%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : PUZ027-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 : Thu Sep 24 01:59:53 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 26
% Syntax : Number of formulae : 80 ( 12 unt; 15 def)
% Number of atoms : 181 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 186 ( 85 ~; 86 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 18 ( 17 usr; 16 prp; 0-1 aty)
% Number of functors : 14 ( 14 usr; 11 con; 0-1 aty)
% Number of variables : 4 ( 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] :
( a_truth(normal(X))
| a_truth(liar(X))
| a_truth(truthteller(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
( answer(a_and_b_truthteller)
| ~ a_truth(truthteller(b))
| ~ a_truth(truthteller(a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,hypothesis,
( answer(a_truthteller_b_normal)
| ~ a_truth(normal(b))
| ~ a_truth(truthteller(a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,hypothesis,
( answer(a_truthteller_b_liar)
| ~ a_truth(liar(b))
| ~ a_truth(truthteller(a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,hypothesis,
( answer(a_normal_b_truthteller)
| ~ a_truth(truthteller(b))
| ~ a_truth(normal(a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
( answer(a_and_b_normal)
| ~ a_truth(normal(b))
| ~ a_truth(normal(a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
( answer(a_normal_b_liar)
| ~ a_truth(liar(b))
| ~ a_truth(normal(a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,hypothesis,
( answer(a_liar_b_truthteller)
| ~ a_truth(truthteller(b))
| ~ a_truth(liar(a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,hypothesis,
( answer(a_liar_b_normal)
| ~ a_truth(normal(b))
| ~ a_truth(liar(a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,hypothesis,
( answer(a_and_b_liar)
| ~ a_truth(liar(b))
| ~ a_truth(liar(a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
! [Answer] : ~ answer(Answer),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,plain,
! [X0] :
( a_truth(normal(X0))
| a_truth(liar(X0))
| a_truth(truthteller(X0)) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f65,plain,
( answer(a_and_b_truthteller)
| ~ a_truth(truthteller(b))
| ~ a_truth(truthteller(a)) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f66,plain,
( answer(a_truthteller_b_normal)
| ~ a_truth(normal(b))
| ~ a_truth(truthteller(a)) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f67,plain,
( answer(a_truthteller_b_liar)
| ~ a_truth(liar(b))
| ~ a_truth(truthteller(a)) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f68,plain,
( answer(a_normal_b_truthteller)
| ~ a_truth(truthteller(b))
| ~ a_truth(normal(a)) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f69,plain,
( answer(a_and_b_normal)
| ~ a_truth(normal(b))
| ~ a_truth(normal(a)) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f70,plain,
( answer(a_normal_b_liar)
| ~ a_truth(liar(b))
| ~ a_truth(normal(a)) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f71,plain,
( answer(a_liar_b_truthteller)
| ~ a_truth(truthteller(b))
| ~ a_truth(liar(a)) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f72,plain,
( answer(a_liar_b_normal)
| ~ a_truth(normal(b))
| ~ a_truth(liar(a)) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f73,plain,
( answer(a_and_b_liar)
| ~ a_truth(liar(b))
| ~ a_truth(liar(a)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f74,plain,
! [X0] : ~ answer(X0),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f75,definition,
( sQ0_spl
<=> a_truth(truthteller(a)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f78,definition,
( sQ1_spl
<=> a_truth(truthteller(b)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f81,definition,
( sQ2_spl
<=> answer(a_and_b_truthteller) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ2_spl
| answer(a_and_b_truthteller) ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f65,f75,f78,f81]) ).
fof(f85,definition,
( sQ3_spl
<=> a_truth(normal(b)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f87,plain,
( sQ3_spl
| ~ a_truth(normal(b)) ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,definition,
( sQ4_spl
<=> answer(a_truthteller_b_normal) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f89,plain,
( ~ sQ4_spl
| answer(a_truthteller_b_normal) ),
inference(component_clause,[status(thm)],[f88]) ).
fof(f91,plain,
( sQ4_spl
| ~ sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f66,f75,f85,f88]) ).
fof(f92,definition,
( sQ5_spl
<=> a_truth(liar(b)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f95,definition,
( sQ6_spl
<=> answer(a_truthteller_b_liar) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f96,plain,
( ~ sQ6_spl
| answer(a_truthteller_b_liar) ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f98,plain,
( sQ6_spl
| ~ sQ5_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f67,f75,f92,f95]) ).
fof(f99,definition,
( sQ7_spl
<=> a_truth(normal(a)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f101,plain,
( sQ7_spl
| ~ a_truth(normal(a)) ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,definition,
( sQ8_spl
<=> answer(a_normal_b_truthteller) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f103,plain,
( ~ sQ8_spl
| answer(a_normal_b_truthteller) ),
inference(component_clause,[status(thm)],[f102]) ).
fof(f105,plain,
( sQ8_spl
| ~ sQ1_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f68,f99,f78,f102]) ).
fof(f106,definition,
( sQ9_spl
<=> answer(a_and_b_normal) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f107,plain,
( ~ sQ9_spl
| answer(a_and_b_normal) ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f109,plain,
( sQ9_spl
| ~ sQ3_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f69,f99,f85,f106]) ).
fof(f110,definition,
( sQ10_spl
<=> answer(a_normal_b_liar) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f111,plain,
( ~ sQ10_spl
| answer(a_normal_b_liar) ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f113,plain,
( sQ10_spl
| ~ sQ5_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f70,f99,f92,f110]) ).
fof(f114,definition,
( sQ11_spl
<=> a_truth(liar(a)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f117,definition,
( sQ12_spl
<=> answer(a_liar_b_truthteller) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ12_spl
| answer(a_liar_b_truthteller) ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( sQ12_spl
| ~ sQ1_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f71,f114,f78,f117]) ).
fof(f121,definition,
( sQ13_spl
<=> answer(a_liar_b_normal) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ13_spl
| answer(a_liar_b_normal) ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( sQ13_spl
| ~ sQ3_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f72,f114,f85,f121]) ).
fof(f125,definition,
( sQ14_spl
<=> answer(a_and_b_liar) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ14_spl
| answer(a_and_b_liar) ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ14_spl
| ~ sQ5_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f73,f114,f92,f125]) ).
fof(f129,plain,
( sQ3_spl
| a_truth(liar(b))
| a_truth(truthteller(b)) ),
inference(resolution,[status(thm)],[f87,f33]) ).
fof(f130,plain,
( sQ3_spl
| sQ5_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f129,f78,f92,f85]) ).
fof(f131,plain,
( ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f126,f74]) ).
fof(f132,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f131]) ).
fof(f133,plain,
( ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f122,f74]) ).
fof(f134,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f133]) ).
fof(f135,plain,
( ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f118,f74]) ).
fof(f136,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f135]) ).
fof(f137,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f111,f74]) ).
fof(f138,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f137]) ).
fof(f139,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f107,f74]) ).
fof(f140,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f139]) ).
fof(f141,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f103,f74]) ).
fof(f142,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f141]) ).
fof(f143,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f96,f74]) ).
fof(f144,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f143]) ).
fof(f145,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f89,f74]) ).
fof(f146,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f145]) ).
fof(f147,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f82,f74]) ).
fof(f148,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f147]) ).
fof(f149,plain,
( sQ7_spl
| a_truth(liar(a))
| a_truth(truthteller(a)) ),
inference(resolution,[status(thm)],[f101,f33]) ).
fof(f150,plain,
( sQ7_spl
| sQ11_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f149,f75,f114,f99]) ).
fof(f151,plain,
$false,
inference(sat_refutation,[status(thm)],[f84,f91,f98,f105,f109,f113,f120,f124,f128,f130,f132,f134,f136,f138,f140,f142,f144,f146,f148,f150]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ027-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n005.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 03:45:48 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.048564 seconds
% 0.13/0.41 % CPU time: 0.114841 seconds
% 0.13/0.41 % Total memory used: 17.340 MB
% 0.13/0.41 % Net memory used: 17.185 MB
%------------------------------------------------------------------------------