%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : REL010+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 : n008.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 02:03:52 PM UTC 2026
% Result : Theorem 0.15s 0.64s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 14
% Syntax : Number of formulae : 113 ( 110 unt; 0 def)
% Number of atoms : 116 ( 115 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 3 ~; 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 : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 161 ( 7 sgn 60 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux4_definiton_of_meet,axiom,
! [X1,X2] : meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux4_definiton_of_meet) ).
fof(def_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(maddux1_join_commutativity,axiom,
! [X1,X2] : join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux1_join_commutativity) ).
fof(maddux2_join_associativity,axiom,
! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',maddux2_join_associativity) ).
fof(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(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(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(goals,conjecture,
! [X1,X2,X3] :
( meet(composition(X1,X2),X3) = zero
=> meet(X2,composition(converse(X1),X3)) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(composition_distributivity,axiom,
! [X1,X2,X3] : composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_distributivity) ).
fof(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(composition_associativity,axiom,
! [X1,X2,X3] : composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001+0.ax',composition_associativity) ).
fof(c_0_14,plain,
! [X8,X9] : meet(X8,X9) = complement(join(complement(X8),complement(X9))),
inference(variable_rename,[status(thm)],[maddux4_definiton_of_meet]) ).
fof(c_0_15,plain,
! [X34] : top = join(X34,complement(X34)),
inference(variable_rename,[status(thm)],[def_top]) ).
fof(c_0_16,plain,
! [X7] : zero = meet(X7,complement(X7)),
inference(variable_rename,[status(thm)],[def_zero]) ).
cnf(c_0_17,plain,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
top = join(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,plain,
zero = meet(X1,complement(X1)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_20,plain,
! [X35,X36] : join(X35,X36) = join(X36,X35),
inference(variable_rename,[status(thm)],[maddux1_join_commutativity]) ).
fof(c_0_21,plain,
! [X37,X38,X39] : join(X37,join(X38,X39)) = join(join(X37,X38),X39),
inference(variable_rename,[status(thm)],[maddux2_join_associativity]) ).
cnf(c_0_22,plain,
complement(top) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_23,plain,
join(X1,X2) = join(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_24,plain,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,plain,
join(zero,top) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_22]),c_0_23]) ).
fof(c_0_26,plain,
! [X32,X33] : X32 = join(complement(join(complement(X32),complement(X33))),complement(join(complement(X32),X33))),
inference(variable_rename,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
cnf(c_0_27,plain,
join(zero,join(top,X1)) = join(top,X1),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_29,plain,
meet(top,zero) = zero,
inference(spm,[status(thm)],[c_0_19,c_0_22]) ).
cnf(c_0_30,plain,
meet(X1,X2) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_23]),c_0_17]) ).
cnf(c_0_31,plain,
join(zero,join(X1,top)) = join(X1,top),
inference(spm,[status(thm)],[c_0_27,c_0_23]) ).
cnf(c_0_32,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_24,c_0_18]) ).
cnf(c_0_33,plain,
join(X1,join(X2,complement(join(X1,X2)))) = top,
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_34,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[c_0_28,c_0_17]) ).
cnf(c_0_35,plain,
meet(zero,top) = zero,
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,plain,
join(top,complement(zero)) = join(top,top),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_23]) ).
cnf(c_0_37,plain,
join(X1,join(zero,complement(X1))) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_18]),c_0_22]),c_0_23]) ).
cnf(c_0_38,plain,
join(zero,complement(join(top,top))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_23]),c_0_36]) ).
cnf(c_0_39,plain,
join(top,top) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_24]),c_0_23]),c_0_25]) ).
cnf(c_0_40,plain,
join(zero,zero) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_22]) ).
fof(c_0_41,plain,
! [X30,X31] : converse(join(X30,X31)) = join(converse(X30),converse(X31)),
inference(variable_rename,[status(thm)],[converse_additivity]) ).
fof(c_0_42,plain,
! [X29] : converse(converse(X29)) = X29,
inference(variable_rename,[status(thm)],[converse_idempotence]) ).
cnf(c_0_43,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(spm,[status(thm)],[c_0_24,c_0_40]) ).
cnf(c_0_44,plain,
join(zero,meet(X1,complement(complement(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_18]),c_0_22]),c_0_23]) ).
cnf(c_0_45,plain,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_46,plain,
converse(converse(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_47,plain,
complement(join(zero,complement(X1))) = meet(top,X1),
inference(spm,[status(thm)],[c_0_17,c_0_22]) ).
cnf(c_0_48,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_49,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,plain,
meet(meet(top,X1),join(zero,complement(X1))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_47]),c_0_30]) ).
cnf(c_0_51,plain,
complement(complement(X1)) = meet(top,X1),
inference(rw,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,plain,
join(top,join(top,X1)) = join(top,X1),
inference(spm,[status(thm)],[c_0_24,c_0_39]) ).
cnf(c_0_53,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(spm,[status(thm)],[c_0_49,c_0_18]) ).
cnf(c_0_54,plain,
join(zero,meet(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_19]),c_0_17]) ).
cnf(c_0_55,plain,
meet(meet(top,X1),complement(X1)) = zero,
inference(rw,[status(thm)],[c_0_50,c_0_48]) ).
cnf(c_0_56,plain,
meet(X1,meet(top,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_48]),c_0_51]) ).
cnf(c_0_57,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_58,plain,
join(top,converse(top)) = converse(top),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_59,plain,
join(complement(X1),join(complement(X2),meet(X1,X2))) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_17]),c_0_24]) ).
cnf(c_0_60,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[c_0_54,c_0_48]) ).
cnf(c_0_61,plain,
meet(top,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_55]),c_0_17]),c_0_48]),c_0_30]),c_0_56]) ).
cnf(c_0_62,plain,
complement(join(complement(X1),meet(X2,X3))) = meet(X1,join(complement(X2),complement(X3))),
inference(spm,[status(thm)],[c_0_17,c_0_17]) ).
cnf(c_0_63,plain,
converse(top) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_46]),c_0_23]),c_0_58]) ).
cnf(c_0_64,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_23]),c_0_18]),c_0_23]) ).
cnf(c_0_65,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_51,c_0_61]) ).
cnf(c_0_66,plain,
complement(join(meet(X1,X2),complement(X3))) = meet(join(complement(X1),complement(X2)),X3),
inference(spm,[status(thm)],[c_0_17,c_0_17]) ).
cnf(c_0_67,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_61]),c_0_22]),c_0_48]) ).
cnf(c_0_68,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(rw,[status(thm)],[c_0_53,c_0_63]) ).
cnf(c_0_69,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_70,plain,
complement(join(X1,complement(X2))) = meet(complement(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_61]),c_0_22]),c_0_48]) ).
cnf(c_0_71,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_17]),c_0_23]) ).
cnf(c_0_72,plain,
meet(X1,complement(converse(complement(converse(complement(X1)))))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_68]),c_0_22]) ).
cnf(c_0_73,plain,
join(X1,join(complement(X1),X2)) = top,
inference(rw,[status(thm)],[c_0_32,c_0_69]) ).
cnf(c_0_74,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_48]) ).
cnf(c_0_75,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_65,c_0_70]) ).
cnf(c_0_76,plain,
meet(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_65]),c_0_48]) ).
cnf(c_0_77,plain,
meet(X1,join(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_73]),c_0_51]),c_0_61]),c_0_22]),c_0_74]) ).
cnf(c_0_78,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_51]),c_0_61]),c_0_51]),c_0_61]) ).
cnf(c_0_79,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_77,c_0_23]) ).
cnf(c_0_80,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_78]),c_0_46]),c_0_46]) ).
fof(c_0_81,plain,
! [X27,X28] : join(composition(converse(X27),complement(composition(X27,X28))),complement(X28)) = complement(X28),
inference(variable_rename,[status(thm)],[converse_cancellativity]) ).
cnf(c_0_82,plain,
converse(complement(converse(complement(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_30]),c_0_76]) ).
cnf(c_0_83,plain,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
fof(c_0_84,plain,
! [X25,X26] : converse(composition(X25,X26)) = composition(converse(X26),converse(X25)),
inference(variable_rename,[status(thm)],[converse_multiplicativity]) ).
cnf(c_0_85,plain,
complement(converse(complement(X1))) = converse(X1),
inference(spm,[status(thm)],[c_0_46,c_0_82]) ).
cnf(c_0_86,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_83,c_0_23]) ).
cnf(c_0_87,plain,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
inference(split_conjunct,[status(thm)],[c_0_84]) ).
cnf(c_0_88,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[c_0_65,c_0_85]) ).
cnf(c_0_89,plain,
join(converse(zero),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_48]),c_0_46]) ).
cnf(c_0_90,plain,
join(converse(complement(X1)),composition(X2,converse(complement(composition(X1,X2))))) = converse(complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_46]),c_0_88]),c_0_88]),c_0_88]) ).
cnf(c_0_91,plain,
converse(zero) = zero,
inference(spm,[status(thm)],[c_0_74,c_0_89]) ).
cnf(c_0_92,plain,
complement(join(zero,zero)) = meet(top,top),
inference(spm,[status(thm)],[c_0_47,c_0_22]) ).
cnf(c_0_93,plain,
composition(X1,converse(complement(composition(top,X1)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_22]),c_0_91]),c_0_48]),c_0_91]) ).
cnf(c_0_94,plain,
complement(zero) = meet(top,top),
inference(rw,[status(thm)],[c_0_92,c_0_40]) ).
fof(c_0_95,negated_conjecture,
~ ! [X1,X2,X3] :
( meet(composition(X1,X2),X3) = zero
=> meet(X2,composition(converse(X1),X3)) = zero ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_96,plain,
! [X22,X23,X24] : composition(join(X22,X23),X24) = join(composition(X22,X24),composition(X23,X24)),
inference(variable_rename,[status(thm)],[composition_distributivity]) ).
cnf(c_0_97,plain,
converse(composition(X1,top)) = composition(top,converse(X1)),
inference(spm,[status(thm)],[c_0_87,c_0_63]) ).
cnf(c_0_98,plain,
composition(converse(complement(composition(top,top))),top) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_93]),c_0_94]),c_0_60]),c_0_63]) ).
fof(c_0_99,plain,
! [X10,X11,X12] : join(meet(composition(X10,X11),X12),composition(meet(X10,composition(X12,converse(X11))),meet(X11,composition(converse(X10),X12)))) = composition(meet(X10,composition(X12,converse(X11))),meet(X11,composition(converse(X10),X12))),
inference(variable_rename,[status(thm)],[dedekind_law]) ).
fof(c_0_100,negated_conjecture,
( meet(esk2_0,composition(converse(esk1_0),esk3_0)) != zero
& meet(composition(esk1_0,esk2_0),esk3_0) = zero ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_95])])])]) ).
fof(c_0_101,plain,
! [X19,X20,X21] : composition(X19,composition(X20,X21)) = composition(composition(X19,X20),X21),
inference(variable_rename,[status(thm)],[composition_associativity]) ).
cnf(c_0_102,plain,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_103,plain,
composition(top,complement(composition(top,top))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_91]),c_0_46]) ).
cnf(c_0_104,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_99]) ).
cnf(c_0_105,negated_conjecture,
meet(composition(esk1_0,esk2_0),esk3_0) = zero,
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_106,plain,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_107,plain,
composition(X1,complement(composition(top,top))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_48]),c_0_69]),c_0_103]) ).
cnf(c_0_108,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_104,c_0_46]) ).
cnf(c_0_109,negated_conjecture,
meet(esk3_0,composition(esk1_0,esk2_0)) = zero,
inference(rw,[status(thm)],[c_0_105,c_0_30]) ).
cnf(c_0_110,plain,
composition(X1,zero) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_107]) ).
cnf(c_0_111,negated_conjecture,
meet(esk2_0,composition(converse(esk1_0),esk3_0)) != zero,
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_112,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_110]),c_0_74]),c_0_110]),c_0_30]),c_0_111]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL010+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n008.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 03:58:40 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.45 Running first-order theorem proving
% 0.15/0.45 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
% 0.15/0.64 % Version: 3.5.1
% 0.15/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.64 % Starting sh5l with 300s (1) cores
% 0.15/0.64 % sh5l with pid 96341 completed with status 0
% 0.15/0.64 % Result found by sh5l
% 0.15/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.64 % Starting sh5l with 300s (1) cores
% 0.15/0.64 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.15/0.64 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.15/0.64 % Search class: FUUPM-FFMF21-DFFFFFNN
% 0.15/0.64 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.64 % Starting SubtermCWHack with 28s (1) cores
% 0.15/0.64 % SubtermCWHack with pid 96349 completed with status 0
% 0.15/0.64 % Result found by SubtermCWHack
% 0.15/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.64 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.64 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.64 % Starting sh5l with 300s (1) cores
% 0.15/0.64 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.15/0.64 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.15/0.64 % Search class: FUUPM-FFMF21-DFFFFFNN
% 0.15/0.64 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.64 % Starting SubtermCWHack with 28s (1) cores
% 0.15/0.64 % Preprocessing time : 0.002 s
% 0.15/0.64
% 0.15/0.64 % Proof found!
% 0.15/0.64 % SZS status Theorem
% 0.15/0.64 % SZS output start CNFRefutation
% See solution above
% 0.15/0.64 % Parsed axioms : 17
% 0.15/0.64 % Removed by relevancy pruning/SinE : 1
% 0.15/0.64 % Initial clauses : 17
% 0.15/0.64 % Removed in clause preprocessing : 0
% 0.15/0.64 % Initial clauses in saturation : 17
% 0.15/0.64 % Processed clauses : 859
% 0.15/0.64 % ...of these trivial : 498
% 0.15/0.64 % ...subsumed : 60
% 0.15/0.64 % ...remaining for further processing : 300
% 0.15/0.64 % Other redundant clauses eliminated : 0
% 0.15/0.64 % Clauses deleted for lack of memory : 0
% 0.15/0.64 % Backward-subsumed : 0
% 0.15/0.64 % Backward-rewritten : 107
% 0.15/0.64 % Generated clauses : 14688
% 0.15/0.64 % ...of the previous two non-redundant : 6702
% 0.15/0.64 % ...aggressively subsumed : 0
% 0.15/0.64 % Contextual simplify-reflections : 0
% 0.15/0.64 % Paramodulations : 14688
% 0.15/0.64 % Factorizations : 0
% 0.15/0.64 % NegExts : 0
% 0.15/0.64 % Equation resolutions : 0
% 0.15/0.64 % Disequality decompositions : 0
% 0.15/0.64 % Total rewrite steps : 26150
% 0.15/0.64 % ...of those cached : 21629
% 0.15/0.64 % Propositional unsat checks : 0
% 0.15/0.64 % Propositional check models : 0
% 0.15/0.64 % Propositional check unsatisfiable : 0
% 0.15/0.64 % Propositional clauses : 0
% 0.15/0.64 % Propositional clauses after purity: 0
% 0.15/0.64 % Propositional unsat core size : 0
% 0.15/0.64 % Propositional preprocessing time : 0.000
% 0.15/0.64 % Propositional encoding time : 0.000
% 0.15/0.64 % Propositional solver time : 0.000
% 0.15/0.64 % Success case prop preproc time : 0.000
% 0.15/0.64 % Success case prop encoding time : 0.000
% 0.15/0.64 % Success case prop solver time : 0.000
% 0.15/0.64 % Current number of processed clauses : 193
% 0.15/0.64 % Positive orientable unit clauses : 188
% 0.15/0.64 % Positive unorientable unit clauses: 4
% 0.15/0.64 % Negative unit clauses : 1
% 0.15/0.64 % Non-unit-clauses : 0
% 0.15/0.64 % Current number of unprocessed clauses: 5607
% 0.15/0.64 % ...number of literals in the above : 5607
% 0.15/0.64 % Current number of archived formulas : 0
% 0.15/0.64 % Current number of archived clauses : 107
% 0.15/0.64 % Clause-clause subsumption calls (NU) : 0
% 0.15/0.64 % Rec. Clause-clause subsumption calls : 0
% 0.15/0.64 % Non-unit clause-clause subsumptions : 0
% 0.15/0.64 % Unit Clause-clause subsumption calls : 4
% 0.15/0.64 % Rewrite failures with RHS unbound : 0
% 0.15/0.64 % BW rewrite match attempts : 422
% 0.15/0.64 % BW rewrite match successes : 120
% 0.15/0.64 % Condensation attempts : 0
% 0.15/0.64 % Condensation successes : 0
% 0.15/0.64 % Termbank termtop insertions : 145755
% 0.15/0.64 % Search garbage collected termcells : 37
% 0.15/0.64
% 0.15/0.64 % -------------------------------------------------
% 0.15/0.64 % User time : 0.102 s
% 0.15/0.64 % System time : 0.018 s
% 0.15/0.64 % Total time : 0.120 s
% 0.15/0.64 % Maximum resident set size: 3652 pages
% 0.15/0.64
% 0.15/0.64 % -------------------------------------------------
% 0.15/0.64 % User time : 0.105 s
% 0.15/0.64 % System time : 0.025 s
% 0.15/0.64 % Total time : 0.129 s
% 0.15/0.64 % Maximum resident set size: 4864 pages
% 0.15/0.64 % E exiting
%------------------------------------------------------------------------------