TSTP Solution File: PUZ027-1 by CSE---1.6
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : PUZ027-1 : 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 : n010.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 13:10:57 EDT 2023
% Result : Unsatisfiable 0.69s 0.78s
% Output : CNFRefutation 0.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ027-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 21:48:50 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.57 start to proof:theBenchmark
% 0.69/0.77 %-------------------------------------------
% 0.69/0.77 % File :CSE---1.6
% 0.69/0.77 % Problem :theBenchmark
% 0.69/0.77 % Transform :cnf
% 0.69/0.77 % Format :tptp:raw
% 0.69/0.77 % Command :java -jar mcs_scs.jar %d %s
% 0.69/0.77
% 0.69/0.77 % Result :Theorem 0.140000s
% 0.69/0.77 % Output :CNFRefutation 0.140000s
% 0.69/0.77 %-------------------------------------------
% 0.69/0.77 %--------------------------------------------------------------------------
% 0.69/0.77 % File : PUZ027-1 : TPTP v8.1.2. Released v1.0.0.
% 0.69/0.77 % Domain : Puzzles
% 0.69/0.77 % Problem : Knights and Knaves #42
% 0.69/0.77 % Version : Especial.
% 0.69/0.77 % English : There is an island with exactly three types of people -
% 0.69/0.77 % truthtellers who always tell the truth, and liars who always
% 0.69/0.77 % lie, and normals who sometimes tell the truth and sometimes
% 0.69/0.77 % lie. Liars are said to be of the lowest rank, normals are
% 0.69/0.77 % middle rank, and truthtellers of the highest rank. Two people
% 0.69/0.77 % A and B on the island make the following statements. A: I am
% 0.69/0.77 % of lower rank than B. B: That's not true! What are the ranks
% 0.69/0.77 % of A and B, and which of the two statements are true? Answer:
% 0.69/0.77 % A is a normal and B is a normal.
% 0.69/0.77
% 0.69/0.77 % Refs : [Smu78] Smullyan (1978), What is the Name of this Book?
% 0.69/0.77 % Source : [ANL]
% 0.69/0.77 % Names : Problem 42 [Smu78]
% 0.69/0.77 % : tandl42.ver1.in [ANL]
% 0.69/0.77
% 0.69/0.77 % Status : Unsatisfiable
% 0.69/0.77 % Rating : 0.00 v2.0.0
% 0.69/0.77 % Syntax : Number of clauses : 32 ( 4 unt; 9 nHn; 29 RR)
% 0.69/0.77 % Number of literals : 88 ( 0 equ; 53 neg)
% 0.69/0.77 % Maximal clause size : 4 ( 2 avg)
% 0.69/0.77 % Maximal term depth : 3 ( 1 avg)
% 0.69/0.77 % Number of predicates : 2 ( 2 usr; 0 prp; 1-1 aty)
% 0.69/0.77 % Number of functors : 17 ( 17 usr; 11 con; 0-2 aty)
% 0.69/0.77 % Number of variables : 36 ( 3 sgn)
% 0.69/0.77 % SPC : CNF_UNS_RFO_NEQ_NHN
% 0.69/0.77
% 0.69/0.77 % Comments :
% 0.69/0.77 %--------------------------------------------------------------------------
% 0.69/0.78 %----Include axioms on truthtellers, liars and normal people
% 0.69/0.78 include('Axioms/PUZ003-0.ax').
% 0.69/0.78 %--------------------------------------------------------------------------
% 0.69/0.78 %----The next 12 clause define lower thand and not lower than
% 0.69/0.78 cnf(not_lower_is_irreflexive,axiom,
% 0.69/0.78 a_truth(not_lower(X,X)) ).
% 0.69/0.78
% 0.69/0.78 cnf(not_not_lower_and_lower,axiom,
% 0.69/0.78 ( ~ a_truth(not_lower(X,Y))
% 0.69/0.78 | ~ a_truth(lower(X,Y)) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(not_lower_or_lower,axiom,
% 0.69/0.78 ( a_truth(not_lower(X,Y))
% 0.69/0.78 | a_truth(lower(X,Y)) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(liars_lowest,axiom,
% 0.69/0.78 ( ~ a_truth(lower(X,Y))
% 0.69/0.78 | ~ a_truth(liar(X))
% 0.69/0.78 | a_truth(normal(Y))
% 0.69/0.78 | a_truth(truthteller(Y)) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(truthtellers_highest,axiom,
% 0.69/0.78 ( ~ a_truth(lower(X,Y))
% 0.69/0.78 | ~ a_truth(normal(X))
% 0.69/0.78 | a_truth(truthteller(Y)) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(truthtellers_lower_than_no_one,axiom,
% 0.69/0.78 ( ~ a_truth(lower(X,Y))
% 0.69/0.78 | ~ a_truth(truthteller(X)) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(normal_and_liars_lower_than_truthtellers,axiom,
% 0.69/0.78 ( ~ a_truth(lower(X,Y))
% 0.69/0.78 | ~ a_truth(truthteller(Y))
% 0.69/0.78 | a_truth(normal(X))
% 0.69/0.78 | a_truth(liar(X)) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(liars_lower_than_normal,axiom,
% 0.69/0.78 ( ~ a_truth(lower(X,Y))
% 0.69/0.78 | ~ a_truth(normal(Y))
% 0.69/0.78 | a_truth(liar(X)) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(no_one_lower_than_liars,axiom,
% 0.69/0.78 ( ~ a_truth(lower(X,Y))
% 0.69/0.78 | ~ a_truth(liar(Y)) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(not_lower_than_truthteller,axiom,
% 0.69/0.78 ( ~ a_truth(not_lower(X,Y))
% 0.69/0.78 | ~ a_truth(truthteller(X))
% 0.69/0.78 | a_truth(truthteller(Y))
% 0.69/0.78 | a_truth(lower(Y,X)) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(not_lower_than_liar,axiom,
% 0.69/0.78 ( ~ a_truth(not_lower(X,Y))
% 0.69/0.78 | ~ a_truth(liar(X))
% 0.69/0.78 | a_truth(liar(Y))
% 0.69/0.78 | a_truth(lower(Y,X)) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(not_lower_than_normal,axiom,
% 0.69/0.78 ( ~ a_truth(not_lower(X,Y))
% 0.69/0.78 | ~ a_truth(normal(X))
% 0.69/0.78 | a_truth(normal(Y))
% 0.69/0.78 | a_truth(lower(Y,X)) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(a_says_a_lower_than_b,hypothesis,
% 0.69/0.78 a_truth(says(a,lower(a,b))) ).
% 0.69/0.78
% 0.69/0.78 cnf(b_says_a_not_lower_than_b,hypothesis,
% 0.69/0.78 a_truth(says(b,not_lower(a,b))) ).
% 0.69/0.78
% 0.69/0.78 %----This is an honest way of doing this. A simpler version could simply
% 0.69/0.78 %----prove that A is a normal and B is a normal.
% 0.69/0.78 cnf(a_and_b_truthteller,hypothesis,
% 0.69/0.78 ( ~ a_truth(truthteller(a))
% 0.69/0.78 | ~ a_truth(truthteller(b))
% 0.69/0.78 | answer(a_and_b_truthteller) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(a_truthteller_b_normal,hypothesis,
% 0.69/0.78 ( ~ a_truth(truthteller(a))
% 0.69/0.78 | ~ a_truth(normal(b))
% 0.69/0.78 | answer(a_truthteller_b_normal) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(a_truthteller_b_liar,hypothesis,
% 0.69/0.78 ( ~ a_truth(truthteller(a))
% 0.69/0.78 | ~ a_truth(liar(b))
% 0.69/0.78 | answer(a_truthteller_b_liar) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(a_normal_b_truthteller,hypothesis,
% 0.69/0.78 ( ~ a_truth(normal(a))
% 0.69/0.78 | ~ a_truth(truthteller(b))
% 0.69/0.78 | answer(a_normal_b_truthteller) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(a_and_b_normal,hypothesis,
% 0.69/0.78 ( ~ a_truth(normal(a))
% 0.69/0.78 | ~ a_truth(normal(b))
% 0.69/0.78 | answer(a_and_b_normal) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(a_normal_b_liar,hypothesis,
% 0.69/0.78 ( ~ a_truth(normal(a))
% 0.69/0.78 | ~ a_truth(liar(b))
% 0.69/0.78 | answer(a_normal_b_liar) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(a_liar_b_truthteller,hypothesis,
% 0.69/0.78 ( ~ a_truth(liar(a))
% 0.69/0.78 | ~ a_truth(truthteller(b))
% 0.69/0.78 | answer(a_liar_b_truthteller) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(a_liar_b_normal,hypothesis,
% 0.69/0.78 ( ~ a_truth(liar(a))
% 0.69/0.78 | ~ a_truth(normal(b))
% 0.69/0.78 | answer(a_liar_b_normal) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(a_and_b_liar,hypothesis,
% 0.69/0.78 ( ~ a_truth(liar(a))
% 0.69/0.78 | ~ a_truth(liar(b))
% 0.69/0.78 | answer(a_and_b_liar) ) ).
% 0.69/0.78
% 0.69/0.78 cnf(prove_there_is_an_answer,negated_conjecture,
% 0.69/0.78 ~ answer(Answer) ).
% 0.69/0.78
% 0.69/0.78 %--------------------------------------------------------------------------
% 0.69/0.78 %-------------------------------------------
% 0.69/0.78 % Proof found
% 0.69/0.78 % SZS status Theorem for theBenchmark
% 0.69/0.78 % SZS output start Proof
% 0.69/0.78 %ClaNum:32(EqnAxiom:0)
% 0.69/0.78 %VarNum:80(SingletonVarNum:36)
% 0.69/0.78 %MaxLitNum:4
% 0.69/0.78 %MaxfuncDepth:2
% 0.69/0.78 %SharedTerms:38
% 0.69/0.78 %goalClause: 4
% 0.69/0.78 %singleGoalClaCount:1
% 0.69/0.78 [2]P1(f16(a2,f13(a2,a3)))
% 0.69/0.78 [3]P1(f16(a3,f1(a2,a3)))
% 0.69/0.78 [4]~P2(x41)
% 0.69/0.78 [1]P1(f1(x11,x11))
% 0.69/0.78 [15]~P1(f14(x151))+~P1(f17(x151))
% 0.69/0.78 [16]~P1(f15(x161))+~P1(f17(x161))
% 0.69/0.78 [17]~P1(f15(x171))+~P1(f14(x171))
% 0.69/0.78 [18]P1(f13(x181,x182))+P1(f1(x181,x182))
% 0.69/0.78 [19]~P1(f17(x191))+~P1(f13(x191,x192))
% 0.69/0.78 [20]~P1(f14(x201))+~P1(f13(x202,x201))
% 0.69/0.78 [29]~P1(f13(x291,x292))+~P1(f1(x291,x292))
% 0.69/0.78 [5]P2(a4)+~P1(f17(a2))+~P1(f17(a3))
% 0.69/0.78 [6]P2(a7)+~P1(f15(a3))+~P1(f17(a2))
% 0.69/0.78 [7]P2(a8)+~P1(f14(a3))+~P1(f17(a2))
% 0.69/0.78 [8]P2(a9)+~P1(f15(a2))+~P1(f17(a3))
% 0.69/0.78 [9]P2(a5)+~P1(f15(a2))+~P1(f15(a3))
% 0.69/0.78 [10]P2(a10)+~P1(f14(a3))+~P1(f15(a2))
% 0.69/0.78 [11]P2(a11)+~P1(f14(a2))+~P1(f17(a3))
% 0.69/0.78 [12]P2(a12)+~P1(f14(a2))+~P1(f15(a3))
% 0.69/0.78 [13]P2(a6)+~P1(f14(a2))+~P1(f14(a3))
% 0.69/0.78 [14]P1(f14(x141))+P1(f15(x141))+P1(f17(x141))
% 0.69/0.78 [21]P1(x211)+~P1(f16(x212,x211))+~P1(f17(x212))
% 0.69/0.78 [22]~P1(x221)+~P1(f16(x222,x221))+~P1(f14(x222))
% 0.69/0.78 [24]~P1(f13(x242,x241))+P1(f17(x241))+~P1(f15(x242))
% 0.69/0.78 [25]~P1(f13(x251,x252))+P1(f14(x251))+~P1(f15(x252))
% 0.69/0.78 [23]P1(x231)+P1(f15(x232))+~P1(f16(x232,x231))+P1(f14(x232))
% 0.69/0.78 [26]~P1(x262)+P1(f15(x261))+~P1(f16(x261,x262))+P1(f17(x261))
% 0.69/0.78 [27]P1(f15(x271))+~P1(f13(x272,x271))+P1(f17(x271))+~P1(f14(x272))
% 0.69/0.78 [28]P1(f15(x281))+~P1(f13(x281,x282))+P1(f14(x281))+~P1(f17(x282))
% 0.69/0.78 [30]~P1(f17(x302))+~P1(f1(x302,x301))+P1(f17(x301))+P1(f13(x301,x302))
% 0.69/0.78 [31]~P1(f14(x312))+~P1(f1(x312,x311))+P1(f14(x311))+P1(f13(x311,x312))
% 0.69/0.78 [32]~P1(f15(x322))+~P1(f1(x322,x321))+P1(f15(x321))+P1(f13(x321,x322))
% 0.69/0.78 %EqnAxiom
% 0.69/0.78
% 0.69/0.78 %-------------------------------------------
% 0.69/0.78 cnf(33,plain,
% 0.69/0.78 (~P1(f13(x331,x331))),
% 0.69/0.78 inference(scs_inference,[],[1,29])).
% 0.69/0.78 cnf(36,plain,
% 0.69/0.78 (~P2(x361)),
% 0.69/0.78 inference(rename_variables,[],[4])).
% 0.69/0.78 cnf(37,plain,
% 0.69/0.78 (~P1(f15(a3))+~P1(f14(a2))),
% 0.69/0.78 inference(scs_inference,[],[4,36,2,1,29,22,13,12])).
% 0.69/0.78 cnf(38,plain,
% 0.69/0.78 (~P2(x381)),
% 0.69/0.78 inference(rename_variables,[],[4])).
% 0.69/0.78 cnf(39,plain,
% 0.69/0.78 (~P1(f17(a3))+~P1(f14(a2))),
% 0.69/0.78 inference(scs_inference,[],[4,36,38,2,1,29,22,13,12,11])).
% 0.69/0.78 cnf(40,plain,
% 0.69/0.78 (~P2(x401)),
% 0.69/0.78 inference(rename_variables,[],[4])).
% 0.69/0.78 cnf(42,plain,
% 0.69/0.78 (~P2(x421)),
% 0.69/0.78 inference(rename_variables,[],[4])).
% 0.69/0.78 cnf(43,plain,
% 0.69/0.78 (~P1(f15(a3))+~P1(f15(a2))),
% 0.69/0.78 inference(scs_inference,[],[4,36,38,40,42,2,1,29,22,13,12,11,10,9])).
% 0.69/0.78 cnf(44,plain,
% 0.69/0.78 (~P2(x441)),
% 0.69/0.78 inference(rename_variables,[],[4])).
% 0.69/0.78 cnf(45,plain,
% 0.69/0.78 (~P1(f17(a3))+~P1(f15(a2))),
% 0.69/0.78 inference(scs_inference,[],[4,36,38,40,42,44,2,1,29,22,13,12,11,10,9,8])).
% 0.69/0.78 cnf(52,plain,
% 0.69/0.78 (~P1(f17(a2))+~P1(f15(a3))),
% 0.69/0.78 inference(scs_inference,[],[4,6])).
% 0.69/0.78 cnf(61,plain,
% 0.69/0.78 (P1(f13(a2,a3))+~P1(f17(a2))),
% 0.69/0.78 inference(scs_inference,[],[2,21])).
% 0.69/0.78 cnf(65,plain,
% 0.69/0.78 (~P1(f1(a2,a3))+~P1(f14(a3))),
% 0.69/0.78 inference(scs_inference,[],[1,33,3,31,22])).
% 0.69/0.78 cnf(82,plain,
% 0.69/0.78 (~P1(f16(x821,f13(x822,x822)))+P1(f14(x821))+P1(f15(x821))),
% 0.69/0.78 inference(scs_inference,[],[33,23])).
% 0.69/0.78 cnf(92,plain,
% 0.69/0.78 (P1(f15(x921))+P1(f17(x921))+~P1(f13(x922,x921))),
% 0.69/0.78 inference(scs_inference,[],[20,14])).
% 0.69/0.78 cnf(95,plain,
% 0.69/0.78 (~P1(f1(a2,a3))+~P1(f17(a2))),
% 0.69/0.78 inference(scs_inference,[],[61,29])).
% 0.69/0.78 cnf(96,plain,
% 0.69/0.78 (P1(f13(a2,a3))+~P1(f14(a3))),
% 0.69/0.78 inference(scs_inference,[],[65,18])).
% 0.69/0.78 cnf(100,plain,
% 0.69/0.78 (P1(f14(a3))+P1(f15(a3))+~P1(f17(a2))),
% 0.69/0.78 inference(scs_inference,[],[3,95,23])).
% 0.69/0.78 cnf(101,plain,
% 0.69/0.78 (~P1(f14(a3))),
% 0.69/0.78 inference(scs_inference,[],[96,20])).
% 0.69/0.78 cnf(105,plain,
% 0.69/0.78 (P1(f15(a3))+~P1(f17(a2))),
% 0.69/0.78 inference(scs_inference,[],[101,100])).
% 0.69/0.78 cnf(120,plain,
% 0.69/0.78 (~P1(f17(a2))),
% 0.69/0.78 inference(scs_inference,[],[105,52])).
% 0.69/0.78 cnf(144,plain,
% 0.69/0.78 (P1(f17(a3))+P1(f15(a3))),
% 0.69/0.78 inference(scs_inference,[],[101,120,82,92,14])).
% 0.69/0.78 cnf(148,plain,
% 0.69/0.78 (P1(f15(a2))+P1(f14(a2))),
% 0.69/0.78 inference(scs_inference,[],[120,14])).
% 0.69/0.78 cnf(166,plain,
% 0.69/0.78 (P1(f17(a3))+~P1(f14(a2))),
% 0.69/0.78 inference(scs_inference,[],[144,37])).
% 0.69/0.78 cnf(167,plain,
% 0.69/0.78 (P1(f15(a2))+~P1(f17(a3))),
% 0.69/0.78 inference(scs_inference,[],[148,39])).
% 0.69/0.78 cnf(177,plain,
% 0.69/0.78 (~P1(f17(a3))),
% 0.69/0.79 inference(scs_inference,[],[167,45])).
% 0.69/0.79 cnf(178,plain,
% 0.69/0.79 (P1(f15(a3))),
% 0.69/0.79 inference(scs_inference,[],[177,144])).
% 0.69/0.79 cnf(179,plain,
% 0.69/0.79 (~P1(f14(a2))),
% 0.69/0.79 inference(scs_inference,[],[177,166])).
% 0.69/0.79 cnf(181,plain,
% 0.69/0.79 (~P1(f15(a2))),
% 0.69/0.79 inference(scs_inference,[],[178,43])).
% 0.69/0.79 cnf(183,plain,
% 0.69/0.79 (P1(f15(a2))),
% 0.69/0.79 inference(scs_inference,[],[179,148])).
% 0.69/0.79 cnf(186,plain,
% 0.69/0.79 ($false),
% 0.69/0.79 inference(scs_inference,[],[183,181]),
% 0.69/0.79 ['proof']).
% 0.69/0.79 % SZS output end Proof
% 0.69/0.79 % Total time :0.140000s
%------------------------------------------------------------------------------