%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ026-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 2.08s 1.15s
% Output : Refutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 26
% Syntax : Number of formulae : 110 ( 16 unt; 11 def)
% Number of atoms : 251 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 263 ( 122 ~; 130 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 12 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( a_truth(truthteller(X0))
| a_truth(liar(X0))
| a_truth(normal(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',person_is_one_type) ).
fof(f5,axiom,
! [X0,X1] :
( ~ a_truth(says(X0,X1))
| ~ a_truth(truthteller(X0))
| a_truth(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',truthtellers_tell_truth) ).
fof(f7,axiom,
! [X0,X1] :
( ~ a_truth(X0)
| ~ a_truth(says(X1,X0))
| a_truth(truthteller(X1))
| a_truth(normal(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',truthtellers_and_normal_tell_truth) ).
fof(f10,axiom,
! [X0] :
( a_truth(not_normal(X0))
| a_truth(normal(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',normal_or_not_normal) ).
fof(f11,axiom,
! [X2,X0,X1] :
( ~ people(X0,X1,X2)
| ~ a_truth(truthteller(X0))
| ~ a_truth(truthteller(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_two_truthtellers1) ).
fof(f13,axiom,
! [X2,X0,X1] :
( ~ people(X0,X1,X2)
| ~ a_truth(liar(X0))
| ~ a_truth(liar(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_two_liars1) ).
fof(f15,axiom,
! [X2,X0,X1] :
( ~ people(X0,X1,X2)
| ~ a_truth(normal(X0))
| ~ a_truth(normal(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_two_normal1) ).
fof(f16,axiom,
! [X2,X0,X1] :
( ~ people(X0,X1,X2)
| ~ a_truth(normal(X0))
| ~ a_truth(normal(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_two_normal2) ).
fof(f17,axiom,
people(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_b_c_are_people) ).
fof(f18,axiom,
people(b,c,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_c_a_are_people) ).
fof(f19,axiom,
people(c,b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_b_a_are_people) ).
fof(f20,axiom,
a_truth(says(a,normal(a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_says_a_normal) ).
fof(f21,axiom,
a_truth(says(b,normal(a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_says_a_normal) ).
fof(f22,axiom,
a_truth(says(c,not_normal(c))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_says_c_not_normal) ).
fof(f23,negated_conjecture,
! [X2,X0,X1] :
( ~ a_truth(liar(X0))
| ~ a_truth(normal(X1))
| ~ a_truth(truthteller(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_one_of_each) ).
fof(f25,definition,
( spl0_1
<=> ! [X2] : ~ a_truth(truthteller(X2)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f26,plain,
( ! [X2] : ~ a_truth(truthteller(X2))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f25]) ).
fof(f28,definition,
( spl0_2
<=> ! [X1] : ~ a_truth(normal(X1)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f29,plain,
( ! [X1] : ~ a_truth(normal(X1))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f31,definition,
( spl0_3
<=> ! [X0] : ~ a_truth(liar(X0)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f32,plain,
( ! [X0] : ~ a_truth(liar(X0))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f31]) ).
fof(f33,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f23,f31,f28,f25]) ).
fof(f35,plain,
( ! [X0] :
( a_truth(liar(X0))
| a_truth(truthteller(X0)) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f1,f29]) ).
fof(f37,plain,
( ~ a_truth(truthteller(a))
| a_truth(normal(a)) ),
inference(resolution,[],[f5,f20]) ).
fof(f38,plain,
( ~ a_truth(truthteller(b))
| a_truth(normal(a)) ),
inference(resolution,[],[f5,f21]) ).
fof(f40,plain,
( ~ a_truth(truthteller(b))
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f38,f29]) ).
fof(f41,plain,
( ~ a_truth(truthteller(a))
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f37,f29]) ).
fof(f48,plain,
( ~ a_truth(truthteller(c))
| ~ a_truth(truthteller(b)) ),
inference(resolution,[],[f11,f19]) ).
fof(f53,plain,
( ~ a_truth(liar(a))
| ~ a_truth(liar(b)) ),
inference(resolution,[],[f13,f17]) ).
fof(f57,definition,
( spl0_4
<=> a_truth(liar(b)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f58,plain,
( ~ a_truth(liar(b))
| spl0_4 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f60,definition,
( spl0_5
<=> a_truth(liar(a)) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f61,plain,
( ~ a_truth(liar(a))
| spl0_5 ),
inference(avatar_component_clause,[],[f60]) ).
fof(f62,plain,
( ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f53,f60,f57]) ).
fof(f63,plain,
( a_truth(truthteller(b))
| ~ spl0_2
| spl0_4 ),
inference(resolution,[],[f58,f35]) ).
fof(f64,plain,
( $false
| ~ spl0_2
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f63,f40]) ).
fof(f65,plain,
( ~ spl0_2
| spl0_4 ),
inference(avatar_contradiction_clause,[],[f64]) ).
fof(f70,plain,
( a_truth(truthteller(a))
| ~ spl0_2
| spl0_5 ),
inference(resolution,[],[f61,f35]) ).
fof(f71,plain,
( $false
| ~ spl0_2
| spl0_5 ),
inference(forward_subsumption_resolution,[],[f70,f41]) ).
fof(f72,plain,
( ~ spl0_2
| spl0_5 ),
inference(avatar_contradiction_clause,[],[f71]) ).
fof(f77,definition,
( spl0_7
<=> a_truth(truthteller(c)) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f78,plain,
( ~ a_truth(truthteller(c))
| spl0_7 ),
inference(avatar_component_clause,[],[f77]) ).
fof(f81,definition,
( spl0_8
<=> a_truth(normal(a)) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f82,plain,
( a_truth(normal(a))
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f84,definition,
( spl0_9
<=> a_truth(truthteller(b)) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
fof(f85,plain,
( ~ a_truth(truthteller(b))
| spl0_9 ),
inference(avatar_component_clause,[],[f84]) ).
fof(f88,definition,
( spl0_10
<=> a_truth(truthteller(a)) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
fof(f89,plain,
( ~ a_truth(truthteller(a))
| spl0_10 ),
inference(avatar_component_clause,[],[f88]) ).
fof(f90,plain,
( spl0_8
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f37,f88,f81]) ).
fof(f96,plain,
( ~ a_truth(normal(a))
| spl0_8 ),
inference(avatar_component_clause,[],[f81]) ).
fof(f98,plain,
( ~ spl0_9
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f48,f77,f84]) ).
fof(f107,plain,
( ! [X0] :
( a_truth(normal(X0))
| a_truth(truthteller(X0)) )
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f1,f32]) ).
fof(f109,plain,
( a_truth(truthteller(a))
| ~ spl0_3
| spl0_8 ),
inference(resolution,[],[f107,f96]) ).
fof(f110,plain,
( $false
| ~ spl0_3
| spl0_8
| spl0_10 ),
inference(forward_subsumption_resolution,[],[f109,f89]) ).
fof(f111,plain,
( ~ spl0_3
| spl0_8
| spl0_10 ),
inference(avatar_contradiction_clause,[],[f110]) ).
fof(f113,plain,
( ~ a_truth(normal(b))
| ~ a_truth(normal(c)) ),
inference(resolution,[],[f15,f18]) ).
fof(f116,definition,
( spl0_12
<=> a_truth(normal(b)) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
fof(f117,plain,
( ~ a_truth(normal(b))
| spl0_12 ),
inference(avatar_component_clause,[],[f116]) ).
fof(f119,definition,
( spl0_13
<=> a_truth(normal(c)) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f120,plain,
( ~ a_truth(normal(c))
| spl0_13 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f122,plain,
( ~ spl0_13
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f113,f116,f119]) ).
fof(f125,plain,
( ~ a_truth(normal(a))
| ~ a_truth(normal(c)) ),
inference(resolution,[],[f16,f17]) ).
fof(f126,plain,
( ~ a_truth(normal(b))
| ~ a_truth(normal(a)) ),
inference(resolution,[],[f16,f18]) ).
fof(f129,plain,
( ~ a_truth(normal(b))
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[],[f126,f82]) ).
fof(f132,plain,
( ~ spl0_12
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f129,f81,f116]) ).
fof(f133,plain,
( a_truth(truthteller(b))
| ~ spl0_3
| spl0_12 ),
inference(resolution,[],[f117,f107]) ).
fof(f134,plain,
( $false
| ~ spl0_3
| spl0_9
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f133,f85]) ).
fof(f135,plain,
( ~ spl0_3
| spl0_9
| spl0_12 ),
inference(avatar_contradiction_clause,[],[f134]) ).
fof(f141,plain,
( a_truth(truthteller(c))
| ~ spl0_3
| spl0_13 ),
inference(resolution,[],[f120,f107]) ).
fof(f142,plain,
( $false
| ~ spl0_3
| spl0_7
| spl0_13 ),
inference(forward_subsumption_resolution,[],[f141,f78]) ).
fof(f143,plain,
( ~ spl0_3
| spl0_7
| spl0_13 ),
inference(avatar_contradiction_clause,[],[f142]) ).
fof(f145,plain,
( ! [X0] :
( a_truth(normal(X0))
| a_truth(liar(X0)) )
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f1,f26]) ).
fof(f148,plain,
( a_truth(liar(b))
| ~ spl0_1
| spl0_12 ),
inference(resolution,[],[f145,f117]) ).
fof(f150,plain,
( $false
| ~ spl0_1
| spl0_4
| spl0_12 ),
inference(forward_subsumption_resolution,[],[f148,f58]) ).
fof(f151,plain,
( ~ spl0_1
| spl0_4
| spl0_12 ),
inference(avatar_contradiction_clause,[],[f150]) ).
fof(f152,plain,
( ! [X0,X1] :
( ~ a_truth(says(X1,X0))
| ~ a_truth(X0)
| a_truth(normal(X1)) )
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f7,f26]) ).
fof(f156,plain,
( ~ a_truth(not_normal(c))
| a_truth(normal(c))
| ~ spl0_1 ),
inference(resolution,[],[f152,f22]) ).
fof(f157,plain,
( a_truth(normal(c))
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f156,f10]) ).
fof(f159,plain,
( $false
| ~ spl0_1
| spl0_13 ),
inference(forward_subsumption_resolution,[],[f157,f120]) ).
fof(f160,plain,
( ~ spl0_1
| spl0_13 ),
inference(avatar_contradiction_clause,[],[f159]) ).
fof(f163,plain,
( ~ spl0_13
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f125,f81,f119]) ).
fof(f168,plain,
( a_truth(liar(a))
| ~ spl0_1
| spl0_8 ),
inference(resolution,[],[f96,f145]) ).
fof(f169,plain,
( $false
| ~ spl0_1
| spl0_5
| spl0_8 ),
inference(forward_subsumption_resolution,[],[f168,f61]) ).
fof(f170,plain,
( ~ spl0_1
| spl0_5
| spl0_8 ),
inference(avatar_contradiction_clause,[],[f169]) ).
cnf(s1,plain,
( spl0_1
| spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f33]) ).
cnf(s2,plain,
( ~ spl0_4
| ~ spl0_5 ),
inference(sat_conversion,[],[f62]) ).
cnf(s3,plain,
( ~ spl0_2
| spl0_4 ),
inference(sat_conversion,[],[f65]) ).
cnf(s5,plain,
( ~ spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f72]) ).
cnf(s8,plain,
( spl0_8
| ~ spl0_10 ),
inference(sat_conversion,[],[f90]) ).
cnf(s11,plain,
( ~ spl0_7
| ~ spl0_9 ),
inference(sat_conversion,[],[f98]) ).
cnf(s19,plain,
( ~ spl0_3
| spl0_8
| spl0_10 ),
inference(sat_conversion,[],[f111]) ).
cnf(s21,plain,
( ~ spl0_12
| ~ spl0_13 ),
inference(sat_conversion,[],[f122]) ).
cnf(s24,plain,
( ~ spl0_8
| ~ spl0_12 ),
inference(sat_conversion,[],[f132]) ).
cnf(s26,plain,
( ~ spl0_3
| spl0_9
| spl0_12 ),
inference(sat_conversion,[],[f135]) ).
cnf(s27,plain,
( ~ spl0_3
| spl0_7
| spl0_13 ),
inference(sat_conversion,[],[f143]) ).
cnf(s28,plain,
( ~ spl0_1
| spl0_4
| spl0_12 ),
inference(sat_conversion,[],[f151]) ).
cnf(s29,plain,
( ~ spl0_1
| spl0_13 ),
inference(sat_conversion,[],[f160]) ).
cnf(s32,plain,
( ~ spl0_8
| ~ spl0_13 ),
inference(sat_conversion,[],[f163]) ).
cnf(s34,plain,
( ~ spl0_1
| spl0_5
| spl0_8 ),
inference(sat_conversion,[],[f170]) ).
cnf(s35,plain,
( spl0_8
| ~ spl0_3 ),
inference(rat,[],[s19,s8]) ).
cnf(s36,plain,
~ spl0_3,
inference(rat,[],[s11,s26,s27,s24,s32,s35]) ).
cnf(s37,plain,
~ spl0_2,
inference(rat,[],[s2,s3,s5]) ).
cnf(s38,plain,
spl0_1,
inference(rat,[],[s1,s36,s37]) ).
cnf(s40,plain,
spl0_13,
inference(rat,[],[s29,s38]) ).
cnf(s41,plain,
~ spl0_8,
inference(rat,[],[s32,s40]) ).
cnf(s42,plain,
~ spl0_12,
inference(rat,[],[s21,s40]) ).
cnf(s45,plain,
spl0_5,
inference(rat,[],[s34,s38,s41]) ).
cnf(s46,plain,
spl0_4,
inference(rat,[],[s28,s38,s42]) ).
cnf(s47,plain,
$false,
inference(rat,[],[s2,s45,s46]) ).
fof(f171,plain,
$false,
inference(avatar_sat_refutation,[],[s47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ026-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n009.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 22:30:30 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.08/1.15 % (2473871)Input is clausal, will run a generic CNF schedule.
% 2.08/1.15 % (2473880)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2632408944:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.08/1.15 % (2473880)First to succeed.
% 2.08/1.15 % (2473880)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2473871"
% 2.08/1.15 % (2473878)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=252679412:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.08/1.15 % (2473876)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=3924765904:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.08/1.15 % (2473877)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=212069466:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.08/1.15 % (2473879)lrs+10_1_sil=8000:sp=occurrence:random_seed=1110727679:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.08/1.15 % (2473882)dis-21_1_sil=8000:lcm=predicate:random_seed=625803401: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)
% 2.08/1.15 % (2473881)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2143014680:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.08/1.15 % (2473879)Also succeeded, but the first one will report.
% 2.08/1.15 % (2473882)Also succeeded, but the first one will report.
% 2.08/1.15 % (2473881)Also succeeded, but the first one will report.
% 2.08/1.15 % (2473880)Refutation found. Thanks to Tanya!
% 2.08/1.15 % SZS status Unsatisfiable for theBenchmark
% 2.08/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.54/1.24 % (2473880)------------------------------
% 2.54/1.24 % (2473880)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.24 % (2473880)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.24 % (2473880)CaDiCaL version: 2.1.3
% 2.54/1.24 % (2473880)Termination reason: Refutation
% 2.54/1.24 % (2473880)Time elapsed: 0.003 s
% 2.54/1.24 % (2473880)Peak memory usage: 89 MB
% 2.54/1.24 % (2473880)Instructions burned: 4 (million)
% 2.54/1.24 % (2473880)------------------------------
% 2.54/1.24 % (2473880)------------------------------
% 2.54/1.24 % (2473871)Success in time 0.287 s
% 2.54/1.24 % Vampire exiting
%------------------------------------------------------------------------------