%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : REL033-3 : 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 : n009.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 05:04:26 PM UTC 2026
% Result : Unsatisfiable 74.57s 43.48s
% Output : CNFRefutation 74.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 18
% Syntax : Number of clauses : 202 ( 202 unt; 0 nHn; 15 RR)
% Number of literals : 202 ( 201 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 345 ( 33 sgn)
% Comments :
%------------------------------------------------------------------------------
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(converse_idempotence_8,axiom,
converse(converse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',converse_idempotence_8) ).
cnf(composition_identity_6,axiom,
composition(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',composition_identity_6) ).
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(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(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(def_top_12,axiom,
top = join(X1,complement(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',def_top_12) ).
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(def_zero_13,axiom,
zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',def_zero_13) ).
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(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(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(modular_law_1_15,axiom,
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_15) ).
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(goals_17,negated_conjecture,
composition(sk1,top) = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
cnf(goals_18,negated_conjecture,
composition(meet(sk1,sk2),sk3) != meet(sk1,composition(sk2,sk3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_18) ).
cnf(c_0_18,axiom,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
converse_multiplicativity_10 ).
cnf(c_0_19,axiom,
converse(converse(X1)) = X1,
converse_idempotence_8 ).
cnf(c_0_20,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,axiom,
composition(X1,one) = X1,
composition_identity_6 ).
cnf(c_0_22,plain,
composition(converse(one),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_19]) ).
cnf(c_0_23,axiom,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
converse_cancellativity_11 ).
cnf(c_0_24,axiom,
join(X1,X2) = join(X2,X1),
maddux1_join_commutativity_1 ).
cnf(c_0_25,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,axiom,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
maddux2_join_associativity_2 ).
cnf(c_0_27,axiom,
top = join(X1,complement(X1)),
def_top_12 ).
cnf(c_0_28,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_22,c_0_25]) ).
cnf(c_0_30,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
join(X1,join(X2,complement(join(X1,X2)))) = top,
inference(spm,[status(thm)],[c_0_27,c_0_26]) ).
cnf(c_0_32,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_25]),c_0_29]) ).
cnf(c_0_33,axiom,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
maddux3_a_kind_of_de_Morgan_3 ).
cnf(c_0_34,axiom,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
maddux4_definiton_of_meet_4 ).
cnf(c_0_35,plain,
join(top,complement(complement(X1))) = join(X1,top),
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
cnf(c_0_36,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_27]),c_0_24]) ).
cnf(c_0_37,axiom,
zero = meet(X1,complement(X1)),
def_zero_13 ).
cnf(c_0_38,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,plain,
join(X1,top) = top,
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_40,plain,
complement(top) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_27]),c_0_37]) ).
cnf(c_0_41,plain,
join(zero,meet(X1,top)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_24]) ).
cnf(c_0_42,plain,
meet(X1,X2) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_24]),c_0_34]) ).
cnf(c_0_43,plain,
complement(join(zero,complement(X1))) = meet(top,X1),
inference(spm,[status(thm)],[c_0_34,c_0_40]) ).
cnf(c_0_44,plain,
join(zero,complement(complement(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_32]),c_0_37]) ).
cnf(c_0_45,plain,
join(zero,meet(top,X1)) = X1,
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,plain,
meet(top,complement(X1)) = complement(X1),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,plain,
join(zero,complement(X1)) = complement(X1),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_48,plain,
complement(complement(X1)) = meet(top,X1),
inference(rw,[status(thm)],[c_0_43,c_0_47]) ).
cnf(c_0_49,plain,
meet(top,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44,c_0_47]),c_0_48]) ).
cnf(c_0_50,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_51,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_32,c_0_50]) ).
cnf(c_0_52,plain,
complement(complement(X1)) = meet(X1,X1),
inference(spm,[status(thm)],[c_0_34,c_0_32]) ).
cnf(c_0_53,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_26,c_0_51]) ).
cnf(c_0_54,plain,
join(zero,meet(X1,X1)) = X1,
inference(spm,[status(thm)],[c_0_44,c_0_52]) ).
cnf(c_0_55,plain,
join(X1,meet(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_38]),c_0_24]) ).
cnf(c_0_56,plain,
complement(join(X1,complement(X2))) = meet(complement(X1),X2),
inference(spm,[status(thm)],[c_0_34,c_0_50]) ).
cnf(c_0_57,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_52]),c_0_54]) ).
cnf(c_0_58,axiom,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
converse_additivity_9 ).
cnf(c_0_59,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_55,c_0_42]) ).
cnf(c_0_60,plain,
complement(join(complement(X1),X2)) = meet(complement(X2),X1),
inference(spm,[status(thm)],[c_0_56,c_0_24]) ).
cnf(c_0_61,plain,
join(X1,join(X2,complement(X1))) = join(top,X2),
inference(spm,[status(thm)],[c_0_30,c_0_24]) ).
cnf(c_0_62,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_24,c_0_39]) ).
cnf(c_0_63,plain,
join(zero,X1) = X1,
inference(rw,[status(thm)],[c_0_54,c_0_57]) ).
cnf(c_0_64,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(spm,[status(thm)],[c_0_58,c_0_19]) ).
cnf(c_0_65,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_26,c_0_59]) ).
cnf(c_0_66,plain,
join(meet(X1,X2),meet(complement(X2),X1)) = X1,
inference(rw,[status(thm)],[c_0_38,c_0_60]) ).
cnf(c_0_67,plain,
join(X1,join(X2,complement(X1))) = top,
inference(rw,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_68,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_24,c_0_63]) ).
cnf(c_0_69,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(spm,[status(thm)],[c_0_64,c_0_27]) ).
cnf(c_0_70,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_71,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_38,c_0_67]),c_0_48]),c_0_49]),c_0_40]),c_0_68]) ).
cnf(c_0_72,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_24]),c_0_26]) ).
cnf(c_0_73,plain,
converse(join(one,X1)) = join(one,converse(X1)),
inference(spm,[status(thm)],[c_0_58,c_0_25]) ).
cnf(c_0_74,plain,
meet(complement(X1),complement(X2)) = complement(join(X1,X2)),
inference(spm,[status(thm)],[c_0_56,c_0_50]) ).
cnf(c_0_75,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_69,c_0_62]) ).
cnf(c_0_76,plain,
meet(X1,complement(meet(X1,X2))) = meet(complement(X2),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_70]),c_0_60]),c_0_48]),c_0_49]),c_0_42]) ).
cnf(c_0_77,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_50,c_0_56]) ).
cnf(c_0_78,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_55]),c_0_42]) ).
cnf(c_0_79,plain,
join(X1,join(X2,meet(X1,X3))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_72,c_0_55]) ).
cnf(c_0_80,plain,
join(one,converse(complement(one))) = converse(top),
inference(spm,[status(thm)],[c_0_73,c_0_27]) ).
cnf(c_0_81,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_70,c_0_74]) ).
cnf(c_0_82,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(rw,[status(thm)],[c_0_69,c_0_75]) ).
cnf(c_0_83,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_76,c_0_76]),c_0_77]),c_0_50]),c_0_42]),c_0_78]) ).
cnf(c_0_84,plain,
join(meet(X1,X2),complement(X2)) = join(complement(X2),X1),
inference(spm,[status(thm)],[c_0_79,c_0_66]) ).
cnf(c_0_85,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_59]),c_0_42]) ).
cnf(c_0_86,plain,
join(one,converse(complement(one))) = top,
inference(rw,[status(thm)],[c_0_80,c_0_75]) ).
cnf(c_0_87,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_40]),c_0_68]) ).
cnf(c_0_88,plain,
meet(X1,join(complement(X1),X2)) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_85]) ).
cnf(c_0_89,plain,
meet(X1,top) = X1,
inference(spm,[status(thm)],[c_0_42,c_0_49]) ).
cnf(c_0_90,plain,
join(one,complement(converse(complement(one)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_86]),c_0_40]),c_0_68]) ).
cnf(c_0_91,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_87]),c_0_19]),c_0_19]) ).
cnf(c_0_92,plain,
meet(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_82]),c_0_89]),c_0_42]) ).
cnf(c_0_93,plain,
join(X1,converse(meet(X2,converse(X1)))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_59]),c_0_19]) ).
cnf(c_0_94,plain,
meet(complement(one),converse(complement(one))) = complement(one),
inference(spm,[status(thm)],[c_0_56,c_0_90]) ).
cnf(c_0_95,plain,
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_42]),c_0_92]) ).
cnf(c_0_96,plain,
join(complement(one),converse(complement(one))) = complement(one),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_97,axiom,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
composition_distributivity_7 ).
cnf(c_0_98,plain,
complement(converse(complement(X1))) = converse(X1),
inference(spm,[status(thm)],[c_0_19,c_0_95]) ).
cnf(c_0_99,plain,
converse(complement(one)) = complement(one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_96]),c_0_42]),c_0_94]) ).
cnf(c_0_100,plain,
join(X1,composition(X2,X1)) = composition(join(one,X2),X1),
inference(spm,[status(thm)],[c_0_97,c_0_29]) ).
cnf(c_0_101,plain,
join(one,converse(meet(one,X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_55]),c_0_25]) ).
cnf(c_0_102,plain,
complement(join(X1,join(X2,complement(X3)))) = meet(complement(join(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_56,c_0_26]) ).
cnf(c_0_103,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(spm,[status(thm)],[c_0_77,c_0_50]) ).
cnf(c_0_104,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[c_0_50,c_0_98]) ).
cnf(c_0_105,plain,
converse(join(complement(one),X1)) = join(complement(one),converse(X1)),
inference(spm,[status(thm)],[c_0_58,c_0_99]) ).
cnf(c_0_106,plain,
join(X1,meet(X2,complement(X1))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_70,c_0_42]) ).
cnf(c_0_107,plain,
join(X1,composition(converse(meet(one,X2)),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_29]) ).
cnf(c_0_108,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_26,c_0_55]) ).
cnf(c_0_109,plain,
composition(top,converse(X1)) = converse(composition(X1,top)),
inference(spm,[status(thm)],[c_0_18,c_0_75]) ).
cnf(c_0_110,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_102,c_0_103]),c_0_56]),c_0_56]) ).
cnf(c_0_111,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_104,c_0_105]),c_0_60]),c_0_104]),c_0_60]),c_0_42]),c_0_42]) ).
cnf(c_0_112,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_106,c_0_74]) ).
cnf(c_0_113,plain,
join(X1,composition(X1,meet(one,X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_107]),c_0_19]),c_0_18]),c_0_19]) ).
cnf(c_0_114,plain,
join(X1,meet(X2,meet(X1,X3))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_59]),c_0_55]) ).
cnf(c_0_115,plain,
composition(top,join(one,converse(X1))) = converse(composition(join(one,X1),top)),
inference(spm,[status(thm)],[c_0_109,c_0_73]) ).
cnf(c_0_116,plain,
composition(join(X1,converse(X2)),converse(X3)) = converse(composition(X3,join(converse(X1),X2))),
inference(spm,[status(thm)],[c_0_18,c_0_64]) ).
cnf(c_0_117,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_110,c_0_50]) ).
cnf(c_0_118,plain,
meet(one,converse(X1)) = converse(meet(one,X1)),
inference(spm,[status(thm)],[c_0_111,c_0_50]) ).
cnf(c_0_119,plain,
meet(join(X1,X2),join(X2,complement(X1))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_112]),c_0_42]),c_0_71]) ).
cnf(c_0_120,plain,
join(X1,composition(X1,meet(X2,one))) = X1,
inference(spm,[status(thm)],[c_0_113,c_0_85]) ).
cnf(c_0_121,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_122,plain,
join(X1,composition(meet(one,X2),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_55]),c_0_29]) ).
cnf(c_0_123,plain,
join(X1,meet(X2,meet(X3,X1))) = X1,
inference(spm,[status(thm)],[c_0_114,c_0_85]) ).
cnf(c_0_124,plain,
join(X1,composition(X2,X1)) = composition(join(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_29]),c_0_24]) ).
cnf(c_0_125,plain,
composition(top,join(one,converse(X1))) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_115,c_0_100]),c_0_62]),c_0_75]) ).
cnf(c_0_126,axiom,
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),
modular_law_1_15 ).
cnf(c_0_127,plain,
converse(join(composition(converse(X1),X2),X3)) = join(composition(converse(X2),X1),converse(X3)),
inference(spm,[status(thm)],[c_0_58,c_0_20]) ).
cnf(c_0_128,plain,
join(composition(X1,converse(X2)),converse(composition(X2,X3))) = converse(composition(X2,join(converse(X1),X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_18]),c_0_116]) ).
cnf(c_0_129,plain,
meet(converse(meet(one,X1)),X2) = meet(one,meet(converse(X1),X2)),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_130,plain,
meet(X1,composition(X1,meet(X2,one))) = composition(X1,meet(X2,one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_83]) ).
cnf(c_0_131,plain,
composition(meet(one,composition(X1,converse(X2))),meet(X2,X1)) = meet(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_25]),c_0_29]),c_0_29]),c_0_29]),c_0_122]) ).
cnf(c_0_132,plain,
meet(X1,meet(X2,meet(X3,X1))) = meet(X2,meet(X3,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_123]),c_0_42]) ).
cnf(c_0_133,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_42]),c_0_117]) ).
cnf(c_0_134,plain,
meet(X1,join(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_71,c_0_24]) ).
cnf(c_0_135,plain,
join(X1,composition(top,X1)) = composition(top,X1),
inference(spm,[status(thm)],[c_0_124,c_0_62]) ).
cnf(c_0_136,axiom,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
composition_associativity_5 ).
cnf(c_0_137,plain,
composition(top,join(one,X1)) = top,
inference(spm,[status(thm)],[c_0_125,c_0_19]) ).
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_42]),c_0_42]) ).
cnf(c_0_139,plain,
composition(converse(X1),top) = converse(composition(top,X1)),
inference(spm,[status(thm)],[c_0_20,c_0_75]) ).
cnf(c_0_140,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_128]),c_0_19]),c_0_19]),c_0_19]),c_0_19]) ).
cnf(c_0_141,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_142,plain,
converse(complement(join(converse(X1),X2))) = complement(join(X1,converse(X2))),
inference(spm,[status(thm)],[c_0_104,c_0_64]) ).
cnf(c_0_143,plain,
join(converse(complement(X1)),complement(X2)) = complement(meet(converse(X1),X2)),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_144,plain,
join(complement(X1),converse(complement(X2))) = complement(meet(X1,converse(X2))),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_145,plain,
meet(converse(meet(X1,one)),X2) = meet(one,meet(converse(X1),X2)),
inference(spm,[status(thm)],[c_0_129,c_0_42]) ).
cnf(c_0_146,plain,
meet(X1,converse(meet(one,X1))) = meet(X1,one),
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_130,c_0_131]),c_0_29]),c_0_118]),c_0_129]),c_0_132]),c_0_133]),c_0_42]),c_0_118]) ).
cnf(c_0_147,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_117,c_0_71]) ).
cnf(c_0_148,plain,
meet(X1,composition(top,X1)) = X1,
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_149,plain,
composition(top,composition(join(one,X1),X2)) = composition(top,X2),
inference(spm,[status(thm)],[c_0_136,c_0_137]) ).
cnf(c_0_150,plain,
composition(X1,meet(X2,converse(composition(top,X1)))) = composition(X1,X2),
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_49]),c_0_49]),c_0_89]),c_0_140]),c_0_55]) ).
cnf(c_0_151,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_141,c_0_42]),c_0_42]) ).
cnf(c_0_152,plain,
composition(top,top) = top,
inference(spm,[status(thm)],[c_0_62,c_0_135]) ).
cnf(c_0_153,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_142,c_0_143]),c_0_50]),c_0_144]),c_0_50]) ).
cnf(c_0_154,plain,
converse(meet(X1,one)) = meet(X1,one),
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_145,c_0_146]),c_0_42]),c_0_118]),c_0_85]),c_0_118]),c_0_85]),c_0_19]),c_0_133]),c_0_42]),c_0_118]),c_0_146]),c_0_85]) ).
cnf(c_0_155,plain,
meet(X1,composition(top,join(X2,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_71]) ).
cnf(c_0_156,plain,
composition(top,join(X1,composition(X2,X1))) = composition(top,X1),
inference(spm,[status(thm)],[c_0_149,c_0_100]) ).
cnf(c_0_157,plain,
composition(X1,converse(composition(top,X1))) = composition(X1,top),
inference(spm,[status(thm)],[c_0_150,c_0_49]) ).
cnf(c_0_158,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_117,c_0_134]) ).
cnf(c_0_159,plain,
meet(X1,composition(X1,top)) = 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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_49]),c_0_75]),c_0_49]),c_0_136]),c_0_152]),c_0_55]),c_0_75]),c_0_49]),c_0_136]),c_0_152]) ).
cnf(c_0_160,plain,
converse(meet(one,X1)) = meet(X1,one),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_42]),c_0_118]),c_0_25]) ).
cnf(c_0_161,plain,
converse(meet(X1,converse(X2))) = meet(converse(X1),X2),
inference(spm,[status(thm)],[c_0_19,c_0_153]) ).
cnf(c_0_162,plain,
meet(composition(X1,X2),composition(top,X2)) = composition(X1,X2),
inference(spm,[status(thm)],[c_0_155,c_0_156]) ).
cnf(c_0_163,plain,
composition(X1,join(converse(composition(top,X1)),X2)) = composition(X1,top),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_157]),c_0_140]),c_0_62]) ).
cnf(c_0_164,plain,
join(meet(X1,X2),meet(X2,complement(X1))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_50]),c_0_24]) ).
cnf(c_0_165,plain,
meet(X1,composition(join(X1,X2),top)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_159]),c_0_134]) ).
cnf(c_0_166,plain,
join(composition(X1,composition(X2,X3)),composition(X4,X3)) = composition(join(composition(X1,X2),X4),X3),
inference(spm,[status(thm)],[c_0_97,c_0_136]) ).
cnf(c_0_167,plain,
meet(one,converse(X1)) = meet(X1,one),
inference(rw,[status(thm)],[c_0_118,c_0_160]) ).
cnf(c_0_168,plain,
meet(X1,meet(composition(X2,X3),composition(X2,meet(X3,composition(converse(X2),meet(X1,composition(X2,X3))))))) = meet(X1,composition(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_85]),c_0_55]),c_0_117]) ).
cnf(c_0_169,plain,
meet(converse(X1),composition(converse(X2),X3)) = converse(meet(X1,composition(converse(X3),X2))),
inference(spm,[status(thm)],[c_0_161,c_0_20]) ).
cnf(c_0_170,plain,
meet(composition(top,X1),composition(X2,X1)) = composition(X2,X1),
inference(spm,[status(thm)],[c_0_42,c_0_162]) ).
cnf(c_0_171,plain,
composition(converse(join(composition(X1,top),X2)),X1) = composition(top,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_163]),c_0_20]),c_0_75]),c_0_109]),c_0_19]) ).
cnf(c_0_172,plain,
join(X1,composition(join(X1,X2),top)) = composition(join(X1,X2),top),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_164,c_0_165]),c_0_106]) ).
cnf(c_0_173,plain,
composition(join(composition(X1,top),X2),top) = composition(join(X1,X2),top),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_152]),c_0_97]) ).
cnf(c_0_174,plain,
composition(converse(composition(X1,top)),X2) = composition(top,composition(converse(X1),X2)),
inference(spm,[status(thm)],[c_0_136,c_0_109]) ).
cnf(c_0_175,plain,
join(meet(X1,one),converse(X1)) = converse(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_167]),c_0_24]) ).
cnf(c_0_176,plain,
meet(X1,composition(converse(X2),composition(X2,X1))) = meet(X1,converse(composition(top,X2))),
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_168,c_0_139]),c_0_19]),c_0_150]),c_0_49]),c_0_169]),c_0_170]),c_0_20]) ).
cnf(c_0_177,plain,
meet(converse(X1),converse(X2)) = converse(meet(X1,X2)),
inference(spm,[status(thm)],[c_0_153,c_0_19]) ).
cnf(c_0_178,plain,
composition(converse(X1),composition(X2,converse(X3))) = converse(composition(X3,composition(converse(X2),X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_20]),c_0_136]) ).
cnf(c_0_179,plain,
composition(top,composition(converse(join(X1,X2)),X1)) = composition(top,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_172]),c_0_173]),c_0_174]) ).
cnf(c_0_180,plain,
join(meet(one,X1),converse(X1)) = converse(X1),
inference(spm,[status(thm)],[c_0_175,c_0_42]) ).
cnf(c_0_181,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_153,c_0_176]),c_0_177]),c_0_19]),c_0_178]),c_0_19]) ).
cnf(c_0_182,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_183,plain,
join(meet(one,composition(X1,X2)),composition(meet(X1,converse(X2)),meet(X2,converse(X1)))) = composition(meet(X1,converse(X2)),meet(X2,converse(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_21]),c_0_29]),c_0_29]),c_0_42]) ).
cnf(c_0_184,plain,
meet(X1,composition(X1,meet(one,X2))) = composition(X1,meet(one,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_113]),c_0_83]) ).
cnf(c_0_185,plain,
join(X1,composition(meet(X2,one),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_59]),c_0_29]) ).
cnf(c_0_186,plain,
composition(top,composition(X1,meet(one,X1))) = composition(top,meet(one,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179,c_0_180]),c_0_19]) ).
cnf(c_0_187,plain,
meet(X1,composition(X1,composition(X2,converse(X2)))) = meet(X1,converse(composition(X2,top))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_19]),c_0_109]) ).
cnf(c_0_188,plain,
composition(converse(X1),meet(one,X2)) = converse(composition(meet(X2,one),X1)),
inference(spm,[status(thm)],[c_0_20,c_0_160]) ).
cnf(c_0_189,plain,
composition(meet(one,composition(X1,top)),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_49]),c_0_75]) ).
cnf(c_0_190,plain,
composition(top,composition(X1,converse(X1))) = converse(composition(X1,top)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_182,c_0_157]),c_0_136]) ).
cnf(c_0_191,plain,
composition(meet(X1,one),meet(one,X1)) = meet(one,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(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_183,c_0_184]),c_0_29]),c_0_118]),c_0_78]),c_0_160]),c_0_25]),c_0_42]),c_0_78]),c_0_185]),c_0_118]),c_0_78]),c_0_160]),c_0_25]),c_0_42]),c_0_78]) ).
cnf(c_0_192,plain,
converse(composition(X1,top)) = composition(top,meet(one,composition(X1,top))),
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_186,c_0_187]),c_0_29]),c_0_118]),c_0_160]),c_0_42]),c_0_136]),c_0_188]),c_0_42]),c_0_189]),c_0_190]),c_0_118]),c_0_160]),c_0_42]) ).
cnf(c_0_193,plain,
meet(X1,composition(top,meet(one,X2))) = composition(X1,meet(one,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_181,c_0_160]),c_0_191]),c_0_184]) ).
cnf(c_0_194,plain,
meet(X1,composition(X1,composition(X2,converse(X2)))) = composition(X1,meet(one,composition(X2,top))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_187,c_0_192]),c_0_193]) ).
cnf(c_0_195,plain,
meet(X1,composition(X2,composition(converse(X2),X1))) = meet(X1,composition(X2,top)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_19]),c_0_109]),c_0_19]) ).
cnf(c_0_196,plain,
composition(meet(one,composition(X1,top)),X2) = meet(X2,composition(X1,top)),
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_153,c_0_194]),c_0_188]),c_0_42]),c_0_19]),c_0_178]),c_0_19]),c_0_195]) ).
cnf(c_0_197,negated_conjecture,
composition(sk1,top) = sk1,
goals_17 ).
cnf(c_0_198,negated_conjecture,
composition(meet(one,sk1),X1) = meet(X1,sk1),
inference(spm,[status(thm)],[c_0_196,c_0_197]) ).
cnf(c_0_199,negated_conjecture,
composition(meet(sk1,sk2),sk3) != meet(sk1,composition(sk2,sk3)),
goals_18 ).
cnf(c_0_200,negated_conjecture,
meet(sk1,composition(X1,X2)) = composition(meet(X1,sk1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_198]),c_0_198]),c_0_42]) ).
cnf(c_0_201,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_199,c_0_200]),c_0_42])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL033-3 : 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 : n009.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 01:42:41 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 74.57/43.48 % Version : CSE_E---1.7
% 74.57/43.48 % Problem : theBenchmark.p
% 74.57/43.48 % SZS status Unsatisfiable for theBenchmark.p
% 74.57/43.48 % SZS output start CNFRefutation
% See solution above
% 74.88/43.79 % Total time : 31.968s
%------------------------------------------------------------------------------