%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : REL035+2 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n012.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 5 05:04:27 PM UTC 2026
% Result : Theorem 279.59s 89.49s
% Output : CNFRefutation 279.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 17
% Syntax : Number of formulae : 256 ( 253 unt; 0 def)
% Number of atoms : 259 ( 258 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 3 ~; 0 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 8 ( 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 : 417 ( 52 sgn 74 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(converse_multiplicativity,axiom,
! [X1,X2] : converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_multiplicativity) ).
fof(converse_idempotence,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
fof(composition_identity,axiom,
! [X1] : composition(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_identity) ).
fof(converse_cancellativity,axiom,
! [X1,X2] : join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).
fof(maddux1_join_commutativity,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux1_join_commutativity) ).
fof(maddux2_join_associativity,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux2_join_associativity) ).
fof(def_top,axiom,
! [X1] : top = join(X1,complement(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',def_top) ).
fof(maddux3_a_kind_of_de_Morgan,axiom,
! [X1,X2] : X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux3_a_kind_of_de_Morgan) ).
fof(maddux4_definiton_of_meet,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',maddux4_definiton_of_meet) ).
fof(def_zero,axiom,
! [X1] : zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',def_zero) ).
fof(converse_additivity,axiom,
! [X1,X2] : converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',converse_additivity) ).
fof(goals,conjecture,
! [X1,X2,X3] :
( composition(X1,top) = X1
=> composition(meet(X2,converse(X1)),meet(X1,X3)) = composition(X2,meet(X1,X3)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
fof(composition_associativity,axiom,
! [X1,X2,X3] : composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax',composition_associativity) ).
fof(modular_law_2,axiom,
! [X1,X2,X3] : join(meet(composition(X1,X2),X3),meet(composition(meet(X1,composition(X3,converse(X2))),X2),X3)) = meet(composition(meet(X1,composition(X3,converse(X2))),X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+1.ax',modular_law_2) ).
fof(modular_law_1,axiom,
! [X1,X2,X3] : join(meet(composition(X1,X2),X3),meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3)) = meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+1.ax',modular_law_1) ).
fof(dedekind_law,axiom,
! [X1,X2,X3] : join(meet(composition(X1,X2),X3),composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3)))) = composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3))),
file('/export/starexec/sandbox/benchmark/Axioms/REL001+1.ax',dedekind_law) ).
fof(c_0_17,plain,
! [X60,X61] : converse(composition(X60,X61)) = composition(converse(X61),converse(X60)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
fof(c_0_18,plain,
! [X57] : converse(converse(X57)) = X57,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
cnf(c_0_19,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_20,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_21,plain,
! [X53] : composition(X53,one) = X53,
inference(variable_rename,[status(thm)],[composition_identity]) ).
cnf(c_0_22,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,plain,
composition(X1,one) = X1,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_24,plain,
! [X62,X63] : join(composition(converse(X62),complement(composition(X62,X63))),complement(X63)) = complement(X63),
inference(variable_rename,[status(thm)],[converse_cancellativity]) ).
fof(c_0_25,plain,
! [X41,X42] : join(X41,X42) = join(X42,X41),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_0_26,plain,
composition(converse(one),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_20]) ).
fof(c_0_27,plain,
! [X43,X44,X45] : join(X43,join(X44,X45)) = join(join(X43,X44),X45),
inference(variable_rename,[status(thm)],[maddux2_join_associativity]) ).
fof(c_0_28,plain,
! [X64] : top = join(X64,complement(X64)),
inference(variable_rename,[status(thm)],[def_top]) ).
cnf(c_0_29,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_30,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_23,c_0_26]) ).
cnf(c_0_32,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
top = join(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_34,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_26,c_0_31]) ).
fof(c_0_36,plain,
! [X46,X47] : X46 = join(complement(join(complement(X46),complement(X47))),complement(join(complement(X46),X47))),
inference(variable_rename,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
fof(c_0_37,plain,
! [X48,X49] : meet(X48,X49) = complement(join(complement(X48),complement(X49))),
inference(variable_rename,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_0_38,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,plain,
join(X1,join(X2,complement(join(X1,X2)))) = top,
inference(spm,[status(thm)],[c_0_33,c_0_32]) ).
cnf(c_0_40,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_31]),c_0_35]) ).
fof(c_0_41,plain,
! [X65] : zero = meet(X65,complement(X65)),
inference(variable_rename,[status(thm)],[def_zero]) ).
cnf(c_0_42,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
cnf(c_0_43,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[c_0_37]) ).
cnf(c_0_44,plain,
join(top,complement(complement(X1))) = join(X1,top),
inference(spm,[status(thm)],[c_0_38,c_0_33]) ).
cnf(c_0_45,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_33]),c_0_30]) ).
cnf(c_0_46,plain,
zero = meet(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_47,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,plain,
join(X1,top) = top,
inference(rw,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,plain,
complement(top) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_33]),c_0_46]) ).
cnf(c_0_50,plain,
join(zero,meet(X1,top)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_30]) ).
cnf(c_0_51,plain,
meet(X1,X2) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_30]),c_0_43]) ).
cnf(c_0_52,plain,
complement(join(zero,complement(X1))) = meet(top,X1),
inference(spm,[status(thm)],[c_0_43,c_0_49]) ).
cnf(c_0_53,plain,
join(zero,complement(complement(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_40]),c_0_46]) ).
cnf(c_0_54,plain,
join(zero,meet(top,X1)) = X1,
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_55,plain,
meet(top,complement(X1)) = complement(X1),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_56,plain,
join(zero,complement(X1)) = complement(X1),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_57,plain,
complement(complement(X1)) = meet(top,X1),
inference(rw,[status(thm)],[c_0_52,c_0_56]) ).
cnf(c_0_58,plain,
meet(top,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_56]),c_0_57]) ).
cnf(c_0_59,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_60,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_40,c_0_59]) ).
cnf(c_0_61,plain,
complement(complement(X1)) = meet(X1,X1),
inference(spm,[status(thm)],[c_0_43,c_0_40]) ).
cnf(c_0_62,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_32,c_0_60]) ).
cnf(c_0_63,plain,
join(zero,meet(X1,X1)) = X1,
inference(spm,[status(thm)],[c_0_53,c_0_61]) ).
fof(c_0_64,plain,
! [X58,X59] : converse(join(X58,X59)) = join(converse(X58),converse(X59)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
cnf(c_0_65,plain,
join(X1,meet(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_47]),c_0_30]) ).
cnf(c_0_66,plain,
complement(join(X1,complement(X2))) = meet(complement(X1),X2),
inference(spm,[status(thm)],[c_0_43,c_0_59]) ).
cnf(c_0_67,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_61]),c_0_63]) ).
cnf(c_0_68,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_64]) ).
cnf(c_0_69,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_65,c_0_51]) ).
cnf(c_0_70,plain,
complement(join(complement(X1),X2)) = meet(complement(X2),X1),
inference(spm,[status(thm)],[c_0_66,c_0_30]) ).
cnf(c_0_71,plain,
join(X1,join(X2,complement(X1))) = join(top,X2),
inference(spm,[status(thm)],[c_0_38,c_0_30]) ).
cnf(c_0_72,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_30,c_0_48]) ).
cnf(c_0_73,plain,
join(zero,X1) = X1,
inference(rw,[status(thm)],[c_0_63,c_0_67]) ).
cnf(c_0_74,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(spm,[status(thm)],[c_0_68,c_0_20]) ).
cnf(c_0_75,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_32,c_0_69]) ).
cnf(c_0_76,plain,
join(meet(X1,X2),meet(complement(X2),X1)) = X1,
inference(rw,[status(thm)],[c_0_47,c_0_70]) ).
cnf(c_0_77,plain,
join(X1,join(X2,complement(X1))) = top,
inference(rw,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_78,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_73]) ).
cnf(c_0_79,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(spm,[status(thm)],[c_0_74,c_0_33]) ).
cnf(c_0_80,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_81,plain,
meet(X1,join(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_77]),c_0_57]),c_0_58]),c_0_49]),c_0_78]) ).
cnf(c_0_82,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_30]),c_0_32]) ).
cnf(c_0_83,plain,
meet(complement(X1),complement(X2)) = complement(join(X1,X2)),
inference(spm,[status(thm)],[c_0_66,c_0_59]) ).
cnf(c_0_84,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_79,c_0_72]) ).
cnf(c_0_85,plain,
meet(X1,complement(meet(X1,X2))) = meet(complement(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_80]),c_0_70]),c_0_57]),c_0_58]),c_0_51]) ).
cnf(c_0_86,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_59,c_0_66]) ).
cnf(c_0_87,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_65]),c_0_51]) ).
cnf(c_0_88,plain,
join(X1,join(X2,meet(X1,X3))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_82,c_0_65]) ).
cnf(c_0_89,plain,
converse(join(one,X1)) = join(one,converse(X1)),
inference(spm,[status(thm)],[c_0_68,c_0_31]) ).
cnf(c_0_90,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_80,c_0_83]) ).
cnf(c_0_91,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(rw,[status(thm)],[c_0_79,c_0_84]) ).
cnf(c_0_92,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_85,c_0_85]),c_0_86]),c_0_59]),c_0_51]),c_0_87]) ).
cnf(c_0_93,plain,
join(meet(X1,X2),complement(X2)) = join(complement(X2),X1),
inference(spm,[status(thm)],[c_0_88,c_0_76]) ).
cnf(c_0_94,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_69]),c_0_51]) ).
cnf(c_0_95,plain,
join(one,converse(complement(one))) = converse(top),
inference(spm,[status(thm)],[c_0_89,c_0_33]) ).
fof(c_0_96,negated_conjecture,
~ ! [X1,X2,X3] :
( composition(X1,top) = X1
=> composition(meet(X2,converse(X1)),meet(X1,X3)) = composition(X2,meet(X1,X3)) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_97,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_49]),c_0_78]) ).
cnf(c_0_98,plain,
meet(X1,join(complement(X1),X2)) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_94]) ).
cnf(c_0_99,plain,
meet(X1,top) = X1,
inference(spm,[status(thm)],[c_0_51,c_0_58]) ).
cnf(c_0_100,plain,
join(one,converse(complement(one))) = top,
inference(rw,[status(thm)],[c_0_95,c_0_84]) ).
fof(c_0_101,plain,
! [X54,X55,X56] : composition(join(X54,X55),X56) = join(composition(X54,X56),composition(X55,X56)),
inference(variable_rename,[status(thm)],[composition_distributivity]) ).
fof(c_0_102,negated_conjecture,
( composition(esk1_0,top) = esk1_0
& composition(meet(esk2_0,converse(esk1_0)),meet(esk1_0,esk3_0)) != composition(esk2_0,meet(esk1_0,esk3_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_96])])]) ).
cnf(c_0_103,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_97]),c_0_20]),c_0_20]) ).
cnf(c_0_104,plain,
meet(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_91]),c_0_99]),c_0_51]) ).
cnf(c_0_105,plain,
join(one,complement(converse(complement(one)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_100]),c_0_49]),c_0_78]) ).
cnf(c_0_106,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_107,negated_conjecture,
composition(esk1_0,top) = esk1_0,
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_108,plain,
converse(complement(converse(complement(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_103]),c_0_51]),c_0_104]) ).
cnf(c_0_109,plain,
join(X1,converse(meet(X2,converse(X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_69]),c_0_20]) ).
cnf(c_0_110,plain,
meet(complement(one),converse(complement(one))) = complement(one),
inference(spm,[status(thm)],[c_0_66,c_0_105]) ).
cnf(c_0_111,plain,
converse(composition(X1,top)) = composition(top,converse(X1)),
inference(spm,[status(thm)],[c_0_19,c_0_84]) ).
cnf(c_0_112,negated_conjecture,
composition(join(esk1_0,X1),top) = join(esk1_0,composition(X1,top)),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_113,plain,
complement(converse(complement(X1))) = converse(X1),
inference(spm,[status(thm)],[c_0_20,c_0_108]) ).
cnf(c_0_114,plain,
join(complement(one),converse(complement(one))) = complement(one),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_115,negated_conjecture,
converse(join(esk1_0,composition(X1,top))) = composition(top,converse(join(esk1_0,X1))),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_116,plain,
converse(join(X1,one)) = join(one,converse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_31]),c_0_30]) ).
cnf(c_0_117,plain,
converse(complement(X1)) = complement(converse(X1)),
inference(spm,[status(thm)],[c_0_59,c_0_113]) ).
cnf(c_0_118,plain,
converse(complement(one)) = complement(one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_114]),c_0_51]),c_0_110]) ).
fof(c_0_119,plain,
! [X50,X51,X52] : composition(X50,composition(X51,X52)) = composition(composition(X50,X51),X52),
inference(variable_rename,[status(thm)],[composition_associativity]) ).
fof(c_0_120,plain,
! [X72,X73,X74] : join(meet(composition(X72,X73),X74),meet(composition(meet(X72,composition(X74,converse(X73))),X73),X74)) = meet(composition(meet(X72,composition(X74,converse(X73))),X73),X74),
inference(variable_rename,[status(thm)],[modular_law_2]) ).
cnf(c_0_121,plain,
join(composition(X1,converse(X2)),converse(composition(X2,X3))) = composition(join(X1,converse(X3)),converse(X2)),
inference(spm,[status(thm)],[c_0_106,c_0_19]) ).
cnf(c_0_122,negated_conjecture,
composition(top,join(one,converse(esk1_0))) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_35]),c_0_48]),c_0_84]),c_0_116]) ).
cnf(c_0_123,plain,
join(X1,composition(X2,X1)) = composition(join(one,X2),X1),
inference(spm,[status(thm)],[c_0_106,c_0_35]) ).
cnf(c_0_124,plain,
complement(converse(join(complement(X1),X2))) = converse(meet(complement(X2),X1)),
inference(spm,[status(thm)],[c_0_117,c_0_70]) ).
cnf(c_0_125,plain,
converse(join(X1,complement(one))) = join(converse(X1),complement(one)),
inference(spm,[status(thm)],[c_0_68,c_0_118]) ).
cnf(c_0_126,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(spm,[status(thm)],[c_0_86,c_0_59]) ).
fof(c_0_127,plain,
! [X69,X70,X71] : join(meet(composition(X69,X70),X71),meet(composition(X69,meet(X70,composition(converse(X69),X71))),X71)) = meet(composition(X69,meet(X70,composition(converse(X69),X71))),X71),
inference(variable_rename,[status(thm)],[modular_law_1]) ).
cnf(c_0_128,plain,
complement(join(zero,zero)) = meet(top,top),
inference(spm,[status(thm)],[c_0_52,c_0_49]) ).
cnf(c_0_129,plain,
join(zero,zero) = zero,
inference(spm,[status(thm)],[c_0_40,c_0_49]) ).
cnf(c_0_130,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_131,negated_conjecture,
composition(top,converse(esk1_0)) = converse(esk1_0),
inference(spm,[status(thm)],[c_0_111,c_0_107]) ).
cnf(c_0_132,plain,
complement(join(X1,join(X2,complement(X3)))) = meet(complement(join(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_66,c_0_32]) ).
cnf(c_0_133,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(spm,[status(thm)],[c_0_68,c_0_20]) ).
cnf(c_0_134,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_120]) ).
cnf(c_0_135,negated_conjecture,
composition(join(X1,join(one,esk1_0)),top) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_84]),c_0_84]),c_0_48]),c_0_89]),c_0_20]),c_0_84]) ).
cnf(c_0_136,plain,
join(X1,composition(X2,X1)) = composition(join(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_35]),c_0_30]) ).
cnf(c_0_137,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_80,c_0_51]) ).
cnf(c_0_138,plain,
join(X1,composition(meet(one,X2),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_65]),c_0_35]) ).
cnf(c_0_139,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_140,plain,
converse(meet(one,X1)) = meet(one,converse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_124,c_0_125]),c_0_117]),c_0_126]),c_0_59]),c_0_59]),c_0_51]) ).
cnf(c_0_141,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_127]) ).
cnf(c_0_142,plain,
complement(zero) = meet(top,top),
inference(rw,[status(thm)],[c_0_128,c_0_129]) ).
cnf(c_0_143,negated_conjecture,
composition(top,composition(converse(esk1_0),X1)) = composition(converse(esk1_0),X1),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_144,negated_conjecture,
composition(converse(esk1_0),complement(esk1_0)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_107]),c_0_49]),c_0_49]),c_0_73]) ).
cnf(c_0_145,negated_conjecture,
join(converse(esk1_0),composition(X1,converse(esk1_0))) = converse(esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_131]),c_0_72]),c_0_131]) ).
cnf(c_0_146,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_132,c_0_126]),c_0_66]),c_0_66]) ).
cnf(c_0_147,plain,
converse(join(X1,complement(converse(X2)))) = join(converse(X1),complement(X2)),
inference(spm,[status(thm)],[c_0_133,c_0_117]) ).
cnf(c_0_148,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_134,c_0_51]),c_0_51]) ).
cnf(c_0_149,negated_conjecture,
composition(top,top) = top,
inference(spm,[status(thm)],[c_0_135,c_0_72]) ).
cnf(c_0_150,plain,
composition(top,join(one,converse(X1))) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_136]),c_0_72]),c_0_84]),c_0_116]) ).
cnf(c_0_151,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_137,c_0_83]) ).
cnf(c_0_152,plain,
join(X1,composition(X1,meet(one,converse(X2)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_138]),c_0_20]),c_0_139]),c_0_140]) ).
cnf(c_0_153,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_32,c_0_65]) ).
cnf(c_0_154,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_141,c_0_51]),c_0_51]) ).
cnf(c_0_155,plain,
converse(join(composition(converse(X1),X2),X3)) = join(composition(converse(X2),X1),converse(X3)),
inference(spm,[status(thm)],[c_0_68,c_0_22]) ).
cnf(c_0_156,plain,
join(complement(converse(X1)),composition(X2,complement(converse(composition(X1,X2))))) = complement(converse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_19]),c_0_20]) ).
cnf(c_0_157,plain,
converse(composition(top,X1)) = composition(converse(X1),top),
inference(spm,[status(thm)],[c_0_22,c_0_84]) ).
cnf(c_0_158,plain,
complement(zero) = top,
inference(rw,[status(thm)],[c_0_142,c_0_67]) ).
cnf(c_0_159,negated_conjecture,
composition(top,zero) = zero,
inference(spm,[status(thm)],[c_0_143,c_0_144]) ).
cnf(c_0_160,negated_conjecture,
join(esk1_0,composition(esk1_0,converse(X1))) = esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_145]),c_0_20]),c_0_139]) ).
cnf(c_0_161,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_146,c_0_59]) ).
cnf(c_0_162,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_124,c_0_147]),c_0_117]),c_0_126]),c_0_59]),c_0_59]) ).
cnf(c_0_163,negated_conjecture,
meet(X1,composition(X1,top)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_58]),c_0_84]),c_0_58]),c_0_130]),c_0_149]),c_0_65]),c_0_84]),c_0_58]),c_0_130]),c_0_149]) ).
cnf(c_0_164,plain,
composition(top,join(one,X1)) = top,
inference(spm,[status(thm)],[c_0_150,c_0_20]) ).
cnf(c_0_165,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_77]),c_0_49]),c_0_57]),c_0_58]),c_0_51]) ).
cnf(c_0_166,negated_conjecture,
join(esk1_0,composition(meet(esk1_0,X1),top)) = esk1_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_65]),c_0_107]) ).
cnf(c_0_167,plain,
meet(join(X1,X2),join(X2,complement(X1))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_151]),c_0_51]),c_0_81]) ).
cnf(c_0_168,plain,
join(X1,composition(X1,meet(one,X2))) = X1,
inference(spm,[status(thm)],[c_0_152,c_0_20]) ).
fof(c_0_169,plain,
! [X66,X67,X68] : join(meet(composition(X66,X67),X68),composition(meet(X66,composition(X68,converse(X67))),meet(X67,composition(converse(X66),X68)))) = composition(meet(X66,composition(X68,converse(X67))),meet(X67,composition(converse(X66),X68))),
inference(variable_rename,[status(thm)],[dedekind_law]) ).
cnf(c_0_170,plain,
join(X1,meet(X2,meet(X1,X3))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_69]),c_0_65]) ).
cnf(c_0_171,plain,
meet(X1,join(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_81,c_0_30]) ).
cnf(c_0_172,plain,
join(X1,join(X2,X3)) = join(X2,join(X3,X1)),
inference(spm,[status(thm)],[c_0_32,c_0_30]) ).
cnf(c_0_173,plain,
join(meet(composition(X1,top),X2),meet(X2,composition(X1,composition(converse(X1),X2)))) = meet(X2,composition(X1,composition(converse(X1),X2))),
inference(spm,[status(thm)],[c_0_154,c_0_58]) ).
cnf(c_0_174,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_121]),c_0_68]),c_0_19]),c_0_20]),c_0_20]),c_0_20]) ).
cnf(c_0_175,plain,
composition(X1,complement(composition(converse(X1),top))) = 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_156,c_0_157]),c_0_84]),c_0_49]),c_0_73]),c_0_84]),c_0_49]) ).
cnf(c_0_176,plain,
meet(X1,zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_158]),c_0_30]),c_0_72]),c_0_49]) ).
cnf(c_0_177,negated_conjecture,
composition(X1,zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_159]),c_0_73]),c_0_72]),c_0_159]) ).
cnf(c_0_178,negated_conjecture,
composition(meet(X1,converse(esk1_0)),esk1_0) = composition(X1,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_148,c_0_131]),c_0_99]),c_0_58]),c_0_106]),c_0_65]),c_0_58]) ).
cnf(c_0_179,negated_conjecture,
join(esk1_0,composition(esk1_0,X1)) = esk1_0,
inference(spm,[status(thm)],[c_0_160,c_0_20]) ).
cnf(c_0_180,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_161,c_0_81]) ).
cnf(c_0_181,negated_conjecture,
meet(X1,composition(top,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_163]),c_0_20]),c_0_22]),c_0_84]),c_0_51]) ).
cnf(c_0_182,plain,
composition(top,composition(join(one,X1),X2)) = composition(top,X2),
inference(spm,[status(thm)],[c_0_130,c_0_164]) ).
cnf(c_0_183,negated_conjecture,
meet(composition(meet(esk1_0,X1),top),complement(esk1_0)) = zero,
inference(spm,[status(thm)],[c_0_165,c_0_166]) ).
cnf(c_0_184,plain,
converse(meet(X1,converse(X2))) = meet(converse(X1),X2),
inference(spm,[status(thm)],[c_0_162,c_0_51]) ).
cnf(c_0_185,plain,
meet(join(X1,X2),join(complement(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_167,c_0_30]) ).
cnf(c_0_186,plain,
join(X1,composition(X1,meet(X2,one))) = X1,
inference(spm,[status(thm)],[c_0_168,c_0_94]) ).
cnf(c_0_187,plain,
join(meet(composition(X1,X2),X3),composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3)))) = composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3))),
inference(split_conjunct,[status(thm)],[c_0_169]) ).
cnf(c_0_188,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_170,c_0_94]) ).
cnf(c_0_189,plain,
meet(X1,join(X2,join(X1,X3))) = X1,
inference(spm,[status(thm)],[c_0_171,c_0_172]) ).
cnf(c_0_190,plain,
composition(converse(X1),composition(converse(X2),X3)) = composition(converse(composition(X2,X1)),X3),
inference(spm,[status(thm)],[c_0_130,c_0_19]) ).
cnf(c_0_191,plain,
composition(X1,composition(converse(X1),top)) = composition(X1,top),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_58]),c_0_99]),c_0_174]),c_0_72]) ).
cnf(c_0_192,plain,
meet(composition(X1,X2),complement(composition(X1,top))) = 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(spm,[status(thm)],[c_0_154,c_0_175]),c_0_20]),c_0_20]),c_0_176]),c_0_177]),c_0_176]),c_0_78]),c_0_20]),c_0_176]),c_0_177]),c_0_176]) ).
cnf(c_0_193,negated_conjecture,
composition(converse(esk1_0),esk1_0) = composition(top,esk1_0),
inference(spm,[status(thm)],[c_0_178,c_0_58]) ).
cnf(c_0_194,negated_conjecture,
composition(esk1_0,composition(top,X1)) = composition(esk1_0,X1),
inference(spm,[status(thm)],[c_0_130,c_0_107]) ).
cnf(c_0_195,negated_conjecture,
meet(esk1_0,composition(esk1_0,X1)) = composition(esk1_0,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_179]),c_0_51]) ).
cnf(c_0_196,negated_conjecture,
meet(X1,composition(top,join(X2,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_180,c_0_181]),c_0_81]) ).
cnf(c_0_197,plain,
composition(top,join(X1,composition(X2,X1))) = composition(top,X1),
inference(spm,[status(thm)],[c_0_182,c_0_123]) ).
cnf(c_0_198,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_154,c_0_20]) ).
cnf(c_0_199,negated_conjecture,
meet(complement(esk1_0),composition(meet(esk1_0,X1),top)) = zero,
inference(spm,[status(thm)],[c_0_51,c_0_183]) ).
cnf(c_0_200,plain,
meet(zero,X1) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_158]),c_0_72]),c_0_49]) ).
cnf(c_0_201,plain,
meet(converse(X1),converse(X2)) = converse(meet(X2,X1)),
inference(spm,[status(thm)],[c_0_162,c_0_20]) ).
cnf(c_0_202,plain,
meet(converse(X1),meet(X2,converse(X3))) = meet(converse(meet(X3,X1)),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_184]),c_0_161]),c_0_162]) ).
cnf(c_0_203,plain,
meet(X1,composition(X1,meet(X2,one))) = composition(X1,meet(X2,one)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_186]),c_0_98]),c_0_51]) ).
cnf(c_0_204,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_187,c_0_31]),c_0_35]),c_0_35]),c_0_35]),c_0_138]) ).
cnf(c_0_205,plain,
meet(X1,meet(X2,meet(X3,X1))) = meet(X2,meet(X3,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_188]),c_0_51]) ).
cnf(c_0_206,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(spm,[status(thm)],[c_0_51,c_0_161]) ).
cnf(c_0_207,plain,
converse(join(complement(one),X1)) = join(complement(one),converse(X1)),
inference(spm,[status(thm)],[c_0_68,c_0_118]) ).
cnf(c_0_208,plain,
meet(meet(X1,X2),join(X1,X3)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_189,c_0_153]) ).
cnf(c_0_209,plain,
join(meet(X1,X2),meet(X2,complement(X1))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_59]),c_0_30]) ).
cnf(c_0_210,plain,
meet(X1,meet(composition(X2,X3),composition(X2,meet(X3,composition(converse(X2),meet(X1,composition(X2,X3))))))) = meet(X1,composition(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_94]),c_0_65]),c_0_161]) ).
cnf(c_0_211,plain,
composition(converse(X1),composition(X1,top)) = composition(converse(X1),top),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_190,c_0_191]),c_0_22]),c_0_130]) ).
cnf(c_0_212,plain,
composition(X1,meet(X2,composition(converse(X1),top))) = composition(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_58]),c_0_99]),c_0_174]),c_0_65]) ).
cnf(c_0_213,plain,
meet(composition(X1,top),composition(X1,X2)) = composition(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_192]),c_0_59]),c_0_73]) ).
cnf(c_0_214,negated_conjecture,
composition(converse(esk1_0),top) = composition(top,esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_193]),c_0_157]),c_0_193]) ).
cnf(c_0_215,negated_conjecture,
composition(esk1_0,esk1_0) = esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_173,c_0_193]),c_0_107]),c_0_67]),c_0_194]),c_0_195]),c_0_179]),c_0_194]),c_0_195]) ).
cnf(c_0_216,negated_conjecture,
meet(composition(X1,X2),composition(top,X2)) = composition(X1,X2),
inference(spm,[status(thm)],[c_0_196,c_0_197]) ).
cnf(c_0_217,negated_conjecture,
composition(converse(meet(esk1_0,X1)),complement(esk1_0)) = 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_198,c_0_199]),c_0_99]),c_0_177]),c_0_51]),c_0_200]),c_0_78]),c_0_177]),c_0_51]),c_0_200]) ).
cnf(c_0_218,plain,
converse(meet(X1,meet(X2,converse(X3)))) = meet(converse(meet(X1,X2)),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_201,c_0_184]),c_0_161]),c_0_202]) ).
cnf(c_0_219,plain,
meet(one,meet(X1,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_203,c_0_204]),c_0_35]),c_0_161]),c_0_205]),c_0_206]),c_0_51]) ).
cnf(c_0_220,plain,
converse(meet(X1,one)) = meet(one,converse(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_98]),c_0_207]),c_0_98]),c_0_51]) ).
cnf(c_0_221,plain,
meet(X1,meet(X2,join(X1,X3))) = meet(X1,X2),
inference(rw,[status(thm)],[c_0_208,c_0_161]) ).
cnf(c_0_222,negated_conjecture,
join(X1,composition(top,X1)) = composition(top,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_209,c_0_181]),c_0_137]) ).
cnf(c_0_223,plain,
meet(X1,composition(converse(X2),composition(X2,X1))) = meet(X1,composition(converse(X2),top)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_210,c_0_211]),c_0_20]),c_0_212]),c_0_213]),c_0_213]) ).
cnf(c_0_224,negated_conjecture,
composition(converse(esk1_0),composition(top,X1)) = composition(top,composition(esk1_0,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_214]),c_0_130]) ).
cnf(c_0_225,negated_conjecture,
composition(esk1_0,composition(esk1_0,X1)) = composition(esk1_0,X1),
inference(spm,[status(thm)],[c_0_130,c_0_215]) ).
cnf(c_0_226,negated_conjecture,
meet(composition(top,X1),composition(X2,X1)) = composition(X2,X1),
inference(spm,[status(thm)],[c_0_51,c_0_216]) ).
cnf(c_0_227,negated_conjecture,
meet(composition(meet(esk1_0,X1),X2),complement(esk1_0)) = 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(spm,[status(thm)],[c_0_198,c_0_217]),c_0_20]),c_0_20]),c_0_176]),c_0_177]),c_0_176]),c_0_78]),c_0_20]),c_0_176]),c_0_177]),c_0_176]) ).
cnf(c_0_228,negated_conjecture,
composition(meet(converse(esk1_0),X1),esk1_0) = composition(X1,esk1_0),
inference(spm,[status(thm)],[c_0_178,c_0_51]) ).
cnf(c_0_229,plain,
meet(converse(X1),composition(converse(X2),top)) = converse(meet(composition(top,X2),X1)),
inference(spm,[status(thm)],[c_0_201,c_0_157]) ).
cnf(c_0_230,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_218,c_0_219]),c_0_220]),c_0_140]),c_0_161]),c_0_51]),c_0_219]) ).
cnf(c_0_231,plain,
join(meet(one,composition(X1,X2)),composition(meet(X1,converse(X2)),meet(X2,converse(X1)))) = composition(meet(X1,converse(X2)),meet(X2,converse(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_187,c_0_23]),c_0_35]),c_0_35]),c_0_51]) ).
cnf(c_0_232,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_185,c_0_168]),c_0_98]),c_0_51]) ).
cnf(c_0_233,plain,
join(X1,composition(meet(X2,one),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_69]),c_0_35]) ).
cnf(c_0_234,negated_conjecture,
meet(X1,meet(X2,composition(top,X1))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_221,c_0_222]) ).
cnf(c_0_235,negated_conjecture,
meet(esk1_0,composition(top,X1)) = composition(esk1_0,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_223,c_0_224]),c_0_20]),c_0_194]),c_0_225]),c_0_226]),c_0_20]),c_0_107]),c_0_51]) ).
cnf(c_0_236,plain,
composition(X1,join(X2,composition(converse(X1),top))) = composition(X1,top),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_174,c_0_191]),c_0_174]),c_0_48]) ).
cnf(c_0_237,negated_conjecture,
join(esk1_0,composition(meet(esk1_0,X1),X2)) = esk1_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_227]),c_0_59]),c_0_73]),c_0_59]) ).
cnf(c_0_238,negated_conjecture,
composition(converse(meet(X1,esk1_0)),esk1_0) = composition(converse(X1),esk1_0),
inference(spm,[status(thm)],[c_0_228,c_0_201]) ).
cnf(c_0_239,plain,
meet(X1,composition(X1,composition(converse(X2),X2))) = meet(composition(top,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_223]),c_0_229]),c_0_20]),c_0_22]),c_0_139]),c_0_130]),c_0_51]) ).
cnf(c_0_240,plain,
converse(meet(one,X1)) = meet(X1,one),
inference(rw,[status(thm)],[c_0_140,c_0_230]) ).
cnf(c_0_241,plain,
composition(meet(X1,one),meet(one,X1)) = meet(one,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_231,c_0_232]),c_0_35]),c_0_140]),c_0_230]),c_0_94]),c_0_31]),c_0_51]),c_0_87]),c_0_233]),c_0_140]),c_0_230]),c_0_94]),c_0_31]),c_0_51]),c_0_87]) ).
cnf(c_0_242,negated_conjecture,
meet(X1,meet(composition(X1,top),X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_161,c_0_163]) ).
cnf(c_0_243,negated_conjecture,
meet(X1,composition(esk1_0,X1)) = meet(X1,esk1_0),
inference(spm,[status(thm)],[c_0_234,c_0_235]) ).
cnf(c_0_244,plain,
composition(converse(join(X1,composition(X2,top))),X2) = composition(top,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_236]),c_0_22]),c_0_84]),c_0_20]) ).
cnf(c_0_245,negated_conjecture,
join(esk1_0,composition(meet(X1,esk1_0),X2)) = esk1_0,
inference(spm,[status(thm)],[c_0_237,c_0_94]) ).
cnf(c_0_246,negated_conjecture,
composition(converse(esk1_0),meet(X1,esk1_0)) = composition(converse(esk1_0),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_238]),c_0_22]) ).
cnf(c_0_247,plain,
meet(composition(top,meet(one,X1)),X2) = composition(X2,meet(one,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_239,c_0_240]),c_0_241]),c_0_232]) ).
cnf(c_0_248,negated_conjecture,
meet(X1,composition(esk1_0,composition(X1,top))) = meet(X1,esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_242,c_0_243]),c_0_242]) ).
cnf(c_0_249,negated_conjecture,
composition(top,meet(X1,esk1_0)) = composition(converse(esk1_0),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_244,c_0_245]),c_0_246]) ).
cnf(c_0_250,negated_conjecture,
composition(X1,meet(one,esk1_0)) = meet(converse(esk1_0),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_247,c_0_248]),c_0_249]),c_0_23]) ).
cnf(c_0_251,negated_conjecture,
composition(meet(one,esk1_0),X1) = meet(X1,esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_250]),c_0_201]),c_0_20]),c_0_140]),c_0_230]),c_0_51]) ).
cnf(c_0_252,negated_conjecture,
composition(meet(converse(esk1_0),X1),X2) = composition(X1,meet(X2,esk1_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_250]),c_0_251]) ).
cnf(c_0_253,negated_conjecture,
composition(meet(esk2_0,converse(esk1_0)),meet(esk1_0,esk3_0)) != composition(esk2_0,meet(esk1_0,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_254,negated_conjecture,
composition(meet(X1,converse(esk1_0)),X2) = composition(X1,meet(X2,esk1_0)),
inference(spm,[status(thm)],[c_0_252,c_0_51]) ).
cnf(c_0_255,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_253,c_0_254]),c_0_161]),c_0_51]),c_0_87])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : REL035+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.07/0.24 % Computer : n012.cluster.edu
% 0.07/0.24 % Model : x86_64 x86_64
% 0.07/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.24 % Memory : 8042.1875MB
% 0.07/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.24 % CPULimit : 300
% 0.07/0.24 % WCLimit : 300
% 0.07/0.24 % DateTime : Tue May 5 01:43:01 EDT 2026
% 0.07/0.24 % CPUTime :
% 0.07/0.25 % start to proof: theBenchmark
% 279.59/89.49 % Version : CSE_E---1.7
% 279.59/89.49 % Problem : theBenchmark.p
% 279.59/89.49 % SZS status Theorem for theBenchmark.p
% 279.59/89.49 % SZS output start CNFRefutation
% See solution above
% 279.99/89.89 % Total time : 73.511s
%------------------------------------------------------------------------------