%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ081^3 : TPTP v9.3.1. Released v3.6.0.
% 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 08:20:51 AM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 66 ( 11 unt; 0 typ; 4 def)
% Number of atoms : 290 ( 69 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 244 ( 70 ~; 49 |; 11 &; 101 @)
% ( 4 <=>; 7 =>; 0 <=; 2 <~>)
% Maximal formula depth : 7 ( 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 : 15 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 54 ( 0 sgn 46 !; 8 ?; 54 :)
% 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_6,type,
vAND: $o > $o > $o ).
thf(func_def_7,type,
vNOT: $o > $o ).
thf(f1,axiom,
! [X0: $i] :
( ( knight @ X0 )
<~> ( knave @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knights_xor_knaves) ).
thf(f2,axiom,
! [X0: $i,X1: $o] :
( ( ( says @ X0 @ X1 )
& ( knight @ X0 ) )
=> X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knights_tell_truth) ).
thf(f3,axiom,
! [X0: $i,X1: $o] :
( ( ( says @ X0 @ X1 )
& ( knave @ X0 ) )
=> ~ X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',knaves_lie) ).
thf(f4,axiom,
says @ zoey @ ( knave @ mel ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zoey_speaks) ).
thf(f6,conjecture,
? [X1: $i,X0: $i] :
( ( knight @ X0 )
& ( knave @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',who_is_knight_and_knave) ).
thf(f7,negated_conjecture,
~ ? [X1: $i,X0: $i] :
( ( knight @ X0 )
& ( knave @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
! [X0: $i] :
( ( knight @ X0 )
<~> ( knave @ X0 ) ),
inference(rectify,[],[f1]) ).
thf(f9,plain,
! [X0: $i] :
( ( knight @ X0 )
!= ( knave @ X0 ) ),
inference(fool_elimination,[],[f8]) ).
thf(f12,plain,
! [X0: $i,X1: $o] :
( ( ( says @ X0 @ X1 )
& ( knight @ X0 ) )
=> X1 ),
inference(rectify,[],[f2]) ).
thf(f13,plain,
! [X1: $o,X0: $i] :
( ( ( ( knight @ X0 )
= $true )
& ( ( says @ X0 @ X1 )
= $true ) )
=> ( $true = X1 ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
! [X0: $i,X1: $o] :
( ( ( says @ X0 @ X1 )
& ( knave @ X0 ) )
=> ~ X1 ),
inference(rectify,[],[f3]) ).
thf(f15,plain,
! [X0: $i,X1: $o] :
( ( ( ( knave @ X0 )
= $true )
& ( ( says @ X0 @ X1 )
= $true ) )
=> ( $true != X1 ) ),
inference(fool_elimination,[],[f14]) ).
thf(f16,plain,
~ ? [X0: $i,X1: $i] :
( ( knight @ X1 )
& ( knave @ X0 ) ),
inference(rectify,[],[f7]) ).
thf(f17,plain,
~ ? [X1: $i,X0: $i] :
( ( ( knave @ X0 )
= $true )
& ( ( knight @ X1 )
= $true ) ),
inference(fool_elimination,[],[f16]) ).
thf(f18,plain,
says @ zoey @ ( knave @ mel ),
inference(rectify,[],[f4]) ).
thf(f19,plain,
( ( says @ zoey @ ( knave @ mel ) )
= $true ),
inference(fool_elimination,[],[f18]) ).
thf(f20,plain,
! [X0: $i,X1: $o] :
( ( ( ( knave @ X0 )
= $true )
& ( ( says @ X0 @ X1 )
= $true ) )
=> ( $true != X1 ) ),
inference(flattening,[],[f15]) ).
thf(f21,plain,
! [X1: $o,X0: $i] :
( ( $true = X1 )
| ( ( knight @ X0 )
!= $true )
| ( ( says @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f22,plain,
! [X1: $o,X0: $i] :
( ( $true = X1 )
| ( ( knight @ X0 )
!= $true )
| ( ( says @ X0 @ X1 )
!= $true ) ),
inference(flattening,[],[f21]) ).
thf(f23,plain,
! [X0: $i,X1: $o] :
( ( $true != X1 )
| ( ( knave @ X0 )
!= $true )
| ( ( says @ X0 @ X1 )
!= $true ) ),
inference(ennf_transformation,[],[f20]) ).
thf(f24,plain,
! [X0: $i,X1: $o] :
( ( ( says @ X0 @ X1 )
!= $true )
| ( $true != X1 )
| ( ( knave @ X0 )
!= $true ) ),
inference(flattening,[],[f23]) ).
thf(f25,plain,
! [X1: $i,X0: $i] :
( ( ( knight @ X1 )
!= $true )
| ( ( knave @ X0 )
!= $true ) ),
inference(ennf_transformation,[],[f17]) ).
thf(f26,plain,
! [X0: $i,X1: $i] :
( ( ( knight @ X0 )
!= $true )
| ( ( knave @ X1 )
!= $true ) ),
inference(rectify,[],[f25]) ).
thf(f27,plain,
! [X0: $o,X1: $i] :
( ( $true = X0 )
| ( ( knight @ X1 )
!= $true )
| ( $true
!= ( says @ X1 @ X0 ) ) ),
inference(rectify,[],[f22]) ).
thf(f28,plain,
! [X0: $i] :
( ( knight @ X0 )
!= ( knave @ X0 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f29,plain,
! [X0: $i,X1: $o] :
( ( ( says @ X0 @ X1 )
!= $true )
| ( $true != X1 )
| ( ( knave @ X0 )
!= $true ) ),
inference(cnf_transformation,[],[f24]) ).
thf(f31,plain,
! [X0: $i,X1: $i] :
( ( ( knight @ X0 )
!= $true )
| ( ( knave @ X1 )
!= $true ) ),
inference(cnf_transformation,[],[f26]) ).
thf(f32,plain,
( ( says @ zoey @ ( knave @ mel ) )
= $true ),
inference(cnf_transformation,[],[f19]) ).
thf(f33,plain,
! [X0: $o,X1: $i] :
( ( $true
!= ( says @ X1 @ X0 ) )
| ( ( knight @ X1 )
!= $true )
| ( $true = X0 ) ),
inference(cnf_transformation,[],[f27]) ).
thf(f36,plain,
! [X0: $i] :
( ( ( says @ X0 @ $true )
!= $true )
| ( ( knave @ X0 )
!= $true ) ),
inference(equality_resolution,[],[f29]) ).
thf(f37,plain,
! [X0: $i] :
( ( ( knight @ X0 )
= $true )
| ( ( knave @ X0 )
= $true ) ),
inference(xor_proxy_clausification,[],[f28]) ).
thf(f40,definition,
( spl0_1
<=> ! [X1: $i] :
( ( knave @ X1 )
!= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f41,plain,
( ! [X1: $i] :
( ( knave @ X1 )
!= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f43,definition,
( spl0_2
<=> ! [X0: $i] :
( ( knight @ X0 )
!= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f44,plain,
( ! [X0: $i] :
( ( knight @ X0 )
!= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f43]) ).
thf(f45,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f31,f43,f40]) ).
thf(f46,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( knave @ X0 )
= $true ) )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f44,f37]) ).
thf(f47,plain,
( ! [X0: $i] :
( ( knave @ X0 )
= $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f46]) ).
thf(f51,plain,
( ( ( says @ zoey @ $true )
= $true )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f32,f47]) ).
thf(f52,plain,
( ( ( knight @ zoey )
!= $true )
| ( $true != $true )
| ( ( knave @ mel )
= $true ) ),
inference(constrained_superposition,[],[f33,f32]) ).
thf(f53,plain,
( ( ( knave @ mel )
= $true )
| ( ( knight @ zoey )
!= $true ) ),
inference(trivial_inequality_removal,[],[f52]) ).
thf(f54,plain,
( ( $true != $true )
| ( ( knave @ zoey )
!= $true )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f36,f51]) ).
thf(f55,plain,
( ( ( knave @ zoey )
!= $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f54]) ).
thf(f56,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f55,f47]) ).
thf(f57,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f56]) ).
thf(f59,definition,
( spl0_3
<=> ( ( knave @ mel )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f61,plain,
( ( ( knave @ mel )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f59]) ).
thf(f63,definition,
( spl0_4
<=> ( ( knight @ zoey )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
thf(f65,plain,
( ( ( knight @ zoey )
!= $true )
| spl0_4 ),
inference(avatar_component_clause,[],[f63]) ).
thf(f66,plain,
( spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f53,f63,f59]) ).
thf(f68,plain,
( ( ( knave @ zoey )
= $true )
| ( $true != $true )
| spl0_4 ),
inference(constrained_superposition,[],[f65,f37]) ).
thf(f69,plain,
( ( ( knave @ zoey )
= $true )
| spl0_4 ),
inference(trivial_inequality_removal,[],[f68]) ).
thf(f70,plain,
( $false
| ~ spl0_1
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f69,f41]) ).
thf(f71,plain,
( ~ spl0_1
| spl0_4 ),
inference(avatar_contradiction_clause,[],[f70]) ).
thf(f72,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f61,f41]) ).
thf(f73,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f72]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f45]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f57]) ).
cnf(s3,plain,
( spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f66]) ).
cnf(s4,plain,
( ~ spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f71]) ).
cnf(s5,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(sat_conversion,[],[f73]) ).
cnf(s6,plain,
spl0_1,
inference(rat,[],[s1,s2]) ).
cnf(s7,plain,
~ spl0_3,
inference(rat,[],[s5,s6]) ).
cnf(s8,plain,
spl0_4,
inference(rat,[],[s4,s6]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s3,s8,s7]) ).
thf(f74,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ081^3 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n007.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:19:41 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 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
% 0.20/0.29 % (3343301)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.29 % (3343308)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2040820023:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.29 % (3343308)Refutation not found, incomplete strategy
% 0.20/0.29 % (3343308)------------------------------
% 0.20/0.29 % (3343308)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (3343308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (3343308)CaDiCaL version: 2.1.3
% 0.20/0.29 % (3343308)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.29 % (3343308)Time elapsed: 0.001 s
% 0.20/0.29 % (3343308)Peak memory usage: 12 MB
% 0.20/0.29 % (3343308)Instructions burned: 2 (million)
% 0.20/0.29 % (3343308)------------------------------
% 0.20/0.29 % (3343308)------------------------------
% 0.20/0.29 % (3343312)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.29 % (3343312)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
% 0.20/0.29 % (3343311)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=980853990:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.29 % (3343306)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3562799910:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.29 % (3343307)lrs+10_16_si=on:nwc=1.5:random_seed=2462824611:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.29 % (3343309)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=704195604: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)
% 0.20/0.29 % (3343310)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1434007704:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.29 % (3343312)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=3307817673:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.29 % (3343307) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3343301-3343307"...
% 0.20/0.29 % (3343306) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3343301-3343306"...
% 0.20/0.29 % (3343310) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3343301-3343310"...
% 0.20/0.29 % (3343311) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3343301-3343311"...
% 0.20/0.29 % (3343307)...printing done.
% 0.20/0.29 % (3343306)...printing done.
% 0.20/0.29 % (3343312) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3343301-3343312"...
% 0.20/0.29 % (3343310)...printing done.
% 0.20/0.29 % (3343306)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.29 % (3343306)------------------------------
% 0.20/0.29 % (3343306)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (3343306)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (3343306)CaDiCaL version: 2.1.3
% 0.20/0.29 % (3343306)Termination reason: Refutation
% 0.20/0.29 % (3343306)Time elapsed: 0.004 s
% 0.20/0.29 % (3343306)Peak memory usage: 13 MB
% 0.20/0.29 % (3343306)Instructions burned: 4 (million)
% 0.20/0.29 % (3343301)Success in time 0.043 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------