TSTP Solution File: REL020+2 by E-SAT---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : REL020+2 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 02:32:13 EDT 2024
% Result : Theorem 86.41s 11.39s
% Output : CNFRefutation 86.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 16
% Syntax : Number of formulae : 217 ( 214 unt; 0 def)
% Number of atoms : 220 ( 219 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 : 7 ( 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 : 391 ( 33 sgn 70 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(converse_multiplicativity,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).
fof(converse_idempotence,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
fof(composition_identity,axiom,
! [X1] : composition(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_identity) ).
fof(converse_cancellativity,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).
fof(maddux1_join_commutativity,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',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/benchmark/Axioms/REL001+0.ax',maddux2_join_associativity) ).
fof(def_top,axiom,
! [X1] : top = join(X1,complement(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',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/benchmark/Axioms/REL001+0.ax',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/benchmark/Axioms/REL001+0.ax',maddux4_definiton_of_meet) ).
fof(converse_additivity,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',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/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
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/benchmark/Axioms/REL001+1.ax',modular_law_2) ).
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/benchmark/Axioms/REL001+1.ax',modular_law_1) ).
fof(composition_associativity,axiom,
! [X1,X2,X3] : composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',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/benchmark/Axioms/REL001+1.ax',dedekind_law) ).
fof(goals,conjecture,
! [X1,X2] :
( composition(X1,top) = X1
=> composition(meet(X1,one),X2) = meet(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c_0_16,plain,
! [X23,X24] : converse(composition(X23,X24)) = composition(converse(X24),converse(X23)),
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,
! [X25] : composition(X25,one) = X25,
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,
! [X29,X30] : join(composition(converse(X29),complement(composition(X29,X30))),complement(X30)) = complement(X30),
inference(variable_rename,[status(thm)],[converse_cancellativity]) ).
fof(c_0_24,plain,
! [X31,X32] : join(X31,X32) = join(X32,X31),
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,
! [X33,X34,X35] : join(X33,join(X34,X35)) = join(join(X33,X34),X35),
inference(variable_rename,[status(thm)],[maddux2_join_associativity]) ).
fof(c_0_27,plain,
! [X26] : top = join(X26,complement(X26)),
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,
! [X27,X28] : X27 = join(complement(join(complement(X27),complement(X28))),complement(join(complement(X27),X28))),
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]) ).
cnf(c_0_56,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_57,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_50,c_0_56]) ).
cnf(c_0_58,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_39,c_0_57]) ).
cnf(c_0_59,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_31,c_0_58]) ).
cnf(c_0_60,plain,
complement(join(X1,complement(X2))) = meet(complement(X1),X2),
inference(spm,[status(thm)],[c_0_41,c_0_57]) ).
fof(c_0_61,plain,
! [X37,X38] : converse(join(X37,X38)) = join(converse(X37),converse(X38)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
cnf(c_0_62,plain,
join(X1,meet(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_44]),c_0_29]) ).
cnf(c_0_63,plain,
complement(join(complement(X1),X2)) = meet(complement(X2),X1),
inference(spm,[status(thm)],[c_0_60,c_0_29]) ).
cnf(c_0_64,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_57,c_0_60]) ).
cnf(c_0_65,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_66,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_62,c_0_48]) ).
cnf(c_0_67,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_63,c_0_62]),c_0_57]),c_0_64]),c_0_48]) ).
cnf(c_0_68,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(spm,[status(thm)],[c_0_65,c_0_19]) ).
cnf(c_0_69,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_31,c_0_66]) ).
cnf(c_0_70,plain,
join(meet(X1,X2),meet(complement(X2),X1)) = X1,
inference(rw,[status(thm)],[c_0_44,c_0_63]) ).
cnf(c_0_71,plain,
meet(X1,join(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_67,c_0_57]) ).
cnf(c_0_72,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_59,c_0_29]) ).
cnf(c_0_73,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(spm,[status(thm)],[c_0_68,c_0_32]) ).
cnf(c_0_74,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_29,c_0_45]) ).
cnf(c_0_75,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_76,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_77,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_78,plain,
converse(join(one,X1)) = join(one,converse(X1)),
inference(spm,[status(thm)],[c_0_65,c_0_30]) ).
cnf(c_0_79,plain,
meet(complement(X1),complement(X2)) = complement(join(X1,X2)),
inference(spm,[status(thm)],[c_0_60,c_0_57]) ).
cnf(c_0_80,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_81,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_63,c_0_75]),c_0_63]),c_0_57]),c_0_48]) ).
cnf(c_0_82,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_62]),c_0_48]) ).
cnf(c_0_83,plain,
join(X1,join(X2,meet(X1,X3))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_77,c_0_62]) ).
cnf(c_0_84,plain,
meet(top,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_52,c_0_41]) ).
cnf(c_0_85,plain,
join(one,converse(complement(one))) = converse(top),
inference(spm,[status(thm)],[c_0_78,c_0_32]) ).
cnf(c_0_86,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_75,c_0_79]) ).
cnf(c_0_87,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(rw,[status(thm)],[c_0_73,c_0_80]) ).
cnf(c_0_88,plain,
join(X1,complement(top)) = X1,
inference(rw,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_89,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_81,c_0_81]),c_0_64]),c_0_57]),c_0_48]),c_0_82]) ).
cnf(c_0_90,plain,
join(meet(X1,X2),complement(X2)) = join(complement(X2),X1),
inference(spm,[status(thm)],[c_0_83,c_0_70]) ).
cnf(c_0_91,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_66]),c_0_48]) ).
cnf(c_0_92,plain,
meet(top,X1) = X1,
inference(spm,[status(thm)],[c_0_84,c_0_56]) ).
cnf(c_0_93,plain,
join(one,converse(complement(one))) = top,
inference(rw,[status(thm)],[c_0_85,c_0_80]) ).
cnf(c_0_94,plain,
join(complement(top),X1) = X1,
inference(rw,[status(thm)],[c_0_53,c_0_56]) ).
cnf(c_0_95,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_88]) ).
cnf(c_0_96,plain,
meet(X1,join(complement(X1),X2)) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]) ).
cnf(c_0_97,plain,
meet(X1,top) = X1,
inference(spm,[status(thm)],[c_0_48,c_0_92]) ).
cnf(c_0_98,plain,
join(one,complement(converse(complement(one)))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_93]),c_0_88]) ).
fof(c_0_99,plain,
! [X20,X21,X22] : composition(join(X20,X21),X22) = join(composition(X20,X22),composition(X21,X22)),
inference(variable_rename,[status(thm)],[composition_distributivity]) ).
cnf(c_0_100,plain,
composition(converse(X1),complement(composition(X1,top))) = complement(top),
inference(spm,[status(thm)],[c_0_33,c_0_94]) ).
cnf(c_0_101,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_95]),c_0_19]),c_0_19]) ).
cnf(c_0_102,plain,
meet(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_87]),c_0_97]),c_0_48]) ).
cnf(c_0_103,plain,
join(X1,converse(meet(X2,converse(X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_66]),c_0_19]) ).
cnf(c_0_104,plain,
meet(complement(one),converse(complement(one))) = complement(one),
inference(spm,[status(thm)],[c_0_60,c_0_98]) ).
cnf(c_0_105,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_106,plain,
composition(top,complement(composition(top,top))) = complement(top),
inference(spm,[status(thm)],[c_0_100,c_0_80]) ).
cnf(c_0_107,plain,
converse(complement(converse(complement(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_101]),c_0_48]),c_0_102]) ).
cnf(c_0_108,plain,
join(complement(one),converse(complement(one))) = complement(one),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
fof(c_0_109,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_110,plain,
composition(X1,complement(composition(top,top))) = complement(top),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_94]),c_0_74]),c_0_106]) ).
cnf(c_0_111,plain,
complement(converse(complement(X1))) = converse(X1),
inference(spm,[status(thm)],[c_0_19,c_0_107]) ).
cnf(c_0_112,plain,
converse(complement(one)) = complement(one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_108]),c_0_48]),c_0_104]) ).
cnf(c_0_113,plain,
join(X1,composition(X2,X1)) = composition(join(one,X2),X1),
inference(spm,[status(thm)],[c_0_105,c_0_34]) ).
cnf(c_0_114,plain,
join(one,converse(meet(one,X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_62]),c_0_30]) ).
fof(c_0_115,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_116,plain,
composition(join(X1,converse(X2)),converse(X3)) = converse(composition(X3,join(converse(X1),X2))),
inference(spm,[status(thm)],[c_0_18,c_0_68]) ).
cnf(c_0_117,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_109]) ).
cnf(c_0_118,plain,
complement(composition(top,top)) = complement(top),
inference(spm,[status(thm)],[c_0_34,c_0_110]) ).
fof(c_0_119,plain,
! [X17,X18,X19] : composition(X17,composition(X18,X19)) = composition(composition(X17,X18),X19),
inference(variable_rename,[status(thm)],[composition_associativity]) ).
cnf(c_0_120,plain,
complement(join(X1,join(X2,complement(X3)))) = meet(complement(join(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_60,c_0_31]) ).
cnf(c_0_121,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(spm,[status(thm)],[c_0_64,c_0_57]) ).
cnf(c_0_122,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[c_0_57,c_0_111]) ).
cnf(c_0_123,plain,
converse(join(complement(one),X1)) = join(complement(one),converse(X1)),
inference(spm,[status(thm)],[c_0_65,c_0_112]) ).
cnf(c_0_124,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_75,c_0_48]) ).
cnf(c_0_125,plain,
join(X1,composition(converse(meet(one,X2)),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_34]) ).
cnf(c_0_126,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_115]) ).
cnf(c_0_127,plain,
converse(join(composition(converse(X1),X2),X3)) = join(composition(converse(X2),X1),converse(X3)),
inference(spm,[status(thm)],[c_0_65,c_0_21]) ).
cnf(c_0_128,plain,
join(composition(X1,converse(X2)),converse(composition(X2,X3))) = converse(composition(X2,join(converse(X1),X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_18]),c_0_116]) ).
cnf(c_0_129,plain,
meet(X1,join(X2,join(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_76,c_0_31]) ).
cnf(c_0_130,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_117,c_0_48]),c_0_48]) ).
cnf(c_0_131,plain,
composition(top,top) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_118]),c_0_88]) ).
cnf(c_0_132,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_133,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_120,c_0_121]),c_0_60]),c_0_60]) ).
cnf(c_0_134,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_122,c_0_123]),c_0_63]),c_0_122]),c_0_63]),c_0_48]),c_0_48]) ).
cnf(c_0_135,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_124,c_0_79]) ).
cnf(c_0_136,plain,
join(X1,composition(X1,meet(one,X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_125]),c_0_19]),c_0_18]),c_0_19]) ).
fof(c_0_137,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_138,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_126,c_0_48]),c_0_48]) ).
cnf(c_0_139,plain,
composition(converse(X1),top) = converse(composition(top,X1)),
inference(spm,[status(thm)],[c_0_21,c_0_80]) ).
cnf(c_0_140,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_19]),c_0_19]),c_0_19]),c_0_19]) ).
cnf(c_0_141,plain,
meet(meet(X1,X2),join(X3,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_129,c_0_66]) ).
cnf(c_0_142,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_130,c_0_131]),c_0_92]),c_0_80]),c_0_92]),c_0_132]),c_0_131]),c_0_62]),c_0_80]),c_0_92]),c_0_132]),c_0_131]) ).
cnf(c_0_143,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_75]),c_0_31]) ).
cnf(c_0_144,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_133,c_0_57]) ).
cnf(c_0_145,plain,
meet(one,converse(X1)) = converse(meet(one,X1)),
inference(spm,[status(thm)],[c_0_134,c_0_57]) ).
cnf(c_0_146,plain,
meet(join(X1,X2),join(X2,complement(X1))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_135]),c_0_48]),c_0_76]) ).
cnf(c_0_147,plain,
join(X1,composition(X1,meet(X2,one))) = X1,
inference(spm,[status(thm)],[c_0_136,c_0_91]) ).
cnf(c_0_148,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_137]) ).
cnf(c_0_149,plain,
join(X1,composition(meet(one,X2),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_62]),c_0_34]) ).
cnf(c_0_150,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_66]),c_0_66]) ).
cnf(c_0_151,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_138,c_0_139]),c_0_97]),c_0_92]),c_0_140]),c_0_62]),c_0_92]) ).
cnf(c_0_152,plain,
meet(X1,join(X2,composition(X1,top))) = X1,
inference(spm,[status(thm)],[c_0_141,c_0_142]) ).
cnf(c_0_153,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_31,c_0_62]) ).
cnf(c_0_154,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_96,c_0_143]),c_0_96]),c_0_57]),c_0_48]) ).
cnf(c_0_155,plain,
join(X1,join(X2,meet(X3,X1))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_77,c_0_66]) ).
cnf(c_0_156,plain,
meet(converse(meet(one,X1)),X2) = meet(one,meet(converse(X1),X2)),
inference(spm,[status(thm)],[c_0_144,c_0_145]) ).
cnf(c_0_157,plain,
meet(X1,composition(X1,meet(X2,one))) = composition(X1,meet(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_89]) ).
cnf(c_0_158,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(spm,[status(thm)],[c_0_148,c_0_30]),c_0_34]),c_0_34]),c_0_34]),c_0_149]) ).
cnf(c_0_159,plain,
meet(X1,meet(X2,meet(X3,X1))) = meet(X2,meet(X3,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_150]),c_0_48]) ).
cnf(c_0_160,plain,
composition(X1,converse(composition(top,X1))) = composition(X1,top),
inference(spm,[status(thm)],[c_0_151,c_0_92]) ).
cnf(c_0_161,plain,
meet(X1,composition(join(X2,X1),top)) = X1,
inference(spm,[status(thm)],[c_0_152,c_0_105]) ).
cnf(c_0_162,plain,
complement(meet(X1,join(X2,complement(X3)))) = join(complement(X1),meet(complement(X2),X3)),
inference(spm,[status(thm)],[c_0_121,c_0_60]) ).
cnf(c_0_163,plain,
meet(complement(X1),join(complement(X2),X3)) = complement(join(meet(complement(X3),X2),X1)),
inference(spm,[status(thm)],[c_0_63,c_0_63]) ).
cnf(c_0_164,plain,
meet(join(X1,X2),join(meet(X1,X3),X2)) = join(meet(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_153]),c_0_48]) ).
cnf(c_0_165,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(join(X2,X3),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_72]),c_0_155]) ).
cnf(c_0_166,plain,
converse(complement(join(converse(X1),X2))) = complement(join(X1,converse(X2))),
inference(spm,[status(thm)],[c_0_122,c_0_68]) ).
cnf(c_0_167,plain,
join(converse(complement(X1)),complement(X2)) = complement(meet(converse(X1),X2)),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_168,plain,
join(complement(X1),converse(complement(X2))) = complement(meet(X1,converse(X2))),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_169,plain,
meet(converse(meet(X1,one)),X2) = meet(one,meet(converse(X1),X2)),
inference(spm,[status(thm)],[c_0_156,c_0_48]) ).
cnf(c_0_170,plain,
meet(X1,converse(meet(one,X1))) = meet(X1,one),
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_157,c_0_158]),c_0_34]),c_0_145]),c_0_156]),c_0_159]),c_0_48]),c_0_144]),c_0_145]) ).
cnf(c_0_171,plain,
composition(X1,join(converse(composition(top,X1)),X2)) = composition(X1,top),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_160]),c_0_140]),c_0_74]) ).
cnf(c_0_172,plain,
composition(top,converse(X1)) = converse(composition(X1,top)),
inference(spm,[status(thm)],[c_0_18,c_0_80]) ).
cnf(c_0_173,plain,
meet(X1,composition(join(X1,X2),top)) = X1,
inference(spm,[status(thm)],[c_0_161,c_0_29]) ).
cnf(c_0_174,plain,
join(composition(X1,composition(X2,X3)),composition(X4,X3)) = composition(join(composition(X1,X2),X4),X3),
inference(spm,[status(thm)],[c_0_105,c_0_132]) ).
cnf(c_0_175,plain,
join(X1,composition(meet(X2,X1),meet(X3,one))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_147]),c_0_66]) ).
cnf(c_0_176,plain,
join(meet(X1,X2),X3) = join(X3,meet(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_163]),c_0_57]),c_0_57]),c_0_57]),c_0_57]) ).
cnf(c_0_177,plain,
join(meet(X1,X2),meet(X1,X3)) = meet(join(X2,X3),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_62]),c_0_165]),c_0_48]),c_0_154]) ).
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_166,c_0_167]),c_0_57]),c_0_168]),c_0_57]) ).
cnf(c_0_179,plain,
converse(meet(X1,one)) = meet(X1,one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_48]),c_0_145]),c_0_91]),c_0_145]),c_0_91]),c_0_19]),c_0_48]),c_0_144]),c_0_145]),c_0_170]),c_0_91]) ).
cnf(c_0_180,plain,
composition(converse(join(composition(X1,top),X2)),X1) = 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_21,c_0_171]),c_0_21]),c_0_80]),c_0_172]),c_0_19]) ).
cnf(c_0_181,plain,
join(X1,composition(join(X1,X2),top)) = composition(join(X1,X2),top),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_173]),c_0_29]) ).
cnf(c_0_182,plain,
composition(join(composition(X1,top),X2),top) = composition(join(X1,X2),top),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_131]),c_0_105]) ).
cnf(c_0_183,plain,
composition(converse(composition(X1,top)),X2) = composition(top,composition(converse(X1),X2)),
inference(spm,[status(thm)],[c_0_132,c_0_172]) ).
cnf(c_0_184,plain,
join(meet(X1,one),converse(X1)) = converse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_175,c_0_158]),c_0_34]),c_0_34]),c_0_29]) ).
cnf(c_0_185,plain,
join(meet(composition(top,X1),X2),meet(X2,composition(X2,composition(converse(X1),X1)))) = meet(X2,composition(X2,composition(converse(X1),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_92]),c_0_132]),c_0_132]) ).
cnf(c_0_186,plain,
join(meet(X1,X2),meet(X2,X3)) = meet(join(X3,X1),X2),
inference(spm,[status(thm)],[c_0_176,c_0_177]) ).
cnf(c_0_187,plain,
join(meet(composition(top,X1),X2),composition(X2,composition(converse(X1),meet(X1,composition(top,X2))))) = composition(X2,composition(converse(X1),meet(X1,composition(top,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_80]),c_0_92]),c_0_132]),c_0_92]),c_0_132]) ).
cnf(c_0_188,plain,
join(meet(one,composition(X1,X2)),composition(meet(X1,converse(X2)),meet(X2,converse(X1)))) = composition(meet(X1,converse(X2)),meet(X2,converse(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_22]),c_0_34]),c_0_34]),c_0_48]) ).
cnf(c_0_189,plain,
meet(X1,composition(X1,meet(one,X2))) = composition(X1,meet(one,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_136]),c_0_89]) ).
cnf(c_0_190,plain,
converse(meet(one,X1)) = meet(X1,one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_179]),c_0_48]),c_0_145]),c_0_30]) ).
cnf(c_0_191,plain,
join(X1,composition(meet(X2,one),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_66]),c_0_34]) ).
cnf(c_0_192,plain,
composition(top,composition(converse(join(X1,X2)),X1)) = composition(top,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_181]),c_0_182]),c_0_183]) ).
cnf(c_0_193,plain,
join(meet(one,X1),converse(X1)) = converse(X1),
inference(spm,[status(thm)],[c_0_184,c_0_48]) ).
cnf(c_0_194,plain,
meet(X1,composition(X1,composition(converse(X2),X2))) = meet(composition(top,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_185,c_0_186]),c_0_174]),c_0_45]) ).
cnf(c_0_195,plain,
composition(X1,meet(one,composition(top,X1))) = 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_187,c_0_30]),c_0_22]),c_0_92]),c_0_34]),c_0_136]),c_0_34]) ).
cnf(c_0_196,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_197,plain,
composition(meet(X1,one),meet(one,X1)) = meet(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(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_188,c_0_189]),c_0_34]),c_0_145]),c_0_82]),c_0_190]),c_0_30]),c_0_48]),c_0_82]),c_0_191]),c_0_145]),c_0_82]),c_0_190]),c_0_30]),c_0_48]),c_0_82]) ).
cnf(c_0_198,plain,
composition(top,composition(X1,meet(one,X1))) = composition(top,meet(one,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_192,c_0_193]),c_0_19]) ).
cnf(c_0_199,plain,
meet(X1,composition(X1,composition(X2,converse(X2)))) = meet(converse(composition(X2,top)),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_19]),c_0_172]) ).
cnf(c_0_200,plain,
composition(converse(X1),meet(one,X2)) = converse(composition(meet(X2,one),X1)),
inference(spm,[status(thm)],[c_0_21,c_0_190]) ).
cnf(c_0_201,plain,
composition(meet(one,composition(X1,top)),X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_195]),c_0_19]),c_0_172]),c_0_145]),c_0_19]) ).
cnf(c_0_202,plain,
composition(top,composition(X1,converse(X1))) = converse(composition(X1,top)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_160]),c_0_132]) ).
cnf(c_0_203,plain,
meet(composition(top,meet(one,X1)),X2) = composition(X2,meet(one,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_190]),c_0_197]),c_0_189]) ).
cnf(c_0_204,plain,
converse(composition(X1,top)) = composition(top,meet(one,composition(X1,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(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_198,c_0_199]),c_0_34]),c_0_48]),c_0_145]),c_0_190]),c_0_48]),c_0_132]),c_0_200]),c_0_48]),c_0_201]),c_0_202]),c_0_48]),c_0_145]),c_0_190]),c_0_48]) ).
cnf(c_0_205,plain,
meet(composition(X1,meet(one,X2)),X3) = composition(meet(X1,X3),meet(one,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_203]),c_0_203]) ).
cnf(c_0_206,plain,
join(meet(composition(X1,top),X2),meet(X2,composition(X1,composition(converse(X1),X2)))) = meet(X2,composition(X1,composition(converse(X1),X2))),
inference(spm,[status(thm)],[c_0_138,c_0_92]) ).
fof(c_0_207,negated_conjecture,
~ ! [X1,X2] :
( composition(X1,top) = X1
=> composition(meet(X1,one),X2) = meet(X1,X2) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_208,plain,
meet(X1,composition(X1,composition(X2,converse(X2)))) = composition(X1,meet(one,composition(X2,top))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_199,c_0_204]),c_0_205]),c_0_92]) ).
cnf(c_0_209,plain,
composition(converse(X1),composition(X2,converse(X3))) = converse(composition(X3,composition(converse(X2),X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_21]),c_0_132]) ).
cnf(c_0_210,plain,
meet(X1,composition(X2,composition(converse(X2),X1))) = meet(composition(X2,top),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_206,c_0_186]),c_0_140]),c_0_45]) ).
fof(c_0_211,negated_conjecture,
( composition(esk1_0,top) = esk1_0
& composition(meet(esk1_0,one),esk2_0) != meet(esk1_0,esk2_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_207])])])]) ).
cnf(c_0_212,plain,
composition(meet(one,composition(X1,top)),X2) = meet(composition(X1,top),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_208]),c_0_200]),c_0_48]),c_0_19]),c_0_209]),c_0_19]),c_0_210]) ).
cnf(c_0_213,negated_conjecture,
composition(esk1_0,top) = esk1_0,
inference(split_conjunct,[status(thm)],[c_0_211]) ).
cnf(c_0_214,negated_conjecture,
composition(meet(esk1_0,one),esk2_0) != meet(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_211]) ).
cnf(c_0_215,negated_conjecture,
composition(meet(esk1_0,one),X1) = meet(esk1_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_212,c_0_213]),c_0_48]) ).
cnf(c_0_216,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_214,c_0_215])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : REL020+2 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon May 20 08:01:23 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.21/0.48 Running first-order model finding
% 0.21/0.48 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/benchmark/theBenchmark.p
% 86.41/11.39 # Version: 3.1.0
% 86.41/11.39 # Preprocessing class: FSMSSMSSSSSNFFN.
% 86.41/11.39 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 86.41/11.39 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 86.41/11.39 # Starting new_bool_3 with 300s (1) cores
% 86.41/11.39 # Starting new_bool_1 with 300s (1) cores
% 86.41/11.39 # Starting sh5l with 300s (1) cores
% 86.41/11.39 # new_bool_3 with pid 32677 completed with status 0
% 86.41/11.39 # Result found by new_bool_3
% 86.41/11.39 # Preprocessing class: FSMSSMSSSSSNFFN.
% 86.41/11.39 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 86.41/11.39 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 86.41/11.39 # Starting new_bool_3 with 300s (1) cores
% 86.41/11.39 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 86.41/11.39 # Search class: FUUPM-FFMF21-DFFFFFNN
% 86.41/11.39 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 86.41/11.39 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 181s (1) cores
% 86.41/11.39 # H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with pid 32684 completed with status 0
% 86.41/11.39 # Result found by H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S
% 86.41/11.39 # Preprocessing class: FSMSSMSSSSSNFFN.
% 86.41/11.39 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 86.41/11.39 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 86.41/11.39 # Starting new_bool_3 with 300s (1) cores
% 86.41/11.39 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 86.41/11.39 # Search class: FUUPM-FFMF21-DFFFFFNN
% 86.41/11.39 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 86.41/11.39 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 181s (1) cores
% 86.41/11.39 # Preprocessing time : 0.001 s
% 86.41/11.39 # Presaturation interreduction done
% 86.41/11.39
% 86.41/11.39 # Proof found!
% 86.41/11.39 # SZS status Theorem
% 86.41/11.39 # SZS output start CNFRefutation
% See solution above
% 86.41/11.39 # Parsed axioms : 17
% 86.41/11.39 # Removed by relevancy pruning/SinE : 1
% 86.41/11.39 # Initial clauses : 17
% 86.41/11.39 # Removed in clause preprocessing : 0
% 86.41/11.39 # Initial clauses in saturation : 17
% 86.41/11.39 # Processed clauses : 25141
% 86.41/11.39 # ...of these trivial : 13088
% 86.41/11.39 # ...subsumed : 9771
% 86.41/11.39 # ...remaining for further processing : 2282
% 86.41/11.39 # Other redundant clauses eliminated : 0
% 86.41/11.39 # Clauses deleted for lack of memory : 0
% 86.41/11.39 # Backward-subsumed : 0
% 86.41/11.39 # Backward-rewritten : 541
% 86.41/11.39 # Generated clauses : 964209
% 86.41/11.39 # ...of the previous two non-redundant : 579058
% 86.41/11.39 # ...aggressively subsumed : 0
% 86.41/11.39 # Contextual simplify-reflections : 0
% 86.41/11.39 # Paramodulations : 964209
% 86.41/11.39 # Factorizations : 0
% 86.41/11.39 # NegExts : 0
% 86.41/11.39 # Equation resolutions : 0
% 86.41/11.39 # Disequality decompositions : 0
% 86.41/11.39 # Total rewrite steps : 2500892
% 86.41/11.39 # ...of those cached : 2183602
% 86.41/11.39 # Propositional unsat checks : 0
% 86.41/11.39 # Propositional check models : 0
% 86.41/11.39 # Propositional check unsatisfiable : 0
% 86.41/11.39 # Propositional clauses : 0
% 86.41/11.39 # Propositional clauses after purity: 0
% 86.41/11.39 # Propositional unsat core size : 0
% 86.41/11.39 # Propositional preprocessing time : 0.000
% 86.41/11.39 # Propositional encoding time : 0.000
% 86.41/11.39 # Propositional solver time : 0.000
% 86.41/11.39 # Success case prop preproc time : 0.000
% 86.41/11.39 # Success case prop encoding time : 0.000
% 86.41/11.39 # Success case prop solver time : 0.000
% 86.41/11.39 # Current number of processed clauses : 1724
% 86.41/11.39 # Positive orientable unit clauses : 1703
% 86.41/11.39 # Positive unorientable unit clauses: 21
% 86.41/11.39 # Negative unit clauses : 0
% 86.41/11.39 # Non-unit-clauses : 0
% 86.41/11.39 # Current number of unprocessed clauses: 550373
% 86.41/11.39 # ...number of literals in the above : 550373
% 86.41/11.39 # Current number of archived formulas : 0
% 86.41/11.39 # Current number of archived clauses : 558
% 86.41/11.39 # Clause-clause subsumption calls (NU) : 0
% 86.41/11.39 # Rec. Clause-clause subsumption calls : 0
% 86.41/11.39 # Non-unit clause-clause subsumptions : 0
% 86.41/11.39 # Unit Clause-clause subsumption calls : 267
% 86.41/11.39 # Rewrite failures with RHS unbound : 0
% 86.41/11.39 # BW rewrite match attempts : 11332
% 86.41/11.39 # BW rewrite match successes : 1102
% 86.41/11.39 # Condensation attempts : 0
% 86.41/11.39 # Condensation successes : 0
% 86.41/11.39 # Termbank termtop insertions : 19104155
% 86.41/11.39 # Search garbage collected termcells : 32
% 86.41/11.39
% 86.41/11.39 # -------------------------------------------------
% 86.41/11.39 # User time : 10.217 s
% 86.41/11.39 # System time : 0.455 s
% 86.41/11.39 # Total time : 10.672 s
% 86.41/11.39 # Maximum resident set size: 1776 pages
% 86.41/11.39
% 86.41/11.39 # -------------------------------------------------
% 86.41/11.39 # User time : 10.218 s
% 86.41/11.39 # System time : 0.458 s
% 86.41/11.39 # Total time : 10.676 s
% 86.41/11.39 # Maximum resident set size: 1756 pages
% 86.41/11.39 % E---3.1 exiting
%------------------------------------------------------------------------------