%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : REL029-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 273.88s 36.23s
% Output : CNFRefutation 273.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 16
% Syntax : Number of clauses : 161 ( 161 unt; 0 nHn; 32 RR)
% Number of literals : 161 ( 160 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 196 ( 11 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(composition_identity_6,axiom,
composition(X1,one) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',composition_identity_6) ).
cnf(converse_idempotence_8,axiom,
converse(converse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',converse_idempotence_8) ).
cnf(converse_cancellativity_11,axiom,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',converse_cancellativity_11) ).
cnf(maddux1_join_commutativity_1,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',maddux1_join_commutativity_1) ).
cnf(def_zero_13,axiom,
zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',def_zero_13) ).
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_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(maddux2_join_associativity_2,axiom,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',maddux2_join_associativity_2) ).
cnf(converse_additivity_9,axiom,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',converse_additivity_9) ).
cnf(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(goals_15,negated_conjecture,
join(sk2,one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_15) ).
cnf(goals_14,negated_conjecture,
join(sk1,one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).
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(goals_16,negated_conjecture,
meet(composition(sk1,sk3),composition(sk2,sk3)) != composition(meet(sk1,sk2),sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_16) ).
cnf(c_0_16,axiom,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
converse_multiplicativity_10 ).
cnf(c_0_17,axiom,
composition(X1,one) = X1,
composition_identity_6 ).
cnf(c_0_18,plain,
composition(converse(one),converse(X1)) = converse(X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,axiom,
converse(converse(X1)) = X1,
converse_idempotence_8 ).
cnf(c_0_20,plain,
composition(converse(one),X1) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,axiom,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
converse_cancellativity_11 ).
cnf(c_0_22,axiom,
join(X1,X2) = join(X2,X1),
maddux1_join_commutativity_1 ).
cnf(c_0_23,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_17,c_0_20]) ).
cnf(c_0_24,axiom,
zero = meet(X1,complement(X1)),
def_zero_13 ).
cnf(c_0_25,axiom,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
maddux4_definiton_of_meet_4 ).
cnf(c_0_26,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_20,c_0_23]) ).
cnf(c_0_28,plain,
zero = complement(join(complement(X1),complement(complement(X1)))),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,axiom,
top = join(X1,complement(X1)),
def_top_12 ).
cnf(c_0_30,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_23]),c_0_27]) ).
cnf(c_0_31,plain,
complement(top) = zero,
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,axiom,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
maddux3_a_kind_of_de_Morgan_3 ).
cnf(c_0_33,axiom,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
maddux2_join_associativity_2 ).
cnf(c_0_34,plain,
join(zero,zero) = zero,
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[c_0_32,c_0_22]) ).
cnf(c_0_36,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,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_35,c_0_30]),c_0_29]),c_0_31]),c_0_22]) ).
cnf(c_0_38,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_39,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_40,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_39]) ).
cnf(c_0_41,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_33,c_0_40]) ).
cnf(c_0_42,plain,
join(top,zero) = top,
inference(spm,[status(thm)],[c_0_29,c_0_31]) ).
cnf(c_0_43,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_33,c_0_29]) ).
cnf(c_0_44,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_35]),c_0_22]) ).
cnf(c_0_45,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_41,c_0_22]) ).
cnf(c_0_46,plain,
join(top,join(zero,X1)) = join(top,X1),
inference(spm,[status(thm)],[c_0_33,c_0_42]) ).
cnf(c_0_47,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_30]),c_0_29]) ).
cnf(c_0_48,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,axiom,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
converse_additivity_9 ).
cnf(c_0_50,plain,
join(top,X1) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_37]),c_0_47]) ).
cnf(c_0_51,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_48,c_0_39]) ).
cnf(c_0_52,plain,
join(converse(top),converse(X1)) = converse(top),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_53,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_35,c_0_35]),c_0_39]),c_0_22]),c_0_33]),c_0_51]) ).
cnf(c_0_54,plain,
join(X1,top) = top,
inference(spm,[status(thm)],[c_0_22,c_0_50]) ).
cnf(c_0_55,plain,
join(converse(top),X1) = converse(top),
inference(spm,[status(thm)],[c_0_52,c_0_19]) ).
cnf(c_0_56,plain,
join(X1,complement(join(X1,complement(X2)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_53,c_0_39]) ).
cnf(c_0_57,plain,
join(converse(X1),converse(complement(X1))) = converse(top),
inference(spm,[status(thm)],[c_0_49,c_0_29]) ).
cnf(c_0_58,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_59,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_56]),c_0_41]) ).
cnf(c_0_60,plain,
join(converse(X1),converse(complement(X1))) = top,
inference(rw,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_61,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_38]) ).
cnf(c_0_62,plain,
join(converse(X1),complement(converse(complement(X1)))) = converse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_31]),c_0_61]) ).
cnf(c_0_63,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_62]),c_0_19]),c_0_19]) ).
cnf(c_0_64,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(spm,[status(thm)],[c_0_60,c_0_19]) ).
cnf(c_0_65,axiom,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
composition_distributivity_7 ).
cnf(c_0_66,plain,
join(converse(zero),converse(X1)) = converse(X1),
inference(spm,[status(thm)],[c_0_49,c_0_38]) ).
cnf(c_0_67,plain,
join(complement(X1),converse(complement(converse(X1)))) = complement(X1),
inference(spm,[status(thm)],[c_0_63,c_0_39]) ).
cnf(c_0_68,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_64]),c_0_31]),c_0_61]) ).
cnf(c_0_69,negated_conjecture,
join(sk2,one) = one,
goals_15 ).
cnf(c_0_70,plain,
join(X1,join(complement(X1),X2)) = top,
inference(rw,[status(thm)],[c_0_43,c_0_50]) ).
cnf(c_0_71,plain,
composition(converse(X1),join(converse(X2),converse(X3))) = join(composition(converse(X1),converse(X2)),composition(converse(X1),converse(X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_65]),c_0_49]),c_0_16]),c_0_16]),c_0_49]) ).
cnf(c_0_72,plain,
join(converse(zero),X1) = X1,
inference(spm,[status(thm)],[c_0_66,c_0_19]) ).
cnf(c_0_73,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_51,c_0_67]),c_0_39]),c_0_22]),c_0_68]) ).
cnf(c_0_74,negated_conjecture,
join(one,converse(sk2)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_69]),c_0_23]),c_0_22]),c_0_23]) ).
cnf(c_0_75,negated_conjecture,
join(sk1,one) = one,
goals_14 ).
cnf(c_0_76,negated_conjecture,
join(sk2,join(one,X1)) = join(one,X1),
inference(spm,[status(thm)],[c_0_33,c_0_69]) ).
cnf(c_0_77,plain,
join(X1,join(X2,complement(X1))) = top,
inference(spm,[status(thm)],[c_0_70,c_0_22]) ).
cnf(c_0_78,plain,
composition(converse(X1),join(one,converse(X2))) = join(converse(X1),composition(converse(X1),converse(X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_23]),c_0_17]),c_0_22]),c_0_22]) ).
cnf(c_0_79,negated_conjecture,
join(X1,composition(sk2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_69]),c_0_27]),c_0_22]),c_0_27]) ).
cnf(c_0_80,plain,
join(converse(complement(X1)),composition(converse(complement(composition(X2,X1))),X2)) = converse(complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_26]),c_0_16]),c_0_19]) ).
cnf(c_0_81,plain,
converse(zero) = zero,
inference(spm,[status(thm)],[c_0_61,c_0_72]) ).
cnf(c_0_82,plain,
converse(complement(converse(X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_39,c_0_73]) ).
cnf(c_0_83,negated_conjecture,
join(X1,composition(converse(sk2),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_74]),c_0_27]),c_0_27]) ).
cnf(c_0_84,negated_conjecture,
join(one,converse(sk1)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_75]),c_0_23]),c_0_22]),c_0_23]) ).
cnf(c_0_85,negated_conjecture,
join(one,complement(sk2)) = top,
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_86,plain,
composition(X1,join(one,converse(X2))) = join(X1,composition(X1,converse(X2))),
inference(spm,[status(thm)],[c_0_78,c_0_19]) ).
cnf(c_0_87,negated_conjecture,
join(X1,join(composition(sk2,X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_33,c_0_79]) ).
cnf(c_0_88,plain,
composition(converse(complement(composition(X1,top))),X1) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_31]),c_0_81]),c_0_38]),c_0_81]) ).
cnf(c_0_89,plain,
converse(complement(X1)) = complement(converse(X1)),
inference(spm,[status(thm)],[c_0_19,c_0_82]) ).
cnf(c_0_90,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_49,c_0_83]),c_0_16]),c_0_19]) ).
cnf(c_0_91,negated_conjecture,
join(X1,composition(converse(sk1),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_84]),c_0_27]),c_0_27]) ).
cnf(c_0_92,plain,
join(X1,join(X2,X3)) = join(X2,join(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_22]),c_0_33]) ).
cnf(c_0_93,negated_conjecture,
join(X1,composition(complement(sk2),X1)) = composition(top,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_85]),c_0_27]) ).
cnf(c_0_94,plain,
composition(X1,join(one,X2)) = join(X1,composition(X1,X2)),
inference(spm,[status(thm)],[c_0_86,c_0_19]) ).
cnf(c_0_95,negated_conjecture,
join(X1,composition(converse(sk2),composition(sk2,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_83]),c_0_79]) ).
cnf(c_0_96,plain,
join(composition(X1,X2),composition(complement(X1),X2)) = composition(top,X2),
inference(spm,[status(thm)],[c_0_65,c_0_29]) ).
cnf(c_0_97,plain,
composition(complement(composition(top,converse(X1))),X1) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_89]),c_0_16]),c_0_58]) ).
cnf(c_0_98,axiom,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
composition_associativity_5 ).
cnf(c_0_99,plain,
join(complement(X1),join(X1,X2)) = top,
inference(spm,[status(thm)],[c_0_70,c_0_39]) ).
cnf(c_0_100,negated_conjecture,
join(X1,composition(X1,sk2)) = X1,
inference(spm,[status(thm)],[c_0_90,c_0_19]) ).
cnf(c_0_101,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_49,c_0_91]),c_0_16]),c_0_19]) ).
cnf(c_0_102,negated_conjecture,
join(X1,join(X2,composition(complement(sk2),X1))) = join(X2,composition(top,X1)),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_103,negated_conjecture,
join(X1,composition(X1,composition(converse(sk2),sk2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_17]),c_0_17]) ).
cnf(c_0_104,plain,
composition(top,composition(converse(X1),X1)) = composition(top,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_39]),c_0_98]),c_0_38]) ).
cnf(c_0_105,negated_conjecture,
join(complement(X1),composition(top,X1)) = top,
inference(spm,[status(thm)],[c_0_99,c_0_93]) ).
cnf(c_0_106,negated_conjecture,
join(sk1,join(one,X1)) = join(one,X1),
inference(spm,[status(thm)],[c_0_33,c_0_75]) ).
cnf(c_0_107,negated_conjecture,
join(X1,composition(sk1,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_75]),c_0_27]),c_0_22]),c_0_27]) ).
cnf(c_0_108,negated_conjecture,
join(X1,join(composition(X1,sk2),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_33,c_0_100]) ).
cnf(c_0_109,negated_conjecture,
join(X1,composition(X1,sk1)) = X1,
inference(spm,[status(thm)],[c_0_101,c_0_19]) ).
cnf(c_0_110,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_59,c_0_22]) ).
cnf(c_0_111,negated_conjecture,
join(complement(sk2),composition(converse(sk2),sk2)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_103]),c_0_104]),c_0_105]),c_0_22]) ).
cnf(c_0_112,negated_conjecture,
join(one,complement(sk1)) = top,
inference(spm,[status(thm)],[c_0_106,c_0_77]) ).
cnf(c_0_113,negated_conjecture,
join(X1,join(composition(sk1,X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_33,c_0_107]) ).
cnf(c_0_114,negated_conjecture,
join(X1,composition(X1,composition(sk2,sk1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_100]),c_0_98]) ).
cnf(c_0_115,negated_conjecture,
join(one,converse(complement(sk2))) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_85]),c_0_23]),c_0_58]) ).
cnf(c_0_116,negated_conjecture,
composition(converse(sk2),sk2) = sk2,
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_110,c_0_111]),c_0_31]),c_0_61]),c_0_39]),c_0_22]),c_0_83]) ).
cnf(c_0_117,negated_conjecture,
join(X1,join(X2,composition(X1,sk1))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_92,c_0_109]) ).
cnf(c_0_118,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_65,c_0_105]),c_0_98]),c_0_22]) ).
cnf(c_0_119,negated_conjecture,
join(X1,composition(complement(sk1),X1)) = composition(top,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_112]),c_0_27]) ).
cnf(c_0_120,negated_conjecture,
join(X1,composition(converse(sk1),composition(sk1,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_91]),c_0_107]) ).
cnf(c_0_121,negated_conjecture,
join(X1,join(X2,composition(X1,composition(sk2,sk1)))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_92,c_0_114]) ).
cnf(c_0_122,negated_conjecture,
join(X1,composition(converse(complement(sk2)),X1)) = composition(top,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_115]),c_0_27]) ).
cnf(c_0_123,negated_conjecture,
converse(sk2) = sk2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_116]),c_0_19]),c_0_116]) ).
cnf(c_0_124,negated_conjecture,
join(complement(X1),composition(top,composition(X1,sk1))) = join(complement(X1),composition(top,sk1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117,c_0_118]),c_0_22]) ).
cnf(c_0_125,negated_conjecture,
join(complement(sk2),composition(top,sk1)) = join(sk1,complement(sk2)),
inference(spm,[status(thm)],[c_0_117,c_0_93]) ).
cnf(c_0_126,negated_conjecture,
join(X1,join(X2,composition(complement(sk1),X1))) = join(X2,composition(top,X1)),
inference(spm,[status(thm)],[c_0_92,c_0_119]) ).
cnf(c_0_127,negated_conjecture,
join(X1,composition(X1,composition(converse(sk1),sk1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_120]),c_0_17]),c_0_17]) ).
cnf(c_0_128,plain,
composition(X1,join(converse(X2),converse(X3))) = join(composition(X1,converse(X2)),composition(X1,converse(X3))),
inference(spm,[status(thm)],[c_0_71,c_0_19]) ).
cnf(c_0_129,negated_conjecture,
join(complement(sk2),composition(sk2,sk1)) = join(sk1,complement(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(spm,[status(thm)],[c_0_121,c_0_122]),c_0_89]),c_0_123]),c_0_124]),c_0_125]),c_0_89]),c_0_123]),c_0_22]) ).
cnf(c_0_130,negated_conjecture,
join(complement(X1),complement(composition(X1,sk1))) = complement(composition(X1,sk1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_109]),c_0_22]) ).
cnf(c_0_131,negated_conjecture,
join(complement(sk1),composition(converse(sk1),sk1)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_104]),c_0_105]),c_0_22]) ).
cnf(c_0_132,plain,
composition(X1,join(converse(X2),X3)) = join(composition(X1,converse(X2)),composition(X1,X3)),
inference(spm,[status(thm)],[c_0_128,c_0_19]) ).
cnf(c_0_133,negated_conjecture,
complement(composition(sk2,sk1)) = join(complement(sk1),complement(sk2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_129]),c_0_110]),c_0_22]),c_0_130]) ).
cnf(c_0_134,negated_conjecture,
composition(converse(sk1),sk1) = sk1,
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_110,c_0_131]),c_0_31]),c_0_61]),c_0_39]),c_0_22]),c_0_91]) ).
cnf(c_0_135,plain,
composition(X1,join(X2,X3)) = join(composition(X1,X2),composition(X1,X3)),
inference(spm,[status(thm)],[c_0_132,c_0_19]) ).
cnf(c_0_136,negated_conjecture,
join(complement(X1),complement(composition(sk2,X1))) = complement(composition(sk2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_79]),c_0_22]) ).
cnf(c_0_137,negated_conjecture,
meet(composition(sk1,sk3),composition(sk2,sk3)) != composition(meet(sk1,sk2),sk3),
inference(fof_simplification,[status(thm)],[goals_16]) ).
cnf(c_0_138,negated_conjecture,
composition(sk2,sk1) = complement(join(complement(sk1),complement(sk2))),
inference(spm,[status(thm)],[c_0_39,c_0_133]) ).
cnf(c_0_139,negated_conjecture,
converse(sk1) = sk1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_134]),c_0_19]),c_0_134]) ).
cnf(c_0_140,negated_conjecture,
join(X1,complement(join(composition(sk2,X1),X2))) = join(X1,complement(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_59]),c_0_87]) ).
cnf(c_0_141,plain,
join(composition(X1,X2),composition(X1,complement(X2))) = composition(X1,top),
inference(spm,[status(thm)],[c_0_135,c_0_29]) ).
cnf(c_0_142,negated_conjecture,
join(X1,complement(composition(sk2,complement(X1)))) = complement(composition(sk2,complement(X1))),
inference(spm,[status(thm)],[c_0_136,c_0_39]) ).
cnf(c_0_143,negated_conjecture,
join(complement(X1),complement(composition(sk1,X1))) = complement(composition(sk1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_107]),c_0_22]) ).
cnf(c_0_144,negated_conjecture,
meet(composition(sk1,sk3),composition(sk2,sk3)) != composition(meet(sk1,sk2),sk3),
c_0_137 ).
cnf(c_0_145,negated_conjecture,
composition(sk1,sk2) = complement(join(complement(sk1),complement(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_16,c_0_138]),c_0_89]),c_0_49]),c_0_89]),c_0_139]),c_0_89]),c_0_123]),c_0_139]),c_0_123]) ).
cnf(c_0_146,negated_conjecture,
composition(complement(join(complement(sk1),complement(sk2))),X1) = composition(sk2,composition(sk1,X1)),
inference(spm,[status(thm)],[c_0_98,c_0_138]) ).
cnf(c_0_147,negated_conjecture,
complement(composition(sk2,complement(X1))) = join(X1,complement(composition(sk2,top))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_142]) ).
cnf(c_0_148,negated_conjecture,
join(X1,complement(join(composition(sk1,X1),X2))) = join(X1,complement(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_59]),c_0_113]) ).
cnf(c_0_149,negated_conjecture,
join(X1,complement(composition(sk1,complement(X1)))) = complement(composition(sk1,complement(X1))),
inference(spm,[status(thm)],[c_0_143,c_0_39]) ).
cnf(c_0_150,negated_conjecture,
join(X1,join(X2,composition(sk1,X1))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_92,c_0_107]) ).
cnf(c_0_151,negated_conjecture,
complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))) != composition(complement(join(complement(sk1),complement(sk2))),sk3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_144,c_0_25]),c_0_25]) ).
cnf(c_0_152,negated_conjecture,
composition(sk2,composition(sk1,X1)) = composition(sk1,composition(sk2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_145]),c_0_146]) ).
cnf(c_0_153,negated_conjecture,
composition(sk2,complement(X1)) = complement(join(X1,complement(composition(sk2,top)))),
inference(spm,[status(thm)],[c_0_39,c_0_147]) ).
cnf(c_0_154,negated_conjecture,
complement(composition(sk1,complement(X1))) = join(X1,complement(composition(sk1,top))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_141]),c_0_149]) ).
cnf(c_0_155,negated_conjecture,
join(X1,complement(join(X2,composition(sk1,X1)))) = join(X1,complement(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_150]),c_0_110]) ).
cnf(c_0_156,negated_conjecture,
composition(sk1,composition(sk2,sk3)) != complement(join(complement(composition(sk1,sk3)),complement(composition(sk2,sk3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_151,c_0_146]),c_0_152]) ).
cnf(c_0_157,negated_conjecture,
composition(sk2,X1) = complement(join(complement(X1),complement(composition(sk2,top)))),
inference(spm,[status(thm)],[c_0_153,c_0_39]) ).
cnf(c_0_158,negated_conjecture,
composition(sk1,complement(X1)) = complement(join(X1,complement(composition(sk1,top)))),
inference(spm,[status(thm)],[c_0_39,c_0_154]) ).
cnf(c_0_159,negated_conjecture,
join(complement(X1),complement(composition(sk1,top))) = complement(composition(sk1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_155,c_0_141]),c_0_143]) ).
cnf(c_0_160,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)],[c_0_156,c_0_157]),c_0_158]),c_0_33]),c_0_22]),c_0_159]),c_0_157]),c_0_39]),c_0_33]),c_0_92]),c_0_41])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL029-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 04:02:38 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 273.88/36.23 % Version: 3.5.1
% 273.88/36.23 % Preprocessing class: FSMSSMSSSSSNFFN.
% 273.88/36.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 273.88/36.23 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 273.88/36.23 % Starting new_bool_3 with 300s (1) cores
% 273.88/36.23 % Starting new_bool_1 with 300s (1) cores
% 273.88/36.23 % Starting sh5l with 300s (1) cores
% 273.88/36.23 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 4101725 completed with status 0
% 273.88/36.23 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 273.88/36.23 % Preprocessing class: FSMSSMSSSSSNFFN.
% 273.88/36.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 273.88/36.23 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 273.88/36.23 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 273.88/36.23 % No SInE strategy applied
% 273.88/36.23 % Search class: FUUPM-FFSF21-MFFFFFNN
% 273.88/36.23 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 273.88/36.23 % Starting SubtermCWHack with 136s (1) cores
% 273.88/36.23 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 273.88/36.23 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 273.88/36.23 % Starting G-E--_060_C18_F1_PI_SE_CS_SP_CO_S0Y with 136s (1) cores
% 273.88/36.23 % Starting U----_043_B31_F1_PI_AE_CS_SP_S2S with 136s (1) cores
% 273.88/36.23 % H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with pid 4101731 completed with status 0
% 273.88/36.23 % Result found by H----_047_B31_F1_PI_AE_R4_CS_SP_S2S
% 273.88/36.23 % Preprocessing class: FSMSSMSSSSSNFFN.
% 273.88/36.23 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 273.88/36.23 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 273.88/36.23 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 273.88/36.23 % No SInE strategy applied
% 273.88/36.23 % Search class: FUUPM-FFSF21-MFFFFFNN
% 273.88/36.23 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 273.88/36.23 % Starting SubtermCWHack with 136s (1) cores
% 273.88/36.23 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 273.88/36.23 % Starting H----_047_B31_F1_PI_AE_R4_CS_SP_S2S with 136s (1) cores
% 273.88/36.23 % Preprocessing time : 0.001 s
% 273.88/36.23
% 273.88/36.23 % Proof found!
% 273.88/36.23 % SZS status Unsatisfiable
% 273.88/36.23 % SZS output start CNFRefutation
% See solution above
% 273.88/36.23 % Parsed axioms : 16
% 273.88/36.23 % Removed by relevancy pruning/SinE : 0
% 273.88/36.23 % Initial clauses : 16
% 273.88/36.23 % Removed in clause preprocessing : 1
% 273.88/36.23 % Initial clauses in saturation : 15
% 273.88/36.23 % Processed clauses : 53433
% 273.88/36.23 % ...of these trivial : 35337
% 273.88/36.23 % ...subsumed : 15258
% 273.88/36.23 % ...remaining for further processing : 2838
% 273.88/36.23 % Other redundant clauses eliminated : 0
% 273.88/36.23 % Clauses deleted for lack of memory : 0
% 273.88/36.23 % Backward-subsumed : 1
% 273.88/36.23 % Backward-rewritten : 661
% 273.88/36.23 % Generated clauses : 1734655
% 273.88/36.23 % ...of the previous two non-redundant : 873884
% 273.88/36.23 % ...aggressively subsumed : 0
% 273.88/36.23 % Contextual simplify-reflections : 0
% 273.88/36.23 % Paramodulations : 1734655
% 273.88/36.23 % Factorizations : 0
% 273.88/36.23 % NegExts : 0
% 273.88/36.23 % Equation resolutions : 0
% 273.88/36.23 % Disequality decompositions : 0
% 273.88/36.23 % Total rewrite steps : 5372154
% 273.88/36.23 % ...of those cached : 4898891
% 273.88/36.23 % Propositional unsat checks : 0
% 273.88/36.23 % Propositional check models : 0
% 273.88/36.23 % Propositional check unsatisfiable : 0
% 273.88/36.23 % Propositional clauses : 0
% 273.88/36.23 % Propositional clauses after purity: 0
% 273.88/36.23 % Propositional unsat core size : 0
% 273.88/36.23 % Propositional preprocessing time : 0.000
% 273.88/36.23 % Propositional encoding time : 0.000
% 273.88/36.23 % Propositional solver time : 0.000
% 273.88/36.23 % Success case prop preproc time : 0.000
% 273.88/36.23 % Success case prop encoding time : 0.000
% 273.88/36.23 % Success case prop solver time : 0.000
% 273.88/36.23 % Current number of processed clauses : 2176
% 273.88/36.23 % Positive orientable unit clauses : 2150
% 273.88/36.23 % Positive unorientable unit clauses: 26
% 273.88/36.23 % Negative unit clauses : 0
% 273.88/36.23 % Non-unit-clauses : 0
% 273.88/36.23 % Current number of unprocessed clauses: 813160
% 273.88/36.23 % ...number of literals in the above : 813160
% 273.88/36.23 % Current number of archived formulas : 0
% 273.88/36.23 % Current number of archived clauses : 663
% 273.88/36.23 % Clause-clause subsumption calls (NU) : 0
% 273.88/36.23 % Rec. Clause-clause subsumption calls : 0
% 273.88/36.23 % Non-unit clause-clause subsumptions : 0
% 273.88/36.23 % Unit Clause-clause subsumption calls : 579
% 273.88/36.23 % Rewrite failures with RHS unbound : 10328
% 273.88/36.23 % BW rewrite match attempts : 89969
% 273.88/36.23 % BW rewrite match successes : 4933
% 273.88/36.23 % Condensation attempts : 0
% 273.88/36.23 % Condensation successes : 0
% 273.88/36.23 % Termbank termtop insertions : 32309134
% 273.88/36.23 % Search garbage collected termcells : 2
% 273.88/36.23
% 273.88/36.23 % -------------------------------------------------
% 273.88/36.23 % User time : 33.554 s
% 273.88/36.23 % System time : 1.264 s
% 273.88/36.23 % Total time : 34.818 s
% 273.88/36.23 % Maximum resident set size: 3644 pages
% 273.88/36.23
% 273.88/36.23 % -------------------------------------------------
% 273.88/36.23 % User time : 167.691 s
% 273.88/36.23 % System time : 6.386 s
% 273.88/36.23 % Total time : 174.076 s
% 273.88/36.23 % Maximum resident set size: 4864 pages
% 273.88/36.23 % E exiting
%------------------------------------------------------------------------------