TSTP Solution File: PUZ024-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : PUZ024-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 13:10:56 EDT 2023
% Result : Unsatisfiable 0.19s 0.63s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : PUZ024-1 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 22:31:32 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof:theBenchmark
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 % File :CSE---1.6
% 0.19/0.62 % Problem :theBenchmark
% 0.19/0.62 % Transform :cnf
% 0.19/0.62 % Format :tptp:raw
% 0.19/0.62 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.62
% 0.19/0.62 % Result :Theorem 0.000000s
% 0.19/0.62 % Output :CNFRefutation 0.000000s
% 0.19/0.62 %-------------------------------------------
% 0.19/0.63 %--------------------------------------------------------------------------
% 0.19/0.63 % File : PUZ024-1 : TPTP v8.1.2. Released v1.0.0.
% 0.19/0.63 % Domain : Puzzles
% 0.19/0.63 % Problem : Knights and Knaves #31
% 0.19/0.63 % Version : Especial.
% 0.19/0.63 % English : There is an island with exactly two types of people -
% 0.19/0.63 % truthtellers who always tell the truth and liars who always lie.
% 0.19/0.63 % There are a group of three people, A, B, and C on the island. A
% 0.19/0.63 % and B make the following statements. A: All of us are liars;
% 0.19/0.63 % B: Exactly one of us is a truthteller. What are A, B, and C?
% 0.19/0.63 % Answer: A is a liar, B is a truthteller, and C is a liar.
% 0.19/0.63
% 0.19/0.63 % Refs : [Smu78] Smullyan (1978), What is the Name of this Book?
% 0.19/0.63 % Source : [ANL]
% 0.19/0.63 % Names : Problem 31 [Smu78]
% 0.19/0.63 % : tandl31.ver1.in [ANL]
% 0.19/0.63
% 0.19/0.63 % Status : Unsatisfiable
% 0.19/0.63 % Rating : 0.00 v6.3.0, 0.14 v6.2.0, 0.00 v2.0.0
% 0.19/0.63 % Syntax : Number of clauses : 20 ( 6 unt; 6 nHn; 19 RR)
% 0.19/0.63 % Number of literals : 60 ( 0 equ; 37 neg)
% 0.19/0.63 % Maximal clause size : 5 ( 3 avg)
% 0.19/0.63 % Maximal term depth : 2 ( 1 avg)
% 0.19/0.63 % Number of predicates : 2 ( 2 usr; 0 prp; 1-3 aty)
% 0.19/0.63 % Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% 0.19/0.63 % Number of variables : 35 ( 3 sgn)
% 0.19/0.63 % SPC : CNF_UNS_RFO_NEQ_NHN
% 0.19/0.63
% 0.19/0.63 % Comments :
% 0.19/0.63 %--------------------------------------------------------------------------
% 0.19/0.63 %----Include axioms for truthtellers and liars
% 0.19/0.63 include('Axioms/PUZ002-0.ax').
% 0.19/0.63 %--------------------------------------------------------------------------
% 0.19/0.63 %----The next 6 clauses define what is meant by exactly one
% 0.19/0.63 %----is a truthteller.
% 0.19/0.63 cnf(one_says_one_truthteller,axiom,
% 0.19/0.63 ( ~ a_truth(says(X,one_truthteller))
% 0.19/0.63 | ~ people(X,Y,Z)
% 0.19/0.63 | ~ a_truth(truthteller(X))
% 0.19/0.63 | ~ a_truth(truthteller(Y))
% 0.19/0.63 | ~ a_truth(truthteller(Z)) ) ).
% 0.19/0.63
% 0.19/0.63 cnf(one_is_the_truth_teller,axiom,
% 0.19/0.63 ( ~ a_truth(one_truthteller)
% 0.19/0.63 | ~ people(X,Y,Z)
% 0.19/0.63 | a_truth(truthteller(X))
% 0.19/0.63 | a_truth(truthteller(Y))
% 0.19/0.63 | a_truth(truthteller(Z)) ) ).
% 0.19/0.63
% 0.19/0.63 cnf(one_is_not_the_truthteller,axiom,
% 0.19/0.63 ( ~ a_truth(one_truthteller)
% 0.19/0.63 | ~ people(X,Y,Z)
% 0.19/0.63 | ~ a_truth(truthteller(Y))
% 0.19/0.63 | ~ a_truth(truthteller(X))
% 0.19/0.63 | ~ a_truth(truthteller(Z)) ) ).
% 0.19/0.63
% 0.19/0.63 cnf(one_truthteller_two_liars,axiom,
% 0.19/0.63 ( ~ a_truth(one_truthteller)
% 0.19/0.63 | ~ people(X,Y,Z)
% 0.19/0.63 | ~ a_truth(liar(X))
% 0.19/0.63 | ~ a_truth(truthteller(Y))
% 0.19/0.63 | a_truth(liar(Z)) ) ).
% 0.19/0.63
% 0.19/0.63 cnf(two_truthtellers,axiom,
% 0.19/0.63 ( a_truth(one_truthteller)
% 0.19/0.63 | ~ people(X,Y,Z)
% 0.19/0.63 | ~ a_truth(liar(X))
% 0.19/0.63 | ~ a_truth(truthteller(Y))
% 0.19/0.63 | a_truth(truthteller(Z)) ) ).
% 0.19/0.63
% 0.19/0.63 cnf(three_liars,axiom,
% 0.19/0.63 ( a_truth(one_truthteller)
% 0.19/0.63 | ~ people(X,Y,Z)
% 0.19/0.63 | ~ a_truth(liar(X))
% 0.19/0.63 | ~ a_truth(liar(Y))
% 0.19/0.63 | a_truth(liar(Z)) ) ).
% 0.19/0.63
% 0.19/0.63 %----If x says that 'all of us' are liars then, all the persons may
% 0.19/0.63 %----be liars.
% 0.19/0.63 cnf(speaker_is_lying,axiom,
% 0.19/0.63 ( ~ a_truth(says(X,all_are_liars))
% 0.19/0.63 | ~ people(X,Y,Z)
% 0.19/0.63 | ~ a_truth(truthteller(X)) ) ).
% 0.19/0.63
% 0.19/0.63 cnf(all_truthtellers,axiom,
% 0.19/0.63 ( a_truth(all_are_liars)
% 0.19/0.63 | ~ people(X,Y,Z)
% 0.19/0.63 | a_truth(truthteller(X))
% 0.19/0.63 | a_truth(truthteller(Y))
% 0.19/0.63 | a_truth(truthteller(Z)) ) ).
% 0.19/0.63
% 0.19/0.63 cnf(b_c_a_people,hypothesis,
% 0.19/0.63 people(b,c,a) ).
% 0.19/0.63
% 0.19/0.63 cnf(a_c_b_people,hypothesis,
% 0.19/0.63 people(a,c,b) ).
% 0.19/0.63
% 0.19/0.63 cnf(c_b_a_people,hypothesis,
% 0.19/0.63 people(c,b,a) ).
% 0.19/0.63
% 0.19/0.63 cnf(a_says_all_are_liars,hypothesis,
% 0.19/0.63 a_truth(says(a,all_are_liars)) ).
% 0.19/0.63
% 0.19/0.63 cnf(b_says_one_truthteller,hypothesis,
% 0.19/0.63 a_truth(says(b,one_truthteller)) ).
% 0.19/0.63
% 0.19/0.63 %----This is an honest way of doing this. A simpler version could simply
% 0.19/0.63 %----prove that A and C are a liars, and B is a truthteller
% 0.19/0.63 cnf(prove_there_is_a_truthteller,negated_conjecture,
% 0.19/0.63 ~ a_truth(truthteller(Truthteller)) ).
% 0.19/0.63
% 0.19/0.63 %--------------------------------------------------------------------------
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 % Proof found
% 0.19/0.63 % SZS status Theorem for theBenchmark
% 0.19/0.63 % SZS output start Proof
% 0.19/0.63 %ClaNum:20(EqnAxiom:0)
% 0.19/0.63 %VarNum:33(SingletonVarNum:17)
% 0.19/0.63 %MaxLitNum:5
% 0.19/0.63 %MaxfuncDepth:1
% 0.19/0.63 %SharedTerms:15
% 0.19/0.63 %goalClause: 6
% 0.19/0.63 %singleGoalClaCount:1
% 0.19/0.63 [3]P2(a1,a5,a2)
% 0.19/0.63 [4]P2(a5,a1,a2)
% 0.19/0.63 [5]P2(a2,a5,a1)
% 0.19/0.63 [1]P1(f7(a1,a4))
% 0.19/0.63 [2]P1(f7(a2,a3))
% 0.19/0.63 [6]~P1(f8(x61))
% 0.19/0.63 [7]P1(f6(x71))+P1(f8(x71))
% 0.19/0.63 [9]P1(x91)+~P1(f7(x92,x91))+P1(f6(x92))
% 0.19/0.63 [10]~P1(x102)+~P1(f7(x101,x102))+P1(f8(x101))
% 0.19/0.63 [12]~P1(x121)+~P1(f7(x122,x121))+~P1(f6(x122))
% 0.19/0.63 [13]~P2(x133,x132,x131)+P1(a3)+P1(f8(x131))+P1(f8(x132))+P1(f8(x133))
% 0.19/0.63 [14]~P2(x143,x142,x141)+P1(f8(x141))+P1(f8(x142))+P1(f8(x143))+~P1(a4)
% 0.19/0.63 [16]~P2(x163,x162,x161)+P1(a4)+P1(f6(x161))+~P1(f6(x162))+~P1(f6(x163))
% 0.19/0.63 %EqnAxiom
% 0.19/0.63
% 0.19/0.63 %-------------------------------------------
% 0.19/0.63 cnf(21,plain,
% 0.19/0.63 (P1(f6(x211))),
% 0.19/0.63 inference(scs_inference,[],[6,7])).
% 0.19/0.63 cnf(23,plain,
% 0.19/0.63 (~P1(a3)+P1(f8(a2))),
% 0.19/0.63 inference(scs_inference,[],[6,1,2,7,12,10])).
% 0.19/0.63 cnf(34,plain,
% 0.19/0.63 (~P1(f8(x341))),
% 0.19/0.63 inference(rename_variables,[],[6])).
% 0.19/0.63 cnf(35,plain,
% 0.19/0.63 (P1(f8(a5))+P1(f8(a2))),
% 0.19/0.63 inference(scs_inference,[],[6,34,3,1,21,12,10,23,13])).
% 0.19/0.63 cnf(40,plain,
% 0.19/0.63 (P1(f8(a2))),
% 0.19/0.63 inference(scs_inference,[],[6,35])).
% 0.19/0.63 cnf(49,plain,
% 0.19/0.63 ($false),
% 0.19/0.63 inference(scs_inference,[],[40,6]),
% 0.19/0.63 ['proof']).
% 0.19/0.63 % SZS output end Proof
% 0.19/0.63 % Total time :0.000000s
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