TSTP Solution File: REL029+1 by E-SAT---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : REL029+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n013.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 02:32:22 EDT 2024
% Result : Theorem 8.04s 1.50s
% Output : CNFRefutation 8.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 14
% Syntax : Number of formulae : 175 ( 172 unt; 0 def)
% Number of atoms : 181 ( 180 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 9 ( 3 ~; 0 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 274 ( 20 sgn 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(converse_multiplicativity,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).
fof(converse_idempotence,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
fof(composition_identity,axiom,
! [X1] : composition(X1,one) = X1,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).
fof(maddux1_join_commutativity,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/REL001+0.ax',maddux2_join_associativity) ).
fof(def_top,axiom,
! [X1] : top = join(X1,complement(X1)),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/REL001+0.ax',maddux4_definiton_of_meet) ).
fof(def_zero,axiom,
! [X1] : zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_zero) ).
fof(goals,conjecture,
! [X1,X2,X3] :
( ( join(X1,one) = one
& join(X2,one) = one )
=> meet(composition(X1,X3),composition(X2,X3)) = composition(meet(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(composition_distributivity,axiom,
! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
fof(converse_additivity,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_additivity) ).
fof(composition_associativity,axiom,
! [X1,X2,X3] : composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_associativity) ).
fof(c_0_14,plain,
! [X14,X15] : converse(composition(X14,X15)) = composition(converse(X15),converse(X14)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
fof(c_0_15,plain,
! [X30] : converse(converse(X30)) = X30,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
cnf(c_0_16,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_18,plain,
! [X10] : composition(X10,one) = X10,
inference(variable_rename,[status(thm)],[composition_identity]) ).
cnf(c_0_19,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_21,plain,
! [X16,X17] : join(composition(converse(X16),complement(composition(X16,X17))),complement(X17)) = complement(X17),
inference(variable_rename,[status(thm)],[converse_cancellativity]) ).
fof(c_0_22,plain,
! [X21,X22] : join(X21,X22) = join(X22,X21),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_0_23,plain,
composition(converse(one),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_17]) ).
fof(c_0_24,plain,
! [X23,X24,X25] : join(X23,join(X24,X25)) = join(join(X23,X24),X25),
inference(variable_rename,[status(thm)],[maddux2_join_associativity]) ).
fof(c_0_25,plain,
! [X31] : top = join(X31,complement(X31)),
inference(variable_rename,[status(thm)],[def_top]) ).
cnf(c_0_26,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_20,c_0_23]) ).
cnf(c_0_29,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
top = join(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_32,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_23,c_0_28]) ).
fof(c_0_33,plain,
! [X26,X27] : X26 = join(complement(join(complement(X26),complement(X27))),complement(join(complement(X26),X27))),
inference(variable_rename,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
fof(c_0_34,plain,
! [X18,X19] : meet(X18,X19) = complement(join(complement(X18),complement(X19))),
inference(variable_rename,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_0_35,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,plain,
join(X1,join(X2,complement(join(X1,X2)))) = top,
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
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_31,c_0_32]),c_0_28]),c_0_32]) ).
fof(c_0_38,plain,
! [X20] : zero = meet(X20,complement(X20)),
inference(variable_rename,[status(thm)],[def_zero]) ).
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_33]) ).
cnf(c_0_40,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,plain,
join(top,complement(complement(X1))) = join(X1,top),
inference(spm,[status(thm)],[c_0_35,c_0_30]) ).
cnf(c_0_42,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_30]),c_0_27]) ).
cnf(c_0_43,plain,
zero = meet(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_45,plain,
join(X1,top) = top,
inference(rw,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,plain,
complement(top) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_30]),c_0_43]) ).
cnf(c_0_47,plain,
join(zero,meet(X1,top)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46]),c_0_27]) ).
cnf(c_0_48,plain,
meet(X1,X2) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_27]),c_0_40]) ).
cnf(c_0_49,plain,
complement(join(zero,complement(X1))) = meet(top,X1),
inference(spm,[status(thm)],[c_0_40,c_0_46]) ).
cnf(c_0_50,plain,
join(zero,complement(complement(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_37]),c_0_43]) ).
cnf(c_0_51,plain,
join(zero,meet(top,X1)) = 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_49,c_0_50]) ).
cnf(c_0_53,plain,
join(zero,complement(X1)) = complement(X1),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_54,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_50,c_0_53]) ).
cnf(c_0_55,plain,
complement(complement(X1)) = meet(X1,X1),
inference(spm,[status(thm)],[c_0_40,c_0_37]) ).
cnf(c_0_56,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_37,c_0_54]) ).
fof(c_0_57,negated_conjecture,
~ ! [X1,X2,X3] :
( ( join(X1,one) = one
& join(X2,one) = one )
=> meet(composition(X1,X3),composition(X2,X3)) = composition(meet(X1,X2),X3) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_58,plain,
join(zero,meet(X1,X1)) = X1,
inference(spm,[status(thm)],[c_0_50,c_0_55]) ).
cnf(c_0_59,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_29,c_0_56]) ).
cnf(c_0_60,plain,
complement(join(X1,complement(X2))) = meet(complement(X1),X2),
inference(spm,[status(thm)],[c_0_40,c_0_54]) ).
fof(c_0_61,plain,
! [X11,X12,X13] : composition(join(X11,X12),X13) = join(composition(X11,X13),composition(X12,X13)),
inference(variable_rename,[status(thm)],[composition_distributivity]) ).
fof(c_0_62,negated_conjecture,
( join(esk1_0,one) = one
& join(esk2_0,one) = one
& meet(composition(esk1_0,esk3_0),composition(esk2_0,esk3_0)) != composition(meet(esk1_0,esk2_0),esk3_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_57])])])]) ).
fof(c_0_63,plain,
! [X28,X29] : converse(join(X28,X29)) = join(converse(X28),converse(X29)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
cnf(c_0_64,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_55]),c_0_58]) ).
cnf(c_0_65,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_27]),c_0_29]) ).
cnf(c_0_66,plain,
join(X1,meet(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_44]),c_0_27]) ).
cnf(c_0_67,plain,
complement(join(complement(X1),X2)) = meet(complement(X2),X1),
inference(spm,[status(thm)],[c_0_60,c_0_27]) ).
cnf(c_0_68,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_69,negated_conjecture,
join(esk2_0,one) = one,
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_70,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_71,plain,
join(X1,join(X2,complement(X1))) = join(top,X2),
inference(spm,[status(thm)],[c_0_35,c_0_27]) ).
cnf(c_0_72,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_27,c_0_45]) ).
cnf(c_0_73,plain,
join(zero,X1) = X1,
inference(rw,[status(thm)],[c_0_58,c_0_64]) ).
cnf(c_0_74,plain,
join(X1,join(X2,meet(X1,X3))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_75,plain,
join(meet(X1,X2),meet(complement(X2),X1)) = X1,
inference(rw,[status(thm)],[c_0_44,c_0_67]) ).
cnf(c_0_76,plain,
join(X1,composition(X2,X1)) = composition(join(one,X2),X1),
inference(spm,[status(thm)],[c_0_68,c_0_32]) ).
cnf(c_0_77,negated_conjecture,
join(one,esk2_0) = one,
inference(rw,[status(thm)],[c_0_69,c_0_27]) ).
cnf(c_0_78,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_66,c_0_48]) ).
cnf(c_0_79,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(spm,[status(thm)],[c_0_70,c_0_17]) ).
cnf(c_0_80,plain,
join(X1,join(X2,complement(X1))) = top,
inference(rw,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_81,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_73]) ).
cnf(c_0_82,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_54,c_0_60]) ).
cnf(c_0_83,plain,
join(meet(X1,X2),complement(X2)) = join(complement(X2),X1),
inference(spm,[status(thm)],[c_0_74,c_0_75]) ).
cnf(c_0_84,negated_conjecture,
join(X1,composition(esk2_0,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_32]) ).
cnf(c_0_85,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_86,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_29,c_0_78]) ).
cnf(c_0_87,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(spm,[status(thm)],[c_0_79,c_0_30]) ).
cnf(c_0_88,plain,
meet(X1,join(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_80]),c_0_54]),c_0_46]),c_0_81]) ).
cnf(c_0_89,plain,
complement(join(X1,join(X2,complement(X3)))) = meet(complement(join(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_60,c_0_29]) ).
cnf(c_0_90,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(spm,[status(thm)],[c_0_82,c_0_54]) ).
cnf(c_0_91,plain,
meet(X1,complement(meet(X2,X1))) = meet(complement(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_83]),c_0_67]),c_0_48]) ).
cnf(c_0_92,negated_conjecture,
join(X1,composition(X1,converse(esk2_0))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_84]),c_0_17]),c_0_85]) ).
cnf(c_0_93,plain,
meet(complement(X1),complement(X2)) = complement(join(X1,X2)),
inference(spm,[status(thm)],[c_0_60,c_0_54]) ).
cnf(c_0_94,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_86,c_0_75]) ).
cnf(c_0_95,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_87,c_0_72]) ).
cnf(c_0_96,plain,
meet(X1,join(X2,join(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_88,c_0_29]) ).
cnf(c_0_97,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_89,c_0_90]),c_0_60]),c_0_60]) ).
cnf(c_0_98,plain,
meet(X1,join(X2,complement(X1))) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_82]),c_0_54]) ).
cnf(c_0_99,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_78]),c_0_48]) ).
cnf(c_0_100,plain,
join(X1,join(X2,X3)) = join(X2,join(X3,X1)),
inference(spm,[status(thm)],[c_0_29,c_0_27]) ).
cnf(c_0_101,negated_conjecture,
join(X1,composition(converse(esk2_0),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_92]),c_0_32]),c_0_32]) ).
cnf(c_0_102,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_93]),c_0_54]),c_0_54]),c_0_27]) ).
cnf(c_0_103,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_94,c_0_93]) ).
cnf(c_0_104,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(rw,[status(thm)],[c_0_87,c_0_95]) ).
cnf(c_0_105,plain,
meet(meet(X1,X2),join(X3,X1)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_96,c_0_66]) ).
cnf(c_0_106,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_97,c_0_54]) ).
cnf(c_0_107,plain,
meet(X1,join(complement(X1),X2)) = meet(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_83]),c_0_48]),c_0_99]) ).
cnf(c_0_108,plain,
complement(join(zero,zero)) = meet(top,top),
inference(spm,[status(thm)],[c_0_49,c_0_46]) ).
cnf(c_0_109,plain,
join(zero,zero) = zero,
inference(spm,[status(thm)],[c_0_37,c_0_46]) ).
cnf(c_0_110,plain,
join(composition(X1,X2),join(X3,composition(X4,X2))) = join(X3,composition(join(X4,X1),X2)),
inference(spm,[status(thm)],[c_0_100,c_0_68]) ).
cnf(c_0_111,negated_conjecture,
join(X1,composition(X1,esk2_0)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_101]),c_0_17]),c_0_16]),c_0_17]) ).
cnf(c_0_112,plain,
meet(X1,join(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_88,c_0_27]) ).
cnf(c_0_113,plain,
meet(join(X1,X2),join(X2,complement(X1))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_102]),c_0_88]) ).
cnf(c_0_114,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_46]),c_0_81]) ).
cnf(c_0_115,plain,
meet(X1,meet(X2,join(X3,X1))) = meet(X1,X2),
inference(rw,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_116,plain,
meet(complement(X1),join(X1,X2)) = meet(X2,complement(X1)),
inference(spm,[status(thm)],[c_0_107,c_0_54]) ).
cnf(c_0_117,plain,
complement(zero) = meet(top,top),
inference(rw,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_118,negated_conjecture,
join(X1,composition(join(X1,X2),esk2_0)) = join(composition(X2,esk2_0),X1),
inference(spm,[status(thm)],[c_0_110,c_0_111]) ).
cnf(c_0_119,plain,
meet(X1,join(X2,join(X1,X3))) = X1,
inference(spm,[status(thm)],[c_0_112,c_0_65]) ).
cnf(c_0_120,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_29,c_0_66]) ).
cnf(c_0_121,plain,
meet(join(X1,X2),join(complement(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_113,c_0_27]) ).
cnf(c_0_122,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_114]),c_0_17]),c_0_17]) ).
cnf(c_0_123,plain,
meet(top,X1) = X1,
inference(spm,[status(thm)],[c_0_52,c_0_54]) ).
cnf(c_0_124,negated_conjecture,
meet(esk2_0,meet(X1,one)) = meet(esk2_0,X1),
inference(spm,[status(thm)],[c_0_115,c_0_77]) ).
cnf(c_0_125,plain,
meet(join(X1,X2),complement(X1)) = meet(X2,complement(X1)),
inference(spm,[status(thm)],[c_0_48,c_0_116]) ).
cnf(c_0_126,plain,
join(complement(one),composition(converse(X1),complement(X1))) = complement(one),
inference(spm,[status(thm)],[c_0_31,c_0_20]) ).
cnf(c_0_127,plain,
complement(zero) = top,
inference(rw,[status(thm)],[c_0_117,c_0_64]) ).
cnf(c_0_128,negated_conjecture,
join(X1,composition(complement(X1),esk2_0)) = join(X1,composition(top,esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_30]),c_0_27]) ).
cnf(c_0_129,negated_conjecture,
meet(X1,composition(X1,esk2_0)) = composition(X1,esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_111]),c_0_98]),c_0_48]) ).
cnf(c_0_130,plain,
meet(meet(X1,X2),join(X1,X3)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_131,plain,
join(X1,composition(X2,X1)) = composition(join(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_32]),c_0_27]) ).
cnf(c_0_132,plain,
converse(complement(converse(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_121,c_0_122]),c_0_54]),c_0_104]),c_0_123]),c_0_54]) ).
cnf(c_0_133,negated_conjecture,
meet(esk2_0,meet(one,X1)) = meet(esk2_0,X1),
inference(spm,[status(thm)],[c_0_124,c_0_48]) ).
cnf(c_0_134,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_54]),c_0_48]),c_0_43]),c_0_54]),c_0_48]) ).
cnf(c_0_135,plain,
meet(X1,zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_127]),c_0_27]),c_0_72]),c_0_46]) ).
cnf(c_0_136,negated_conjecture,
meet(composition(top,esk2_0),X1) = composition(X1,esk2_0),
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_128]),c_0_107]),c_0_54]),c_0_48]),c_0_129]) ).
cnf(c_0_137,plain,
meet(join(X1,X2),meet(X1,X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_48,c_0_130]) ).
cnf(c_0_138,plain,
join(X1,composition(top,X1)) = composition(top,X1),
inference(spm,[status(thm)],[c_0_131,c_0_72]) ).
cnf(c_0_139,negated_conjecture,
join(esk1_0,one) = one,
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_140,plain,
converse(complement(X1)) = complement(converse(X1)),
inference(spm,[status(thm)],[c_0_17,c_0_132]) ).
cnf(c_0_141,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(spm,[status(thm)],[c_0_70,c_0_17]) ).
cnf(c_0_142,negated_conjecture,
meet(esk2_0,composition(converse(X1),complement(X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_135]) ).
cnf(c_0_143,negated_conjecture,
meet(composition(X1,esk2_0),X2) = composition(meet(X1,X2),esk2_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_136]),c_0_136]) ).
cnf(c_0_144,plain,
meet(composition(top,X1),meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_137,c_0_138]) ).
cnf(c_0_145,negated_conjecture,
join(one,esk1_0) = one,
inference(rw,[status(thm)],[c_0_139,c_0_27]) ).
cnf(c_0_146,plain,
complement(converse(join(complement(X1),X2))) = converse(meet(complement(X2),X1)),
inference(spm,[status(thm)],[c_0_140,c_0_67]) ).
cnf(c_0_147,plain,
converse(join(X1,complement(converse(X2)))) = join(converse(X1),complement(X2)),
inference(spm,[status(thm)],[c_0_141,c_0_140]) ).
cnf(c_0_148,negated_conjecture,
meet(esk2_0,composition(complement(converse(X1)),X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_54]),c_0_140]) ).
cnf(c_0_149,negated_conjecture,
meet(X1,composition(X2,esk2_0)) = composition(meet(X2,X1),esk2_0),
inference(spm,[status(thm)],[c_0_48,c_0_143]) ).
cnf(c_0_150,negated_conjecture,
composition(meet(esk2_0,X1),esk2_0) = meet(esk2_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_143]),c_0_123]) ).
cnf(c_0_151,negated_conjecture,
join(X1,composition(esk1_0,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_145]),c_0_32]) ).
cnf(c_0_152,plain,
converse(meet(converse(X1),X2)) = meet(converse(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_140]),c_0_90]),c_0_54]),c_0_54]) ).
cnf(c_0_153,negated_conjecture,
meet(esk2_0,complement(converse(esk2_0))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_48]),c_0_150]) ).
cnf(c_0_154,negated_conjecture,
join(X1,composition(X1,converse(esk1_0))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_151]),c_0_17]),c_0_85]) ).
cnf(c_0_155,plain,
converse(meet(X1,converse(X2))) = meet(converse(X1),X2),
inference(spm,[status(thm)],[c_0_152,c_0_48]) ).
cnf(c_0_156,negated_conjecture,
meet(esk2_0,converse(esk2_0)) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_153]),c_0_54]),c_0_48]),c_0_73]) ).
cnf(c_0_157,negated_conjecture,
join(X1,composition(converse(esk1_0),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_154]),c_0_32]),c_0_32]) ).
cnf(c_0_158,negated_conjecture,
converse(esk2_0) = esk2_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_156]),c_0_48]),c_0_156]) ).
cnf(c_0_159,negated_conjecture,
composition(meet(one,X1),esk2_0) = meet(esk2_0,X1),
inference(spm,[status(thm)],[c_0_143,c_0_32]) ).
cnf(c_0_160,negated_conjecture,
meet(X1,composition(converse(esk1_0),X1)) = composition(converse(esk1_0),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_157]),c_0_98]),c_0_48]) ).
cnf(c_0_161,negated_conjecture,
composition(converse(X1),esk2_0) = converse(composition(esk2_0,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_158]) ).
cnf(c_0_162,negated_conjecture,
composition(converse(esk1_0),esk2_0) = meet(esk2_0,converse(esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_20]),c_0_20]) ).
cnf(c_0_163,negated_conjecture,
meet(converse(composition(esk2_0,X1)),X2) = composition(meet(converse(X1),X2),esk2_0),
inference(spm,[status(thm)],[c_0_143,c_0_161]) ).
cnf(c_0_164,plain,
meet(converse(X1),converse(X2)) = converse(meet(X2,X1)),
inference(spm,[status(thm)],[c_0_152,c_0_17]) ).
fof(c_0_165,plain,
! [X7,X8,X9] : composition(X7,composition(X8,X9)) = composition(composition(X7,X8),X9),
inference(variable_rename,[status(thm)],[composition_associativity]) ).
cnf(c_0_166,negated_conjecture,
composition(converse(esk2_0),esk1_0) = meet(esk1_0,converse(esk2_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_162]),c_0_155]),c_0_48]) ).
cnf(c_0_167,negated_conjecture,
meet(composition(esk2_0,X1),X2) = composition(esk2_0,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_155,c_0_163]),c_0_164]),c_0_161]),c_0_17]),c_0_17]) ).
cnf(c_0_168,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_165]) ).
cnf(c_0_169,negated_conjecture,
composition(esk2_0,esk1_0) = meet(esk1_0,esk2_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_166,c_0_158]),c_0_158]) ).
cnf(c_0_170,negated_conjecture,
meet(composition(esk1_0,esk3_0),composition(esk2_0,esk3_0)) != composition(meet(esk1_0,esk2_0),esk3_0),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_171,negated_conjecture,
meet(X1,composition(esk2_0,X2)) = composition(esk2_0,meet(X1,X2)),
inference(spm,[status(thm)],[c_0_48,c_0_167]) ).
cnf(c_0_172,negated_conjecture,
meet(X1,composition(esk1_0,X1)) = composition(esk1_0,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_151]),c_0_98]),c_0_48]) ).
cnf(c_0_173,negated_conjecture,
composition(esk2_0,composition(esk1_0,X1)) = composition(meet(esk1_0,esk2_0),X1),
inference(spm,[status(thm)],[c_0_168,c_0_169]) ).
cnf(c_0_174,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_171]),c_0_48]),c_0_172]),c_0_173])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : REL029+1 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.13 % Command : run_E %s %d THM
% 0.14/0.34 % Computer : n013.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon May 20 08:08:53 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.21/0.47 Running first-order model finding
% 0.21/0.47 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/benchmark/theBenchmark.p
% 8.04/1.50 # Version: 3.1.0
% 8.04/1.50 # Preprocessing class: FSMSSMSSSSSNFFN.
% 8.04/1.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.04/1.50 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.04/1.50 # Starting new_bool_3 with 300s (1) cores
% 8.04/1.50 # Starting new_bool_1 with 300s (1) cores
% 8.04/1.50 # Starting sh5l with 300s (1) cores
% 8.04/1.50 # sh5l with pid 12895 completed with status 0
% 8.04/1.50 # Result found by sh5l
% 8.04/1.50 # Preprocessing class: FSMSSMSSSSSNFFN.
% 8.04/1.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.04/1.50 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.04/1.50 # Starting new_bool_3 with 300s (1) cores
% 8.04/1.50 # Starting new_bool_1 with 300s (1) cores
% 8.04/1.50 # Starting sh5l with 300s (1) cores
% 8.04/1.50 # SinE strategy is gf500_gu_R04_F100_L20000
% 8.04/1.50 # Search class: FUUPM-FFSF21-MFFFFFNN
% 8.04/1.50 # Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 8.04/1.50 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S2S with 135s (1) cores
% 8.04/1.50 # H----_047_C09_12_F1_AE_ND_CS_SP_S2S with pid 12903 completed with status 0
% 8.04/1.50 # Result found by H----_047_C09_12_F1_AE_ND_CS_SP_S2S
% 8.04/1.50 # Preprocessing class: FSMSSMSSSSSNFFN.
% 8.04/1.50 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 8.04/1.50 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 8.04/1.50 # Starting new_bool_3 with 300s (1) cores
% 8.04/1.50 # Starting new_bool_1 with 300s (1) cores
% 8.04/1.50 # Starting sh5l with 300s (1) cores
% 8.04/1.50 # SinE strategy is gf500_gu_R04_F100_L20000
% 8.04/1.50 # Search class: FUUPM-FFSF21-MFFFFFNN
% 8.04/1.50 # Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 8.04/1.50 # Starting H----_047_C09_12_F1_AE_ND_CS_SP_S2S with 135s (1) cores
% 8.04/1.50 # Preprocessing time : 0.001 s
% 8.04/1.50 # Presaturation interreduction done
% 8.04/1.50
% 8.04/1.50 # Proof found!
% 8.04/1.50 # SZS status Theorem
% 8.04/1.50 # SZS output start CNFRefutation
% See solution above
% 8.04/1.50 # Parsed axioms : 14
% 8.04/1.50 # Removed by relevancy pruning/SinE : 0
% 8.04/1.50 # Initial clauses : 16
% 8.04/1.50 # Removed in clause preprocessing : 0
% 8.04/1.50 # Initial clauses in saturation : 16
% 8.04/1.50 # Processed clauses : 6367
% 8.04/1.50 # ...of these trivial : 3943
% 8.04/1.50 # ...subsumed : 1330
% 8.04/1.50 # ...remaining for further processing : 1094
% 8.04/1.50 # Other redundant clauses eliminated : 0
% 8.04/1.50 # Clauses deleted for lack of memory : 0
% 8.04/1.50 # Backward-subsumed : 0
% 8.04/1.50 # Backward-rewritten : 282
% 8.04/1.50 # Generated clauses : 154782
% 8.04/1.50 # ...of the previous two non-redundant : 76494
% 8.04/1.50 # ...aggressively subsumed : 0
% 8.04/1.50 # Contextual simplify-reflections : 0
% 8.04/1.50 # Paramodulations : 154782
% 8.04/1.50 # Factorizations : 0
% 8.04/1.50 # NegExts : 0
% 8.04/1.50 # Equation resolutions : 0
% 8.04/1.50 # Disequality decompositions : 0
% 8.04/1.50 # Total rewrite steps : 257023
% 8.04/1.50 # ...of those cached : 215076
% 8.04/1.50 # Propositional unsat checks : 0
% 8.04/1.50 # Propositional check models : 0
% 8.04/1.50 # Propositional check unsatisfiable : 0
% 8.04/1.50 # Propositional clauses : 0
% 8.04/1.50 # Propositional clauses after purity: 0
% 8.04/1.50 # Propositional unsat core size : 0
% 8.04/1.50 # Propositional preprocessing time : 0.000
% 8.04/1.50 # Propositional encoding time : 0.000
% 8.04/1.50 # Propositional solver time : 0.000
% 8.04/1.50 # Success case prop preproc time : 0.000
% 8.04/1.50 # Success case prop encoding time : 0.000
% 8.04/1.50 # Success case prop solver time : 0.000
% 8.04/1.50 # Current number of processed clauses : 796
% 8.04/1.50 # Positive orientable unit clauses : 784
% 8.04/1.50 # Positive unorientable unit clauses: 12
% 8.04/1.50 # Negative unit clauses : 0
% 8.04/1.50 # Non-unit-clauses : 0
% 8.04/1.50 # Current number of unprocessed clauses: 69200
% 8.04/1.50 # ...number of literals in the above : 69200
% 8.04/1.50 # Current number of archived formulas : 0
% 8.04/1.50 # Current number of archived clauses : 298
% 8.04/1.50 # Clause-clause subsumption calls (NU) : 0
% 8.04/1.50 # Rec. Clause-clause subsumption calls : 0
% 8.04/1.50 # Non-unit clause-clause subsumptions : 0
% 8.04/1.50 # Unit Clause-clause subsumption calls : 48
% 8.04/1.50 # Rewrite failures with RHS unbound : 0
% 8.04/1.50 # BW rewrite match attempts : 2340
% 8.04/1.50 # BW rewrite match successes : 383
% 8.04/1.50 # Condensation attempts : 0
% 8.04/1.50 # Condensation successes : 0
% 8.04/1.50 # Termbank termtop insertions : 1592034
% 8.04/1.50 # Search garbage collected termcells : 45
% 8.04/1.50
% 8.04/1.50 # -------------------------------------------------
% 8.04/1.50 # User time : 0.908 s
% 8.04/1.50 # System time : 0.055 s
% 8.04/1.50 # Total time : 0.963 s
% 8.04/1.50 # Maximum resident set size: 1760 pages
% 8.04/1.50
% 8.04/1.50 # -------------------------------------------------
% 8.04/1.50 # User time : 0.909 s
% 8.04/1.50 # System time : 0.057 s
% 8.04/1.50 # Total time : 0.966 s
% 8.04/1.50 # Maximum resident set size: 1712 pages
% 8.04/1.50 % E---3.1 exiting
%------------------------------------------------------------------------------