TSTP Solution File: REL022+2 by E---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1
% Problem : REL022+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n015.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 19:13:36 EDT 2023
% Result : Theorem 491.62s 63.40s
% Output : CNFRefutation 491.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 17
% Syntax : Number of formulae : 249 ( 246 unt; 0 def)
% Number of atoms : 252 ( 251 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 3 ~; 0 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 410 ( 46 sgn; 72 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(converse_multiplicativity,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/export/starexec/sandbox/tmp/tmp.KKWVEfxoRz/E---3.1_10899.p',converse_multiplicativity) ).
fof(converse_idempotence,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/export/starexec/sandbox/tmp/tmp.KKWVEfxoRz/E---3.1_10899.p',converse_idempotence) ).
fof(composition_identity,axiom,
! [X1] : composition(X1,one) = X1,
file('/export/starexec/sandbox/tmp/tmp.KKWVEfxoRz/E---3.1_10899.p',composition_identity) ).
fof(maddux2_join_associativity,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/export/starexec/sandbox/tmp/tmp.KKWVEfxoRz/E---3.1_10899.p',maddux2_join_associativity) ).
fof(def_top,axiom,
! [X1] : top = join(X1,complement(X1)),
file('/export/starexec/sandbox/tmp/tmp.KKWVEfxoRz/E---3.1_10899.p',def_top) ).
fof(converse_cancellativity,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/export/starexec/sandbox/tmp/tmp.KKWVEfxoRz/E---3.1_10899.p',converse_cancellativity) ).
fof(maddux1_join_commutativity,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/tmp/tmp.KKWVEfxoRz/E---3.1_10899.p',maddux1_join_commutativity) ).
fof(maddux3_a_kind_of_de_Morgan,axiom,
! [X1,X2] : X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
file('/export/starexec/sandbox/tmp/tmp.KKWVEfxoRz/E---3.1_10899.p',maddux3_a_kind_of_de_Morgan) ).
fof(maddux4_definiton_of_meet,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/export/starexec/sandbox/tmp/tmp.KKWVEfxoRz/E---3.1_10899.p',maddux4_definiton_of_meet) ).
fof(def_zero,axiom,
! [X1] : zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox/tmp/tmp.KKWVEfxoRz/E---3.1_10899.p',def_zero) ).
fof(converse_additivity,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/export/starexec/sandbox/tmp/tmp.KKWVEfxoRz/E---3.1_10899.p',converse_additivity) ).
fof(composition_distributivity,axiom,
! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/export/starexec/sandbox/tmp/tmp.KKWVEfxoRz/E---3.1_10899.p',composition_distributivity) ).
fof(goals,conjecture,
! [X1,X2] :
( composition(X1,top) = X1
=> join(meet(X1,X2),composition(meet(X1,one),X2)) = composition(meet(X1,one),X2) ),
file('/export/starexec/sandbox/tmp/tmp.KKWVEfxoRz/E---3.1_10899.p',goals) ).
fof(modular_law_1,axiom,
! [X1,X2,X3] : join(meet(composition(X1,X2),X3),meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3)) = meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3),
file('/export/starexec/sandbox/tmp/tmp.KKWVEfxoRz/E---3.1_10899.p',modular_law_1) ).
fof(modular_law_2,axiom,
! [X1,X2,X3] : join(meet(composition(X1,X2),X3),meet(composition(meet(X1,composition(X3,converse(X2))),X2),X3)) = meet(composition(meet(X1,composition(X3,converse(X2))),X2),X3),
file('/export/starexec/sandbox/tmp/tmp.KKWVEfxoRz/E---3.1_10899.p',modular_law_2) ).
fof(composition_associativity,axiom,
! [X1,X2,X3] : composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/export/starexec/sandbox/tmp/tmp.KKWVEfxoRz/E---3.1_10899.p',composition_associativity) ).
fof(dedekind_law,axiom,
! [X1,X2,X3] : join(meet(composition(X1,X2),X3),composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3)))) = composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3))),
file('/export/starexec/sandbox/tmp/tmp.KKWVEfxoRz/E---3.1_10899.p',dedekind_law) ).
fof(c_0_17,plain,
! [X13,X14] : converse(composition(X13,X14)) = composition(converse(X14),converse(X13)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
fof(c_0_18,plain,
! [X38] : converse(converse(X38)) = X38,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
cnf(c_0_19,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_20,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_21,plain,
! [X9] : composition(X9,one) = X9,
inference(variable_rename,[status(thm)],[composition_identity]) ).
cnf(c_0_22,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_24,plain,
! [X30,X31,X32] : join(X30,join(X31,X32)) = join(join(X30,X31),X32),
inference(variable_rename,[status(thm)],[maddux2_join_associativity]) ).
fof(c_0_25,plain,
! [X37] : top = join(X37,complement(X37)),
inference(variable_rename,[status(thm)],[def_top]) ).
fof(c_0_26,plain,
! [X15,X16] : join(composition(converse(X15),complement(composition(X15,X16))),complement(X16)) = complement(X16),
inference(variable_rename,[status(thm)],[converse_cancellativity]) ).
fof(c_0_27,plain,
! [X28,X29] : join(X28,X29) = join(X29,X28),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_0_28,plain,
composition(converse(one),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_20]) ).
cnf(c_0_29,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
top = join(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_23,c_0_28]) ).
cnf(c_0_34,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_28,c_0_33]) ).
fof(c_0_37,plain,
! [X33,X34] : X33 = join(complement(join(complement(X33),complement(X34))),complement(join(complement(X33),X34))),
inference(variable_rename,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
fof(c_0_38,plain,
! [X26,X27] : meet(X26,X27) = complement(join(complement(X26),complement(X27))),
inference(variable_rename,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_0_39,plain,
join(X1,join(X2,complement(X1))) = join(top,X2),
inference(spm,[status(thm)],[c_0_34,c_0_32]) ).
cnf(c_0_40,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_33]),c_0_36]) ).
fof(c_0_41,plain,
! [X39] : zero = meet(X39,complement(X39)),
inference(variable_rename,[status(thm)],[def_zero]) ).
cnf(c_0_42,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_43,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,plain,
join(top,complement(complement(X1))) = join(X1,top),
inference(spm,[status(thm)],[c_0_34,c_0_30]) ).
cnf(c_0_45,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_30]) ).
cnf(c_0_46,plain,
zero = meet(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_47,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,plain,
join(X1,top) = top,
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,plain,
complement(top) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_30]),c_0_46]) ).
cnf(c_0_50,plain,
join(zero,meet(X1,top)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_32]) ).
cnf(c_0_51,plain,
meet(X1,X2) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_32]),c_0_43]) ).
cnf(c_0_52,plain,
complement(join(zero,complement(X1))) = meet(top,X1),
inference(spm,[status(thm)],[c_0_43,c_0_49]) ).
cnf(c_0_53,plain,
join(zero,complement(complement(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_40]),c_0_46]) ).
cnf(c_0_54,plain,
join(zero,meet(top,X1)) = X1,
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_55,plain,
meet(top,complement(X1)) = complement(X1),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_56,plain,
join(zero,complement(X1)) = complement(X1),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_57,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_53,c_0_56]) ).
cnf(c_0_58,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_40,c_0_57]) ).
cnf(c_0_59,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_29,c_0_58]) ).
fof(c_0_60,plain,
! [X35,X36] : converse(join(X35,X36)) = join(converse(X35),converse(X36)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
cnf(c_0_61,plain,
complement(complement(X1)) = meet(X1,X1),
inference(spm,[status(thm)],[c_0_43,c_0_40]) ).
cnf(c_0_62,plain,
join(X1,meet(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_47]),c_0_32]) ).
cnf(c_0_63,plain,
complement(join(X1,complement(X2))) = meet(complement(X1),X2),
inference(spm,[status(thm)],[c_0_43,c_0_57]) ).
cnf(c_0_64,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_65,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_32,c_0_48]) ).
cnf(c_0_66,plain,
join(zero,meet(X1,X1)) = X1,
inference(spm,[status(thm)],[c_0_53,c_0_61]) ).
cnf(c_0_67,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_62,c_0_51]) ).
cnf(c_0_68,plain,
complement(join(complement(X1),X2)) = meet(complement(X2),X1),
inference(spm,[status(thm)],[c_0_63,c_0_32]) ).
cnf(c_0_69,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(spm,[status(thm)],[c_0_64,c_0_20]) ).
cnf(c_0_70,plain,
join(X1,join(X2,complement(X1))) = top,
inference(rw,[status(thm)],[c_0_39,c_0_65]) ).
cnf(c_0_71,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_61]),c_0_66]) ).
cnf(c_0_72,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_29,c_0_67]) ).
cnf(c_0_73,plain,
join(meet(X1,X2),meet(complement(X2),X1)) = X1,
inference(rw,[status(thm)],[c_0_47,c_0_68]) ).
cnf(c_0_74,plain,
join(X1,converse(top)) = converse(top),
inference(spm,[status(thm)],[c_0_69,c_0_48]) ).
cnf(c_0_75,plain,
join(complement(X1),join(X2,X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_47]),c_0_29]) ).
cnf(c_0_76,plain,
join(X1,zero) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_71]),c_0_32]),c_0_30]),c_0_49]) ).
fof(c_0_77,plain,
! [X10,X11,X12] : composition(join(X10,X11),X12) = join(composition(X10,X12),composition(X11,X12)),
inference(variable_rename,[status(thm)],[composition_distributivity]) ).
cnf(c_0_78,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_79,plain,
meet(complement(X1),complement(X2)) = complement(join(X1,X2)),
inference(spm,[status(thm)],[c_0_63,c_0_57]) ).
cnf(c_0_80,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_65,c_0_74]) ).
cnf(c_0_81,plain,
meet(X1,join(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_75]),c_0_49]),c_0_76]) ).
cnf(c_0_82,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_32]),c_0_29]) ).
cnf(c_0_83,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_77]) ).
cnf(c_0_84,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_85,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_30]),c_0_80]) ).
cnf(c_0_86,plain,
meet(X1,complement(meet(X1,X2))) = meet(complement(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_78]),c_0_68]),c_0_57]),c_0_51]) ).
cnf(c_0_87,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_57,c_0_63]) ).
cnf(c_0_88,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_62]),c_0_51]) ).
cnf(c_0_89,plain,
join(X1,join(X2,meet(X1,X3))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_82,c_0_62]) ).
cnf(c_0_90,plain,
join(X1,composition(X2,X1)) = composition(join(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_36]),c_0_32]) ).
cnf(c_0_91,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_49]),c_0_76]) ).
cnf(c_0_92,plain,
meet(X1,join(X2,complement(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_86,c_0_86]),c_0_87]),c_0_57]),c_0_51]),c_0_88]) ).
cnf(c_0_93,plain,
join(meet(X1,X2),complement(X2)) = join(complement(X2),X1),
inference(spm,[status(thm)],[c_0_89,c_0_73]) ).
cnf(c_0_94,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_67]),c_0_51]) ).
cnf(c_0_95,plain,
meet(top,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_56]),c_0_57]) ).
cnf(c_0_96,plain,
composition(join(X1,one),top) = top,
inference(spm,[status(thm)],[c_0_90,c_0_65]) ).
cnf(c_0_97,plain,
join(one,complement(converse(complement(one)))) = one,
inference(spm,[status(thm)],[c_0_91,c_0_33]) ).
cnf(c_0_98,plain,
meet(X1,join(complement(X1),X2)) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94]) ).
cnf(c_0_99,plain,
meet(X1,top) = X1,
inference(spm,[status(thm)],[c_0_51,c_0_95]) ).
fof(c_0_100,negated_conjecture,
~ ! [X1,X2] :
( composition(X1,top) = X1
=> join(meet(X1,X2),composition(meet(X1,one),X2)) = composition(meet(X1,one),X2) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_101,plain,
complement(join(zero,zero)) = meet(top,top),
inference(spm,[status(thm)],[c_0_52,c_0_49]) ).
cnf(c_0_102,plain,
join(zero,zero) = zero,
inference(spm,[status(thm)],[c_0_40,c_0_49]) ).
cnf(c_0_103,plain,
composition(top,top) = top,
inference(spm,[status(thm)],[c_0_96,c_0_65]) ).
cnf(c_0_104,plain,
join(X1,converse(meet(X2,converse(X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_67]),c_0_20]) ).
cnf(c_0_105,plain,
meet(complement(one),converse(complement(one))) = complement(one),
inference(spm,[status(thm)],[c_0_63,c_0_97]) ).
cnf(c_0_106,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_91]),c_0_20]),c_0_20]) ).
cnf(c_0_107,plain,
meet(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_85]),c_0_99]),c_0_51]) ).
fof(c_0_108,plain,
! [X20,X21,X22] : join(meet(composition(X20,X21),X22),meet(composition(X20,meet(X21,composition(converse(X20),X22))),X22)) = meet(composition(X20,meet(X21,composition(converse(X20),X22))),X22),
inference(variable_rename,[status(thm)],[modular_law_1]) ).
fof(c_0_109,negated_conjecture,
( composition(esk1_0,top) = esk1_0
& join(meet(esk1_0,esk2_0),composition(meet(esk1_0,one),esk2_0)) != composition(meet(esk1_0,one),esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_100])])]) ).
cnf(c_0_110,plain,
complement(zero) = meet(top,top),
inference(rw,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_111,plain,
composition(top,zero) = 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(spm,[status(thm)],[c_0_35,c_0_103]),c_0_49]),c_0_80]),c_0_49]),c_0_90]),c_0_65]),c_0_49]) ).
cnf(c_0_112,plain,
join(complement(one),converse(complement(one))) = complement(one),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_113,plain,
converse(complement(converse(complement(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_106]),c_0_51]),c_0_107]) ).
cnf(c_0_114,plain,
join(meet(composition(X1,X2),X3),meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3)) = meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_115,negated_conjecture,
composition(esk1_0,top) = esk1_0,
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_116,plain,
join(zero,X1) = X1,
inference(rw,[status(thm)],[c_0_66,c_0_71]) ).
cnf(c_0_117,plain,
complement(zero) = top,
inference(rw,[status(thm)],[c_0_110,c_0_71]) ).
cnf(c_0_118,plain,
composition(join(X1,one),zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_111]),c_0_90]),c_0_65]),c_0_111]) ).
fof(c_0_119,plain,
! [X23,X24,X25] : join(meet(composition(X23,X24),X25),meet(composition(meet(X23,composition(X25,converse(X24))),X24),X25)) = meet(composition(meet(X23,composition(X25,converse(X24))),X24),X25),
inference(variable_rename,[status(thm)],[modular_law_2]) ).
cnf(c_0_120,plain,
converse(complement(one)) = complement(one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_112]),c_0_51]),c_0_105]) ).
cnf(c_0_121,plain,
complement(converse(complement(X1))) = converse(X1),
inference(spm,[status(thm)],[c_0_20,c_0_113]) ).
cnf(c_0_122,plain,
join(meet(composition(X1,X2),X3),meet(X3,composition(X1,meet(X2,composition(converse(X1),X3))))) = meet(X3,composition(X1,meet(X2,composition(converse(X1),X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_51]),c_0_51]) ).
cnf(c_0_123,negated_conjecture,
composition(converse(esk1_0),complement(esk1_0)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_115]),c_0_49]),c_0_49]),c_0_116]) ).
cnf(c_0_124,plain,
meet(X1,zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_117]),c_0_48]),c_0_49]) ).
cnf(c_0_125,plain,
composition(X1,zero) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_116]),c_0_118]) ).
cnf(c_0_126,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(spm,[status(thm)],[c_0_64,c_0_20]) ).
cnf(c_0_127,plain,
join(meet(composition(X1,X2),X3),meet(composition(meet(X1,composition(X3,converse(X2))),X2),X3)) = meet(composition(meet(X1,composition(X3,converse(X2))),X2),X3),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
fof(c_0_128,plain,
! [X6,X7,X8] : composition(X6,composition(X7,X8)) = composition(composition(X6,X7),X8),
inference(variable_rename,[status(thm)],[composition_associativity]) ).
cnf(c_0_129,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_130,plain,
! [X17,X18,X19] : join(meet(composition(X17,X18),X19),composition(meet(X17,composition(X19,converse(X18))),meet(X18,composition(converse(X17),X19)))) = composition(meet(X17,composition(X19,converse(X18))),meet(X18,composition(converse(X17),X19))),
inference(variable_rename,[status(thm)],[dedekind_law]) ).
cnf(c_0_131,plain,
join(complement(one),converse(X1)) = converse(join(complement(one),X1)),
inference(spm,[status(thm)],[c_0_64,c_0_120]) ).
cnf(c_0_132,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[c_0_57,c_0_121]) ).
cnf(c_0_133,negated_conjecture,
meet(composition(esk1_0,X1),complement(esk1_0)) = 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_122,c_0_123]),c_0_124]),c_0_125]),c_0_124]),c_0_76]),c_0_124]),c_0_125]),c_0_124]) ).
cnf(c_0_134,plain,
join(converse(zero),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_116]),c_0_20]) ).
cnf(c_0_135,plain,
meet(X1,join(X2,join(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_81,c_0_29]) ).
cnf(c_0_136,plain,
join(meet(composition(X1,X2),X3),meet(X3,composition(meet(X1,composition(X3,converse(X2))),X2))) = meet(X3,composition(meet(X1,composition(X3,converse(X2))),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_127,c_0_51]),c_0_51]) ).
cnf(c_0_137,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_128]) ).
cnf(c_0_138,plain,
complement(join(X1,join(X2,complement(X3)))) = meet(complement(join(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_63,c_0_29]) ).
cnf(c_0_139,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(spm,[status(thm)],[c_0_87,c_0_57]) ).
cnf(c_0_140,plain,
composition(converse(X1),top) = converse(composition(top,X1)),
inference(spm,[status(thm)],[c_0_22,c_0_80]) ).
cnf(c_0_141,plain,
join(one,converse(X1)) = converse(join(one,X1)),
inference(spm,[status(thm)],[c_0_64,c_0_33]) ).
cnf(c_0_142,plain,
join(X1,composition(X1,converse(X2))) = composition(X1,converse(join(X2,one))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_90]),c_0_129]),c_0_129]) ).
cnf(c_0_143,plain,
join(meet(composition(X1,X2),X3),composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3)))) = composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3))),
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_144,plain,
meet(one,converse(complement(X1))) = converse(meet(one,complement(X1))),
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_68,c_0_131]),c_0_132]),c_0_68]),c_0_132]),c_0_51]),c_0_51]) ).
cnf(c_0_145,negated_conjecture,
meet(complement(esk1_0),composition(esk1_0,X1)) = zero,
inference(spm,[status(thm)],[c_0_51,c_0_133]) ).
cnf(c_0_146,plain,
converse(zero) = zero,
inference(spm,[status(thm)],[c_0_76,c_0_134]) ).
cnf(c_0_147,plain,
meet(meet(X1,X2),join(X3,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_135,c_0_67]) ).
cnf(c_0_148,plain,
meet(X1,composition(X1,top)) = 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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_103]),c_0_95]),c_0_80]),c_0_95]),c_0_137]),c_0_103]),c_0_62]),c_0_80]),c_0_95]),c_0_137]),c_0_103]) ).
cnf(c_0_149,plain,
meet(meet(complement(X1),X2),X3) = meet(complement(X1),meet(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_63]),c_0_63]) ).
cnf(c_0_150,plain,
meet(X1,join(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_81,c_0_32]) ).
cnf(c_0_151,plain,
converse(composition(top,join(one,X1))) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_140]),c_0_65]),c_0_32]),c_0_141]),c_0_140]) ).
cnf(c_0_152,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_70]),c_0_49]),c_0_57]),c_0_51]) ).
cnf(c_0_153,plain,
join(X1,composition(X1,X2)) = composition(X1,join(X2,one)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_20]),c_0_69]),c_0_33]) ).
cnf(c_0_154,plain,
composition(meet(one,composition(X1,converse(X2))),meet(X2,X1)) = meet(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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_33]),c_0_36]),c_0_36]),c_0_90]),c_0_36]),c_0_32]),c_0_62]),c_0_36]) ).
cnf(c_0_155,plain,
meet(one,converse(X1)) = converse(meet(one,X1)),
inference(spm,[status(thm)],[c_0_144,c_0_57]) ).
cnf(c_0_156,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_29,c_0_62]) ).
cnf(c_0_157,negated_conjecture,
meet(esk1_0,composition(esk1_0,X1)) = composition(esk1_0,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_145]),c_0_76]),c_0_51]) ).
cnf(c_0_158,negated_conjecture,
composition(converse(complement(esk1_0)),esk1_0) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_123]),c_0_146]) ).
cnf(c_0_159,plain,
meet(X1,join(X2,composition(X1,top))) = X1,
inference(spm,[status(thm)],[c_0_147,c_0_148]) ).
cnf(c_0_160,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_149,c_0_57]) ).
cnf(c_0_161,plain,
meet(X1,composition(join(X2,one),X1)) = X1,
inference(spm,[status(thm)],[c_0_150,c_0_90]) ).
cnf(c_0_162,plain,
composition(top,join(one,X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_151]),c_0_80]) ).
cnf(c_0_163,plain,
converse(complement(join(converse(X1),X2))) = complement(join(X1,converse(X2))),
inference(spm,[status(thm)],[c_0_132,c_0_69]) ).
cnf(c_0_164,plain,
join(converse(complement(X1)),complement(X2)) = complement(meet(converse(X1),X2)),
inference(spm,[status(thm)],[c_0_139,c_0_132]) ).
cnf(c_0_165,plain,
join(complement(X1),converse(complement(X2))) = complement(meet(X1,converse(X2))),
inference(spm,[status(thm)],[c_0_139,c_0_132]) ).
cnf(c_0_166,plain,
meet(composition(X1,X2),complement(composition(X1,join(X2,one)))) = zero,
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_167,plain,
composition(converse(meet(one,X1)),meet(X1,one)) = meet(X1,one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_36]),c_0_155]) ).
cnf(c_0_168,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_78,c_0_51]) ).
cnf(c_0_169,negated_conjecture,
join(esk1_0,join(composition(esk1_0,X1),X2)) = join(esk1_0,X2),
inference(spm,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_170,negated_conjecture,
composition(complement(esk1_0),top) = complement(esk1_0),
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_158]),c_0_20]),c_0_110]),c_0_71]),c_0_153]),c_0_65]) ).
cnf(c_0_171,plain,
join(composition(X1,converse(X2)),converse(X3)) = converse(join(composition(X2,converse(X1)),X3)),
inference(spm,[status(thm)],[c_0_64,c_0_129]) ).
cnf(c_0_172,plain,
composition(join(X1,converse(X2)),converse(X3)) = converse(composition(X3,join(converse(X1),X2))),
inference(spm,[status(thm)],[c_0_19,c_0_69]) ).
cnf(c_0_173,plain,
meet(X1,composition(join(X2,X1),top)) = X1,
inference(spm,[status(thm)],[c_0_159,c_0_83]) ).
cnf(c_0_174,plain,
composition(top,converse(X1)) = converse(composition(X1,top)),
inference(spm,[status(thm)],[c_0_19,c_0_80]) ).
cnf(c_0_175,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_160,c_0_81]) ).
cnf(c_0_176,plain,
meet(X1,composition(top,X1)) = X1,
inference(spm,[status(thm)],[c_0_161,c_0_65]) ).
cnf(c_0_177,plain,
composition(top,join(X1,one)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_90]),c_0_23]) ).
cnf(c_0_178,plain,
converse(meet(converse(X1),X2)) = meet(X1,converse(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_163,c_0_164]),c_0_57]),c_0_165]),c_0_57]) ).
cnf(c_0_179,plain,
meet(X1,converse(meet(one,complement(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_166,c_0_167]),c_0_32]),c_0_67]),c_0_23]),c_0_132]),c_0_160]),c_0_155]),c_0_86]),c_0_51]) ).
cnf(c_0_180,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_168,c_0_79]) ).
cnf(c_0_181,negated_conjecture,
join(esk1_0,composition(join(esk1_0,X1),X2)) = join(esk1_0,composition(X1,X2)),
inference(spm,[status(thm)],[c_0_169,c_0_83]) ).
cnf(c_0_182,negated_conjecture,
composition(complement(esk1_0),composition(top,X1)) = composition(complement(esk1_0),X1),
inference(spm,[status(thm)],[c_0_137,c_0_170]) ).
cnf(c_0_183,plain,
meet(complement(X1),join(X1,X2)) = meet(X2,complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_79]),c_0_57]),c_0_57]) ).
cnf(c_0_184,plain,
converse(join(composition(X1,converse(X2)),composition(X1,X3))) = converse(composition(X1,join(converse(X2),X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_19]),c_0_171]),c_0_172]) ).
cnf(c_0_185,plain,
meet(composition(X1,X2),composition(X1,top)) = composition(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_153]),c_0_137]),c_0_96]) ).
cnf(c_0_186,plain,
composition(meet(one,composition(X1,top)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_95]),c_0_80]) ).
cnf(c_0_187,plain,
composition(meet(X1,converse(composition(X2,top))),X2) = composition(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_136,c_0_174]),c_0_99]),c_0_95]),c_0_83]),c_0_62]),c_0_95]) ).
cnf(c_0_188,plain,
meet(X1,composition(top,join(X2,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_176]),c_0_81]) ).
cnf(c_0_189,plain,
composition(top,composition(join(X1,one),X2)) = composition(top,X2),
inference(spm,[status(thm)],[c_0_137,c_0_177]) ).
cnf(c_0_190,plain,
converse(meet(X1,converse(X2))) = meet(converse(X1),X2),
inference(spm,[status(thm)],[c_0_20,c_0_178]) ).
cnf(c_0_191,plain,
join(X1,converse(meet(one,X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_179]),c_0_76]),c_0_57]) ).
cnf(c_0_192,plain,
meet(converse(meet(one,X1)),X2) = meet(one,meet(converse(X1),X2)),
inference(spm,[status(thm)],[c_0_160,c_0_155]) ).
cnf(c_0_193,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_67]),c_0_67]) ).
cnf(c_0_194,plain,
meet(join(X1,X2),join(X2,complement(X1))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_180]),c_0_51]),c_0_81]) ).
cnf(c_0_195,negated_conjecture,
join(esk1_0,composition(complement(esk1_0),X1)) = join(esk1_0,composition(top,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_85]),c_0_132]),c_0_20]) ).
cnf(c_0_196,negated_conjecture,
composition(complement(esk1_0),join(X1,one)) = complement(esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_177]),c_0_170]) ).
cnf(c_0_197,plain,
meet(join(X1,X2),complement(X1)) = meet(X2,complement(X1)),
inference(spm,[status(thm)],[c_0_51,c_0_183]) ).
cnf(c_0_198,plain,
join(composition(X1,converse(X2)),composition(X1,X3)) = composition(X1,join(converse(X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_184]),c_0_20]) ).
cnf(c_0_199,plain,
meet(complement(composition(X1,top)),composition(X1,X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_185]),c_0_46]) ).
cnf(c_0_200,negated_conjecture,
composition(meet(esk1_0,one),esk1_0) = esk1_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_115]),c_0_51]) ).
cnf(c_0_201,negated_conjecture,
composition(esk1_0,composition(top,X1)) = composition(esk1_0,X1),
inference(spm,[status(thm)],[c_0_137,c_0_115]) ).
cnf(c_0_202,plain,
composition(converse(meet(one,composition(X1,top))),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_155]),c_0_36]) ).
cnf(c_0_203,plain,
meet(composition(X1,X2),composition(top,X2)) = composition(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_90]),c_0_189]) ).
cnf(c_0_204,plain,
converse(meet(X1,meet(X2,converse(X3)))) = meet(converse(meet(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_190,c_0_160]) ).
cnf(c_0_205,plain,
meet(one,meet(X1,converse(X1))) = converse(meet(one,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_191]),c_0_192]),c_0_51]) ).
cnf(c_0_206,plain,
meet(X1,meet(X2,meet(X3,X1))) = meet(X2,meet(X3,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_193]),c_0_51]) ).
cnf(c_0_207,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(spm,[status(thm)],[c_0_51,c_0_160]) ).
cnf(c_0_208,plain,
join(X1,join(meet(complement(X1),X2),X3)) = join(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_78]),c_0_29]) ).
cnf(c_0_209,plain,
meet(X1,meet(composition(top,X1),X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_160,c_0_176]) ).
cnf(c_0_210,negated_conjecture,
meet(composition(top,X1),complement(esk1_0)) = composition(complement(esk1_0),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_195]),c_0_32]),c_0_153]),c_0_196]),c_0_197]) ).
cnf(c_0_211,plain,
join(composition(X1,X2),composition(X1,meet(X2,converse(composition(top,X1))))) = composition(X1,meet(X2,converse(composition(top,X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_122,c_0_140]),c_0_95]),c_0_95]),c_0_99]) ).
cnf(c_0_212,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_198,c_0_20]) ).
cnf(c_0_213,plain,
join(meet(X1,X2),meet(complement(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_73,c_0_51]) ).
cnf(c_0_214,negated_conjecture,
meet(esk1_0,complement(composition(meet(esk1_0,one),top))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_199,c_0_200]),c_0_51]) ).
cnf(c_0_215,negated_conjecture,
join(esk1_0,composition(X1,top)) = composition(join(X1,esk1_0),top),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_115]),c_0_32]) ).
cnf(c_0_216,negated_conjecture,
composition(esk1_0,join(one,X1)) = esk1_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_162]),c_0_115]) ).
cnf(c_0_217,plain,
meet(X1,meet(composition(X2,X3),composition(meet(X2,composition(meet(X1,composition(X2,X3)),converse(X3))),X3))) = meet(X1,composition(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_94]),c_0_62]),c_0_160]) ).
cnf(c_0_218,plain,
composition(meet(one,composition(top,X1)),converse(X1)) = converse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_202]),c_0_140]),c_0_155]),c_0_129]) ).
cnf(c_0_219,plain,
meet(composition(top,X1),composition(X2,X1)) = composition(X2,X1),
inference(spm,[status(thm)],[c_0_51,c_0_203]) ).
cnf(c_0_220,plain,
converse(meet(one,X1)) = meet(one,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_205]),c_0_20]),c_0_192]),c_0_51]),c_0_205]) ).
cnf(c_0_221,plain,
meet(X1,meet(join(X2,join(X3,X1)),X4)) = meet(X4,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_206,c_0_135]),c_0_207]) ).
cnf(c_0_222,plain,
composition(meet(one,X1),meet(one,X1)) = meet(one,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_33]),c_0_23]) ).
cnf(c_0_223,plain,
meet(X1,join(meet(X1,X2),X3)) = meet(join(X2,X3),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_208]),c_0_98]),c_0_57]),c_0_51]) ).
cnf(c_0_224,negated_conjecture,
meet(X1,composition(complement(esk1_0),X1)) = meet(X1,complement(esk1_0)),
inference(spm,[status(thm)],[c_0_209,c_0_210]) ).
cnf(c_0_225,plain,
composition(converse(X1),meet(X2,converse(X3))) = converse(composition(meet(converse(X2),X3),X1)),
inference(spm,[status(thm)],[c_0_19,c_0_178]) ).
cnf(c_0_226,plain,
composition(X1,meet(X2,converse(composition(top,X1)))) = composition(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_211,c_0_212]),c_0_62]) ).
cnf(c_0_227,plain,
meet(converse(X1),converse(X2)) = converse(meet(X1,X2)),
inference(spm,[status(thm)],[c_0_178,c_0_20]) ).
cnf(c_0_228,negated_conjecture,
complement(composition(meet(esk1_0,one),top)) = complement(esk1_0),
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_213,c_0_214]),c_0_79]),c_0_215]),c_0_32]),c_0_62]),c_0_115]),c_0_116]) ).
cnf(c_0_229,negated_conjecture,
composition(esk1_0,join(X1,one)) = esk1_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_216,c_0_90]),c_0_23]) ).
cnf(c_0_230,plain,
meet(composition(X1,X2),composition(join(X3,X1),X2)) = composition(X1,X2),
inference(spm,[status(thm)],[c_0_81,c_0_83]) ).
cnf(c_0_231,plain,
meet(one,composition(converse(X1),X1)) = meet(one,composition(top,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_217,c_0_218]),c_0_95]),c_0_219]) ).
cnf(c_0_232,plain,
converse(meet(X1,one)) = meet(X1,one),
inference(spm,[status(thm)],[c_0_220,c_0_221]) ).
cnf(c_0_233,plain,
composition(meet(X1,one),meet(X1,one)) = meet(X1,one),
inference(spm,[status(thm)],[c_0_222,c_0_94]) ).
cnf(c_0_234,negated_conjecture,
meet(X1,join(composition(complement(esk1_0),X1),X2)) = meet(join(complement(esk1_0),X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_223,c_0_224]),c_0_223]),c_0_51]) ).
cnf(c_0_235,plain,
composition(converse(X1),meet(X2,composition(X1,top))) = composition(converse(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_225,c_0_226]),c_0_174]),c_0_227]),c_0_22]) ).
cnf(c_0_236,negated_conjecture,
composition(meet(esk1_0,one),top) = esk1_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_228]),c_0_57]) ).
cnf(c_0_237,negated_conjecture,
join(esk1_0,composition(meet(esk1_0,X1),X2)) = esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_62]),c_0_153]),c_0_229]) ).
cnf(c_0_238,plain,
meet(composition(X1,X2),composition(meet(X1,X3),X2)) = composition(meet(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_230,c_0_62]),c_0_51]) ).
cnf(c_0_239,plain,
meet(one,composition(top,meet(X1,one))) = meet(X1,one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_231,c_0_232]),c_0_233]),c_0_94]) ).
cnf(c_0_240,negated_conjecture,
meet(X1,join(complement(esk1_0),composition(X2,X1))) = meet(X1,composition(join(complement(esk1_0),X2),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_83]),c_0_51]) ).
cnf(c_0_241,negated_conjecture,
composition(meet(esk1_0,one),meet(X1,esk1_0)) = composition(meet(esk1_0,one),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_235,c_0_236]),c_0_232]),c_0_232]) ).
cnf(c_0_242,negated_conjecture,
meet(esk1_0,composition(meet(esk1_0,X1),X2)) = composition(meet(esk1_0,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_237]),c_0_92]) ).
cnf(c_0_243,plain,
meet(X1,composition(meet(X2,one),X1)) = composition(meet(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_238,c_0_239]),c_0_36]) ).
cnf(c_0_244,plain,
join(complement(X1),meet(X1,X2)) = join(complement(X1),X2),
inference(spm,[status(thm)],[c_0_78,c_0_57]) ).
cnf(c_0_245,plain,
meet(X1,composition(join(one,X2),X1)) = X1,
inference(spm,[status(thm)],[c_0_161,c_0_32]) ).
cnf(c_0_246,negated_conjecture,
join(meet(esk1_0,esk2_0),composition(meet(esk1_0,one),esk2_0)) != composition(meet(esk1_0,one),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_247,negated_conjecture,
composition(meet(esk1_0,one),X1) = meet(X1,esk1_0),
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_240,c_0_241]),c_0_160]),c_0_98]),c_0_51]),c_0_242]),c_0_243]),c_0_244]),c_0_32]),c_0_245]) ).
cnf(c_0_248,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_246,c_0_247]),c_0_51]),c_0_58]),c_0_247]),c_0_51])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : REL022+2 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 2400
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Oct 2 15:31:31 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.49 Running first-order theorem proving
% 0.21/0.49 Running: /export/starexec/sandbox/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/sandbox/tmp/tmp.KKWVEfxoRz/E---3.1_10899.p
% 491.62/63.40 # Version: 3.1pre001
% 491.62/63.40 # Preprocessing class: FSMSSMSSSSSNFFN.
% 491.62/63.40 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 491.62/63.40 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 491.62/63.40 # Starting new_bool_3 with 300s (1) cores
% 491.62/63.40 # Starting new_bool_1 with 300s (1) cores
% 491.62/63.40 # Starting sh5l with 300s (1) cores
% 491.62/63.40 # sh5l with pid 10984 completed with status 0
% 491.62/63.40 # Result found by sh5l
% 491.62/63.40 # Preprocessing class: FSMSSMSSSSSNFFN.
% 491.62/63.40 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 491.62/63.40 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 491.62/63.40 # Starting new_bool_3 with 300s (1) cores
% 491.62/63.40 # Starting new_bool_1 with 300s (1) cores
% 491.62/63.40 # Starting sh5l with 300s (1) cores
% 491.62/63.40 # SinE strategy is gf500_gu_R04_F100_L20000
% 491.62/63.40 # Search class: FUUPM-FFMF21-DFFFFFNN
% 491.62/63.40 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 491.62/63.40 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 163s (1) cores
% 491.62/63.40 # H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with pid 10988 completed with status 0
% 491.62/63.40 # Result found by H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S
% 491.62/63.40 # Preprocessing class: FSMSSMSSSSSNFFN.
% 491.62/63.40 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 491.62/63.40 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 491.62/63.40 # Starting new_bool_3 with 300s (1) cores
% 491.62/63.40 # Starting new_bool_1 with 300s (1) cores
% 491.62/63.40 # Starting sh5l with 300s (1) cores
% 491.62/63.40 # SinE strategy is gf500_gu_R04_F100_L20000
% 491.62/63.40 # Search class: FUUPM-FFMF21-DFFFFFNN
% 491.62/63.40 # Scheduled 6 strats onto 1 cores with 300 seconds (300 total)
% 491.62/63.40 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 163s (1) cores
% 491.62/63.40 # Preprocessing time : 0.001 s
% 491.62/63.40 # Presaturation interreduction done
% 491.62/63.40
% 491.62/63.40 # Proof found!
% 491.62/63.40 # SZS status Theorem
% 491.62/63.40 # SZS output start CNFRefutation
% See solution above
% 491.62/63.40 # Parsed axioms : 17
% 491.62/63.40 # Removed by relevancy pruning/SinE : 0
% 491.62/63.40 # Initial clauses : 18
% 491.62/63.40 # Removed in clause preprocessing : 0
% 491.62/63.40 # Initial clauses in saturation : 18
% 491.62/63.40 # Processed clauses : 63829
% 491.62/63.40 # ...of these trivial : 36114
% 491.62/63.40 # ...subsumed : 23514
% 491.62/63.40 # ...remaining for further processing : 4201
% 491.62/63.40 # Other redundant clauses eliminated : 0
% 491.62/63.40 # Clauses deleted for lack of memory : 228525
% 491.62/63.40 # Backward-subsumed : 1
% 491.62/63.40 # Backward-rewritten : 930
% 491.62/63.40 # Generated clauses : 3294869
% 491.62/63.40 # ...of the previous two non-redundant : 2077316
% 491.62/63.40 # ...aggressively subsumed : 0
% 491.62/63.40 # Contextual simplify-reflections : 0
% 491.62/63.40 # Paramodulations : 3294869
% 491.62/63.40 # Factorizations : 0
% 491.62/63.40 # NegExts : 0
% 491.62/63.40 # Equation resolutions : 0
% 491.62/63.40 # Total rewrite steps : 9365337
% 491.62/63.40 # Propositional unsat checks : 0
% 491.62/63.40 # Propositional check models : 0
% 491.62/63.40 # Propositional check unsatisfiable : 0
% 491.62/63.40 # Propositional clauses : 0
% 491.62/63.40 # Propositional clauses after purity: 0
% 491.62/63.40 # Propositional unsat core size : 0
% 491.62/63.40 # Propositional preprocessing time : 0.000
% 491.62/63.40 # Propositional encoding time : 0.000
% 491.62/63.40 # Propositional solver time : 0.000
% 491.62/63.40 # Success case prop preproc time : 0.000
% 491.62/63.40 # Success case prop encoding time : 0.000
% 491.62/63.40 # Success case prop solver time : 0.000
% 491.62/63.40 # Current number of processed clauses : 3252
% 491.62/63.40 # Positive orientable unit clauses : 3209
% 491.62/63.40 # Positive unorientable unit clauses: 43
% 491.62/63.40 # Negative unit clauses : 0
% 491.62/63.40 # Non-unit-clauses : 0
% 491.62/63.40 # Current number of unprocessed clauses: 1239887
% 491.62/63.40 # ...number of literals in the above : 1239887
% 491.62/63.40 # Current number of archived formulas : 0
% 491.62/63.40 # Current number of archived clauses : 949
% 491.62/63.40 # Clause-clause subsumption calls (NU) : 0
% 491.62/63.40 # Rec. Clause-clause subsumption calls : 0
% 491.62/63.40 # Non-unit clause-clause subsumptions : 0
% 491.62/63.40 # Unit Clause-clause subsumption calls : 1643
% 491.62/63.40 # Rewrite failures with RHS unbound : 0
% 491.62/63.40 # BW rewrite match attempts : 30651
% 491.62/63.40 # BW rewrite match successes : 1725
% 491.62/63.40 # Condensation attempts : 0
% 491.62/63.40 # Condensation successes : 0
% 491.62/63.40 # Termbank termtop insertions : 70183402
% 491.62/63.40
% 491.62/63.40 # -------------------------------------------------
% 491.62/63.40 # User time : 60.540 s
% 491.62/63.40 # System time : 1.510 s
% 491.62/63.40 # Total time : 62.050 s
% 491.62/63.40 # Maximum resident set size: 1764 pages
% 491.62/63.40
% 491.62/63.40 # -------------------------------------------------
% 491.62/63.40 # User time : 60.542 s
% 491.62/63.40 # System time : 1.514 s
% 491.62/63.40 # Total time : 62.055 s
% 491.62/63.40 # Maximum resident set size: 1724 pages
% 491.62/63.40 % E---3.1 exiting
% 491.62/63.40 % E---3.1 exiting
%------------------------------------------------------------------------------