TSTP Solution File: REL040+4 by E-SAT---3.1
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1
% Problem : REL040+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 2400s
% WCLimit : 300s
% DateTime : Tue Oct 10 19:14:30 EDT 2023
% Result : Theorem 938.38s 119.18s
% Output : CNFRefutation 938.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 15
% Syntax : Number of formulae : 214 ( 209 unt; 0 def)
% Number of atoms : 222 ( 221 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 8 ~; 3 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 441 ( 32 sgn; 70 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(converse_multiplicativity,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/export/starexec/sandbox2/tmp/tmp.CHSC5DR2WN/E---3.1_13872.p',converse_multiplicativity) ).
fof(composition_identity,axiom,
! [X1] : composition(X1,one) = X1,
file('/export/starexec/sandbox2/tmp/tmp.CHSC5DR2WN/E---3.1_13872.p',composition_identity) ).
fof(converse_idempotence,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/export/starexec/sandbox2/tmp/tmp.CHSC5DR2WN/E---3.1_13872.p',converse_idempotence) ).
fof(converse_cancellativity,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/export/starexec/sandbox2/tmp/tmp.CHSC5DR2WN/E---3.1_13872.p',converse_cancellativity) ).
fof(maddux1_join_commutativity,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/tmp/tmp.CHSC5DR2WN/E---3.1_13872.p',maddux1_join_commutativity) ).
fof(composition_distributivity,axiom,
! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/export/starexec/sandbox2/tmp/tmp.CHSC5DR2WN/E---3.1_13872.p',composition_distributivity) ).
fof(maddux2_join_associativity,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/export/starexec/sandbox2/tmp/tmp.CHSC5DR2WN/E---3.1_13872.p',maddux2_join_associativity) ).
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/sandbox2/tmp/tmp.CHSC5DR2WN/E---3.1_13872.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/sandbox2/tmp/tmp.CHSC5DR2WN/E---3.1_13872.p',maddux4_definiton_of_meet) ).
fof(converse_additivity,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/export/starexec/sandbox2/tmp/tmp.CHSC5DR2WN/E---3.1_13872.p',converse_additivity) ).
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/sandbox2/tmp/tmp.CHSC5DR2WN/E---3.1_13872.p',dedekind_law) ).
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/sandbox2/tmp/tmp.CHSC5DR2WN/E---3.1_13872.p',modular_law_2) ).
fof(composition_associativity,axiom,
! [X1,X2,X3] : composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/export/starexec/sandbox2/tmp/tmp.CHSC5DR2WN/E---3.1_13872.p',composition_associativity) ).
fof(goals,conjecture,
! [X1,X2,X3] :
( join(composition(converse(X1),X1),one) = one
=> ( join(composition(X1,meet(X2,X3)),meet(composition(X1,X2),composition(X1,X3))) = meet(composition(X1,X2),composition(X1,X3))
& join(meet(composition(X1,X2),composition(X1,X3)),composition(X1,meet(X2,X3))) = composition(X1,meet(X2,X3)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CHSC5DR2WN/E---3.1_13872.p',goals) ).
fof(modular_law_1,axiom,
! [X1,X2,X3] : join(meet(composition(X1,X2),X3),meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3)) = meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3),
file('/export/starexec/sandbox2/tmp/tmp.CHSC5DR2WN/E---3.1_13872.p',modular_law_1) ).
fof(c_0_15,plain,
! [X13,X14] : converse(composition(X13,X14)) = composition(converse(X14),converse(X13)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
fof(c_0_16,plain,
! [X33] : composition(X33,one) = X33,
inference(variable_rename,[status(thm)],[composition_identity]) ).
cnf(c_0_17,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,plain,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_19,plain,
! [X34] : converse(converse(X34)) = X34,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
cnf(c_0_20,plain,
composition(converse(one),converse(X1)) = converse(X1),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_22,plain,
composition(converse(one),X1) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
fof(c_0_23,plain,
! [X37,X38] : join(composition(converse(X37),complement(composition(X37,X38))),complement(X38)) = complement(X38),
inference(variable_rename,[status(thm)],[converse_cancellativity]) ).
fof(c_0_24,plain,
! [X26,X27] : join(X26,X27) = join(X27,X26),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
fof(c_0_25,plain,
! [X10,X11,X12] : composition(join(X10,X11),X12) = join(composition(X10,X12),composition(X11,X12)),
inference(variable_rename,[status(thm)],[composition_distributivity]) ).
cnf(c_0_26,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_27,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_22,c_0_26]) ).
fof(c_0_31,plain,
! [X28,X29,X30] : join(X28,join(X29,X30)) = join(join(X28,X29),X30),
inference(variable_rename,[status(thm)],[maddux2_join_associativity]) ).
cnf(c_0_32,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
join(X1,composition(X2,X1)) = composition(join(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_28]) ).
fof(c_0_34,plain,
! [X35,X36] : X35 = join(complement(join(complement(X35),complement(X36))),complement(join(complement(X35),X36))),
inference(variable_rename,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
fof(c_0_35,plain,
! [X24,X25] : meet(X24,X25) = complement(join(complement(X24),complement(X25))),
inference(variable_rename,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_0_36,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_30]),c_0_26]),c_0_30]) ).
cnf(c_0_38,plain,
join(X1,X1) = composition(join(one,one),X1),
inference(spm,[status(thm)],[c_0_33,c_0_30]) ).
cnf(c_0_39,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_41,plain,
join(composition(join(X1,one),X2),X3) = join(X2,join(composition(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_36,c_0_33]) ).
cnf(c_0_42,plain,
composition(join(one,one),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_43,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,plain,
join(complement(X1),join(complement(X1),X2)) = join(complement(X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_30]) ).
cnf(c_0_45,plain,
complement(complement(X1)) = meet(X1,X1),
inference(spm,[status(thm)],[c_0_40,c_0_37]) ).
cnf(c_0_46,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_40]),c_0_28]) ).
cnf(c_0_47,plain,
meet(X1,X2) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_28]),c_0_40]) ).
cnf(c_0_48,plain,
join(meet(X1,X1),join(meet(X1,X1),X2)) = join(meet(X1,X1),X2),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,plain,
join(meet(X1,X2),meet(complement(X2),X1)) = X1,
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_50,plain,
join(X1,meet(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_28]) ).
cnf(c_0_51,plain,
join(X1,join(meet(X1,X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_36,c_0_50]) ).
cnf(c_0_52,plain,
join(meet(complement(X1),X2),meet(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_28,c_0_49]) ).
fof(c_0_53,plain,
! [X31,X32] : converse(join(X31,X32)) = join(converse(X31),converse(X32)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
cnf(c_0_54,plain,
complement(join(complement(X1),meet(X2,X3))) = meet(X1,join(complement(X2),complement(X3))),
inference(spm,[status(thm)],[c_0_40,c_0_40]) ).
cnf(c_0_55,plain,
join(complement(X1),meet(X1,complement(X1))) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_38]),c_0_42]),c_0_47]) ).
cnf(c_0_56,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_57,plain,
join(X1,meet(X1,complement(X1))) = join(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_49]),c_0_47]) ).
cnf(c_0_58,plain,
join(meet(X1,X2),complement(join(complement(X2),X1))) = X2,
inference(spm,[status(thm)],[c_0_43,c_0_47]) ).
cnf(c_0_59,plain,
meet(X1,join(meet(X1,X1),complement(X1))) = meet(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_45]),c_0_45]),c_0_28]) ).
cnf(c_0_60,plain,
complement(join(meet(X1,X2),complement(X3))) = meet(join(complement(X1),complement(X2)),X3),
inference(spm,[status(thm)],[c_0_40,c_0_40]) ).
cnf(c_0_61,plain,
join(complement(X1),composition(join(converse(X2),converse(X3)),complement(composition(join(X2,X3),X1)))) = complement(X1),
inference(spm,[status(thm)],[c_0_32,c_0_56]) ).
cnf(c_0_62,plain,
join(X1,join(meet(X1,complement(X1)),X2)) = join(X1,join(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_57]),c_0_36]) ).
cnf(c_0_63,plain,
composition(join(one,one),meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_42,c_0_40]) ).
cnf(c_0_64,plain,
join(meet(X1,X2),complement(join(X2,complement(X1)))) = X1,
inference(spm,[status(thm)],[c_0_43,c_0_28]) ).
cnf(c_0_65,plain,
join(meet(X1,X1),complement(join(X1,X1))) = join(meet(X1,X1),complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]),c_0_38]),c_0_42]),c_0_47]),c_0_28]),c_0_57]) ).
cnf(c_0_66,plain,
join(complement(X1),complement(join(X1,X1))) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_38]),c_0_26]),c_0_26]),c_0_42]) ).
cnf(c_0_67,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_28]),c_0_36]) ).
cnf(c_0_68,plain,
join(X1,join(X1,X1)) = join(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_38]),c_0_63]),c_0_57]),c_0_57]) ).
cnf(c_0_69,plain,
join(meet(X1,X2),complement(join(X1,complement(X2)))) = X2,
inference(spm,[status(thm)],[c_0_64,c_0_47]) ).
cnf(c_0_70,plain,
join(X1,complement(join(X1,X1))) = join(X1,complement(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_65]),c_0_51]) ).
cnf(c_0_71,plain,
meet(X1,join(X1,X1)) = meet(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_66]),c_0_45]) ).
cnf(c_0_72,plain,
join(X1,join(X2,join(X1,X1))) = join(X2,join(X1,X1)),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_73,plain,
join(X1,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_71]),c_0_69]) ).
cnf(c_0_74,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_73]),c_0_73]) ).
cnf(c_0_75,plain,
join(X1,meet(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_52]),c_0_28]) ).
cnf(c_0_76,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_36,c_0_75]) ).
cnf(c_0_77,plain,
join(complement(X1),meet(X2,X1)) = join(complement(X1),X2),
inference(spm,[status(thm)],[c_0_76,c_0_52]) ).
cnf(c_0_78,plain,
meet(X1,composition(join(one,one),X1)) = meet(X1,X1),
inference(spm,[status(thm)],[c_0_71,c_0_38]) ).
cnf(c_0_79,plain,
join(meet(X1,X1),complement(X1)) = join(X1,complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_73]),c_0_30]),c_0_28]),c_0_73]),c_0_30]),c_0_28]) ).
cnf(c_0_80,plain,
complement(join(X1,complement(X1))) = meet(X1,complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_79]),c_0_38]),c_0_73]),c_0_30]),c_0_47]) ).
cnf(c_0_81,plain,
join(meet(X1,X2),meet(X2,complement(X1))) = X2,
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_82,plain,
join(X1,meet(meet(X1,X2),X3)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_75]),c_0_75]) ).
cnf(c_0_83,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_80]),c_0_45]),c_0_45]),c_0_47]),c_0_81]) ).
cnf(c_0_84,plain,
complement(join(meet(X1,X2),meet(X3,X3))) = meet(join(complement(X1),complement(X2)),complement(X3)),
inference(spm,[status(thm)],[c_0_60,c_0_45]) ).
cnf(c_0_85,plain,
join(X1,meet(meet(X2,X1),X3)) = X1,
inference(spm,[status(thm)],[c_0_82,c_0_47]) ).
cnf(c_0_86,plain,
meet(X1,join(X1,complement(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_59,c_0_79]),c_0_83]) ).
cnf(c_0_87,plain,
join(complement(X1),meet(X1,X2)) = join(complement(X1),X2),
inference(spm,[status(thm)],[c_0_77,c_0_47]) ).
cnf(c_0_88,plain,
complement(join(X1,X2)) = meet(complement(X1),complement(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_83]),c_0_83]),c_0_38]),c_0_73]),c_0_30]) ).
cnf(c_0_89,plain,
complement(meet(X1,X2)) = meet(join(complement(X1),complement(X2)),join(complement(X1),complement(X2))),
inference(spm,[status(thm)],[c_0_45,c_0_40]) ).
cnf(c_0_90,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[c_0_28,c_0_36]) ).
cnf(c_0_91,plain,
join(X1,join(complement(X1),X2)) = join(X1,complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_36]),c_0_87]) ).
cnf(c_0_92,plain,
meet(X1,join(complement(X2),complement(X1))) = meet(X1,complement(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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_77]),c_0_88]),c_0_45]),c_0_83]),c_0_45]),c_0_83]),c_0_89]),c_0_83]) ).
cnf(c_0_93,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_45,c_0_83]) ).
cnf(c_0_94,plain,
join(X1,join(X2,complement(X2))) = join(X2,complement(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_36]),c_0_91]) ).
cnf(c_0_95,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_96,plain,
join(X1,join(X2,meet(X1,X3))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_67,c_0_75]) ).
cnf(c_0_97,plain,
join(X1,complement(X1)) = join(X2,complement(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_94]),c_0_94]) ).
cnf(c_0_98,plain,
join(meet(X1,X2),join(complement(join(complement(X1),X2)),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_36,c_0_43]) ).
cnf(c_0_99,plain,
meet(X1,join(complement(X1),X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_95,c_0_28]) ).
cnf(c_0_100,plain,
join(X1,join(X2,complement(X1))) = join(X1,complement(X1)),
inference(spm,[status(thm)],[c_0_91,c_0_96]) ).
cnf(c_0_101,plain,
meet(X1,join(X2,complement(X2))) = X1,
inference(spm,[status(thm)],[c_0_86,c_0_97]) ).
cnf(c_0_102,plain,
join(X1,composition(X2,X1)) = composition(join(one,X2),X1),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_103,plain,
join(converse(X1),converse(meet(X1,X2))) = converse(X1),
inference(spm,[status(thm)],[c_0_56,c_0_75]) ).
cnf(c_0_104,plain,
join(X1,meet(X2,join(complement(X1),X3))) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_77]),c_0_98]) ).
cnf(c_0_105,plain,
join(meet(X1,X2),meet(complement(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_49,c_0_47]) ).
cnf(c_0_106,plain,
join(meet(X1,complement(X2)),meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_81]) ).
cnf(c_0_107,plain,
meet(X1,join(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_45]),c_0_83]),c_0_28]),c_0_101]),c_0_45]),c_0_83]) ).
cnf(c_0_108,plain,
join(X1,composition(meet(one,X2),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_75]),c_0_30]) ).
cnf(c_0_109,plain,
join(X1,converse(meet(converse(X1),X2))) = X1,
inference(spm,[status(thm)],[c_0_103,c_0_21]) ).
cnf(c_0_110,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_104]),c_0_99]),c_0_45]),c_0_83]) ).
cnf(c_0_111,plain,
meet(X1,join(meet(complement(X1),X2),X3)) = meet(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_76]),c_0_99]) ).
cnf(c_0_112,plain,
join(meet(X1,X2),join(meet(complement(X1),X2),X3)) = join(X2,X3),
inference(spm,[status(thm)],[c_0_36,c_0_105]) ).
cnf(c_0_113,plain,
join(X1,meet(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_106]),c_0_28]) ).
cnf(c_0_114,plain,
meet(X1,composition(meet(one,X2),X1)) = composition(meet(one,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_47]) ).
cnf(c_0_115,plain,
join(X1,converse(meet(X2,converse(X1)))) = X1,
inference(spm,[status(thm)],[c_0_109,c_0_47]) ).
cnf(c_0_116,plain,
meet(meet(X1,X2),meet(X3,X1)) = meet(meet(X1,X2),X3),
inference(spm,[status(thm)],[c_0_110,c_0_49]) ).
cnf(c_0_117,plain,
meet(X1,join(meet(X1,X2),X3)) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_45]),c_0_83]) ).
cnf(c_0_118,plain,
join(X1,join(X2,meet(X3,X1))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_67,c_0_113]) ).
cnf(c_0_119,plain,
join(converse(X1),converse(meet(X1,X1))) = converse(X1),
inference(spm,[status(thm)],[c_0_56,c_0_50]) ).
cnf(c_0_120,plain,
join(X1,composition(X1,converse(meet(one,X2)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_114]),c_0_17]),c_0_21]) ).
cnf(c_0_121,plain,
meet(X1,converse(meet(X2,converse(X1)))) = converse(meet(X2,converse(X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_115]),c_0_47]) ).
fof(c_0_122,plain,
! [X15,X16,X17] : join(meet(composition(X15,X16),X17),composition(meet(X15,composition(X17,converse(X16))),meet(X16,composition(converse(X15),X17)))) = composition(meet(X15,composition(X17,converse(X16))),meet(X16,composition(converse(X15),X17))),
inference(variable_rename,[status(thm)],[dedekind_law]) ).
cnf(c_0_123,plain,
meet(meet(X1,X2),meet(X1,X3)) = meet(meet(X1,X2),X3),
inference(spm,[status(thm)],[c_0_116,c_0_47]) ).
fof(c_0_124,plain,
! [X21,X22,X23] : join(meet(composition(X21,X22),X23),meet(composition(meet(X21,composition(X23,converse(X22))),X22),X23)) = meet(composition(meet(X21,composition(X23,converse(X22))),X22),X23),
inference(variable_rename,[status(thm)],[modular_law_2]) ).
cnf(c_0_125,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_107,c_0_76]),c_0_47]) ).
cnf(c_0_126,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_74]),c_0_118]) ).
cnf(c_0_127,plain,
join(one,converse(meet(one,one))) = one,
inference(spm,[status(thm)],[c_0_119,c_0_26]) ).
cnf(c_0_128,plain,
join(X1,composition(X1,meet(X2,one))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_26]),c_0_21]) ).
cnf(c_0_129,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_122]) ).
cnf(c_0_130,plain,
meet(meet(X1,X2),X3) = meet(meet(X1,X3),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_123]),c_0_123]) ).
cnf(c_0_131,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_76,c_0_81]) ).
cnf(c_0_132,plain,
join(composition(converse(X1),converse(X2)),composition(converse(X1),converse(X3))) = composition(converse(X1),join(converse(X2),converse(X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_29]),c_0_17]),c_0_56]),c_0_17]),c_0_17]) ).
cnf(c_0_133,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_124]) ).
cnf(c_0_134,plain,
join(meet(X1,X2),meet(X1,X3)) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_75]),c_0_126]),c_0_117]) ).
cnf(c_0_135,plain,
meet(complement(X1),join(X2,X1)) = meet(complement(X1),X2),
inference(spm,[status(thm)],[c_0_95,c_0_93]) ).
cnf(c_0_136,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_76,c_0_105]) ).
cnf(c_0_137,plain,
complement(meet(X1,X2)) = join(complement(X1),complement(X2)),
inference(rw,[status(thm)],[c_0_89,c_0_83]) ).
cnf(c_0_138,plain,
meet(X1,join(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_91]),c_0_45]),c_0_83]),c_0_28]),c_0_101]),c_0_45]),c_0_83]) ).
cnf(c_0_139,plain,
meet(X1,converse(meet(converse(X1),X2))) = converse(meet(converse(X1),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_109]),c_0_47]) ).
cnf(c_0_140,plain,
join(one,join(converse(meet(one,one)),X1)) = join(one,X1),
inference(spm,[status(thm)],[c_0_36,c_0_127]) ).
cnf(c_0_141,plain,
meet(X1,composition(X1,meet(X2,one))) = composition(X1,meet(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_128]),c_0_47]) ).
cnf(c_0_142,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_129,c_0_26]),c_0_30]),c_0_30]),c_0_108]),c_0_30]) ).
cnf(c_0_143,plain,
meet(meet(X1,X2),X3) = meet(X2,meet(X1,X3)),
inference(spm,[status(thm)],[c_0_47,c_0_130]) ).
cnf(c_0_144,plain,
meet(X1,meet(X2,X1)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_131]),c_0_99]),c_0_45]),c_0_83]) ).
fof(c_0_145,plain,
! [X7,X8,X9] : composition(X7,composition(X8,X9)) = composition(composition(X7,X8),X9),
inference(variable_rename,[status(thm)],[composition_associativity]) ).
fof(c_0_146,negated_conjecture,
~ ! [X1,X2,X3] :
( join(composition(converse(X1),X1),one) = one
=> ( join(composition(X1,meet(X2,X3)),meet(composition(X1,X2),composition(X1,X3))) = meet(composition(X1,X2),composition(X1,X3))
& join(meet(composition(X1,X2),composition(X1,X3)),composition(X1,meet(X2,X3))) = composition(X1,meet(X2,X3)) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_147,plain,
! [X18,X19,X20] : join(meet(composition(X18,X19),X20),meet(composition(X18,meet(X19,composition(converse(X18),X20))),X20)) = meet(composition(X18,meet(X19,composition(converse(X18),X20))),X20),
inference(variable_rename,[status(thm)],[modular_law_1]) ).
cnf(c_0_148,plain,
join(composition(converse(X1),converse(X2)),composition(converse(X1),X3)) = composition(converse(X1),join(converse(X2),X3)),
inference(spm,[status(thm)],[c_0_132,c_0_21]) ).
cnf(c_0_149,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_133,c_0_47]),c_0_47]) ).
cnf(c_0_150,plain,
join(meet(X1,X2),meet(X2,X3)) = meet(X2,join(X1,X3)),
inference(spm,[status(thm)],[c_0_134,c_0_47]) ).
cnf(c_0_151,plain,
meet(join(X1,X2),join(X1,complement(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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_137]),c_0_45]),c_0_83]),c_0_137]),c_0_45]),c_0_83]),c_0_47]),c_0_47]),c_0_138]) ).
cnf(c_0_152,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_36,c_0_113]) ).
cnf(c_0_153,plain,
join(X1,composition(X1,meet(one,X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_139]),c_0_26]),c_0_21]) ).
cnf(c_0_154,plain,
join(one,converse(meet(one,X1))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_103]),c_0_127]),c_0_83]) ).
cnf(c_0_155,plain,
meet(X1,meet(one,converse(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(spm,[status(thm)],[c_0_141,c_0_142]),c_0_30]),c_0_143]),c_0_144]),c_0_47]),c_0_143]) ).
cnf(c_0_156,plain,
join(X1,meet(X2,meet(X1,X3))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_113]),c_0_75]) ).
cnf(c_0_157,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_145]) ).
fof(c_0_158,negated_conjecture,
( join(composition(converse(esk1_0),esk1_0),one) = one
& ( join(composition(esk1_0,meet(esk2_0,esk3_0)),meet(composition(esk1_0,esk2_0),composition(esk1_0,esk3_0))) != meet(composition(esk1_0,esk2_0),composition(esk1_0,esk3_0))
| join(meet(composition(esk1_0,esk2_0),composition(esk1_0,esk3_0)),composition(esk1_0,meet(esk2_0,esk3_0))) != composition(esk1_0,meet(esk2_0,esk3_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_146])])]) ).
cnf(c_0_159,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_147]) ).
cnf(c_0_160,plain,
join(composition(X1,converse(X2)),composition(X1,X3)) = composition(X1,join(converse(X2),X3)),
inference(spm,[status(thm)],[c_0_148,c_0_21]) ).
cnf(c_0_161,plain,
meet(X1,composition(meet(X2,composition(X1,converse(X3))),X3)) = meet(X1,composition(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_149,c_0_150]),c_0_29]),c_0_75]) ).
cnf(c_0_162,plain,
meet(join(X1,X2),join(X2,complement(X1))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_96]),c_0_88]),c_0_137]),c_0_104]) ).
cnf(c_0_163,plain,
join(X1,composition(meet(X2,X1),meet(one,X3))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_153]),c_0_113]) ).
cnf(c_0_164,plain,
meet(one,converse(meet(one,X1))) = converse(meet(one,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_154]),c_0_47]) ).
cnf(c_0_165,plain,
meet(one,converse(X1)) = meet(X1,one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_21]),c_0_47]),c_0_143]),c_0_155]),c_0_47]) ).
cnf(c_0_166,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_136]),c_0_99]),c_0_45]),c_0_83]) ).
cnf(c_0_167,plain,
join(meet(X1,X2),composition(meet(X1,X2),meet(one,composition(converse(X1),X2)))) = composition(meet(X1,X2),meet(one,composition(converse(X1),X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_18]),c_0_26]),c_0_18]),c_0_26]),c_0_18]) ).
cnf(c_0_168,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_156]),c_0_47]) ).
cnf(c_0_169,plain,
meet(X1,composition(X1,meet(one,X2))) = composition(X1,meet(one,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_153]),c_0_47]) ).
cnf(c_0_170,plain,
join(composition(X1,composition(X2,X3)),composition(X4,X3)) = composition(join(composition(X1,X2),X4),X3),
inference(spm,[status(thm)],[c_0_29,c_0_157]) ).
cnf(c_0_171,negated_conjecture,
join(composition(converse(esk1_0),esk1_0),one) = one,
inference(split_conjunct,[status(thm)],[c_0_158]) ).
cnf(c_0_172,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_159,c_0_47]),c_0_47]) ).
cnf(c_0_173,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_160,c_0_21]) ).
cnf(c_0_174,plain,
meet(X1,composition(meet(X2,composition(X1,X3)),converse(X3))) = meet(X1,composition(X2,converse(X3))),
inference(spm,[status(thm)],[c_0_161,c_0_21]) ).
cnf(c_0_175,plain,
meet(X1,composition(meet(X2,X1),meet(one,X3))) = composition(meet(X2,X1),meet(one,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_163]),c_0_95]) ).
cnf(c_0_176,plain,
converse(meet(one,X1)) = meet(one,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_164,c_0_165]),c_0_47]),c_0_166]) ).
cnf(c_0_177,plain,
composition(meet(one,X1),meet(one,X1)) = meet(one,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_26]),c_0_30]),c_0_108]),c_0_30]) ).
cnf(c_0_178,plain,
meet(X1,meet(X2,composition(X1,meet(one,X3)))) = meet(X2,composition(X1,meet(one,X3))),
inference(spm,[status(thm)],[c_0_168,c_0_169]) ).
cnf(c_0_179,plain,
join(X1,composition(X2,composition(X3,X1))) = composition(join(one,composition(X2,X3)),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_170,c_0_30]),c_0_28]),c_0_28]) ).
cnf(c_0_180,negated_conjecture,
join(one,composition(converse(esk1_0),esk1_0)) = one,
inference(rw,[status(thm)],[c_0_171,c_0_28]) ).
cnf(c_0_181,plain,
meet(meet(X1,X2),meet(X3,X2)) = meet(meet(X1,X2),X3),
inference(spm,[status(thm)],[c_0_110,c_0_105]) ).
cnf(c_0_182,plain,
meet(X1,composition(X2,meet(X3,composition(converse(X2),X1)))) = meet(X1,composition(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_172,c_0_150]),c_0_173]),c_0_75]) ).
cnf(c_0_183,plain,
join(X1,composition(meet(one,X2),meet(X3,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_152,c_0_108]),c_0_113]) ).
cnf(c_0_184,plain,
meet(X1,composition(X2,meet(one,X3))) = composition(meet(X1,X2),meet(one,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_175]),c_0_176]),c_0_157]),c_0_177]),c_0_169]),c_0_176]),c_0_143]),c_0_178]) ).
cnf(c_0_185,negated_conjecture,
join(X1,composition(converse(esk1_0),composition(esk1_0,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_180]),c_0_30]) ).
cnf(c_0_186,plain,
join(meet(composition(X1,converse(X2)),X3),composition(meet(X1,composition(X3,X2)),meet(converse(X2),composition(converse(X1),X3)))) = composition(meet(X1,composition(X3,X2)),meet(converse(X2),composition(converse(X1),X3))),
inference(spm,[status(thm)],[c_0_129,c_0_21]) ).
cnf(c_0_187,negated_conjecture,
meet(one,composition(converse(esk1_0),esk1_0)) = composition(converse(esk1_0),esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_180]),c_0_47]) ).
cnf(c_0_188,plain,
meet(meet(X1,X2),meet(X2,X3)) = meet(meet(X1,X2),X3),
inference(spm,[status(thm)],[c_0_181,c_0_47]) ).
cnf(c_0_189,plain,
meet(X1,composition(converse(X2),meet(X3,composition(X2,X1)))) = meet(X1,composition(converse(X2),X3)),
inference(spm,[status(thm)],[c_0_182,c_0_21]) ).
cnf(c_0_190,plain,
meet(X1,composition(meet(one,X2),meet(X3,X1))) = composition(meet(one,X2),meet(X3,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_183]),c_0_95]) ).
cnf(c_0_191,plain,
composition(meet(one,X1),composition(meet(one,X1),X2)) = composition(meet(one,X1),X2),
inference(spm,[status(thm)],[c_0_157,c_0_177]) ).
cnf(c_0_192,plain,
meet(X1,meet(X2,composition(meet(one,X3),X1))) = meet(X2,composition(meet(one,X3),X1)),
inference(spm,[status(thm)],[c_0_168,c_0_114]) ).
cnf(c_0_193,plain,
meet(X1,meet(one,X2)) = composition(meet(X1,one),meet(one,X2)),
inference(spm,[status(thm)],[c_0_184,c_0_30]) ).
cnf(c_0_194,negated_conjecture,
meet(X1,composition(converse(esk1_0),composition(esk1_0,X1))) = composition(converse(esk1_0),composition(esk1_0,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_185]),c_0_47]) ).
cnf(c_0_195,negated_conjecture,
composition(converse(esk1_0),composition(esk1_0,converse(esk1_0))) = converse(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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_186,c_0_187]),c_0_30]),c_0_83]),c_0_26]),c_0_30]),c_0_83]),c_0_157]),c_0_185]),c_0_26]),c_0_30]),c_0_83]),c_0_157]) ).
cnf(c_0_196,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_188,c_0_143]),c_0_143]),c_0_168]) ).
cnf(c_0_197,plain,
meet(complement(X1),join(X1,X2)) = meet(complement(X1),X2),
inference(spm,[status(thm)],[c_0_135,c_0_28]) ).
cnf(c_0_198,plain,
meet(X1,composition(meet(one,X2),X3)) = composition(meet(one,X2),meet(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_190]),c_0_176]),c_0_191]),c_0_114]),c_0_176]),c_0_143]),c_0_192]) ).
cnf(c_0_199,negated_conjecture,
meet(X1,composition(converse(esk1_0),esk1_0)) = composition(meet(X1,one),composition(converse(esk1_0),esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_193,c_0_194]),c_0_18]),c_0_18]) ).
cnf(c_0_200,negated_conjecture,
composition(esk1_0,composition(converse(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(spm,[status(thm)],[c_0_17,c_0_195]),c_0_21]),c_0_17]),c_0_21]),c_0_21]),c_0_157]) ).
cnf(c_0_201,plain,
join(X1,meet(X2,meet(complement(X1),X3))) = join(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_136,c_0_196]) ).
cnf(c_0_202,plain,
meet(join(X1,X2),meet(complement(X1),X3)) = meet(X2,meet(complement(X1),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_197]),c_0_143]) ).
cnf(c_0_203,negated_conjecture,
meet(X1,composition(converse(esk1_0),composition(esk1_0,X2))) = composition(converse(esk1_0),composition(esk1_0,meet(X1,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_198,c_0_199]),c_0_83]),c_0_30]),c_0_157]),c_0_83]),c_0_30]),c_0_157]) ).
cnf(c_0_204,negated_conjecture,
composition(esk1_0,composition(converse(esk1_0),composition(esk1_0,X1))) = composition(esk1_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_200]),c_0_157]) ).
cnf(c_0_205,negated_conjecture,
( join(composition(esk1_0,meet(esk2_0,esk3_0)),meet(composition(esk1_0,esk2_0),composition(esk1_0,esk3_0))) != meet(composition(esk1_0,esk2_0),composition(esk1_0,esk3_0))
| join(meet(composition(esk1_0,esk2_0),composition(esk1_0,esk3_0)),composition(esk1_0,meet(esk2_0,esk3_0))) != composition(esk1_0,meet(esk2_0,esk3_0)) ),
inference(split_conjunct,[status(thm)],[c_0_158]) ).
cnf(c_0_206,plain,
join(X1,meet(join(X1,X2),X3)) = join(X1,meet(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_202]),c_0_201]) ).
cnf(c_0_207,negated_conjecture,
meet(composition(esk1_0,X1),composition(esk1_0,meet(X2,X1))) = meet(composition(esk1_0,X1),composition(esk1_0,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_203]),c_0_21]),c_0_204]),c_0_21]) ).
cnf(c_0_208,negated_conjecture,
( join(composition(esk1_0,meet(esk2_0,esk3_0)),meet(composition(esk1_0,esk2_0),composition(esk1_0,esk3_0))) != meet(composition(esk1_0,esk2_0),composition(esk1_0,esk3_0))
| join(composition(esk1_0,meet(esk2_0,esk3_0)),meet(composition(esk1_0,esk2_0),composition(esk1_0,esk3_0))) != composition(esk1_0,meet(esk2_0,esk3_0)) ),
inference(rw,[status(thm)],[c_0_205,c_0_28]) ).
cnf(c_0_209,plain,
join(X1,meet(X2,X3)) = meet(join(X1,X2),join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_138]),c_0_206]) ).
cnf(c_0_210,negated_conjecture,
meet(composition(esk1_0,X1),composition(esk1_0,meet(X1,X2))) = composition(esk1_0,meet(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_166]),c_0_83]),c_0_47]) ).
cnf(c_0_211,negated_conjecture,
meet(composition(esk1_0,esk2_0),composition(esk1_0,esk3_0)) != composition(esk1_0,meet(esk2_0,esk3_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_208,c_0_209]),c_0_173]),c_0_28]),c_0_209]),c_0_73]),c_0_138]),c_0_173]),c_0_28]),c_0_209]),c_0_28]),c_0_73]),c_0_47]),c_0_107]),c_0_209]),c_0_173]),c_0_28]),c_0_209]),c_0_73]),c_0_138]),c_0_173]),c_0_28]),c_0_209]),c_0_28]),c_0_73]),c_0_47]),c_0_107])]) ).
cnf(c_0_212,negated_conjecture,
meet(composition(esk1_0,X1),composition(esk1_0,X2)) = composition(esk1_0,meet(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_207,c_0_47]),c_0_210]) ).
cnf(c_0_213,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_211,c_0_212])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : REL040+4 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.10 % Command : run_E %s %d THM
% 0.09/0.30 % Computer : n016.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 2400
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon Oct 2 15:46:51 EDT 2023
% 0.09/0.31 % CPUTime :
% 0.15/0.41 Running first-order model finding
% 0.15/0.41 Running: /export/starexec/sandbox2/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/sandbox2/tmp/tmp.CHSC5DR2WN/E---3.1_13872.p
% 938.38/119.18 # Version: 3.1pre001
% 938.38/119.18 # Preprocessing class: FSMSSMSSSSSNFFN.
% 938.38/119.18 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 938.38/119.18 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 938.38/119.18 # Starting new_bool_3 with 300s (1) cores
% 938.38/119.18 # Starting new_bool_1 with 300s (1) cores
% 938.38/119.18 # Starting sh5l with 300s (1) cores
% 938.38/119.18 # new_bool_3 with pid 13950 completed with status 0
% 938.38/119.18 # Result found by new_bool_3
% 938.38/119.18 # Preprocessing class: FSMSSMSSSSSNFFN.
% 938.38/119.18 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 938.38/119.18 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 938.38/119.18 # Starting new_bool_3 with 300s (1) cores
% 938.38/119.18 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 938.38/119.18 # Search class: FUHPM-FFMF21-DFFFFFNN
% 938.38/119.18 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 938.38/119.18 # Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 181s (1) cores
% 938.38/119.18 # H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with pid 13956 completed with status 0
% 938.38/119.18 # Result found by H----_047_B31_F1_PI_AE_R4_CS_SP_S2S
% 938.38/119.18 # Preprocessing class: FSMSSMSSSSSNFFN.
% 938.38/119.18 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 938.38/119.18 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 938.38/119.18 # Starting new_bool_3 with 300s (1) cores
% 938.38/119.18 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 938.38/119.18 # Search class: FUHPM-FFMF21-DFFFFFNN
% 938.38/119.18 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 938.38/119.18 # Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 181s (1) cores
% 938.38/119.18 # Preprocessing time : 0.001 s
% 938.38/119.18
% 938.38/119.18 # Proof found!
% 938.38/119.18 # SZS status Theorem
% 938.38/119.18 # SZS output start CNFRefutation
% See solution above
% 938.38/119.18 # Parsed axioms : 17
% 938.38/119.18 # Removed by relevancy pruning/SinE : 2
% 938.38/119.18 # Initial clauses : 16
% 938.38/119.18 # Removed in clause preprocessing : 0
% 938.38/119.18 # Initial clauses in saturation : 16
% 938.38/119.18 # Processed clauses : 81688
% 938.38/119.18 # ...of these trivial : 30646
% 938.38/119.18 # ...subsumed : 47248
% 938.38/119.18 # ...remaining for further processing : 3794
% 938.38/119.18 # Other redundant clauses eliminated : 0
% 938.38/119.18 # Clauses deleted for lack of memory : 339365
% 938.38/119.18 # Backward-subsumed : 15
% 938.38/119.18 # Backward-rewritten : 1049
% 938.38/119.18 # Generated clauses : 3710004
% 938.38/119.18 # ...of the previous two non-redundant : 2893305
% 938.38/119.18 # ...aggressively subsumed : 0
% 938.38/119.18 # Contextual simplify-reflections : 0
% 938.38/119.18 # Paramodulations : 3710004
% 938.38/119.18 # Factorizations : 0
% 938.38/119.18 # NegExts : 0
% 938.38/119.18 # Equation resolutions : 0
% 938.38/119.18 # Total rewrite steps : 16172481
% 938.38/119.18 # Propositional unsat checks : 0
% 938.38/119.18 # Propositional check models : 0
% 938.38/119.18 # Propositional check unsatisfiable : 0
% 938.38/119.18 # Propositional clauses : 0
% 938.38/119.18 # Propositional clauses after purity: 0
% 938.38/119.18 # Propositional unsat core size : 0
% 938.38/119.18 # Propositional preprocessing time : 0.000
% 938.38/119.18 # Propositional encoding time : 0.000
% 938.38/119.18 # Propositional solver time : 0.000
% 938.38/119.18 # Success case prop preproc time : 0.000
% 938.38/119.18 # Success case prop encoding time : 0.000
% 938.38/119.18 # Success case prop solver time : 0.000
% 938.38/119.18 # Current number of processed clauses : 2730
% 938.38/119.18 # Positive orientable unit clauses : 2362
% 938.38/119.18 # Positive unorientable unit clauses: 368
% 938.38/119.18 # Negative unit clauses : 0
% 938.38/119.18 # Non-unit-clauses : 0
% 938.38/119.18 # Current number of unprocessed clauses: 1277256
% 938.38/119.18 # ...number of literals in the above : 1277256
% 938.38/119.18 # Current number of archived formulas : 0
% 938.38/119.18 # Current number of archived clauses : 1064
% 938.38/119.18 # Clause-clause subsumption calls (NU) : 0
% 938.38/119.18 # Rec. Clause-clause subsumption calls : 0
% 938.38/119.18 # Non-unit clause-clause subsumptions : 0
% 938.38/119.18 # Unit Clause-clause subsumption calls : 8183
% 938.38/119.18 # Rewrite failures with RHS unbound : 13586
% 938.38/119.18 # BW rewrite match attempts : 100636
% 938.38/119.18 # BW rewrite match successes : 14952
% 938.38/119.18 # Condensation attempts : 0
% 938.38/119.18 # Condensation successes : 0
% 938.38/119.18 # Termbank termtop insertions : 92288985
% 938.38/119.18
% 938.38/119.18 # -------------------------------------------------
% 938.38/119.18 # User time : 114.254 s
% 938.38/119.18 # System time : 2.001 s
% 938.38/119.18 # Total time : 116.255 s
% 938.38/119.18 # Maximum resident set size: 1744 pages
% 938.38/119.18
% 938.38/119.18 # -------------------------------------------------
% 938.38/119.18 # User time : 114.257 s
% 938.38/119.18 # System time : 2.006 s
% 938.38/119.18 # Total time : 116.263 s
% 938.38/119.18 # Maximum resident set size: 1728 pages
% 938.38/119.18 % E---3.1 exiting
%------------------------------------------------------------------------------