%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : REL041+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 : n007.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 05:04:29 PM UTC 2026
% Result : Theorem 51.29s 30.26s
% Output : CNFRefutation 51.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 17
% Syntax : Number of formulae : 201 ( 198 unt; 0 def)
% Number of atoms : 204 ( 203 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 3 ~; 0 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 327 ( 29 sgn 72 !; 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(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(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(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(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(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(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(goals,conjecture,
! [X1] :
( join(composition(converse(X1),X1),one) = one
=> ! [X2] : meet(composition(X1,X2),composition(X1,complement(X2))) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
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(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,
! [X59,X60] : converse(composition(X59,X60)) = composition(converse(X60),converse(X59)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
fof(c_0_18,plain,
! [X56] : converse(converse(X56)) = X56,
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,
! [X52] : composition(X52,one) = X52,
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,
! [X42,X43,X44] : join(X42,join(X43,X44)) = join(join(X42,X43),X44),
inference(variable_rename,[status(thm)],[maddux2_join_associativity]) ).
fof(c_0_25,plain,
! [X63] : top = join(X63,complement(X63)),
inference(variable_rename,[status(thm)],[def_top]) ).
fof(c_0_26,plain,
! [X61,X62] : join(composition(converse(X61),complement(composition(X61,X62))),complement(X62)) = complement(X62),
inference(variable_rename,[status(thm)],[converse_cancellativity]) ).
fof(c_0_27,plain,
! [X40,X41] : join(X40,X41) = join(X41,X40),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_0_28,plain,
composition(converse(one),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_20]) ).
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(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_23,c_0_28]) ).
cnf(c_0_34,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_28,c_0_33]) ).
fof(c_0_37,plain,
! [X45,X46] : X45 = join(complement(join(complement(X45),complement(X46))),complement(join(complement(X45),X46))),
inference(variable_rename,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
fof(c_0_38,plain,
! [X47,X48] : meet(X47,X48) = complement(join(complement(X47),complement(X48))),
inference(variable_rename,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_0_39,plain,
join(X1,join(X2,complement(X1))) = join(top,X2),
inference(spm,[status(thm)],[c_0_34,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_35,c_0_36]),c_0_33]),c_0_36]) ).
fof(c_0_41,plain,
! [X64] : zero = meet(X64,complement(X64)),
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_37]) ).
cnf(c_0_43,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_44,plain,
join(top,complement(complement(X1))) = join(X1,top),
inference(spm,[status(thm)],[c_0_34,c_0_30]) ).
cnf(c_0_45,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),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_30]),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_32]) ).
cnf(c_0_51,plain,
meet(X1,X2) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_32]),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)) = X1,
inference(rw,[status(thm)],[c_0_53,c_0_56]) ).
cnf(c_0_58,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_40,c_0_57]) ).
cnf(c_0_59,plain,
complement(complement(X1)) = meet(X1,X1),
inference(spm,[status(thm)],[c_0_43,c_0_40]) ).
cnf(c_0_60,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_29,c_0_58]) ).
cnf(c_0_61,plain,
join(zero,meet(X1,X1)) = X1,
inference(spm,[status(thm)],[c_0_53,c_0_59]) ).
fof(c_0_62,plain,
! [X57,X58] : converse(join(X57,X58)) = join(converse(X57),converse(X58)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
cnf(c_0_63,plain,
join(X1,meet(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_47]),c_0_32]) ).
cnf(c_0_64,plain,
complement(join(X1,complement(X2))) = meet(complement(X1),X2),
inference(spm,[status(thm)],[c_0_43,c_0_57]) ).
cnf(c_0_65,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_59]),c_0_61]) ).
cnf(c_0_66,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_67,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_63,c_0_51]) ).
cnf(c_0_68,plain,
complement(join(complement(X1),X2)) = meet(complement(X2),X1),
inference(spm,[status(thm)],[c_0_64,c_0_32]) ).
cnf(c_0_69,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_32,c_0_48]) ).
cnf(c_0_70,plain,
join(zero,X1) = X1,
inference(rw,[status(thm)],[c_0_61,c_0_65]) ).
cnf(c_0_71,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(spm,[status(thm)],[c_0_66,c_0_20]) ).
cnf(c_0_72,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_29,c_0_67]) ).
cnf(c_0_73,plain,
join(meet(X1,X2),meet(complement(X2),X1)) = X1,
inference(rw,[status(thm)],[c_0_47,c_0_68]) ).
cnf(c_0_74,plain,
join(X1,join(X2,complement(X1))) = top,
inference(rw,[status(thm)],[c_0_39,c_0_69]) ).
cnf(c_0_75,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_70]) ).
cnf(c_0_76,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(spm,[status(thm)],[c_0_71,c_0_30]) ).
cnf(c_0_77,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_78,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_47,c_0_74]),c_0_57]),c_0_49]),c_0_75]) ).
cnf(c_0_79,plain,
converse(join(one,X1)) = join(one,converse(X1)),
inference(spm,[status(thm)],[c_0_66,c_0_33]) ).
cnf(c_0_80,plain,
meet(complement(X1),complement(X2)) = complement(join(X1,X2)),
inference(spm,[status(thm)],[c_0_64,c_0_57]) ).
cnf(c_0_81,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_76,c_0_69]) ).
cnf(c_0_82,plain,
meet(X1,complement(meet(X1,X2))) = meet(complement(X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_77]),c_0_68]),c_0_57]),c_0_51]) ).
cnf(c_0_83,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_57,c_0_64]) ).
cnf(c_0_84,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_63]),c_0_51]) ).
cnf(c_0_85,plain,
join(one,converse(complement(one))) = converse(top),
inference(spm,[status(thm)],[c_0_79,c_0_30]) ).
cnf(c_0_86,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_77,c_0_80]) ).
cnf(c_0_87,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(rw,[status(thm)],[c_0_76,c_0_81]) ).
cnf(c_0_88,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_82]),c_0_83]),c_0_57]),c_0_51]),c_0_84]) ).
cnf(c_0_89,plain,
meet(top,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_56]),c_0_57]) ).
cnf(c_0_90,plain,
join(one,converse(complement(one))) = top,
inference(rw,[status(thm)],[c_0_85,c_0_81]) ).
cnf(c_0_91,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_49]),c_0_75]) ).
cnf(c_0_92,plain,
meet(X1,join(complement(X1),X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_88,c_0_32]) ).
cnf(c_0_93,plain,
meet(X1,top) = X1,
inference(spm,[status(thm)],[c_0_51,c_0_89]) ).
cnf(c_0_94,plain,
join(one,complement(converse(complement(one)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_90]),c_0_49]),c_0_75]) ).
fof(c_0_95,plain,
! [X53,X54,X55] : composition(join(X53,X54),X55) = join(composition(X53,X55),composition(X54,X55)),
inference(variable_rename,[status(thm)],[composition_distributivity]) ).
cnf(c_0_96,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_91]),c_0_20]),c_0_20]) ).
cnf(c_0_97,plain,
meet(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_87]),c_0_93]) ).
cnf(c_0_98,plain,
join(X1,converse(meet(X2,converse(X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_67]),c_0_20]) ).
cnf(c_0_99,plain,
meet(complement(one),converse(complement(one))) = complement(one),
inference(spm,[status(thm)],[c_0_64,c_0_94]) ).
cnf(c_0_100,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_101,plain,
converse(complement(converse(complement(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_96]),c_0_51]),c_0_97]) ).
cnf(c_0_102,plain,
join(complement(one),converse(complement(one))) = complement(one),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_103,plain,
join(X1,composition(X2,X1)) = composition(join(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_36]),c_0_32]) ).
cnf(c_0_104,plain,
complement(converse(complement(X1))) = converse(X1),
inference(spm,[status(thm)],[c_0_20,c_0_101]) ).
cnf(c_0_105,plain,
converse(complement(one)) = complement(one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_102]),c_0_51]),c_0_99]) ).
cnf(c_0_106,plain,
composition(join(X1,one),top) = top,
inference(spm,[status(thm)],[c_0_103,c_0_69]) ).
cnf(c_0_107,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[c_0_57,c_0_104]) ).
cnf(c_0_108,plain,
converse(join(complement(one),X1)) = join(complement(one),converse(X1)),
inference(spm,[status(thm)],[c_0_66,c_0_105]) ).
cnf(c_0_109,plain,
converse(composition(top,X1)) = composition(converse(X1),top),
inference(spm,[status(thm)],[c_0_22,c_0_81]) ).
cnf(c_0_110,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(spm,[status(thm)],[c_0_66,c_0_20]) ).
cnf(c_0_111,plain,
composition(top,top) = top,
inference(spm,[status(thm)],[c_0_106,c_0_69]) ).
cnf(c_0_112,plain,
join(complement(X1),join(X2,X1)) = top,
inference(spm,[status(thm)],[c_0_74,c_0_57]) ).
fof(c_0_113,plain,
! [X68,X69,X70] : join(meet(composition(X68,X69),X70),meet(composition(X68,meet(X69,composition(converse(X68),X70))),X70)) = meet(composition(X68,meet(X69,composition(converse(X68),X70))),X70),
inference(variable_rename,[status(thm)],[modular_law_1]) ).
cnf(c_0_114,plain,
meet(one,converse(complement(X1))) = converse(meet(one,complement(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_107,c_0_108]),c_0_68]),c_0_107]),c_0_68]),c_0_51]),c_0_51]) ).
cnf(c_0_115,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_116,plain,
converse(join(X1,one)) = join(one,converse(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_33]),c_0_32]) ).
fof(c_0_117,plain,
! [X71,X72,X73] : join(meet(composition(X71,X72),X73),meet(composition(meet(X71,composition(X73,converse(X72))),X72),X73)) = meet(composition(meet(X71,composition(X73,converse(X72))),X72),X73),
inference(variable_rename,[status(thm)],[modular_law_2]) ).
cnf(c_0_118,plain,
complement(composition(converse(X1),top)) = converse(complement(composition(top,X1))),
inference(spm,[status(thm)],[c_0_107,c_0_109]) ).
cnf(c_0_119,plain,
join(converse(zero),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_70]),c_0_20]) ).
cnf(c_0_120,plain,
converse(composition(X1,top)) = composition(top,converse(X1)),
inference(spm,[status(thm)],[c_0_19,c_0_81]) ).
cnf(c_0_121,plain,
composition(top,zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_111]),c_0_49]),c_0_81]),c_0_49]),c_0_103]),c_0_69]),c_0_49]) ).
cnf(c_0_122,plain,
join(X1,complement(meet(X2,X1))) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_67]),c_0_32]) ).
fof(c_0_123,negated_conjecture,
~ ! [X1] :
( join(composition(converse(X1),X1),one) = one
=> ! [X2] : meet(composition(X1,X2),composition(X1,complement(X2))) = zero ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_124,plain,
complement(join(X1,join(X2,complement(X3)))) = meet(complement(join(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_64,c_0_29]) ).
cnf(c_0_125,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(spm,[status(thm)],[c_0_83,c_0_57]) ).
cnf(c_0_126,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_113]) ).
cnf(c_0_127,plain,
meet(one,converse(X1)) = converse(meet(one,X1)),
inference(spm,[status(thm)],[c_0_114,c_0_57]) ).
cnf(c_0_128,plain,
join(X1,composition(X1,converse(X2))) = composition(X1,join(one,converse(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_103]),c_0_115]),c_0_116]),c_0_115]) ).
cnf(c_0_129,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_117]) ).
cnf(c_0_130,plain,
composition(X1,converse(complement(composition(top,X1)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_118]),c_0_49]),c_0_20]),c_0_70]),c_0_49]) ).
cnf(c_0_131,plain,
converse(zero) = zero,
inference(spm,[status(thm)],[c_0_75,c_0_119]) ).
cnf(c_0_132,plain,
complement(composition(top,converse(X1))) = converse(complement(composition(X1,top))),
inference(spm,[status(thm)],[c_0_107,c_0_120]) ).
cnf(c_0_133,plain,
complement(zero) = top,
inference(spm,[status(thm)],[c_0_30,c_0_56]) ).
cnf(c_0_134,plain,
composition(X1,zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_121]),c_0_48]),c_0_121]),c_0_75]) ).
cnf(c_0_135,plain,
meet(complement(X1),meet(X2,X1)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_122]),c_0_49]) ).
fof(c_0_136,negated_conjecture,
( join(composition(converse(esk1_0),esk1_0),one) = one
& meet(composition(esk1_0,esk2_0),composition(esk1_0,complement(esk2_0))) != zero ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_123])])]) ).
cnf(c_0_137,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_124,c_0_125]),c_0_64]),c_0_64]) ).
cnf(c_0_138,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_126,c_0_51]),c_0_51]) ).
cnf(c_0_139,plain,
meet(one,composition(converse(X1),top)) = converse(meet(one,composition(top,X1))),
inference(spm,[status(thm)],[c_0_127,c_0_109]) ).
cnf(c_0_140,plain,
join(X1,composition(X1,X2)) = composition(X1,join(one,X2)),
inference(spm,[status(thm)],[c_0_128,c_0_20]) ).
cnf(c_0_141,plain,
join(one,converse(meet(one,X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_63]),c_0_33]) ).
cnf(c_0_142,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_129,c_0_51]),c_0_51]) ).
cnf(c_0_143,plain,
composition(converse(complement(composition(X1,top))),X1) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_130]),c_0_131]),c_0_132]),c_0_20]) ).
cnf(c_0_144,plain,
meet(X1,zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_133]),c_0_48]),c_0_49]) ).
cnf(c_0_145,plain,
composition(zero,X1) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_134]),c_0_131]),c_0_131]) ).
cnf(c_0_146,plain,
meet(X1,complement(join(X2,X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_80]),c_0_57]) ).
cnf(c_0_147,negated_conjecture,
join(composition(converse(esk1_0),esk1_0),one) = one,
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_148,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_67]),c_0_51]) ).
cnf(c_0_149,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_137,c_0_57]) ).
cnf(c_0_150,plain,
composition(X1,converse(meet(one,composition(top,X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_23]),c_0_93]),c_0_89]),c_0_140]),c_0_141]),c_0_23]),c_0_89]) ).
cnf(c_0_151,plain,
meet(composition(X1,X2),complement(composition(top,X2))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_143]),c_0_118]),c_0_20]),c_0_118]),c_0_20]),c_0_144]),c_0_145]),c_0_144]),c_0_75]),c_0_118]),c_0_20]),c_0_144]),c_0_145]),c_0_144]) ).
cnf(c_0_152,plain,
join(X1,join(meet(complement(X1),X2),X3)) = join(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_77]),c_0_29]) ).
cnf(c_0_153,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_32]),c_0_29]) ).
fof(c_0_154,plain,
! [X49,X50,X51] : composition(X49,composition(X50,X51)) = composition(composition(X49,X50),X51),
inference(variable_rename,[status(thm)],[composition_associativity]) ).
cnf(c_0_155,plain,
meet(X1,complement(join(X2,join(X3,X1)))) = zero,
inference(spm,[status(thm)],[c_0_146,c_0_29]) ).
cnf(c_0_156,negated_conjecture,
join(one,composition(converse(esk1_0),esk1_0)) = one,
inference(rw,[status(thm)],[c_0_147,c_0_32]) ).
cnf(c_0_157,plain,
meet(composition(X1,X2),complement(composition(X1,join(one,X2)))) = zero,
inference(spm,[status(thm)],[c_0_146,c_0_140]) ).
cnf(c_0_158,plain,
meet(X1,meet(composition(X2,X3),composition(meet(X2,composition(meet(X1,composition(X2,X3)),converse(X3))),X3))) = meet(X1,composition(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_148]),c_0_63]),c_0_149]) ).
cnf(c_0_159,plain,
composition(meet(one,composition(top,X1)),converse(X1)) = converse(X1),
inference(spm,[status(thm)],[c_0_115,c_0_150]) ).
cnf(c_0_160,plain,
meet(composition(top,X1),composition(X2,X1)) = composition(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_151]),c_0_57]),c_0_70]) ).
cnf(c_0_161,plain,
meet(X1,join(meet(X1,X2),X3)) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_152]),c_0_92]),c_0_57]) ).
cnf(c_0_162,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_60,c_0_32]) ).
cnf(c_0_163,plain,
join(X1,join(X2,meet(X3,X1))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_153,c_0_67]) ).
cnf(c_0_164,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_154]) ).
cnf(c_0_165,plain,
join(meet(composition(X1,X2),X3),meet(X3,composition(X1,meet(composition(converse(X1),X3),X2)))) = meet(X3,composition(X1,meet(composition(converse(X1),X3),X2))),
inference(spm,[status(thm)],[c_0_138,c_0_51]) ).
cnf(c_0_166,negated_conjecture,
meet(composition(converse(esk1_0),esk1_0),complement(join(X1,one))) = zero,
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_167,plain,
complement(join(one,converse(X1))) = converse(complement(join(one,X1))),
inference(spm,[status(thm)],[c_0_107,c_0_79]) ).
cnf(c_0_168,plain,
complement(join(X1,converse(complement(X2)))) = meet(complement(X1),converse(X2)),
inference(spm,[status(thm)],[c_0_64,c_0_107]) ).
cnf(c_0_169,plain,
join(meet(X1,X2),meet(X2,complement(X1))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_57]),c_0_32]) ).
cnf(c_0_170,plain,
meet(complement(X1),composition(X1,meet(one,X2))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_157,c_0_63]),c_0_23]),c_0_51]) ).
cnf(c_0_171,negated_conjecture,
meet(one,composition(converse(esk1_0),esk1_0)) = composition(converse(esk1_0),esk1_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_156]),c_0_51]) ).
cnf(c_0_172,plain,
meet(one,composition(converse(X1),X1)) = meet(one,composition(top,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_89]),c_0_160]) ).
cnf(c_0_173,plain,
meet(X1,join(X2,meet(X1,X3))) = meet(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_163]) ).
cnf(c_0_174,plain,
join(meet(composition(top,X1),X2),meet(X2,composition(X2,composition(converse(X1),X1)))) = meet(X2,composition(X2,composition(converse(X1),X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_89]),c_0_164]),c_0_164]) ).
cnf(c_0_175,plain,
meet(X1,join(meet(X2,X1),X3)) = meet(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_161,c_0_51]) ).
cnf(c_0_176,plain,
join(composition(X1,X2),composition(X3,composition(X4,X2))) = composition(join(X1,composition(X3,X4)),X2),
inference(spm,[status(thm)],[c_0_100,c_0_164]) ).
fof(c_0_177,plain,
! [X65,X66,X67] : join(meet(composition(X65,X66),X67),composition(meet(X65,composition(X67,converse(X66))),meet(X66,composition(converse(X65),X67)))) = composition(meet(X65,composition(X67,converse(X66))),meet(X66,composition(converse(X65),X67))),
inference(variable_rename,[status(thm)],[dedekind_law]) ).
cnf(c_0_178,negated_conjecture,
meet(esk1_0,composition(esk1_0,complement(join(X1,one)))) = 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(spm,[status(thm)],[c_0_165,c_0_166]),c_0_134]),c_0_144]),c_0_75]),c_0_134]),c_0_144]),c_0_51]) ).
cnf(c_0_179,plain,
complement(join(converse(complement(X1)),X2)) = meet(complement(X2),converse(X1)),
inference(spm,[status(thm)],[c_0_68,c_0_107]) ).
cnf(c_0_180,plain,
meet(complement(one),converse(X1)) = converse(meet(complement(one),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_64]) ).
cnf(c_0_181,plain,
meet(X1,composition(X1,meet(one,X2))) = composition(X1,meet(one,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_170]),c_0_57]),c_0_70]),c_0_51]) ).
cnf(c_0_182,negated_conjecture,
meet(one,composition(top,esk1_0)) = composition(converse(esk1_0),esk1_0),
inference(rw,[status(thm)],[c_0_171,c_0_172]) ).
cnf(c_0_183,plain,
meet(X1,composition(X1,composition(converse(X2),X2))) = meet(X1,composition(top,X2)),
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_174]),c_0_84]),c_0_175]),c_0_176]),c_0_69]) ).
cnf(c_0_184,plain,
converse(complement(join(converse(X1),X2))) = complement(join(X1,converse(X2))),
inference(spm,[status(thm)],[c_0_107,c_0_71]) ).
cnf(c_0_185,plain,
join(converse(complement(X1)),complement(X2)) = complement(meet(converse(X1),X2)),
inference(spm,[status(thm)],[c_0_125,c_0_107]) ).
cnf(c_0_186,plain,
join(complement(X1),converse(complement(X2))) = complement(meet(X1,converse(X2))),
inference(spm,[status(thm)],[c_0_125,c_0_107]) ).
cnf(c_0_187,plain,
join(X1,complement(meet(X1,X2))) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_63]),c_0_32]) ).
cnf(c_0_188,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_177]) ).
cnf(c_0_189,negated_conjecture,
meet(esk1_0,composition(esk1_0,converse(meet(complement(one),X1)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_178,c_0_179]),c_0_180]) ).
cnf(c_0_190,plain,
meet(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = composition(converse(X2),complement(composition(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_35]),c_0_51]) ).
cnf(c_0_191,negated_conjecture,
composition(X1,composition(converse(esk1_0),esk1_0)) = meet(X1,composition(top,esk1_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_182]),c_0_183]) ).
cnf(c_0_192,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_184,c_0_185]),c_0_57]),c_0_186]),c_0_57]) ).
cnf(c_0_193,plain,
meet(complement(X1),meet(X1,X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_187]),c_0_49]) ).
cnf(c_0_194,plain,
join(meet(composition(X1,X2),composition(X3,X4)),composition(meet(X1,composition(X3,composition(X4,converse(X2)))),meet(X2,composition(converse(X1),composition(X3,X4))))) = composition(meet(X1,composition(X3,composition(X4,converse(X2)))),meet(X2,composition(converse(X1),composition(X3,X4)))),
inference(spm,[status(thm)],[c_0_188,c_0_164]) ).
cnf(c_0_195,negated_conjecture,
meet(esk1_0,composition(esk1_0,composition(converse(complement(X1)),X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_189,c_0_190]),c_0_23]),c_0_22]) ).
cnf(c_0_196,negated_conjecture,
composition(converse(esk1_0),composition(esk1_0,X1)) = meet(X1,composition(converse(esk1_0),top)),
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_191]),c_0_192]),c_0_109]),c_0_22]),c_0_164]) ).
cnf(c_0_197,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(spm,[status(thm)],[c_0_193,c_0_57]) ).
cnf(c_0_198,negated_conjecture,
meet(composition(esk1_0,esk2_0),composition(esk1_0,complement(esk2_0))) != zero,
inference(split_conjunct,[status(thm)],[c_0_136]) ).
cnf(c_0_199,negated_conjecture,
meet(composition(esk1_0,X1),composition(esk1_0,complement(X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(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_194,c_0_195]),c_0_107]),c_0_20]),c_0_107]),c_0_20]),c_0_196]),c_0_197]),c_0_134]),c_0_75]),c_0_107]),c_0_20]),c_0_196]),c_0_197]),c_0_134]) ).
cnf(c_0_200,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_198,c_0_199])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL041+2 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n007.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 01:43:24 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 51.29/30.26 % Version : CSE_E---1.7
% 51.29/30.26 % Problem : theBenchmark.p
% 51.29/30.26 % SZS status Theorem for theBenchmark.p
% 51.29/30.26 % SZS output start CNFRefutation
% See solution above
% 51.49/30.48 % Total time : 22.418s
%------------------------------------------------------------------------------