%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ024-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : Tue Sep 29 12:31:15 PM UTC 2026
% Result : Unsatisfiable 3.39s 1.24s
% Output : Refutation 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 24 ( 11 unt; 2 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 48 ( 22 ~; 24 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 3 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(truthteller(X0))
| a_truth(liar(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',truthteller_or_liar) ).
fof(f4,axiom,
! [X0,X1] :
( ~ a_truth(liar(X0))
| ~ a_truth(says(X0,X1))
| ~ a_truth(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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/sandbox/benchmark/theBenchmark.p',all_truthtellers) ).
fof(f15,axiom,
people(b,c,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_c_a_people) ).
fof(f18,axiom,
a_truth(says(a,all_are_liars)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_says_all_are_liars) ).
fof(f20,negated_conjecture,
! [X0] : ~ a_truth(truthteller(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_a_truthteller) ).
fof(f22,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(f23,plain,
( ! [X2,X0,X1] :
( ~ people(X0,X1,X2)
| a_truth(truthteller(X2))
| a_truth(truthteller(X1))
| a_truth(truthteller(X0)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f22]) ).
fof(f25,definition,
( spl0_2
<=> a_truth(all_are_liars) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f28,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f14,f25,f22]) ).
fof(f50,plain,
! [X0] : a_truth(liar(X0)),
inference(forward_subsumption_resolution,[],[f1,f20]) ).
fof(f51,plain,
! [X0,X1] :
( ~ a_truth(says(X0,X1))
| ~ a_truth(X1) ),
inference(forward_subsumption_resolution,[],[f4,f50]) ).
fof(f52,plain,
~ a_truth(all_are_liars),
inference(resolution,[],[f51,f18]) ).
fof(f56,plain,
( ! [X2,X0,X1] :
( ~ people(X0,X1,X2)
| a_truth(truthteller(X1))
| a_truth(truthteller(X0)) )
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f23,f20]) ).
fof(f57,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f52,f25]) ).
fof(f58,plain,
( ! [X2,X0,X1] :
( ~ people(X0,X1,X2)
| a_truth(truthteller(X0)) )
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f56,f20]) ).
fof(f59,plain,
( ! [X2,X0,X1] : ~ people(X0,X1,X2)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f58,f20]) ).
fof(f60,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f59,f15]) ).
fof(f63,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f60]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f28]) ).
cnf(s8,plain,
~ spl0_2,
inference(sat_conversion,[],[f57]) ).
cnf(s10,plain,
~ spl0_1,
inference(sat_conversion,[],[f63]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s1,s8,s10]) ).
fof(f64,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ024-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 22:28:40 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.39/1.24 % (1836265)Input is clausal, will run a generic CNF schedule.
% 3.39/1.24 % (1836272)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1402353696:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.39/1.24 % (1836276)dis-21_1_sil=8000:lcm=predicate:random_seed=1052049049:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.39/1.24 % (1836275)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3366884941:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.39/1.24 % (1836271)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=597491211:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.39/1.24 % (1836274)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3370120752:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.39/1.24 % (1836273)lrs+10_1_sil=8000:sp=occurrence:random_seed=2578645571:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.39/1.24 % (1836270)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2800920444:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.39/1.24 % (1836274)Also succeeded, but the first one will report.
% 3.39/1.24 % (1836275)First to succeed.
% 3.39/1.24 % (1836273)Also succeeded, but the first one will report.
% 3.39/1.24 % (1836276)Also succeeded, but the first one will report.
% 3.39/1.24 % (1836275)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1836265"
% 3.39/1.24 % (1836275)Refutation found. Thanks to Tanya!
% 3.39/1.24 % SZS status Unsatisfiable for theBenchmark
% 3.39/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 3.39/1.24 % (1836275)------------------------------
% 3.39/1.24 % (1836275)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.39/1.24 % (1836275)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.39/1.24 % (1836275)CaDiCaL version: 2.1.3
% 3.39/1.24 % (1836275)Termination reason: Refutation
% 3.39/1.24 % (1836275)Time elapsed: 0.003 s
% 3.39/1.24 % (1836275)Peak memory usage: 89 MB
% 3.39/1.24 % (1836275)Instructions burned: 1 (million)
% 3.39/1.24 % (1836275)------------------------------
% 3.39/1.24 % (1836275)------------------------------
% 3.39/1.24 % (1836265)Success in time 0.426 s
% 3.39/1.24 % Vampire exiting
%------------------------------------------------------------------------------