%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : PUZ024-1 : TPTP v8.2.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n015.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 : Mon Jun 24 13:42:05 EDT 2024
% Result : Unsatisfiable 58.61s 58.78s
% Output : CNFRefutation 59.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : PUZ024-1 : TPTP v8.2.0. Released v1.0.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Jun 18 10:40:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.20/0.56 start to proof:theBenchmark
% 58.52/58.75 %-------------------------------------------
% 58.52/58.75 % File :CSE---1.7
% 58.52/58.75 % Problem :theBenchmark
% 58.52/58.75 % Transform :cnf
% 58.52/58.75 % Format :tptp:raw
% 58.52/58.75 % Command :java -jar mcs_scs.jar %d %s
% 58.52/58.75
% 58.52/58.75 % Result :Theorem 58.000000s
% 58.52/58.75 % Output :CNFRefutation 58.000000s
% 58.52/58.75 %-------------------------------------------
% 58.52/58.77 %--------------------------------------------------------------------------
% 58.52/58.77 % File : PUZ024-1 : TPTP v8.2.0. Released v1.0.0.
% 58.52/58.77 % Domain : Puzzles
% 58.52/58.78 % Problem : Knights and Knaves #31
% 58.52/58.78 % Version : Especial.
% 58.52/58.78 % English : There is an island with exactly two types of people -
% 58.52/58.78 % truthtellers who always tell the truth and liars who always lie.
% 58.52/58.78 % There are a group of three people, A, B, and C on the island. A
% 58.52/58.78 % and B make the following statements. A: All of us are liars;
% 58.52/58.78 % B: Exactly one of us is a truthteller. What are A, B, and C?
% 58.52/58.78 % Answer: A is a liar, B is a truthteller, and C is a liar.
% 58.52/58.78
% 58.52/58.78 % Refs : [Smu78] Smullyan (1978), What is the Name of this Book?
% 58.52/58.78 % Source : [ANL]
% 58.52/58.78 % Names : Problem 31 [Smu78]
% 58.52/58.78 % : tandl31.ver1.in [ANL]
% 58.52/58.78
% 58.52/58.78 % Status : Unsatisfiable
% 58.52/58.78 % Rating : 0.00 v6.3.0, 0.14 v6.2.0, 0.00 v2.0.0
% 58.52/58.78 % Syntax : Number of clauses : 20 ( 6 unt; 6 nHn; 19 RR)
% 58.52/58.78 % Number of literals : 60 ( 0 equ; 37 neg)
% 58.52/58.78 % Maximal clause size : 5 ( 3 avg)
% 58.52/58.78 % Maximal term depth : 2 ( 1 avg)
% 58.52/58.78 % Number of predicates : 2 ( 2 usr; 0 prp; 1-3 aty)
% 58.52/58.78 % Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% 58.52/58.78 % Number of variables : 35 ( 3 sgn)
% 58.52/58.78 % SPC : CNF_UNS_RFO_NEQ_NHN
% 58.52/58.78
% 58.52/58.78 % Comments :
% 58.52/58.78 %--------------------------------------------------------------------------
% 58.52/58.78 %----Include axioms for truthtellers and liars
% 58.52/58.78 include('Axioms/PUZ002-0.ax').
% 58.52/58.78 %--------------------------------------------------------------------------
% 58.52/58.78 %----The next 6 clauses define what is meant by exactly one
% 58.52/58.78 %----is a truthteller.
% 58.52/58.78 cnf(one_says_one_truthteller,axiom,
% 58.52/58.78 ( ~ a_truth(says(X,one_truthteller))
% 58.52/58.78 | ~ people(X,Y,Z)
% 58.52/58.78 | ~ a_truth(truthteller(X))
% 58.52/58.78 | ~ a_truth(truthteller(Y))
% 58.52/58.78 | ~ a_truth(truthteller(Z)) ) ).
% 58.52/58.78
% 58.52/58.78 cnf(one_is_the_truth_teller,axiom,
% 58.52/58.78 ( ~ a_truth(one_truthteller)
% 58.52/58.78 | ~ people(X,Y,Z)
% 58.52/58.78 | a_truth(truthteller(X))
% 58.52/58.78 | a_truth(truthteller(Y))
% 58.52/58.78 | a_truth(truthteller(Z)) ) ).
% 58.52/58.78
% 58.52/58.78 cnf(one_is_not_the_truthteller,axiom,
% 58.52/58.78 ( ~ a_truth(one_truthteller)
% 58.52/58.78 | ~ people(X,Y,Z)
% 58.52/58.78 | ~ a_truth(truthteller(Y))
% 58.52/58.78 | ~ a_truth(truthteller(X))
% 58.52/58.78 | ~ a_truth(truthteller(Z)) ) ).
% 58.52/58.78
% 58.52/58.78 cnf(one_truthteller_two_liars,axiom,
% 58.52/58.78 ( ~ a_truth(one_truthteller)
% 58.52/58.78 | ~ people(X,Y,Z)
% 58.52/58.78 | ~ a_truth(liar(X))
% 58.52/58.78 | ~ a_truth(truthteller(Y))
% 58.52/58.78 | a_truth(liar(Z)) ) ).
% 58.52/58.78
% 58.52/58.78 cnf(two_truthtellers,axiom,
% 58.52/58.78 ( a_truth(one_truthteller)
% 58.52/58.78 | ~ people(X,Y,Z)
% 58.52/58.78 | ~ a_truth(liar(X))
% 58.52/58.78 | ~ a_truth(truthteller(Y))
% 58.52/58.78 | a_truth(truthteller(Z)) ) ).
% 58.52/58.78
% 58.52/58.78 cnf(three_liars,axiom,
% 58.52/58.78 ( a_truth(one_truthteller)
% 58.52/58.78 | ~ people(X,Y,Z)
% 58.52/58.78 | ~ a_truth(liar(X))
% 58.52/58.78 | ~ a_truth(liar(Y))
% 58.52/58.78 | a_truth(liar(Z)) ) ).
% 58.52/58.78
% 58.52/58.78 %----If x says that 'all of us' are liars then, all the persons may
% 58.52/58.78 %----be liars.
% 58.52/58.78 cnf(speaker_is_lying,axiom,
% 58.52/58.78 ( ~ a_truth(says(X,all_are_liars))
% 58.52/58.78 | ~ people(X,Y,Z)
% 58.52/58.78 | ~ a_truth(truthteller(X)) ) ).
% 58.52/58.78
% 58.52/58.78 cnf(all_truthtellers,axiom,
% 58.52/58.78 ( a_truth(all_are_liars)
% 58.52/58.78 | ~ people(X,Y,Z)
% 58.52/58.78 | a_truth(truthteller(X))
% 58.52/58.78 | a_truth(truthteller(Y))
% 58.52/58.78 | a_truth(truthteller(Z)) ) ).
% 58.52/58.78
% 58.52/58.78 cnf(b_c_a_people,hypothesis,
% 58.52/58.78 people(b,c,a) ).
% 58.52/58.78
% 58.52/58.78 cnf(a_c_b_people,hypothesis,
% 58.52/58.78 people(a,c,b) ).
% 58.52/58.78
% 58.52/58.78 cnf(c_b_a_people,hypothesis,
% 58.52/58.78 people(c,b,a) ).
% 58.52/58.78
% 58.52/58.78 cnf(a_says_all_are_liars,hypothesis,
% 58.52/58.78 a_truth(says(a,all_are_liars)) ).
% 58.61/58.78
% 58.61/58.78 cnf(b_says_one_truthteller,hypothesis,
% 58.61/58.78 a_truth(says(b,one_truthteller)) ).
% 58.61/58.78
% 58.61/58.78 %----This is an honest way of doing this. A simpler version could simply
% 58.61/58.78 %----prove that A and C are a liars, and B is a truthteller
% 58.61/58.78 cnf(prove_there_is_a_truthteller,negated_conjecture,
% 58.61/58.78 ~ a_truth(truthteller(Truthteller)) ).
% 58.61/58.78
% 58.61/58.78 %--------------------------------------------------------------------------
% 58.61/58.78 %-------------------------------------------
% 58.61/58.78 % Proof found
% 58.61/58.78 % SZS status Theorem for theBenchmark
% 58.61/58.78 % SZS output start Proof
% 58.61/58.79 %ClaNum:20(EqnAxiom:0)
% 58.61/58.79 %VarNum:33(SingletonVarNum:17)
% 58.61/58.79 %MaxLitNum:5
% 58.61/58.79 %MaxfuncDepth:1
% 58.61/58.79 %SharedTerms:15
% 58.61/58.79 %goalClause: 6
% 58.61/58.79 %singleGoalClaCount:1
% 58.61/58.79 [3]P2(a1,a5,a2)
% 58.61/58.79 [4]P2(a5,a1,a2)
% 58.61/58.79 [5]P2(a2,a5,a1)
% 58.61/58.79 [1]P1(f7(a1,a4))
% 58.61/58.79 [2]P1(f7(a2,a3))
% 58.61/58.79 [6]~P1(f8(x61))
% 58.61/58.79 [7]P1(f6(x71))+P1(f8(x71))
% 58.61/58.79 [9]P1(x91)+~P1(f7(x92,x91))+P1(f6(x92))
% 58.61/58.79 [10]~P1(x102)+~P1(f7(x101,x102))+P1(f8(x101))
% 58.61/58.79 [12]~P1(x121)+~P1(f7(x122,x121))+~P1(f6(x122))
% 58.61/58.79 [13]~P2(x133,x132,x131)+P1(a3)+P1(f8(x131))+P1(f8(x132))+P1(f8(x133))
% 58.61/58.79 [14]~P2(x143,x142,x141)+P1(f8(x141))+P1(f8(x142))+P1(f8(x143))+~P1(a4)
% 58.61/58.79 [16]~P2(x163,x162,x161)+P1(a4)+P1(f6(x161))+~P1(f6(x162))+~P1(f6(x163))
% 58.61/58.79 %EqnAxiom
% 58.61/58.79
% 58.61/58.79 %-------------------------------------------
% 58.76/59.02 cnf(21,plain,
% 58.76/59.02 (P1(f6(x211))),
% 58.76/59.02 inference(scs_inference,[],[6,7])).
% 58.76/59.02 cnf(26,plain,
% 58.76/59.02 (~P1(a3)),
% 58.76/59.02 inference(scs_inference,[],[21,2,12])).
% 58.76/59.02 cnf(31,plain,
% 58.76/59.02 (~P2(x311,x312,x313)+P1(f8(x313))+P1(f8(x312))+P1(f8(x311))),
% 58.76/59.02 inference(scs_inference,[],[26,13])).
% 58.76/59.02 cnf(374606,plain,
% 58.76/59.02 (P1(f8(a5))+P1(f8(a2))),
% 58.76/59.02 inference(scs_inference,[],[6,3,1,21,12,31])).
% 58.76/59.02 cnf(374610,plain,
% 58.76/59.02 (P1(f8(a2))),
% 58.76/59.02 inference(scs_inference,[],[6,374606])).
% 58.76/59.02 cnf(374614,plain,
% 58.76/59.02 ($false),
% 58.76/59.02 inference(scs_inference,[],[374610,6]),
% 58.76/59.02 ['proof']).
% 59.04/59.22 % SZS output end Proof
% 59.04/59.22 % Total time :58.000000s
%------------------------------------------------------------------------------