%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : REL026-4 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:04:21 PM UTC 2026
% Result : Unsatisfiable 199.27s 65.19s
% Output : CNFRefutation 199.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 17
% Syntax : Number of clauses : 169 ( 164 unt; 0 nHn; 32 RR)
% Number of literals : 174 ( 173 equ; 10 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 11 ( 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 : 233 ( 15 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(composition_identity_6,axiom,
composition(X1,one) = X1,
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',composition_identity_6) ).
cnf(converse_idempotence_8,axiom,
converse(converse(X1)) = X1,
file('/export/starexec/sandbox2/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/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(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(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(goals_17,negated_conjecture,
join(sk1,one) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_17) ).
cnf(modular_law_1_15,axiom,
join(meet(composition(X1,X2),X3),meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3)) = meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-1.ax',modular_law_1_15) ).
cnf(composition_associativity_5,axiom,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-0.ax',composition_associativity_5) ).
cnf(modular_law_2_16,axiom,
join(meet(composition(X1,X2),X3),meet(composition(meet(X1,composition(X3,converse(X2))),X2),X3)) = meet(composition(meet(X1,composition(X3,converse(X2))),X2),X3),
file('/export/starexec/sandbox2/benchmark/Axioms/REL001-1.ax',modular_law_2_16) ).
cnf(goals_18,negated_conjecture,
( join(composition(sk1,sk2),meet(composition(sk1,top),sk2)) != meet(composition(sk1,top),sk2)
| join(meet(composition(sk1,top),sk2),composition(sk1,sk2)) != composition(sk1,sk2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_18) ).
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(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_44,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_42,c_0_23]) ).
cnf(c_0_45,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_46,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_34,c_0_30]) ).
cnf(c_0_47,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_48,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_45,c_0_40]) ).
cnf(c_0_49,axiom,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
converse_additivity_9 ).
cnf(c_0_50,axiom,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
composition_distributivity_7 ).
cnf(c_0_51,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_31]),c_0_30]) ).
cnf(c_0_52,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_47]),c_0_23]),c_0_48]) ).
cnf(c_0_53,plain,
join(converse(zero),converse(X1)) = converse(X1),
inference(spm,[status(thm)],[c_0_49,c_0_39]) ).
cnf(c_0_54,plain,
join(X1,composition(X2,X1)) = composition(join(X2,one),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_28]),c_0_23]) ).
cnf(c_0_55,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_51,c_0_40]) ).
cnf(c_0_56,plain,
join(X1,complement(join(X1,complement(X2)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_52,c_0_40]) ).
cnf(c_0_57,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_39]) ).
cnf(c_0_58,plain,
join(converse(zero),X1) = X1,
inference(spm,[status(thm)],[c_0_53,c_0_20]) ).
cnf(c_0_59,plain,
composition(join(X1,one),top) = top,
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_60,plain,
join(converse(top),converse(X1)) = converse(top),
inference(spm,[status(thm)],[c_0_49,c_0_55]) ).
cnf(c_0_61,negated_conjecture,
join(sk1,one) = one,
goals_17 ).
cnf(c_0_62,axiom,
join(meet(composition(X1,X2),X3),meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3)) = meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3),
modular_law_1_15 ).
cnf(c_0_63,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_42]) ).
cnf(c_0_64,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_27]),c_0_17]),c_0_20]) ).
cnf(c_0_65,plain,
converse(zero) = zero,
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_66,plain,
composition(top,top) = top,
inference(spm,[status(thm)],[c_0_59,c_0_55]) ).
cnf(c_0_67,plain,
join(X1,top) = top,
inference(spm,[status(thm)],[c_0_23,c_0_55]) ).
cnf(c_0_68,plain,
join(converse(top),X1) = converse(top),
inference(spm,[status(thm)],[c_0_60,c_0_20]) ).
cnf(c_0_69,plain,
join(composition(join(X1,X2),X3),X4) = join(composition(X1,X3),join(composition(X2,X3),X4)),
inference(spm,[status(thm)],[c_0_34,c_0_50]) ).
cnf(c_0_70,negated_conjecture,
join(one,sk1) = one,
inference(rw,[status(thm)],[c_0_61,c_0_23]) ).
cnf(c_0_71,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))),complement(X3)))) = complement(join(complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))),complement(X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]) ).
cnf(c_0_72,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_63,c_0_23]) ).
cnf(c_0_73,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[c_0_23,c_0_34]) ).
cnf(c_0_74,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_64,c_0_32]),c_0_65]),c_0_39]),c_0_65]) ).
cnf(c_0_75,plain,
composition(converse(top),zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_66]),c_0_32]),c_0_32]),c_0_39]),c_0_32]) ).
cnf(c_0_76,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_77,negated_conjecture,
join(X1,join(composition(sk1,X1),X2)) = join(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_28]),c_0_28]) ).
cnf(c_0_78,plain,
join(complement(join(complement(composition(X1,X2)),complement(X3))),complement(join(complement(X3),complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3))))))))) = complement(join(complement(X3),complement(composition(X1,complement(join(complement(X2),complement(composition(converse(X1),X3)))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_23]),c_0_23]) ).
cnf(c_0_79,plain,
join(X1,join(complement(join(X2,X1)),X3)) = join(X1,join(complement(X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_72]),c_0_34]) ).
cnf(c_0_80,plain,
join(X1,complement(join(X2,join(X3,X1)))) = join(X1,complement(join(X2,X3))),
inference(spm,[status(thm)],[c_0_63,c_0_73]) ).
cnf(c_0_81,plain,
join(X1,join(complement(join(X1,X2)),X3)) = join(X1,join(complement(X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_63]),c_0_34]) ).
cnf(c_0_82,plain,
composition(converse(X1),complement(composition(X1,top))) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_74]),c_0_65]),c_0_20]) ).
cnf(c_0_83,plain,
composition(top,zero) = zero,
inference(rw,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_84,negated_conjecture,
join(X1,composition(sk1,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_77]),c_0_41]),c_0_23]) ).
cnf(c_0_85,plain,
join(converse(X1),converse(complement(X1))) = converse(top),
inference(spm,[status(thm)],[c_0_49,c_0_30]) ).
cnf(c_0_86,negated_conjecture,
join(one,converse(sk1)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_70]),c_0_24]),c_0_24]) ).
cnf(c_0_87,axiom,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
composition_associativity_5 ).
cnf(c_0_88,plain,
join(complement(X1),join(complement(composition(X2,X3)),complement(composition(X2,complement(join(complement(X3),complement(composition(converse(X2),X1)))))))) = join(complement(composition(X2,X3)),complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_78]),c_0_40]),c_0_40]),c_0_47]),c_0_79]),c_0_40]),c_0_34]),c_0_80]),c_0_23]),c_0_81]) ).
cnf(c_0_89,plain,
composition(X1,complement(composition(converse(X1),top))) = zero,
inference(spm,[status(thm)],[c_0_82,c_0_20]) ).
cnf(c_0_90,plain,
complement(zero) = top,
inference(spm,[status(thm)],[c_0_30,c_0_39]) ).
cnf(c_0_91,plain,
composition(X1,zero) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_83]),c_0_39]),c_0_55]),c_0_83]) ).
cnf(c_0_92,negated_conjecture,
join(complement(X1),complement(composition(sk1,X1))) = complement(composition(sk1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_84]),c_0_23]) ).
cnf(c_0_93,plain,
join(converse(X1),converse(complement(X1))) = top,
inference(rw,[status(thm)],[c_0_85,c_0_76]) ).
cnf(c_0_94,negated_conjecture,
join(X1,join(X2,composition(sk1,X1))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_77,c_0_23]) ).
cnf(c_0_95,negated_conjecture,
join(X1,join(composition(converse(sk1),X1),X2)) = join(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_86]),c_0_28]),c_0_28]) ).
cnf(c_0_96,plain,
join(composition(X1,composition(X2,X3)),composition(X4,X3)) = composition(join(composition(X1,X2),X4),X3),
inference(spm,[status(thm)],[c_0_50,c_0_87]) ).
cnf(c_0_97,plain,
join(composition(X1,top),complement(composition(X1,X2))) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_20]),c_0_40]),c_0_90]),c_0_67]),c_0_32]),c_0_91]),c_0_90]),c_0_67]),c_0_67]),c_0_20]),c_0_40]),c_0_23]) ).
cnf(c_0_98,negated_conjecture,
join(X1,complement(composition(sk1,complement(X1)))) = complement(composition(sk1,complement(X1))),
inference(spm,[status(thm)],[c_0_92,c_0_40]) ).
cnf(c_0_99,plain,
join(converse(X1),complement(converse(complement(X1)))) = converse(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_93]),c_0_32]),c_0_57]) ).
cnf(c_0_100,negated_conjecture,
join(X1,composition(converse(sk1),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_84]) ).
cnf(c_0_101,plain,
composition(join(composition(X1,top),X2),top) = composition(join(X1,X2),top),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_66]),c_0_50]) ).
cnf(c_0_102,plain,
join(composition(X1,top),composition(X1,X2)) = composition(X1,top),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_97]),c_0_32]),c_0_57]),c_0_40]) ).
cnf(c_0_103,negated_conjecture,
complement(composition(sk1,complement(composition(sk1,top)))) = top,
inference(spm,[status(thm)],[c_0_98,c_0_97]) ).
cnf(c_0_104,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_99]),c_0_20]),c_0_20]) ).
cnf(c_0_105,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(spm,[status(thm)],[c_0_93,c_0_20]) ).
cnf(c_0_106,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_100]),c_0_17]),c_0_20]) ).
cnf(c_0_107,plain,
join(composition(X1,X2),composition(X1,complement(join(complement(X2),complement(composition(converse(X1),top)))))) = composition(X1,complement(join(complement(X2),complement(composition(converse(X1),top))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_32]),c_0_57]),c_0_40]),c_0_39]),c_0_40]),c_0_39]),c_0_40]) ).
cnf(c_0_108,plain,
composition(join(X1,composition(X1,X2)),top) = composition(X1,top),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_87]),c_0_66]) ).
cnf(c_0_109,negated_conjecture,
composition(sk1,complement(composition(sk1,top))) = 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_36,c_0_103]),c_0_55]),c_0_32]),c_0_55]),c_0_32]),c_0_39]) ).
cnf(c_0_110,plain,
join(complement(X1),converse(complement(converse(X1)))) = complement(X1),
inference(spm,[status(thm)],[c_0_104,c_0_40]) ).
cnf(c_0_111,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_105]),c_0_32]),c_0_57]) ).
cnf(c_0_112,negated_conjecture,
join(X1,composition(X1,sk1)) = X1,
inference(spm,[status(thm)],[c_0_106,c_0_20]) ).
cnf(c_0_113,negated_conjecture,
join(one,join(sk1,X1)) = join(one,X1),
inference(spm,[status(thm)],[c_0_34,c_0_70]) ).
cnf(c_0_114,plain,
join(X1,join(complement(X1),X2)) = top,
inference(rw,[status(thm)],[c_0_46,c_0_55]) ).
cnf(c_0_115,plain,
composition(X1,composition(converse(X1),top)) = composition(X1,top),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_107]),c_0_32]),c_0_39]),c_0_40]),c_0_87]),c_0_87]),c_0_66]),c_0_32]),c_0_39]),c_0_40]),c_0_108]) ).
cnf(c_0_116,negated_conjecture,
composition(join(sk1,converse(sk1)),top) = composition(sk1,top),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_109]),c_0_40]),c_0_90]),c_0_50]),c_0_40]) ).
cnf(c_0_117,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_48,c_0_110]),c_0_40]),c_0_23]),c_0_111]) ).
cnf(c_0_118,negated_conjecture,
join(X1,join(composition(X1,sk1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_112]) ).
cnf(c_0_119,negated_conjecture,
join(one,complement(sk1)) = join(one,top),
inference(spm,[status(thm)],[c_0_113,c_0_30]) ).
cnf(c_0_120,plain,
join(complement(X1),join(X1,X2)) = top,
inference(spm,[status(thm)],[c_0_114,c_0_40]) ).
cnf(c_0_121,plain,
join(X1,composition(top,X1)) = composition(top,X1),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_122,negated_conjecture,
composition(converse(sk1),top) = composition(sk1,top),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_115]),c_0_50]),c_0_23]),c_0_116]) ).
cnf(c_0_123,plain,
converse(complement(converse(X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_40,c_0_117]) ).
cnf(c_0_124,negated_conjecture,
join(X1,composition(join(X1,X2),sk1)) = join(X1,composition(X2,sk1)),
inference(spm,[status(thm)],[c_0_118,c_0_50]) ).
cnf(c_0_125,negated_conjecture,
join(one,complement(sk1)) = top,
inference(rw,[status(thm)],[c_0_119,c_0_67]) ).
cnf(c_0_126,plain,
join(composition(top,X1),complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_121]),c_0_23]) ).
cnf(c_0_127,negated_conjecture,
composition(top,converse(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_17,c_0_122]),c_0_17]),c_0_76]),c_0_76]),c_0_20]) ).
cnf(c_0_128,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[c_0_20,c_0_123]) ).
cnf(c_0_129,negated_conjecture,
join(X1,composition(complement(X1),sk1)) = join(X1,composition(top,sk1)),
inference(spm,[status(thm)],[c_0_124,c_0_30]) ).
cnf(c_0_130,negated_conjecture,
join(X1,composition(join(X2,X1),sk1)) = join(X1,composition(X2,sk1)),
inference(spm,[status(thm)],[c_0_124,c_0_23]) ).
cnf(c_0_131,negated_conjecture,
join(one,converse(complement(sk1))) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_125]),c_0_24]),c_0_76]) ).
cnf(c_0_132,negated_conjecture,
join(composition(top,sk1),converse(complement(sk1))) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_128]) ).
cnf(c_0_133,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_134,plain,
join(X1,composition(top,complement(X1))) = top,
inference(spm,[status(thm)],[c_0_114,c_0_121]) ).
cnf(c_0_135,negated_conjecture,
join(complement(X1),complement(composition(X1,sk1))) = complement(composition(X1,sk1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_112]),c_0_23]) ).
cnf(c_0_136,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_63,c_0_129]),c_0_63]) ).
cnf(c_0_137,negated_conjecture,
join(sk1,converse(complement(sk1))) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_23]),c_0_132]),c_0_28]),c_0_23]) ).
cnf(c_0_138,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_133,c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]) ).
cnf(c_0_139,plain,
composition(top,composition(top,X1)) = composition(top,X1),
inference(spm,[status(thm)],[c_0_87,c_0_66]) ).
cnf(c_0_140,plain,
join(converse(X1),composition(converse(complement(X1)),top)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_134]),c_0_76]),c_0_17]),c_0_76]) ).
cnf(c_0_141,plain,
join(converse(X1),converse(complement(join(X1,X2)))) = join(converse(X1),converse(complement(X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_63]),c_0_49]) ).
cnf(c_0_142,negated_conjecture,
complement(composition(complement(X1),sk1)) = join(X1,complement(composition(top,sk1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_40]),c_0_136]) ).
cnf(c_0_143,negated_conjecture,
join(sk1,converse(sk1)) = sk1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_137]),c_0_32]),c_0_57]),c_0_128]),c_0_40]) ).
cnf(c_0_144,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_138,c_0_23]),c_0_23]) ).
cnf(c_0_145,plain,
composition(top,complement(composition(top,X1))) = complement(composition(top,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_139]),c_0_76]),c_0_121]) ).
cnf(c_0_146,plain,
join(X1,composition(complement(X1),top)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_128]),c_0_20]),c_0_20]) ).
cnf(c_0_147,plain,
join(X1,converse(complement(join(converse(X1),X2)))) = join(X1,converse(complement(X2))),
inference(spm,[status(thm)],[c_0_141,c_0_20]) ).
cnf(c_0_148,negated_conjecture,
complement(join(X1,complement(composition(top,sk1)))) = composition(complement(X1),sk1),
inference(spm,[status(thm)],[c_0_40,c_0_142]) ).
cnf(c_0_149,negated_conjecture,
converse(sk1) = sk1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_143]),c_0_20]),c_0_23]),c_0_143]) ).
cnf(c_0_150,plain,
complement(join(complement(composition(X1,X2)),complement(composition(complement(join(complement(X1),complement(composition(X1,composition(X2,converse(X2)))))),X2)))) = composition(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_144,c_0_41]),c_0_40]),c_0_87]),c_0_87]),c_0_43]) ).
cnf(c_0_151,plain,
composition(converse(complement(composition(top,X1))),top) = converse(complement(composition(top,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_145]),c_0_76]) ).
cnf(c_0_152,plain,
join(X1,complement(composition(complement(X1),top))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_146]),c_0_32]),c_0_57]) ).
cnf(c_0_153,negated_conjecture,
join(X1,composition(sk1,complement(X1))) = join(X1,composition(sk1,top)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_147,c_0_148]),c_0_128]),c_0_17]),c_0_149]),c_0_20]),c_0_40]),c_0_17]),c_0_149]),c_0_76]) ).
cnf(c_0_154,plain,
complement(composition(converse(X1),top)) = converse(complement(composition(top,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(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_150,c_0_151]),c_0_128]),c_0_40]),c_0_17]),c_0_76]),c_0_128]),c_0_40]),c_0_17]),c_0_76]),c_0_76]),c_0_66]),c_0_151]),c_0_128]),c_0_40]),c_0_17]),c_0_76]),c_0_50]),c_0_41]),c_0_152]) ).
cnf(c_0_155,negated_conjecture,
( join(composition(sk1,sk2),meet(composition(sk1,top),sk2)) != meet(composition(sk1,top),sk2)
| join(meet(composition(sk1,top),sk2),composition(sk1,sk2)) != composition(sk1,sk2) ),
goals_18 ).
cnf(c_0_156,negated_conjecture,
complement(composition(sk1,complement(X1))) = join(X1,complement(composition(sk1,top))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_153]),c_0_63]),c_0_98]) ).
cnf(c_0_157,negated_conjecture,
complement(composition(sk1,top)) = converse(complement(composition(top,sk1))),
inference(spm,[status(thm)],[c_0_154,c_0_149]) ).
cnf(c_0_158,plain,
join(composition(converse(X1),converse(X2)),composition(converse(X1),converse(X3))) = composition(converse(X1),join(converse(X2),converse(X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_17]),c_0_49]),c_0_17]),c_0_17]) ).
cnf(c_0_159,negated_conjecture,
( join(complement(join(complement(composition(sk1,top)),complement(sk2))),composition(sk1,sk2)) != composition(sk1,sk2)
| join(composition(sk1,sk2),complement(join(complement(composition(sk1,top)),complement(sk2)))) != complement(join(complement(composition(sk1,top)),complement(sk2))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_155,c_0_26]),c_0_26]),c_0_26]) ).
cnf(c_0_160,negated_conjecture,
complement(composition(sk1,complement(X1))) = join(X1,converse(complement(composition(top,sk1)))),
inference(rw,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_161,plain,
join(composition(X1,converse(X2)),composition(X1,converse(X3))) = composition(X1,join(converse(X2),converse(X3))),
inference(spm,[status(thm)],[c_0_158,c_0_20]) ).
cnf(c_0_162,negated_conjecture,
( join(composition(sk1,sk2),complement(join(complement(sk2),complement(composition(sk1,top))))) != complement(join(complement(sk2),complement(composition(sk1,top))))
| join(composition(sk1,sk2),complement(join(complement(sk2),complement(composition(sk1,top))))) != composition(sk1,sk2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_159,c_0_23]),c_0_23]),c_0_23]),c_0_23]) ).
cnf(c_0_163,negated_conjecture,
complement(composition(sk1,X1)) = join(complement(X1),converse(complement(composition(top,sk1)))),
inference(spm,[status(thm)],[c_0_160,c_0_40]) ).
cnf(c_0_164,plain,
join(composition(X1,converse(X2)),composition(X1,X3)) = composition(X1,join(converse(X2),X3)),
inference(spm,[status(thm)],[c_0_161,c_0_20]) ).
cnf(c_0_165,negated_conjecture,
( join(composition(sk1,sk2),complement(join(complement(sk2),converse(complement(composition(top,sk1)))))) != complement(join(complement(sk2),converse(complement(composition(top,sk1)))))
| join(composition(sk1,sk2),complement(join(complement(sk2),converse(complement(composition(top,sk1)))))) != composition(sk1,sk2) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_162,c_0_157]),c_0_157]),c_0_157]) ).
cnf(c_0_166,negated_conjecture,
complement(join(complement(X1),converse(complement(composition(top,sk1))))) = composition(sk1,X1),
inference(spm,[status(thm)],[c_0_40,c_0_163]) ).
cnf(c_0_167,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_164,c_0_20]) ).
cnf(c_0_168,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)],[c_0_165,c_0_166]),c_0_167]),c_0_41]),c_0_166]),c_0_166]),c_0_167]),c_0_41])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : REL026-4 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n004.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 01:41:32 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 199.27/65.19 % Version : CSE_E---1.7
% 199.27/65.19 % Problem : theBenchmark.p
% 199.27/65.19 % SZS status Unsatisfiable for theBenchmark.p
% 199.27/65.19 % SZS output start CNFRefutation
% See solution above
% 199.64/65.55 % Total time : 51.812s
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