey )
!= $true ) ),
inference(equality_resolution,[],[f32]) ).
thf(f40,plain,
( ( $true
!= ( knight @ mel ) )
| ( ( knight @ zoey )
!= $true ) ),
inference(equality_resolution,[],[f39]) ).
thf(f41,plain,
! [X1: $i > $o] :
( ( ( X1 @ mel )
!= $true )
| ( knave != X1 )
| ( ( knave @ zoey )
!= $true ) ),
inference(equality_resolution,[],[f31]) ).
thf(f42,plain,
( ( ( knave @ mel )
!= $true )
| ( ( knave @ zoey )
!= $true ) ),
inference(equality_resolution,[],[f41]) ).
thf(f43,plain,
! [X1: $i > $o] :
( ( ( X1 @ mel )
!= $true )
| ( knight != X1 )
| ( ( knave @ zoey )
!= $true ) ),
inference(equality_resolution,[],[f30]) ).
thf(f44,plain,
( ( ( knave @ zoey )
!= $true )
| ( $true
!= ( knight @ mel ) ) ),
inference(equality_resolution,[],[f43]) ).
thf(f46,plain,
! [X0: $i] :
( ( ( knave @ X0 )
= $true )
| ( ( knight @ X0 )
= $true ) ),
inference(xor_proxy_clausification,[],[f28]) ).
thf(f54,definition,
( spl0_2
<=> ( ( knave @ zoey )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f56,plain,
( ( ( knave @ zoey )
!= $true )
| spl0_2 ),
inference(avatar_component_clause,[],[f54]) ).
thf(f58,definition,
( spl0_3
<=> ( $true
= ( knight @ mel ) ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f60,plain,
( ( $true
!= ( knight @ mel ) )
| spl0_3 ),
inference(avatar_component_clause,[],[f58]) ).
thf(f61,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f44,f58,f54]) ).
thf(f63,definition,
( spl0_4
<=> ( ( knave @ mel )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
thf(f65,plain,
( ( ( knave @ mel )
!= $true )
| spl0_4 ),
inference(avatar_component_clause,[],[f63]) ).
thf(f66,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f42,f63,f54]) ).
thf(f68,definition,
( spl0_5
<=> ( ( knight @ zoey )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
thf(f70,plain,
( ( ( knight @ zoey )
!= $true )
| spl0_5 ),
inference(avatar_component_clause,[],[f68]) ).
thf(f71,plain,
( ~ spl0_5
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f40,f58,f68]) ).
thf(f72,plain,
( ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f38,f68,f63]) ).
thf(f223,plain,
( ( ( knight @ zoey )
= $true )
| ( $true != $true )
| spl0_2 ),
inference(superposition,[],[f56,f46]) ).
thf(f224,plain,
( ( ( knight @ zoey )
= $true )
| spl0_2 ),
inference(trivial_inequality_removal,[],[f223]) ).
thf(f225,plain,
( $false
| spl0_2
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f224,f70]) ).
thf(f226,plain,
( spl0_2
| spl0_5 ),
inference(avatar_contradiction_clause,[],[f225]) ).
thf(f238,plain,
( ( $true
= ( knight @ mel ) )
| ( $true != $true )
| spl0_4 ),
inference(superposition,[],[f65,f46]) ).
thf(f239,plain,
( ( $true
= ( knight @ mel ) )
| spl0_4 ),
inference(trivial_inequality_removal,[],[f238]) ).
thf(f240,plain,
( $false
| spl0_3
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f239,f60]) ).
thf(f241,plain,
( spl0_3
| spl0_4 ),
inference(avatar_contradiction_clause,[],[f240]) ).
cnf(s2,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f61]) ).
cnf(s3,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(sat_conversion,[],[f66]) ).
cnf(s4,plain,
( ~ spl0_3
| ~ spl0_5 ),
inference(sat_conversion,[],[f71]) ).
cnf(s5,plain,
( ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f72]) ).
cnf(s32,plain,
( spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f226]) ).
cnf(s35,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f241]) ).
cnf(s36,plain,
~ spl0_5,
inference(rat,[],[s35,s4,s5]) ).
cnf(s37,plain,
spl0_2,
inference(rat,[],[s32,s36]) ).
cnf(s40,plain,
~ spl0_4,
inference(rat,[],[s3,s37]) ).
cnf(s41,plain,
~ spl0_3,
inference(rat,[],[s2,s37]) ).
cnf(s42,plain,
$false,
inference(rat,[],[s35,s40,s41]) ).
thf(f242,plain,
$false,
inference(avatar_sat_refutation,[],[s42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ081^2 : TPTP v9.3.1. Bugfixed v7.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n002.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:24:07 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 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
% 0.21/0.28 % (1263504)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.28 % (1263512)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=2725839994: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)
% 0.21/0.28 % (1263512) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1263504-1263512"...
% 0.21/0.28 % (1263515)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.28 % (1263515)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
% 0.21/0.28 % (1263512)...printing done.
% 0.21/0.28 % (1263512)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Theorem for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (1263512)------------------------------
% 0.21/0.28 % (1263512)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (1263512)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (1263512)CaDiCaL version: 2.1.3
% 0.21/0.28 % (1263512)Termination reason: Refutation
% 0.21/0.28 % (1263512)Time elapsed: 0.004 s
% 0.21/0.28 % (1263512)Peak memory usage: 13 MB
% 0.21/0.28 % (1263512)Instructions burned: 9 (million)
% 0.21/0.28 % (1263504)Success in time 0.035 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------