%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PUZ081_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 : Tue Sep 29 12:32:15 PM UTC 2026
% Result : Theorem 0.20s 0.48s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 70 ( 8 unt; 0 typ; 6 def)
% Number of atoms : 182 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 144 ( 69 ~; 57 |; 7 &)
% ( 6 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 61 ( 45 fml; 16 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 10 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 41 ( 0 sgn 37 !; 4 ?; 41 :)
% Comments :
%------------------------------------------------------------------------------
tff(pred_def_3,type,
says: ( $i * $o ) > $o ).
tff(f1,axiom,
! [X0: $i] :
( knight(X0)
<~> knave(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knights_xor_knaves) ).
tff(f2,axiom,
! [X0: $i,X1: $o] :
( ( knight(X0)
& says(X0,(X1)) )
=> (X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knights_tell_truth) ).
tff(f3,axiom,
! [X0: $i,X1: $o] :
( ( knave(X0)
& says(X0,(X1)) )
=> ~ (X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',knaves_lie) ).
tff(f4,axiom,
says(zoey,knave(mel)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zoey_speaks) ).
tff(f5,axiom,
says(mel,
( ~ knave(zoey)
& ~ knave(mel) )),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mel_speaks) ).
tff(f6,conjecture,
? [X0: $i,X1: $i] :
( knight(X0)
& knave(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',who_is_knight_and_knave) ).
tff(f7,negated_conjecture,
~ ? [X0: $i,X1: $i] :
( knight(X0)
& knave(X1) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f8,plain,
! [X0: $i,X1: $o] :
( ( knight(X0)
& says(X0,(X1)) )
=> (X1) ),
inference(rectify,[],[f2]) ).
tff(f9,plain,
! [X0: $i,X1: $o] :
( ( knave(X0)
& says(X0,(X1)) )
=> ~ (X1) ),
inference(rectify,[],[f3]) ).
tff(f10,plain,
! [X0: $i,X1: $o] :
( (X1)
| ~ knight(X0)
| ~ says(X0,(X1)) ),
inference(ennf_transformation,[],[f8]) ).
tff(f11,plain,
! [X0: $i,X1: $o] :
( (X1)
| ~ knight(X0)
| ~ says(X0,(X1)) ),
inference(flattening,[],[f10]) ).
tff(f12,plain,
! [X0: $i,X1: $o] :
( ~ (X1)
| ~ knave(X0)
| ~ says(X0,(X1)) ),
inference(ennf_transformation,[],[f9]) ).
tff(f13,plain,
! [X0: $i,X1: $o] :
( ~ (X1)
| ~ knave(X0)
| ~ says(X0,(X1)) ),
inference(flattening,[],[f12]) ).
tff(f14,plain,
! [X0: $i,X1: $i] :
( ~ knight(X0)
| ~ knave(X1) ),
inference(ennf_transformation,[],[f7]) ).
tff(f15,plain,
! [X0: $i] :
( knave(X0)
| knight(X0) ),
inference(cnf_transformation,[],[f1]) ).
tff(f17,plain,
! [X0: $i] :
( ~ says(X0,$false)
| ~ knight(X0) ),
inference(cnf_transformation,[],[f11]) ).
tff(f18,plain,
! [X0: $i] :
( ~ says(X0,$true)
| ~ knave(X0) ),
inference(cnf_transformation,[],[f13]) ).
tff(f19,plain,
( ~ knave(mel)
| says(zoey,$true) ),
inference(cnf_transformation,[],[f4]) ).
tff(f20,plain,
( knave(mel)
| says(zoey,$false) ),
inference(cnf_transformation,[],[f4]) ).
tff(f21,plain,
( ~ knave(mel)
| says(mel,$false) ),
inference(cnf_transformation,[],[f5]) ).
tff(f24,plain,
! [X0: $i,X1: $i] :
( ~ knave(X1)
| ~ knight(X0) ),
inference(cnf_transformation,[],[f14]) ).
tff(f28,plain,
! [X0: $i] :
( knave(X0)
| ~ knight(X0) ),
inference(consistent_polarity_flipping,[],[f15]) ).
tff(f29,plain,
! [X0: $i] :
( says(X0,$false)
| knight(X0) ),
inference(consistent_polarity_flipping,[],[f17]) ).
tff(f30,plain,
! [X0: $i] :
( says(X0,$true)
| ~ knave(X0) ),
inference(consistent_polarity_flipping,[],[f18]) ).
tff(f31,plain,
( knave(mel)
| ~ says(zoey,$false) ),
inference(consistent_polarity_flipping,[],[f20]) ).
tff(f32,plain,
( ~ knave(mel)
| ~ says(zoey,$true) ),
inference(consistent_polarity_flipping,[],[f19]) ).
tff(f35,plain,
( ~ knave(mel)
| ~ says(mel,$false) ),
inference(consistent_polarity_flipping,[],[f21]) ).
tff(f36,plain,
! [X0: $i,X1: $i] :
( ~ knave(X1)
| knight(X0) ),
inference(consistent_polarity_flipping,[],[f24]) ).
tff(f38,definition,
( spl0_1
<=> ! [X0: $i] : knight(X0) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f39,plain,
( ! [X0: $i] : knight(X0)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f38]) ).
tff(f41,definition,
( spl0_2
<=> ! [X1: $i] : ~ knave(X1) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f42,plain,
( ! [X1: $i] : ~ knave(X1)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f41]) ).
tff(f43,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f36,f41,f38]) ).
tff(f45,definition,
( spl0_3
<=> says(mel,$false) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
tff(f47,plain,
( ~ says(mel,$false)
| spl0_3 ),
inference(avatar_component_clause,[],[f45]) ).
tff(f49,definition,
( spl0_4
<=> knave(mel) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
tff(f51,plain,
( ~ knave(mel)
| spl0_4 ),
inference(avatar_component_clause,[],[f49]) ).
tff(f52,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f35,f49,f45]) ).
tff(f64,definition,
( spl0_7
<=> says(zoey,$true) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
tff(f66,plain,
( ~ says(zoey,$true)
| spl0_7 ),
inference(avatar_component_clause,[],[f64]) ).
tff(f67,plain,
( ~ spl0_7
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f32,f49,f64]) ).
tff(f69,definition,
( spl0_8
<=> says(zoey,$false) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
tff(f71,plain,
( ~ says(zoey,$false)
| spl0_8 ),
inference(avatar_component_clause,[],[f69]) ).
tff(f72,plain,
( ~ spl0_8
| spl0_4 ),
inference(avatar_split_clause,[],[f31,f49,f69]) ).
tff(f73,plain,
( ! [X0: $i] : ~ knight(X0)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f28,f42]) ).
tff(f74,plain,
( ! [X0: $i] : says(X0,$false)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f29,f73]) ).
tff(f75,plain,
( $false
| ~ spl0_2
| spl0_3 ),
inference(backward_subsumption_resolution,[],[f47,f74]) ).
tff(f76,plain,
( $false
| ~ spl0_2
| spl0_8 ),
inference(backward_subsumption_resolution,[],[f71,f74]) ).
tff(f77,plain,
( ~ spl0_2
| spl0_3 ),
inference(avatar_contradiction_clause,[],[f75]) ).
tff(f78,plain,
( ~ spl0_2
| spl0_8 ),
inference(avatar_contradiction_clause,[],[f76]) ).
tff(f79,plain,
( ! [X0: $i] : knave(X0)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f28,f39]) ).
tff(f80,plain,
( $false
| ~ spl0_1
| spl0_4 ),
inference(backward_subsumption_resolution,[],[f51,f79]) ).
tff(f81,plain,
( ~ spl0_1
| spl0_4 ),
inference(avatar_contradiction_clause,[],[f80]) ).
tff(f82,plain,
( ! [X0: $i] : says(X0,$true)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f30,f79]) ).
tff(f84,plain,
( $false
| ~ spl0_1
| spl0_7 ),
inference(backward_subsumption_resolution,[],[f66,f82]) ).
tff(f86,plain,
( ~ spl0_1
| spl0_7 ),
inference(avatar_contradiction_clause,[],[f84]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f43]) ).
cnf(s2,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f52]) ).
cnf(s5,plain,
( ~ spl0_4
| ~ spl0_7 ),
inference(sat_conversion,[],[f67]) ).
cnf(s6,plain,
( spl0_4
| ~ spl0_8 ),
inference(sat_conversion,[],[f72]) ).
cnf(s7,plain,
( ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f77]) ).
cnf(s8,plain,
( ~ spl0_2
| spl0_8 ),
inference(sat_conversion,[],[f78]) ).
cnf(s9,plain,
( ~ spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f81]) ).
cnf(s11,plain,
( ~ spl0_1
| spl0_7 ),
inference(sat_conversion,[],[f86]) ).
cnf(s12,plain,
~ spl0_2,
inference(rat,[],[s2,s6,s7,s8]) ).
cnf(s13,plain,
spl0_1,
inference(rat,[],[s1,s12]) ).
cnf(s14,plain,
spl0_7,
inference(rat,[],[s11,s13]) ).
cnf(s16,plain,
spl0_4,
inference(rat,[],[s9,s13]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s5,s14,s16]) ).
tff(f87,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ081_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.40 % Computer : n026.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sun Sep 27 22:43:11 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.43 Running first-order model finding
% 0.14/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.48 % (3279683)Will run a generic schedule for satisfiability detection.
% 0.20/0.48 % (3279688)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3711652148_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.48 % Detected minimum model sizes of [1,1]
% 0.20/0.48 % Detected maximum model sizes of [2,2]
% 0.20/0.48 % TRYING [1,1]
% 0.20/0.48 % TRYING [1,2]
% 0.20/0.48 % TRYING [2,2]
% 0.20/0.48 % (3279688)Cannot enumerate next child to try in an incomplete setup
% 0.20/0.48 % (3279688)Refutation not found, incomplete strategy
% 0.20/0.48 % (3279688)------------------------------
% 0.20/0.48 % (3279688)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.48 % (3279688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.48 % (3279688)CaDiCaL version: 2.1.3
% 0.20/0.48 % (3279688)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.48 % (3279688)Time elapsed: 0.001 s
% 0.20/0.48 % (3279688)Peak memory usage: 11 MB
% 0.20/0.48 % (3279688)Instructions burned: 2 (million)
% 0.20/0.48 % (3279688)------------------------------
% 0.20/0.48 % (3279688)------------------------------
% 0.20/0.48 % (3279689)% WARNING: option uhcvi not known.
% 0.20/0.48 % (3279689)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1171453218:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.48 % (3279690)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2466118277:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.48 % (3279691)dis+10_1_sil=32000:sp=arity:random_seed=2106792827:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.48 % (3279692)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=240277776:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.48 % (3279693)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=319241:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.48 % (3279694)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3244956327:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.48 % (3279689) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3279683-3279689"...
% 0.20/0.48 % (3279692) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3279683-3279692"...
% 0.20/0.48 % (3279689)...printing done.
% 0.20/0.48 % (3279689)Refutation found. Thanks to Tanya!
% 0.20/0.48 % SZS status Theorem for theBenchmark
% 0.20/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.48 % (3279689)------------------------------
% 0.20/0.48 % (3279689)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.48 % (3279689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.48 % (3279689)CaDiCaL version: 2.1.3
% 0.20/0.48 % (3279689)Termination reason: Refutation
% 0.20/0.48 % (3279689)Time elapsed: 0.002 s
% 0.20/0.48 % (3279689)Peak memory usage: 12 MB
% 0.20/0.48 % (3279689)Instructions burned: 2 (million)
% 0.20/0.48 % (3279683)Success in time 0.034 s
% 0.20/0.48 % Vampire exiting
%------------------------------------------------------------------------------