TSTP Solution File: LAT014-1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : LAT014-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n027.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 05:57:11 EDT 2023
% Result : Unsatisfiable 0.19s 0.62s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT014-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.12/0.34 % Computer : n027.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 : Thu Aug 24 07:27:02 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.56 start to proof:theBenchmark
% 0.19/0.61 %-------------------------------------------
% 0.19/0.61 % File :CSE---1.6
% 0.19/0.61 % Problem :theBenchmark
% 0.19/0.61 % Transform :cnf
% 0.19/0.61 % Format :tptp:raw
% 0.19/0.61 % Command :java -jar mcs_scs.jar %d %s
% 0.19/0.61
% 0.19/0.61 % Result :Theorem 0.010000s
% 0.19/0.61 % Output :CNFRefutation 0.010000s
% 0.19/0.61 %-------------------------------------------
% 0.19/0.62 %--------------------------------------------------------------------------
% 0.19/0.62 % File : LAT014-1 : TPTP v8.1.2. Released v2.2.0.
% 0.19/0.62 % Domain : Lattice Theory
% 0.19/0.62 % Problem : McKenzie's 4-basis for lattice theory, part 3 (of 3)
% 0.19/0.62 % Version : [MP96] (equality) axioms.
% 0.19/0.62 % English : This is part of a proof that McKenzie's 4-basis axiomatizes
% 0.19/0.62 % lattice theory. We prove half of the standard basis.
% 0.19/0.62 % The other half follows by duality. In this part we prove
% 0.19/0.62 % absorbtion of meet.
% 0.19/0.62
% 0.19/0.62 % Refs : [McC98] McCune (1998), Email to G. Sutcliffe
% 0.19/0.62 % : [MP96] McCune & Padmanabhan (1996), Automated Deduction in Eq
% 0.19/0.62 % Source : [McC98]
% 0.19/0.62 % Names : LT-9 [MP96]
% 0.19/0.62
% 0.19/0.62 % Status : Unsatisfiable
% 0.19/0.62 % Rating : 0.00 v7.4.0, 0.04 v7.3.0, 0.00 v6.0.0, 0.10 v5.5.0, 0.05 v5.4.0, 0.00 v5.1.0, 0.13 v5.0.0, 0.07 v4.1.0, 0.09 v4.0.1, 0.07 v4.0.0, 0.08 v3.7.0, 0.00 v2.2.1
% 0.19/0.62 % Syntax : Number of clauses : 5 ( 5 unt; 0 nHn; 1 RR)
% 0.19/0.62 % Number of literals : 5 ( 5 equ; 1 neg)
% 0.19/0.62 % Maximal clause size : 1 ( 1 avg)
% 0.19/0.62 % Maximal term depth : 4 ( 2 avg)
% 0.19/0.62 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 0.19/0.62 % Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% 0.19/0.62 % Number of variables : 12 ( 8 sgn)
% 0.19/0.62 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 0.19/0.62
% 0.19/0.62 % Comments :
% 0.19/0.62 %--------------------------------------------------------------------------
% 0.19/0.62 %----McKenzie's self-dual (independent) absorptive 4-basis for lattice theory.
% 0.19/0.62 cnf(mckenzie1,axiom,
% 0.19/0.62 join(X,meet(Y,meet(X,Z))) = X ).
% 0.19/0.62
% 0.19/0.62 cnf(mckenzie2,axiom,
% 0.19/0.62 meet(X,join(Y,join(X,Z))) = X ).
% 0.19/0.62
% 0.19/0.62 cnf(mckenzie3,axiom,
% 0.19/0.62 join(join(meet(X,Y),meet(Y,Z)),Y) = Y ).
% 0.19/0.62
% 0.19/0.62 cnf(mckenzie4,axiom,
% 0.19/0.62 meet(meet(join(X,Y),join(Y,Z)),Y) = Y ).
% 0.19/0.62
% 0.19/0.62 %----Denial of conclusion:
% 0.19/0.62 cnf(prove_absorbtion,negated_conjecture,
% 0.19/0.62 meet(a,join(a,b)) != a ).
% 0.19/0.62
% 0.19/0.62 %--------------------------------------------------------------------------
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 % Proof found
% 0.19/0.62 % SZS status Theorem for theBenchmark
% 0.19/0.62 % SZS output start Proof
% 0.19/0.62 %ClaNum:12(EqnAxiom:7)
% 0.19/0.62 %VarNum:22(SingletonVarNum:12)
% 0.19/0.62 %MaxLitNum:1
% 0.19/0.62 %MaxfuncDepth:3
% 0.19/0.62 %SharedTerms:5
% 0.19/0.62 %goalClause: 12
% 0.19/0.62 %singleGoalClaCount:1
% 0.19/0.62 [12]~E(f4(a2,f1(a2,a3)),a2)
% 0.19/0.62 [8]E(f4(x81,f1(x82,f1(x81,x83))),x81)
% 0.19/0.62 [9]E(f1(x91,f4(x92,f4(x91,x93))),x91)
% 0.19/0.62 [10]E(f4(f4(f1(x101,x102),f1(x102,x103)),x102),x102)
% 0.19/0.62 [11]E(f1(f1(f4(x111,x112),f4(x112,x113)),x112),x112)
% 0.19/0.62 %EqnAxiom
% 0.19/0.62 [1]E(x11,x11)
% 0.19/0.62 [2]E(x22,x21)+~E(x21,x22)
% 0.19/0.62 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.19/0.62 [4]~E(x41,x42)+E(f1(x41,x43),f1(x42,x43))
% 0.19/0.62 [5]~E(x51,x52)+E(f1(x53,x51),f1(x53,x52))
% 0.19/0.62 [6]~E(x61,x62)+E(f4(x61,x63),f4(x62,x63))
% 0.19/0.62 [7]~E(x71,x72)+E(f4(x73,x71),f4(x73,x72))
% 0.19/0.62
% 0.19/0.62 %-------------------------------------------
% 0.19/0.62 cnf(14,plain,
% 0.19/0.62 (~E(f4(a2,f1(a2,a3)),f4(a2,f1(x141,f1(a2,x142))))),
% 0.19/0.62 inference(scs_inference,[],[12,8,2,3])).
% 0.19/0.62 cnf(25,plain,
% 0.19/0.62 ($false),
% 0.19/0.62 inference(scs_inference,[],[14,11,2,7]),
% 0.19/0.62 ['proof']).
% 0.19/0.62 % SZS output end Proof
% 0.19/0.62 % Total time :0.010000s
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