%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : PUZ026-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 : Sun Sep 27 08:23:07 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 60 ( 17 unt; 0 def)
% Number of atoms : 133 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 138 ( 65 ~; 73 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 11 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a_b_c_are_people,axiom,
people(a,b,c),
file('theBenchmark.p',a_b_c_are_people) ).
cnf(c_1,plain,
people(a,b,c),
inference(clausify,[status(thm)],[a_b_c_are_people]) ).
fof(not_two_normal2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ a_truth(normal(VAR_2))
| ~ a_truth(normal(VAR_0))
| ~ people(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',not_two_normal2) ).
cnf(c_2,plain,
( ~ a_truth(normal(C))
| ~ a_truth(normal(A))
| ~ people(A,B,C) ),
inference(clausify,[status(thm)],[not_two_normal2]) ).
fof(not_two_normal1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ a_truth(normal(VAR_1))
| ~ a_truth(normal(VAR_0))
| ~ people(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',not_two_normal1) ).
cnf(c_3,plain,
( ~ a_truth(normal(B))
| ~ a_truth(normal(A))
| ~ people(A,B,C) ),
inference(clausify,[status(thm)],[not_two_normal1]) ).
fof(not_two_liars1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ a_truth(liar(VAR_1))
| ~ a_truth(liar(VAR_0))
| ~ people(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',not_two_liars1) ).
cnf(c_5,plain,
( ~ a_truth(liar(B))
| ~ a_truth(liar(A))
| ~ people(A,B,C) ),
inference(clausify,[status(thm)],[not_two_liars1]) ).
fof(not_two_truthtellers1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ a_truth(truthteller(VAR_1))
| ~ a_truth(truthteller(VAR_0))
| ~ people(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',not_two_truthtellers1) ).
cnf(c_7,plain,
( ~ a_truth(truthteller(B))
| ~ a_truth(truthteller(A))
| ~ people(A,B,C) ),
inference(clausify,[status(thm)],[not_two_truthtellers1]) ).
fof(b_c_a_are_people,axiom,
people(b,c,a),
file('theBenchmark.p',b_c_a_are_people) ).
cnf(c_8,plain,
people(b,c,a),
inference(clausify,[status(thm)],[b_c_a_are_people]) ).
cnf(c_10,plain,
( ~ a_truth(truthteller(c))
| ~ a_truth(truthteller(b)) ),
inference(resolve,[status(thm)],[c_8,c_7]) ).
cnf(c_12,plain,
( ~ a_truth(normal(c))
| ~ a_truth(normal(b)) ),
inference(resolve,[status(thm)],[c_8,c_3]) ).
cnf(c_15,plain,
( ~ a_truth(liar(b))
| ~ a_truth(liar(a)) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_17,plain,
( ~ a_truth(normal(b))
| ~ a_truth(normal(a)) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_18,plain,
( ~ a_truth(normal(c))
| ~ a_truth(normal(a)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(prove_one_of_each,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ a_truth(truthteller(VAR_2))
| ~ a_truth(normal(VAR_1))
| ~ a_truth(liar(VAR_0)) ),
file('theBenchmark.p',prove_one_of_each) ).
cnf(c_19,plain,
( ~ a_truth(truthteller(C))
| ~ a_truth(normal(B))
| ~ a_truth(liar(A)) ),
inference(clausify,[status(thm)],[prove_one_of_each]) ).
fof(c_says_c_not_normal,axiom,
a_truth(says(c,not_normal(c))),
file('theBenchmark.p',c_says_c_not_normal) ).
cnf(c_20,plain,
a_truth(says(c,not_normal(c))),
inference(clausify,[status(thm)],[c_says_c_not_normal]) ).
fof(b_says_a_normal,axiom,
a_truth(says(b,normal(a))),
file('theBenchmark.p',b_says_a_normal) ).
cnf(c_21,plain,
a_truth(says(b,normal(a))),
inference(clausify,[status(thm)],[b_says_a_normal]) ).
fof(a_says_a_normal,axiom,
a_truth(says(a,normal(a))),
file('theBenchmark.p',a_says_a_normal) ).
cnf(c_22,plain,
a_truth(says(a,normal(a))),
inference(clausify,[status(thm)],[a_says_a_normal]) ).
fof(normal_or_not_normal,axiom,
! [VAR_0] :
( a_truth(normal(VAR_0))
| a_truth(not_normal(VAR_0)) ),
file('theBenchmark.p',normal_or_not_normal) ).
cnf(c_23,plain,
( a_truth(normal(A))
| a_truth(not_normal(A)) ),
inference(clausify,[status(thm)],[normal_or_not_normal]) ).
fof(liars_and_normal_lie,axiom,
! [VAR_0,VAR_1] :
( a_truth(normal(VAR_1))
| a_truth(liar(VAR_1))
| ~ a_truth(says(VAR_1,VAR_0))
| a_truth(VAR_0) ),
file('theBenchmark.p',liars_and_normal_lie) ).
cnf(c_25,plain,
( a_truth(normal(B))
| a_truth(liar(B))
| ~ a_truth(says(B,A))
| a_truth(A) ),
inference(clausify,[status(thm)],[liars_and_normal_lie]) ).
fof(truthtellers_and_normal_tell_truth,axiom,
! [VAR_0,VAR_1] :
( a_truth(normal(VAR_1))
| a_truth(truthteller(VAR_1))
| ~ a_truth(says(VAR_1,VAR_0))
| ~ a_truth(VAR_0) ),
file('theBenchmark.p',truthtellers_and_normal_tell_truth) ).
cnf(c_26,plain,
( a_truth(normal(B))
| a_truth(truthteller(B))
| ~ a_truth(says(B,A))
| ~ a_truth(A) ),
inference(clausify,[status(thm)],[truthtellers_and_normal_tell_truth]) ).
fof(liars_lie,axiom,
! [VAR_0,VAR_1] :
( ~ a_truth(VAR_1)
| ~ a_truth(says(VAR_0,VAR_1))
| ~ a_truth(liar(VAR_0)) ),
file('theBenchmark.p',liars_lie) ).
cnf(c_27,plain,
( ~ a_truth(B)
| ~ a_truth(says(A,B))
| ~ a_truth(liar(A)) ),
inference(clausify,[status(thm)],[liars_lie]) ).
fof(person_is_one_type,axiom,
! [VAR_0] :
( a_truth(normal(VAR_0))
| a_truth(liar(VAR_0))
| a_truth(truthteller(VAR_0)) ),
file('theBenchmark.p',person_is_one_type) ).
cnf(c_32,plain,
( a_truth(normal(A))
| a_truth(liar(A))
| a_truth(truthteller(A)) ),
inference(clausify,[status(thm)],[person_is_one_type]) ).
cnf(c_82,plain,
( a_truth(normal(a))
| a_truth(liar(a))
| a_truth(normal(a)) ),
inference(resolve,[status(thm)],[c_25,c_22]) ).
cnf(c_36,plain,
( a_truth(liar(a))
| a_truth(normal(a)) ),
inference(copy,[status(thm)],[c_82]) ).
cnf(c_37,plain,
( a_truth(normal(b))
| a_truth(liar(b))
| a_truth(normal(a)) ),
inference(resolve,[status(thm)],[c_25,c_21]) ).
cnf(c_38,plain,
( a_truth(normal(b))
| a_truth(truthteller(b))
| ~ a_truth(normal(a)) ),
inference(resolve,[status(thm)],[c_26,c_21]) ).
cnf(c_41,plain,
( ~ a_truth(not_normal(c))
| ~ a_truth(liar(c)) ),
inference(resolve,[status(thm)],[c_27,c_20]) ).
cnf(c_50,plain,
( ~ a_truth(truthteller(B))
| ~ a_truth(normal(A))
| a_truth(normal(a)) ),
inference(resolve,[status(thm)],[c_36,c_19]) ).
cnf(c_51,plain,
( a_truth(normal(c))
| ~ a_truth(liar(c)) ),
inference(resolve,[status(thm)],[c_41,c_23]) ).
cnf(c_83,plain,
( a_truth(normal(c))
| a_truth(truthteller(c))
| a_truth(normal(c)) ),
inference(resolve,[status(thm)],[c_51,c_32]) ).
cnf(c_52,plain,
( a_truth(truthteller(c))
| a_truth(normal(c)) ),
inference(copy,[status(thm)],[c_83]) ).
cnf(c_54,plain,
( ~ a_truth(liar(a))
| a_truth(normal(b))
| a_truth(normal(a)) ),
inference(resolve,[status(thm)],[c_37,c_15]) ).
cnf(c_84,plain,
( a_truth(normal(a))
| a_truth(normal(b))
| a_truth(normal(a)) ),
inference(resolve,[status(thm)],[c_54,c_36]) ).
cnf(c_63,plain,
( a_truth(normal(b))
| a_truth(normal(a)) ),
inference(copy,[status(thm)],[c_84]) ).
cnf(c_85,plain,
( ~ a_truth(truthteller(A))
| a_truth(normal(a))
| a_truth(normal(a)) ),
inference(resolve,[status(thm)],[c_63,c_50]) ).
cnf(c_64,plain,
( ~ a_truth(truthteller(A))
| a_truth(normal(a)) ),
inference(copy,[status(thm)],[c_85]) ).
cnf(c_65,plain,
( ~ a_truth(normal(c))
| a_truth(normal(a)) ),
inference(resolve,[status(thm)],[c_63,c_12]) ).
cnf(c_66,plain,
( a_truth(normal(c))
| a_truth(normal(a)) ),
inference(resolve,[status(thm)],[c_64,c_52]) ).
cnf(c_86,plain,
( a_truth(normal(a))
| a_truth(normal(a)) ),
inference(resolve,[status(thm)],[c_66,c_65]) ).
cnf(c_67,plain,
a_truth(normal(a)),
inference(copy,[status(thm)],[c_86]) ).
cnf(c_69,plain,
( a_truth(normal(b))
| a_truth(truthteller(b)) ),
inference(resolve,[status(thm)],[c_67,c_38]) ).
cnf(c_70,plain,
~ a_truth(normal(c)),
inference(resolve,[status(thm)],[c_67,c_18]) ).
cnf(c_71,plain,
~ a_truth(normal(b)),
inference(resolve,[status(thm)],[c_67,c_17]) ).
cnf(c_77,plain,
a_truth(truthteller(c)),
inference(resolve,[status(thm)],[c_70,c_52]) ).
cnf(c_79,plain,
a_truth(truthteller(b)),
inference(resolve,[status(thm)],[c_71,c_69]) ).
cnf(c_87,plain,
~ a_truth(truthteller(c)),
inference(resolve,[status(thm)],[c_79,c_10]) ).
cnf(c_81,plain,
$false,
inference(resolve,[status(thm)],[c_77,c_87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ026-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n003.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
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 05:06:39 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 2081387 was started by sandbox2 on n003,
% 0.10/0.36 % Sat Sep 26 05:06:39 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.36
% 0.10/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.38
% 0.12/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.38
% 0.12/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.12/0.38 % Length of proof is 39.
% 0.12/0.38 % Level of proof is 9.
% 0.12/0.38 % Maximum clause weight is 12.000.
% 0.12/0.38 % Given clauses 50.
% 0.12/0.38
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------