%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : REL026-2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:03:59 PM UTC 2026
% Result : Unsatisfiable 27.66s 4.65s
% Output : CNFRefutation 27.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 15
% Syntax : Number of clauses : 140 ( 135 unt; 0 nHn; 36 RR)
% Number of literals : 145 ( 144 equ; 10 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 161 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(converse_multiplicativity_10,axiom,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',converse_multiplicativity_10) ).
cnf(converse_idempotence_8,axiom,
converse(converse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',converse_idempotence_8) ).
cnf(composition_identity_6,axiom,
composition(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',composition_identity_6) ).
cnf(converse_cancellativity_11,axiom,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',converse_cancellativity_11) ).
cnf(maddux1_join_commutativity_1,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',maddux1_join_commutativity_1) ).
cnf(def_zero_13,axiom,
zero = meet(X1,complement(X1)),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/REL001-0.ax',maddux4_definiton_of_meet_4) ).
cnf(def_top_12,axiom,
top = join(X1,complement(X1)),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/Axioms/REL001-0.ax',maddux2_join_associativity_2) ).
cnf(composition_distributivity_7,axiom,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',composition_distributivity_7) ).
cnf(converse_additivity_9,axiom,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',converse_additivity_9) ).
cnf(goals_14,negated_conjecture,
join(sk1,one) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_14) ).
cnf(composition_associativity_5,axiom,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',composition_associativity_5) ).
cnf(goals_15,negated_conjecture,
( join(meet(composition(sk1,top),sk2),composition(sk1,sk2)) != composition(sk1,sk2)
| join(composition(sk1,sk2),meet(composition(sk1,top),sk2)) != meet(composition(sk1,top),sk2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_15) ).
cnf(c_0_15,axiom,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
converse_multiplicativity_10 ).
cnf(c_0_16,axiom,
converse(converse(X1)) = X1,
converse_idempotence_8 ).
cnf(c_0_17,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,axiom,
composition(X1,one) = X1,
composition_identity_6 ).
cnf(c_0_19,plain,
composition(converse(one),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_16]) ).
cnf(c_0_20,axiom,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
converse_cancellativity_11 ).
cnf(c_0_21,axiom,
join(X1,X2) = join(X2,X1),
maddux1_join_commutativity_1 ).
cnf(c_0_22,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,axiom,
zero = meet(X1,complement(X1)),
def_zero_13 ).
cnf(c_0_24,axiom,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
maddux4_definiton_of_meet_4 ).
cnf(c_0_25,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_19,c_0_22]) ).
cnf(c_0_27,plain,
zero = complement(join(complement(X1),complement(complement(X1)))),
inference(rw,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,axiom,
top = join(X1,complement(X1)),
def_top_12 ).
cnf(c_0_29,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_22]),c_0_26]) ).
cnf(c_0_30,plain,
complement(top) = zero,
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,axiom,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
maddux3_a_kind_of_de_Morgan_3 ).
cnf(c_0_32,axiom,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
maddux2_join_associativity_2 ).
cnf(c_0_33,plain,
join(zero,zero) = zero,
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[c_0_31,c_0_21]) ).
cnf(c_0_35,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,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_34,c_0_28]),c_0_29]),c_0_30]),c_0_21]) ).
cnf(c_0_37,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_39,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_29,c_0_38]) ).
cnf(c_0_40,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_32,c_0_28]) ).
cnf(c_0_41,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_32,c_0_39]) ).
cnf(c_0_42,axiom,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
composition_distributivity_7 ).
cnf(c_0_43,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_29]),c_0_28]) ).
cnf(c_0_44,axiom,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
converse_additivity_9 ).
cnf(c_0_45,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_34]),c_0_21]) ).
cnf(c_0_46,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_41,c_0_21]) ).
cnf(c_0_47,plain,
join(X1,composition(X2,X1)) = composition(join(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_26]),c_0_21]) ).
cnf(c_0_48,negated_conjecture,
join(sk1,one) = one,
goals_14 ).
cnf(c_0_49,plain,
join(X1,top) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_28]),c_0_43]) ).
cnf(c_0_50,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(spm,[status(thm)],[c_0_44,c_0_16]) ).
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,negated_conjecture,
join(X1,composition(sk1,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_26]) ).
cnf(c_0_53,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_54,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_21,c_0_49]) ).
cnf(c_0_55,plain,
join(X1,converse(top)) = converse(top),
inference(spm,[status(thm)],[c_0_50,c_0_49]) ).
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_32,c_0_21]),c_0_32]) ).
cnf(c_0_57,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_51,c_0_38]) ).
cnf(c_0_58,plain,
join(X1,composition(X2,X1)) = composition(join(one,X2),X1),
inference(spm,[status(thm)],[c_0_42,c_0_26]) ).
cnf(c_0_59,negated_conjecture,
join(X1,composition(X1,converse(sk1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_52]),c_0_16]),c_0_53]) ).
cnf(c_0_60,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_61,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_34,c_0_34]),c_0_38]),c_0_56]),c_0_21]),c_0_57]) ).
cnf(c_0_62,negated_conjecture,
join(X1,composition(converse(sk1),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_26]),c_0_26]) ).
cnf(c_0_63,plain,
composition(converse(X1),top) = converse(composition(top,X1)),
inference(spm,[status(thm)],[c_0_17,c_0_60]) ).
cnf(c_0_64,plain,
composition(top,converse(X1)) = converse(composition(X1,top)),
inference(spm,[status(thm)],[c_0_15,c_0_60]) ).
cnf(c_0_65,plain,
join(X1,complement(join(X1,complement(X2)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_61,c_0_38]) ).
cnf(c_0_66,negated_conjecture,
join(X1,composition(X1,sk1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_62]),c_0_16]),c_0_15]),c_0_16]) ).
cnf(c_0_67,plain,
composition(X1,complement(converse(composition(top,X1)))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_63]),c_0_30]),c_0_16]),c_0_37]),c_0_30]) ).
cnf(c_0_68,plain,
converse(composition(top,top)) = composition(top,top),
inference(spm,[status(thm)],[c_0_64,c_0_60]) ).
cnf(c_0_69,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_65]),c_0_41]) ).
cnf(c_0_70,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_28]),c_0_60]) ).
cnf(c_0_71,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_21,c_0_37]) ).
cnf(c_0_72,negated_conjecture,
join(X1,join(composition(X1,sk1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_32,c_0_66]) ).
cnf(c_0_73,plain,
composition(top,complement(composition(top,top))) = zero,
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_74,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_30]),c_0_71]) ).
cnf(c_0_75,negated_conjecture,
join(X1,composition(join(X1,X2),sk1)) = join(X1,composition(X2,sk1)),
inference(spm,[status(thm)],[c_0_72,c_0_42]) ).
cnf(c_0_76,plain,
composition(X1,complement(composition(top,top))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_73]),c_0_37]),c_0_54]),c_0_73]) ).
cnf(c_0_77,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_74]),c_0_16]),c_0_16]) ).
cnf(c_0_78,plain,
join(X1,join(complement(X1),X2)) = top,
inference(rw,[status(thm)],[c_0_40,c_0_54]) ).
cnf(c_0_79,plain,
join(X1,composition(top,X1)) = composition(top,X1),
inference(spm,[status(thm)],[c_0_58,c_0_49]) ).
cnf(c_0_80,negated_conjecture,
join(X1,composition(complement(X1),sk1)) = join(X1,composition(top,sk1)),
inference(spm,[status(thm)],[c_0_75,c_0_28]) ).
cnf(c_0_81,plain,
complement(composition(top,top)) = zero,
inference(spm,[status(thm)],[c_0_26,c_0_76]) ).
cnf(c_0_82,negated_conjecture,
join(X1,join(X2,composition(X1,sk1))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_56,c_0_66]) ).
cnf(c_0_83,plain,
join(X1,composition(complement(one),X1)) = composition(top,X1),
inference(spm,[status(thm)],[c_0_58,c_0_28]) ).
cnf(c_0_84,plain,
join(complement(X1),complement(join(X1,X2))) = complement(X1),
inference(spm,[status(thm)],[c_0_45,c_0_38]) ).
cnf(c_0_85,plain,
join(complement(X1),converse(complement(converse(X1)))) = complement(X1),
inference(spm,[status(thm)],[c_0_77,c_0_38]) ).
cnf(c_0_86,plain,
join(X1,composition(top,complement(X1))) = top,
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_87,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_66]),c_0_21]) ).
cnf(c_0_88,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_69,c_0_80]),c_0_69]) ).
cnf(c_0_89,axiom,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
composition_associativity_5 ).
cnf(c_0_90,plain,
composition(top,top) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_81]),c_0_71]) ).
cnf(c_0_91,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_69,c_0_21]) ).
cnf(c_0_92,negated_conjecture,
join(composition(top,sk1),complement(one)) = join(sk1,complement(one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_21]) ).
cnf(c_0_93,negated_conjecture,
join(complement(sk1),complement(one)) = complement(sk1),
inference(spm,[status(thm)],[c_0_84,c_0_48]) ).
cnf(c_0_94,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_85]),c_0_38]),c_0_21]),c_0_74]) ).
cnf(c_0_95,plain,
join(composition(top,X1),complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_38]),c_0_21]) ).
cnf(c_0_96,negated_conjecture,
join(X1,complement(composition(top,sk1))) = complement(composition(complement(X1),sk1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_38]),c_0_88]) ).
cnf(c_0_97,plain,
composition(top,composition(top,X1)) = composition(top,X1),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_98,plain,
join(complement(X1),complement(composition(top,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_84,c_0_79]) ).
cnf(c_0_99,negated_conjecture,
join(complement(one),complement(composition(top,sk1))) = complement(sk1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_91]),c_0_21]),c_0_93]) ).
cnf(c_0_100,plain,
converse(complement(converse(X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_38,c_0_94]) ).
cnf(c_0_101,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X2),complement(X1)))) = X1,
inference(spm,[status(thm)],[c_0_34,c_0_21]) ).
cnf(c_0_102,negated_conjecture,
complement(composition(complement(composition(top,sk1)),sk1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97]) ).
cnf(c_0_103,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(spm,[status(thm)],[c_0_44,c_0_16]) ).
cnf(c_0_104,negated_conjecture,
complement(composition(sk1,sk1)) = complement(sk1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_96]),c_0_38]) ).
cnf(c_0_105,negated_conjecture,
join(one,complement(composition(top,sk1))) = join(sk1,complement(composition(top,sk1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_99]),c_0_38]),c_0_38]),c_0_21]),c_0_21]) ).
cnf(c_0_106,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[c_0_16,c_0_100]) ).
cnf(c_0_107,negated_conjecture,
composition(complement(composition(top,sk1)),sk1) = 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_101,c_0_102]),c_0_54]),c_0_30]),c_0_49]),c_0_30]),c_0_37]) ).
cnf(c_0_108,plain,
join(converse(zero),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_37]),c_0_16]) ).
cnf(c_0_109,plain,
join(composition(X1,X2),composition(X3,composition(X4,X2))) = composition(join(X1,composition(X3,X4)),X2),
inference(spm,[status(thm)],[c_0_42,c_0_89]) ).
cnf(c_0_110,negated_conjecture,
composition(sk1,sk1) = sk1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_104]),c_0_101]) ).
cnf(c_0_111,plain,
join(complement(one),composition(converse(X1),complement(X1))) = complement(one),
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_112,negated_conjecture,
complement(composition(complement(one),sk1)) = complement(composition(complement(sk1),sk1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_96]),c_0_96]) ).
cnf(c_0_113,plain,
converse(complement(one)) = complement(one),
inference(spm,[status(thm)],[c_0_106,c_0_22]) ).
cnf(c_0_114,negated_conjecture,
composition(complement(composition(complement(X1),sk1)),sk1) = composition(X1,sk1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_107]),c_0_71]),c_0_96]) ).
cnf(c_0_115,plain,
converse(zero) = zero,
inference(spm,[status(thm)],[c_0_71,c_0_108]) ).
cnf(c_0_116,negated_conjecture,
composition(join(X1,composition(X2,sk1)),sk1) = composition(join(X1,X2),sk1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_42]) ).
cnf(c_0_117,plain,
join(complement(one),composition(converse(complement(X1)),X1)) = complement(one),
inference(spm,[status(thm)],[c_0_111,c_0_38]) ).
cnf(c_0_118,negated_conjecture,
composition(complement(one),sk1) = composition(complement(sk1),sk1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_112]),c_0_101]) ).
cnf(c_0_119,plain,
join(complement(one),converse(X1)) = converse(join(complement(one),X1)),
inference(spm,[status(thm)],[c_0_44,c_0_113]) ).
cnf(c_0_120,negated_conjecture,
composition(complement(composition(X1,sk1)),sk1) = composition(complement(X1),sk1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_114]),c_0_89]),c_0_110]) ).
cnf(c_0_121,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_17,c_0_67]),c_0_115]),c_0_64]),c_0_16]) ).
cnf(c_0_122,plain,
complement(zero) = top,
inference(spm,[status(thm)],[c_0_28,c_0_37]) ).
cnf(c_0_123,plain,
composition(converse(composition(X1,top)),X2) = composition(top,composition(converse(X1),X2)),
inference(spm,[status(thm)],[c_0_89,c_0_64]) ).
cnf(c_0_124,negated_conjecture,
composition(converse(complement(sk1)),sk1) = composition(complement(sk1),sk1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_118]),c_0_119]),c_0_21]),c_0_93]) ).
cnf(c_0_125,plain,
converse(composition(top,composition(converse(X1),X2))) = composition(converse(X2),composition(X1,top)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_17]),c_0_89]) ).
cnf(c_0_126,negated_conjecture,
composition(top,composition(converse(sk1),sk1)) = composition(top,sk1),
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_106]),c_0_38]),c_0_123]) ).
cnf(c_0_127,negated_conjecture,
composition(converse(sk1),sk1) = sk1,
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_124]),c_0_114]),c_0_110]),c_0_106]),c_0_38]) ).
cnf(c_0_128,negated_conjecture,
( join(meet(composition(sk1,top),sk2),composition(sk1,sk2)) != composition(sk1,sk2)
| join(composition(sk1,sk2),meet(composition(sk1,top),sk2)) != meet(composition(sk1,top),sk2) ),
inference(fof_simplification,[status(thm)],[goals_15]) ).
cnf(c_0_129,negated_conjecture,
composition(converse(sk1),composition(sk1,top)) = converse(composition(top,sk1)),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_130,negated_conjecture,
converse(sk1) = sk1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_127]),c_0_127]) ).
cnf(c_0_131,negated_conjecture,
composition(sk1,composition(sk1,X1)) = composition(sk1,X1),
inference(spm,[status(thm)],[c_0_89,c_0_110]) ).
cnf(c_0_132,negated_conjecture,
( join(meet(composition(sk1,top),sk2),composition(sk1,sk2)) != composition(sk1,sk2)
| join(composition(sk1,sk2),meet(composition(sk1,top),sk2)) != meet(composition(sk1,top),sk2) ),
c_0_128 ).
cnf(c_0_133,negated_conjecture,
converse(composition(top,sk1)) = composition(sk1,top),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_129,c_0_130]),c_0_131]) ).
cnf(c_0_134,negated_conjecture,
( join(composition(sk1,sk2),complement(join(complement(composition(sk1,top)),complement(sk2)))) != complement(join(complement(composition(sk1,top)),complement(sk2)))
| join(complement(join(complement(composition(sk1,top)),complement(sk2))),composition(sk1,sk2)) != composition(sk1,sk2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_132,c_0_24]),c_0_24]),c_0_24]) ).
cnf(c_0_135,plain,
converse(complement(composition(converse(X1),X2))) = complement(composition(converse(X2),X1)),
inference(spm,[status(thm)],[c_0_106,c_0_17]) ).
cnf(c_0_136,negated_conjecture,
converse(complement(composition(top,sk1))) = complement(composition(sk1,top)),
inference(spm,[status(thm)],[c_0_106,c_0_133]) ).
cnf(c_0_137,negated_conjecture,
( join(composition(sk1,sk2),complement(join(complement(sk2),complement(composition(sk1,top))))) != composition(sk1,sk2)
| join(composition(sk1,sk2),complement(join(complement(sk2),complement(composition(sk1,top))))) != complement(join(complement(sk2),complement(composition(sk1,top)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_21]),c_0_21]),c_0_21]),c_0_21]) ).
cnf(c_0_138,negated_conjecture,
join(X1,complement(composition(sk1,top))) = complement(composition(sk1,complement(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_96]),c_0_106]),c_0_135]),c_0_136]),c_0_130]) ).
cnf(c_0_139,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)],[c_0_137,c_0_138]),c_0_38]),c_0_38]),c_0_39]),c_0_138]),c_0_38]),c_0_38]),c_0_138]),c_0_38]),c_0_38]),c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL026-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.20/0.46 % Computer : n001.cluster.edu
% 0.20/0.46 % Model : x86_64 x86_64
% 0.20/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.46 % Memory : 8046.5625MB
% 0.20/0.46 % OS : Linux 6.8.0-71-generic
% 0.20/0.46 % CPULimit : 300
% 0.20/0.46 % WCLimit : 300
% 0.20/0.46 % DateTime : Mon Sep 21 04:07:43 UTC 2026
% 0.20/0.46 % CPUTime :
% 0.20/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.53 Running first-order theorem proving
% 0.25/0.53 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 27.66/4.65 % Version: 3.5.1
% 27.66/4.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 27.66/4.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 27.66/4.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 27.66/4.65 % Starting new_bool_3 with 300s (1) cores
% 27.66/4.65 % Starting new_bool_1 with 300s (1) cores
% 27.66/4.65 % Starting sh5l with 300s (1) cores
% 27.66/4.65 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2153671 completed with status 0
% 27.66/4.65 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 27.66/4.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 27.66/4.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 27.66/4.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 27.66/4.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 27.66/4.65 % No SInE strategy applied
% 27.66/4.65 % Search class: FUHPM-FFSF21-MFFFFFNN
% 27.66/4.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 27.66/4.65 % Starting SubtermCWHack with 136s (1) cores
% 27.66/4.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 27.66/4.65 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 136s (1) cores
% 27.66/4.65 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S2S with 136s (1) cores
% 27.66/4.65 % Starting new_bool_3 with 136s (1) cores
% 27.66/4.65 % H----_047_C09_12_F1_AE_ND_CS_SP_S2S with pid 2153681 completed with status 0
% 27.66/4.65 % Result found by H----_047_C09_12_F1_AE_ND_CS_SP_S2S
% 27.66/4.65 % Preprocessing class: FSMSSMSSSSSNFFN.
% 27.66/4.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 27.66/4.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 27.66/4.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 27.66/4.65 % No SInE strategy applied
% 27.66/4.65 % Search class: FUHPM-FFSF21-MFFFFFNN
% 27.66/4.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 27.66/4.65 % Starting SubtermCWHack with 136s (1) cores
% 27.66/4.65 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 27.66/4.65 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_S2S with 136s (1) cores
% 27.66/4.65 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S2S with 136s (1) cores
% 27.66/4.65 % Preprocessing time : 0.002 s
% 27.66/4.65 % Presaturation interreduction done
% 27.66/4.65
% 27.66/4.65 % Proof found!
% 27.66/4.65 % SZS status Unsatisfiable
% 27.66/4.65 % SZS output start CNFRefutation
% See solution above
% 27.66/4.65 % Parsed axioms : 15
% 27.66/4.65 % Removed by relevancy pruning/SinE : 0
% 27.66/4.65 % Initial clauses : 15
% 27.66/4.65 % Removed in clause preprocessing : 1
% 27.66/4.65 % Initial clauses in saturation : 14
% 27.66/4.65 % Processed clauses : 6082
% 27.66/4.65 % ...of these trivial : 4107
% 27.66/4.65 % ...subsumed : 1027
% 27.66/4.65 % ...remaining for further processing : 948
% 27.66/4.65 % Other redundant clauses eliminated : 0
% 27.66/4.65 % Clauses deleted for lack of memory : 0
% 27.66/4.65 % Backward-subsumed : 0
% 27.66/4.65 % Backward-rewritten : 205
% 27.66/4.65 % Generated clauses : 199387
% 27.66/4.65 % ...of the previous two non-redundant : 107978
% 27.66/4.65 % ...aggressively subsumed : 0
% 27.66/4.65 % Contextual simplify-reflections : 0
% 27.66/4.65 % Paramodulations : 199387
% 27.66/4.65 % Factorizations : 0
% 27.66/4.65 % NegExts : 0
% 27.66/4.65 % Equation resolutions : 0
% 27.66/4.65 % Disequality decompositions : 0
% 27.66/4.65 % Total rewrite steps : 476188
% 27.66/4.65 % ...of those cached : 408600
% 27.66/4.65 % Propositional unsat checks : 0
% 27.66/4.65 % Propositional check models : 0
% 27.66/4.65 % Propositional check unsatisfiable : 0
% 27.66/4.65 % Propositional clauses : 0
% 27.66/4.65 % Propositional clauses after purity: 0
% 27.66/4.65 % Propositional unsat core size : 0
% 27.66/4.65 % Propositional preprocessing time : 0.000
% 27.66/4.65 % Propositional encoding time : 0.000
% 27.66/4.65 % Propositional solver time : 0.000
% 27.66/4.65 % Success case prop preproc time : 0.000
% 27.66/4.65 % Success case prop encoding time : 0.000
% 27.66/4.65 % Success case prop solver time : 0.000
% 27.66/4.65 % Current number of processed clauses : 729
% 27.66/4.65 % Positive orientable unit clauses : 715
% 27.66/4.65 % Positive unorientable unit clauses: 14
% 27.66/4.65 % Negative unit clauses : 0
% 27.66/4.65 % Non-unit-clauses : 0
% 27.66/4.65 % Current number of unprocessed clauses: 100828
% 27.66/4.65 % ...number of literals in the above : 100828
% 27.66/4.65 % Current number of archived formulas : 0
% 27.66/4.65 % Current number of archived clauses : 220
% 27.66/4.65 % Clause-clause subsumption calls (NU) : 0
% 27.66/4.65 % Rec. Clause-clause subsumption calls : 0
% 27.66/4.65 % Non-unit clause-clause subsumptions : 0
% 27.66/4.65 % Unit Clause-clause subsumption calls : 146
% 27.66/4.65 % Rewrite failures with RHS unbound : 0
% 27.66/4.65 % BW rewrite match attempts : 6054
% 27.66/4.65 % BW rewrite match successes : 499
% 27.66/4.65 % Condensation attempts : 0
% 27.66/4.65 % Condensation successes : 0
% 27.66/4.65 % Termbank termtop insertions : 2950035
% 27.66/4.65 % Search garbage collected termcells : 5
% 27.66/4.65
% 27.66/4.65 % -------------------------------------------------
% 27.66/4.65 % User time : 3.738 s
% 27.66/4.65 % System time : 0.185 s
% 27.66/4.65 % Total time : 3.922 s
% 27.66/4.65 % Maximum resident set size: 3592 pages
% 27.66/4.65
% 27.66/4.65 % -------------------------------------------------
% 27.66/4.65 % User time : 18.513 s
% 27.66/4.65 % System time : 0.889 s
% 27.66/4.65 % Total time : 19.401 s
% 27.66/4.65 % Maximum resident set size: 4864 pages
% 27.66/4.65 % E exiting
%------------------------------------------------------------------------------