%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : REL044+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 02:04:08 PM UTC 2026
% Result : Theorem 3.13s 0.88s
% Output : CNFRefutation 3.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 13
% Syntax : Number of formulae : 119 ( 116 unt; 0 def)
% Number of atoms : 122 ( 121 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 0 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 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 : 191 ( 16 sgn 58 !; 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/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(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(def_zero,axiom,
! [X1] : zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/Axioms/REL001+0.ax',converse_additivity) ).
fof(converse_idempotence,axiom,
! [X1] : converse(converse(X1)) = X1,
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/REL001+0.ax',converse_cancellativity) ).
fof(goals,conjecture,
! [X1,X2,X3] :
( join(composition(complement(X1),X2),complement(X3)) = complement(X3)
=> join(composition(X3,converse(X2)),X1) = X1 ),
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(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(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(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(c_0_13,plain,
! [X12,X13] : X12 = join(complement(join(complement(X12),complement(X13))),complement(join(complement(X12),X13))),
inference(variable_rename,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
fof(c_0_14,plain,
! [X14,X15] : meet(X14,X15) = complement(join(complement(X14),complement(X15))),
inference(variable_rename,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_0_15,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_17,plain,
! [X7,X8] : join(X7,X8) = join(X8,X7),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_0_18,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_20,plain,
! [X38] : zero = meet(X38,complement(X38)),
inference(variable_rename,[status(thm)],[def_zero]) ).
cnf(c_0_21,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_16]),c_0_19]) ).
cnf(c_0_22,plain,
meet(X1,X2) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_19]),c_0_16]) ).
cnf(c_0_23,plain,
zero = meet(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,plain,
join(meet(X1,X2),meet(complement(X2),X1)) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
join(zero,meet(X1,complement(complement(X1)))) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_23]) ).
cnf(c_0_26,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_23]),c_0_22]),c_0_19]),c_0_25]) ).
fof(c_0_27,plain,
! [X9,X10,X11] : join(X9,join(X10,X11)) = join(join(X9,X10),X11),
inference(variable_rename,[status(thm)],[maddux2_join_associativity]) ).
cnf(c_0_28,plain,
complement(join(X1,complement(X2))) = meet(complement(X1),X2),
inference(spm,[status(thm)],[c_0_16,c_0_26]) ).
cnf(c_0_29,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_30,plain,
join(zero,meet(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_23]),c_0_16]) ).
cnf(c_0_31,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_26,c_0_28]) ).
cnf(c_0_32,plain,
meet(meet(X1,X2),join(complement(X1),complement(X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_16]),c_0_22]) ).
cnf(c_0_33,plain,
join(zero,join(meet(X1,X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
join(X1,complement(X1)) = complement(zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_23]),c_0_26]) ).
cnf(c_0_35,plain,
meet(zero,join(complement(X1),complement(complement(X1)))) = zero,
inference(spm,[status(thm)],[c_0_32,c_0_23]) ).
cnf(c_0_36,plain,
join(X1,complement(meet(X1,X1))) = complement(zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_34]) ).
cnf(c_0_37,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[c_0_19,c_0_29]) ).
cnf(c_0_38,plain,
meet(zero,join(zero,complement(zero))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_35]),c_0_16]),c_0_23]),c_0_19]) ).
cnf(c_0_39,plain,
join(X1,complement(zero)) = complement(zero),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_31]),c_0_26]),c_0_37]),c_0_19]),c_0_34]) ).
cnf(c_0_40,plain,
join(zero,meet(zero,complement(join(zero,complement(zero))))) = zero,
inference(spm,[status(thm)],[c_0_21,c_0_38]) ).
cnf(c_0_41,plain,
meet(zero,complement(X1)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_39]),c_0_26]),c_0_22]) ).
cnf(c_0_42,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_19]),c_0_29]) ).
cnf(c_0_43,plain,
join(zero,zero) = zero,
inference(rw,[status(thm)],[c_0_40,c_0_41]) ).
fof(c_0_44,plain,
! [X19,X20] : converse(join(X19,X20)) = join(converse(X19),converse(X20)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
fof(c_0_45,plain,
! [X37] : converse(converse(X37)) = X37,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
cnf(c_0_46,plain,
join(zero,join(X1,meet(X2,X2))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_42,c_0_30]) ).
cnf(c_0_47,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(spm,[status(thm)],[c_0_29,c_0_43]) ).
cnf(c_0_48,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_49,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_50,plain,
join(zero,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_30]) ).
cnf(c_0_51,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_52,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[c_0_30,c_0_50]) ).
cnf(c_0_53,plain,
join(complement(zero),X1) = complement(zero),
inference(spm,[status(thm)],[c_0_19,c_0_39]) ).
cnf(c_0_54,plain,
join(X1,converse(complement(zero))) = converse(complement(zero)),
inference(spm,[status(thm)],[c_0_51,c_0_39]) ).
cnf(c_0_55,plain,
join(X1,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_52]),c_0_26]),c_0_26]) ).
cnf(c_0_56,plain,
converse(complement(zero)) = complement(zero),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_57,plain,
meet(meet(X1,X2),join(complement(X2),complement(X1))) = zero,
inference(spm,[status(thm)],[c_0_32,c_0_19]) ).
cnf(c_0_58,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(spm,[status(thm)],[c_0_31,c_0_26]) ).
cnf(c_0_59,plain,
join(meet(X1,X2),complement(join(complement(X2),X1))) = X2,
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_60,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_55]),c_0_29]),c_0_55]) ).
cnf(c_0_61,plain,
complement(join(complement(X1),X2)) = meet(complement(X2),X1),
inference(spm,[status(thm)],[c_0_28,c_0_19]) ).
cnf(c_0_62,plain,
join(X1,converse(complement(converse(X1)))) = complement(zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_34]),c_0_56]) ).
cnf(c_0_63,plain,
meet(meet(X1,X2),complement(meet(X2,X1))) = zero,
inference(rw,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_64,plain,
meet(complement(X1),complement(X2)) = complement(join(X1,X2)),
inference(spm,[status(thm)],[c_0_28,c_0_26]) ).
cnf(c_0_65,plain,
join(zero,meet(complement(zero),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_39]),c_0_26]),c_0_19]) ).
fof(c_0_66,plain,
! [X21,X22] : join(composition(converse(X21),complement(composition(X21,X22))),complement(X22)) = complement(X22),
inference(variable_rename,[status(thm)],[converse_cancellativity]) ).
cnf(c_0_67,plain,
complement(join(complement(X1),meet(X2,X3))) = meet(X1,join(complement(X2),complement(X3))),
inference(spm,[status(thm)],[c_0_16,c_0_16]) ).
cnf(c_0_68,plain,
join(X1,meet(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_24]),c_0_19]) ).
cnf(c_0_69,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_26]),c_0_22]) ).
cnf(c_0_70,plain,
meet(join(X1,X2),complement(join(X2,X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_64]),c_0_26]),c_0_22]) ).
cnf(c_0_71,plain,
join(X1,join(complement(X1),X2)) = complement(zero),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_34]),c_0_53]) ).
cnf(c_0_72,plain,
meet(complement(zero),X1) = X1,
inference(rw,[status(thm)],[c_0_65,c_0_50]) ).
cnf(c_0_73,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_74,plain,
meet(X1,join(X1,complement(X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_26]),c_0_26]) ).
cnf(c_0_75,plain,
meet(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_69]),c_0_26]),c_0_50]) ).
cnf(c_0_76,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_71]),c_0_29]),c_0_61]),c_0_72]),c_0_22]) ).
cnf(c_0_77,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_73,c_0_19]) ).
cnf(c_0_78,plain,
meet(X1,join(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_74,c_0_26]) ).
cnf(c_0_79,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_75]),c_0_26]),c_0_26]) ).
fof(c_0_80,negated_conjecture,
~ ! [X1,X2,X3] :
( join(composition(complement(X1),X2),complement(X3)) = complement(X3)
=> join(composition(X3,converse(X2)),X1) = X1 ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_81,plain,
meet(X1,composition(converse(X2),complement(composition(X2,X1)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_26]),c_0_22]) ).
cnf(c_0_82,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_78,c_0_19]) ).
cnf(c_0_83,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_79]),c_0_49]),c_0_49]) ).
fof(c_0_84,negated_conjecture,
( join(composition(esk3_0,converse(esk2_0)),esk1_0) != esk1_0
& join(composition(complement(esk1_0),esk2_0),complement(esk3_0)) = complement(esk3_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_80])])])]) ).
fof(c_0_85,plain,
! [X16,X17,X18] : composition(join(X16,X17),X18) = join(composition(X16,X18),composition(X17,X18)),
inference(variable_rename,[status(thm)],[composition_distributivity]) ).
cnf(c_0_86,plain,
composition(converse(X1),complement(composition(X1,complement(zero)))) = zero,
inference(spm,[status(thm)],[c_0_72,c_0_81]) ).
cnf(c_0_87,plain,
converse(complement(converse(complement(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_22]),c_0_75]) ).
fof(c_0_88,plain,
! [X23,X24,X25] : join(meet(composition(X23,X24),X25),composition(meet(X23,composition(X25,converse(X24))),meet(X24,composition(converse(X23),X25)))) = composition(meet(X23,composition(X25,converse(X24))),meet(X24,composition(converse(X23),X25))),
inference(variable_rename,[status(thm)],[dedekind_law]) ).
cnf(c_0_89,negated_conjecture,
join(composition(complement(esk1_0),esk2_0),complement(esk3_0)) = complement(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
fof(c_0_90,plain,
! [X32,X33,X34] : composition(X32,composition(X33,X34)) = composition(composition(X32,X33),X34),
inference(variable_rename,[status(thm)],[composition_associativity]) ).
cnf(c_0_91,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_92,plain,
composition(complement(zero),complement(composition(complement(zero),complement(zero)))) = zero,
inference(spm,[status(thm)],[c_0_86,c_0_56]) ).
cnf(c_0_93,plain,
complement(converse(complement(X1))) = converse(X1),
inference(spm,[status(thm)],[c_0_49,c_0_87]) ).
cnf(c_0_94,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_88]) ).
cnf(c_0_95,negated_conjecture,
join(complement(esk3_0),composition(complement(esk1_0),esk2_0)) = complement(esk3_0),
inference(rw,[status(thm)],[c_0_89,c_0_19]) ).
cnf(c_0_96,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_97,plain,
composition(X1,complement(composition(complement(zero),complement(zero)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_50]),c_0_53]),c_0_92]) ).
cnf(c_0_98,plain,
meet(X1,complement(join(X1,X2))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_71]),c_0_26]),c_0_26]),c_0_22]) ).
cnf(c_0_99,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[c_0_26,c_0_93]) ).
cnf(c_0_100,plain,
join(meet(composition(converse(X1),X2),X3),composition(meet(converse(X1),composition(X3,converse(X2))),meet(X2,composition(X1,X3)))) = composition(meet(converse(X1),composition(X3,converse(X2))),meet(X2,composition(X1,X3))),
inference(spm,[status(thm)],[c_0_94,c_0_49]) ).
cnf(c_0_101,negated_conjecture,
meet(esk3_0,composition(complement(esk1_0),esk2_0)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_95]),c_0_26]),c_0_22]) ).
cnf(c_0_102,plain,
composition(X1,zero) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_97]) ).
cnf(c_0_103,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_50]) ).
fof(c_0_104,plain,
! [X35,X36] : converse(composition(X35,X36)) = composition(converse(X36),converse(X35)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
cnf(c_0_105,plain,
meet(converse(X1),converse(complement(join(X1,X2)))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_48]),c_0_99]) ).
cnf(c_0_106,plain,
join(meet(X1,X2),meet(complement(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_24,c_0_22]) ).
cnf(c_0_107,negated_conjecture,
meet(esk2_0,composition(converse(complement(esk1_0)),esk3_0)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_102]),c_0_103]),c_0_102]),c_0_22]) ).
cnf(c_0_108,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_109,plain,
meet(converse(meet(X1,X2)),converse(complement(X2))) = zero,
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_110,negated_conjecture,
meet(esk2_0,complement(composition(converse(complement(esk1_0)),esk3_0))) = esk2_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_107]),c_0_50]) ).
cnf(c_0_111,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(spm,[status(thm)],[c_0_108,c_0_49]) ).
cnf(c_0_112,plain,
join(X1,join(X2,meet(X1,X3))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_42,c_0_68]) ).
cnf(c_0_113,negated_conjecture,
meet(converse(esk2_0),composition(converse(esk3_0),complement(esk1_0))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_26]),c_0_111]) ).
cnf(c_0_114,negated_conjecture,
join(composition(esk3_0,converse(esk2_0)),esk1_0) != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_115,plain,
join(meet(X1,X2),complement(X2)) = join(complement(X2),X1),
inference(spm,[status(thm)],[c_0_112,c_0_24]) ).
cnf(c_0_116,negated_conjecture,
meet(composition(esk3_0,converse(esk2_0)),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_100,c_0_113]),c_0_49]),c_0_49]),c_0_49]),c_0_101]),c_0_102]),c_0_103]),c_0_49]),c_0_49]),c_0_101]),c_0_102]) ).
cnf(c_0_117,negated_conjecture,
join(esk1_0,composition(esk3_0,converse(esk2_0))) != esk1_0,
inference(rw,[status(thm)],[c_0_114,c_0_19]) ).
cnf(c_0_118,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_116]),c_0_26]),c_0_50]),c_0_26]),c_0_117]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL044+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 04:08:27 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 3.13/0.88 % Version: 3.5.1
% 3.13/0.88 % Preprocessing class: FSMSSMSSSSSNFFN.
% 3.13/0.88 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.13/0.88 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.13/0.88 % Starting new_bool_3 with 300s (1) cores
% 3.13/0.88 % Starting new_bool_1 with 300s (1) cores
% 3.13/0.88 % Starting sh5l with 300s (1) cores
% 3.13/0.88 % sh5l with pid 939361 completed with status 0
% 3.13/0.88 % Result found by sh5l
% 3.13/0.88 % Preprocessing class: FSMSSMSSSSSNFFN.
% 3.13/0.88 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.13/0.88 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.13/0.88 % Starting new_bool_3 with 300s (1) cores
% 3.13/0.88 % Starting new_bool_1 with 300s (1) cores
% 3.13/0.88 % Starting sh5l with 300s (1) cores
% 3.13/0.88 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 3.13/0.88 % SinE strategy is gf500_gu_R04_F100_L20000
% 3.13/0.88 % Search class: FUUPM-FFMF21-DFFFFFNN
% 3.13/0.88 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 3.13/0.88 % Starting SubtermCWHack with 28s (1) cores
% 3.13/0.88 % SubtermCWHack with pid 939369 completed with status 0
% 3.13/0.88 % Result found by SubtermCWHack
% 3.13/0.88 % Preprocessing class: FSMSSMSSSSSNFFN.
% 3.13/0.88 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.13/0.88 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.13/0.88 % Starting new_bool_3 with 300s (1) cores
% 3.13/0.88 % Starting new_bool_1 with 300s (1) cores
% 3.13/0.88 % Starting sh5l with 300s (1) cores
% 3.13/0.88 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 3.13/0.88 % SinE strategy is gf500_gu_R04_F100_L20000
% 3.13/0.88 % Search class: FUUPM-FFMF21-DFFFFFNN
% 3.13/0.88 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 3.13/0.88 % Starting SubtermCWHack with 28s (1) cores
% 3.13/0.88 % Preprocessing time : 0.001 s
% 3.13/0.88
% 3.13/0.88 % Proof found!
% 3.13/0.88 % SZS status Theorem
% 3.13/0.88 % SZS output start CNFRefutation
% See solution above
% 3.13/0.88 % Parsed axioms : 17
% 3.13/0.88 % Removed by relevancy pruning/SinE : 2
% 3.13/0.88 % Initial clauses : 16
% 3.13/0.88 % Removed in clause preprocessing : 0
% 3.13/0.88 % Initial clauses in saturation : 16
% 3.13/0.88 % Processed clauses : 1983
% 3.13/0.88 % ...of these trivial : 1129
% 3.13/0.88 % ...subsumed : 524
% 3.13/0.88 % ...remaining for further processing : 330
% 3.13/0.88 % Other redundant clauses eliminated : 0
% 3.13/0.88 % Clauses deleted for lack of memory : 0
% 3.13/0.88 % Backward-subsumed : 0
% 3.13/0.88 % Backward-rewritten : 48
% 3.13/0.88 % Generated clauses : 35368
% 3.13/0.88 % ...of the previous two non-redundant : 14471
% 3.13/0.88 % ...aggressively subsumed : 0
% 3.13/0.88 % Contextual simplify-reflections : 0
% 3.13/0.88 % Paramodulations : 35368
% 3.13/0.88 % Factorizations : 0
% 3.13/0.88 % NegExts : 0
% 3.13/0.88 % Equation resolutions : 0
% 3.13/0.88 % Disequality decompositions : 0
% 3.13/0.88 % Total rewrite steps : 54139
% 3.13/0.88 % ...of those cached : 45236
% 3.13/0.88 % Propositional unsat checks : 0
% 3.13/0.88 % Propositional check models : 0
% 3.13/0.88 % Propositional check unsatisfiable : 0
% 3.13/0.88 % Propositional clauses : 0
% 3.13/0.88 % Propositional clauses after purity: 0
% 3.13/0.88 % Propositional unsat core size : 0
% 3.13/0.88 % Propositional preprocessing time : 0.000
% 3.13/0.88 % Propositional encoding time : 0.000
% 3.13/0.88 % Propositional solver time : 0.000
% 3.13/0.88 % Success case prop preproc time : 0.000
% 3.13/0.88 % Success case prop encoding time : 0.000
% 3.13/0.88 % Success case prop solver time : 0.000
% 3.13/0.88 % Current number of processed clauses : 282
% 3.13/0.88 % Positive orientable unit clauses : 276
% 3.13/0.88 % Positive unorientable unit clauses: 5
% 3.13/0.88 % Negative unit clauses : 1
% 3.13/0.88 % Non-unit-clauses : 0
% 3.13/0.88 % Current number of unprocessed clauses: 12270
% 3.13/0.88 % ...number of literals in the above : 12270
% 3.13/0.88 % Current number of archived formulas : 0
% 3.13/0.88 % Current number of archived clauses : 48
% 3.13/0.88 % Clause-clause subsumption calls (NU) : 0
% 3.13/0.88 % Rec. Clause-clause subsumption calls : 0
% 3.13/0.88 % Non-unit clause-clause subsumptions : 0
% 3.13/0.88 % Unit Clause-clause subsumption calls : 6
% 3.13/0.88 % Rewrite failures with RHS unbound : 0
% 3.13/0.88 % BW rewrite match attempts : 585
% 3.13/0.88 % BW rewrite match successes : 61
% 3.13/0.88 % Condensation attempts : 0
% 3.13/0.88 % Condensation successes : 0
% 3.13/0.88 % Termbank termtop insertions : 336358
% 3.13/0.88 % Search garbage collected termcells : 43
% 3.13/0.88
% 3.13/0.88 % -------------------------------------------------
% 3.13/0.88 % User time : 0.400 s
% 3.13/0.88 % System time : 0.020 s
% 3.13/0.88 % Total time : 0.420 s
% 3.13/0.88 % Maximum resident set size: 3652 pages
% 3.13/0.88
% 3.13/0.88 % -------------------------------------------------
% 3.13/0.88 % User time : 0.402 s
% 3.13/0.88 % System time : 0.025 s
% 3.13/0.88 % Total time : 0.427 s
% 3.13/0.88 % Maximum resident set size: 4864 pages
% 3.13/0.88 % E exiting
%------------------------------------------------------------------------------