%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : LAT039-2 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n018.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 10:18:01 EDT 2024
% Result : Unsatisfiable 0.51s 0.60s
% Output : CNFRefutation 0.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT039-2 : TPTP v8.2.0. Released v2.4.0.
% 0.03/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n018.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 Jun 22 00:50:54 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.51/0.57 start to proof:theBenchmark
% 0.51/0.60 %-------------------------------------------
% 0.51/0.60 % File :CSE---1.7
% 0.51/0.60 % Problem :theBenchmark
% 0.51/0.60 % Transform :cnf
% 0.51/0.60 % Format :tptp:raw
% 0.51/0.60 % Command :java -jar mcs_scs.jar %d %s
% 0.51/0.60
% 0.51/0.60 % Result :Theorem 0.000000s
% 0.51/0.60 % Output :CNFRefutation 0.000000s
% 0.51/0.60 %-------------------------------------------
% 0.51/0.60 %--------------------------------------------------------------------------
% 0.51/0.60 % File : LAT039-2 : TPTP v8.2.0. Released v2.4.0.
% 0.51/0.60 % Domain : Lattice Theory
% 0.51/0.60 % Problem : Every distributive lattice is modular
% 0.51/0.60 % Version : [McC88] (equality) axioms.
% 0.51/0.60 % English : Theorem formulation : Modularity is expressed by:
% 0.51/0.60 % x <= y -> x v (y & z) = (x v y) & (x v z)
% 0.51/0.60
% 0.51/0.60 % Refs : [DeN00] DeNivelle (2000), Email to G. Sutcliffe
% 0.51/0.60 % [McC88] McCune (1988), Challenge Equality Problems in Lattice
% 0.51/0.60 % Source : [DeN00]
% 0.51/0.60 % Names : lattice-mod-3 [DeN00]
% 0.51/0.60
% 0.51/0.60 % Status : Unsatisfiable
% 0.51/0.60 % Rating : 0.05 v8.2.0, 0.04 v8.1.0, 0.05 v7.5.0, 0.04 v7.4.0, 0.09 v7.3.0, 0.05 v7.1.0, 0.06 v7.0.0, 0.05 v6.3.0, 0.12 v6.2.0, 0.14 v6.1.0, 0.06 v6.0.0, 0.10 v5.5.0, 0.05 v5.4.0, 0.00 v2.4.0
% 0.51/0.60 % Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 2 RR)
% 0.51/0.60 % Number of literals : 12 ( 12 equ; 1 neg)
% 0.51/0.60 % Maximal clause size : 1 ( 1 avg)
% 0.51/0.60 % Maximal term depth : 3 ( 2 avg)
% 0.51/0.60 % Number of predicates : 1 ( 0 usr; 0 prp; 2-2 aty)
% 0.51/0.60 % Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% 0.51/0.60 % Number of variables : 22 ( 2 sgn)
% 0.51/0.60 % SPC : CNF_UNS_RFO_PEQ_UEQ
% 0.51/0.60
% 0.51/0.60 % Comments :
% 0.51/0.60 %--------------------------------------------------------------------------
% 0.51/0.60 %----Include lattice theory axioms
% 0.51/0.60 include('Axioms/LAT001-0.ax').
% 0.51/0.60 %--------------------------------------------------------------------------
% 0.51/0.60 cnf(dist_join,hypothesis,
% 0.51/0.60 join(X,meet(Y,Z)) = meet(join(X,Y),join(X,Z)) ).
% 0.51/0.60
% 0.51/0.60 cnf(dist_meet,hypothesis,
% 0.51/0.60 meet(X,join(Y,Z)) = join(meet(X,Y),meet(X,Z)) ).
% 0.51/0.60
% 0.51/0.60 cnf(lhs,hypothesis,
% 0.51/0.60 join(xx,yy) = yy ).
% 0.51/0.60
% 0.51/0.60 cnf(rhs,negated_conjecture,
% 0.51/0.60 join(xx,meet(yy,zz)) != meet(join(xx,yy),join(xx,zz)) ).
% 0.51/0.60
% 0.51/0.60 %--------------------------------------------------------------------------
% 0.51/0.60 %-------------------------------------------
% 0.51/0.60 % Proof found
% 0.51/0.60 % SZS status Theorem for theBenchmark
% 0.51/0.60 % SZS output start Proof
% 0.51/0.61 %ClaNum:19(EqnAxiom:7)
% 0.51/0.61 %VarNum:48(SingletonVarNum:22)
% 0.51/0.61 %MaxLitNum:1
% 0.51/0.61 %MaxfuncDepth:2
% 0.51/0.61 %SharedTerms:10
% 0.51/0.61 %goalClause: 19
% 0.51/0.61 %singleGoalClaCount:1
% 0.51/0.61 [8]E(f2(a1,a4),a4)
% 0.51/0.61 [19]~E(f3(f2(a1,a4),f2(a1,a5)),f2(a1,f3(a4,a5)))
% 0.51/0.61 [9]E(f3(x91,x91),x91)
% 0.51/0.61 [10]E(f2(x101,x101),x101)
% 0.51/0.61 [11]E(f3(x111,x112),f3(x112,x111))
% 0.51/0.61 [12]E(f2(x121,x122),f2(x122,x121))
% 0.51/0.61 [13]E(f3(x131,f2(x131,x132)),x131)
% 0.51/0.61 [14]E(f2(x141,f3(x141,x142)),x141)
% 0.51/0.61 [15]E(f3(f3(x151,x152),x153),f3(x151,f3(x152,x153)))
% 0.51/0.61 [16]E(f2(f2(x161,x162),x163),f2(x161,f2(x162,x163)))
% 0.51/0.61 [17]E(f2(f3(x171,x172),f3(x171,x173)),f3(x171,f2(x172,x173)))
% 0.51/0.61 [18]E(f3(f2(x181,x182),f2(x181,x183)),f2(x181,f3(x182,x183)))
% 0.51/0.61 %EqnAxiom
% 0.51/0.61 [1]E(x11,x11)
% 0.51/0.61 [2]E(x22,x21)+~E(x21,x22)
% 0.51/0.61 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.51/0.61 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.51/0.61 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.51/0.61 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63))
% 0.51/0.61 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72))
% 0.51/0.61
% 0.51/0.61 %-------------------------------------------
% 0.51/0.61 cnf(20,plain,
% 0.51/0.61 ($false),
% 0.51/0.61 inference(scs_inference,[],[19,18]),
% 0.51/0.61 ['proof']).
% 0.51/0.61 % SZS output end Proof
% 0.51/0.61 % Total time :0.000000s
%------------------------------------------------------------------------------