%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : REL029-10 : TPTP v9.2.1. Released v7.3.0.
% 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 : n004.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 05:04:23 PM UTC 2026
% Result : Unsatisfiable 17.84s 11.63s
% Output : CNFRefutation 17.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 19
% Syntax : Number of clauses : 188 ( 188 unt; 0 nHn; 38 RR)
% Number of literals : 188 ( 187 equ; 4 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 : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 254 ( 18 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(converse_multiplicativity_10,axiom,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
cnf(converse_idempotence_8,axiom,
converse(converse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence_8) ).
cnf(composition_identity_6,axiom,
composition(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity_6) ).
cnf(maddux2_join_associativity_2,axiom,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
cnf(def_top_12,axiom,
top = join(X1,complement(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top_12) ).
cnf(converse_cancellativity_11,axiom,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity_11) ).
cnf(maddux1_join_commutativity_1,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
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/theBenchmark.p',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/theBenchmark.p',maddux4_definiton_of_meet_4) ).
cnf(def_zero_13,axiom,
zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero_13) ).
cnf(converse_additivity_9,axiom,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_additivity_9) ).
cnf(goals_18,negated_conjecture,
join(sk2,one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_18) ).
cnf(composition_distributivity_7,axiom,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_distributivity_7) ).
cnf(goals_17,negated_conjecture,
join(sk1,one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
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/theBenchmark.p',modular_law_1_15) ).
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/theBenchmark.p',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/theBenchmark.p',dedekind_law_14) ).
cnf(composition_associativity_5,axiom,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity_5) ).
cnf(goals_19,negated_conjecture,
tuple(join(meet(composition(sk1,sk3),composition(sk2,sk3)),composition(meet(sk1,sk2),sk3)),join(composition(meet(sk1,sk2),sk3),meet(composition(sk1,sk3),composition(sk2,sk3)))) != tuple(composition(meet(sk1,sk2),sk3),meet(composition(sk1,sk3),composition(sk2,sk3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_19) ).
cnf(c_0_19,axiom,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
converse_multiplicativity_10 ).
cnf(c_0_20,axiom,
converse(converse(X1)) = X1,
converse_idempotence_8 ).
cnf(c_0_21,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,axiom,
composition(X1,one) = X1,
composition_identity_6 ).
cnf(c_0_23,plain,
composition(converse(one),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_20]) ).
cnf(c_0_24,axiom,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
maddux2_join_associativity_2 ).
cnf(c_0_25,axiom,
top = join(X1,complement(X1)),
def_top_12 ).
cnf(c_0_26,axiom,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
converse_cancellativity_11 ).
cnf(c_0_27,axiom,
join(X1,X2) = join(X2,X1),
maddux1_join_commutativity_1 ).
cnf(c_0_28,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_23,c_0_28]) ).
cnf(c_0_32,plain,
join(X1,join(X2,complement(X1))) = join(top,X2),
inference(spm,[status(thm)],[c_0_29,c_0_27]) ).
cnf(c_0_33,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_28]),c_0_31]) ).
cnf(c_0_34,axiom,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
maddux3_a_kind_of_de_Morgan_3 ).
cnf(c_0_35,axiom,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
maddux4_definiton_of_meet_4 ).
cnf(c_0_36,plain,
join(top,complement(complement(X1))) = join(X1,top),
inference(spm,[status(thm)],[c_0_29,c_0_25]) ).
cnf(c_0_37,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_25]) ).
cnf(c_0_38,axiom,
zero = meet(X1,complement(X1)),
def_zero_13 ).
cnf(c_0_39,plain,
join(meet(X1,X2),complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_40,plain,
join(X1,top) = top,
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,plain,
complement(top) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_25]),c_0_38]) ).
cnf(c_0_42,plain,
join(zero,meet(X1,top)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]),c_0_27]) ).
cnf(c_0_43,plain,
meet(X1,X2) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_27]),c_0_35]) ).
cnf(c_0_44,plain,
complement(join(zero,complement(X1))) = meet(top,X1),
inference(spm,[status(thm)],[c_0_35,c_0_41]) ).
cnf(c_0_45,plain,
join(zero,complement(complement(X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_33]),c_0_38]) ).
cnf(c_0_46,plain,
join(zero,meet(top,X1)) = X1,
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,plain,
meet(top,complement(X1)) = complement(X1),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_48,plain,
join(zero,complement(X1)) = complement(X1),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_49,plain,
complement(complement(X1)) = meet(top,X1),
inference(rw,[status(thm)],[c_0_44,c_0_48]) ).
cnf(c_0_50,plain,
meet(top,X1) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_48]),c_0_49]) ).
cnf(c_0_51,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_52,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_33,c_0_51]) ).
cnf(c_0_53,plain,
complement(complement(X1)) = meet(X1,X1),
inference(spm,[status(thm)],[c_0_35,c_0_33]) ).
cnf(c_0_54,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_24,c_0_52]) ).
cnf(c_0_55,plain,
join(zero,meet(X1,X1)) = X1,
inference(spm,[status(thm)],[c_0_45,c_0_53]) ).
cnf(c_0_56,plain,
join(X1,meet(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_39]),c_0_27]) ).
cnf(c_0_57,plain,
complement(join(X1,complement(X2))) = meet(complement(X1),X2),
inference(spm,[status(thm)],[c_0_35,c_0_51]) ).
cnf(c_0_58,plain,
meet(X1,X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_53]),c_0_55]) ).
cnf(c_0_59,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_56,c_0_43]) ).
cnf(c_0_60,plain,
complement(join(complement(X1),X2)) = meet(complement(X2),X1),
inference(spm,[status(thm)],[c_0_57,c_0_27]) ).
cnf(c_0_61,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_27,c_0_40]) ).
cnf(c_0_62,plain,
join(zero,X1) = X1,
inference(rw,[status(thm)],[c_0_55,c_0_58]) ).
cnf(c_0_63,axiom,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
converse_additivity_9 ).
cnf(c_0_64,plain,
join(X1,join(meet(X2,X1),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_24,c_0_59]) ).
cnf(c_0_65,plain,
join(meet(X1,X2),meet(complement(X2),X1)) = X1,
inference(rw,[status(thm)],[c_0_39,c_0_60]) ).
cnf(c_0_66,plain,
join(X1,join(X2,complement(X1))) = top,
inference(rw,[status(thm)],[c_0_32,c_0_61]) ).
cnf(c_0_67,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_62]) ).
cnf(c_0_68,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(spm,[status(thm)],[c_0_63,c_0_20]) ).
cnf(c_0_69,plain,
join(X1,meet(complement(X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_70,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_39,c_0_66]),c_0_49]),c_0_50]),c_0_41]),c_0_67]) ).
cnf(c_0_71,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(spm,[status(thm)],[c_0_68,c_0_25]) ).
cnf(c_0_72,plain,
complement(meet(complement(X1),X2)) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_51,c_0_57]) ).
cnf(c_0_73,negated_conjecture,
join(sk2,one) = one,
goals_18 ).
cnf(c_0_74,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_69]),c_0_60]),c_0_49]),c_0_50]),c_0_43]) ).
cnf(c_0_75,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_56]),c_0_43]) ).
cnf(c_0_76,plain,
meet(complement(X1),complement(X2)) = complement(join(X1,X2)),
inference(spm,[status(thm)],[c_0_57,c_0_51]) ).
cnf(c_0_77,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_71,c_0_61]) ).
cnf(c_0_78,plain,
complement(join(X1,join(X2,complement(X3)))) = meet(complement(join(X1,X2)),X3),
inference(spm,[status(thm)],[c_0_57,c_0_24]) ).
cnf(c_0_79,plain,
join(complement(X1),complement(X2)) = complement(meet(X1,X2)),
inference(spm,[status(thm)],[c_0_72,c_0_51]) ).
cnf(c_0_80,negated_conjecture,
join(sk2,join(one,X1)) = join(one,X1),
inference(spm,[status(thm)],[c_0_24,c_0_73]) ).
cnf(c_0_81,axiom,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
composition_distributivity_7 ).
cnf(c_0_82,negated_conjecture,
join(sk1,one) = one,
goals_17 ).
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_74,c_0_74]),c_0_72]),c_0_51]),c_0_43]),c_0_75]) ).
cnf(c_0_84,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_69,c_0_76]) ).
cnf(c_0_85,plain,
meet(X1,join(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_70,c_0_27]) ).
cnf(c_0_86,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(rw,[status(thm)],[c_0_71,c_0_77]) ).
cnf(c_0_87,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_78,c_0_79]),c_0_57]),c_0_57]) ).
cnf(c_0_88,negated_conjecture,
join(sk2,join(X1,one)) = join(X1,one),
inference(spm,[status(thm)],[c_0_80,c_0_27]) ).
cnf(c_0_89,plain,
join(X1,composition(X2,X1)) = composition(join(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_31]),c_0_27]) ).
cnf(c_0_90,negated_conjecture,
join(sk1,join(one,X1)) = join(one,X1),
inference(spm,[status(thm)],[c_0_24,c_0_82]) ).
cnf(c_0_91,plain,
meet(join(X1,X2),join(X1,complement(X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_43]),c_0_85]) ).
cnf(c_0_92,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_86]),c_0_41]),c_0_67]) ).
cnf(c_0_93,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_87,c_0_51]) ).
cnf(c_0_94,negated_conjecture,
meet(sk2,one) = sk2,
inference(spm,[status(thm)],[c_0_85,c_0_73]) ).
cnf(c_0_95,negated_conjecture,
join(one,complement(sk2)) = join(top,one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_29]),c_0_27]) ).
cnf(c_0_96,plain,
composition(join(X1,one),top) = top,
inference(spm,[status(thm)],[c_0_89,c_0_61]) ).
cnf(c_0_97,plain,
complement(join(zero,zero)) = meet(top,top),
inference(spm,[status(thm)],[c_0_44,c_0_41]) ).
cnf(c_0_98,plain,
join(zero,zero) = zero,
inference(spm,[status(thm)],[c_0_33,c_0_41]) ).
cnf(c_0_99,negated_conjecture,
join(sk1,join(X1,one)) = join(X1,one),
inference(spm,[status(thm)],[c_0_90,c_0_27]) ).
cnf(c_0_100,plain,
meet(join(X1,X2),join(complement(X2),X1)) = X1,
inference(spm,[status(thm)],[c_0_91,c_0_27]) ).
cnf(c_0_101,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_92]),c_0_20]),c_0_20]) ).
cnf(c_0_102,negated_conjecture,
meet(sk2,meet(one,X1)) = meet(sk2,X1),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_103,plain,
meet(X1,join(complement(X1),X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_83,c_0_27]) ).
cnf(c_0_104,negated_conjecture,
join(one,complement(sk2)) = top,
inference(rw,[status(thm)],[c_0_95,c_0_61]) ).
cnf(c_0_105,plain,
composition(top,top) = top,
inference(spm,[status(thm)],[c_0_96,c_0_61]) ).
cnf(c_0_106,plain,
complement(zero) = meet(top,top),
inference(rw,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_107,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(spm,[status(thm)],[c_0_63,c_0_20]) ).
cnf(c_0_108,negated_conjecture,
meet(sk1,one) = sk1,
inference(spm,[status(thm)],[c_0_85,c_0_82]) ).
cnf(c_0_109,negated_conjecture,
join(one,complement(sk1)) = join(top,one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_99]),c_0_27]) ).
cnf(c_0_110,plain,
converse(complement(converse(X1))) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_49]),c_0_50]),c_0_27]),c_0_86]),c_0_50]),c_0_49]),c_0_50]) ).
cnf(c_0_111,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_112,negated_conjecture,
meet(sk2,join(complement(one),X1)) = meet(sk2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_102]) ).
cnf(c_0_113,negated_conjecture,
meet(sk2,complement(one)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_104]),c_0_41]),c_0_43]) ).
cnf(c_0_114,plain,
composition(top,zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_105]),c_0_41]),c_0_77]),c_0_41]),c_0_89]),c_0_61]),c_0_41]) ).
cnf(c_0_115,plain,
complement(zero) = top,
inference(rw,[status(thm)],[c_0_106,c_0_58]) ).
cnf(c_0_116,plain,
join(converse(zero),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_62]),c_0_20]) ).
cnf(c_0_117,negated_conjecture,
meet(sk1,meet(one,X1)) = meet(sk1,X1),
inference(spm,[status(thm)],[c_0_93,c_0_108]) ).
cnf(c_0_118,negated_conjecture,
join(one,complement(sk1)) = top,
inference(rw,[status(thm)],[c_0_109,c_0_61]) ).
cnf(c_0_119,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[c_0_20,c_0_110]) ).
cnf(c_0_120,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_111,c_0_43]),c_0_43]) ).
cnf(c_0_121,negated_conjecture,
meet(sk2,composition(converse(X1),complement(X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_30]),c_0_113]),c_0_22]) ).
cnf(c_0_122,plain,
composition(X1,zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_114]),c_0_40]),c_0_114]),c_0_67]) ).
cnf(c_0_123,plain,
meet(X1,zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_115]),c_0_40]),c_0_41]) ).
cnf(c_0_124,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_125,plain,
join(complement(X1),composition(X2,complement(composition(converse(X2),X1)))) = complement(X1),
inference(spm,[status(thm)],[c_0_30,c_0_20]) ).
cnf(c_0_126,plain,
converse(zero) = zero,
inference(spm,[status(thm)],[c_0_67,c_0_116]) ).
cnf(c_0_127,negated_conjecture,
meet(sk1,join(complement(one),X1)) = meet(sk1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_103]),c_0_117]) ).
cnf(c_0_128,negated_conjecture,
meet(sk1,complement(one)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_118]),c_0_41]),c_0_43]) ).
cnf(c_0_129,plain,
converse(complement(join(converse(X1),X2))) = complement(join(X1,converse(X2))),
inference(spm,[status(thm)],[c_0_119,c_0_68]) ).
cnf(c_0_130,plain,
join(converse(complement(X1)),complement(X2)) = complement(meet(converse(X1),X2)),
inference(spm,[status(thm)],[c_0_79,c_0_119]) ).
cnf(c_0_131,plain,
join(complement(X1),converse(complement(X2))) = complement(meet(X1,converse(X2))),
inference(spm,[status(thm)],[c_0_79,c_0_119]) ).
cnf(c_0_132,negated_conjecture,
meet(composition(X1,sk2),complement(X1)) = zero,
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_120,c_0_121]),c_0_122]),c_0_123]),c_0_67]),c_0_122]),c_0_123]) ).
cnf(c_0_133,plain,
join(X1,join(meet(X1,X2),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_24,c_0_56]) ).
cnf(c_0_134,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_124,c_0_43]),c_0_43]) ).
cnf(c_0_135,negated_conjecture,
meet(sk2,composition(X1,converse(complement(X1)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_125]),c_0_113]),c_0_22]),c_0_119]) ).
cnf(c_0_136,plain,
composition(zero,X1) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_122]),c_0_126]),c_0_126]) ).
cnf(c_0_137,plain,
join(meet(composition(converse(X1),X2),X3),meet(X3,composition(converse(X1),meet(X2,composition(X1,X3))))) = meet(X3,composition(converse(X1),meet(X2,composition(X1,X3)))),
inference(spm,[status(thm)],[c_0_120,c_0_20]) ).
cnf(c_0_138,negated_conjecture,
meet(sk1,composition(converse(X1),complement(X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_30]),c_0_128]),c_0_22]) ).
cnf(c_0_139,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_129,c_0_130]),c_0_51]),c_0_131]),c_0_51]) ).
cnf(c_0_140,negated_conjecture,
meet(X1,composition(X1,sk2)) = composition(X1,sk2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_132]),c_0_49]),c_0_50]),c_0_62]) ).
cnf(c_0_141,plain,
join(X1,meet(X2,meet(X1,X3))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_59]),c_0_56]) ).
cnf(c_0_142,plain,
join(meet(X1,X2),meet(complement(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_65,c_0_43]) ).
cnf(c_0_143,negated_conjecture,
meet(X1,composition(sk2,complement(X1))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_136]),c_0_123]),c_0_67]),c_0_136]),c_0_123]),c_0_43]) ).
cnf(c_0_144,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_145,negated_conjecture,
meet(composition(X1,sk1),complement(X1)) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_137,c_0_138]),c_0_20]),c_0_20]),c_0_122]),c_0_123]),c_0_67]),c_0_20]),c_0_122]),c_0_123]) ).
cnf(c_0_146,plain,
join(meet(one,composition(X1,X2)),meet(one,composition(X1,meet(X2,converse(X1))))) = meet(one,composition(X1,meet(X2,converse(X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_22]),c_0_43]) ).
cnf(c_0_147,negated_conjecture,
meet(X1,composition(converse(sk2),X1)) = composition(converse(sk2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_140]),c_0_21]),c_0_21]) ).
cnf(c_0_148,negated_conjecture,
join(X1,meet(X2,composition(X1,sk2))) = X1,
inference(spm,[status(thm)],[c_0_141,c_0_140]) ).
cnf(c_0_149,negated_conjecture,
meet(X1,composition(sk2,X1)) = composition(sk2,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_142,c_0_143]),c_0_49]),c_0_50]),c_0_67]),c_0_49]),c_0_50]) ).
cnf(c_0_150,plain,
join(X1,composition(X1,converse(X2))) = composition(X1,converse(join(X2,one))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_89]),c_0_144]),c_0_144]) ).
cnf(c_0_151,negated_conjecture,
meet(X1,composition(X1,sk1)) = composition(X1,sk1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_145]),c_0_49]),c_0_50]),c_0_62]) ).
cnf(c_0_152,negated_conjecture,
join(X1,join(composition(X1,sk2),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_133,c_0_140]) ).
cnf(c_0_153,negated_conjecture,
meet(one,composition(converse(sk2),sk2)) = converse(sk2),
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_146,c_0_147]),c_0_22]),c_0_20]),c_0_43]),c_0_94]),c_0_148]),c_0_20]),c_0_43]),c_0_94]) ).
cnf(c_0_154,negated_conjecture,
meet(X1,composition(X1,converse(sk2))) = composition(X1,converse(sk2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_149]),c_0_144]),c_0_144]) ).
cnf(c_0_155,plain,
join(X1,composition(X1,X2)) = composition(X1,join(X2,one)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_150,c_0_20]),c_0_68]),c_0_28]) ).
cnf(c_0_156,plain,
join(one,converse(X1)) = converse(join(one,X1)),
inference(spm,[status(thm)],[c_0_63,c_0_28]) ).
cnf(c_0_157,negated_conjecture,
meet(X1,composition(converse(sk1),X1)) = composition(converse(sk1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_151]),c_0_21]),c_0_21]) ).
cnf(c_0_158,negated_conjecture,
join(X1,meet(X2,composition(X1,sk1))) = X1,
inference(spm,[status(thm)],[c_0_141,c_0_151]) ).
cnf(c_0_159,negated_conjecture,
join(X1,composition(join(X1,X2),sk2)) = join(X1,composition(X2,sk2)),
inference(spm,[status(thm)],[c_0_152,c_0_81]) ).
cnf(c_0_160,negated_conjecture,
composition(sk2,converse(sk2)) = sk2,
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_137,c_0_153]),c_0_20]),c_0_22]),c_0_58]),c_0_20]),c_0_154]),c_0_155]),c_0_27]),c_0_156]),c_0_27]),c_0_73]),c_0_28]),c_0_22]),c_0_20]),c_0_154]) ).
cnf(c_0_161,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_162,negated_conjecture,
meet(one,composition(converse(sk1),sk1)) = converse(sk1),
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_146,c_0_157]),c_0_22]),c_0_20]),c_0_43]),c_0_108]),c_0_158]),c_0_20]),c_0_43]),c_0_108]) ).
cnf(c_0_163,negated_conjecture,
join(X1,composition(complement(X1),sk2)) = join(X1,composition(top,sk2)),
inference(spm,[status(thm)],[c_0_159,c_0_25]) ).
cnf(c_0_164,plain,
composition(converse(X1),top) = converse(composition(top,X1)),
inference(spm,[status(thm)],[c_0_21,c_0_77]) ).
cnf(c_0_165,negated_conjecture,
converse(sk2) = sk2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_160]),c_0_160]) ).
cnf(c_0_166,negated_conjecture,
composition(sk1,converse(sk1)) = sk1,
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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_22]),c_0_58]),c_0_28]),c_0_22]),c_0_58]),c_0_155]),c_0_27]),c_0_156]),c_0_27]),c_0_82]),c_0_28]),c_0_22]),c_0_28]),c_0_22]),c_0_58]) ).
cnf(c_0_167,negated_conjecture,
meet(X1,composition(top,sk2)) = composition(X1,sk2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_163]),c_0_103]),c_0_49]),c_0_50]),c_0_140]) ).
cnf(c_0_168,negated_conjecture,
converse(composition(top,sk2)) = composition(sk2,top),
inference(spm,[status(thm)],[c_0_164,c_0_165]) ).
cnf(c_0_169,negated_conjecture,
composition(sk2,converse(X1)) = converse(composition(X1,sk2)),
inference(spm,[status(thm)],[c_0_19,c_0_165]) ).
cnf(c_0_170,negated_conjecture,
converse(sk1) = sk1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_166]),c_0_166]) ).
cnf(c_0_171,negated_conjecture,
meet(sk2,converse(X1)) = converse(meet(sk2,X1)),
inference(spm,[status(thm)],[c_0_139,c_0_165]) ).
cnf(c_0_172,axiom,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
composition_associativity_5 ).
cnf(c_0_173,negated_conjecture,
tuple(join(meet(composition(sk1,sk3),composition(sk2,sk3)),composition(meet(sk1,sk2),sk3)),join(composition(meet(sk1,sk2),sk3),meet(composition(sk1,sk3),composition(sk2,sk3)))) != tuple(composition(meet(sk1,sk2),sk3),meet(composition(sk1,sk3),composition(sk2,sk3))),
goals_19 ).
cnf(c_0_174,negated_conjecture,
meet(X1,composition(sk2,top)) = composition(sk2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_139,c_0_167]),c_0_21]),c_0_165]),c_0_168]) ).
cnf(c_0_175,negated_conjecture,
converse(composition(sk1,sk2)) = composition(sk2,sk1),
inference(spm,[status(thm)],[c_0_169,c_0_170]) ).
cnf(c_0_176,negated_conjecture,
composition(sk1,sk2) = meet(sk1,sk2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_167]),c_0_31]),c_0_167]) ).
cnf(c_0_177,negated_conjecture,
converse(meet(sk1,sk2)) = meet(sk1,sk2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_170]),c_0_43]),c_0_43]) ).
cnf(c_0_178,plain,
composition(converse(X1),composition(converse(X2),X3)) = composition(converse(composition(X2,X1)),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_21]),c_0_172]),c_0_21]) ).
cnf(c_0_179,negated_conjecture,
tuple(join(composition(meet(sk1,sk2),sk3),meet(composition(sk1,sk3),composition(sk2,sk3))),join(composition(meet(sk1,sk2),sk3),meet(composition(sk1,sk3),composition(sk2,sk3)))) != tuple(composition(meet(sk1,sk2),sk3),meet(composition(sk1,sk3),composition(sk2,sk3))),
inference(rw,[status(thm)],[c_0_173,c_0_27]) ).
cnf(c_0_180,negated_conjecture,
meet(X1,composition(sk2,X2)) = composition(sk2,meet(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_174]),c_0_174]) ).
cnf(c_0_181,negated_conjecture,
meet(X1,composition(sk1,X1)) = composition(sk1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_157,c_0_170]),c_0_170]) ).
cnf(c_0_182,plain,
join(composition(X1,X2),composition(X3,composition(X4,X2))) = composition(join(X1,composition(X3,X4)),X2),
inference(spm,[status(thm)],[c_0_81,c_0_172]) ).
cnf(c_0_183,negated_conjecture,
composition(sk2,sk1) = meet(sk1,sk2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_175,c_0_176]),c_0_177]) ).
cnf(c_0_184,negated_conjecture,
composition(converse(composition(X1,sk2)),X2) = composition(sk2,composition(converse(X1),X2)),
inference(spm,[status(thm)],[c_0_178,c_0_165]) ).
cnf(c_0_185,negated_conjecture,
tuple(composition(meet(sk1,sk2),sk3),composition(sk2,composition(sk1,sk3))) != tuple(composition(meet(sk1,sk2),sk3),composition(meet(sk1,sk2),sk3)),
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(rw,[status(thm)],[c_0_179,c_0_180]),c_0_43]),c_0_181]),c_0_182]),c_0_183]),c_0_52]),c_0_180]),c_0_43]),c_0_181]),c_0_182]),c_0_183]),c_0_52]),c_0_180]),c_0_43]),c_0_181]) ).
cnf(c_0_186,negated_conjecture,
composition(sk2,composition(sk1,X1)) = composition(meet(sk1,sk2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_184,c_0_176]),c_0_177]),c_0_170]) ).
cnf(c_0_187,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_185,c_0_186])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : REL029-10 : TPTP v9.2.1. Released v7.3.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n004.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 01:42:02 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 17.84/11.63 % Version : CSE_E---1.7
% 17.84/11.63 % Problem : theBenchmark.p
% 17.84/11.63 % SZS status Unsatisfiable for theBenchmark.p
% 17.84/11.63 % SZS output start CNFRefutation
% See solution above
% 17.94/11.71 % Total time : 8.468s
%------------------------------------------------------------------------------