TSTP Solution File: LAT181-1 by E---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : LAT181-1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n024.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 : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 18:07:56 EDT 2023
% Result : Unsatisfiable 665.17s 86.53s
% Output : CNFRefutation 665.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 13
% Syntax : Number of clauses : 144 ( 130 unt; 0 nHn; 19 RR)
% Number of literals : 165 ( 164 equ; 23 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 321 ( 37 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox2/tmp/tmp.MWtZWjVEjS/E---3.1_8765.p',absorption1) ).
cnf(complement_join,axiom,
join(X1,complement(X1)) = one,
file('/export/starexec/sandbox2/tmp/tmp.MWtZWjVEjS/E---3.1_8765.p',complement_join) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/tmp/tmp.MWtZWjVEjS/E---3.1_8765.p',commutativity_of_join) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox2/tmp/tmp.MWtZWjVEjS/E---3.1_8765.p',commutativity_of_meet) ).
cnf(associativity_of_meet,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
file('/export/starexec/sandbox2/tmp/tmp.MWtZWjVEjS/E---3.1_8765.p',associativity_of_meet) ).
cnf(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox2/tmp/tmp.MWtZWjVEjS/E---3.1_8765.p',absorption2) ).
cnf(equation_H4,axiom,
meet(X1,join(X2,meet(X1,join(X3,X4)))) = meet(X1,join(X2,meet(join(X1,meet(X2,X4)),join(X3,X4)))),
file('/export/starexec/sandbox2/tmp/tmp.MWtZWjVEjS/E---3.1_8765.p',equation_H4) ).
cnf(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox2/tmp/tmp.MWtZWjVEjS/E---3.1_8765.p',idempotence_of_meet) ).
cnf(associativity_of_join,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
file('/export/starexec/sandbox2/tmp/tmp.MWtZWjVEjS/E---3.1_8765.p',associativity_of_join) ).
cnf(idempotence_of_join,axiom,
join(X1,X1) = X1,
file('/export/starexec/sandbox2/tmp/tmp.MWtZWjVEjS/E---3.1_8765.p',idempotence_of_join) ).
cnf(meet_join_complement,axiom,
( complement(X1) = X2
| meet(X1,X2) != zero
| join(X1,X2) != one ),
file('/export/starexec/sandbox2/tmp/tmp.MWtZWjVEjS/E---3.1_8765.p',meet_join_complement) ).
cnf(complement_meet,axiom,
meet(X1,complement(X1)) = zero,
file('/export/starexec/sandbox2/tmp/tmp.MWtZWjVEjS/E---3.1_8765.p',complement_meet) ).
cnf(prove_distributivity,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
file('/export/starexec/sandbox2/tmp/tmp.MWtZWjVEjS/E---3.1_8765.p',prove_distributivity) ).
cnf(c_0_13,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_14,axiom,
join(X1,complement(X1)) = one,
complement_join ).
cnf(c_0_15,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_16,plain,
meet(X1,one) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_18,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_19,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_20,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_21,plain,
meet(one,X1) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,axiom,
meet(X1,join(X2,meet(X1,join(X3,X4)))) = meet(X1,join(X2,meet(join(X1,meet(X2,X4)),join(X3,X4)))),
equation_H4 ).
cnf(c_0_24,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_25,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_26,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_27,plain,
join(one,X1) = one,
inference(spm,[status(thm)],[c_0_13,c_0_21]) ).
cnf(c_0_28,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_17]) ).
cnf(c_0_29,plain,
meet(X1,join(X2,meet(join(X1,X2),join(X3,X2)))) = meet(X1,join(X2,meet(X1,join(X3,X2)))),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_30,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_13]),c_0_26]) ).
cnf(c_0_31,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_32,plain,
join(X1,join(complement(X1),X2)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_14]),c_0_27]) ).
cnf(c_0_33,plain,
join(X1,one) = one,
inference(spm,[status(thm)],[c_0_27,c_0_15]) ).
cnf(c_0_34,plain,
join(meet(X1,X2),meet(X2,join(X3,X1))) = meet(X2,join(X3,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_28]),c_0_15]) ).
cnf(c_0_35,plain,
meet(X1,join(complement(X1),meet(X1,join(X2,complement(X1))))) = meet(X1,join(complement(X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_14]),c_0_21]),c_0_30]) ).
cnf(c_0_36,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_31,c_0_17]) ).
cnf(c_0_37,plain,
join(complement(X1),join(X2,X1)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_32]),c_0_33]),c_0_26]) ).
cnf(c_0_38,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_26,c_0_25]) ).
cnf(c_0_39,plain,
meet(X1,meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_18]) ).
cnf(c_0_40,plain,
join(X1,join(X2,X3)) = join(X2,join(X3,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_15]) ).
cnf(c_0_41,plain,
join(meet(X1,join(X2,complement(X1))),meet(X1,join(complement(X1),X2))) = meet(X1,join(complement(X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_18]),c_0_36]),c_0_17]) ).
cnf(c_0_42,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_43,plain,
join(X1,complement(meet(X2,X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_25]),c_0_15]) ).
cnf(c_0_44,plain,
join(meet(X1,X2),join(X3,meet(X2,join(meet(X1,X2),X4)))) = join(meet(X2,join(meet(X1,X2),X4)),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]) ).
cnf(c_0_45,plain,
join(meet(X1,join(complement(X1),X2)),meet(X1,join(X2,complement(X1)))) = meet(X1,join(complement(X1),X2)),
inference(spm,[status(thm)],[c_0_15,c_0_41]) ).
cnf(c_0_46,axiom,
( complement(X1) = X2
| meet(X1,X2) != zero
| join(X1,X2) != one ),
meet_join_complement ).
cnf(c_0_47,plain,
meet(X1,join(X2,meet(X3,join(X1,meet(X2,X3))))) = meet(X1,join(X2,meet(X1,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_42]),c_0_17]) ).
cnf(c_0_48,plain,
join(complement(meet(X1,X2)),meet(X2,join(meet(X1,X2),X3))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_39]),c_0_15]) ).
cnf(c_0_49,plain,
join(meet(X1,X2),meet(X2,join(complement(X2),meet(X1,X2)))) = meet(X2,join(complement(X2),meet(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_15]),c_0_42]) ).
cnf(c_0_50,plain,
( complement(X1) = X2
| meet(X2,X1) != zero
| join(X1,X2) != one ),
inference(spm,[status(thm)],[c_0_46,c_0_17]) ).
cnf(c_0_51,axiom,
meet(X1,complement(X1)) = zero,
complement_meet ).
cnf(c_0_52,plain,
meet(X1,join(X2,meet(X3,join(meet(X2,X3),X1)))) = meet(X1,join(X2,meet(X1,X3))),
inference(spm,[status(thm)],[c_0_47,c_0_15]) ).
cnf(c_0_53,plain,
meet(X1,meet(join(X2,meet(join(X1,meet(X2,X3)),join(X4,X3))),X5)) = meet(X1,meet(join(X2,meet(X1,join(X4,X3))),X5)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_23]),c_0_18]) ).
cnf(c_0_54,plain,
join(complement(meet(X1,X2)),meet(X2,join(complement(X2),meet(X1,X2)))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_31]) ).
cnf(c_0_55,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_15]),c_0_14])]) ).
cnf(c_0_56,plain,
meet(complement(meet(X1,X2)),join(X1,meet(X2,complement(meet(X1,X2))))) = meet(join(X1,X2),complement(meet(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_14]),c_0_16]),c_0_17]),c_0_17]) ).
cnf(c_0_57,plain,
join(meet(X1,X2),meet(join(X3,X1),X2)) = meet(join(X3,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_22]),c_0_15]) ).
cnf(c_0_58,plain,
( meet(join(X1,meet(join(X2,meet(X1,X3)),join(X4,X3))),X5) = complement(X2)
| join(X2,meet(join(X1,meet(join(X2,meet(X1,X3)),join(X4,X3))),X5)) != one
| meet(X2,meet(join(X1,meet(X2,join(X4,X3))),X5)) != zero ),
inference(spm,[status(thm)],[c_0_46,c_0_53]) ).
cnf(c_0_59,plain,
join(complement(meet(X1,complement(X2))),meet(complement(X2),join(X2,meet(X1,complement(X2))))) = one,
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_60,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_61,plain,
join(X1,meet(join(X1,X2),complement(meet(X1,X2)))) = join(X1,meet(X2,complement(meet(X1,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_56]),c_0_26]),c_0_57]) ).
cnf(c_0_62,plain,
join(X1,complement(meet(X1,X2))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_20]),c_0_15]) ).
cnf(c_0_63,plain,
meet(X1,zero) = zero,
inference(spm,[status(thm)],[c_0_31,c_0_51]) ).
cnf(c_0_64,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_51]) ).
cnf(c_0_65,plain,
( X1 = X2
| join(complement(X2),X1) != one
| meet(complement(X2),X1) != zero ),
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_58,c_0_59]),c_0_60]),c_0_59]),c_0_21]),c_0_55]),c_0_60]),c_0_59]),c_0_21]),c_0_21]) ).
cnf(c_0_66,plain,
join(X1,meet(join(complement(X1),X2),complement(meet(X1,join(complement(X1),X2))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_32]),c_0_21]),c_0_62]) ).
cnf(c_0_67,plain,
meet(X1,meet(X2,complement(meet(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_51,c_0_18]) ).
cnf(c_0_68,plain,
meet(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_63,c_0_17]) ).
cnf(c_0_69,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_64,c_0_15]) ).
cnf(c_0_70,plain,
join(X1,complement(meet(X2,meet(X3,X1)))) = one,
inference(spm,[status(thm)],[c_0_43,c_0_18]) ).
cnf(c_0_71,plain,
meet(join(X1,X2),join(X2,X1)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_30]) ).
cnf(c_0_72,plain,
meet(join(X1,X2),complement(meet(complement(X1),join(X1,X2)))) = X1,
inference(cn,[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_65,c_0_66]),c_0_55]),c_0_55]),c_0_55]),c_0_55]),c_0_67])]) ).
cnf(c_0_73,plain,
meet(X1,meet(X2,complement(meet(X2,X1)))) = zero,
inference(spm,[status(thm)],[c_0_67,c_0_17]) ).
cnf(c_0_74,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_51]),c_0_68]) ).
cnf(c_0_75,plain,
complement(zero) = one,
inference(spm,[status(thm)],[c_0_14,c_0_69]) ).
cnf(c_0_76,plain,
join(X1,join(X2,complement(meet(X3,join(X2,X1))))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_26]) ).
cnf(c_0_77,plain,
join(X1,complement(meet(complement(X1),join(X1,X2)))) = complement(meet(complement(X1),join(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_72]),c_0_15]) ).
cnf(c_0_78,plain,
meet(complement(X1),meet(X2,X1)) = zero,
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_16]),c_0_18]) ).
cnf(c_0_79,plain,
join(X1,complement(meet(complement(X2),join(X2,X1)))) = one,
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_80,plain,
meet(X1,meet(X2,join(X3,meet(join(meet(X1,X2),meet(X3,X4)),join(X5,X4))))) = meet(X1,meet(X2,join(X3,meet(X1,meet(X2,join(X5,X4)))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_23]),c_0_18]),c_0_18]) ).
cnf(c_0_81,plain,
( meet(X1,X2) = X2
| join(complement(X2),meet(X1,X2)) != one ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_78]),c_0_55]) ).
cnf(c_0_82,plain,
join(X1,complement(meet(complement(X2),join(X1,X2)))) = one,
inference(spm,[status(thm)],[c_0_79,c_0_15]) ).
cnf(c_0_83,plain,
( complement(meet(X1,join(X2,meet(join(meet(X3,X1),meet(X2,X4)),join(X5,X4))))) = X3
| join(X3,meet(X1,join(X2,meet(join(meet(X3,X1),meet(X2,X4)),join(X5,X4))))) != one
| meet(X3,meet(X1,join(X2,meet(X3,meet(X1,join(X5,X4)))))) != zero ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_80]),c_0_15]) ).
cnf(c_0_84,plain,
( meet(X1,join(meet(X2,X1),X3)) = meet(X2,X1)
| join(meet(X2,X1),complement(meet(X1,join(meet(X2,X1),X3)))) != one ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_39]),c_0_15]) ).
cnf(c_0_85,plain,
join(X1,complement(meet(X2,join(X1,complement(X2))))) = one,
inference(spm,[status(thm)],[c_0_82,c_0_55]) ).
cnf(c_0_86,plain,
( complement(X1) = X2
| join(X2,X1) != one
| meet(X2,X1) != zero ),
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_83,c_0_27]),c_0_21]),c_0_27]),c_0_16]),c_0_21]),c_0_27]),c_0_16]),c_0_16]) ).
cnf(c_0_87,plain,
join(X1,join(X2,complement(join(X2,X1)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_30]),c_0_15]),c_0_26]) ).
cnf(c_0_88,plain,
meet(X1,join(complement(X1),meet(X2,X1))) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_15]) ).
cnf(c_0_89,plain,
( complement(join(X1,complement(join(X1,X2)))) = X2
| meet(X2,join(X1,complement(join(X1,X2)))) != zero ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_90,plain,
complement(one) = zero,
inference(spm,[status(thm)],[c_0_51,c_0_21]) ).
cnf(c_0_91,plain,
meet(join(X1,X2),join(X1,complement(join(X1,X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_13]),c_0_15]) ).
cnf(c_0_92,plain,
( join(X1,complement(join(X1,X2))) = complement(X2)
| meet(X2,join(X1,complement(join(X1,X2)))) != zero ),
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_87]),c_0_90]),c_0_64]),c_0_90]),c_0_64]),c_0_17]) ).
cnf(c_0_93,plain,
meet(X1,join(X2,complement(join(X2,X1)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_91]) ).
cnf(c_0_94,plain,
( join(X1,complement(join(X1,X2))) = complement(X2)
| meet(X2,X1) != zero ),
inference(rw,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_95,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_26,c_0_20]) ).
cnf(c_0_96,plain,
( join(X1,complement(join(X1,X2))) = complement(X2)
| meet(X1,X2) != zero ),
inference(spm,[status(thm)],[c_0_94,c_0_17]) ).
cnf(c_0_97,plain,
meet(X1,complement(join(X1,X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_13]),c_0_17]) ).
cnf(c_0_98,plain,
meet(join(X1,X2),join(meet(X1,X3),X2)) = join(meet(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_95]),c_0_17]) ).
cnf(c_0_99,plain,
meet(X1,complement(meet(complement(X1),join(X1,X2)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_72]),c_0_17]) ).
cnf(c_0_100,plain,
meet(join(X1,X2),complement(meet(complement(X2),join(X1,X2)))) = X2,
inference(spm,[status(thm)],[c_0_72,c_0_15]) ).
cnf(c_0_101,plain,
join(X1,complement(join(X1,complement(join(X1,X2))))) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_55]) ).
cnf(c_0_102,plain,
meet(X1,meet(X2,join(X3,meet(X1,X2)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_103,plain,
meet(X1,join(meet(X1,X2),meet(X3,X1))) = join(meet(X1,X2),meet(X3,X1)),
inference(spm,[status(thm)],[c_0_98,c_0_25]) ).
cnf(c_0_104,plain,
meet(complement(X1),complement(meet(X1,join(complement(X1),X2)))) = complement(X1),
inference(spm,[status(thm)],[c_0_99,c_0_55]) ).
cnf(c_0_105,plain,
complement(join(X1,complement(join(X1,X2)))) = meet(complement(X1),join(X1,X2)),
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_55]),c_0_17]),c_0_91]),c_0_17]) ).
cnf(c_0_106,plain,
meet(X1,join(X2,meet(X3,join(X1,meet(X2,meet(X3,X4)))))) = meet(X1,join(X2,meet(X1,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_20]),c_0_17]) ).
cnf(c_0_107,plain,
meet(X1,join(meet(X2,X3),meet(X1,X2))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_108,plain,
meet(complement(X1),complement(meet(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_104,c_0_88]) ).
cnf(c_0_109,plain,
join(X1,meet(complement(X1),join(X1,X2))) = join(X1,X2),
inference(rw,[status(thm)],[c_0_101,c_0_105]) ).
cnf(c_0_110,plain,
meet(X1,join(meet(X2,X3),meet(X2,join(X1,meet(X2,X3))))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_24]),c_0_107]) ).
cnf(c_0_111,plain,
join(complement(X1),complement(meet(X2,X1))) = complement(meet(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_108]),c_0_15]) ).
cnf(c_0_112,plain,
join(meet(X1,X2),meet(X1,complement(meet(X1,X2)))) = 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(spm,[status(thm)],[c_0_109,c_0_110]),c_0_17]),c_0_15]),c_0_14]),c_0_16]),c_0_15]),c_0_20]) ).
cnf(c_0_113,plain,
complement(meet(complement(X1),join(X1,X2))) = join(X1,complement(join(X1,X2))),
inference(spm,[status(thm)],[c_0_55,c_0_105]) ).
cnf(c_0_114,plain,
join(complement(X1),complement(meet(X1,X2))) = complement(meet(X1,X2)),
inference(spm,[status(thm)],[c_0_111,c_0_17]) ).
cnf(c_0_115,plain,
join(meet(X1,X2),meet(X1,meet(X2,X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_18]) ).
cnf(c_0_116,plain,
join(X1,meet(X2,complement(meet(X2,X1)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_38,c_0_112]) ).
cnf(c_0_117,plain,
complement(meet(X1,complement(meet(X1,X2)))) = join(complement(X1),meet(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_55]),c_0_55]) ).
cnf(c_0_118,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_26,c_0_30]),c_0_26]),c_0_26]) ).
cnf(c_0_119,plain,
join(meet(X1,X2),meet(X2,X1)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_24]),c_0_18]),c_0_36]),c_0_18]),c_0_36]) ).
cnf(c_0_120,plain,
( join(complement(X1),meet(X1,X2)) = X2
| join(X2,X1) != one ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_116]),c_0_117]),c_0_73])]) ).
cnf(c_0_121,plain,
join(X1,join(X2,complement(join(X1,X2)))) = one,
inference(spm,[status(thm)],[c_0_14,c_0_26]) ).
cnf(c_0_122,plain,
complement(join(X1,complement(join(X2,X1)))) = meet(complement(X1),join(X2,X1)),
inference(spm,[status(thm)],[c_0_105,c_0_15]) ).
cnf(c_0_123,plain,
meet(X1,join(X2,complement(join(X1,X2)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_93,c_0_15]) ).
cnf(c_0_124,plain,
join(X1,join(X2,meet(X3,join(X2,X1)))) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_71]),c_0_26]) ).
cnf(c_0_125,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_25,c_0_39]),c_0_15]) ).
cnf(c_0_126,plain,
join(meet(X1,X2),join(X3,meet(X2,X1))) = join(meet(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_30]) ).
cnf(c_0_127,plain,
join(X1,join(X2,meet(X1,X3))) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_30]),c_0_95]) ).
cnf(c_0_128,plain,
join(meet(X1,X2),meet(complement(X2),join(X1,X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_122]),c_0_17]),c_0_123]),c_0_15]) ).
cnf(c_0_129,plain,
join(X1,meet(X2,join(meet(X3,X2),X1))) = join(X1,meet(X3,X2)),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_130,plain,
join(meet(X1,X2),X3) = join(X3,meet(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_119]),c_0_126]) ).
cnf(c_0_131,plain,
join(complement(X1),meet(X2,X1)) = join(complement(X1),X2),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
cnf(c_0_132,plain,
join(X1,meet(X2,join(X1,meet(X2,X3)))) = join(X1,meet(X3,X2)),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_133,plain,
meet(X1,join(X2,meet(join(X1,X2),join(X3,join(X2,X4))))) = meet(X1,join(X2,meet(X1,join(X3,join(X2,X4))))),
inference(spm,[status(thm)],[c_0_23,c_0_13]) ).
cnf(c_0_134,plain,
meet(X1,join(complement(X1),meet(X1,X2))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_88,c_0_17]) ).
cnf(c_0_135,plain,
meet(X1,join(complement(X1),X2)) = meet(X2,X1),
inference(rw,[status(thm)],[c_0_88,c_0_131]) ).
cnf(c_0_136,plain,
join(complement(X1),meet(X1,X2)) = join(complement(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_131]),c_0_19]) ).
cnf(c_0_137,plain,
meet(X1,join(X2,join(complement(X1),X3))) = meet(join(X2,X3),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_14]),c_0_21]),c_0_118]),c_0_134]),c_0_135]) ).
cnf(c_0_138,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_136,c_0_55]) ).
cnf(c_0_139,plain,
meet(X1,join(meet(X1,X2),meet(X1,X3))) = join(meet(X1,X2),meet(X1,X3)),
inference(spm,[status(thm)],[c_0_98,c_0_20]) ).
cnf(c_0_140,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(join(X2,X3),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_137]),c_0_55]),c_0_17]) ).
cnf(c_0_141,negated_conjecture,
meet(a,join(b,c)) != join(meet(a,b),meet(a,c)),
prove_distributivity ).
cnf(c_0_142,plain,
join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(meet(X1,X2),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_139,c_0_140]),c_0_17]) ).
cnf(c_0_143,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_141,c_0_142]),c_0_15]),c_0_140]),c_0_15]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT181-1 : TPTP v8.1.2. Released v3.1.0.
% 0.12/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 2400
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Oct 2 10:11:57 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.MWtZWjVEjS/E---3.1_8765.p
% 665.17/86.53 # Version: 3.1pre001
% 665.17/86.53 # Preprocessing class: FSSSSMSSSSSNFFN.
% 665.17/86.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 665.17/86.53 # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 665.17/86.53 # Starting new_bool_3 with 300s (1) cores
% 665.17/86.53 # Starting new_bool_1 with 300s (1) cores
% 665.17/86.53 # Starting sh5l with 300s (1) cores
% 665.17/86.53 # sh5l with pid 8858 completed with status 0
% 665.17/86.53 # Result found by sh5l
% 665.17/86.53 # Preprocessing class: FSSSSMSSSSSNFFN.
% 665.17/86.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 665.17/86.53 # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 665.17/86.53 # Starting new_bool_3 with 300s (1) cores
% 665.17/86.53 # Starting new_bool_1 with 300s (1) cores
% 665.17/86.53 # Starting sh5l with 300s (1) cores
% 665.17/86.53 # SinE strategy is gf500_gu_R04_F100_L20000
% 665.17/86.53 # Search class: FHUPM-FFSF21-MFFFFFNN
% 665.17/86.53 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 665.17/86.53 # Starting G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S with 163s (1) cores
% 665.17/86.53 # G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S with pid 8863 completed with status 0
% 665.17/86.53 # Result found by G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S
% 665.17/86.53 # Preprocessing class: FSSSSMSSSSSNFFN.
% 665.17/86.53 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 665.17/86.53 # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 665.17/86.53 # Starting new_bool_3 with 300s (1) cores
% 665.17/86.53 # Starting new_bool_1 with 300s (1) cores
% 665.17/86.53 # Starting sh5l with 300s (1) cores
% 665.17/86.53 # SinE strategy is gf500_gu_R04_F100_L20000
% 665.17/86.53 # Search class: FHUPM-FFSF21-MFFFFFNN
% 665.17/86.53 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 665.17/86.53 # Starting G----_X1276__C12_02_nc_F1_AE_CS_SP_S5PRR_S2S with 163s (1) cores
% 665.17/86.53 # Preprocessing time : 0.001 s
% 665.17/86.53 # Presaturation interreduction done
% 665.17/86.53
% 665.17/86.53 # Proof found!
% 665.17/86.53 # SZS status Unsatisfiable
% 665.17/86.53 # SZS output start CNFRefutation
% See solution above
% 665.17/86.53 # Parsed axioms : 13
% 665.17/86.53 # Removed by relevancy pruning/SinE : 0
% 665.17/86.53 # Initial clauses : 13
% 665.17/86.53 # Removed in clause preprocessing : 0
% 665.17/86.53 # Initial clauses in saturation : 13
% 665.17/86.53 # Processed clauses : 40321
% 665.17/86.53 # ...of these trivial : 12083
% 665.17/86.53 # ...subsumed : 26523
% 665.17/86.53 # ...remaining for further processing : 1715
% 665.17/86.53 # Other redundant clauses eliminated : 0
% 665.17/86.53 # Clauses deleted for lack of memory : 48766
% 665.17/86.53 # Backward-subsumed : 9
% 665.17/86.53 # Backward-rewritten : 855
% 665.17/86.53 # Generated clauses : 2497094
% 665.17/86.53 # ...of the previous two non-redundant : 1611506
% 665.17/86.53 # ...aggressively subsumed : 0
% 665.17/86.53 # Contextual simplify-reflections : 0
% 665.17/86.53 # Paramodulations : 2497030
% 665.17/86.53 # Factorizations : 0
% 665.17/86.53 # NegExts : 0
% 665.17/86.53 # Equation resolutions : 64
% 665.17/86.53 # Total rewrite steps : 7489161
% 665.17/86.53 # Propositional unsat checks : 0
% 665.17/86.53 # Propositional check models : 0
% 665.17/86.53 # Propositional check unsatisfiable : 0
% 665.17/86.53 # Propositional clauses : 0
% 665.17/86.53 # Propositional clauses after purity: 0
% 665.17/86.53 # Propositional unsat core size : 0
% 665.17/86.53 # Propositional preprocessing time : 0.000
% 665.17/86.53 # Propositional encoding time : 0.000
% 665.17/86.53 # Propositional solver time : 0.000
% 665.17/86.53 # Success case prop preproc time : 0.000
% 665.17/86.53 # Success case prop encoding time : 0.000
% 665.17/86.53 # Success case prop solver time : 0.000
% 665.17/86.53 # Current number of processed clauses : 838
% 665.17/86.53 # Positive orientable unit clauses : 678
% 665.17/86.53 # Positive unorientable unit clauses: 10
% 665.17/86.53 # Negative unit clauses : 0
% 665.17/86.53 # Non-unit-clauses : 150
% 665.17/86.53 # Current number of unprocessed clauses: 1020839
% 665.17/86.53 # ...number of literals in the above : 1160705
% 665.17/86.53 # Current number of archived formulas : 0
% 665.17/86.53 # Current number of archived clauses : 877
% 665.17/86.53 # Clause-clause subsumption calls (NU) : 77510
% 665.17/86.53 # Rec. Clause-clause subsumption calls : 74572
% 665.17/86.53 # Non-unit clause-clause subsumptions : 16959
% 665.17/86.53 # Unit Clause-clause subsumption calls : 1926
% 665.17/86.53 # Rewrite failures with RHS unbound : 0
% 665.17/86.53 # BW rewrite match attempts : 97056
% 665.17/86.53 # BW rewrite match successes : 1563
% 665.17/86.53 # Condensation attempts : 0
% 665.17/86.53 # Condensation successes : 0
% 665.17/86.53 # Termbank termtop insertions : 85579469
% 665.17/86.53
% 665.17/86.53 # -------------------------------------------------
% 665.17/86.53 # User time : 81.142 s
% 665.17/86.53 # System time : 1.640 s
% 665.17/86.53 # Total time : 82.783 s
% 665.17/86.53 # Maximum resident set size: 1668 pages
% 665.17/86.53
% 665.17/86.53 # -------------------------------------------------
% 665.17/86.53 # User time : 81.145 s
% 665.17/86.53 # System time : 1.644 s
% 665.17/86.53 # Total time : 82.788 s
% 665.17/86.53 # Maximum resident set size: 1676 pages
% 665.17/86.53 % E---3.1 exiting
% 665.17/86.53 % E---3.1 exiting
%------------------------------------------------------------------------------