%------------------------------------------------------------------------------
% 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/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 : Unsatisfiable 259.16s 38.48s
% Output : CNFRefutation 259.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 17
% Syntax : Number of clauses : 139 ( 139 unt; 0 nHn; 24 RR)
% Number of literals : 139 ( 138 equ; 3 neg)
% Maximal clause size : 1 ( 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 : 204 ( 16 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(maddux3_a_kind_of_de_Morgan_3,axiom,
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_3) ).
cnf(maddux4_definiton_of_meet_4,axiom,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',maddux4_definiton_of_meet_4) ).
cnf(maddux1_join_commutativity_1,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',maddux1_join_commutativity_1) ).
cnf(def_top_12,axiom,
top = join(X1,complement(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',def_top_12) ).
cnf(def_zero_13,axiom,
zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',def_zero_13) ).
cnf(maddux2_join_associativity_2,axiom,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',maddux2_join_associativity_2) ).
cnf(converse_additivity_9,axiom,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',converse_additivity_9) ).
cnf(converse_idempotence_8,axiom,
converse(converse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',converse_idempotence_8) ).
cnf(converse_cancellativity_11,axiom,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',converse_cancellativity_11) ).
cnf(goals_18,negated_conjecture,
composition(sk2,top) = sk2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_18) ).
cnf(converse_multiplicativity_10,axiom,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',converse_multiplicativity_10) ).
cnf(composition_distributivity_7,axiom,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',composition_distributivity_7) ).
cnf(composition_associativity_5,axiom,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',composition_associativity_5) ).
cnf(modular_law_2_16,axiom,
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_16) ).
cnf(dedekind_law_14,axiom,
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_14) ).
cnf(goals_17,negated_conjecture,
composition(sk1,top) = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
cnf(goals_19,negated_conjecture,
composition(meet(sk1,sk2),top) != meet(sk1,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_19) ).
cnf(c_0_17,axiom,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
maddux3_a_kind_of_de_Morgan_3 ).
cnf(c_0_18,axiom,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
maddux4_definiton_of_meet_4 ).
cnf(c_0_19,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,axiom,
join(X1,X2) = join(X2,X1),
maddux1_join_commutativity_1 ).
cnf(c_0_21,axiom,
top = join(X1,complement(X1)),
def_top_12 ).
cnf(c_0_22,axiom,
zero = meet(X1,complement(X1)),
def_zero_13 ).
cnf(c_0_23,plain,
join(meet(X1,X2),meet(X1,complement(X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_18]),c_0_20]) ).
cnf(c_0_24,plain,
complement(top) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_21]),c_0_22]) ).
cnf(c_0_25,plain,
join(meet(X1,top),meet(X1,zero)) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,plain,
meet(X1,X2) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_20]),c_0_18]) ).
cnf(c_0_27,plain,
join(zero,meet(X1,complement(complement(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_21]),c_0_24]),c_0_20]) ).
cnf(c_0_28,plain,
join(meet(X1,top),meet(zero,X1)) = X1,
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,plain,
join(zero,meet(top,complement(zero))) = top,
inference(spm,[status(thm)],[c_0_27,c_0_24]) ).
cnf(c_0_30,plain,
complement(zero) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_22]),c_0_26]),c_0_20]),c_0_29]) ).
cnf(c_0_31,axiom,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
maddux2_join_associativity_2 ).
cnf(c_0_32,plain,
join(top,zero) = top,
inference(spm,[status(thm)],[c_0_21,c_0_24]) ).
cnf(c_0_33,plain,
complement(join(top,complement(X1))) = meet(zero,X1),
inference(spm,[status(thm)],[c_0_18,c_0_30]) ).
cnf(c_0_34,plain,
join(top,join(zero,X1)) = join(top,X1),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,plain,
join(zero,meet(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_22]),c_0_18]) ).
cnf(c_0_36,plain,
complement(join(top,top)) = meet(zero,zero),
inference(spm,[status(thm)],[c_0_33,c_0_30]) ).
cnf(c_0_37,plain,
join(top,meet(X1,X1)) = join(top,X1),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,plain,
join(top,top) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_36]),c_0_31]),c_0_37]),c_0_32]) ).
cnf(c_0_39,plain,
meet(zero,zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_38]),c_0_24]) ).
cnf(c_0_40,plain,
join(zero,zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_39]),c_0_30]),c_0_32]),c_0_24]) ).
cnf(c_0_41,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(spm,[status(thm)],[c_0_31,c_0_40]) ).
cnf(c_0_42,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_41,c_0_27]) ).
cnf(c_0_43,plain,
join(complement(X1),join(complement(X2),meet(X1,X2))) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_18]),c_0_31]) ).
cnf(c_0_44,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[c_0_35,c_0_42]) ).
cnf(c_0_45,plain,
join(X1,join(X2,complement(join(X1,X2)))) = top,
inference(spm,[status(thm)],[c_0_21,c_0_31]) ).
cnf(c_0_46,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_20]),c_0_21]),c_0_20]) ).
cnf(c_0_47,plain,
join(X1,top) = top,
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_48,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_42]) ).
cnf(c_0_49,plain,
complement(join(zero,complement(X1))) = meet(top,X1),
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_50,plain,
meet(X1,top) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_47]),c_0_24]),c_0_48]) ).
cnf(c_0_51,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_31,c_0_21]) ).
cnf(c_0_52,plain,
complement(complement(X1)) = meet(top,X1),
inference(rw,[status(thm)],[c_0_49,c_0_42]) ).
cnf(c_0_53,plain,
meet(top,X1) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_50]) ).
cnf(c_0_54,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_55,plain,
join(X1,join(X2,complement(X1))) = join(top,X2),
inference(spm,[status(thm)],[c_0_51,c_0_20]) ).
cnf(c_0_56,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_20,c_0_47]) ).
cnf(c_0_57,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,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_54,c_0_50]),c_0_24]),c_0_20]),c_0_42]) ).
cnf(c_0_59,plain,
join(X1,join(X2,complement(X1))) = top,
inference(rw,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_60,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_61,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_19,c_0_59]),c_0_52]),c_0_53]),c_0_24]),c_0_48]) ).
cnf(c_0_62,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_20]),c_0_31]) ).
cnf(c_0_63,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_60,c_0_44]),c_0_52]),c_0_53]),c_0_52]),c_0_53]) ).
cnf(c_0_64,plain,
meet(X1,join(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_61,c_0_20]) ).
cnf(c_0_65,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_31]),c_0_63]) ).
cnf(c_0_66,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_23]),c_0_26]) ).
cnf(c_0_67,plain,
join(X1,meet(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_23]),c_0_20]) ).
cnf(c_0_68,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_66,c_0_26]) ).
cnf(c_0_69,axiom,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
converse_additivity_9 ).
cnf(c_0_70,axiom,
converse(converse(X1)) = X1,
converse_idempotence_8 ).
cnf(c_0_71,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_72,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_73,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_74,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_31,c_0_71]) ).
cnf(c_0_75,plain,
join(top,join(top,X1)) = join(top,X1),
inference(spm,[status(thm)],[c_0_31,c_0_38]) ).
cnf(c_0_76,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(spm,[status(thm)],[c_0_72,c_0_21]) ).
cnf(c_0_77,plain,
complement(join(complement(X1),X2)) = meet(X1,complement(X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_50]),c_0_24]),c_0_48]) ).
cnf(c_0_78,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_74,c_0_23]) ).
cnf(c_0_79,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_80,plain,
join(top,converse(top)) = converse(top),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_81,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_77,c_0_78]),c_0_77]),c_0_52]),c_0_53]) ).
cnf(c_0_82,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_78,c_0_26]) ).
cnf(c_0_83,plain,
meet(complement(X1),complement(X2)) = complement(join(X1,X2)),
inference(spm,[status(thm)],[c_0_58,c_0_57]) ).
cnf(c_0_84,plain,
converse(top) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_80]),c_0_70]),c_0_20]),c_0_80]) ).
cnf(c_0_85,plain,
meet(X1,join(X2,complement(X1))) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_60]),c_0_57]) ).
cnf(c_0_86,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_87,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(rw,[status(thm)],[c_0_76,c_0_84]) ).
cnf(c_0_88,plain,
meet(X1,join(complement(X1),X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_85,c_0_20]) ).
cnf(c_0_89,plain,
meet(converse(X1),converse(join(X2,X1))) = converse(X1),
inference(spm,[status(thm)],[c_0_61,c_0_69]) ).
cnf(c_0_90,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_24]),c_0_48]) ).
cnf(c_0_91,plain,
meet(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_87]),c_0_50]) ).
cnf(c_0_92,plain,
converse(complement(converse(complement(converse(X1))))) = converse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_26]),c_0_91]) ).
cnf(c_0_93,axiom,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
converse_cancellativity_11 ).
cnf(c_0_94,plain,
complement(converse(complement(converse(X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_92]),c_0_70]) ).
cnf(c_0_95,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_93,c_0_20]) ).
cnf(c_0_96,negated_conjecture,
composition(sk2,top) = sk2,
goals_18 ).
cnf(c_0_97,plain,
converse(complement(converse(X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_57,c_0_94]) ).
cnf(c_0_98,plain,
meet(join(complement(X1),complement(X2)),X3) = meet(complement(meet(X1,X2)),X3),
inference(rw,[status(thm)],[c_0_54,c_0_58]) ).
cnf(c_0_99,axiom,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
converse_multiplicativity_10 ).
cnf(c_0_100,negated_conjecture,
join(zero,composition(converse(sk2),complement(sk2))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_24]),c_0_24]) ).
cnf(c_0_101,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[c_0_70,c_0_97]) ).
cnf(c_0_102,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_98]),c_0_50]) ).
cnf(c_0_103,plain,
converse(composition(X1,top)) = composition(top,converse(X1)),
inference(spm,[status(thm)],[c_0_99,c_0_84]) ).
cnf(c_0_104,axiom,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
composition_distributivity_7 ).
cnf(c_0_105,negated_conjecture,
composition(converse(sk2),complement(sk2)) = zero,
inference(rw,[status(thm)],[c_0_100,c_0_42]) ).
cnf(c_0_106,plain,
converse(complement(join(converse(X1),X2))) = complement(join(X1,converse(X2))),
inference(spm,[status(thm)],[c_0_101,c_0_72]) ).
cnf(c_0_107,plain,
join(converse(complement(X1)),complement(X2)) = complement(meet(converse(X1),X2)),
inference(spm,[status(thm)],[c_0_102,c_0_101]) ).
cnf(c_0_108,plain,
join(complement(X1),converse(complement(X2))) = complement(meet(X1,converse(X2))),
inference(spm,[status(thm)],[c_0_102,c_0_101]) ).
cnf(c_0_109,axiom,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
composition_associativity_5 ).
cnf(c_0_110,negated_conjecture,
composition(top,converse(sk2)) = converse(sk2),
inference(spm,[status(thm)],[c_0_103,c_0_96]) ).
cnf(c_0_111,negated_conjecture,
composition(join(converse(sk2),X1),complement(sk2)) = composition(X1,complement(sk2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_42]) ).
cnf(c_0_112,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_106,c_0_107]),c_0_57]),c_0_108]),c_0_57]) ).
cnf(c_0_113,negated_conjecture,
composition(top,composition(converse(sk2),X1)) = composition(converse(sk2),X1),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_114,axiom,
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),
modular_law_2_16 ).
cnf(c_0_115,axiom,
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))),
dedekind_law_14 ).
cnf(c_0_116,negated_conjecture,
composition(meet(converse(sk2),X1),complement(sk2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_67]),c_0_105]) ).
cnf(c_0_117,plain,
meet(converse(X1),converse(X2)) = converse(meet(X1,X2)),
inference(spm,[status(thm)],[c_0_112,c_0_70]) ).
cnf(c_0_118,negated_conjecture,
composition(top,zero) = zero,
inference(spm,[status(thm)],[c_0_113,c_0_105]) ).
cnf(c_0_119,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_114,c_0_26]),c_0_26]) ).
cnf(c_0_120,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_115,c_0_84]),c_0_53]),c_0_53]) ).
cnf(c_0_121,negated_conjecture,
composition(converse(meet(sk2,X1)),complement(sk2)) = zero,
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_122,negated_conjecture,
composition(X1,zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_118]),c_0_42]),c_0_56]),c_0_118]) ).
cnf(c_0_123,negated_conjecture,
join(meet(sk2,X1),meet(X1,composition(meet(sk2,composition(X1,top)),top))) = meet(X1,composition(meet(sk2,composition(X1,top)),top)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_96]),c_0_84]),c_0_84]) ).
cnf(c_0_124,negated_conjecture,
composition(sk1,top) = sk1,
goals_17 ).
cnf(c_0_125,plain,
join(meet(X1,X2),meet(X2,complement(X1))) = X2,
inference(spm,[status(thm)],[c_0_23,c_0_26]) ).
cnf(c_0_126,negated_conjecture,
meet(complement(sk2),composition(meet(sk2,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_120,c_0_121]),c_0_26]),c_0_122]),c_0_48]),c_0_122]) ).
cnf(c_0_127,plain,
meet(X1,join(meet(X2,complement(X1)),X3)) = meet(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_74]),c_0_88]) ).
cnf(c_0_128,plain,
join(meet(X1,X2),join(meet(X1,complement(X2)),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_31,c_0_23]) ).
cnf(c_0_129,plain,
join(X1,join(X2,meet(X3,X1))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_62,c_0_71]) ).
cnf(c_0_130,negated_conjecture,
join(meet(sk1,sk2),meet(sk1,composition(meet(sk1,sk2),top))) = meet(sk1,composition(meet(sk1,sk2),top)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_26]),c_0_26]),c_0_26]) ).
cnf(c_0_131,negated_conjecture,
meet(sk2,composition(meet(sk2,X1),top)) = composition(meet(sk2,X1),top),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_52]),c_0_53]),c_0_26]),c_0_42]) ).
cnf(c_0_132,negated_conjecture,
composition(meet(sk1,sk2),top) != meet(sk1,sk2),
inference(fof_simplification,[status(thm)],[goals_19]) ).
cnf(c_0_133,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_127,c_0_128]),c_0_52]),c_0_53]) ).
cnf(c_0_134,negated_conjecture,
join(meet(sk1,sk2),composition(meet(sk1,sk2),top)) = composition(meet(sk1,sk2),top),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_71]) ).
cnf(c_0_135,negated_conjecture,
meet(sk2,composition(meet(X1,sk2),top)) = composition(meet(X1,sk2),top),
inference(spm,[status(thm)],[c_0_131,c_0_68]) ).
cnf(c_0_136,negated_conjecture,
join(sk1,composition(X1,top)) = composition(join(X1,sk1),top),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_124]),c_0_20]) ).
cnf(c_0_137,negated_conjecture,
composition(meet(sk1,sk2),top) != meet(sk1,sk2),
c_0_132 ).
cnf(c_0_138,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_133,c_0_134]),c_0_135]),c_0_136]),c_0_20]),c_0_67]),c_0_124]),c_0_26]),c_0_137]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL019-2 : 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 : n009.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 04:00:42 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 259.16/38.48 % Version: 3.5.1
% 259.16/38.48 % Preprocessing class: FSMSSMSSSSSNFFN.
% 259.16/38.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 259.16/38.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 259.16/38.48 % Starting new_bool_3 with 300s (1) cores
% 259.16/38.48 % Starting new_bool_1 with 300s (1) cores
% 259.16/38.48 % Starting sh5l with 300s (1) cores
% 259.16/38.48 % sh5l with pid 800877 completed with status 0
% 259.16/38.48 % Result found by sh5l
% 259.16/38.48 % Preprocessing class: FSMSSMSSSSSNFFN.
% 259.16/38.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 259.16/38.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 259.16/38.48 % Starting new_bool_3 with 300s (1) cores
% 259.16/38.48 % Starting new_bool_1 with 300s (1) cores
% 259.16/38.48 % Starting sh5l with 300s (1) cores
% 259.16/38.48 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 259.16/38.48 % SinE strategy is gf500_gu_R04_F100_L20000
% 259.16/38.48 % Search class: FUUPM-FFMF21-DFFFFFNN
% 259.16/38.48 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 259.16/38.48 % Starting SubtermCWHack with 28s (1) cores
% 259.16/38.48 % SubtermCWHack with pid 800883 completed with status 8
% 259.16/38.48 % Starting sh5l with 31s (1) cores
% 259.16/38.48 % sh5l with pid 800912 completed with status 0
% 259.16/38.48 % Result found by sh5l
% 259.16/38.48 % Preprocessing class: FSMSSMSSSSSNFFN.
% 259.16/38.48 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 259.16/38.48 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 259.16/38.48 % Starting new_bool_3 with 300s (1) cores
% 259.16/38.48 % Starting new_bool_1 with 300s (1) cores
% 259.16/38.48 % Starting sh5l with 300s (1) cores
% 259.16/38.48 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 259.16/38.48 % SinE strategy is gf500_gu_R04_F100_L20000
% 259.16/38.48 % Search class: FUUPM-FFMF21-DFFFFFNN
% 259.16/38.48 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 259.16/38.48 % Starting SubtermCWHack with 28s (1) cores
% 259.16/38.48 % SubtermCWHack with pid 800883 completed with status 8
% 259.16/38.48 % Starting sh5l with 31s (1) cores
% 259.16/38.48 % Preprocessing time : 0.002 s
% 259.16/38.48 % Presaturation interreduction done
% 259.16/38.48
% 259.16/38.48 % Proof found!
% 259.16/38.48 % SZS status Unsatisfiable
% 259.16/38.48 % SZS output start CNFRefutation
% See solution above
% 259.16/38.48 % Parsed axioms : 19
% 259.16/38.48 % Removed by relevancy pruning/SinE : 1
% 259.16/38.48 % Initial clauses : 18
% 259.16/38.48 % Removed in clause preprocessing : 0
% 259.16/38.48 % Initial clauses in saturation : 18
% 259.16/38.48 % Processed clauses : 6355
% 259.16/38.48 % ...of these trivial : 3362
% 259.16/38.48 % ...subsumed : 983
% 259.16/38.48 % ...remaining for further processing : 2010
% 259.16/38.48 % Other redundant clauses eliminated : 0
% 259.16/38.48 % Clauses deleted for lack of memory : 0
% 259.16/38.48 % Backward-subsumed : 0
% 259.16/38.48 % Backward-rewritten : 647
% 259.16/38.48 % Generated clauses : 278855
% 259.16/38.48 % ...of the previous two non-redundant : 145664
% 259.16/38.48 % ...aggressively subsumed : 0
% 259.16/38.48 % Contextual simplify-reflections : 0
% 259.16/38.48 % Paramodulations : 278855
% 259.16/38.48 % Factorizations : 0
% 259.16/38.48 % NegExts : 0
% 259.16/38.48 % Equation resolutions : 0
% 259.16/38.48 % Disequality decompositions : 0
% 259.16/38.48 % Total rewrite steps : 734373
% 259.16/38.48 % ...of those cached : 648449
% 259.16/38.48 % Propositional unsat checks : 0
% 259.16/38.48 % Propositional check models : 0
% 259.16/38.48 % Propositional check unsatisfiable : 0
% 259.16/38.48 % Propositional clauses : 0
% 259.16/38.48 % Propositional clauses after purity: 0
% 259.16/38.48 % Propositional unsat core size : 0
% 259.16/38.48 % Propositional preprocessing time : 0.000
% 259.16/38.48 % Propositional encoding time : 0.000
% 259.16/38.48 % Propositional solver time : 0.000
% 259.16/38.48 % Success case prop preproc time : 0.000
% 259.16/38.48 % Success case prop encoding time : 0.000
% 259.16/38.48 % Success case prop solver time : 0.000
% 259.16/38.48 % Current number of processed clauses : 1345
% 259.16/38.48 % Positive orientable unit clauses : 1333
% 259.16/38.48 % Positive unorientable unit clauses: 11
% 259.16/38.48 % Negative unit clauses : 1
% 259.16/38.48 % Non-unit-clauses : 0
% 259.16/38.48 % Current number of unprocessed clauses: 137002
% 259.16/38.48 % ...number of literals in the above : 137002
% 259.16/38.48 % Current number of archived formulas : 0
% 259.16/38.48 % Current number of archived clauses : 665
% 259.16/38.48 % Clause-clause subsumption calls (NU) : 0
% 259.16/38.48 % Rec. Clause-clause subsumption calls : 0
% 259.16/38.48 % Non-unit clause-clause subsumptions : 0
% 259.16/38.48 % Unit Clause-clause subsumption calls : 115
% 259.16/38.48 % Rewrite failures with RHS unbound : 0
% 259.16/38.48 % BW rewrite match attempts : 7438
% 259.16/38.48 % BW rewrite match successes : 646
% 259.16/38.48 % Condensation attempts : 6355
% 259.16/38.48 % Condensation successes : 0
% 259.16/38.48 % Termbank termtop insertions : 6204531
% 259.16/38.48 % Search garbage collected termcells : 5
% 259.16/38.48
% 259.16/38.48 % -------------------------------------------------
% 259.16/38.48 % User time : 35.851 s
% 259.16/38.48 % System time : 1.290 s
% 259.16/38.48 % Total time : 37.141 s
% 259.16/38.48 % Maximum resident set size: 3648 pages
% 259.16/38.48
% 259.16/38.48 % -------------------------------------------------
% 259.16/38.48 % User time : 35.855 s
% 259.16/38.48 % System time : 1.293 s
% 259.16/38.48 % Total time : 37.149 s
% 259.16/38.48 % Maximum resident set size: 4608 pages
% 259.16/38.48 % E exiting
%------------------------------------------------------------------------------