%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ023-1 : 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 0.17s 1.31s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 56 ( 15 unt; 8 def)
% Number of atoms : 109 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 107 ( 54 ~; 45 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 9 prp; 0-1 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 2 ( 0 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( a_truth(liar(X0))
| a_truth(truthteller(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',truthteller_or_liar) ).
fof(f18,axiom,
( ~ a_truth(liar(b))
| ~ a_truth(liar(c))
| an_answer(b_and_c_liars) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_and_c_liars) ).
fof(f19,axiom,
( ~ a_truth(liar(b))
| ~ a_truth(truthteller(c))
| an_answer(b_liar_and_c_truthteller) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_liar_and_c_truthteller) ).
fof(f20,axiom,
( ~ a_truth(truthteller(b))
| ~ a_truth(liar(c))
| an_answer(b_truthteller_and_c_liar) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_truthteller_and_c_liar) ).
fof(f21,axiom,
( ~ a_truth(truthteller(b))
| ~ a_truth(truthteller(c))
| an_answer(b_and_c_truthtellers) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_and_c_truthtellers) ).
fof(f22,negated_conjecture,
! [X0] : ~ an_answer(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_is_an_answer) ).
fof(f24,definition,
( spl0_1
<=> an_answer(b_and_c_truthtellers) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f25,plain,
( an_answer(b_and_c_truthtellers)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f27,definition,
( spl0_2
<=> a_truth(truthteller(c)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f30,definition,
( spl0_3
<=> a_truth(truthteller(b)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f32,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f21,f30,f27,f24]) ).
fof(f34,definition,
( spl0_4
<=> an_answer(b_truthteller_and_c_liar) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f35,plain,
( an_answer(b_truthteller_and_c_liar)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f37,definition,
( spl0_5
<=> a_truth(liar(c)) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f38,plain,
( ~ a_truth(liar(c))
| spl0_5 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f39,plain,
( spl0_4
| ~ spl0_5
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f20,f30,f37,f34]) ).
fof(f41,definition,
( spl0_6
<=> an_answer(b_liar_and_c_truthteller) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f42,plain,
( an_answer(b_liar_and_c_truthteller)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f44,definition,
( spl0_7
<=> a_truth(liar(b)) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f45,plain,
( ~ a_truth(liar(b))
| spl0_7 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f46,plain,
( spl0_6
| ~ spl0_2
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f19,f44,f27,f41]) ).
fof(f48,definition,
( spl0_8
<=> an_answer(b_and_c_liars) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f49,plain,
( an_answer(b_and_c_liars)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f50,plain,
( spl0_8
| ~ spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f18,f44,f37,f48]) ).
fof(f94,plain,
( a_truth(truthteller(c))
| spl0_5 ),
inference(resolution,[],[f1,f38]) ).
fof(f95,plain,
( spl0_2
| spl0_5 ),
inference(avatar_split_clause,[],[f94,f37,f27]) ).
fof(f96,plain,
( a_truth(truthteller(b))
| spl0_7 ),
inference(resolution,[],[f45,f1]) ).
fof(f97,plain,
( spl0_3
| spl0_7 ),
inference(avatar_split_clause,[],[f96,f44,f30]) ).
fof(f98,plain,
( $false
| ~ spl0_8 ),
inference(resolution,[],[f49,f22]) ).
fof(f99,plain,
~ spl0_8,
inference(avatar_contradiction_clause,[],[f98]) ).
fof(f101,plain,
( $false
| ~ spl0_6 ),
inference(resolution,[],[f42,f22]) ).
fof(f102,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f101]) ).
fof(f104,plain,
( $false
| ~ spl0_4 ),
inference(resolution,[],[f35,f22]) ).
fof(f105,plain,
~ spl0_4,
inference(avatar_contradiction_clause,[],[f104]) ).
fof(f106,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f25,f22]) ).
fof(f107,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f106]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f32]) ).
cnf(s2,plain,
( ~ spl0_3
| spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f39]) ).
cnf(s3,plain,
( ~ spl0_2
| spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f46]) ).
cnf(s4,plain,
( ~ spl0_5
| ~ spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f50]) ).
cnf(s14,plain,
( spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f95]) ).
cnf(s15,plain,
( spl0_3
| spl0_7 ),
inference(sat_conversion,[],[f97]) ).
cnf(s16,plain,
~ spl0_8,
inference(sat_conversion,[],[f99]) ).
cnf(s19,plain,
~ spl0_6,
inference(sat_conversion,[],[f102]) ).
cnf(s21,plain,
~ spl0_4,
inference(sat_conversion,[],[f105]) ).
cnf(s23,plain,
~ spl0_1,
inference(sat_conversion,[],[f107]) ).
cnf(s24,plain,
( ~ spl0_5
| ~ spl0_7 ),
inference(rat,[],[s4,s16]) ).
cnf(s25,plain,
( ~ spl0_2
| ~ spl0_7 ),
inference(rat,[],[s3,s19]) ).
cnf(s26,plain,
( ~ spl0_3
| ~ spl0_5 ),
inference(rat,[],[s2,s21]) ).
cnf(s27,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(rat,[],[s1,s23]) ).
cnf(s28,plain,
~ spl0_5,
inference(rat,[],[s15,s26,s24]) ).
cnf(s29,plain,
spl0_2,
inference(rat,[],[s14,s28]) ).
cnf(s30,plain,
~ spl0_7,
inference(rat,[],[s25,s29]) ).
cnf(s31,plain,
~ spl0_3,
inference(rat,[],[s27,s29]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s15,s30,s31]) ).
fof(f108,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ023-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % 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 22:28:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 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
% 0.17/1.31 % (1835861)Input is clausal, will run a generic CNF schedule.
% 0.17/1.31 % (1835872)dis-21_1_sil=8000:lcm=predicate:random_seed=2377015347: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)
% 0.17/1.31 % (1835872)First to succeed.
% 0.17/1.31 % (1835872)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1835861"
% 0.17/1.31 % (1835871)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=967202831:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.17/1.31 % (1835867)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3586540602:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.17/1.31 % (1835869)lrs+10_1_sil=8000:sp=occurrence:random_seed=3570715909:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.17/1.31 % (1835870)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2079438395:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.17/1.31 % (1835866)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=3845605549:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.17/1.31 % (1835868)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=514423320:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.17/1.31 % (1835870)Also succeeded, but the first one will report.
% 0.17/1.31 % (1835869)Also succeeded, but the first one will report.
% 0.17/1.31 % (1835871)Also succeeded, but the first one will report.
% 0.17/1.31 % (1835872)Refutation found. Thanks to Tanya!
% 0.17/1.31 % SZS status Unsatisfiable for theBenchmark
% 0.17/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.31 % (1835872)------------------------------
% 0.17/1.31 % (1835872)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.31 % (1835872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.31 % (1835872)CaDiCaL version: 2.1.3
% 0.17/1.31 % (1835872)Termination reason: Refutation
% 0.17/1.31 % (1835872)Time elapsed: 0.002 s
% 0.17/1.31 % (1835872)Peak memory usage: 89 MB
% 0.17/1.31 % (1835872)Instructions burned: 2 (million)
% 0.17/1.31 % (1835872)------------------------------
% 0.17/1.31 % (1835872)------------------------------
% 0.17/1.31 % (1835861)Success in time 0.27 s
% 0.17/1.31 % Vampire exiting
%------------------------------------------------------------------------------