%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : PUZ026-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 0.14s 5.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 27
% Syntax : Number of formulae : 109 ( 13 unt; 10 def)
% Number of atoms : 285 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 348 ( 172 ~; 166 |; 0 &)
% ( 10 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 12 usr; 11 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 111 ( 111 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] :
( a_truth(normal(X))
| a_truth(liar(X))
| a_truth(truthteller(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] :
( ~ a_truth(liar(X))
| ~ a_truth(truthteller(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( a_truth(normal(Y))
| a_truth(truthteller(Y))
| ~ a_truth(says(Y,X))
| ~ a_truth(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( a_truth(normal(Y))
| a_truth(liar(Y))
| ~ a_truth(says(Y,X))
| a_truth(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X] :
( a_truth(normal(X))
| a_truth(not_normal(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y,Z] :
( ~ a_truth(truthteller(Y))
| ~ a_truth(truthteller(X))
| ~ people(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,Z] :
( ~ a_truth(liar(Y))
| ~ a_truth(liar(X))
| ~ people(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y,Z] :
( ~ a_truth(liar(Z))
| ~ a_truth(liar(X))
| ~ people(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y,Z] :
( ~ a_truth(normal(Y))
| ~ a_truth(normal(X))
| ~ people(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y,Z] :
( ~ a_truth(normal(Z))
| ~ a_truth(normal(X))
| ~ people(X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
people(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
people(b,c,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
people(c,b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
a_truth(says(a,normal(a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
a_truth(says(b,normal(a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
a_truth(says(c,not_normal(c))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
! [Liar,Normal,Truthteller] :
( ~ a_truth(truthteller(Truthteller))
| ~ a_truth(normal(Normal))
| ~ a_truth(liar(Liar)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,plain,
! [X0] :
( a_truth(normal(X0))
| a_truth(liar(X0))
| a_truth(truthteller(X0)) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f26,plain,
! [X0] :
( ~ a_truth(liar(X0))
| ~ a_truth(truthteller(X0)) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f32,plain,
! [Y] :
( a_truth(normal(Y))
| a_truth(truthteller(Y))
| ! [X] :
( ~ a_truth(says(Y,X))
| ~ a_truth(X) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f33,plain,
! [X0,X1] :
( a_truth(normal(X1))
| a_truth(truthteller(X1))
| ~ a_truth(says(X1,X0))
| ~ a_truth(X0) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
! [Y] :
( a_truth(normal(Y))
| a_truth(liar(Y))
| ! [X] :
( ~ a_truth(says(Y,X))
| a_truth(X) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f35,plain,
! [X0,X1] :
( a_truth(normal(X1))
| a_truth(liar(X1))
| ~ a_truth(says(X1,X0))
| a_truth(X0) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,plain,
! [X0] :
( a_truth(normal(X0))
| a_truth(not_normal(X0)) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f38,plain,
! [Y] :
( ~ a_truth(truthteller(Y))
| ! [X] :
( ~ a_truth(truthteller(X))
| ! [Z] : ~ people(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ a_truth(truthteller(X1))
| ~ a_truth(truthteller(X0))
| ~ people(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f42,plain,
! [Y] :
( ~ a_truth(liar(Y))
| ! [X] :
( ~ a_truth(liar(X))
| ! [Z] : ~ people(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ a_truth(liar(X1))
| ~ a_truth(liar(X0))
| ~ people(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [Z] :
( ~ a_truth(liar(Z))
| ! [X] :
( ~ a_truth(liar(X))
| ! [Y] : ~ people(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ~ a_truth(liar(X2))
| ~ a_truth(liar(X0))
| ~ people(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [Y] :
( ~ a_truth(normal(Y))
| ! [X] :
( ~ a_truth(normal(X))
| ! [Z] : ~ people(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ~ a_truth(normal(X1))
| ~ a_truth(normal(X0))
| ~ people(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [Z] :
( ~ a_truth(normal(Z))
| ! [X] :
( ~ a_truth(normal(X))
| ! [Y] : ~ people(X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ~ a_truth(normal(X2))
| ~ a_truth(normal(X0))
| ~ people(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
people(a,b,c),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f51,plain,
people(b,c,a),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f52,plain,
people(c,b,a),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f53,plain,
a_truth(says(a,normal(a))),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f54,plain,
a_truth(says(b,normal(a))),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f55,plain,
a_truth(says(c,not_normal(c))),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f56,plain,
( ! [Truthteller] : ~ a_truth(truthteller(Truthteller))
| ! [Normal] : ~ a_truth(normal(Normal))
| ! [Liar] : ~ a_truth(liar(Liar)) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ~ a_truth(truthteller(X2))
| ~ a_truth(normal(X1))
| ~ a_truth(liar(X0)) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,definition,
! [X0] :
( sQ0_spl
<=> ~ a_truth(liar(X0)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f59,plain,
! [X0] :
( ~ sQ0_spl
| ~ a_truth(liar(X0)) ),
inference(component_clause,[status(thm)],[f58]) ).
fof(f61,definition,
! [X1] :
( sQ1_spl
<=> ~ a_truth(normal(X1)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f62,plain,
! [X0] :
( ~ sQ1_spl
| ~ a_truth(normal(X0)) ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,definition,
! [X2] :
( sQ2_spl
<=> ~ a_truth(truthteller(X2)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f65,plain,
! [X0] :
( ~ sQ2_spl
| ~ a_truth(truthteller(X0)) ),
inference(component_clause,[status(thm)],[f64]) ).
fof(f67,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f57,f58,f61,f64]) ).
fof(f68,plain,
! [X0] :
( ~ sQ2_spl
| a_truth(normal(X0))
| a_truth(liar(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f24,f65]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| a_truth(liar(X1))
| ~ a_truth(normal(X0))
| ~ people(X0,X1,X2) ),
inference(resolution,[status(thm)],[f47,f68]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| a_truth(liar(X2))
| ~ a_truth(normal(X0))
| ~ people(X0,X1,X2) ),
inference(resolution,[status(thm)],[f49,f68]) ).
fof(f72,plain,
! [X0,X1] :
( ~ sQ2_spl
| a_truth(normal(X1))
| ~ a_truth(says(X1,X0))
| ~ a_truth(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f33,f65]) ).
fof(f73,plain,
( ~ sQ2_spl
| a_truth(normal(c))
| ~ a_truth(not_normal(c)) ),
inference(resolution,[status(thm)],[f72,f55]) ).
fof(f76,definition,
( sQ3_spl
<=> a_truth(not_normal(c)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( sQ3_spl
| ~ a_truth(not_normal(c)) ),
inference(component_clause,[status(thm)],[f76]) ).
fof(f79,definition,
( sQ4_spl
<=> a_truth(normal(c)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( ~ sQ4_spl
| a_truth(normal(c)) ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f81,plain,
( sQ4_spl
| ~ a_truth(normal(c)) ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,plain,
( ~ sQ2_spl
| sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f73,f76,f79,f64]) ).
fof(f83,definition,
( sQ5_spl
<=> a_truth(normal(a)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ5_spl
| a_truth(normal(a)) ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,definition,
( sQ6_spl
<=> a_truth(normal(b)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f87,plain,
( ~ sQ6_spl
| a_truth(normal(b)) ),
inference(component_clause,[status(thm)],[f86]) ).
fof(f92,plain,
( a_truth(normal(b))
| a_truth(liar(b))
| a_truth(normal(a)) ),
inference(resolution,[status(thm)],[f35,f54]) ).
fof(f93,plain,
( a_truth(normal(a))
| a_truth(liar(a))
| a_truth(normal(a)) ),
inference(resolution,[status(thm)],[f35,f53]) ).
fof(f98,definition,
( sQ8_spl
<=> a_truth(liar(b)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f101,plain,
( sQ6_spl
| sQ8_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f92,f83,f98,f86]) ).
fof(f102,definition,
( sQ9_spl
<=> a_truth(liar(a)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f103,plain,
( ~ sQ9_spl
| a_truth(liar(a)) ),
inference(component_clause,[status(thm)],[f102]) ).
fof(f105,plain,
( sQ9_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f93,f83,f102]) ).
fof(f108,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f87,f62]) ).
fof(f109,plain,
( ~ sQ6_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f108]) ).
fof(f115,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f103,f59]) ).
fof(f116,plain,
( ~ sQ9_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f115]) ).
fof(f129,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ sQ2_spl
| a_truth(liar(X0))
| ~ people(c,X0,X1) ),
inference(resolution,[status(thm)],[f70,f80]) ).
fof(f131,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| a_truth(liar(b)) ),
inference(resolution,[status(thm)],[f129,f52]) ).
fof(f132,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ sQ2_spl
| a_truth(liar(X1))
| ~ people(c,X0,X1) ),
inference(resolution,[status(thm)],[f71,f80]) ).
fof(f134,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| a_truth(liar(a)) ),
inference(resolution,[status(thm)],[f132,f52]) ).
fof(f147,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ a_truth(normal(X0))
| ~ people(X0,X1,c) ),
inference(resolution,[status(thm)],[f49,f80]) ).
fof(f163,plain,
( ~ sQ4_spl
| ~ a_truth(normal(a)) ),
inference(resolution,[status(thm)],[f147,f50]) ).
fof(f172,plain,
! [X0,X1] :
( ~ sQ4_spl
| ~ sQ2_spl
| ~ a_truth(liar(X0))
| ~ people(X0,X1,a) ),
inference(resolution,[status(thm)],[f45,f134]) ).
fof(f173,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ2_spl
| ~ people(b,X0,a) ),
inference(resolution,[status(thm)],[f172,f131]) ).
fof(f175,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f51,f173]) ).
fof(f176,plain,
( ~ sQ4_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f175]) ).
fof(f177,plain,
( ~ sQ4_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f163,f83,f79]) ).
fof(f184,plain,
( sQ3_spl
| a_truth(normal(c)) ),
inference(resolution,[status(thm)],[f78,f37]) ).
fof(f185,plain,
( sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f184,f79,f76]) ).
fof(f194,plain,
! [X0] :
( ~ sQ0_spl
| a_truth(normal(X0))
| a_truth(truthteller(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f24,f59]) ).
fof(f195,plain,
( sQ4_spl
| ~ sQ0_spl
| a_truth(truthteller(c)) ),
inference(resolution,[status(thm)],[f194,f81]) ).
fof(f203,plain,
! [X0,X1] :
( sQ4_spl
| ~ sQ0_spl
| ~ a_truth(truthteller(X0))
| ~ people(X0,c,X1) ),
inference(resolution,[status(thm)],[f39,f195]) ).
fof(f206,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| a_truth(truthteller(X1))
| ~ a_truth(normal(X0))
| ~ people(X0,X1,X2) ),
inference(resolution,[status(thm)],[f47,f194]) ).
fof(f207,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ sQ0_spl
| a_truth(truthteller(X0))
| ~ people(a,X0,X1) ),
inference(resolution,[status(thm)],[f206,f84]) ).
fof(f209,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| a_truth(truthteller(b)) ),
inference(resolution,[status(thm)],[f207,f50]) ).
fof(f216,definition,
( sQ11_spl
<=> a_truth(truthteller(b)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f217,plain,
( ~ sQ11_spl
| a_truth(truthteller(b)) ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f225,plain,
! [X0] :
( sQ4_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ people(b,c,X0) ),
inference(resolution,[status(thm)],[f209,f203]) ).
fof(f232,plain,
( sQ4_spl
| ~ sQ0_spl
| ~ sQ5_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f51,f225]) ).
fof(f233,plain,
( sQ4_spl
| ~ sQ0_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f232]) ).
fof(f242,plain,
! [X0] :
( ~ sQ1_spl
| a_truth(liar(X0))
| a_truth(truthteller(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f24,f62]) ).
fof(f254,plain,
( ~ sQ11_spl
| ~ a_truth(liar(b)) ),
inference(resolution,[status(thm)],[f217,f26]) ).
fof(f258,plain,
( ~ sQ11_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f254,f98,f216]) ).
fof(f259,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f84,f62]) ).
fof(f260,plain,
( ~ sQ5_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f259]) ).
fof(f274,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| a_truth(truthteller(X1))
| ~ a_truth(liar(X0))
| ~ people(X0,X1,X2) ),
inference(resolution,[status(thm)],[f43,f242]) ).
fof(f279,plain,
! [X0,X1] :
( ~ sQ9_spl
| ~ sQ1_spl
| a_truth(truthteller(X0))
| ~ people(a,X0,X1) ),
inference(resolution,[status(thm)],[f274,f103]) ).
fof(f285,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| a_truth(truthteller(b)) ),
inference(resolution,[status(thm)],[f279,f50]) ).
fof(f286,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f285,f216,f61,f102]) ).
fof(f287,plain,
$false,
inference(sat_refutation,[status(thm)],[f67,f82,f101,f105,f109,f116,f176,f177,f185,f233,f258,f260,f286]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ026-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n014.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Mon Sep 21 03:45:56 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.39 % Drodi V4.1.1
% 0.14/5.41 % Refutation found
% 0.14/5.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.43 % Elapsed time: 0.041510 seconds
% 0.14/5.43 % CPU time: 0.138109 seconds
% 0.14/5.43 % Total memory used: 14.906 MB
% 0.14/5.43 % Net memory used: 14.629 MB
%------------------------------------------------------------------------------