TSTP Solution File: PUZ023-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : PUZ023-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n023.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 0.11s 0.52s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07 % Problem : PUZ023-1 : TPTP v8.1.2. Released v1.0.0.
% 0.02/0.08 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.07/0.27 % Computer : n023.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 300
% 0.07/0.27 % DateTime : Sat Aug 26 22:27:56 EDT 2023
% 0.07/0.27 % CPUTime :
% 0.11/0.42 start to proof:theBenchmark
% 0.11/0.51 %-------------------------------------------
% 0.11/0.51 % File :CSE---1.6
% 0.11/0.51 % Problem :theBenchmark
% 0.11/0.51 % Transform :cnf
% 0.11/0.51 % Format :tptp:raw
% 0.11/0.51 % Command :java -jar mcs_scs.jar %d %s
% 0.11/0.51
% 0.11/0.51 % Result :Theorem 0.040000s
% 0.11/0.51 % Output :CNFRefutation 0.040000s
% 0.11/0.51 %-------------------------------------------
% 0.11/0.52 %--------------------------------------------------------------------------
% 0.11/0.52 % File : PUZ023-1 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.52 % Domain : Puzzles
% 0.11/0.52 % Problem : Knights and Knaves #27
% 0.11/0.52 % Version : Especial.
% 0.11/0.52 % English : There is an island with exactly two types of people :
% 0.11/0.52 % truthtellers who always tell the truth and liars who always
% 0.11/0.52 % lie. There are a group of three people, A, B, and C on the
% 0.11/0.52 % island. A stranger passes by and asks A, "How many
% 0.11/0.52 % truthtellers are among you ?" A answers indistinctly. So the
% 0.11/0.52 % stranger asks B, "what did A say?". B replies "A said that
% 0.11/0.52 % there is exactly one truthteller among us." Then C says,
% 0.11/0.52 % "Don't believe B; he is lying!" What are B and C. Answer:
% 0.11/0.52 % B is a liar and C is a truth-teller.
% 0.11/0.52
% 0.11/0.52 % Refs : [Smu78] Smullyan (1978), What is the Name of this Book?
% 0.11/0.52 % Source : [ANL]
% 0.11/0.52 % Names : Problem 27 [Smu78]
% 0.11/0.52 % : tandl27.ver1.in [ANL]
% 0.11/0.52
% 0.11/0.52 % Status : Unsatisfiable
% 0.11/0.52 % Rating : 0.00 v2.0.0
% 0.11/0.52 % Syntax : Number of clauses : 22 ( 5 unt; 6 nHn; 21 RR)
% 0.11/0.52 % Number of literals : 65 ( 0 equ; 39 neg)
% 0.11/0.52 % Maximal clause size : 5 ( 2 avg)
% 0.11/0.52 % Maximal term depth : 3 ( 1 avg)
% 0.11/0.52 % Number of predicates : 3 ( 3 usr; 0 prp; 1-3 aty)
% 0.11/0.52 % Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% 0.11/0.52 % Number of variables : 32 ( 4 sgn)
% 0.11/0.52 % SPC : CNF_UNS_RFO_NEQ_NHN
% 0.11/0.52
% 0.11/0.52 % Comments :
% 0.11/0.52 %--------------------------------------------------------------------------
% 0.11/0.52 %----Include axioms for truthtellers and liars
% 0.11/0.52 include('Axioms/PUZ002-0.ax').
% 0.11/0.52 %--------------------------------------------------------------------------
% 0.11/0.52 cnf(one_is_the_truthteller,axiom,
% 0.11/0.52 ( ~ people(X,Y,Z)
% 0.11/0.52 | ~ a_truth(one_truthteller)
% 0.11/0.52 | a_truth(truthteller(X))
% 0.11/0.52 | a_truth(truthteller(Y))
% 0.11/0.52 | a_truth(truthteller(Z)) ) ).
% 0.11/0.52
% 0.11/0.52 cnf(two_truthtellers1,axiom,
% 0.11/0.52 ( ~ people(X,Y,Z)
% 0.11/0.52 | ~ a_truth(truthteller(X))
% 0.11/0.52 | ~ a_truth(truthteller(Y))
% 0.11/0.52 | ~ a_truth(one_truthteller) ) ).
% 0.11/0.52
% 0.11/0.52 cnf(two_truthtellers2,axiom,
% 0.11/0.52 ( ~ people(X,Y,Z)
% 0.11/0.52 | ~ a_truth(truthteller(X))
% 0.11/0.52 | ~ a_truth(truthteller(Z))
% 0.11/0.52 | ~ a_truth(one_truthteller) ) ).
% 0.11/0.52
% 0.11/0.52 cnf(two_truthtellers3,axiom,
% 0.11/0.52 ( ~ people(X,Y,Z)
% 0.11/0.52 | ~ a_truth(truthteller(Y))
% 0.11/0.52 | ~ a_truth(truthteller(Z))
% 0.11/0.52 | ~ a_truth(one_truthteller) ) ).
% 0.11/0.52
% 0.11/0.52 cnf(identify_one_truthteller1,axiom,
% 0.11/0.52 ( ~ people(X,Y,Z)
% 0.11/0.52 | a_truth(one_truthteller)
% 0.11/0.52 | ~ a_truth(truthteller(X))
% 0.11/0.52 | a_truth(truthteller(Y))
% 0.11/0.52 | a_truth(truthteller(Z)) ) ).
% 0.11/0.52
% 0.11/0.52 cnf(identify_one_truthteller2,axiom,
% 0.11/0.52 ( ~ people(X,Y,Z)
% 0.11/0.52 | a_truth(one_truthteller)
% 0.11/0.52 | ~ a_truth(truthteller(Y))
% 0.11/0.52 | a_truth(truthteller(X))
% 0.11/0.52 | a_truth(truthteller(Z)) ) ).
% 0.11/0.52
% 0.11/0.52 cnf(identify_one_truthteller3,axiom,
% 0.11/0.52 ( ~ people(X,Y,Z)
% 0.11/0.52 | a_truth(one_truthteller)
% 0.11/0.52 | ~ a_truth(truthteller(Z))
% 0.11/0.52 | a_truth(truthteller(Y))
% 0.11/0.52 | a_truth(truthteller(X)) ) ).
% 0.11/0.52
% 0.11/0.52 cnf(a_b_and_c_are_people,hypothesis,
% 0.11/0.52 people(a,b,c) ).
% 0.11/0.52
% 0.11/0.52 cnf(a_says_garbage,hypothesis,
% 0.11/0.52 a_truth(says(a,garbage)) ).
% 0.11/0.52
% 0.11/0.52 cnf(b_says_a_says_one_truthteller,hypothesis,
% 0.11/0.52 a_truth(says(b,says(a,one_truthteller))) ).
% 0.11/0.52
% 0.11/0.52 cnf(c_says_b_lies,hypothesis,
% 0.11/0.52 a_truth(says(c,liar(b))) ).
% 0.11/0.52
% 0.11/0.52 %----This is an honest way of doing this. A simpler version could simply
% 0.11/0.52 %----prove that B is a liar and C is a truth-teller.
% 0.11/0.52 cnf(b_and_c_liars,hypothesis,
% 0.11/0.52 ( ~ a_truth(liar(b))
% 0.11/0.52 | ~ a_truth(liar(c))
% 0.11/0.52 | an_answer(b_and_c_liars) ) ).
% 0.11/0.52
% 0.11/0.52 cnf(b_liar_and_c_truthteller,hypothesis,
% 0.11/0.52 ( ~ a_truth(liar(b))
% 0.11/0.52 | ~ a_truth(truthteller(c))
% 0.11/0.52 | an_answer(b_liar_and_c_truthteller) ) ).
% 0.11/0.52
% 0.11/0.52 cnf(b_truthteller_and_c_liar,hypothesis,
% 0.11/0.52 ( ~ a_truth(truthteller(b))
% 0.11/0.52 | ~ a_truth(liar(c))
% 0.11/0.52 | an_answer(b_truthteller_and_c_liar) ) ).
% 0.11/0.52
% 0.11/0.52 cnf(b_and_c_truthtellers,hypothesis,
% 0.11/0.52 ( ~ a_truth(truthteller(b))
% 0.11/0.52 | ~ a_truth(truthteller(c))
% 0.11/0.52 | an_answer(b_and_c_truthtellers) ) ).
% 0.11/0.52
% 0.11/0.52 cnf(prove_there_is_an_answer,negated_conjecture,
% 0.11/0.52 ~ an_answer(X) ).
% 0.11/0.52
% 0.11/0.52 %--------------------------------------------------------------------------
% 0.11/0.52 %-------------------------------------------
% 0.11/0.52 % Proof found
% 0.11/0.52 % SZS status Theorem for theBenchmark
% 0.11/0.52 % SZS output start Proof
% 0.11/0.52 %ClaNum:22(EqnAxiom:0)
% 0.11/0.52 %VarNum:60(SingletonVarNum:32)
% 0.11/0.52 %MaxLitNum:5
% 0.11/0.52 %MaxfuncDepth:2
% 0.11/0.52 %SharedTerms:31
% 0.11/0.52 %goalClause: 5
% 0.11/0.52 %singleGoalClaCount:1
% 0.11/0.52 [3]P2(a1,a4,a3)
% 0.11/0.52 [1]P1(f9(a1,a2))
% 0.11/0.52 [2]P1(f9(a3,f10(a4)))
% 0.11/0.52 [4]P1(f9(a4,f9(a1,a11)))
% 0.11/0.52 [5]~P3(x51)
% 0.11/0.52 [6]P1(f10(x61))+P1(f12(x61))
% 0.11/0.52 [11]~P1(f10(x111))+~P1(f12(x111))
% 0.11/0.52 [7]P3(a5)+~P1(f10(a4))+~P1(f10(a3))
% 0.11/0.52 [8]P3(a6)+~P1(f12(a3))+~P1(f10(a4))
% 0.11/0.52 [9]P3(a8)+~P1(f12(a4))+~P1(f10(a3))
% 0.11/0.52 [10]P3(a7)+~P1(f12(a4))+~P1(f12(a3))
% 0.11/0.52 [12]P1(x121)+~P1(f9(x122,x121))+P1(f10(x122))
% 0.11/0.52 [13]~P1(x132)+~P1(f9(x131,x132))+P1(f12(x131))
% 0.11/0.52 [14]P1(x141)+~P1(f9(x142,x141))+~P1(f12(x142))
% 0.11/0.52 [15]~P1(x151)+~P1(f9(x152,x151))+~P1(f10(x152))
% 0.11/0.52 [17]~P2(x173,x172,x171)+~P1(a11)+~P1(f12(x171))+~P1(f12(x172))
% 0.11/0.52 [18]~P2(x182,x183,x181)+~P1(a11)+~P1(f12(x181))+~P1(f12(x182))
% 0.11/0.52 [19]~P2(x192,x191,x193)+~P1(a11)+~P1(f12(x191))+~P1(f12(x192))
% 0.11/0.52 [16]~P2(x163,x162,x161)+P1(f12(x161))+P1(f12(x162))+P1(f12(x163))+~P1(a11)
% 0.11/0.52 [20]~P2(x203,x202,x201)+P1(a11)+P1(f12(x201))+P1(f12(x202))+~P1(f12(x203))
% 0.11/0.52 [21]~P2(x212,x213,x211)+P1(a11)+P1(f12(x211))+P1(f12(x212))+~P1(f12(x213))
% 0.11/0.52 [22]~P2(x222,x221,x223)+P1(a11)+P1(f12(x221))+P1(f12(x222))+~P1(f12(x223))
% 0.11/0.52 %EqnAxiom
% 0.11/0.52
% 0.11/0.52 %-------------------------------------------
% 0.11/0.53 cnf(39,plain,
% 0.11/0.53 (~P1(f10(a3))+~P1(f10(a4))),
% 0.11/0.53 inference(scs_inference,[],[5,7])).
% 0.11/0.53 cnf(40,plain,
% 0.11/0.53 (~P1(f10(a4))+~P1(f12(a3))),
% 0.11/0.53 inference(scs_inference,[],[5,8])).
% 0.11/0.53 cnf(41,plain,
% 0.11/0.53 (~P1(f10(a3))+~P1(f12(a4))),
% 0.11/0.53 inference(scs_inference,[],[5,9])).
% 0.11/0.53 cnf(43,plain,
% 0.11/0.53 (P1(f10(a4))+~P1(f12(a3))),
% 0.11/0.53 inference(scs_inference,[],[2,14])).
% 0.11/0.53 cnf(55,plain,
% 0.11/0.53 (P1(f10(a4))+P1(f10(a3))),
% 0.11/0.53 inference(scs_inference,[],[2,4,14,12])).
% 0.11/0.53 cnf(64,plain,
% 0.11/0.53 (P1(f12(x641))+~P1(f9(x641,f9(a1,a2)))),
% 0.11/0.53 inference(scs_inference,[],[3,1,16,15,13])).
% 0.11/0.53 cnf(70,plain,
% 0.11/0.53 (P1(f12(a3))+~P1(f10(a4))),
% 0.11/0.53 inference(scs_inference,[],[39,6])).
% 0.11/0.53 cnf(76,plain,
% 0.11/0.53 (~P1(f10(a4))),
% 0.11/0.53 inference(scs_inference,[],[40,70])).
% 0.11/0.53 cnf(77,plain,
% 0.11/0.53 (~P1(f12(a3))),
% 0.11/0.53 inference(scs_inference,[],[76,43])).
% 0.11/0.53 cnf(79,plain,
% 0.11/0.53 (P1(f10(a3))),
% 0.11/0.53 inference(scs_inference,[],[76,55])).
% 0.11/0.53 cnf(81,plain,
% 0.11/0.53 (P1(f12(a4))),
% 0.11/0.53 inference(scs_inference,[],[76,6])).
% 0.11/0.53 cnf(109,plain,
% 0.11/0.53 ($false),
% 0.11/0.53 inference(scs_inference,[],[77,79,81,64,41]),
% 0.11/0.53 ['proof']).
% 0.11/0.53 % SZS output end Proof
% 0.11/0.53 % Total time :0.040000s
%------------------------------------------------------------------------------