TSTP Solution File: LAT012-1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LAT012-1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 : 600s
% DateTime : Sun Jul 17 05:58:53 EDT 2022
% Result : Unsatisfiable 0.50s 0.70s
% Output : CNFRefutation 0.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 25
% Syntax : Number of clauses : 91 ( 51 unt; 0 nHn; 45 RR)
% Number of literals : 151 ( 150 equ; 62 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 206 ( 49 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(mckenzie1,axiom,
join(X,meet(Y,meet(X,Z))) = X ).
cnf(mckenzie2,axiom,
meet(X,join(Y,join(X,Z))) = X ).
cnf(mckenzie3,axiom,
join(join(meet(X,Y),meet(Y,Z)),Y) = Y ).
cnf(mckenzie4,axiom,
meet(meet(join(X,Y),join(Y,Z)),Y) = Y ).
cnf(prove_commutativity_of_meet,negated_conjecture,
meet(b,a) != meet(a,b) ).
cnf(refute_0_0,plain,
meet(meet(join(X_14,meet(X_4,X_14)),join(meet(X_4,X_14),X_16)),meet(X_4,X_14)) = meet(X_4,X_14),
inference(subst,[],[mckenzie4:[bind(X,$fot(X_14)),bind(Y,$fot(meet(X_4,X_14))),bind(Z,$fot(X_16))]]) ).
cnf(refute_0_1,plain,
join(X_3,meet(X_4,meet(X_3,join(Y,join(X_3,Z))))) = X_3,
inference(subst,[],[mckenzie1:[bind(X,$fot(X_3)),bind(Y,$fot(X_4)),bind(Z,$fot(join(Y,join(X_3,Z))))]]) ).
cnf(refute_0_2,plain,
meet(X_3,join(Y,join(X_3,Z))) = X_3,
inference(subst,[],[mckenzie2:[bind(X,$fot(X_3))]]) ).
cnf(refute_0_3,plain,
( join(X_3,meet(X_4,meet(X_3,join(Y,join(X_3,Z))))) != X_3
| meet(X_3,join(Y,join(X_3,Z))) != X_3
| join(X_3,meet(X_4,X_3)) = X_3 ),
introduced(tautology,[equality,[$cnf( $equal(join(X_3,meet(X_4,meet(X_3,join(Y,join(X_3,Z))))),X_3) ),[0,1,1],$fot(X_3)]]) ).
cnf(refute_0_4,plain,
( join(X_3,meet(X_4,meet(X_3,join(Y,join(X_3,Z))))) != X_3
| join(X_3,meet(X_4,X_3)) = X_3 ),
inference(resolve,[$cnf( $equal(meet(X_3,join(Y,join(X_3,Z))),X_3) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
join(X_3,meet(X_4,X_3)) = X_3,
inference(resolve,[$cnf( $equal(join(X_3,meet(X_4,meet(X_3,join(Y,join(X_3,Z))))),X_3) )],[refute_0_1,refute_0_4]) ).
cnf(refute_0_6,plain,
join(X_14,meet(X_4,X_14)) = X_14,
inference(subst,[],[refute_0_5:[bind(X_3,$fot(X_14))]]) ).
cnf(refute_0_7,plain,
( join(X_14,meet(X_4,X_14)) != X_14
| meet(meet(join(X_14,meet(X_4,X_14)),join(meet(X_4,X_14),X_16)),meet(X_4,X_14)) != meet(X_4,X_14)
| meet(meet(X_14,join(meet(X_4,X_14),X_16)),meet(X_4,X_14)) = meet(X_4,X_14) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(join(X_14,meet(X_4,X_14)),join(meet(X_4,X_14),X_16)),meet(X_4,X_14)),meet(X_4,X_14)) ),[0,0,0],$fot(X_14)]]) ).
cnf(refute_0_8,plain,
( meet(meet(join(X_14,meet(X_4,X_14)),join(meet(X_4,X_14),X_16)),meet(X_4,X_14)) != meet(X_4,X_14)
| meet(meet(X_14,join(meet(X_4,X_14),X_16)),meet(X_4,X_14)) = meet(X_4,X_14) ),
inference(resolve,[$cnf( $equal(join(X_14,meet(X_4,X_14)),X_14) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
meet(meet(X_14,join(meet(X_4,X_14),X_16)),meet(X_4,X_14)) = meet(X_4,X_14),
inference(resolve,[$cnf( $equal(meet(meet(join(X_14,meet(X_4,X_14)),join(meet(X_4,X_14),X_16)),meet(X_4,X_14)),meet(X_4,X_14)) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
meet(meet(X_93,join(meet(X_94,X_93),X_94)),meet(X_94,X_93)) = meet(X_94,X_93),
inference(subst,[],[refute_0_9:[bind(X_14,$fot(X_93)),bind(X_16,$fot(X_94)),bind(X_4,$fot(X_94))]]) ).
cnf(refute_0_11,plain,
join(join(meet(X_21,X_22),meet(X_22,join(Y,join(X_22,Z)))),X_22) = X_22,
inference(subst,[],[mckenzie3:[bind(X,$fot(X_21)),bind(Y,$fot(X_22)),bind(Z,$fot(join(Y,join(X_22,Z))))]]) ).
cnf(refute_0_12,plain,
meet(X_22,join(Y,join(X_22,Z))) = X_22,
inference(subst,[],[mckenzie2:[bind(X,$fot(X_22))]]) ).
cnf(refute_0_13,plain,
( join(join(meet(X_21,X_22),meet(X_22,join(Y,join(X_22,Z)))),X_22) != X_22
| meet(X_22,join(Y,join(X_22,Z))) != X_22
| join(join(meet(X_21,X_22),X_22),X_22) = X_22 ),
introduced(tautology,[equality,[$cnf( $equal(join(join(meet(X_21,X_22),meet(X_22,join(Y,join(X_22,Z)))),X_22),X_22) ),[0,0,1],$fot(X_22)]]) ).
cnf(refute_0_14,plain,
( join(join(meet(X_21,X_22),meet(X_22,join(Y,join(X_22,Z)))),X_22) != X_22
| join(join(meet(X_21,X_22),X_22),X_22) = X_22 ),
inference(resolve,[$cnf( $equal(meet(X_22,join(Y,join(X_22,Z))),X_22) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
join(join(meet(X_21,X_22),X_22),X_22) = X_22,
inference(resolve,[$cnf( $equal(join(join(meet(X_21,X_22),meet(X_22,join(Y,join(X_22,Z)))),X_22),X_22) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
join(join(X_9,X_4),meet(X_4,join(X_9,X_4))) = join(X_9,X_4),
inference(subst,[],[refute_0_5:[bind(X_3,$fot(join(X_9,X_4)))]]) ).
cnf(refute_0_17,plain,
meet(X,join(Y,join(X,meet(X_4,meet(X,X_5))))) = X,
inference(subst,[],[mckenzie2:[bind(Z,$fot(meet(X_4,meet(X,X_5))))]]) ).
cnf(refute_0_18,plain,
join(X,meet(X_4,meet(X,X_5))) = X,
inference(subst,[],[mckenzie1:[bind(Y,$fot(X_4)),bind(Z,$fot(X_5))]]) ).
cnf(refute_0_19,plain,
( join(X,meet(X_4,meet(X,X_5))) != X
| meet(X,join(Y,join(X,meet(X_4,meet(X,X_5))))) != X
| meet(X,join(Y,X)) = X ),
introduced(tautology,[equality,[$cnf( $equal(meet(X,join(Y,join(X,meet(X_4,meet(X,X_5))))),X) ),[0,1,1],$fot(X)]]) ).
cnf(refute_0_20,plain,
( meet(X,join(Y,join(X,meet(X_4,meet(X,X_5))))) != X
| meet(X,join(Y,X)) = X ),
inference(resolve,[$cnf( $equal(join(X,meet(X_4,meet(X,X_5))),X) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
meet(X,join(Y,X)) = X,
inference(resolve,[$cnf( $equal(meet(X,join(Y,join(X,meet(X_4,meet(X,X_5))))),X) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
meet(X_4,join(X_9,X_4)) = X_4,
inference(subst,[],[refute_0_21:[bind(X,$fot(X_4)),bind(Y,$fot(X_9))]]) ).
cnf(refute_0_23,plain,
( join(join(X_9,X_4),meet(X_4,join(X_9,X_4))) != join(X_9,X_4)
| meet(X_4,join(X_9,X_4)) != X_4
| join(join(X_9,X_4),X_4) = join(X_9,X_4) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(X_9,X_4),meet(X_4,join(X_9,X_4))),join(X_9,X_4)) ),[0,1],$fot(X_4)]]) ).
cnf(refute_0_24,plain,
( join(join(X_9,X_4),meet(X_4,join(X_9,X_4))) != join(X_9,X_4)
| join(join(X_9,X_4),X_4) = join(X_9,X_4) ),
inference(resolve,[$cnf( $equal(meet(X_4,join(X_9,X_4)),X_4) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
join(join(X_9,X_4),X_4) = join(X_9,X_4),
inference(resolve,[$cnf( $equal(join(join(X_9,X_4),meet(X_4,join(X_9,X_4))),join(X_9,X_4)) )],[refute_0_16,refute_0_24]) ).
cnf(refute_0_26,plain,
join(join(meet(X_21,X_22),X_22),X_22) = join(meet(X_21,X_22),X_22),
inference(subst,[],[refute_0_25:[bind(X_4,$fot(X_22)),bind(X_9,$fot(meet(X_21,X_22)))]]) ).
cnf(refute_0_27,plain,
( join(join(meet(X_21,X_22),X_22),X_22) != X_22
| join(join(meet(X_21,X_22),X_22),X_22) != join(meet(X_21,X_22),X_22)
| join(meet(X_21,X_22),X_22) = X_22 ),
introduced(tautology,[equality,[$cnf( $equal(join(join(meet(X_21,X_22),X_22),X_22),X_22) ),[0],$fot(join(meet(X_21,X_22),X_22))]]) ).
cnf(refute_0_28,plain,
( join(join(meet(X_21,X_22),X_22),X_22) != X_22
| join(meet(X_21,X_22),X_22) = X_22 ),
inference(resolve,[$cnf( $equal(join(join(meet(X_21,X_22),X_22),X_22),join(meet(X_21,X_22),X_22)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
join(meet(X_21,X_22),X_22) = X_22,
inference(resolve,[$cnf( $equal(join(join(meet(X_21,X_22),X_22),X_22),X_22) )],[refute_0_15,refute_0_28]) ).
cnf(refute_0_30,plain,
join(meet(X_24,join(Y,X_24)),join(Y,X_24)) = join(Y,X_24),
inference(subst,[],[refute_0_29:[bind(X_21,$fot(X_24)),bind(X_22,$fot(join(Y,X_24)))]]) ).
cnf(refute_0_31,plain,
meet(X_24,join(Y,X_24)) = X_24,
inference(subst,[],[refute_0_21:[bind(X,$fot(X_24))]]) ).
cnf(refute_0_32,plain,
( join(meet(X_24,join(Y,X_24)),join(Y,X_24)) != join(Y,X_24)
| meet(X_24,join(Y,X_24)) != X_24
| join(X_24,join(Y,X_24)) = join(Y,X_24) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_24,join(Y,X_24)),join(Y,X_24)),join(Y,X_24)) ),[0,0],$fot(X_24)]]) ).
cnf(refute_0_33,plain,
( join(meet(X_24,join(Y,X_24)),join(Y,X_24)) != join(Y,X_24)
| join(X_24,join(Y,X_24)) = join(Y,X_24) ),
inference(resolve,[$cnf( $equal(meet(X_24,join(Y,X_24)),X_24) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
join(X_24,join(Y,X_24)) = join(Y,X_24),
inference(resolve,[$cnf( $equal(join(meet(X_24,join(Y,X_24)),join(Y,X_24)),join(Y,X_24)) )],[refute_0_30,refute_0_33]) ).
cnf(refute_0_35,plain,
join(meet(X_47,Z),join(X_47,meet(X_47,Z))) = join(X_47,meet(X_47,Z)),
inference(subst,[],[refute_0_34:[bind(Y,$fot(X_47)),bind(X_24,$fot(meet(X_47,Z)))]]) ).
cnf(refute_0_36,plain,
join(X,meet(meet(join(X_14,meet(X,Z)),join(meet(X,Z),X_16)),meet(X,Z))) = X,
inference(subst,[],[mckenzie1:[bind(Y,$fot(meet(join(X_14,meet(X,Z)),join(meet(X,Z),X_16))))]]) ).
cnf(refute_0_37,plain,
meet(meet(join(X_14,meet(X,Z)),join(meet(X,Z),X_16)),meet(X,Z)) = meet(X,Z),
inference(subst,[],[mckenzie4:[bind(X,$fot(X_14)),bind(Y,$fot(meet(X,Z))),bind(Z,$fot(X_16))]]) ).
cnf(refute_0_38,plain,
( join(X,meet(meet(join(X_14,meet(X,Z)),join(meet(X,Z),X_16)),meet(X,Z))) != X
| meet(meet(join(X_14,meet(X,Z)),join(meet(X,Z),X_16)),meet(X,Z)) != meet(X,Z)
| join(X,meet(X,Z)) = X ),
introduced(tautology,[equality,[$cnf( $equal(join(X,meet(meet(join(X_14,meet(X,Z)),join(meet(X,Z),X_16)),meet(X,Z))),X) ),[0,1],$fot(meet(X,Z))]]) ).
cnf(refute_0_39,plain,
( join(X,meet(meet(join(X_14,meet(X,Z)),join(meet(X,Z),X_16)),meet(X,Z))) != X
| join(X,meet(X,Z)) = X ),
inference(resolve,[$cnf( $equal(meet(meet(join(X_14,meet(X,Z)),join(meet(X,Z),X_16)),meet(X,Z)),meet(X,Z)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
join(X,meet(X,Z)) = X,
inference(resolve,[$cnf( $equal(join(X,meet(meet(join(X_14,meet(X,Z)),join(meet(X,Z),X_16)),meet(X,Z))),X) )],[refute_0_36,refute_0_39]) ).
cnf(refute_0_41,plain,
join(X_47,meet(X_47,Z)) = X_47,
inference(subst,[],[refute_0_40:[bind(X,$fot(X_47))]]) ).
cnf(refute_0_42,plain,
( join(X_47,meet(X_47,Z)) != X_47
| join(meet(X_47,Z),join(X_47,meet(X_47,Z))) != join(X_47,meet(X_47,Z))
| join(meet(X_47,Z),X_47) = join(X_47,meet(X_47,Z)) ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_47,Z),join(X_47,meet(X_47,Z))),join(X_47,meet(X_47,Z))) ),[0,1],$fot(X_47)]]) ).
cnf(refute_0_43,plain,
( join(meet(X_47,Z),join(X_47,meet(X_47,Z))) != join(X_47,meet(X_47,Z))
| join(meet(X_47,Z),X_47) = join(X_47,meet(X_47,Z)) ),
inference(resolve,[$cnf( $equal(join(X_47,meet(X_47,Z)),X_47) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
join(meet(X_47,Z),X_47) = join(X_47,meet(X_47,Z)),
inference(resolve,[$cnf( $equal(join(meet(X_47,Z),join(X_47,meet(X_47,Z))),join(X_47,meet(X_47,Z))) )],[refute_0_35,refute_0_43]) ).
cnf(refute_0_45,plain,
( join(X_47,meet(X_47,Z)) != X_47
| join(meet(X_47,Z),X_47) != join(X_47,meet(X_47,Z))
| join(meet(X_47,Z),X_47) = X_47 ),
introduced(tautology,[equality,[$cnf( $equal(join(meet(X_47,Z),X_47),join(X_47,meet(X_47,Z))) ),[1],$fot(X_47)]]) ).
cnf(refute_0_46,plain,
( join(meet(X_47,Z),X_47) != join(X_47,meet(X_47,Z))
| join(meet(X_47,Z),X_47) = X_47 ),
inference(resolve,[$cnf( $equal(join(X_47,meet(X_47,Z)),X_47) )],[refute_0_41,refute_0_45]) ).
cnf(refute_0_47,plain,
join(meet(X_47,Z),X_47) = X_47,
inference(resolve,[$cnf( $equal(join(meet(X_47,Z),X_47),join(X_47,meet(X_47,Z))) )],[refute_0_44,refute_0_46]) ).
cnf(refute_0_48,plain,
join(meet(X_94,X_93),X_94) = X_94,
inference(subst,[],[refute_0_47:[bind(Z,$fot(X_93)),bind(X_47,$fot(X_94))]]) ).
cnf(refute_0_49,plain,
( join(meet(X_94,X_93),X_94) != X_94
| meet(meet(X_93,join(meet(X_94,X_93),X_94)),meet(X_94,X_93)) != meet(X_94,X_93)
| meet(meet(X_93,X_94),meet(X_94,X_93)) = meet(X_94,X_93) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(X_93,join(meet(X_94,X_93),X_94)),meet(X_94,X_93)),meet(X_94,X_93)) ),[0,0,1],$fot(X_94)]]) ).
cnf(refute_0_50,plain,
( meet(meet(X_93,join(meet(X_94,X_93),X_94)),meet(X_94,X_93)) != meet(X_94,X_93)
| meet(meet(X_93,X_94),meet(X_94,X_93)) = meet(X_94,X_93) ),
inference(resolve,[$cnf( $equal(join(meet(X_94,X_93),X_94),X_94) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
meet(meet(X_93,X_94),meet(X_94,X_93)) = meet(X_94,X_93),
inference(resolve,[$cnf( $equal(meet(meet(X_93,join(meet(X_94,X_93),X_94)),meet(X_94,X_93)),meet(X_94,X_93)) )],[refute_0_10,refute_0_50]) ).
cnf(refute_0_52,plain,
meet(meet(meet(X_128,X_127),meet(X_127,X_128)),meet(meet(X_127,X_128),meet(X_128,X_127))) = meet(meet(X_127,X_128),meet(X_128,X_127)),
inference(subst,[],[refute_0_51:[bind(X_93,$fot(meet(X_128,X_127))),bind(X_94,$fot(meet(X_127,X_128)))]]) ).
cnf(refute_0_53,plain,
meet(meet(X_127,X_128),meet(X_128,X_127)) = meet(X_128,X_127),
inference(subst,[],[refute_0_51:[bind(X_93,$fot(X_127)),bind(X_94,$fot(X_128))]]) ).
cnf(refute_0_54,plain,
( meet(meet(X_127,X_128),meet(X_128,X_127)) != meet(X_128,X_127)
| meet(meet(meet(X_128,X_127),meet(X_127,X_128)),meet(meet(X_127,X_128),meet(X_128,X_127))) != meet(meet(X_127,X_128),meet(X_128,X_127))
| meet(meet(meet(X_128,X_127),meet(X_127,X_128)),meet(X_128,X_127)) = meet(meet(X_127,X_128),meet(X_128,X_127)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(meet(X_128,X_127),meet(X_127,X_128)),meet(meet(X_127,X_128),meet(X_128,X_127))),meet(meet(X_127,X_128),meet(X_128,X_127))) ),[0,1],$fot(meet(X_128,X_127))]]) ).
cnf(refute_0_55,plain,
( meet(meet(meet(X_128,X_127),meet(X_127,X_128)),meet(meet(X_127,X_128),meet(X_128,X_127))) != meet(meet(X_127,X_128),meet(X_128,X_127))
| meet(meet(meet(X_128,X_127),meet(X_127,X_128)),meet(X_128,X_127)) = meet(meet(X_127,X_128),meet(X_128,X_127)) ),
inference(resolve,[$cnf( $equal(meet(meet(X_127,X_128),meet(X_128,X_127)),meet(X_128,X_127)) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
meet(meet(meet(X_128,X_127),meet(X_127,X_128)),meet(X_128,X_127)) = meet(meet(X_127,X_128),meet(X_128,X_127)),
inference(resolve,[$cnf( $equal(meet(meet(meet(X_128,X_127),meet(X_127,X_128)),meet(meet(X_127,X_128),meet(X_128,X_127))),meet(meet(X_127,X_128),meet(X_128,X_127))) )],[refute_0_52,refute_0_55]) ).
cnf(refute_0_57,plain,
meet(meet(X_128,X_127),meet(X_127,X_128)) = meet(X_127,X_128),
inference(subst,[],[refute_0_51:[bind(X_93,$fot(X_128)),bind(X_94,$fot(X_127))]]) ).
cnf(refute_0_58,plain,
meet(meet(Y,X_27),join(Y,meet(Y,X_27))) = meet(Y,X_27),
inference(subst,[],[refute_0_21:[bind(X,$fot(meet(Y,X_27)))]]) ).
cnf(refute_0_59,plain,
join(Y,meet(Y,X_27)) = Y,
inference(subst,[],[refute_0_40:[bind(X,$fot(Y)),bind(Z,$fot(X_27))]]) ).
cnf(refute_0_60,plain,
( join(Y,meet(Y,X_27)) != Y
| meet(meet(Y,X_27),join(Y,meet(Y,X_27))) != meet(Y,X_27)
| meet(meet(Y,X_27),Y) = meet(Y,X_27) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(Y,X_27),join(Y,meet(Y,X_27))),meet(Y,X_27)) ),[0,1],$fot(Y)]]) ).
cnf(refute_0_61,plain,
( meet(meet(Y,X_27),join(Y,meet(Y,X_27))) != meet(Y,X_27)
| meet(meet(Y,X_27),Y) = meet(Y,X_27) ),
inference(resolve,[$cnf( $equal(join(Y,meet(Y,X_27)),Y) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
meet(meet(Y,X_27),Y) = meet(Y,X_27),
inference(resolve,[$cnf( $equal(meet(meet(Y,X_27),join(Y,meet(Y,X_27))),meet(Y,X_27)) )],[refute_0_58,refute_0_61]) ).
cnf(refute_0_63,plain,
meet(meet(meet(X_128,X_127),meet(X_127,X_128)),meet(X_128,X_127)) = meet(meet(X_128,X_127),meet(X_127,X_128)),
inference(subst,[],[refute_0_62:[bind(Y,$fot(meet(X_128,X_127))),bind(X_27,$fot(meet(X_127,X_128)))]]) ).
cnf(refute_0_64,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_65,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_66,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_68,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
( meet(meet(X_128,X_127),meet(X_127,X_128)) != meet(X_127,X_128)
| meet(meet(meet(X_128,X_127),meet(X_127,X_128)),meet(X_128,X_127)) != meet(meet(X_128,X_127),meet(X_127,X_128))
| meet(meet(meet(X_128,X_127),meet(X_127,X_128)),meet(X_128,X_127)) = meet(X_127,X_128) ),
inference(subst,[],[refute_0_68:[bind(X0,$fot(meet(meet(meet(X_128,X_127),meet(X_127,X_128)),meet(X_128,X_127)))),bind(Y0,$fot(meet(meet(X_128,X_127),meet(X_127,X_128)))),bind(Z0,$fot(meet(X_127,X_128)))]]) ).
cnf(refute_0_70,plain,
( meet(meet(X_128,X_127),meet(X_127,X_128)) != meet(X_127,X_128)
| meet(meet(meet(X_128,X_127),meet(X_127,X_128)),meet(X_128,X_127)) = meet(X_127,X_128) ),
inference(resolve,[$cnf( $equal(meet(meet(meet(X_128,X_127),meet(X_127,X_128)),meet(X_128,X_127)),meet(meet(X_128,X_127),meet(X_127,X_128))) )],[refute_0_63,refute_0_69]) ).
cnf(refute_0_71,plain,
meet(meet(meet(X_128,X_127),meet(X_127,X_128)),meet(X_128,X_127)) = meet(X_127,X_128),
inference(resolve,[$cnf( $equal(meet(meet(X_128,X_127),meet(X_127,X_128)),meet(X_127,X_128)) )],[refute_0_57,refute_0_70]) ).
cnf(refute_0_72,plain,
( meet(meet(meet(X_128,X_127),meet(X_127,X_128)),meet(X_128,X_127)) != meet(X_127,X_128)
| meet(meet(meet(X_128,X_127),meet(X_127,X_128)),meet(X_128,X_127)) != meet(meet(X_127,X_128),meet(X_128,X_127))
| meet(X_127,X_128) = meet(meet(X_127,X_128),meet(X_128,X_127)) ),
introduced(tautology,[equality,[$cnf( $equal(meet(meet(meet(X_128,X_127),meet(X_127,X_128)),meet(X_128,X_127)),meet(meet(X_127,X_128),meet(X_128,X_127))) ),[0],$fot(meet(X_127,X_128))]]) ).
cnf(refute_0_73,plain,
( meet(meet(meet(X_128,X_127),meet(X_127,X_128)),meet(X_128,X_127)) != meet(meet(X_127,X_128),meet(X_128,X_127))
| meet(X_127,X_128) = meet(meet(X_127,X_128),meet(X_128,X_127)) ),
inference(resolve,[$cnf( $equal(meet(meet(meet(X_128,X_127),meet(X_127,X_128)),meet(X_128,X_127)),meet(X_127,X_128)) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
( meet(X_127,X_128) != meet(meet(X_127,X_128),meet(X_128,X_127))
| meet(meet(X_127,X_128),meet(X_128,X_127)) != meet(X_128,X_127)
| meet(X_127,X_128) = meet(X_128,X_127) ),
introduced(tautology,[equality,[$cnf( ~ $equal(meet(X_127,X_128),meet(X_128,X_127)) ),[0],$fot(meet(meet(X_127,X_128),meet(X_128,X_127)))]]) ).
cnf(refute_0_75,plain,
( meet(X_127,X_128) != meet(meet(X_127,X_128),meet(X_128,X_127))
| meet(X_127,X_128) = meet(X_128,X_127) ),
inference(resolve,[$cnf( $equal(meet(meet(X_127,X_128),meet(X_128,X_127)),meet(X_128,X_127)) )],[refute_0_53,refute_0_74]) ).
cnf(refute_0_76,plain,
( meet(meet(meet(X_128,X_127),meet(X_127,X_128)),meet(X_128,X_127)) != meet(meet(X_127,X_128),meet(X_128,X_127))
| meet(X_127,X_128) = meet(X_128,X_127) ),
inference(resolve,[$cnf( $equal(meet(X_127,X_128),meet(meet(X_127,X_128),meet(X_128,X_127))) )],[refute_0_73,refute_0_75]) ).
cnf(refute_0_77,plain,
meet(X_127,X_128) = meet(X_128,X_127),
inference(resolve,[$cnf( $equal(meet(meet(meet(X_128,X_127),meet(X_127,X_128)),meet(X_128,X_127)),meet(meet(X_127,X_128),meet(X_128,X_127))) )],[refute_0_56,refute_0_76]) ).
cnf(refute_0_78,plain,
( meet(X_127,X_128) != meet(X_128,X_127)
| meet(X_128,X_127) = meet(X_127,X_128) ),
inference(subst,[],[refute_0_66:[bind(X0,$fot(meet(X_127,X_128))),bind(Y0,$fot(meet(X_128,X_127)))]]) ).
cnf(refute_0_79,plain,
meet(X_128,X_127) = meet(X_127,X_128),
inference(resolve,[$cnf( $equal(meet(X_127,X_128),meet(X_128,X_127)) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
meet(b,a) = meet(a,b),
inference(subst,[],[refute_0_79:[bind(X_127,$fot(a)),bind(X_128,$fot(b))]]) ).
cnf(refute_0_81,plain,
( meet(a,b) != meet(a,b)
| meet(b,a) != meet(a,b)
| meet(b,a) = meet(a,b) ),
introduced(tautology,[equality,[$cnf( $equal(meet(b,a),meet(a,b)) ),[1],$fot(meet(a,b))]]) ).
cnf(refute_0_82,plain,
( meet(a,b) != meet(a,b)
| meet(b,a) = meet(a,b) ),
inference(resolve,[$cnf( $equal(meet(b,a),meet(a,b)) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
meet(a,b) != meet(a,b),
inference(resolve,[$cnf( $equal(meet(b,a),meet(a,b)) )],[refute_0_82,prove_commutativity_of_meet]) ).
cnf(refute_0_84,plain,
meet(a,b) = meet(a,b),
introduced(tautology,[refl,[$fot(meet(a,b))]]) ).
cnf(refute_0_85,plain,
$false,
inference(resolve,[$cnf( $equal(meet(a,b),meet(a,b)) )],[refute_0_84,refute_0_83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT012-1 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n004.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 : 600
% 0.12/0.33 % DateTime : Wed Jun 29 13:28:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.50/0.70 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.50/0.70
% 0.50/0.70 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.50/0.70
%------------------------------------------------------------------------------