%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : REL019+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:03:56 PM UTC 2026
% Result : Theorem 245.33s 36.33s
% Output : CNFRefutation 245.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 15
% Syntax : Number of formulae : 152 ( 149 unt; 0 def)
% Number of atoms : 158 ( 157 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 9 ( 3 ~; 0 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 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 : 238 ( 16 sgn 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(def_top,axiom,
! [X1] : top = join(X1,complement(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_top) ).
fof(def_zero,axiom,
! [X1] : zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',def_zero) ).
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(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(converse_idempotence,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',converse_idempotence) ).
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(goals,conjecture,
! [X1,X2] :
( ( composition(X2,top) = X2
& composition(X1,top) = X1 )
=> composition(meet(X1,X2),top) = meet(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
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(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(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(modular_law_2,axiom,
! [X1,X2,X3] : join(meet(composition(X1,X2),X3),meet(composition(meet(X1,composition(X3,converse(X2))),X2),X3)) = meet(composition(meet(X1,composition(X3,converse(X2))),X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+1.ax',modular_law_2) ).
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/benchmark/Axioms/REL001+1.ax',dedekind_law) ).
fof(c_0_15,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]) ).
fof(c_0_16,plain,
! [X6,X7] : meet(X6,X7) = complement(join(complement(X6),complement(X7))),
inference(variable_rename,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_0_17,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_19,plain,
! [X31,X32] : join(X31,X32) = join(X32,X31),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
fof(c_0_20,plain,
! [X27] : top = join(X27,complement(X27)),
inference(variable_rename,[status(thm)],[def_top]) ).
fof(c_0_21,plain,
! [X30] : zero = meet(X30,complement(X30)),
inference(variable_rename,[status(thm)],[def_zero]) ).
cnf(c_0_22,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
top = join(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_25,plain,
zero = meet(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_18]),c_0_23]) ).
cnf(c_0_27,plain,
complement(top) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_24]),c_0_25]) ).
cnf(c_0_28,plain,
join(meet(X1,top),meet(X1,zero)) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_29,plain,
meet(X1,X2) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_23]),c_0_18]) ).
cnf(c_0_30,plain,
join(zero,meet(X1,complement(complement(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_24]),c_0_27]),c_0_23]) ).
cnf(c_0_31,plain,
join(meet(X1,top),meet(zero,X1)) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,plain,
join(zero,meet(top,complement(zero))) = top,
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
fof(c_0_33,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_34,plain,
complement(zero) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_25]),c_0_29]),c_0_23]),c_0_32]) ).
cnf(c_0_35,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_36,plain,
join(top,zero) = top,
inference(spm,[status(thm)],[c_0_24,c_0_27]) ).
cnf(c_0_37,plain,
complement(join(top,complement(X1))) = meet(zero,X1),
inference(spm,[status(thm)],[c_0_18,c_0_34]) ).
cnf(c_0_38,plain,
join(top,join(zero,X1)) = join(top,X1),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,plain,
join(zero,meet(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_25]),c_0_18]) ).
cnf(c_0_40,plain,
complement(join(top,top)) = meet(zero,zero),
inference(spm,[status(thm)],[c_0_37,c_0_34]) ).
cnf(c_0_41,plain,
join(top,meet(X1,X1)) = join(top,X1),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_42,plain,
join(top,top) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_40]),c_0_35]),c_0_41]),c_0_36]) ).
cnf(c_0_43,plain,
meet(zero,zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_42]),c_0_27]) ).
cnf(c_0_44,plain,
join(zero,zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_43]),c_0_34]),c_0_36]),c_0_27]) ).
cnf(c_0_45,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(spm,[status(thm)],[c_0_35,c_0_44]) ).
cnf(c_0_46,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_45,c_0_30]) ).
cnf(c_0_47,plain,
join(complement(X1),join(complement(X2),meet(X1,X2))) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_18]),c_0_35]) ).
cnf(c_0_48,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[c_0_39,c_0_46]) ).
cnf(c_0_49,plain,
join(X1,join(X2,complement(join(X1,X2)))) = top,
inference(spm,[status(thm)],[c_0_24,c_0_35]) ).
cnf(c_0_50,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_23]),c_0_24]),c_0_23]) ).
cnf(c_0_51,plain,
join(X1,top) = top,
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_52,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_46]) ).
cnf(c_0_53,plain,
complement(join(zero,complement(X1))) = meet(top,X1),
inference(spm,[status(thm)],[c_0_18,c_0_27]) ).
cnf(c_0_54,plain,
meet(X1,top) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_51]),c_0_27]),c_0_52]) ).
cnf(c_0_55,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_35,c_0_24]) ).
cnf(c_0_56,plain,
complement(complement(X1)) = meet(top,X1),
inference(rw,[status(thm)],[c_0_53,c_0_46]) ).
cnf(c_0_57,plain,
meet(top,X1) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_54]) ).
cnf(c_0_58,plain,
complement(join(meet(X1,X2),complement(X3))) = meet(join(complement(X1),complement(X2)),X3),
inference(spm,[status(thm)],[c_0_18,c_0_18]) ).
cnf(c_0_59,plain,
join(X1,join(X2,complement(X1))) = join(top,X2),
inference(spm,[status(thm)],[c_0_55,c_0_23]) ).
cnf(c_0_60,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_23,c_0_51]) ).
cnf(c_0_61,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_62,plain,
complement(join(X1,complement(X2))) = meet(complement(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_54]),c_0_27]),c_0_23]),c_0_46]) ).
cnf(c_0_63,plain,
join(X1,join(X2,complement(X1))) = top,
inference(rw,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_64,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_65,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_22,c_0_63]),c_0_56]),c_0_57]),c_0_27]),c_0_52]) ).
cnf(c_0_66,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_23]),c_0_35]) ).
cnf(c_0_67,plain,
join(X1,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_48]),c_0_56]),c_0_57]),c_0_56]),c_0_57]) ).
cnf(c_0_68,plain,
meet(X1,join(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_65,c_0_23]) ).
cnf(c_0_69,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_35]),c_0_67]) ).
cnf(c_0_70,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_26]),c_0_29]) ).
fof(c_0_71,plain,
! [X36,X37] : converse(join(X36,X37)) = join(converse(X36),converse(X37)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
fof(c_0_72,plain,
! [X38] : converse(converse(X38)) = X38,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
cnf(c_0_73,plain,
join(X1,meet(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_26]),c_0_23]) ).
cnf(c_0_74,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_70,c_0_29]) ).
cnf(c_0_75,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
cnf(c_0_76,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_72]) ).
cnf(c_0_77,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_78,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_79,plain,
complement(join(complement(X1),meet(X2,X3))) = meet(X1,join(complement(X2),complement(X3))),
inference(spm,[status(thm)],[c_0_18,c_0_18]) ).
cnf(c_0_80,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_35,c_0_77]) ).
cnf(c_0_81,plain,
join(top,join(top,X1)) = join(top,X1),
inference(spm,[status(thm)],[c_0_35,c_0_42]) ).
cnf(c_0_82,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(spm,[status(thm)],[c_0_78,c_0_24]) ).
cnf(c_0_83,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_54]),c_0_27]),c_0_52]) ).
cnf(c_0_84,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_80,c_0_26]) ).
cnf(c_0_85,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_86,plain,
join(top,converse(top)) = converse(top),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_87,plain,
meet(X1,complement(meet(X2,X1))) = meet(X1,complement(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_83]),c_0_56]),c_0_57]) ).
cnf(c_0_88,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_84,c_0_29]) ).
cnf(c_0_89,plain,
meet(complement(X1),complement(X2)) = complement(join(X1,X2)),
inference(spm,[status(thm)],[c_0_62,c_0_61]) ).
cnf(c_0_90,plain,
converse(top) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_76]),c_0_23]),c_0_86]) ).
cnf(c_0_91,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_64]),c_0_61]) ).
cnf(c_0_92,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_93,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(rw,[status(thm)],[c_0_82,c_0_90]) ).
cnf(c_0_94,plain,
meet(X1,join(complement(X1),X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_91,c_0_23]) ).
cnf(c_0_95,plain,
meet(converse(X1),converse(join(X2,X1))) = converse(X1),
inference(spm,[status(thm)],[c_0_65,c_0_75]) ).
cnf(c_0_96,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_27]),c_0_52]) ).
cnf(c_0_97,plain,
meet(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_93]),c_0_54]) ).
fof(c_0_98,plain,
! [X25,X26] : join(composition(converse(X25),complement(composition(X25,X26))),complement(X26)) = complement(X26),
inference(variable_rename,[status(thm)],[converse_cancellativity]) ).
fof(c_0_99,negated_conjecture,
~ ! [X1,X2] :
( ( composition(X2,top) = X2
& composition(X1,top) = X1 )
=> composition(meet(X1,X2),top) = meet(X1,X2) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_100,plain,
converse(complement(converse(complement(converse(X1))))) = converse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_29]),c_0_97]) ).
cnf(c_0_101,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
fof(c_0_102,negated_conjecture,
( composition(meet(esk1_0,esk2_0),top) != meet(esk1_0,esk2_0)
& composition(esk2_0,top) = esk2_0
& composition(esk1_0,top) = esk1_0 ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_99])])])]) ).
cnf(c_0_103,plain,
complement(converse(complement(converse(X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_100]),c_0_76]) ).
fof(c_0_104,plain,
! [X23,X24] : converse(composition(X23,X24)) = composition(converse(X24),converse(X23)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
cnf(c_0_105,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_101,c_0_23]) ).
cnf(c_0_106,negated_conjecture,
composition(esk2_0,top) = esk2_0,
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_107,plain,
converse(complement(converse(X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_61,c_0_103]) ).
cnf(c_0_108,plain,
meet(join(complement(X1),complement(X2)),X3) = meet(complement(meet(X1,X2)),X3),
inference(rw,[status(thm)],[c_0_58,c_0_62]) ).
cnf(c_0_109,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
fof(c_0_110,plain,
! [X20,X21,X22] : composition(join(X20,X21),X22) = join(composition(X20,X22),composition(X21,X22)),
inference(variable_rename,[status(thm)],[composition_distributivity]) ).
cnf(c_0_111,negated_conjecture,
join(zero,composition(converse(esk2_0),complement(esk2_0))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_27]),c_0_27]) ).
cnf(c_0_112,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[c_0_76,c_0_107]) ).
cnf(c_0_113,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_108]),c_0_54]) ).
fof(c_0_114,plain,
! [X17,X18,X19] : composition(X17,composition(X18,X19)) = composition(composition(X17,X18),X19),
inference(variable_rename,[status(thm)],[composition_associativity]) ).
cnf(c_0_115,plain,
converse(composition(X1,top)) = composition(top,converse(X1)),
inference(spm,[status(thm)],[c_0_109,c_0_90]) ).
cnf(c_0_116,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_117,negated_conjecture,
composition(converse(esk2_0),complement(esk2_0)) = zero,
inference(rw,[status(thm)],[c_0_111,c_0_46]) ).
cnf(c_0_118,plain,
converse(complement(join(converse(X1),X2))) = complement(join(X1,converse(X2))),
inference(spm,[status(thm)],[c_0_112,c_0_78]) ).
cnf(c_0_119,plain,
join(converse(complement(X1)),complement(X2)) = complement(meet(converse(X1),X2)),
inference(spm,[status(thm)],[c_0_113,c_0_112]) ).
cnf(c_0_120,plain,
join(complement(X1),converse(complement(X2))) = complement(meet(X1,converse(X2))),
inference(spm,[status(thm)],[c_0_113,c_0_112]) ).
cnf(c_0_121,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_122,negated_conjecture,
composition(top,converse(esk2_0)) = converse(esk2_0),
inference(spm,[status(thm)],[c_0_115,c_0_106]) ).
fof(c_0_123,plain,
! [X14,X15,X16] : join(meet(composition(X14,X15),X16),meet(composition(meet(X14,composition(X16,converse(X15))),X15),X16)) = meet(composition(meet(X14,composition(X16,converse(X15))),X15),X16),
inference(variable_rename,[status(thm)],[modular_law_2]) ).
fof(c_0_124,plain,
! [X8,X9,X10] : join(meet(composition(X8,X9),X10),composition(meet(X8,composition(X10,converse(X9))),meet(X9,composition(converse(X8),X10)))) = composition(meet(X8,composition(X10,converse(X9))),meet(X9,composition(converse(X8),X10))),
inference(variable_rename,[status(thm)],[dedekind_law]) ).
cnf(c_0_125,negated_conjecture,
composition(join(converse(esk2_0),X1),complement(esk2_0)) = composition(X1,complement(esk2_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_46]) ).
cnf(c_0_126,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_118,c_0_119]),c_0_61]),c_0_120]),c_0_61]) ).
cnf(c_0_127,negated_conjecture,
composition(top,composition(converse(esk2_0),X1)) = composition(converse(esk2_0),X1),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_128,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_123]) ).
cnf(c_0_129,plain,
join(meet(composition(X1,X2),X3),composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3)))) = composition(meet(X1,composition(X3,converse(X2))),meet(X2,composition(converse(X1),X3))),
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_130,negated_conjecture,
composition(meet(converse(esk2_0),X1),complement(esk2_0)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_73]),c_0_117]) ).
cnf(c_0_131,plain,
meet(converse(X1),converse(X2)) = converse(meet(X1,X2)),
inference(spm,[status(thm)],[c_0_126,c_0_76]) ).
cnf(c_0_132,negated_conjecture,
composition(top,zero) = zero,
inference(spm,[status(thm)],[c_0_127,c_0_117]) ).
cnf(c_0_133,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_128,c_0_29]),c_0_29]) ).
cnf(c_0_134,plain,
join(meet(composition(X1,top),X2),composition(meet(X1,composition(X2,top)),composition(converse(X1),X2))) = composition(meet(X1,composition(X2,top)),composition(converse(X1),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_90]),c_0_57]),c_0_57]) ).
cnf(c_0_135,negated_conjecture,
composition(converse(meet(esk2_0,X1)),complement(esk2_0)) = zero,
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_136,negated_conjecture,
composition(X1,zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_132]),c_0_46]),c_0_60]),c_0_132]) ).
cnf(c_0_137,negated_conjecture,
join(meet(esk2_0,X1),meet(X1,composition(meet(esk2_0,composition(X1,top)),top))) = meet(X1,composition(meet(esk2_0,composition(X1,top)),top)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_106]),c_0_90]),c_0_90]) ).
cnf(c_0_138,negated_conjecture,
composition(esk1_0,top) = esk1_0,
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_139,plain,
join(meet(X1,X2),meet(X2,complement(X1))) = X2,
inference(spm,[status(thm)],[c_0_26,c_0_29]) ).
cnf(c_0_140,negated_conjecture,
meet(complement(esk2_0),composition(meet(esk2_0,X1),top)) = zero,
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_29]),c_0_136]),c_0_52]),c_0_136]) ).
cnf(c_0_141,plain,
meet(X1,join(meet(X2,complement(X1)),X3)) = meet(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_80]),c_0_94]) ).
cnf(c_0_142,plain,
join(meet(X1,X2),join(meet(X1,complement(X2)),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_35,c_0_26]) ).
cnf(c_0_143,plain,
join(X1,join(X2,meet(X3,X1))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_66,c_0_77]) ).
cnf(c_0_144,negated_conjecture,
join(meet(esk1_0,esk2_0),meet(esk1_0,composition(meet(esk1_0,esk2_0),top))) = meet(esk1_0,composition(meet(esk1_0,esk2_0),top)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_29]),c_0_29]),c_0_29]) ).
cnf(c_0_145,negated_conjecture,
meet(esk2_0,composition(meet(esk2_0,X1),top)) = composition(meet(esk2_0,X1),top),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_56]),c_0_57]),c_0_29]),c_0_46]) ).
cnf(c_0_146,plain,
meet(X1,join(meet(X2,X1),X3)) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_141,c_0_142]),c_0_56]),c_0_57]) ).
cnf(c_0_147,negated_conjecture,
join(meet(esk1_0,esk2_0),composition(meet(esk1_0,esk2_0),top)) = composition(meet(esk1_0,esk2_0),top),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_77]) ).
cnf(c_0_148,negated_conjecture,
meet(esk2_0,composition(meet(X1,esk2_0),top)) = composition(meet(X1,esk2_0),top),
inference(spm,[status(thm)],[c_0_145,c_0_74]) ).
cnf(c_0_149,negated_conjecture,
join(esk1_0,composition(X1,top)) = composition(join(X1,esk1_0),top),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_138]),c_0_23]) ).
cnf(c_0_150,negated_conjecture,
composition(meet(esk1_0,esk2_0),top) != meet(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_151,negated_conjecture,
$false,
inference(sr,[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_146,c_0_147]),c_0_148]),c_0_149]),c_0_23]),c_0_73]),c_0_138]),c_0_29]),c_0_150]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : REL019+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.44 % Computer : n013.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 04:00:20 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.19/0.51 Running first-order theorem proving
% 0.19/0.51 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 245.33/36.33 % Version: 3.5.1
% 245.33/36.33 % Preprocessing class: FSMSSMSSSSSNFFN.
% 245.33/36.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 245.33/36.33 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 245.33/36.33 % Starting new_bool_3 with 300s (1) cores
% 245.33/36.33 % Starting new_bool_1 with 300s (1) cores
% 245.33/36.33 % Starting sh5l with 300s (1) cores
% 245.33/36.33 % sh5l with pid 4098221 completed with status 0
% 245.33/36.33 % Result found by sh5l
% 245.33/36.33 % Preprocessing class: FSMSSMSSSSSNFFN.
% 245.33/36.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 245.33/36.33 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 245.33/36.33 % Starting new_bool_3 with 300s (1) cores
% 245.33/36.33 % Starting new_bool_1 with 300s (1) cores
% 245.33/36.33 % Starting sh5l with 300s (1) cores
% 245.33/36.33 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 245.33/36.33 % SinE strategy is gf500_gu_R04_F100_L20000
% 245.33/36.33 % Search class: FUUPM-FFMF21-DFFFFFNN
% 245.33/36.33 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 245.33/36.33 % Starting SubtermCWHack with 28s (1) cores
% 245.33/36.33 % SubtermCWHack with pid 4098228 completed with status 8
% 245.33/36.33 % Starting sh5l with 31s (1) cores
% 245.33/36.33 % sh5l with pid 4098396 completed with status 0
% 245.33/36.33 % Result found by sh5l
% 245.33/36.33 % Preprocessing class: FSMSSMSSSSSNFFN.
% 245.33/36.33 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 245.33/36.33 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 245.33/36.33 % Starting new_bool_3 with 300s (1) cores
% 245.33/36.33 % Starting new_bool_1 with 300s (1) cores
% 245.33/36.33 % Starting sh5l with 300s (1) cores
% 245.33/36.33 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 245.33/36.33 % SinE strategy is gf500_gu_R04_F100_L20000
% 245.33/36.33 % Search class: FUUPM-FFMF21-DFFFFFNN
% 245.33/36.33 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 245.33/36.33 % Starting SubtermCWHack with 28s (1) cores
% 245.33/36.33 % SubtermCWHack with pid 4098228 completed with status 8
% 245.33/36.33 % Starting sh5l with 31s (1) cores
% 245.33/36.33 % Preprocessing time : 0.001 s
% 245.33/36.33 % Presaturation interreduction done
% 245.33/36.33
% 245.33/36.33 % Proof found!
% 245.33/36.33 % SZS status Theorem
% 245.33/36.33 % SZS output start CNFRefutation
% See solution above
% 245.33/36.33 % Parsed axioms : 17
% 245.33/36.33 % Removed by relevancy pruning/SinE : 1
% 245.33/36.33 % Initial clauses : 18
% 245.33/36.33 % Removed in clause preprocessing : 0
% 245.33/36.33 % Initial clauses in saturation : 18
% 245.33/36.33 % Processed clauses : 6355
% 245.33/36.33 % ...of these trivial : 3362
% 245.33/36.33 % ...subsumed : 983
% 245.33/36.33 % ...remaining for further processing : 2010
% 245.33/36.33 % Other redundant clauses eliminated : 0
% 245.33/36.33 % Clauses deleted for lack of memory : 0
% 245.33/36.33 % Backward-subsumed : 0
% 245.33/36.33 % Backward-rewritten : 647
% 245.33/36.33 % Generated clauses : 278855
% 245.33/36.33 % ...of the previous two non-redundant : 145664
% 245.33/36.33 % ...aggressively subsumed : 0
% 245.33/36.33 % Contextual simplify-reflections : 0
% 245.33/36.33 % Paramodulations : 278855
% 245.33/36.33 % Factorizations : 0
% 245.33/36.33 % NegExts : 0
% 245.33/36.33 % Equation resolutions : 0
% 245.33/36.33 % Disequality decompositions : 0
% 245.33/36.33 % Total rewrite steps : 734373
% 245.33/36.33 % ...of those cached : 648449
% 245.33/36.33 % Propositional unsat checks : 0
% 245.33/36.33 % Propositional check models : 0
% 245.33/36.33 % Propositional check unsatisfiable : 0
% 245.33/36.33 % Propositional clauses : 0
% 245.33/36.33 % Propositional clauses after purity: 0
% 245.33/36.33 % Propositional unsat core size : 0
% 245.33/36.33 % Propositional preprocessing time : 0.000
% 245.33/36.33 % Propositional encoding time : 0.000
% 245.33/36.33 % Propositional solver time : 0.000
% 245.33/36.33 % Success case prop preproc time : 0.000
% 245.33/36.33 % Success case prop encoding time : 0.000
% 245.33/36.33 % Success case prop solver time : 0.000
% 245.33/36.33 % Current number of processed clauses : 1345
% 245.33/36.33 % Positive orientable unit clauses : 1333
% 245.33/36.33 % Positive unorientable unit clauses: 11
% 245.33/36.33 % Negative unit clauses : 1
% 245.33/36.33 % Non-unit-clauses : 0
% 245.33/36.33 % Current number of unprocessed clauses: 137002
% 245.33/36.33 % ...number of literals in the above : 137002
% 245.33/36.33 % Current number of archived formulas : 0
% 245.33/36.33 % Current number of archived clauses : 665
% 245.33/36.33 % Clause-clause subsumption calls (NU) : 0
% 245.33/36.33 % Rec. Clause-clause subsumption calls : 0
% 245.33/36.33 % Non-unit clause-clause subsumptions : 0
% 245.33/36.33 % Unit Clause-clause subsumption calls : 115
% 245.33/36.33 % Rewrite failures with RHS unbound : 0
% 245.33/36.33 % BW rewrite match attempts : 7438
% 245.33/36.33 % BW rewrite match successes : 646
% 245.33/36.33 % Condensation attempts : 6355
% 245.33/36.33 % Condensation successes : 0
% 245.33/36.33 % Termbank termtop insertions : 6205138
% 245.33/36.33 % Search garbage collected termcells : 42
% 245.33/36.33
% 245.33/36.33 % -------------------------------------------------
% 245.33/36.33 % User time : 32.385 s
% 245.33/36.33 % System time : 1.172 s
% 245.33/36.33 % Total time : 33.557 s
% 245.33/36.33 % Maximum resident set size: 3652 pages
% 245.33/36.33
% 245.33/36.33 % -------------------------------------------------
% 245.33/36.33 % User time : 32.387 s
% 245.33/36.33 % System time : 1.178 s
% 245.33/36.33 % Total time : 33.565 s
% 245.33/36.33 % Maximum resident set size: 4864 pages
% 245.33/36.33 % E exiting
%------------------------------------------------------------------------------