TSTP Solution File: REL021+2 by E-SAT---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : REL021+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n017.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 19:14:13 EDT 2023
% Result : Theorem 527.80s 67.20s
% Output : CNFRefutation 527.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 16
% Syntax : Number of formulae : 271 ( 268 unt; 0 def)
% Number of atoms : 274 ( 273 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 447 ( 54 sgn; 70 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(converse_multiplicativity,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/export/starexec/sandbox/tmp/tmp.wKER6ooVQb/E---3.1_21820.p',converse_multiplicativity) ).
fof(converse_idempotence,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/export/starexec/sandbox/tmp/tmp.wKER6ooVQb/E---3.1_21820.p',converse_idempotence) ).
fof(composition_identity,axiom,
! [X1] : composition(X1,one) = X1,
file('/export/starexec/sandbox/tmp/tmp.wKER6ooVQb/E---3.1_21820.p',composition_identity) ).
fof(converse_cancellativity,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/export/starexec/sandbox/tmp/tmp.wKER6ooVQb/E---3.1_21820.p',converse_cancellativity) ).
fof(maddux1_join_commutativity,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/tmp/tmp.wKER6ooVQb/E---3.1_21820.p',maddux1_join_commutativity) ).
fof(maddux2_join_associativity,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/export/starexec/sandbox/tmp/tmp.wKER6ooVQb/E---3.1_21820.p',maddux2_join_associativity) ).
fof(def_top,axiom,
! [X1] : top = join(X1,complement(X1)),
file('/export/starexec/sandbox/tmp/tmp.wKER6ooVQb/E---3.1_21820.p',def_top) ).
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.wKER6ooVQb/E---3.1_21820.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.wKER6ooVQb/E---3.1_21820.p',maddux4_definiton_of_meet) ).
fof(converse_additivity,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/export/starexec/sandbox/tmp/tmp.wKER6ooVQb/E---3.1_21820.p',converse_additivity) ).
fof(goals,conjecture,
! [X1,X2] :
( composition(X1,top) = X1
=> join(composition(meet(X1,one),X2),meet(X1,X2)) = meet(X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.wKER6ooVQb/E---3.1_21820.p',goals) ).
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.wKER6ooVQb/E---3.1_21820.p',composition_distributivity) ).
fof(composition_associativity,axiom,
! [X1,X2,X3] : composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/export/starexec/sandbox/tmp/tmp.wKER6ooVQb/E---3.1_21820.p',composition_associativity) ).
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.wKER6ooVQb/E---3.1_21820.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.wKER6ooVQb/E---3.1_21820.p',modular_law_2) ).
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.wKER6ooVQb/E---3.1_21820.p',dedekind_law) ).
fof(c_0_16,plain,
! [X28,X29] : converse(composition(X28,X29)) = composition(converse(X29),converse(X28)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
fof(c_0_17,plain,
! [X36] : converse(converse(X36)) = X36,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
cnf(c_0_18,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_20,plain,
! [X30] : composition(X30,one) = X30,
inference(variable_rename,[status(thm)],[composition_identity]) ).
cnf(c_0_21,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,plain,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_23,plain,
! [X34,X35] : join(composition(converse(X34),complement(composition(X34,X35))),complement(X35)) = complement(X35),
inference(variable_rename,[status(thm)],[converse_cancellativity]) ).
fof(c_0_24,plain,
! [X17,X18] : join(X17,X18) = join(X18,X17),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_0_25,plain,
composition(converse(one),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_19]) ).
fof(c_0_26,plain,
! [X19,X20,X21] : join(X19,join(X20,X21)) = join(join(X19,X20),X21),
inference(variable_rename,[status(thm)],[maddux2_join_associativity]) ).
fof(c_0_27,plain,
! [X31] : top = join(X31,complement(X31)),
inference(variable_rename,[status(thm)],[def_top]) ).
cnf(c_0_28,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_22,c_0_25]) ).
cnf(c_0_31,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
top = join(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_25,c_0_30]) ).
fof(c_0_35,plain,
! [X32,X33] : X32 = join(complement(join(complement(X32),complement(X33))),complement(join(complement(X32),X33))),
inference(variable_rename,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
fof(c_0_36,plain,
! [X6,X7] : meet(X6,X7) = complement(join(complement(X6),complement(X7))),
inference(variable_rename,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_0_37,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,plain,
join(X1,join(X2,complement(join(X1,X2)))) = top,
inference(spm,[status(thm)],[c_0_32,c_0_31]) ).
cnf(c_0_39,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_30]),c_0_34]) ).
cnf(c_0_40,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_42,plain,
join(top,complement(complement(X1))) = join(X1,top),
inference(spm,[status(thm)],[c_0_37,c_0_32]) ).
cnf(c_0_43,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_32]),c_0_29]) ).
cnf(c_0_44,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,plain,
join(X1,top) = top,
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_46,plain,
meet(X1,complement(X1)) = complement(top),
inference(spm,[status(thm)],[c_0_41,c_0_32]) ).
cnf(c_0_47,plain,
join(meet(X1,top),complement(top)) = X1,
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_48,plain,
meet(X1,X2) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_29]),c_0_41]) ).
cnf(c_0_49,plain,
join(complement(top),complement(complement(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_39]),c_0_46]) ).
cnf(c_0_50,plain,
complement(complement(X1)) = meet(X1,X1),
inference(spm,[status(thm)],[c_0_41,c_0_39]) ).
cnf(c_0_51,plain,
join(meet(top,X1),complement(top)) = X1,
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,plain,
meet(top,complement(X1)) = complement(X1),
inference(spm,[status(thm)],[c_0_41,c_0_49]) ).
cnf(c_0_53,plain,
join(complement(top),meet(X1,X1)) = X1,
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,plain,
join(complement(X1),complement(top)) = complement(X1),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_55,plain,
join(meet(X1,X1),complement(top)) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_53]) ).
fof(c_0_56,plain,
! [X37,X38] : converse(join(X37,X38)) = join(converse(X37),converse(X38)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
cnf(c_0_57,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_50]),c_0_55]) ).
cnf(c_0_58,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_59,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_50,c_0_57]) ).
fof(c_0_60,negated_conjecture,
~ ! [X1,X2] :
( composition(X1,top) = X1
=> join(composition(meet(X1,one),X2),meet(X1,X2)) = meet(X1,X2) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_61,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(spm,[status(thm)],[c_0_58,c_0_19]) ).
cnf(c_0_62,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_39,c_0_59]) ).
cnf(c_0_63,plain,
join(complement(top),X1) = X1,
inference(rw,[status(thm)],[c_0_53,c_0_57]) ).
fof(c_0_64,negated_conjecture,
( composition(esk1_0,top) = esk1_0
& join(composition(meet(esk1_0,one),esk2_0),meet(esk1_0,esk2_0)) != meet(esk1_0,esk2_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_60])])]) ).
cnf(c_0_65,plain,
join(X1,complement(top)) = X1,
inference(rw,[status(thm)],[c_0_55,c_0_57]) ).
fof(c_0_66,plain,
! [X22,X23,X24] : composition(join(X22,X23),X24) = join(composition(X22,X24),composition(X23,X24)),
inference(variable_rename,[status(thm)],[composition_distributivity]) ).
cnf(c_0_67,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(spm,[status(thm)],[c_0_61,c_0_32]) ).
cnf(c_0_68,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_29,c_0_45]) ).
cnf(c_0_69,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_31,c_0_62]) ).
cnf(c_0_70,plain,
complement(join(X1,complement(X2))) = meet(complement(X1),X2),
inference(spm,[status(thm)],[c_0_41,c_0_59]) ).
cnf(c_0_71,plain,
composition(converse(X1),complement(composition(X1,top))) = complement(top),
inference(spm,[status(thm)],[c_0_33,c_0_63]) ).
cnf(c_0_72,negated_conjecture,
composition(esk1_0,top) = esk1_0,
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_73,plain,
join(X1,converse(complement(top))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_65]),c_0_19]) ).
cnf(c_0_74,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_75,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_76,plain,
join(X1,meet(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_44]),c_0_29]) ).
cnf(c_0_77,plain,
complement(join(complement(X1),X2)) = meet(complement(X2),X1),
inference(spm,[status(thm)],[c_0_70,c_0_29]) ).
cnf(c_0_78,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_59,c_0_70]) ).
cnf(c_0_79,negated_conjecture,
composition(converse(esk1_0),complement(esk1_0)) = complement(top),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_80,plain,
converse(complement(top)) = complement(top),
inference(spm,[status(thm)],[c_0_63,c_0_73]) ).
fof(c_0_81,plain,
! [X25,X26,X27] : composition(X25,composition(X26,X27)) = composition(composition(X25,X26),X27),
inference(variable_rename,[status(thm)],[composition_associativity]) ).
cnf(c_0_82,plain,
join(X1,composition(X2,X1)) = composition(join(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_34]),c_0_29]) ).
cnf(c_0_83,plain,
composition(converse(X1),top) = converse(composition(top,X1)),
inference(spm,[status(thm)],[c_0_21,c_0_75]) ).
cnf(c_0_84,plain,
join(one,converse(X1)) = converse(join(one,X1)),
inference(spm,[status(thm)],[c_0_58,c_0_30]) ).
cnf(c_0_85,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_76,c_0_48]) ).
cnf(c_0_86,plain,
meet(X1,join(X1,complement(X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_76]),c_0_59]),c_0_78]),c_0_48]) ).
fof(c_0_87,plain,
! [X11,X12,X13] : join(meet(composition(X11,X12),X13),meet(composition(X11,meet(X12,composition(converse(X11),X13))),X13)) = meet(composition(X11,meet(X12,composition(converse(X11),X13))),X13),
inference(variable_rename,[status(thm)],[modular_law_1]) ).
cnf(c_0_88,plain,
meet(top,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_52,c_0_41]) ).
cnf(c_0_89,negated_conjecture,
composition(converse(complement(esk1_0)),esk1_0) = complement(top),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_79]),c_0_80]) ).
cnf(c_0_90,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_91,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_82,c_0_83]),c_0_68]),c_0_29]),c_0_84]),c_0_83]) ).
cnf(c_0_92,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_31,c_0_85]) ).
cnf(c_0_93,plain,
join(meet(X1,X2),meet(complement(X2),X1)) = X1,
inference(rw,[status(thm)],[c_0_44,c_0_77]) ).
cnf(c_0_94,plain,
meet(X1,join(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_86,c_0_59]) ).
cnf(c_0_95,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_69,c_0_29]) ).
cnf(c_0_96,plain,
join(X1,join(X2,complement(X1))) = join(top,X2),
inference(spm,[status(thm)],[c_0_37,c_0_29]) ).
cnf(c_0_97,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_87]) ).
cnf(c_0_98,plain,
meet(top,X1) = X1,
inference(spm,[status(thm)],[c_0_88,c_0_57]) ).
cnf(c_0_99,negated_conjecture,
composition(join(converse(complement(esk1_0)),X1),esk1_0) = composition(X1,esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_89]),c_0_63]) ).
cnf(c_0_100,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(rw,[status(thm)],[c_0_67,c_0_75]) ).
cnf(c_0_101,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_102,negated_conjecture,
composition(esk1_0,composition(top,X1)) = composition(esk1_0,X1),
inference(spm,[status(thm)],[c_0_90,c_0_72]) ).
cnf(c_0_103,plain,
composition(top,join(one,X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_91]),c_0_75]) ).
cnf(c_0_104,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_105,plain,
meet(complement(X1),complement(X2)) = complement(join(X1,X2)),
inference(spm,[status(thm)],[c_0_70,c_0_59]) ).
cnf(c_0_106,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_107,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_29]),c_0_31]) ).
cnf(c_0_108,plain,
join(X1,join(X2,complement(X1))) = top,
inference(rw,[status(thm)],[c_0_96,c_0_68]) ).
cnf(c_0_109,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(spm,[status(thm)],[c_0_58,c_0_19]) ).
cnf(c_0_110,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_97,c_0_48]),c_0_48]) ).
cnf(c_0_111,plain,
meet(X1,top) = X1,
inference(spm,[status(thm)],[c_0_48,c_0_98]) ).
cnf(c_0_112,negated_conjecture,
composition(converse(esk1_0),esk1_0) = composition(top,esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_19]),c_0_59]) ).
cnf(c_0_113,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_61,c_0_82]),c_0_101]),c_0_101]) ).
cnf(c_0_114,negated_conjecture,
composition(esk1_0,join(one,X1)) = esk1_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_72]) ).
cnf(c_0_115,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_116,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_77,c_0_104]),c_0_77]),c_0_59]),c_0_48]) ).
cnf(c_0_117,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_76]),c_0_48]) ).
cnf(c_0_118,plain,
join(X1,join(X2,meet(X1,X3))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_107,c_0_76]) ).
cnf(c_0_119,plain,
join(complement(X1),join(X2,X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_44]),c_0_31]) ).
cnf(c_0_120,plain,
join(converse(X1),composition(X2,converse(X3))) = converse(join(X1,composition(X3,converse(X2)))),
inference(spm,[status(thm)],[c_0_58,c_0_101]) ).
cnf(c_0_121,plain,
composition(join(converse(X1),X2),converse(X3)) = converse(composition(X3,join(X1,converse(X2)))),
inference(spm,[status(thm)],[c_0_18,c_0_109]) ).
cnf(c_0_122,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_110,c_0_83]),c_0_111]),c_0_98]),c_0_98]) ).
cnf(c_0_123,negated_conjecture,
converse(composition(top,esk1_0)) = composition(top,esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_112]),c_0_112]) ).
cnf(c_0_124,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_113,c_0_19]),c_0_61]),c_0_30]) ).
cnf(c_0_125,negated_conjecture,
composition(esk1_0,join(X1,one)) = esk1_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_82]),c_0_22]) ).
cnf(c_0_126,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_100]),c_0_65]) ).
cnf(c_0_127,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_116,c_0_116]),c_0_78]),c_0_59]),c_0_48]),c_0_117]) ).
cnf(c_0_128,plain,
join(meet(X1,X2),complement(X2)) = join(complement(X2),X1),
inference(spm,[status(thm)],[c_0_118,c_0_93]) ).
cnf(c_0_129,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_85]),c_0_48]) ).
cnf(c_0_130,plain,
join(complement(X1),join(X1,X2)) = top,
inference(spm,[status(thm)],[c_0_119,c_0_29]) ).
cnf(c_0_131,plain,
composition(join(X1,one),top) = top,
inference(spm,[status(thm)],[c_0_82,c_0_68]) ).
cnf(c_0_132,plain,
converse(join(composition(X1,X2),composition(X1,converse(X3)))) = converse(composition(X1,join(X2,converse(X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_18]),c_0_120]),c_0_121]) ).
cnf(c_0_133,negated_conjecture,
composition(esk1_0,esk1_0) = 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_122,c_0_72]),c_0_123]),c_0_98]),c_0_102]),c_0_124]),c_0_125]),c_0_123]),c_0_98]),c_0_102]) ).
cnf(c_0_134,negated_conjecture,
composition(esk1_0,converse(join(one,X1))) = esk1_0,
inference(spm,[status(thm)],[c_0_114,c_0_84]) ).
cnf(c_0_135,plain,
join(one,complement(converse(complement(one)))) = one,
inference(spm,[status(thm)],[c_0_126,c_0_30]) ).
cnf(c_0_136,plain,
meet(X1,join(complement(X1),X2)) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_129]) ).
cnf(c_0_137,plain,
join(X1,complement(meet(X1,X2))) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_44]),c_0_29]) ).
cnf(c_0_138,plain,
composition(top,top) = top,
inference(spm,[status(thm)],[c_0_131,c_0_68]) ).
cnf(c_0_139,negated_conjecture,
converse(composition(esk1_0,join(esk1_0,converse(X1)))) = converse(esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_132,c_0_133]),c_0_124]),c_0_29]),c_0_84]),c_0_134]) ).
cnf(c_0_140,plain,
meet(X1,composition(join(X2,one),X1)) = X1,
inference(spm,[status(thm)],[c_0_94,c_0_82]) ).
cnf(c_0_141,plain,
join(X1,converse(meet(X2,converse(X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_85]),c_0_19]) ).
cnf(c_0_142,plain,
meet(complement(one),converse(complement(one))) = complement(one),
inference(spm,[status(thm)],[c_0_70,c_0_135]) ).
cnf(c_0_143,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_126]),c_0_19]),c_0_19]) ).
cnf(c_0_144,plain,
meet(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_100]),c_0_111]),c_0_48]) ).
cnf(c_0_145,plain,
meet(X1,meet(complement(X1),X2)) = complement(top),
inference(spm,[status(thm)],[c_0_41,c_0_137]) ).
cnf(c_0_146,plain,
composition(top,complement(top)) = complement(top),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_138]),c_0_75]),c_0_82]),c_0_68]) ).
cnf(c_0_147,negated_conjecture,
composition(esk1_0,join(esk1_0,converse(X1))) = esk1_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_139]),c_0_19]) ).
cnf(c_0_148,plain,
meet(X1,composition(top,X1)) = X1,
inference(spm,[status(thm)],[c_0_140,c_0_68]) ).
cnf(c_0_149,plain,
join(X1,join(X2,X3)) = join(X2,join(X3,X1)),
inference(spm,[status(thm)],[c_0_31,c_0_29]) ).
cnf(c_0_150,plain,
join(complement(one),converse(complement(one))) = complement(one),
inference(spm,[status(thm)],[c_0_141,c_0_142]) ).
cnf(c_0_151,plain,
converse(complement(converse(complement(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_143]),c_0_48]),c_0_144]) ).
cnf(c_0_152,plain,
meet(X1,complement(top)) = complement(top),
inference(spm,[status(thm)],[c_0_145,c_0_145]) ).
cnf(c_0_153,plain,
composition(X1,complement(top)) = complement(top),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_146]),c_0_45]),c_0_146]),c_0_65]) ).
cnf(c_0_154,negated_conjecture,
composition(esk1_0,join(esk1_0,X1)) = esk1_0,
inference(spm,[status(thm)],[c_0_147,c_0_19]) ).
cnf(c_0_155,plain,
join(X1,join(X2,composition(top,X1))) = join(composition(top,X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_148]),c_0_149]) ).
cnf(c_0_156,plain,
join(converse(X1),composition(converse(X2),X3)) = converse(join(X1,composition(converse(X3),X2))),
inference(spm,[status(thm)],[c_0_58,c_0_21]) ).
cnf(c_0_157,plain,
converse(complement(one)) = complement(one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_150]),c_0_48]),c_0_142]) ).
cnf(c_0_158,plain,
complement(converse(complement(X1))) = converse(X1),
inference(spm,[status(thm)],[c_0_19,c_0_151]) ).
cnf(c_0_159,negated_conjecture,
meet(composition(esk1_0,X1),complement(esk1_0)) = complement(top),
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_110,c_0_79]),c_0_152]),c_0_153]),c_0_152]),c_0_65]),c_0_152]),c_0_153]),c_0_152]) ).
cnf(c_0_160,plain,
meet(X1,join(X2,join(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_106,c_0_31]) ).
cnf(c_0_161,plain,
meet(X1,composition(X1,join(X2,one))) = X1,
inference(spm,[status(thm)],[c_0_94,c_0_124]) ).
cnf(c_0_162,negated_conjecture,
composition(esk1_0,join(composition(top,esk1_0),X1)) = esk1_0,
inference(spm,[status(thm)],[c_0_154,c_0_155]) ).
cnf(c_0_163,negated_conjecture,
join(composition(top,esk1_0),converse(X1)) = converse(join(X1,composition(top,esk1_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_112]),c_0_112]),c_0_29]) ).
cnf(c_0_164,plain,
join(composition(X1,converse(X2)),converse(X3)) = converse(join(composition(X2,converse(X1)),X3)),
inference(spm,[status(thm)],[c_0_58,c_0_101]) ).
cnf(c_0_165,plain,
composition(join(X1,converse(X2)),converse(X3)) = converse(composition(X3,join(converse(X1),X2))),
inference(spm,[status(thm)],[c_0_18,c_0_61]) ).
cnf(c_0_166,plain,
composition(join(X1,one),X1) = composition(X1,join(X1,one)),
inference(spm,[status(thm)],[c_0_82,c_0_124]) ).
fof(c_0_167,plain,
! [X14,X15,X16] : join(meet(composition(X14,X15),X16),meet(composition(meet(X14,composition(X16,converse(X15))),X15),X16)) = meet(composition(meet(X14,composition(X16,converse(X15))),X15),X16),
inference(variable_rename,[status(thm)],[modular_law_2]) ).
cnf(c_0_168,plain,
join(X1,complement(meet(X2,X1))) = top,
inference(spm,[status(thm)],[c_0_137,c_0_48]) ).
fof(c_0_169,plain,
! [X8,X9,X10] : join(meet(composition(X8,X9),X10),composition(meet(X8,composition(X10,converse(X9))),meet(X9,composition(converse(X8),X10)))) = composition(meet(X8,composition(X10,converse(X9))),meet(X9,composition(converse(X8),X10))),
inference(variable_rename,[status(thm)],[dedekind_law]) ).
cnf(c_0_170,plain,
join(complement(one),converse(X1)) = converse(join(complement(one),X1)),
inference(spm,[status(thm)],[c_0_58,c_0_157]) ).
cnf(c_0_171,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[c_0_59,c_0_158]) ).
cnf(c_0_172,negated_conjecture,
meet(complement(esk1_0),composition(esk1_0,X1)) = complement(top),
inference(spm,[status(thm)],[c_0_48,c_0_159]) ).
cnf(c_0_173,plain,
meet(meet(X1,X2),join(X3,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_160,c_0_85]) ).
cnf(c_0_174,plain,
meet(X1,composition(X1,top)) = X1,
inference(spm,[status(thm)],[c_0_161,c_0_68]) ).
cnf(c_0_175,negated_conjecture,
composition(esk1_0,converse(join(X1,composition(top,esk1_0)))) = esk1_0,
inference(spm,[status(thm)],[c_0_162,c_0_163]) ).
cnf(c_0_176,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_74,c_0_18]),c_0_164]),c_0_165]) ).
cnf(c_0_177,plain,
converse(composition(top,join(X1,converse(X2)))) = composition(join(converse(X1),X2),top),
inference(spm,[status(thm)],[c_0_83,c_0_109]) ).
cnf(c_0_178,plain,
composition(join(one,X1),X1) = composition(X1,join(one,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_101,c_0_166]),c_0_29]),c_0_84]),c_0_18]),c_0_19]),c_0_29]),c_0_84]),c_0_19]) ).
cnf(c_0_179,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_167]) ).
cnf(c_0_180,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(spm,[status(thm)],[c_0_78,c_0_59]) ).
cnf(c_0_181,plain,
meet(X1,meet(X2,complement(X1))) = complement(top),
inference(spm,[status(thm)],[c_0_41,c_0_168]) ).
cnf(c_0_182,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_169]) ).
cnf(c_0_183,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_77,c_0_170]),c_0_171]),c_0_77]),c_0_171]),c_0_48]),c_0_48]) ).
cnf(c_0_184,plain,
complement(join(X1,join(X2,complement(X3)))) = meet(complement(join(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_70,c_0_31]) ).
cnf(c_0_185,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_31,c_0_76]) ).
cnf(c_0_186,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_93,c_0_172]),c_0_65]),c_0_48]) ).
cnf(c_0_187,plain,
meet(X1,join(X2,composition(X1,top))) = X1,
inference(spm,[status(thm)],[c_0_173,c_0_174]) ).
cnf(c_0_188,negated_conjecture,
composition(esk1_0,composition(join(converse(esk1_0),X1),top)) = esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_176]),c_0_29]),c_0_177]) ).
cnf(c_0_189,plain,
composition(join(X1,complement(one)),top) = composition(top,join(X1,complement(one))),
inference(spm,[status(thm)],[c_0_178,c_0_108]) ).
cnf(c_0_190,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_179,c_0_48]),c_0_48]) ).
cnf(c_0_191,plain,
composition(top,converse(X1)) = converse(composition(X1,top)),
inference(spm,[status(thm)],[c_0_18,c_0_75]) ).
cnf(c_0_192,plain,
converse(complement(join(converse(X1),X2))) = complement(join(X1,converse(X2))),
inference(spm,[status(thm)],[c_0_171,c_0_61]) ).
cnf(c_0_193,plain,
join(converse(complement(X1)),complement(X2)) = complement(meet(converse(X1),X2)),
inference(spm,[status(thm)],[c_0_180,c_0_171]) ).
cnf(c_0_194,plain,
join(complement(X1),converse(complement(X2))) = complement(meet(X1,converse(X2))),
inference(spm,[status(thm)],[c_0_180,c_0_171]) ).
cnf(c_0_195,plain,
meet(X1,complement(join(X2,X1))) = complement(top),
inference(spm,[status(thm)],[c_0_181,c_0_105]) ).
cnf(c_0_196,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_182,c_0_30]),c_0_34]),c_0_34]),c_0_82]),c_0_34]),c_0_29]),c_0_76]),c_0_34]) ).
cnf(c_0_197,plain,
meet(one,converse(X1)) = converse(meet(one,X1)),
inference(spm,[status(thm)],[c_0_183,c_0_59]) ).
cnf(c_0_198,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_184,c_0_180]),c_0_70]),c_0_70]) ).
cnf(c_0_199,negated_conjecture,
join(esk1_0,join(composition(esk1_0,X1),X2)) = join(esk1_0,X2),
inference(spm,[status(thm)],[c_0_185,c_0_186]) ).
cnf(c_0_200,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_33,c_0_89]),c_0_19]),c_0_50]),c_0_57]),c_0_124]),c_0_68]) ).
cnf(c_0_201,plain,
meet(X1,composition(join(X2,X1),top)) = X1,
inference(spm,[status(thm)],[c_0_187,c_0_74]) ).
cnf(c_0_202,negated_conjecture,
composition(esk1_0,converse(join(esk1_0,complement(one)))) = esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_188,c_0_189]),c_0_102]),c_0_29]),c_0_170]),c_0_29]) ).
cnf(c_0_203,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_190,c_0_191]),c_0_111]),c_0_98]),c_0_74]),c_0_76]),c_0_98]) ).
cnf(c_0_204,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_192,c_0_193]),c_0_59]),c_0_194]),c_0_59]) ).
cnf(c_0_205,plain,
meet(composition(X1,X2),complement(composition(X1,join(X2,one)))) = complement(top),
inference(spm,[status(thm)],[c_0_195,c_0_124]) ).
cnf(c_0_206,plain,
composition(converse(meet(one,X1)),meet(X1,one)) = meet(X1,one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_34]),c_0_197]) ).
cnf(c_0_207,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_198,c_0_59]) ).
cnf(c_0_208,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_105]),c_0_59]),c_0_59]),c_0_29]) ).
cnf(c_0_209,negated_conjecture,
join(esk1_0,composition(join(esk1_0,X1),X2)) = join(esk1_0,composition(X1,X2)),
inference(spm,[status(thm)],[c_0_199,c_0_74]) ).
cnf(c_0_210,negated_conjecture,
composition(complement(esk1_0),composition(top,X1)) = composition(complement(esk1_0),X1),
inference(spm,[status(thm)],[c_0_90,c_0_200]) ).
cnf(c_0_211,plain,
composition(top,join(X1,one)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_82]),c_0_22]) ).
cnf(c_0_212,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_116,c_0_105]),c_0_59]),c_0_59]) ).
cnf(c_0_213,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_201,c_0_124]),c_0_90]),c_0_131]) ).
cnf(c_0_214,negated_conjecture,
composition(meet(esk1_0,one),esk1_0) = 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_196,c_0_202]),c_0_48]),c_0_48]),c_0_94]),c_0_48]),c_0_94]) ).
cnf(c_0_215,plain,
composition(converse(meet(one,composition(X1,top))),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_203,c_0_197]),c_0_34]) ).
cnf(c_0_216,plain,
converse(meet(X1,converse(X2))) = meet(converse(X1),X2),
inference(spm,[status(thm)],[c_0_19,c_0_204]) ).
cnf(c_0_217,plain,
meet(X1,converse(meet(one,complement(X1)))) = complement(top),
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_205,c_0_206]),c_0_29]),c_0_85]),c_0_22]),c_0_171]),c_0_207]),c_0_197]),c_0_116]),c_0_48]) ).
cnf(c_0_218,plain,
meet(converse(meet(one,X1)),X2) = meet(one,meet(converse(X1),X2)),
inference(spm,[status(thm)],[c_0_207,c_0_197]) ).
cnf(c_0_219,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_85]),c_0_85]) ).
cnf(c_0_220,plain,
meet(join(X1,X2),join(X2,complement(X1))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_208]),c_0_48]),c_0_106]) ).
cnf(c_0_221,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_209,c_0_100]),c_0_171]),c_0_19]) ).
cnf(c_0_222,negated_conjecture,
composition(complement(esk1_0),join(X1,one)) = complement(esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_210,c_0_211]),c_0_200]) ).
cnf(c_0_223,plain,
meet(join(X1,X2),complement(X1)) = meet(X2,complement(X1)),
inference(spm,[status(thm)],[c_0_48,c_0_212]) ).
cnf(c_0_224,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_19,c_0_176]),c_0_19]) ).
cnf(c_0_225,negated_conjecture,
meet(esk1_0,composition(meet(esk1_0,one),top)) = esk1_0,
inference(spm,[status(thm)],[c_0_213,c_0_214]) ).
cnf(c_0_226,plain,
meet(X1,meet(composition(X2,X3),composition(X2,meet(X3,composition(converse(X2),meet(X1,composition(X2,X3))))))) = meet(X1,composition(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_129]),c_0_76]),c_0_207]) ).
cnf(c_0_227,plain,
composition(converse(X1),meet(one,composition(X1,top))) = converse(X1),
inference(spm,[status(thm)],[c_0_21,c_0_215]) ).
cnf(c_0_228,plain,
meet(composition(X1,top),composition(X1,X2)) = composition(X1,X2),
inference(spm,[status(thm)],[c_0_48,c_0_213]) ).
cnf(c_0_229,plain,
converse(meet(X1,meet(X2,converse(X3)))) = meet(converse(meet(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_216,c_0_207]) ).
cnf(c_0_230,plain,
meet(one,meet(X1,converse(X1))) = converse(meet(one,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_93,c_0_217]),c_0_59]),c_0_218]),c_0_65]),c_0_59]),c_0_48]) ).
cnf(c_0_231,plain,
meet(X1,meet(X2,meet(X3,X1))) = meet(X2,meet(X3,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_219]),c_0_48]) ).
cnf(c_0_232,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(spm,[status(thm)],[c_0_48,c_0_207]) ).
cnf(c_0_233,plain,
join(X1,join(meet(complement(X1),X2),X3)) = join(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_104]),c_0_31]) ).
cnf(c_0_234,plain,
meet(X1,meet(composition(top,X1),X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_207,c_0_148]) ).
cnf(c_0_235,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_220,c_0_221]),c_0_29]),c_0_124]),c_0_222]),c_0_223]) ).
cnf(c_0_236,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_224,c_0_19]) ).
cnf(c_0_237,plain,
join(meet(X1,X2),meet(complement(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_93,c_0_48]) ).
cnf(c_0_238,negated_conjecture,
meet(esk1_0,complement(composition(meet(esk1_0,one),top))) = complement(top),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_225]),c_0_46]),c_0_48]) ).
cnf(c_0_239,negated_conjecture,
join(esk1_0,composition(X1,top)) = composition(join(X1,esk1_0),top),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_72]),c_0_29]) ).
cnf(c_0_240,plain,
converse(meet(one,composition(converse(X1),X2))) = meet(one,composition(converse(X2),X1)),
inference(spm,[status(thm)],[c_0_197,c_0_21]) ).
cnf(c_0_241,plain,
meet(one,composition(X1,converse(X1))) = meet(one,composition(X1,top)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_226,c_0_227]),c_0_98]),c_0_228]) ).
cnf(c_0_242,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_229,c_0_230]),c_0_19]),c_0_218]),c_0_48]),c_0_230]) ).
cnf(c_0_243,plain,
meet(X1,meet(join(X2,join(X3,X1)),X4)) = meet(X4,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_231,c_0_160]),c_0_232]) ).
cnf(c_0_244,plain,
composition(meet(one,X1),meet(one,X1)) = meet(one,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_30]),c_0_22]) ).
cnf(c_0_245,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_136,c_0_233]),c_0_136]),c_0_59]),c_0_48]) ).
cnf(c_0_246,negated_conjecture,
meet(X1,composition(complement(esk1_0),X1)) = meet(X1,complement(esk1_0)),
inference(spm,[status(thm)],[c_0_234,c_0_235]) ).
cnf(c_0_247,plain,
composition(converse(X1),meet(X2,converse(X3))) = converse(composition(meet(converse(X2),X3),X1)),
inference(spm,[status(thm)],[c_0_18,c_0_204]) ).
cnf(c_0_248,plain,
composition(X1,meet(X2,converse(composition(top,X1)))) = 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_110,c_0_98]),c_0_83]),c_0_83]),c_0_111]),c_0_236]),c_0_76]) ).
cnf(c_0_249,plain,
meet(converse(X1),converse(X2)) = converse(meet(X1,X2)),
inference(spm,[status(thm)],[c_0_204,c_0_19]) ).
cnf(c_0_250,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_237,c_0_238]),c_0_105]),c_0_239]),c_0_29]),c_0_76]),c_0_72]),c_0_180]),c_0_98]) ).
cnf(c_0_251,plain,
meet(composition(X1,X2),composition(join(X3,X1),X2)) = composition(X1,X2),
inference(spm,[status(thm)],[c_0_106,c_0_74]) ).
cnf(c_0_252,plain,
meet(one,composition(converse(X1),X1)) = meet(one,composition(top,X1)),
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_83]),c_0_197]),c_0_19]),c_0_19]) ).
cnf(c_0_253,plain,
converse(meet(X1,one)) = meet(X1,one),
inference(spm,[status(thm)],[c_0_242,c_0_243]) ).
cnf(c_0_254,plain,
composition(meet(X1,one),meet(X1,one)) = meet(X1,one),
inference(spm,[status(thm)],[c_0_244,c_0_129]) ).
cnf(c_0_255,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_245,c_0_246]),c_0_245]),c_0_48]) ).
cnf(c_0_256,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_247,c_0_248]),c_0_191]),c_0_249]),c_0_21]) ).
cnf(c_0_257,negated_conjecture,
composition(meet(esk1_0,one),top) = esk1_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_250]),c_0_59]) ).
cnf(c_0_258,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_209,c_0_76]),c_0_124]),c_0_125]) ).
cnf(c_0_259,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_251,c_0_76]),c_0_48]) ).
cnf(c_0_260,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_252,c_0_253]),c_0_254]),c_0_129]) ).
cnf(c_0_261,negated_conjecture,
join(composition(meet(esk1_0,one),esk2_0),meet(esk1_0,esk2_0)) != meet(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_262,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_255,c_0_74]),c_0_48]) ).
cnf(c_0_263,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_256,c_0_257]),c_0_253]),c_0_253]) ).
cnf(c_0_264,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_220,c_0_258]),c_0_127]) ).
cnf(c_0_265,plain,
meet(X1,composition(meet(X2,one),X1)) = composition(meet(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_259,c_0_260]),c_0_34]) ).
cnf(c_0_266,plain,
join(complement(X1),meet(X1,X2)) = join(complement(X1),X2),
inference(spm,[status(thm)],[c_0_104,c_0_59]) ).
cnf(c_0_267,plain,
meet(X1,composition(join(one,X2),X1)) = X1,
inference(spm,[status(thm)],[c_0_140,c_0_29]) ).
cnf(c_0_268,negated_conjecture,
join(meet(esk1_0,esk2_0),composition(meet(esk1_0,one),esk2_0)) != meet(esk1_0,esk2_0),
inference(rw,[status(thm)],[c_0_261,c_0_29]) ).
cnf(c_0_269,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_262,c_0_263]),c_0_207]),c_0_136]),c_0_48]),c_0_264]),c_0_265]),c_0_266]),c_0_29]),c_0_267]) ).
cnf(c_0_270,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_268,c_0_269]),c_0_48]),c_0_62])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : REL021+2 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.11 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n017.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 2400
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Oct 2 14:47:41 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.15/0.42 Running first-order model finding
% 0.15/0.42 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.wKER6ooVQb/E---3.1_21820.p
% 527.80/67.20 # Version: 3.1pre001
% 527.80/67.20 # Preprocessing class: FSMSSMSSSSSNFFN.
% 527.80/67.20 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 527.80/67.20 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 527.80/67.20 # Starting new_bool_3 with 300s (1) cores
% 527.80/67.20 # Starting new_bool_1 with 300s (1) cores
% 527.80/67.20 # Starting sh5l with 300s (1) cores
% 527.80/67.20 # new_bool_1 with pid 21899 completed with status 0
% 527.80/67.20 # Result found by new_bool_1
% 527.80/67.20 # Preprocessing class: FSMSSMSSSSSNFFN.
% 527.80/67.20 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 527.80/67.20 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 527.80/67.20 # Starting new_bool_3 with 300s (1) cores
% 527.80/67.20 # Starting new_bool_1 with 300s (1) cores
% 527.80/67.20 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 527.80/67.20 # Search class: FUUPM-FFMF21-DFFFFFNN
% 527.80/67.20 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 527.80/67.20 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 181s (1) cores
% 527.80/67.20 # H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with pid 21904 completed with status 0
% 527.80/67.20 # Result found by H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S
% 527.80/67.20 # Preprocessing class: FSMSSMSSSSSNFFN.
% 527.80/67.20 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 527.80/67.20 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 527.80/67.20 # Starting new_bool_3 with 300s (1) cores
% 527.80/67.20 # Starting new_bool_1 with 300s (1) cores
% 527.80/67.20 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 527.80/67.20 # Search class: FUUPM-FFMF21-DFFFFFNN
% 527.80/67.20 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 527.80/67.20 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 181s (1) cores
% 527.80/67.20 # Preprocessing time : 0.001 s
% 527.80/67.20 # Presaturation interreduction done
% 527.80/67.20
% 527.80/67.20 # Proof found!
% 527.80/67.20 # SZS status Theorem
% 527.80/67.20 # SZS output start CNFRefutation
% See solution above
% 527.80/67.20 # Parsed axioms : 17
% 527.80/67.20 # Removed by relevancy pruning/SinE : 1
% 527.80/67.20 # Initial clauses : 17
% 527.80/67.20 # Removed in clause preprocessing : 0
% 527.80/67.20 # Initial clauses in saturation : 17
% 527.80/67.20 # Processed clauses : 62943
% 527.80/67.20 # ...of these trivial : 34983
% 527.80/67.20 # ...subsumed : 23795
% 527.80/67.20 # ...remaining for further processing : 4165
% 527.80/67.20 # Other redundant clauses eliminated : 0
% 527.80/67.20 # Clauses deleted for lack of memory : 359689
% 527.80/67.20 # Backward-subsumed : 1
% 527.80/67.20 # Backward-rewritten : 890
% 527.80/67.20 # Generated clauses : 3155073
% 527.80/67.20 # ...of the previous two non-redundant : 2049410
% 527.80/67.20 # ...aggressively subsumed : 0
% 527.80/67.20 # Contextual simplify-reflections : 0
% 527.80/67.20 # Paramodulations : 3155073
% 527.80/67.20 # Factorizations : 0
% 527.80/67.20 # NegExts : 0
% 527.80/67.20 # Equation resolutions : 0
% 527.80/67.20 # Total rewrite steps : 8658585
% 527.80/67.20 # Propositional unsat checks : 0
% 527.80/67.20 # Propositional check models : 0
% 527.80/67.20 # Propositional check unsatisfiable : 0
% 527.80/67.20 # Propositional clauses : 0
% 527.80/67.20 # Propositional clauses after purity: 0
% 527.80/67.20 # Propositional unsat core size : 0
% 527.80/67.20 # Propositional preprocessing time : 0.000
% 527.80/67.20 # Propositional encoding time : 0.000
% 527.80/67.20 # Propositional solver time : 0.000
% 527.80/67.20 # Success case prop preproc time : 0.000
% 527.80/67.20 # Success case prop encoding time : 0.000
% 527.80/67.20 # Success case prop solver time : 0.000
% 527.80/67.20 # Current number of processed clauses : 3257
% 527.80/67.20 # Positive orientable unit clauses : 3214
% 527.80/67.20 # Positive unorientable unit clauses: 43
% 527.80/67.20 # Negative unit clauses : 0
% 527.80/67.20 # Non-unit-clauses : 0
% 527.80/67.20 # Current number of unprocessed clauses: 1212815
% 527.80/67.20 # ...number of literals in the above : 1212815
% 527.80/67.20 # Current number of archived formulas : 0
% 527.80/67.20 # Current number of archived clauses : 908
% 527.80/67.20 # Clause-clause subsumption calls (NU) : 0
% 527.80/67.20 # Rec. Clause-clause subsumption calls : 0
% 527.80/67.20 # Non-unit clause-clause subsumptions : 0
% 527.80/67.20 # Unit Clause-clause subsumption calls : 1434
% 527.80/67.20 # Rewrite failures with RHS unbound : 0
% 527.80/67.20 # BW rewrite match attempts : 28736
% 527.80/67.20 # BW rewrite match successes : 1526
% 527.80/67.20 # Condensation attempts : 0
% 527.80/67.20 # Condensation successes : 0
% 527.80/67.20 # Termbank termtop insertions : 69001538
% 527.80/67.20
% 527.80/67.20 # -------------------------------------------------
% 527.80/67.20 # User time : 64.043 s
% 527.80/67.20 # System time : 1.708 s
% 527.80/67.20 # Total time : 65.752 s
% 527.80/67.20 # Maximum resident set size: 1772 pages
% 527.80/67.20
% 527.80/67.20 # -------------------------------------------------
% 527.80/67.20 # User time : 64.049 s
% 527.80/67.20 # System time : 1.709 s
% 527.80/67.20 # Total time : 65.758 s
% 527.80/67.20 # Maximum resident set size: 1728 pages
% 527.80/67.20 % E---3.1 exiting
%------------------------------------------------------------------------------