%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : PUZ024-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 12:31:56 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.45s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 11 unt; 3 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 57 ( 21 ~; 33 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 0 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( a_truth(liar(X0))
| a_truth(truthteller(X0)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PUZ002-0.ax',truthteller_or_liar) ).
fof(f4,axiom,
! [X0,X1] :
( ~ a_truth(says(X0,X1))
| ~ a_truth(liar(X0))
| ~ a_truth(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/PUZ002-0.ax',liars_lie) ).
fof(f14,axiom,
! [X2,X0,X1] :
( a_truth(all_are_liars)
| ~ people(X0,X1,X2)
| a_truth(truthteller(X0))
| a_truth(truthteller(X1))
| a_truth(truthteller(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',all_truthtellers) ).
fof(f15,axiom,
people(b,c,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_c_a_people) ).
fof(f18,axiom,
a_truth(says(a,all_are_liars)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_says_all_are_liars) ).
fof(f20,negated_conjecture,
! [X0] : ~ a_truth(truthteller(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_there_is_a_truthteller) ).
fof(f28,plain,
! [X2,X0,X1] :
( a_truth(all_are_liars)
| people(X0,X1,X2)
| a_truth(truthteller(X0))
| a_truth(truthteller(X1))
| a_truth(truthteller(X2)) ),
inference(consistent_polarity_flipping,[],[f14]) ).
fof(f29,plain,
~ people(b,c,a),
inference(consistent_polarity_flipping,[],[f15]) ).
fof(f33,definition,
( spl0_1
<=> ! [X2,X0,X1] :
( people(X0,X1,X2)
| a_truth(truthteller(X2))
| a_truth(truthteller(X1))
| a_truth(truthteller(X0)) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f34,plain,
( ! [X2,X0,X1] :
( a_truth(truthteller(X2))
| people(X0,X1,X2)
| a_truth(truthteller(X1))
| a_truth(truthteller(X0)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f36,definition,
( spl0_2
<=> a_truth(all_are_liars) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f39,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f28,f36,f33]) ).
fof(f49,plain,
( ~ a_truth(liar(a))
| ~ a_truth(all_are_liars) ),
inference(resolution,[],[f4,f18]) ).
fof(f52,definition,
( spl0_5
<=> a_truth(liar(a)) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f54,plain,
( ~ a_truth(liar(a))
| spl0_5 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f55,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f49,f52,f36]) ).
fof(f56,plain,
( a_truth(truthteller(a))
| spl0_5 ),
inference(resolution,[],[f54,f1]) ).
fof(f57,plain,
( $false
| spl0_5 ),
inference(resolution,[],[f56,f20]) ).
fof(f58,plain,
spl0_5,
inference(avatar_contradiction_clause,[],[f57]) ).
fof(f62,plain,
( ! [X2,X0,X1] :
( a_truth(truthteller(X1))
| people(X0,X1,X2)
| a_truth(truthteller(X0)) )
| ~ spl0_1 ),
inference(resolution,[],[f34,f20]) ).
fof(f63,plain,
( ! [X2,X0,X1] :
( a_truth(truthteller(X0))
| people(X0,X1,X2) )
| ~ spl0_1 ),
inference(resolution,[],[f62,f20]) ).
fof(f64,plain,
( ! [X2,X0,X1] : people(X0,X1,X2)
| ~ spl0_1 ),
inference(resolution,[],[f63,f20]) ).
fof(f65,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f64,f29]) ).
fof(f70,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f65]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f39]) ).
cnf(s4,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(sat_conversion,[],[f55]) ).
cnf(s5,plain,
spl0_5,
inference(sat_conversion,[],[f58]) ).
cnf(s8,plain,
~ spl0_1,
inference(sat_conversion,[],[f70]) ).
cnf(s9,plain,
~ spl0_2,
inference(rat,[],[s4,s5]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s9,s8]) ).
fof(f71,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ024-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.37 % Computer : n019.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sun Sep 27 22:30:33 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.15/0.41 Running first-order model finding
% 0.15/0.41 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
% 0.15/0.45 % (3479834)Will run a generic schedule for satisfiability detection.
% 0.15/0.45 % (3479845)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=344380338:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.45 % (3479845) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3479834-3479845"...
% 0.15/0.45 % (3479845)...printing done.
% 0.15/0.45 % (3479840)% WARNING: option uhcvi not known.
% 0.15/0.45 % (3479845)Refutation found. Thanks to Tanya!
% 0.15/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.45 % (3479845)------------------------------
% 0.15/0.45 % (3479845)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.45 % (3479845)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.45 % (3479845)CaDiCaL version: 2.1.3
% 0.15/0.45 % (3479845)Termination reason: Refutation
% 0.15/0.45 % (3479845)Time elapsed: 0.001 s
% 0.15/0.45 % (3479845)Peak memory usage: 12 MB
% 0.15/0.45 % (3479845)Instructions burned: 1 (million)
% 0.15/0.45 % (3479834)Success in time 0.028 s
% 0.15/0.45 % Vampire exiting
%------------------------------------------------------------------------------