%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT401-2 : TPTP v9.2.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n020.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 : Tue May 5 04:38:29 PM UTC 2026
% Result : Unsatisfiable 32.45s 19.02s
% Output : CNFRefutation 32.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 14
% Syntax : Number of clauses : 194 ( 194 unt; 0 nHn; 92 RR)
% Number of literals : 194 ( 193 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 262 ( 30 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(conjecture_1,negated_conjecture,
upme(a,x2,y2) = upme(a,y2,z2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture_1) ).
cnf(definition_of_upme,axiom,
upme(X1,X2,X3) = meet(X1,join(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_upme) ).
cnf(upme_property_1,axiom,
join(upme(meet(a,X1),X2,X3),meet(X2,X3)) = meet(join(meet(meet(a,X1),X2),X3),join(meet(meet(a,X1),X3),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upme_property_1) ).
cnf(commutativity,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity) ).
cnf(associativity,axiom,
meet(X1,meet(X2,X3)) = meet(meet(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
cnf(absorption_003,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption_003) ).
cnf(absorption,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption) ).
cnf(commutativity_001,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_001) ).
cnf(associativity_002,axiom,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_002) ).
cnf(conjecture,negated_conjecture,
upme(a,x2,y2) = upme(a,x2,z2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture) ).
cnf(upme_property_2,axiom,
upme(X1,X2,X3) = join(upme(X1,X2,meet(a,X3)),upme(X1,X3,meet(a,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upme_property_2) ).
cnf(conjecture_2,negated_conjecture,
upjo(x2,y2,z2) != lojo(x2,y2,z2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture_2) ).
cnf(definition_of_lojo,axiom,
lojo(X1,X2,X3) = join(X1,meet(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_lojo) ).
cnf(definition_of_upjo,axiom,
upjo(X1,X2,X3) = meet(join(X1,X2),join(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',definition_of_upjo) ).
cnf(c_0_14,negated_conjecture,
upme(a,x2,y2) = upme(a,y2,z2),
conjecture_1 ).
cnf(c_0_15,axiom,
upme(X1,X2,X3) = meet(X1,join(X2,X3)),
definition_of_upme ).
cnf(c_0_16,axiom,
join(upme(meet(a,X1),X2,X3),meet(X2,X3)) = meet(join(meet(meet(a,X1),X2),X3),join(meet(meet(a,X1),X3),X2)),
upme_property_1 ).
cnf(c_0_17,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity ).
cnf(c_0_18,axiom,
meet(X1,meet(X2,X3)) = meet(meet(X1,X2),X3),
associativity ).
cnf(c_0_19,negated_conjecture,
meet(a,join(y2,z2)) = meet(a,join(x2,y2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_15]) ).
cnf(c_0_20,axiom,
meet(X1,join(X1,X2)) = X1,
absorption_003 ).
cnf(c_0_21,axiom,
join(X1,meet(X1,X2)) = X1,
absorption ).
cnf(c_0_22,plain,
join(meet(meet(a,X1),join(X2,X3)),meet(X2,X3)) = meet(join(meet(meet(a,X1),X2),X3),join(meet(meet(a,X1),X3),X2)),
inference(rw,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_23,axiom,
join(X1,X2) = join(X2,X1),
commutativity_001 ).
cnf(c_0_24,axiom,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
associativity_002 ).
cnf(c_0_25,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_26,negated_conjecture,
meet(a,meet(join(y2,z2),X1)) = meet(a,meet(join(x2,y2),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_18]) ).
cnf(c_0_27,plain,
meet(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
meet(join(meet(a,meet(X1,X2)),X3),join(meet(a,meet(X1,X3)),X2)) = join(meet(X2,X3),meet(a,meet(X1,join(X2,X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_18]),c_0_18]),c_0_18]),c_0_23]) ).
cnf(c_0_29,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_17]) ).
cnf(c_0_30,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_23]) ).
cnf(c_0_31,plain,
meet(join(X1,X2),join(X1,join(X2,X3))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_24]) ).
cnf(c_0_32,plain,
join(X1,meet(X2,meet(X1,X3))) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_25]) ).
cnf(c_0_33,negated_conjecture,
meet(a,meet(join(x2,y2),join(y2,z2))) = meet(a,join(x2,y2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_19]) ).
cnf(c_0_34,plain,
join(meet(a,meet(X1,X2)),join(X3,join(meet(X2,X3),meet(a,meet(X1,join(X2,X3)))))) = join(meet(a,meet(X1,X2)),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_28]),c_0_24]) ).
cnf(c_0_35,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_24,c_0_29]) ).
cnf(c_0_36,negated_conjecture,
upme(a,x2,y2) = upme(a,x2,z2),
conjecture ).
cnf(c_0_37,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_38,plain,
meet(X1,meet(X2,X1)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_21]),c_0_18]) ).
cnf(c_0_39,plain,
meet(join(X1,X2),join(X1,join(X3,X2))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_31,c_0_23]) ).
cnf(c_0_40,negated_conjecture,
join(x2,join(y2,meet(a,join(x2,y2)))) = join(x2,y2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_24]) ).
cnf(c_0_41,plain,
join(meet(a,meet(X1,X2)),join(X3,meet(a,meet(X1,join(X2,X3))))) = join(meet(a,meet(X1,X2)),X3),
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,negated_conjecture,
meet(a,join(x2,z2)) = meet(a,join(x2,y2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_15]),c_0_15]) ).
cnf(c_0_43,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_27]) ).
cnf(c_0_44,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_23]),c_0_24]) ).
cnf(c_0_45,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_37]) ).
cnf(c_0_46,plain,
meet(X1,meet(X2,join(X3,meet(X1,X2)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_30]) ).
cnf(c_0_47,negated_conjecture,
meet(join(x2,y2),join(x2,meet(a,join(x2,y2)))) = join(x2,meet(a,join(x2,y2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_17]) ).
cnf(c_0_48,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_20]),c_0_24]) ).
cnf(c_0_49,negated_conjecture,
join(y2,join(z2,meet(a,join(x2,y2)))) = join(y2,z2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_19]),c_0_24]) ).
cnf(c_0_50,negated_conjecture,
meet(join(x2,y2),join(y2,meet(a,join(x2,y2)))) = join(y2,meet(a,join(x2,y2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_40]),c_0_17]) ).
cnf(c_0_51,negated_conjecture,
join(z2,join(meet(a,x2),meet(a,join(x2,y2)))) = join(z2,meet(a,x2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_43]),c_0_43]),c_0_23]),c_0_44]) ).
cnf(c_0_52,plain,
join(meet(a,X1),meet(a,X2)) = meet(a,join(meet(a,X2),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_38]),c_0_23]),c_0_21]),c_0_17]),c_0_45]) ).
cnf(c_0_53,negated_conjecture,
meet(a,join(x2,meet(a,join(x2,y2)))) = meet(a,join(x2,y2)),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_54,negated_conjecture,
join(z2,join(y2,meet(a,join(x2,y2)))) = join(y2,z2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_24]),c_0_24]),c_0_23]),c_0_24]),c_0_49]),c_0_48]),c_0_23]),c_0_23]) ).
cnf(c_0_55,negated_conjecture,
join(z2,join(meet(a,y2),meet(a,join(x2,y2)))) = join(z2,meet(a,y2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_19]),c_0_43]),c_0_43]),c_0_43]),c_0_23]),c_0_44]) ).
cnf(c_0_56,negated_conjecture,
meet(a,join(y2,meet(a,join(x2,y2)))) = meet(a,join(x2,y2)),
inference(spm,[status(thm)],[c_0_46,c_0_50]) ).
cnf(c_0_57,negated_conjecture,
join(z2,meet(a,join(x2,y2))) = join(z2,meet(a,x2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52]),c_0_23]),c_0_53]) ).
cnf(c_0_58,axiom,
upme(X1,X2,X3) = join(upme(X1,X2,meet(a,X3)),upme(X1,X3,meet(a,X2))),
upme_property_2 ).
cnf(c_0_59,negated_conjecture,
meet(z2,meet(join(y2,z2),X1)) = meet(z2,X1),
inference(spm,[status(thm)],[c_0_37,c_0_54]) ).
cnf(c_0_60,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_61,negated_conjecture,
join(z2,meet(a,y2)) = join(z2,meet(a,x2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_52]),c_0_23]),c_0_56]),c_0_57]) ).
cnf(c_0_62,plain,
meet(X1,join(X2,X3)) = join(meet(X1,join(X2,meet(a,X3))),meet(X1,join(X3,meet(a,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_15]),c_0_15]),c_0_15]) ).
cnf(c_0_63,plain,
join(meet(X1,X2),meet(X1,meet(X2,X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_64,plain,
join(meet(X1,X2),meet(a,X1)) = meet(X1,join(meet(a,X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_27]),c_0_20]),c_0_23]),c_0_32]),c_0_17]) ).
cnf(c_0_65,negated_conjecture,
meet(z2,meet(X1,join(y2,z2))) = meet(z2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_38]),c_0_59]) ).
cnf(c_0_66,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_17]),c_0_18]) ).
cnf(c_0_67,plain,
join(meet(a,meet(X1,X2)),join(X3,meet(a,meet(X1,join(X3,X2))))) = join(meet(a,meet(X1,X2)),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_28]),c_0_24]),c_0_60]) ).
cnf(c_0_68,negated_conjecture,
meet(a,meet(y2,join(z2,meet(a,x2)))) = meet(a,y2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_61]),c_0_18]) ).
cnf(c_0_69,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(X1,meet(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_38]),c_0_18]),c_0_18]) ).
cnf(c_0_70,plain,
join(meet(X1,meet(a,X2)),meet(X1,meet(X2,join(meet(a,X2),X3)))) = meet(X1,join(meet(a,X2),meet(X2,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_43]),c_0_64]) ).
cnf(c_0_71,negated_conjecture,
meet(a,meet(z2,join(x2,y2))) = meet(a,z2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_19]),c_0_66]),c_0_17]) ).
cnf(c_0_72,negated_conjecture,
join(z2,meet(a,join(meet(a,x2),meet(x2,y2)))) = join(z2,meet(a,meet(x2,y2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_69]),c_0_61]),c_0_69]),c_0_17]),c_0_44]),c_0_52]),c_0_17]),c_0_23]) ).
cnf(c_0_73,plain,
meet(X1,join(meet(a,X2),meet(X2,X3))) = meet(X1,meet(X2,join(meet(a,X2),X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_43]),c_0_64]),c_0_23]),c_0_70]),c_0_64]) ).
cnf(c_0_74,negated_conjecture,
join(y2,join(meet(a,z2),meet(a,meet(x2,z2)))) = join(y2,meet(a,meet(x2,z2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_71]),c_0_17]),c_0_44]),c_0_23]),c_0_17]),c_0_23]) ).
cnf(c_0_75,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_18]) ).
cnf(c_0_76,negated_conjecture,
meet(a,meet(X1,join(y2,z2))) = meet(a,meet(join(x2,y2),X1)),
inference(spm,[status(thm)],[c_0_26,c_0_17]) ).
cnf(c_0_77,plain,
meet(join(X1,meet(a,meet(X2,X3))),join(meet(a,meet(X2,X1)),X3)) = join(meet(X1,X3),meet(a,meet(X2,join(X1,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_23]),c_0_17]) ).
cnf(c_0_78,negated_conjecture,
join(z2,meet(a,meet(x2,y2))) = join(z2,meet(a,x2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73]),c_0_23]),c_0_46]) ).
cnf(c_0_79,negated_conjecture,
join(y2,meet(a,meet(x2,z2))) = join(y2,meet(a,z2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_74,c_0_52]),c_0_23]),c_0_75]) ).
cnf(c_0_80,negated_conjecture,
meet(a,meet(X1,join(y2,z2))) = meet(a,meet(X1,join(x2,y2))),
inference(spm,[status(thm)],[c_0_76,c_0_17]) ).
cnf(c_0_81,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_82,plain,
meet(join(meet(a,meet(X1,X2)),X3),join(X2,meet(a,meet(X1,join(X3,meet(a,meet(X1,X2))))))) = join(meet(a,meet(X1,join(X3,X2))),meet(X2,join(X3,meet(a,meet(X1,X2))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_48]),c_0_24]),c_0_17]),c_0_23]),c_0_75]),c_0_23]),c_0_23]),c_0_17]) ).
cnf(c_0_83,negated_conjecture,
meet(join(y2,meet(a,z2)),join(z2,meet(a,x2))) = join(meet(a,x2),meet(y2,z2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_23]),c_0_79]),c_0_17]),c_0_23]),c_0_80]),c_0_20]),c_0_17]),c_0_23]) ).
cnf(c_0_84,negated_conjecture,
join(x2,join(meet(a,z2),meet(a,meet(y2,z2)))) = join(x2,meet(a,meet(y2,z2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_71]),c_0_17]),c_0_44]),c_0_23]),c_0_17]),c_0_23]) ).
cnf(c_0_85,plain,
meet(X1,meet(X2,join(meet(X2,X1),X3))) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_81,c_0_17]) ).
cnf(c_0_86,plain,
join(meet(a,X1),meet(X2,a)) = meet(a,join(X2,meet(a,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_64]),c_0_27]),c_0_20]),c_0_27]),c_0_21]),c_0_38]),c_0_27]),c_0_45]),c_0_27]),c_0_21]) ).
cnf(c_0_87,plain,
meet(X1,join(X2,join(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_24]) ).
cnf(c_0_88,plain,
meet(X1,join(X2,join(X1,X3))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_30]),c_0_20]) ).
cnf(c_0_89,negated_conjecture,
join(y2,join(meet(a,x2),join(meet(a,z2),meet(y2,z2)))) = join(y2,meet(a,z2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_83]),c_0_24]),c_0_44]) ).
cnf(c_0_90,negated_conjecture,
meet(a,meet(join(x2,z2),X1)) = meet(a,meet(join(x2,y2),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_42]),c_0_18]) ).
cnf(c_0_91,plain,
meet(X1,meet(join(X2,X3),meet(join(X2,meet(a,X3)),X1))) = meet(X1,join(X2,meet(a,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_62]),c_0_18]),c_0_25]) ).
cnf(c_0_92,plain,
join(meet(X1,join(X2,meet(a,X3))),meet(X1,join(meet(a,X2),X3))) = meet(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_62,c_0_23]) ).
cnf(c_0_93,negated_conjecture,
meet(y2,join(meet(a,x2),meet(y2,z2))) = meet(y2,join(z2,meet(a,x2))),
inference(spm,[status(thm)],[c_0_37,c_0_83]) ).
cnf(c_0_94,negated_conjecture,
join(x2,meet(a,meet(y2,z2))) = join(x2,meet(a,z2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_52]),c_0_23]),c_0_75]) ).
cnf(c_0_95,plain,
join(meet(join(X1,meet(a,X2)),X3),meet(X3,join(X2,meet(a,X1)))) = meet(X3,join(X1,X2)),
inference(spm,[status(thm)],[c_0_62,c_0_17]) ).
cnf(c_0_96,plain,
meet(a,join(meet(X1,a),X2)) = meet(a,join(X1,meet(a,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_85]),c_0_86]) ).
cnf(c_0_97,negated_conjecture,
meet(a,meet(x2,meet(z2,join(y2,meet(a,meet(x2,z2)))))) = meet(a,meet(x2,z2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_74]),c_0_18]),c_0_18]) ).
cnf(c_0_98,negated_conjecture,
meet(a,meet(x2,join(y2,meet(a,z2)))) = meet(a,x2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_18]) ).
cnf(c_0_99,negated_conjecture,
meet(a,meet(join(x2,y2),join(x2,meet(a,z2)))) = meet(a,join(x2,meet(a,z2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_17]),c_0_66]),c_0_43]) ).
cnf(c_0_100,negated_conjecture,
meet(a,meet(X1,meet(X2,join(y2,z2)))) = meet(a,meet(join(x2,y2),meet(X1,X2))),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_101,negated_conjecture,
meet(y2,join(x2,meet(y2,z2))) = meet(y2,join(x2,z2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94]),c_0_62]) ).
cnf(c_0_102,negated_conjecture,
meet(a,meet(join(x2,y2),meet(X1,join(x2,z2)))) = meet(a,meet(join(x2,y2),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_38]),c_0_90]) ).
cnf(c_0_103,plain,
meet(a,join(X1,meet(X2,a))) = meet(a,join(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_38]),c_0_43]),c_0_95]) ).
cnf(c_0_104,plain,
join(meet(X1,join(X2,meet(a,X3))),join(meet(X1,join(X3,meet(a,X2))),X4)) = join(meet(X1,join(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_24,c_0_62]) ).
cnf(c_0_105,negated_conjecture,
meet(a,meet(x2,meet(z2,join(y2,meet(a,z2))))) = meet(a,meet(x2,z2)),
inference(rw,[status(thm)],[c_0_97,c_0_79]) ).
cnf(c_0_106,negated_conjecture,
join(y2,meet(a,z2)) = join(y2,meet(a,x2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_98]),c_0_66]),c_0_43]),c_0_66]),c_0_43]),c_0_23]),c_0_79]),c_0_44]),c_0_23]),c_0_63]) ).
cnf(c_0_107,negated_conjecture,
join(x2,join(meet(a,z2),meet(a,join(x2,meet(a,z2))))) = join(x2,meet(a,z2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_99]),c_0_24]) ).
cnf(c_0_108,negated_conjecture,
meet(a,meet(y2,join(x2,z2))) = meet(a,y2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_45]),c_0_101]),c_0_102]),c_0_17]),c_0_30]) ).
cnf(c_0_109,plain,
meet(a,join(X1,meet(a,X2))) = meet(a,join(X1,X2)),
inference(spm,[status(thm)],[c_0_103,c_0_17]) ).
cnf(c_0_110,plain,
join(meet(X1,join(X2,X3)),meet(X4,meet(X5,meet(X1,join(X3,meet(a,X2)))))) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_75]),c_0_62]) ).
cnf(c_0_111,negated_conjecture,
meet(a,meet(x2,meet(z2,join(y2,meet(a,x2))))) = meet(a,meet(x2,z2)),
inference(rw,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_112,negated_conjecture,
meet(a,meet(z2,join(x2,meet(a,z2)))) = meet(a,z2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_107]),c_0_18]) ).
cnf(c_0_113,plain,
join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_21,c_0_24]) ).
cnf(c_0_114,plain,
join(meet(X1,meet(X2,join(X3,meet(a,X4)))),meet(X1,meet(X2,join(X4,meet(a,X3))))) = meet(X1,meet(X2,join(X3,X4))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_18]),c_0_18]),c_0_18]) ).
cnf(c_0_115,negated_conjecture,
meet(a,meet(z2,join(x2,meet(a,meet(y2,z2))))) = meet(a,z2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_84]),c_0_18]) ).
cnf(c_0_116,negated_conjecture,
join(x2,meet(a,z2)) = join(x2,meet(a,y2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_108]),c_0_23]),c_0_94]),c_0_44]),c_0_23]),c_0_63]) ).
cnf(c_0_117,plain,
meet(a,join(meet(a,X1),X2)) = meet(a,join(X2,X1)),
inference(spm,[status(thm)],[c_0_109,c_0_23]) ).
cnf(c_0_118,negated_conjecture,
join(meet(a,meet(x2,z2)),meet(z2,join(x2,y2))) = meet(z2,join(x2,y2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_23]) ).
cnf(c_0_119,negated_conjecture,
join(meet(a,z2),meet(z2,join(x2,meet(a,z2)))) = meet(z2,join(x2,meet(a,z2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_112]),c_0_23]) ).
cnf(c_0_120,plain,
meet(join(X1,X2),join(X2,meet(a,X1))) = join(X2,meet(a,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_27]),c_0_44]),c_0_23]),c_0_113]),c_0_17]) ).
cnf(c_0_121,negated_conjecture,
meet(a,meet(z2,join(x2,meet(y2,z2)))) = meet(a,z2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_63]) ).
cnf(c_0_122,plain,
join(meet(X1,X2),meet(a,X2)) = meet(X2,join(meet(a,X2),X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_27]),c_0_23]),c_0_32]),c_0_30]) ).
cnf(c_0_123,negated_conjecture,
meet(z2,join(meet(a,x2),meet(y2,z2))) = meet(z2,join(y2,meet(a,z2))),
inference(spm,[status(thm)],[c_0_45,c_0_83]) ).
cnf(c_0_124,negated_conjecture,
join(x2,meet(a,meet(y2,z2))) = join(x2,meet(a,y2)),
inference(rw,[status(thm)],[c_0_94,c_0_116]) ).
cnf(c_0_125,negated_conjecture,
meet(a,join(meet(x2,z2),meet(z2,join(x2,y2)))) = meet(a,z2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_71]),c_0_23]) ).
cnf(c_0_126,negated_conjecture,
join(meet(a,z2),meet(z2,join(x2,meet(a,y2)))) = meet(z2,join(x2,meet(a,y2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_119,c_0_116]),c_0_116]) ).
cnf(c_0_127,negated_conjecture,
join(x2,join(y2,meet(a,z2))) = join(x2,y2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_71]),c_0_24]) ).
cnf(c_0_128,negated_conjecture,
meet(join(y2,z2),join(z2,meet(a,join(x2,y2)))) = join(z2,meet(a,join(x2,y2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_49]),c_0_17]) ).
cnf(c_0_129,negated_conjecture,
meet(a,meet(join(x2,y2),join(z2,meet(a,x2)))) = meet(a,join(z2,meet(a,x2))),
inference(spm,[status(thm)],[c_0_90,c_0_120]) ).
cnf(c_0_130,negated_conjecture,
join(x2,meet(z2,join(y2,meet(a,z2)))) = join(x2,meet(y2,z2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_121]),c_0_24]),c_0_122]),c_0_23]) ).
cnf(c_0_131,negated_conjecture,
meet(z2,join(meet(a,x2),meet(y2,z2))) = meet(z2,join(y2,meet(a,x2))),
inference(rw,[status(thm)],[c_0_123,c_0_106]) ).
cnf(c_0_132,plain,
join(meet(X1,join(X2,meet(a,X3))),meet(X1,join(X3,meet(X2,a)))) = meet(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_62,c_0_17]) ).
cnf(c_0_133,negated_conjecture,
meet(join(x2,meet(a,y2)),join(z2,meet(a,x2))) = join(meet(a,y2),meet(x2,z2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_124]),c_0_17]),c_0_23]),c_0_78]),c_0_108]),c_0_23]) ).
cnf(c_0_134,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_135,negated_conjecture,
join(meet(a,z2),meet(x2,z2)) = meet(z2,join(x2,meet(a,y2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_125]),c_0_71]),c_0_43]),c_0_43]),c_0_122]),c_0_23]),c_0_116]),c_0_126]),c_0_71]),c_0_43]) ).
cnf(c_0_136,negated_conjecture,
join(y2,join(meet(a,z2),meet(a,join(x2,y2)))) = join(y2,meet(a,z2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_19]),c_0_43]),c_0_43]),c_0_43]),c_0_23]),c_0_44]) ).
cnf(c_0_137,negated_conjecture,
meet(join(x2,y2),join(y2,meet(a,z2))) = join(y2,meet(a,z2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_127]),c_0_17]) ).
cnf(c_0_138,plain,
meet(join(meet(a,meet(X1,X2)),X3),join(meet(X2,X3),meet(a,meet(X1,join(X2,X3))))) = join(meet(X2,X3),meet(a,meet(X1,join(X2,X3)))),
inference(spm,[status(thm)],[c_0_43,c_0_28]) ).
cnf(c_0_139,negated_conjecture,
meet(join(y2,z2),join(z2,meet(a,x2))) = join(z2,meet(a,x2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_128,c_0_57]),c_0_57]) ).
cnf(c_0_140,negated_conjecture,
meet(a,join(z2,meet(a,x2))) = meet(a,join(x2,y2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_51]),c_0_18]),c_0_129]) ).
cnf(c_0_141,plain,
meet(join(X1,meet(X2,join(X3,X4))),join(X1,meet(X2,join(X3,meet(a,X4))))) = join(X1,meet(X2,join(X3,meet(a,X4)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_62]),c_0_17]) ).
cnf(c_0_142,negated_conjecture,
join(x2,meet(z2,join(y2,meet(a,x2)))) = join(x2,meet(y2,z2)),
inference(rw,[status(thm)],[c_0_130,c_0_106]) ).
cnf(c_0_143,negated_conjecture,
meet(z2,join(x2,meet(y2,z2))) = meet(z2,join(x2,y2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_131]),c_0_94]),c_0_116]),c_0_62]) ).
cnf(c_0_144,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_145,plain,
join(meet(X1,join(X2,meet(X3,a))),meet(X1,join(meet(a,X2),X3))) = meet(X1,join(X3,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_23]),c_0_23]) ).
cnf(c_0_146,negated_conjecture,
meet(z2,join(meet(a,y2),meet(x2,z2))) = meet(z2,join(x2,meet(a,y2))),
inference(spm,[status(thm)],[c_0_45,c_0_133]) ).
cnf(c_0_147,plain,
join(meet(X1,join(X2,meet(a,X3))),join(X4,meet(X1,join(X3,meet(a,X2))))) = join(X4,meet(X1,join(X3,X2))),
inference(spm,[status(thm)],[c_0_134,c_0_62]) ).
cnf(c_0_148,negated_conjecture,
join(meet(x2,z2),meet(z2,join(x2,meet(a,y2)))) = meet(z2,join(x2,meet(a,y2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_135]),c_0_122]),c_0_23]),c_0_116]) ).
cnf(c_0_149,negated_conjecture,
meet(a,meet(z2,join(x2,meet(a,y2)))) = meet(a,z2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_116]),c_0_18]) ).
cnf(c_0_150,negated_conjecture,
meet(a,join(y2,meet(a,z2))) = meet(a,join(x2,y2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_136]),c_0_18]),c_0_137]) ).
cnf(c_0_151,negated_conjecture,
meet(a,join(meet(x2,z2),meet(a,join(x2,y2)))) = meet(a,join(x2,y2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_17]),c_0_30]),c_0_52]),c_0_23]),c_0_140]),c_0_140]),c_0_18]),c_0_46]),c_0_140]),c_0_25]),c_0_17]),c_0_66]),c_0_52]),c_0_23]) ).
cnf(c_0_152,negated_conjecture,
join(x2,join(meet(a,z2),X1)) = join(x2,join(meet(a,y2),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_116]),c_0_24]) ).
cnf(c_0_153,negated_conjecture,
join(meet(a,z2),meet(z2,join(x2,y2))) = meet(z2,join(x2,y2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_71]),c_0_23]) ).
cnf(c_0_154,negated_conjecture,
meet(join(x2,meet(y2,z2)),join(x2,meet(z2,join(x2,y2)))) = join(x2,meet(y2,z2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_23]),c_0_17]) ).
cnf(c_0_155,negated_conjecture,
join(x2,join(meet(y2,z2),meet(z2,join(x2,y2)))) = join(x2,meet(y2,z2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_143]),c_0_24]) ).
cnf(c_0_156,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_24,c_0_144]) ).
cnf(c_0_157,plain,
join(meet(a,X1),meet(X2,a)) = meet(a,join(X2,X1)),
inference(rw,[status(thm)],[c_0_86,c_0_109]) ).
cnf(c_0_158,negated_conjecture,
meet(z2,join(y2,meet(x2,z2))) = meet(z2,join(x2,y2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_18]),c_0_17]),c_0_66]),c_0_79]),c_0_106]),c_0_62]),c_0_23]),c_0_23]) ).
cnf(c_0_159,negated_conjecture,
join(meet(x2,z2),meet(z2,join(x2,y2))) = meet(z2,join(x2,y2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_62]),c_0_23]) ).
cnf(c_0_160,negated_conjecture,
meet(a,join(meet(a,y2),meet(x2,z2))) = meet(a,join(x2,y2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_149]),c_0_17]),c_0_52]),c_0_23]),c_0_150]),c_0_52]),c_0_23]),c_0_151]),c_0_17]),c_0_52]) ).
cnf(c_0_161,negated_conjecture,
join(z2,join(meet(a,y2),X1)) = join(z2,join(meet(a,x2),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_61]),c_0_24]) ).
cnf(c_0_162,plain,
meet(a,meet(X1,meet(X2,join(meet(X2,X3),meet(a,meet(X1,join(X2,X3))))))) = meet(a,meet(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_28]),c_0_18]),c_0_18]),c_0_18]),c_0_18]),c_0_30]) ).
cnf(c_0_163,plain,
meet(join(X1,X2),join(X1,meet(a,X2))) = join(X1,meet(a,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_27]),c_0_24]),c_0_113]),c_0_17]) ).
cnf(c_0_164,plain,
meet(join(meet(a,X1),X2),join(X1,join(meet(a,meet(X1,X2)),X3))) = join(meet(a,X1),meet(join(X1,X3),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_20]),c_0_24]),c_0_20]),c_0_44]),c_0_23]) ).
cnf(c_0_165,plain,
join(X1,join(meet(X2,meet(X1,X3)),X4)) = join(X1,X4),
inference(spm,[status(thm)],[c_0_60,c_0_25]) ).
cnf(c_0_166,negated_conjecture,
join(x2,join(meet(a,y2),meet(z2,join(x2,y2)))) = join(x2,meet(z2,join(x2,y2))),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_167,negated_conjecture,
join(x2,meet(z2,join(x2,y2))) = join(x2,meet(y2,z2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_154]),c_0_24]),c_0_44]),c_0_23]),c_0_155]),c_0_156]) ).
cnf(c_0_168,plain,
join(X1,meet(a,join(X2,X1))) = join(X1,meet(X2,a)),
inference(spm,[status(thm)],[c_0_35,c_0_157]) ).
cnf(c_0_169,negated_conjecture,
join(y2,meet(z2,join(x2,y2))) = join(y2,meet(x2,z2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_158]),c_0_24]),c_0_159]) ).
cnf(c_0_170,negated_conjecture,
meet(a,join(y2,meet(x2,z2))) = meet(a,join(x2,y2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_160]),c_0_79]),c_0_150]),c_0_144]) ).
cnf(c_0_171,negated_conjecture,
join(z2,meet(a,join(X1,y2))) = join(z2,meet(a,join(X1,x2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_157]),c_0_86]),c_0_109]) ).
cnf(c_0_172,negated_conjecture,
meet(a,meet(y2,join(meet(y2,z2),meet(a,join(x2,y2))))) = meet(a,y2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_19]),c_0_43]),c_0_43]),c_0_43]) ).
cnf(c_0_173,negated_conjecture,
meet(join(x2,meet(a,z2)),join(x2,meet(y2,z2))) = join(x2,meet(a,z2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_130]),c_0_46]),c_0_46]),c_0_17]) ).
cnf(c_0_174,plain,
join(meet(X1,join(X2,meet(a,X3))),meet(join(X3,meet(X2,a)),X1)) = meet(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_132,c_0_17]) ).
cnf(c_0_175,negated_conjecture,
meet(join(x2,z2),join(x2,meet(a,y2))) = join(x2,meet(a,y2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_116]),c_0_23]) ).
cnf(c_0_176,plain,
join(meet(a,X1),meet(join(X1,X2),X3)) = meet(join(meet(a,X1),X3),join(X1,X2)),
inference(rw,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_177,plain,
join(X1,join(X2,meet(X3,X1))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_44,c_0_29]) ).
cnf(c_0_178,negated_conjecture,
join(x2,join(meet(a,y2),meet(z2,join(x2,y2)))) = join(x2,meet(y2,z2)),
inference(rw,[status(thm)],[c_0_166,c_0_167]) ).
cnf(c_0_179,negated_conjecture,
join(meet(a,y2),meet(z2,join(x2,y2))) = meet(join(x2,y2),join(z2,meet(a,x2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_169]),c_0_170]),c_0_122]),c_0_23]),c_0_171]),c_0_144]),c_0_17]),c_0_23]) ).
cnf(c_0_180,plain,
join(meet(X1,X2),meet(X2,join(meet(X1,X2),X3))) = meet(X2,join(meet(X1,X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_81]),c_0_23]) ).
cnf(c_0_181,negated_conjecture,
join(meet(a,y2),meet(y2,join(z2,meet(a,x2)))) = join(meet(a,y2),meet(y2,z2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_172]),c_0_66]),c_0_30]),c_0_43]),c_0_64]),c_0_23]),c_0_61]),c_0_66]),c_0_30]),c_0_43]) ).
cnf(c_0_182,negated_conjecture,
meet(join(x2,meet(a,y2)),join(x2,meet(y2,z2))) = join(x2,meet(a,y2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_173,c_0_116]),c_0_116]) ).
cnf(c_0_183,plain,
join(X1,join(X2,join(X1,X3))) = join(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_48]),c_0_24]),c_0_24]) ).
cnf(c_0_184,negated_conjecture,
join(x2,meet(join(x2,z2),join(y2,meet(a,x2)))) = meet(join(x2,y2),join(x2,z2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_175]),c_0_17]),c_0_24]),c_0_176]),c_0_44]),c_0_23]),c_0_61]),c_0_177]),c_0_23]),c_0_17]) ).
cnf(c_0_185,negated_conjecture,
upjo(x2,y2,z2) != lojo(x2,y2,z2),
conjecture_2 ).
cnf(c_0_186,axiom,
lojo(X1,X2,X3) = join(X1,meet(X2,X3)),
definition_of_lojo ).
cnf(c_0_187,axiom,
upjo(X1,X2,X3) = meet(join(X1,X2),join(X1,X3)),
definition_of_upjo ).
cnf(c_0_188,negated_conjecture,
join(x2,meet(join(x2,y2),join(z2,meet(a,x2)))) = join(x2,meet(y2,z2)),
inference(rw,[status(thm)],[c_0_178,c_0_179]) ).
cnf(c_0_189,negated_conjecture,
join(meet(a,y2),meet(y2,z2)) = meet(y2,join(z2,meet(a,x2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_181]),c_0_73]),c_0_23]),c_0_61]),c_0_43]),c_0_181]),c_0_73]),c_0_23]),c_0_61]),c_0_43]) ).
cnf(c_0_190,negated_conjecture,
join(x2,meet(y2,join(z2,meet(a,x2)))) = join(x2,meet(y2,z2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_182]),c_0_24]),c_0_183]),c_0_64]),c_0_23]),c_0_61]) ).
cnf(c_0_191,negated_conjecture,
join(x2,meet(join(x2,y2),join(x2,z2))) = meet(join(x2,y2),join(x2,z2)),
inference(spm,[status(thm)],[c_0_156,c_0_184]) ).
cnf(c_0_192,negated_conjecture,
join(x2,meet(y2,z2)) != meet(join(x2,y2),join(x2,z2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_185,c_0_186]),c_0_187]) ).
cnf(c_0_193,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_188]),c_0_116]),c_0_163]),c_0_24]),c_0_183]),c_0_189]),c_0_190]),c_0_23]),c_0_191]),c_0_192]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT401-2 : TPTP v9.2.1. Released v8.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.17/0.34 % Computer : n020.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon May 4 21:51:50 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 32.45/19.02 % Version : CSE_E---1.7
% 32.45/19.02 % Problem : theBenchmark.p
% 32.45/19.02 % SZS status Unsatisfiable for theBenchmark.p
% 32.45/19.02 % SZS output start CNFRefutation
% See solution above
% 32.67/19.14 % Total time : 14.395s
%------------------------------------------------------------------------------