%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT005-10 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n016.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 04:37:17 PM UTC 2026
% Result : Unsatisfiable 120.10s 59.49s
% Output : CNFRefutation 120.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 57
% Number of leaves : 20
% Syntax : Number of clauses : 213 ( 213 unt; 0 nHn; 51 RR)
% Number of literals : 213 ( 212 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 : 12 ( 12 usr; 7 con; 0-4 aty)
% Number of variables : 345 ( 88 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(complement_meet,axiom,
ifeq(complement(X1,X2),true,meet(X1,X2),n0) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_meet) ).
cnf(complement_of_a_join_b,hypothesis,
complement(r1,join(a,b)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_a_join_b) ).
cnf(ifeq_axiom_002,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_002) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
cnf(associativity_of_join,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_join) ).
cnf(modular,axiom,
ifeq3(meet(X1,X2),X1,meet(X2,join(X1,X3)),join(X1,meet(X3,X2))) = join(X1,meet(X3,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modular) ).
cnf(x_join_0,axiom,
join(X1,n0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_join_0) ).
cnf(x_meet_0,axiom,
meet(X1,n0) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_meet_0) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
cnf(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption1) ).
cnf(ifeq_axiom,axiom,
ifeq3(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption2) ).
cnf(associativity_of_meet,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_meet) ).
cnf(x_meet_1,axiom,
meet(X1,n1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_meet_1) ).
cnf(complement_join,axiom,
ifeq(complement(X1,X2),true,join(X1,X2),n1) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_join) ).
cnf(complement_of_a_meet_b,hypothesis,
complement(r2,meet(a,b)) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement_of_a_meet_b) ).
cnf(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_meet) ).
cnf(x_join_1,axiom,
join(X1,n1) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_join_1) ).
cnf(idempotence_of_join,axiom,
join(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_of_join) ).
cnf(prove_lemma,negated_conjecture,
r1 != meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lemma) ).
cnf(c_0_20,axiom,
ifeq(complement(X1,X2),true,meet(X1,X2),n0) = n0,
complement_meet ).
cnf(c_0_21,hypothesis,
complement(r1,join(a,b)) = true,
complement_of_a_join_b ).
cnf(c_0_22,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom_002 ).
cnf(c_0_23,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_24,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_25,axiom,
ifeq3(meet(X1,X2),X1,meet(X2,join(X1,X3)),join(X1,meet(X3,X2))) = join(X1,meet(X3,X2)),
modular ).
cnf(c_0_26,hypothesis,
meet(r1,join(a,b)) = n0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_27,axiom,
join(X1,n0) = X1,
x_join_0 ).
cnf(c_0_28,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,axiom,
meet(X1,n0) = n0,
x_meet_0 ).
cnf(c_0_30,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_31,hypothesis,
ifeq3(meet(X1,join(a,b)),X1,meet(join(a,b),join(X1,r1)),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_27]) ).
cnf(c_0_32,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_33,axiom,
ifeq3(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_34,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_35,plain,
ifeq3(meet(X1,X2),X1,meet(X2,join(X3,join(X1,X4))),join(X1,meet(join(X4,X3),X2))) = join(X1,meet(join(X4,X3),X2)),
inference(spm,[status(thm)],[c_0_25,c_0_28]) ).
cnf(c_0_36,plain,
join(n0,X1) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_23]) ).
cnf(c_0_37,plain,
meet(n0,X1) = n0,
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_38,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_39,hypothesis,
meet(join(r1,a),join(a,b)) = a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_23]),c_0_33]),c_0_30]) ).
cnf(c_0_40,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_23]) ).
cnf(c_0_41,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_24,c_0_34]) ).
cnf(c_0_42,plain,
meet(X1,join(X2,X3)) = meet(join(X3,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_36]),c_0_33]) ).
cnf(c_0_43,hypothesis,
meet(join(r1,a),meet(join(a,b),X1)) = meet(a,X1),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_44,plain,
meet(join(X1,X2),join(X2,meet(X1,X3))) = join(meet(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_45,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_32,c_0_38]) ).
cnf(c_0_46,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_30]),c_0_38]) ).
cnf(c_0_47,axiom,
meet(X1,n1) = X1,
x_meet_1 ).
cnf(c_0_48,hypothesis,
meet(join(r1,a),join(b,meet(a,X1))) = meet(a,join(b,meet(a,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_23]) ).
cnf(c_0_49,plain,
meet(X1,meet(X2,join(meet(X2,X1),X3))) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_45,c_0_30]) ).
cnf(c_0_50,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_46,c_0_40]) ).
cnf(c_0_51,axiom,
ifeq(complement(X1,X2),true,join(X1,X2),n1) = n1,
complement_join ).
cnf(c_0_52,hypothesis,
complement(r2,meet(a,b)) = true,
complement_of_a_meet_b ).
cnf(c_0_53,plain,
meet(n1,X1) = X1,
inference(spm,[status(thm)],[c_0_47,c_0_30]) ).
cnf(c_0_54,plain,
ifeq3(meet(X1,X2),X1,meet(X2,join(X3,X1)),join(X1,meet(X3,X2))) = join(X1,meet(X3,X2)),
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_55,hypothesis,
meet(join(r1,a),join(b,meet(X1,a))) = meet(a,join(b,meet(X1,a))),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_56,hypothesis,
meet(b,join(r1,a)) = meet(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_39]),c_0_30]),c_0_30]) ).
cnf(c_0_57,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_58,hypothesis,
join(r2,meet(a,b)) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_22]) ).
cnf(c_0_59,plain,
join(n1,X1) = n1,
inference(spm,[status(thm)],[c_0_32,c_0_53]) ).
cnf(c_0_60,plain,
ifeq3(meet(X1,X2),X1,meet(X2,join(X1,X3)),join(meet(X3,X2),X1)) = join(meet(X3,X2),X1),
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_61,hypothesis,
join(meet(X1,a),meet(a,b)) = meet(a,join(b,meet(X1,a))),
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_54,c_0_55]),c_0_38]),c_0_40]),c_0_56]),c_0_33]),c_0_56]) ).
cnf(c_0_62,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_38,c_0_57]) ).
cnf(c_0_63,hypothesis,
join(r2,join(meet(a,b),X1)) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_58]),c_0_59]) ).
cnf(c_0_64,axiom,
join(X1,n1) = n1,
x_join_1 ).
cnf(c_0_65,hypothesis,
meet(a,join(meet(a,b),X1)) = meet(a,join(b,meet(X1,a))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_38]),c_0_30]),c_0_62]),c_0_33]) ).
cnf(c_0_66,hypothesis,
join(meet(a,b),join(X1,join(X2,r2))) = n1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_63]),c_0_64]),c_0_24]) ).
cnf(c_0_67,hypothesis,
meet(a,join(b,meet(a,join(X1,join(r2,X2))))) = a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_47]),c_0_42]),c_0_24]) ).
cnf(c_0_68,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(spm,[status(thm)],[c_0_30,c_0_38]) ).
cnf(c_0_69,hypothesis,
meet(a,join(b,meet(a,join(X1,r2)))) = a,
inference(spm,[status(thm)],[c_0_67,c_0_27]) ).
cnf(c_0_70,plain,
join(X1,meet(X2,meet(X1,X3))) = X1,
inference(spm,[status(thm)],[c_0_34,c_0_68]) ).
cnf(c_0_71,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_38,c_0_32]) ).
cnf(c_0_72,plain,
meet(join(X1,X2),join(X1,join(X2,X3))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_32,c_0_24]) ).
cnf(c_0_73,plain,
ifeq3(meet(X1,X2),X1,X2,join(X1,X2)) = join(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_53]),c_0_64]),c_0_47]) ).
cnf(c_0_74,hypothesis,
meet(a,join(b,meet(a,r2))) = a,
inference(spm,[status(thm)],[c_0_69,c_0_36]) ).
cnf(c_0_75,plain,
join(X1,join(X2,meet(X1,X3))) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_24]) ).
cnf(c_0_76,plain,
ifeq3(meet(X1,X2),X1,meet(X2,join(X1,meet(X3,X4))),join(X1,meet(X3,meet(X4,X2)))) = join(X1,meet(X3,meet(X4,X2))),
inference(spm,[status(thm)],[c_0_25,c_0_38]) ).
cnf(c_0_77,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_34,c_0_30]) ).
cnf(c_0_78,hypothesis,
meet(r1,meet(join(a,b),X1)) = n0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_26]),c_0_37]) ).
cnf(c_0_79,plain,
meet(join(X1,X2),join(X1,join(X3,X2))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_72,c_0_23]) ).
cnf(c_0_80,hypothesis,
join(b,meet(a,r2)) = join(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_75]),c_0_33]),c_0_75]) ).
cnf(c_0_81,plain,
meet(X1,join(meet(X2,X1),meet(X3,X2))) = meet(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_38]),c_0_57]),c_0_33]) ).
cnf(c_0_82,plain,
ifeq3(meet(X1,meet(X2,X3)),meet(X1,X2),meet(X3,join(meet(X1,X2),X4)),join(meet(X1,X2),meet(X4,X3))) = join(meet(X1,X2),meet(X4,X3)),
inference(spm,[status(thm)],[c_0_25,c_0_38]) ).
cnf(c_0_83,hypothesis,
meet(r1,meet(X1,join(a,b))) = n0,
inference(spm,[status(thm)],[c_0_78,c_0_30]) ).
cnf(c_0_84,hypothesis,
meet(join(a,b),join(b,join(X1,meet(a,r2)))) = join(a,b),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_85,plain,
ifeq3(meet(X1,X2),X1,meet(X2,join(X1,X3)),join(X1,meet(X2,X3))) = join(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_25,c_0_30]) ).
cnf(c_0_86,hypothesis,
meet(join(r1,a),join(meet(a,b),meet(X1,b))) = meet(a,b),
inference(spm,[status(thm)],[c_0_81,c_0_56]) ).
cnf(c_0_87,plain,
join(meet(X1,X2),meet(X3,X2)) = meet(X2,join(meet(X1,X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_57]),c_0_33]) ).
cnf(c_0_88,hypothesis,
meet(r1,a) = n0,
inference(spm,[status(thm)],[c_0_83,c_0_32]) ).
cnf(c_0_89,plain,
ifeq3(meet(X1,X2),X1,meet(X2,join(X3,join(X4,X1))),join(X1,meet(join(X3,X4),X2))) = join(X1,meet(join(X3,X4),X2)),
inference(spm,[status(thm)],[c_0_25,c_0_28]) ).
cnf(c_0_90,hypothesis,
meet(a,join(b,join(X1,meet(a,r2)))) = a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_84]),c_0_32]) ).
cnf(c_0_91,plain,
join(X1,meet(join(X1,X2),X3)) = meet(join(X1,X2),join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_32]),c_0_33]) ).
cnf(c_0_92,hypothesis,
meet(join(r1,a),join(meet(a,b),meet(b,X1))) = meet(a,b),
inference(spm,[status(thm)],[c_0_86,c_0_30]) ).
cnf(c_0_93,hypothesis,
meet(a,join(r1,meet(X1,a))) = meet(X1,a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_88]),c_0_27]),c_0_23]) ).
cnf(c_0_94,hypothesis,
join(meet(a,r2),meet(a,join(b,X1))) = a,
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_89,c_0_90]),c_0_38]),c_0_30]),c_0_62]),c_0_30]),c_0_33]),c_0_30]) ).
cnf(c_0_95,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_38,c_0_40]) ).
cnf(c_0_96,hypothesis,
meet(join(r1,a),join(r1,join(meet(a,b),meet(b,X1)))) = join(r1,meet(a,b)),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_97,hypothesis,
meet(a,join(r1,meet(a,X1))) = meet(a,X1),
inference(spm,[status(thm)],[c_0_93,c_0_30]) ).
cnf(c_0_98,plain,
join(meet(X1,X2),meet(X1,meet(X2,X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_38]) ).
cnf(c_0_99,hypothesis,
join(meet(a,r2),meet(a,X1)) = meet(a,join(meet(a,r2),X1)),
inference(spm,[status(thm)],[c_0_91,c_0_94]) ).
cnf(c_0_100,hypothesis,
meet(a,join(r1,join(meet(a,b),meet(b,X1)))) = meet(a,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97]) ).
cnf(c_0_101,hypothesis,
join(meet(a,X1),meet(a,b)) = meet(a,join(b,meet(a,X1))),
inference(spm,[status(thm)],[c_0_61,c_0_30]) ).
cnf(c_0_102,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_103,plain,
join(meet(X1,X2),meet(X1,meet(X3,X2))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_98,c_0_30]) ).
cnf(c_0_104,hypothesis,
meet(a,join(r1,join(meet(a,b),join(meet(a,r2),meet(b,X1))))) = a,
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_99,c_0_100]),c_0_101]),c_0_80]),c_0_32]),c_0_102]),c_0_102]) ).
cnf(c_0_105,plain,
meet(X1,join(meet(X2,X1),meet(X2,X3))) = meet(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_103]),c_0_38]),c_0_57]),c_0_33]) ).
cnf(c_0_106,hypothesis,
meet(a,join(r1,join(meet(a,b),join(meet(a,r2),meet(X1,b))))) = a,
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_107,plain,
meet(X1,meet(X2,X1)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_34]),c_0_38]) ).
cnf(c_0_108,plain,
join(X1,join(X2,meet(X3,join(X1,X2)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_24,c_0_77]) ).
cnf(c_0_109,plain,
join(X1,meet(X2,join(X3,X1))) = meet(join(X3,X1),join(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_40]),c_0_33]) ).
cnf(c_0_110,hypothesis,
meet(a,join(r1,join(meet(a,b),join(meet(X1,b),meet(a,r2))))) = a,
inference(spm,[status(thm)],[c_0_106,c_0_23]) ).
cnf(c_0_111,plain,
join(meet(X1,X2),meet(X3,X1)) = meet(X1,join(meet(X1,X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_107]),c_0_33]) ).
cnf(c_0_112,plain,
join(X1,meet(join(X1,X2),join(X2,X3))) = join(X1,X2),
inference(rw,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_113,plain,
join(X1,meet(X2,join(X1,X3))) = meet(join(X1,X3),join(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_32]),c_0_33]) ).
cnf(c_0_114,hypothesis,
meet(a,join(r1,join(meet(a,b),meet(r2,join(a,meet(b,r2)))))) = a,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_30]),c_0_23]) ).
cnf(c_0_115,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_32]),c_0_24]) ).
cnf(c_0_116,hypothesis,
join(r2,join(X1,meet(a,b))) = n1,
inference(spm,[status(thm)],[c_0_63,c_0_23]) ).
cnf(c_0_117,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_24,c_0_77]) ).
cnf(c_0_118,hypothesis,
join(b,meet(join(a,b),join(meet(a,r2),X1))) = join(a,b),
inference(spm,[status(thm)],[c_0_112,c_0_80]) ).
cnf(c_0_119,plain,
join(meet(X1,X2),meet(join(X1,X3),X2)) = meet(join(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_71]),c_0_23]) ).
cnf(c_0_120,hypothesis,
meet(join(r1,a),join(r1,join(meet(a,b),meet(r2,join(a,meet(b,r2)))))) = join(r1,a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_42]),c_0_24]),c_0_23]),c_0_102]) ).
cnf(c_0_121,plain,
join(X1,join(X2,join(meet(X1,X3),X4))) = join(X1,join(X4,X2)),
inference(spm,[status(thm)],[c_0_41,c_0_28]) ).
cnf(c_0_122,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_115]),c_0_24]),c_0_24]) ).
cnf(c_0_123,hypothesis,
join(a,r2) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_34]),c_0_23]) ).
cnf(c_0_124,plain,
join(X1,join(X2,X3)) = join(X3,join(X2,X1)),
inference(spm,[status(thm)],[c_0_28,c_0_23]) ).
cnf(c_0_125,plain,
join(meet(X1,X2),join(meet(X2,meet(X3,X1)),X4)) = join(meet(X1,X2),X4),
inference(spm,[status(thm)],[c_0_117,c_0_68]) ).
cnf(c_0_126,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_77,c_0_38]) ).
cnf(c_0_127,hypothesis,
join(b,meet(r2,meet(join(a,b),join(X1,a)))) = join(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_42]),c_0_46]) ).
cnf(c_0_128,hypothesis,
join(r1,join(meet(a,b),meet(r2,join(a,meet(b,r2))))) = join(r1,join(a,meet(b,r2))),
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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_120]),c_0_24]),c_0_121]),c_0_23]),c_0_122]),c_0_113]),c_0_123]),c_0_47]),c_0_33]),c_0_24]),c_0_121]),c_0_23]),c_0_122]),c_0_113]),c_0_123]),c_0_47]) ).
cnf(c_0_129,plain,
join(meet(X1,X2),X3) = join(X3,meet(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_111]),c_0_23]),c_0_126]) ).
cnf(c_0_130,hypothesis,
join(b,meet(r2,meet(join(X1,a),join(a,b)))) = join(a,b),
inference(spm,[status(thm)],[c_0_127,c_0_30]) ).
cnf(c_0_131,hypothesis,
meet(join(r1,join(a,meet(b,r2))),join(meet(a,b),meet(r2,join(a,meet(b,r2))))) = join(meet(a,b),meet(r2,join(a,meet(b,r2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_128]),c_0_42]),c_0_129]),c_0_42]),c_0_23]) ).
cnf(c_0_132,hypothesis,
meet(join(a,b),join(b,meet(r2,join(X1,a)))) = join(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_130]),c_0_40]),c_0_33]) ).
cnf(c_0_133,plain,
meet(X1,join(X2,join(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_40,c_0_24]) ).
cnf(c_0_134,hypothesis,
join(r1,join(a,meet(r2,join(b,meet(r2,join(a,meet(b,r2))))))) = join(r1,join(a,meet(b,r2))),
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_34,c_0_131]),c_0_24]),c_0_24]),c_0_121]),c_0_111]),c_0_23]) ).
cnf(c_0_135,plain,
meet(X1,join(X2,join(X1,X3))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_40]),c_0_32]) ).
cnf(c_0_136,hypothesis,
meet(a,join(b,meet(r2,join(X1,a)))) = a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_132]),c_0_32]) ).
cnf(c_0_137,hypothesis,
ifeq3(meet(a,X1),a,X1,join(a,meet(r2,X1))) = join(a,meet(r2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_123]),c_0_47]) ).
cnf(c_0_138,hypothesis,
meet(r2,meet(join(r1,join(a,meet(b,r2))),join(b,meet(r2,join(a,meet(b,r2)))))) = meet(r2,join(b,meet(r2,join(a,meet(b,r2))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_38]),c_0_42]),c_0_23]) ).
cnf(c_0_139,plain,
meet(X1,meet(join(X2,join(X1,X3)),X4)) = meet(X1,X4),
inference(spm,[status(thm)],[c_0_38,c_0_135]) ).
cnf(c_0_140,hypothesis,
meet(a,join(b,meet(r2,join(a,X1)))) = a,
inference(spm,[status(thm)],[c_0_136,c_0_23]) ).
cnf(c_0_141,hypothesis,
meet(join(r1,join(a,meet(b,r2))),join(b,meet(r2,join(a,meet(b,r2))))) = join(a,meet(r2,join(b,meet(r2,join(a,meet(b,r2)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_139]),c_0_140]),c_0_33]) ).
cnf(c_0_142,plain,
join(X1,join(X2,join(X3,meet(X4,join(X1,X2))))) = join(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_72]),c_0_24]),c_0_24]) ).
cnf(c_0_143,hypothesis,
join(b,meet(r2,join(a,meet(b,r2)))) = join(a,b),
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_141]),c_0_24]),c_0_142]),c_0_23]),c_0_113]),c_0_123]),c_0_47]),c_0_75]),c_0_23]) ).
cnf(c_0_144,hypothesis,
meet(join(r1,b),join(a,b)) = b,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_40]),c_0_23]),c_0_33]),c_0_30]) ).
cnf(c_0_145,plain,
ifeq3(meet(X1,X2),X1,meet(join(X1,X3),meet(X2,join(X1,X4))),join(X1,meet(X4,meet(join(X1,X3),X2)))) = join(X1,meet(X4,meet(join(X1,X3),X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_71]),c_0_38]) ).
cnf(c_0_146,hypothesis,
meet(r2,meet(join(a,b),join(a,meet(b,r2)))) = meet(r2,join(a,meet(b,r2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_143]),c_0_38]),c_0_42]),c_0_23]) ).
cnf(c_0_147,hypothesis,
meet(r1,b) = n0,
inference(spm,[status(thm)],[c_0_83,c_0_40]) ).
cnf(c_0_148,hypothesis,
meet(join(r1,b),meet(join(a,b),X1)) = meet(b,X1),
inference(spm,[status(thm)],[c_0_38,c_0_144]) ).
cnf(c_0_149,hypothesis,
meet(join(a,b),join(a,meet(b,r2))) = join(a,meet(b,r2)),
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_145,c_0_146]),c_0_32]),c_0_123]),c_0_47]),c_0_113]),c_0_123]),c_0_47]),c_0_33]),c_0_113]),c_0_123]),c_0_47]) ).
cnf(c_0_150,hypothesis,
join(r1,join(a,b)) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_21]),c_0_22]) ).
cnf(c_0_151,hypothesis,
meet(b,join(r1,meet(X1,b))) = meet(X1,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_147]),c_0_27]),c_0_23]) ).
cnf(c_0_152,hypothesis,
meet(join(r1,b),join(a,meet(b,r2))) = meet(b,join(a,meet(b,r2))),
inference(spm,[status(thm)],[c_0_148,c_0_149]) ).
cnf(c_0_153,hypothesis,
join(r1,join(a,meet(b,r2))) = n1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_143]),c_0_113]),c_0_123]),c_0_47]),c_0_150]) ).
cnf(c_0_154,hypothesis,
meet(b,join(r1,meet(b,X1))) = meet(b,X1),
inference(spm,[status(thm)],[c_0_151,c_0_30]) ).
cnf(c_0_155,hypothesis,
join(r1,meet(b,join(a,meet(b,r2)))) = join(r1,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_152]),c_0_153]),c_0_47]) ).
cnf(c_0_156,hypothesis,
meet(b,join(a,meet(b,r2))) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_40]) ).
cnf(c_0_157,hypothesis,
join(a,meet(b,r2)) = join(a,b),
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_73,c_0_156]),c_0_75]),c_0_23]),c_0_33]),c_0_75]),c_0_23]) ).
cnf(c_0_158,hypothesis,
meet(join(a,b),join(a,join(meet(b,r2),X1))) = join(a,b),
inference(spm,[status(thm)],[c_0_72,c_0_157]) ).
cnf(c_0_159,hypothesis,
meet(join(r1,a),join(r1,b)) = join(r1,meet(a,b)),
inference(spm,[status(thm)],[c_0_113,c_0_56]) ).
cnf(c_0_160,hypothesis,
meet(b,join(a,join(meet(b,r2),X1))) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_158]),c_0_40]) ).
cnf(c_0_161,hypothesis,
meet(b,join(r1,meet(a,b))) = meet(a,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_159]),c_0_30]),c_0_56]) ).
cnf(c_0_162,hypothesis,
join(meet(b,r2),meet(b,join(a,X1))) = b,
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_35,c_0_160]),c_0_38]),c_0_30]),c_0_62]),c_0_42]),c_0_33]),c_0_42]) ).
cnf(c_0_163,hypothesis,
meet(b,meet(join(r1,meet(a,b)),X1)) = meet(a,meet(b,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_161]),c_0_38]) ).
cnf(c_0_164,hypothesis,
join(meet(b,r2),meet(b,X1)) = meet(b,join(meet(b,r2),X1)),
inference(spm,[status(thm)],[c_0_91,c_0_162]) ).
cnf(c_0_165,hypothesis,
meet(b,join(meet(r1,X1),meet(a,b))) = meet(a,b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_44]),c_0_45]) ).
cnf(c_0_166,hypothesis,
meet(b,join(meet(a,b),join(meet(b,r2),meet(r1,X1)))) = b,
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_164,c_0_165]),c_0_111]),c_0_23]),c_0_157]),c_0_40]),c_0_28]) ).
cnf(c_0_167,hypothesis,
meet(b,join(meet(a,b),meet(r2,join(r1,meet(b,r2))))) = b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_87]),c_0_23]) ).
cnf(c_0_168,plain,
meet(join(X1,X2),join(X2,meet(X3,X1))) = join(meet(X3,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_117]),c_0_42]) ).
cnf(c_0_169,hypothesis,
join(meet(a,b),meet(r2,join(r1,meet(b,r2)))) = join(b,meet(r2,join(r1,meet(b,r2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_167]),c_0_117]),c_0_33]),c_0_117]) ).
cnf(c_0_170,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_171,hypothesis,
meet(join(r1,b),join(b,meet(r2,join(r1,meet(b,r2))))) = join(b,meet(r2,join(r1,meet(b,r2)))),
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_168,c_0_169]),c_0_24]),c_0_111]),c_0_23]),c_0_157]),c_0_40]),c_0_129]),c_0_42]),c_0_23]),c_0_169]) ).
cnf(c_0_172,plain,
meet(X1,meet(X2,join(X3,meet(X1,X2)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_38,c_0_40]) ).
cnf(c_0_173,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_24,c_0_170]) ).
cnf(c_0_174,hypothesis,
meet(r2,meet(join(r1,b),join(r1,meet(b,r2)))) = meet(r2,join(r1,meet(b,r2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_171]),c_0_38]),c_0_172]),c_0_46]) ).
cnf(c_0_175,plain,
meet(join(X1,X2),join(X2,join(X3,X1))) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_23]),c_0_24]) ).
cnf(c_0_176,hypothesis,
join(r1,join(b,meet(r2,join(r1,meet(b,r2))))) = join(r1,b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_171]),c_0_24]),c_0_173]) ).
cnf(c_0_177,hypothesis,
meet(join(r1,r2),join(r1,meet(b,r2))) = join(r1,meet(b,r2)),
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_126,c_0_174]),c_0_24]),c_0_109]),c_0_23]),c_0_77]),c_0_42]),c_0_23]),c_0_113]),c_0_42]),c_0_23]) ).
cnf(c_0_178,hypothesis,
meet(join(r1,a),meet(join(r1,b),X1)) = meet(join(r1,meet(a,b)),X1),
inference(spm,[status(thm)],[c_0_38,c_0_159]) ).
cnf(c_0_179,hypothesis,
meet(join(r1,b),join(r1,meet(b,r2))) = join(r1,meet(b,r2)),
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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_176]),c_0_129]),c_0_42]),c_0_23]),c_0_113]),c_0_42]),c_0_23]),c_0_38]),c_0_129]),c_0_42]),c_0_23]),c_0_113]),c_0_42]),c_0_23]),c_0_42]),c_0_23]),c_0_46]),c_0_177]),c_0_177]) ).
cnf(c_0_180,hypothesis,
meet(r2,meet(a,b)) = n0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_52]),c_0_22]) ).
cnf(c_0_181,hypothesis,
meet(join(r1,meet(a,b)),join(r1,meet(b,r2))) = meet(join(r1,a),join(r1,meet(b,r2))),
inference(spm,[status(thm)],[c_0_178,c_0_179]) ).
cnf(c_0_182,hypothesis,
meet(b,meet(X1,join(r1,meet(a,b)))) = meet(X1,meet(a,b)),
inference(spm,[status(thm)],[c_0_46,c_0_161]) ).
cnf(c_0_183,hypothesis,
meet(a,meet(b,r2)) = n0,
inference(rw,[status(thm)],[c_0_180,c_0_68]) ).
cnf(c_0_184,hypothesis,
meet(r1,meet(b,X1)) = n0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_147]),c_0_37]) ).
cnf(c_0_185,plain,
join(X1,meet(join(X2,X1),X3)) = meet(join(X2,X1),join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_40]),c_0_33]) ).
cnf(c_0_186,plain,
meet(X1,meet(X2,meet(X3,join(X4,X1)))) = meet(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_95,c_0_68]) ).
cnf(c_0_187,hypothesis,
meet(join(r1,a),join(r1,meet(b,r2))) = r1,
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_25,c_0_181]),c_0_32]),c_0_38]),c_0_182]),c_0_68]),c_0_183]),c_0_27]),c_0_33]),c_0_38]),c_0_182]),c_0_68]),c_0_183]),c_0_27]) ).
cnf(c_0_188,hypothesis,
meet(b,meet(X1,meet(X2,r1))) = n0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_184]),c_0_29]),c_0_38]) ).
cnf(c_0_189,plain,
join(meet(X1,X2),meet(X2,X3)) = meet(X2,join(meet(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_185,c_0_77]) ).
cnf(c_0_190,hypothesis,
meet(b,meet(r2,meet(X1,join(r1,a)))) = n0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_187]),c_0_38]),c_0_188]),c_0_38]) ).
cnf(c_0_191,plain,
join(X1,join(X2,meet(X3,X1))) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_32]),c_0_24]) ).
cnf(c_0_192,plain,
ifeq3(meet(X1,X2),X1,meet(X2,join(X1,X3)),join(X1,meet(join(X3,meet(X1,X4)),X2))) = join(X1,meet(join(X3,meet(X1,X4)),X2)),
inference(spm,[status(thm)],[c_0_25,c_0_75]) ).
cnf(c_0_193,plain,
meet(X1,join(meet(X2,X1),X3)) = meet(X1,join(meet(X1,X3),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_111]),c_0_189]) ).
cnf(c_0_194,plain,
join(meet(X1,X2),join(X3,meet(X1,meet(X2,X4)))) = join(X3,meet(X1,X2)),
inference(spm,[status(thm)],[c_0_102,c_0_98]) ).
cnf(c_0_195,hypothesis,
meet(b,meet(r2,meet(join(r1,a),X1))) = n0,
inference(spm,[status(thm)],[c_0_190,c_0_30]) ).
cnf(c_0_196,plain,
meet(join(X1,X2),join(meet(X3,X1),X2)) = join(X2,meet(X3,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_191]),c_0_42]) ).
cnf(c_0_197,plain,
meet(X1,join(meet(X2,X1),X3)) = meet(X1,join(meet(X3,X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_129]),c_0_189]) ).
cnf(c_0_198,plain,
meet(X1,join(meet(X2,X1),X3)) = meet(X1,join(X2,meet(X1,X3))),
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_192,c_0_193]),c_0_38]),c_0_107]),c_0_38]),c_0_111]),c_0_194]),c_0_33]),c_0_38]),c_0_111]),c_0_194]) ).
cnf(c_0_199,hypothesis,
meet(b,meet(r2,join(a,meet(X1,r1)))) = n0,
inference(spm,[status(thm)],[c_0_195,c_0_196]) ).
cnf(c_0_200,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X3,meet(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_197,c_0_198]),c_0_198]) ).
cnf(c_0_201,plain,
ifeq3(meet(X1,X2),X2,meet(X1,meet(join(X3,X2),join(X2,X4))),join(X2,meet(X4,meet(X1,join(X3,X2))))) = join(X2,meet(X4,meet(X1,join(X3,X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_50]),c_0_38]) ).
cnf(c_0_202,hypothesis,
meet(b,meet(r2,join(r1,meet(a,r2)))) = n0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_200]),c_0_30]) ).
cnf(c_0_203,hypothesis,
ifeq3(meet(X1,meet(X2,join(a,b))),meet(X1,X2),meet(join(a,b),join(r1,meet(X2,X1))),meet(X1,X2)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_38]),c_0_129]) ).
cnf(c_0_204,hypothesis,
meet(r2,meet(join(a,b),join(r1,meet(a,r2)))) = meet(a,r2),
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_201,c_0_202]),c_0_107]),c_0_30]),c_0_23]),c_0_80]),c_0_27]),c_0_33]),c_0_27]),c_0_42]),c_0_23]) ).
cnf(c_0_205,hypothesis,
meet(join(a,b),join(r1,meet(a,r2))) = meet(a,r2),
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_203,c_0_204]),c_0_38]),c_0_42]),c_0_23]),c_0_62]),c_0_204]),c_0_38]),c_0_42]),c_0_23]),c_0_46]),c_0_204]),c_0_33]) ).
cnf(c_0_206,hypothesis,
meet(b,join(r1,meet(a,r2))) = n0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_205]),c_0_68]),c_0_30]),c_0_183]) ).
cnf(c_0_207,negated_conjecture,
r1 != meet(join(r1,meet(r2,b)),join(r1,meet(r2,a))),
prove_lemma ).
cnf(c_0_208,plain,
join(X1,meet(X2,meet(X3,join(X1,X4)))) = meet(join(X1,X4),join(X1,meet(X2,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_32]),c_0_33]) ).
cnf(c_0_209,hypothesis,
meet(b,meet(X1,join(r1,meet(a,r2)))) = n0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_206]),c_0_29]) ).
cnf(c_0_210,negated_conjecture,
meet(join(r1,meet(a,r2)),join(r1,meet(b,r2))) != r1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_207,c_0_30]),c_0_30]),c_0_30]) ).
cnf(c_0_211,hypothesis,
meet(join(r1,meet(a,r2)),join(r1,meet(b,X1))) = r1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_208,c_0_209]),c_0_27]) ).
cnf(c_0_212,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_210,c_0_211])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT005-10 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n016.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 20:45:36 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 120.10/59.49 % Version : CSE_E---1.7
% 120.10/59.49 % Problem : theBenchmark.p
% 120.10/59.49 % SZS status Unsatisfiable for theBenchmark.p
% 120.10/59.49 % SZS output start CNFRefutation
% See solution above
% 120.90/60.23 % Total time : 39.770s
%------------------------------------------------------------------------------