TSTP Solution File: REL041+2 by E-SAT---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : REL041+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat May 4 09:13:51 EDT 2024
% Result : Theorem 37.22s 5.15s
% Output : CNFRefutation 37.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 15
% Syntax : Number of formulae : 150 ( 147 unt; 0 def)
% Number of atoms : 153 ( 152 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 : 251 ( 19 sgn 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(converse_multiplicativity,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/export/starexec/sandbox2/tmp/tmp.1ltR5mtnub/E---3.1_19755.p',converse_multiplicativity) ).
fof(converse_idempotence,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/export/starexec/sandbox2/tmp/tmp.1ltR5mtnub/E---3.1_19755.p',converse_idempotence) ).
fof(composition_identity,axiom,
! [X1] : composition(X1,one) = X1,
file('/export/starexec/sandbox2/tmp/tmp.1ltR5mtnub/E---3.1_19755.p',composition_identity) ).
fof(converse_cancellativity,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/export/starexec/sandbox2/tmp/tmp.1ltR5mtnub/E---3.1_19755.p',converse_cancellativity) ).
fof(maddux1_join_commutativity,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/tmp/tmp.1ltR5mtnub/E---3.1_19755.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.1ltR5mtnub/E---3.1_19755.p',composition_distributivity) ).
fof(maddux4_definiton_of_meet,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/export/starexec/sandbox2/tmp/tmp.1ltR5mtnub/E---3.1_19755.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.1ltR5mtnub/E---3.1_19755.p',converse_additivity) ).
fof(def_zero,axiom,
! [X1] : zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox2/tmp/tmp.1ltR5mtnub/E---3.1_19755.p',def_zero) ).
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.1ltR5mtnub/E---3.1_19755.p',maddux3_a_kind_of_de_Morgan) ).
fof(maddux2_join_associativity,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/export/starexec/sandbox2/tmp/tmp.1ltR5mtnub/E---3.1_19755.p',maddux2_join_associativity) ).
fof(goals,conjecture,
! [X1] :
( join(composition(converse(X1),X1),one) = one
=> ! [X2] : meet(composition(X1,X2),composition(X1,complement(X2))) = zero ),
file('/export/starexec/sandbox2/tmp/tmp.1ltR5mtnub/E---3.1_19755.p',goals) ).
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.1ltR5mtnub/E---3.1_19755.p',dedekind_law) ).
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.1ltR5mtnub/E---3.1_19755.p',modular_law_1) ).
fof(composition_associativity,axiom,
! [X1,X2,X3] : composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/export/starexec/sandbox2/tmp/tmp.1ltR5mtnub/E---3.1_19755.p',composition_associativity) ).
fof(c_0_15,plain,
! [X24,X25] : converse(composition(X24,X25)) = composition(converse(X25),converse(X24)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
fof(c_0_16,plain,
! [X38] : converse(converse(X38)) = X38,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
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,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_19,plain,
! [X30] : composition(X30,one) = X30,
inference(variable_rename,[status(thm)],[composition_identity]) ).
cnf(c_0_20,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_22,plain,
! [X26,X27] : join(composition(converse(X26),complement(composition(X26,X27))),complement(X27)) = complement(X27),
inference(variable_rename,[status(thm)],[converse_cancellativity]) ).
fof(c_0_23,plain,
! [X31,X32] : join(X31,X32) = join(X32,X31),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_0_24,plain,
composition(converse(one),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_18]) ).
cnf(c_0_25,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_21,c_0_24]) ).
fof(c_0_28,plain,
! [X21,X22,X23] : composition(join(X21,X22),X23) = join(composition(X21,X23),composition(X22,X23)),
inference(variable_rename,[status(thm)],[composition_distributivity]) ).
fof(c_0_29,plain,
! [X7,X8] : meet(X7,X8) = complement(join(complement(X7),complement(X8))),
inference(variable_rename,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_0_30,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_24,c_0_27]) ).
cnf(c_0_32,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_33,plain,
! [X36,X37] : converse(join(X36,X37)) = join(converse(X36),converse(X37)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
fof(c_0_34,plain,
! [X6] : zero = meet(X6,complement(X6)),
inference(variable_rename,[status(thm)],[def_zero]) ).
cnf(c_0_35,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_27]),c_0_31]) ).
cnf(c_0_37,plain,
join(X1,composition(X2,X1)) = composition(join(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_31]),c_0_26]) ).
cnf(c_0_38,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,plain,
zero = meet(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,plain,
complement(complement(X1)) = meet(X1,X1),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
fof(c_0_41,plain,
! [X28,X29] : X28 = join(complement(join(complement(X28),complement(X29))),complement(join(complement(X28),X29))),
inference(variable_rename,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
cnf(c_0_42,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_43,plain,
join(X1,X1) = composition(join(one,one),X1),
inference(spm,[status(thm)],[c_0_37,c_0_31]) ).
cnf(c_0_44,plain,
converse(join(X1,one)) = join(one,converse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_27]),c_0_26]) ).
fof(c_0_45,plain,
! [X33,X34,X35] : join(X33,join(X34,X35)) = join(join(X33,X34),X35),
inference(variable_rename,[status(thm)],[maddux2_join_associativity]) ).
cnf(c_0_46,plain,
join(meet(X1,X2),meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_36,c_0_35]) ).
cnf(c_0_47,plain,
meet(complement(X1),meet(X1,X1)) = zero,
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_48,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_49,plain,
join(X1,X1) = composition(X1,join(one,one)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_38]),c_0_18]),c_0_44]),c_0_27]) ).
cnf(c_0_50,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_51,plain,
join(zero,zero) = zero,
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[c_0_48,c_0_35]) ).
cnf(c_0_53,plain,
composition(complement(X1),join(one,one)) = complement(X1),
inference(spm,[status(thm)],[c_0_49,c_0_36]) ).
cnf(c_0_54,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_55,plain,
join(zero,complement(complement(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_49]),c_0_39]),c_0_53]) ).
cnf(c_0_56,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_57,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_58,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_57]) ).
cnf(c_0_59,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_50,c_0_58]) ).
cnf(c_0_60,plain,
join(X1,meet(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_52]),c_0_26]) ).
cnf(c_0_61,plain,
meet(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_56,c_0_60]) ).
cnf(c_0_62,plain,
complement(join(complement(zero),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_61]),c_0_56]) ).
cnf(c_0_63,plain,
join(complement(zero),X1) = complement(zero),
inference(spm,[status(thm)],[c_0_57,c_0_62]) ).
cnf(c_0_64,plain,
join(X1,complement(zero)) = complement(zero),
inference(spm,[status(thm)],[c_0_26,c_0_63]) ).
cnf(c_0_65,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_56]) ).
cnf(c_0_66,plain,
meet(X1,X2) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_26]),c_0_35]) ).
cnf(c_0_67,plain,
meet(X1,complement(zero)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_64]),c_0_57]),c_0_65]) ).
cnf(c_0_68,plain,
complement(join(X1,complement(X2))) = meet(complement(X1),X2),
inference(spm,[status(thm)],[c_0_35,c_0_57]) ).
cnf(c_0_69,plain,
meet(complement(zero),X1) = X1,
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_70,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_60,c_0_66]) ).
cnf(c_0_71,plain,
complement(join(complement(X1),X2)) = meet(complement(X2),X1),
inference(spm,[status(thm)],[c_0_68,c_0_26]) ).
cnf(c_0_72,plain,
join(X1,complement(X1)) = complement(zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_69]),c_0_57]),c_0_56]) ).
cnf(c_0_73,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(spm,[status(thm)],[c_0_38,c_0_18]) ).
cnf(c_0_74,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_50,c_0_70]) ).
cnf(c_0_75,plain,
join(meet(X1,X2),meet(complement(X2),X1)) = X1,
inference(rw,[status(thm)],[c_0_52,c_0_71]) ).
cnf(c_0_76,plain,
join(X1,join(complement(X1),X2)) = complement(zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_72]),c_0_63]) ).
cnf(c_0_77,plain,
join(converse(complement(zero)),X1) = converse(complement(zero)),
inference(spm,[status(thm)],[c_0_73,c_0_63]) ).
cnf(c_0_78,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_79,plain,
meet(X1,join(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_76]),c_0_57]),c_0_57]),c_0_65]) ).
cnf(c_0_80,plain,
meet(complement(X1),complement(X2)) = complement(join(X1,X2)),
inference(spm,[status(thm)],[c_0_68,c_0_57]) ).
cnf(c_0_81,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(spm,[status(thm)],[c_0_38,c_0_18]) ).
cnf(c_0_82,plain,
converse(complement(zero)) = complement(zero),
inference(spm,[status(thm)],[c_0_64,c_0_77]) ).
cnf(c_0_83,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_71,c_0_78]),c_0_71]),c_0_57]),c_0_66]) ).
cnf(c_0_84,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_57,c_0_68]) ).
cnf(c_0_85,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_52]),c_0_66]) ).
cnf(c_0_86,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_78,c_0_80]) ).
cnf(c_0_87,plain,
join(X1,converse(complement(converse(X1)))) = complement(zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_72]),c_0_82]) ).
cnf(c_0_88,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_83,c_0_83]),c_0_84]),c_0_57]),c_0_66]),c_0_85]) ).
cnf(c_0_89,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_59,c_0_26]) ).
cnf(c_0_90,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_57]),c_0_65]) ).
cnf(c_0_91,plain,
meet(X1,join(complement(X1),X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_88,c_0_26]) ).
cnf(c_0_92,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_79,c_0_89]) ).
cnf(c_0_93,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_90]),c_0_18]),c_0_18]) ).
cnf(c_0_94,plain,
meet(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_87]),c_0_67]) ).
cnf(c_0_95,plain,
converse(complement(converse(complement(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_66]),c_0_94]) ).
cnf(c_0_96,plain,
complement(converse(complement(X1))) = converse(X1),
inference(spm,[status(thm)],[c_0_18,c_0_95]) ).
cnf(c_0_97,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[c_0_57,c_0_96]) ).
cnf(c_0_98,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(spm,[status(thm)],[c_0_84,c_0_57]) ).
cnf(c_0_99,plain,
converse(complement(join(converse(X1),X2))) = complement(join(X1,converse(X2))),
inference(spm,[status(thm)],[c_0_97,c_0_81]) ).
cnf(c_0_100,plain,
join(converse(complement(X1)),complement(X2)) = complement(meet(converse(X1),X2)),
inference(spm,[status(thm)],[c_0_98,c_0_97]) ).
cnf(c_0_101,plain,
join(complement(X1),converse(complement(X2))) = complement(meet(X1,converse(X2))),
inference(spm,[status(thm)],[c_0_98,c_0_97]) ).
cnf(c_0_102,plain,
join(X1,composition(X1,converse(X2))) = composition(X1,join(one,converse(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_37]),c_0_42]),c_0_44]),c_0_42]) ).
cnf(c_0_103,plain,
complement(join(X1,join(X2,complement(X3)))) = meet(complement(join(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_68,c_0_50]) ).
cnf(c_0_104,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_99,c_0_100]),c_0_57]),c_0_101]),c_0_57]) ).
cnf(c_0_105,plain,
join(X1,composition(X1,X2)) = composition(X1,join(one,X2)),
inference(spm,[status(thm)],[c_0_102,c_0_18]) ).
cnf(c_0_106,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_103,c_0_98]),c_0_68]),c_0_68]) ).
cnf(c_0_107,plain,
meet(complement(X1),join(X1,X2)) = meet(X2,complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_80]),c_0_57]),c_0_57]) ).
cnf(c_0_108,plain,
join(complement(one),composition(converse(X1),complement(X1))) = complement(one),
inference(spm,[status(thm)],[c_0_30,c_0_21]) ).
cnf(c_0_109,plain,
join(converse(zero),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_56]),c_0_18]) ).
cnf(c_0_110,plain,
composition(join(X1,one),zero) = composition(X1,zero),
inference(spm,[status(thm)],[c_0_37,c_0_56]) ).
fof(c_0_111,negated_conjecture,
~ ! [X1] :
( join(composition(converse(X1),X1),one) = one
=> ! [X2] : meet(composition(X1,X2),composition(X1,complement(X2))) = zero ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_112,plain,
! [X9,X10,X11] : join(meet(composition(X9,X10),X11),composition(meet(X9,composition(X11,converse(X10))),meet(X10,composition(converse(X9),X11)))) = composition(meet(X9,composition(X11,converse(X10))),meet(X10,composition(converse(X9),X11))),
inference(variable_rename,[status(thm)],[dedekind_law]) ).
cnf(c_0_113,plain,
converse(meet(X1,converse(X2))) = meet(converse(X1),X2),
inference(spm,[status(thm)],[c_0_18,c_0_104]) ).
cnf(c_0_114,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_78,c_0_66]) ).
cnf(c_0_115,plain,
meet(composition(X1,X2),composition(X1,join(one,X2))) = composition(X1,X2),
inference(spm,[status(thm)],[c_0_92,c_0_105]) ).
cnf(c_0_116,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_106,c_0_57]) ).
cnf(c_0_117,plain,
meet(one,composition(converse(X1),complement(X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_57]),c_0_39]),c_0_57]),c_0_66]) ).
cnf(c_0_118,plain,
converse(zero) = zero,
inference(spm,[status(thm)],[c_0_65,c_0_109]) ).
cnf(c_0_119,plain,
composition(join(X1,one),complement(zero)) = complement(zero),
inference(spm,[status(thm)],[c_0_37,c_0_63]) ).
cnf(c_0_120,plain,
composition(join(one,X1),zero) = composition(X1,zero),
inference(spm,[status(thm)],[c_0_110,c_0_26]) ).
fof(c_0_121,negated_conjecture,
( join(composition(converse(esk1_0),esk1_0),one) = one
& meet(composition(esk1_0,esk2_0),composition(esk1_0,complement(esk2_0))) != zero ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_111])])])]) ).
fof(c_0_122,plain,
! [X12,X13,X14] : join(meet(composition(X12,X13),X14),meet(composition(X12,meet(X13,composition(converse(X12),X14))),X14)) = meet(composition(X12,meet(X13,composition(converse(X12),X14))),X14),
inference(variable_rename,[status(thm)],[modular_law_1]) ).
cnf(c_0_123,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_112]) ).
cnf(c_0_124,plain,
meet(converse(X1),composition(converse(X2),X3)) = converse(meet(X1,composition(converse(X3),X2))),
inference(spm,[status(thm)],[c_0_113,c_0_20]) ).
cnf(c_0_125,plain,
meet(X1,complement(meet(X2,X1))) = meet(complement(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_114]),c_0_71]),c_0_57]),c_0_66]) ).
cnf(c_0_126,plain,
meet(X1,composition(X1,meet(one,X2))) = composition(X1,meet(one,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_60]),c_0_21]),c_0_66]) ).
cnf(c_0_127,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_66]),c_0_116]) ).
cnf(c_0_128,plain,
meet(one,composition(X1,converse(complement(X1)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_97]),c_0_18]) ).
cnf(c_0_129,plain,
meet(X1,zero) = zero,
inference(spm,[status(thm)],[c_0_66,c_0_61]) ).
cnf(c_0_130,plain,
converse(composition(X1,zero)) = composition(zero,converse(X1)),
inference(spm,[status(thm)],[c_0_17,c_0_118]) ).
cnf(c_0_131,plain,
composition(converse(X1),zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_119]),c_0_57]),c_0_44]),c_0_57]),c_0_120]),c_0_37]),c_0_26]),c_0_120]),c_0_57]) ).
cnf(c_0_132,negated_conjecture,
join(composition(converse(esk1_0),esk1_0),one) = one,
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_133,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_122]) ).
cnf(c_0_134,plain,
join(meet(composition(X1,converse(X2)),X3),composition(meet(X1,composition(X3,X2)),converse(meet(X2,composition(converse(X3),X1))))) = composition(meet(X1,composition(X3,X2)),converse(meet(X2,composition(converse(X3),X1)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_18]),c_0_124]),c_0_124]) ).
cnf(c_0_135,plain,
meet(complement(X1),composition(X1,meet(one,X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_39]) ).
cnf(c_0_136,plain,
meet(one,meet(X1,composition(X2,converse(complement(X2))))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_129]) ).
cnf(c_0_137,plain,
composition(zero,X1) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_118]),c_0_18]) ).
cnf(c_0_138,negated_conjecture,
join(one,composition(converse(esk1_0),esk1_0)) = one,
inference(rw,[status(thm)],[c_0_132,c_0_26]) ).
fof(c_0_139,plain,
! [X18,X19,X20] : composition(X18,composition(X19,X20)) = composition(composition(X18,X19),X20),
inference(variable_rename,[status(thm)],[composition_associativity]) ).
cnf(c_0_140,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_133,c_0_66]),c_0_66]) ).
cnf(c_0_141,plain,
meet(X1,composition(meet(one,X2),complement(X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(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_134,c_0_135]),c_0_97]),c_0_18]),c_0_97]),c_0_116]),c_0_136]),c_0_118]),c_0_137]),c_0_65]),c_0_97]),c_0_116]),c_0_136]),c_0_118]),c_0_137]),c_0_66]) ).
cnf(c_0_142,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_92,c_0_138]),c_0_66]) ).
cnf(c_0_143,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_139]) ).
cnf(c_0_144,plain,
join(meet(composition(converse(X1),X2),X3),meet(X3,composition(converse(X1),meet(X2,composition(X1,X3))))) = meet(X3,composition(converse(X1),meet(X2,composition(X1,X3)))),
inference(spm,[status(thm)],[c_0_140,c_0_18]) ).
cnf(c_0_145,negated_conjecture,
meet(X1,composition(converse(esk1_0),composition(esk1_0,complement(X1)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_143]) ).
cnf(c_0_146,plain,
composition(X1,zero) = zero,
inference(spm,[status(thm)],[c_0_131,c_0_18]) ).
cnf(c_0_147,negated_conjecture,
meet(composition(esk1_0,esk2_0),composition(esk1_0,complement(esk2_0))) != zero,
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_148,negated_conjecture,
meet(composition(esk1_0,X1),composition(esk1_0,complement(X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_145]),c_0_18]),c_0_18]),c_0_146]),c_0_129]),c_0_65]),c_0_18]),c_0_146]),c_0_129]) ).
cnf(c_0_149,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_147,c_0_148])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : REL041+2 : TPTP v8.1.2. Released v4.0.0.
% 0.02/0.11 % Command : run_E %s %d THM
% 0.10/0.31 % Computer : n017.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri May 3 09:13:36 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.16/0.41 Running first-order model finding
% 0.16/0.41 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.1ltR5mtnub/E---3.1_19755.p
% 37.22/5.15 # Version: 3.1.0
% 37.22/5.15 # Preprocessing class: FSMSSMSSSSSNFFN.
% 37.22/5.15 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 37.22/5.15 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 37.22/5.15 # Starting new_bool_3 with 300s (1) cores
% 37.22/5.15 # Starting new_bool_1 with 300s (1) cores
% 37.22/5.15 # Starting sh5l with 300s (1) cores
% 37.22/5.15 # new_bool_3 with pid 19833 completed with status 0
% 37.22/5.15 # Result found by new_bool_3
% 37.22/5.15 # Preprocessing class: FSMSSMSSSSSNFFN.
% 37.22/5.15 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 37.22/5.15 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 37.22/5.15 # Starting new_bool_3 with 300s (1) cores
% 37.22/5.15 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 37.22/5.15 # Search class: FUUPM-FFMF21-DFFFFFNN
% 37.22/5.15 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 37.22/5.15 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 181s (1) cores
% 37.22/5.15 # H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with pid 19840 completed with status 0
% 37.22/5.15 # Result found by H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S
% 37.22/5.15 # Preprocessing class: FSMSSMSSSSSNFFN.
% 37.22/5.15 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 37.22/5.15 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 37.22/5.15 # Starting new_bool_3 with 300s (1) cores
% 37.22/5.15 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 37.22/5.15 # Search class: FUUPM-FFMF21-DFFFFFNN
% 37.22/5.15 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 37.22/5.15 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 181s (1) cores
% 37.22/5.15 # Preprocessing time : 0.001 s
% 37.22/5.15 # Presaturation interreduction done
% 37.22/5.15
% 37.22/5.15 # Proof found!
% 37.22/5.15 # SZS status Theorem
% 37.22/5.15 # SZS output start CNFRefutation
% See solution above
% 37.22/5.15 # Parsed axioms : 17
% 37.22/5.15 # Removed by relevancy pruning/SinE : 1
% 37.22/5.15 # Initial clauses : 17
% 37.22/5.15 # Removed in clause preprocessing : 0
% 37.22/5.15 # Initial clauses in saturation : 17
% 37.22/5.15 # Processed clauses : 10858
% 37.22/5.15 # ...of these trivial : 5094
% 37.22/5.15 # ...subsumed : 4652
% 37.22/5.15 # ...remaining for further processing : 1112
% 37.22/5.15 # Other redundant clauses eliminated : 0
% 37.22/5.15 # Clauses deleted for lack of memory : 0
% 37.22/5.15 # Backward-subsumed : 0
% 37.22/5.15 # Backward-rewritten : 167
% 37.22/5.15 # Generated clauses : 321197
% 37.22/5.15 # ...of the previous two non-redundant : 202312
% 37.22/5.15 # ...aggressively subsumed : 0
% 37.22/5.15 # Contextual simplify-reflections : 0
% 37.22/5.15 # Paramodulations : 321197
% 37.22/5.15 # Factorizations : 0
% 37.22/5.15 # NegExts : 0
% 37.22/5.15 # Equation resolutions : 0
% 37.22/5.15 # Disequality decompositions : 0
% 37.22/5.15 # Total rewrite steps : 703407
% 37.22/5.15 # ...of those cached : 593836
% 37.22/5.15 # Propositional unsat checks : 0
% 37.22/5.15 # Propositional check models : 0
% 37.22/5.15 # Propositional check unsatisfiable : 0
% 37.22/5.15 # Propositional clauses : 0
% 37.22/5.15 # Propositional clauses after purity: 0
% 37.22/5.15 # Propositional unsat core size : 0
% 37.22/5.15 # Propositional preprocessing time : 0.000
% 37.22/5.15 # Propositional encoding time : 0.000
% 37.22/5.15 # Propositional solver time : 0.000
% 37.22/5.15 # Success case prop preproc time : 0.000
% 37.22/5.15 # Success case prop encoding time : 0.000
% 37.22/5.15 # Success case prop solver time : 0.000
% 37.22/5.15 # Current number of processed clauses : 928
% 37.22/5.15 # Positive orientable unit clauses : 914
% 37.22/5.15 # Positive unorientable unit clauses: 14
% 37.22/5.15 # Negative unit clauses : 0
% 37.22/5.15 # Non-unit-clauses : 0
% 37.22/5.15 # Current number of unprocessed clauses: 189900
% 37.22/5.15 # ...number of literals in the above : 189900
% 37.22/5.15 # Current number of archived formulas : 0
% 37.22/5.15 # Current number of archived clauses : 184
% 37.22/5.15 # Clause-clause subsumption calls (NU) : 0
% 37.22/5.15 # Rec. Clause-clause subsumption calls : 0
% 37.22/5.15 # Non-unit clause-clause subsumptions : 0
% 37.22/5.15 # Unit Clause-clause subsumption calls : 234
% 37.22/5.15 # Rewrite failures with RHS unbound : 0
% 37.22/5.15 # BW rewrite match attempts : 4698
% 37.22/5.15 # BW rewrite match successes : 780
% 37.22/5.15 # Condensation attempts : 0
% 37.22/5.15 # Condensation successes : 0
% 37.22/5.15 # Termbank termtop insertions : 6202151
% 37.22/5.15 # Search garbage collected termcells : 35
% 37.22/5.15
% 37.22/5.15 # -------------------------------------------------
% 37.22/5.15 # User time : 4.432 s
% 37.22/5.15 # System time : 0.204 s
% 37.22/5.15 # Total time : 4.636 s
% 37.22/5.15 # Maximum resident set size: 1756 pages
% 37.22/5.15
% 37.22/5.15 # -------------------------------------------------
% 37.22/5.15 # User time : 4.432 s
% 37.22/5.15 # System time : 0.207 s
% 37.22/5.15 # Total time : 4.639 s
% 37.22/5.15 # Maximum resident set size: 1700 pages
% 37.22/5.15 % E---3.1 exiting
%------------------------------------------------------------------------------