%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : REL029-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:04:02 PM UTC 2026
% Result : Unsatisfiable 192.27s 38.40s
% Output : CNFRefutation 192.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 17
% Syntax : Number of clauses : 143 ( 143 unt; 0 nHn; 34 RR)
% Number of literals : 143 ( 142 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 11 ( 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 : 169 ( 10 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(composition_identity_6,axiom,
composition(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity_6) ).
cnf(converse_idempotence_8,axiom,
converse(converse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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/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(def_zero_13,axiom,
zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero_13) ).
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_top_12,axiom,
top = join(X1,complement(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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/theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
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(goals_17,negated_conjecture,
join(sk1,one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
cnf(goals_18,negated_conjecture,
join(sk2,one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_18) ).
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(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(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(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_17,axiom,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
converse_multiplicativity_10 ).
cnf(c_0_18,axiom,
composition(X1,one) = X1,
composition_identity_6 ).
cnf(c_0_19,plain,
composition(converse(one),converse(X1)) = converse(X1),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,axiom,
converse(converse(X1)) = X1,
converse_idempotence_8 ).
cnf(c_0_21,plain,
composition(converse(one),X1) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,axiom,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
converse_cancellativity_11 ).
cnf(c_0_23,axiom,
join(X1,X2) = join(X2,X1),
maddux1_join_commutativity_1 ).
cnf(c_0_24,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_18,c_0_21]) ).
cnf(c_0_25,axiom,
zero = meet(X1,complement(X1)),
def_zero_13 ).
cnf(c_0_26,axiom,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
maddux4_definiton_of_meet_4 ).
cnf(c_0_27,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_21,c_0_24]) ).
cnf(c_0_29,plain,
zero = complement(join(complement(X1),complement(complement(X1)))),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,axiom,
top = join(X1,complement(X1)),
def_top_12 ).
cnf(c_0_31,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_24]),c_0_28]) ).
cnf(c_0_32,plain,
complement(top) = zero,
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
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,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
maddux2_join_associativity_2 ).
cnf(c_0_35,plain,
join(zero,zero) = zero,
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[c_0_33,c_0_23]) ).
cnf(c_0_37,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,plain,
join(zero,complement(complement(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_31]),c_0_30]),c_0_32]),c_0_23]) ).
cnf(c_0_39,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_40,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_41,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_40]) ).
cnf(c_0_42,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_41]) ).
cnf(c_0_43,plain,
join(top,zero) = top,
inference(spm,[status(thm)],[c_0_30,c_0_32]) ).
cnf(c_0_44,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_34,c_0_30]) ).
cnf(c_0_45,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_36]),c_0_23]) ).
cnf(c_0_46,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_42,c_0_23]) ).
cnf(c_0_47,plain,
join(top,join(zero,X1)) = join(top,X1),
inference(spm,[status(thm)],[c_0_34,c_0_43]) ).
cnf(c_0_48,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_31]),c_0_30]) ).
cnf(c_0_49,negated_conjecture,
join(sk1,one) = one,
goals_17 ).
cnf(c_0_50,negated_conjecture,
join(sk2,one) = one,
goals_18 ).
cnf(c_0_51,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,axiom,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
converse_additivity_9 ).
cnf(c_0_53,plain,
join(top,X1) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_38]),c_0_48]) ).
cnf(c_0_54,negated_conjecture,
join(one,sk1) = one,
inference(rw,[status(thm)],[c_0_49,c_0_23]) ).
cnf(c_0_55,negated_conjecture,
join(one,sk2) = one,
inference(rw,[status(thm)],[c_0_50,c_0_23]) ).
cnf(c_0_56,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_23]),c_0_34]) ).
cnf(c_0_57,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_51,c_0_40]) ).
cnf(c_0_58,plain,
join(converse(top),converse(X1)) = converse(top),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_59,axiom,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
composition_distributivity_7 ).
cnf(c_0_60,negated_conjecture,
join(one,converse(sk1)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_54]),c_0_24]),c_0_24]) ).
cnf(c_0_61,negated_conjecture,
join(one,converse(sk2)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_55]),c_0_24]),c_0_24]) ).
cnf(c_0_62,negated_conjecture,
join(one,join(sk2,X1)) = join(one,X1),
inference(spm,[status(thm)],[c_0_34,c_0_55]) ).
cnf(c_0_63,plain,
join(complement(X1),complement(join(complement(X1),complement(X2)))) = join(complement(X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_36]),c_0_40]),c_0_56]),c_0_23]),c_0_57]) ).
cnf(c_0_64,plain,
join(X1,top) = top,
inference(spm,[status(thm)],[c_0_23,c_0_53]) ).
cnf(c_0_65,plain,
join(converse(top),X1) = converse(top),
inference(spm,[status(thm)],[c_0_58,c_0_20]) ).
cnf(c_0_66,negated_conjecture,
join(X1,composition(converse(sk1),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_28]),c_0_28]) ).
cnf(c_0_67,negated_conjecture,
join(X1,composition(converse(sk2),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_61]),c_0_28]),c_0_28]) ).
cnf(c_0_68,negated_conjecture,
join(one,complement(sk2)) = join(top,one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_30]),c_0_23]) ).
cnf(c_0_69,plain,
join(X1,complement(join(X1,complement(X2)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_63,c_0_40]) ).
cnf(c_0_70,plain,
join(converse(X1),converse(complement(X1))) = converse(top),
inference(spm,[status(thm)],[c_0_52,c_0_30]) ).
cnf(c_0_71,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_72,negated_conjecture,
join(converse(X1),composition(converse(X1),sk1)) = converse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_66]),c_0_17]),c_0_20]) ).
cnf(c_0_73,negated_conjecture,
join(converse(X1),composition(converse(X1),sk2)) = converse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_67]),c_0_17]),c_0_20]) ).
cnf(c_0_74,plain,
join(X1,join(complement(X1),X2)) = top,
inference(rw,[status(thm)],[c_0_44,c_0_53]) ).
cnf(c_0_75,negated_conjecture,
join(one,complement(sk2)) = top,
inference(rw,[status(thm)],[c_0_68,c_0_53]) ).
cnf(c_0_76,negated_conjecture,
join(one,join(sk1,X1)) = join(one,X1),
inference(spm,[status(thm)],[c_0_34,c_0_54]) ).
cnf(c_0_77,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_69]),c_0_42]) ).
cnf(c_0_78,plain,
join(converse(X1),converse(complement(X1))) = top,
inference(rw,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_79,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_39]) ).
cnf(c_0_80,negated_conjecture,
join(X1,composition(X1,sk1)) = X1,
inference(spm,[status(thm)],[c_0_72,c_0_20]) ).
cnf(c_0_81,negated_conjecture,
join(X1,composition(X1,sk2)) = X1,
inference(spm,[status(thm)],[c_0_73,c_0_20]) ).
cnf(c_0_82,plain,
join(complement(X1),join(X1,X2)) = top,
inference(spm,[status(thm)],[c_0_74,c_0_40]) ).
cnf(c_0_83,negated_conjecture,
join(X1,composition(complement(sk2),X1)) = composition(top,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_75]),c_0_28]) ).
cnf(c_0_84,negated_conjecture,
join(one,complement(sk1)) = join(top,one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_30]),c_0_23]) ).
cnf(c_0_85,plain,
join(converse(X1),complement(converse(complement(X1)))) = converse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_32]),c_0_79]) ).
cnf(c_0_86,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_87,plain,
join(composition(X1,X2),composition(complement(X1),X2)) = composition(top,X2),
inference(spm,[status(thm)],[c_0_59,c_0_30]) ).
cnf(c_0_88,negated_conjecture,
join(complement(one),complement(sk1)) = complement(sk1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_54]),c_0_23]) ).
cnf(c_0_89,negated_conjecture,
join(X1,join(composition(X1,sk1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_80]) ).
cnf(c_0_90,negated_conjecture,
join(X1,join(composition(X1,sk2),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_81]) ).
cnf(c_0_91,axiom,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
composition_associativity_5 ).
cnf(c_0_92,negated_conjecture,
join(complement(X1),composition(top,X1)) = top,
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_93,negated_conjecture,
join(one,complement(sk1)) = top,
inference(rw,[status(thm)],[c_0_84,c_0_53]) ).
cnf(c_0_94,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_85]),c_0_20]),c_0_20]) ).
cnf(c_0_95,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(spm,[status(thm)],[c_0_78,c_0_20]) ).
cnf(c_0_96,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),X2)),complement(X3)))) = complement(join(complement(composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),X2)),complement(X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]) ).
cnf(c_0_97,negated_conjecture,
join(X1,join(X2,composition(X1,sk1))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_56,c_0_80]) ).
cnf(c_0_98,plain,
join(X1,composition(complement(one),X1)) = composition(top,X1),
inference(spm,[status(thm)],[c_0_87,c_0_28]) ).
cnf(c_0_99,negated_conjecture,
join(complement(one),join(X1,complement(sk1))) = join(X1,complement(sk1)),
inference(spm,[status(thm)],[c_0_56,c_0_88]) ).
cnf(c_0_100,negated_conjecture,
join(X1,join(composition(X1,composition(sk1,sk2)),X2)) = join(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_89]),c_0_91]) ).
cnf(c_0_101,negated_conjecture,
join(X1,join(X2,composition(X1,sk2))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_56,c_0_81]) ).
cnf(c_0_102,negated_conjecture,
join(composition(top,composition(X1,X2)),composition(complement(X1),X2)) = composition(top,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_92]),c_0_91]),c_0_23]) ).
cnf(c_0_103,negated_conjecture,
join(X1,composition(complement(sk1),X1)) = composition(top,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_93]),c_0_28]) ).
cnf(c_0_104,negated_conjecture,
join(X1,composition(complement(X1),sk1)) = join(X1,composition(top,sk1)),
inference(spm,[status(thm)],[c_0_89,c_0_87]) ).
cnf(c_0_105,plain,
join(complement(X1),converse(complement(converse(X1)))) = complement(X1),
inference(spm,[status(thm)],[c_0_94,c_0_40]) ).
cnf(c_0_106,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_95]),c_0_32]),c_0_79]) ).
cnf(c_0_107,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(X3),complement(composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),X2))))) = complement(join(complement(X3),complement(composition(complement(join(complement(X1),complement(composition(X3,converse(X2))))),X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_23]),c_0_23]) ).
cnf(c_0_108,negated_conjecture,
join(complement(one),composition(top,sk1)) = join(sk1,complement(one)),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_109,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_77,c_0_23]) ).
cnf(c_0_110,plain,
join(composition(X1,X2),join(X3,composition(complement(X1),X2))) = join(X3,composition(top,X2)),
inference(spm,[status(thm)],[c_0_56,c_0_87]) ).
cnf(c_0_111,negated_conjecture,
join(complement(sk1),composition(complement(one),composition(sk1,sk2))) = complement(sk1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_88]),c_0_23]) ).
cnf(c_0_112,negated_conjecture,
join(complement(X1),composition(top,composition(X1,sk2))) = join(complement(X1),composition(top,sk2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_23]) ).
cnf(c_0_113,negated_conjecture,
join(complement(sk1),composition(top,sk2)) = join(sk2,complement(sk1)),
inference(spm,[status(thm)],[c_0_101,c_0_103]) ).
cnf(c_0_114,negated_conjecture,
join(complement(X1),complement(composition(X1,sk1))) = complement(composition(X1,sk1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_80]),c_0_23]) ).
cnf(c_0_115,negated_conjecture,
join(X1,complement(composition(complement(X1),sk1))) = join(X1,complement(composition(top,sk1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_104]),c_0_77]) ).
cnf(c_0_116,plain,
complement(converse(complement(converse(X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_105]),c_0_40]),c_0_23]),c_0_106]) ).
cnf(c_0_117,plain,
join(complement(join(complement(composition(X1,converse(X2))),complement(X3))),complement(join(complement(X3),complement(composition(complement(join(complement(X1),complement(composition(X3,X2)))),converse(X2)))))) = complement(join(complement(X3),complement(composition(complement(join(complement(X1),complement(composition(X3,X2)))),converse(X2))))),
inference(spm,[status(thm)],[c_0_107,c_0_20]) ).
cnf(c_0_118,negated_conjecture,
join(complement(one),complement(composition(top,sk1))) = complement(sk1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_108]),c_0_109]),c_0_88]) ).
cnf(c_0_119,negated_conjecture,
join(X1,composition(sk1,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_54]),c_0_28]),c_0_28]) ).
cnf(c_0_120,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))),
inference(fof_simplification,[status(thm)],[goals_19]) ).
cnf(c_0_121,negated_conjecture,
join(complement(sk1),composition(sk1,sk2)) = join(sk2,complement(sk1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_28]),c_0_112]),c_0_113]),c_0_23]) ).
cnf(c_0_122,negated_conjecture,
join(complement(X1),complement(composition(X1,sk2))) = complement(composition(X1,sk2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_81]),c_0_23]) ).
cnf(c_0_123,negated_conjecture,
complement(composition(complement(X1),sk1)) = join(X1,complement(composition(top,sk1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_40]),c_0_115]) ).
cnf(c_0_124,plain,
converse(complement(converse(X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_40,c_0_116]) ).
cnf(c_0_125,negated_conjecture,
composition(sk1,converse(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(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_117,c_0_118]),c_0_28]),c_0_32]),c_0_79]),c_0_40]),c_0_32]),c_0_40]),c_0_39]),c_0_40]),c_0_119]),c_0_32]),c_0_40]),c_0_39]),c_0_40]) ).
cnf(c_0_126,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))),
c_0_120 ).
cnf(c_0_127,negated_conjecture,
complement(composition(sk1,sk2)) = join(complement(sk1),complement(sk2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_121]),c_0_109]),c_0_122]) ).
cnf(c_0_128,negated_conjecture,
composition(complement(X1),sk1) = complement(join(X1,complement(composition(top,sk1)))),
inference(spm,[status(thm)],[c_0_40,c_0_123]) ).
cnf(c_0_129,plain,
converse(complement(X1)) = complement(converse(X1)),
inference(spm,[status(thm)],[c_0_20,c_0_124]) ).
cnf(c_0_130,negated_conjecture,
converse(sk1) = sk1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_125]),c_0_20]),c_0_20]),c_0_125]) ).
cnf(c_0_131,negated_conjecture,
tuple(join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(complement(join(complement(sk1),complement(sk2))),sk3)),join(composition(complement(join(complement(sk1),complement(sk2))),sk3),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))))) != tuple(composition(complement(join(complement(sk1),complement(sk2))),sk3),complement(join(complement(composition(sk1,sk3)),complement(composition(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)],[c_0_126,c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]) ).
cnf(c_0_132,negated_conjecture,
composition(sk1,sk2) = complement(join(complement(sk1),complement(sk2))),
inference(spm,[status(thm)],[c_0_40,c_0_127]) ).
cnf(c_0_133,negated_conjecture,
composition(sk1,complement(converse(X1))) = complement(join(complement(composition(sk1,top)),converse(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(spm,[status(thm)],[c_0_17,c_0_128]),c_0_129]),c_0_52]),c_0_129]),c_0_17]),c_0_130]),c_0_71]),c_0_130]),c_0_129]),c_0_23]) ).
cnf(c_0_134,negated_conjecture,
join(X1,composition(sk2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_55]),c_0_28]),c_0_28]) ).
cnf(c_0_135,negated_conjecture,
tuple(join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(complement(join(complement(sk1),complement(sk2))),sk3)),join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(complement(join(complement(sk1),complement(sk2))),sk3))) != tuple(composition(complement(join(complement(sk1),complement(sk2))),sk3),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3))))),
inference(rw,[status(thm)],[c_0_131,c_0_23]) ).
cnf(c_0_136,negated_conjecture,
composition(complement(join(complement(sk1),complement(sk2))),X1) = composition(sk1,composition(sk2,X1)),
inference(spm,[status(thm)],[c_0_91,c_0_132]) ).
cnf(c_0_137,negated_conjecture,
composition(sk1,complement(X1)) = complement(join(complement(composition(sk1,top)),X1)),
inference(spm,[status(thm)],[c_0_133,c_0_20]) ).
cnf(c_0_138,negated_conjecture,
join(complement(X1),complement(composition(sk2,X1))) = complement(composition(sk2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_134]),c_0_23]) ).
cnf(c_0_139,negated_conjecture,
tuple(join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(sk1,composition(sk2,sk3))),join(complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),composition(sk1,composition(sk2,sk3)))) != tuple(composition(sk1,composition(sk2,sk3)),complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_135,c_0_136]),c_0_136]),c_0_136]) ).
cnf(c_0_140,negated_conjecture,
composition(sk1,X1) = complement(join(complement(composition(sk1,top)),complement(X1))),
inference(spm,[status(thm)],[c_0_137,c_0_40]) ).
cnf(c_0_141,negated_conjecture,
join(complement(X1),join(X2,complement(composition(sk2,X1)))) = join(X2,complement(composition(sk2,X1))),
inference(spm,[status(thm)],[c_0_56,c_0_138]) ).
cnf(c_0_142,negated_conjecture,
$false,
inference(cn,[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(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_139,c_0_140]),c_0_23]),c_0_40]),c_0_34]),c_0_141]),c_0_140]),c_0_41]),c_0_140]),c_0_23]),c_0_40]),c_0_34]),c_0_141]),c_0_140]),c_0_41]),c_0_140]),c_0_140]),c_0_23]),c_0_40]),c_0_34]),c_0_141])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL029-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/10.47 % Computer : n020.cluster.edu
% 0.18/10.47 % Model : x86_64 x86_64
% 0.18/10.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/10.47 % Memory : 8046.5625MB
% 0.18/10.47 % OS : Linux 6.8.0-71-generic
% 0.18/10.47 % CPULimit : 300
% 0.18/10.47 % WCLimit : 300
% 0.18/10.47 % DateTime : Mon Sep 21 04:04:14 UTC 2026
% 0.18/10.47 % CPUTime :
% 0.18/10.47 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.23/10.54 Running first-order theorem proving
% 0.23/10.54 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
% 192.27/38.40 % Version: 3.5.1
% 192.27/38.40 % Preprocessing class: FSMSSMSSSSSNFFN.
% 192.27/38.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 192.27/38.40 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 192.27/38.40 % Starting new_bool_3 with 300s (1) cores
% 192.27/38.40 % Starting new_bool_1 with 300s (1) cores
% 192.27/38.40 % Starting sh5l with 300s (1) cores
% 192.27/38.40 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1961955 completed with status 0
% 192.27/38.40 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 192.27/38.40 % Preprocessing class: FSMSSMSSSSSNFFN.
% 192.27/38.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 192.27/38.40 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 192.27/38.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 192.27/38.40 % No SInE strategy applied
% 192.27/38.40 % Search class: FUUPM-FFMF21-DFFFFFNN
% 192.27/38.40 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 192.27/38.40 % Starting SubtermCWHack with 136s (1) cores
% 192.27/38.40 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 192.27/38.40 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 192.27/38.40 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S2S with 136s (1) cores
% 192.27/38.40 % Starting new_bool_3 with 136s (1) cores
% 192.27/38.40 % H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with pid 1961963 completed with status 0
% 192.27/38.40 % Result found by H----_047_B31_F1_PI_AE_R4_CS_SP_S2S
% 192.27/38.40 % Preprocessing class: FSMSSMSSSSSNFFN.
% 192.27/38.40 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 192.27/38.40 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 192.27/38.40 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 192.27/38.40 % No SInE strategy applied
% 192.27/38.40 % Search class: FUUPM-FFMF21-DFFFFFNN
% 192.27/38.40 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 192.27/38.40 % Starting SubtermCWHack with 136s (1) cores
% 192.27/38.40 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 192.27/38.40 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 192.27/38.40 % Preprocessing time : 0.002 s
% 192.27/38.40
% 192.27/38.40 % Proof found!
% 192.27/38.40 % SZS status Unsatisfiable
% 192.27/38.40 % SZS output start CNFRefutation
% See solution above
% 192.27/38.40 % Parsed axioms : 19
% 192.27/38.40 % Removed by relevancy pruning/SinE : 0
% 192.27/38.40 % Initial clauses : 19
% 192.27/38.40 % Removed in clause preprocessing : 1
% 192.27/38.40 % Initial clauses in saturation : 18
% 192.27/38.40 % Processed clauses : 35733
% 192.27/38.40 % ...of these trivial : 25127
% 192.27/38.40 % ...subsumed : 8281
% 192.27/38.40 % ...remaining for further processing : 2325
% 192.27/38.40 % Other redundant clauses eliminated : 0
% 192.27/38.40 % Clauses deleted for lack of memory : 0
% 192.27/38.40 % Backward-subsumed : 1
% 192.27/38.40 % Backward-rewritten : 542
% 192.27/38.40 % Generated clauses : 1087333
% 192.27/38.40 % ...of the previous two non-redundant : 539714
% 192.27/38.40 % ...aggressively subsumed : 0
% 192.27/38.40 % Contextual simplify-reflections : 0
% 192.27/38.40 % Paramodulations : 1087333
% 192.27/38.40 % Factorizations : 0
% 192.27/38.40 % NegExts : 0
% 192.27/38.40 % Equation resolutions : 0
% 192.27/38.40 % Disequality decompositions : 0
% 192.27/38.40 % Total rewrite steps : 4223116
% 192.27/38.40 % ...of those cached : 3865927
% 192.27/38.40 % Propositional unsat checks : 0
% 192.27/38.40 % Propositional check models : 0
% 192.27/38.40 % Propositional check unsatisfiable : 0
% 192.27/38.40 % Propositional clauses : 0
% 192.27/38.40 % Propositional clauses after purity: 0
% 192.27/38.40 % Propositional unsat core size : 0
% 192.27/38.40 % Propositional preprocessing time : 0.000
% 192.27/38.40 % Propositional encoding time : 0.000
% 192.27/38.40 % Propositional solver time : 0.000
% 192.27/38.40 % Success case prop preproc time : 0.000
% 192.27/38.40 % Success case prop encoding time : 0.000
% 192.27/38.40 % Success case prop solver time : 0.000
% 192.27/38.40 % Current number of processed clauses : 1782
% 192.27/38.40 % Positive orientable unit clauses : 1760
% 192.27/38.40 % Positive unorientable unit clauses: 22
% 192.27/38.40 % Negative unit clauses : 0
% 192.27/38.40 % Non-unit-clauses : 0
% 192.27/38.40 % Current number of unprocessed clauses: 498924
% 192.27/38.40 % ...number of literals in the above : 498924
% 192.27/38.40 % Current number of archived formulas : 0
% 192.27/38.40 % Current number of archived clauses : 544
% 192.27/38.40 % Clause-clause subsumption calls (NU) : 0
% 192.27/38.40 % Rec. Clause-clause subsumption calls : 0
% 192.27/38.40 % Non-unit clause-clause subsumptions : 0
% 192.27/38.40 % Unit Clause-clause subsumption calls : 1164
% 192.27/38.40 % Rewrite failures with RHS unbound : 4553
% 192.27/38.40 % BW rewrite match attempts : 62321
% 192.27/38.40 % BW rewrite match successes : 2634
% 192.27/38.40 % Condensation attempts : 0
% 192.27/38.40 % Condensation successes : 0
% 192.27/38.40 % Termbank termtop insertions : 24595256
% 192.27/38.40 % Search garbage collected termcells : 2
% 192.27/38.40
% 192.27/38.40 % -------------------------------------------------
% 192.27/38.40 % User time : 25.837 s
% 192.27/38.40 % System time : 0.942 s
% 192.27/38.40 % Total time : 26.779 s
% 192.27/38.40 % Maximum resident set size: 3336 pages
% 192.27/38.40
% 192.27/38.40 % -------------------------------------------------
% 192.27/38.40 % User time : 132.039 s
% 192.27/38.40 % System time : 4.542 s
% 192.27/38.40 % Total time : 136.581 s
% 192.27/38.40 % Maximum resident set size: 4608 pages
% 192.27/38.40 % E exiting
%------------------------------------------------------------------------------