TSTP Solution File: REL028-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : REL028-2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n024.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 : Thu Aug 31 13:36:11 EDT 2023
% Result : Unsatisfiable 3.14s 3.25s
% Output : CNFRefutation 3.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 27
% Syntax : Number of formulae : 184 ( 174 unt; 10 typ; 0 def)
% Number of atoms : 174 ( 173 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 8 ( 5 >; 3 *; 0 +; 0 <<)
% 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 : 215 ( 13 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
join: ( $i * $i ) > $i ).
tff(decl_23,type,
complement: $i > $i ).
tff(decl_24,type,
meet: ( $i * $i ) > $i ).
tff(decl_25,type,
composition: ( $i * $i ) > $i ).
tff(decl_26,type,
one: $i ).
tff(decl_27,type,
converse: $i > $i ).
tff(decl_28,type,
top: $i ).
tff(decl_29,type,
zero: $i ).
tff(decl_30,type,
sk1: $i ).
tff(decl_31,type,
sk2: $i ).
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(converse_idempotence_8,axiom,
converse(converse(X1)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/REL001-0.ax',converse_idempotence_8) ).
cnf(composition_identity_6,axiom,
composition(X1,one) = X1,
file('/export/starexec/sandbox/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/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_18,negated_conjecture,
join(sk2,one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_18) ).
cnf(modular_law_1_15,axiom,
join(meet(composition(X1,X2),X3),meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3)) = meet(composition(X1,meet(X2,composition(converse(X1),X3))),X3),
file('/export/starexec/sandbox/benchmark/Axioms/REL001-1.ax',modular_law_1_15) ).
cnf(goals_17,negated_conjecture,
join(sk1,one) = one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_17) ).
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_19,negated_conjecture,
composition(sk1,sk2) != meet(sk1,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_19) ).
cnf(c_0_17,axiom,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
converse_multiplicativity_10 ).
cnf(c_0_18,axiom,
converse(converse(X1)) = X1,
converse_idempotence_8 ).
cnf(c_0_19,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_20,axiom,
composition(X1,one) = X1,
composition_identity_6 ).
cnf(c_0_21,plain,
composition(converse(one),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_18]) ).
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_20,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_30]),c_0_31]),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(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_34,c_0_30]) ).
cnf(c_0_43,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_41]) ).
cnf(c_0_44,plain,
join(X1,join(X2,complement(X1))) = join(top,X2),
inference(spm,[status(thm)],[c_0_42,c_0_23]) ).
cnf(c_0_45,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_36]),c_0_23]) ).
cnf(c_0_46,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_43,c_0_23]) ).
cnf(c_0_47,plain,
join(top,complement(complement(X1))) = join(X1,top),
inference(spm,[status(thm)],[c_0_42,c_0_30]) ).
cnf(c_0_48,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_31]),c_0_30]) ).
cnf(c_0_49,axiom,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
converse_additivity_9 ).
cnf(c_0_50,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_51,plain,
join(X1,top) = top,
inference(rw,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_52,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(spm,[status(thm)],[c_0_49,c_0_18]) ).
cnf(c_0_53,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X2),complement(X1)))) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_23]) ).
cnf(c_0_54,plain,
join(complement(join(X1,X2)),complement(join(X1,complement(X2)))) = complement(X1),
inference(spm,[status(thm)],[c_0_36,c_0_40]) ).
cnf(c_0_55,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_50,c_0_40]) ).
cnf(c_0_56,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_23,c_0_51]) ).
cnf(c_0_57,plain,
join(X1,converse(top)) = converse(top),
inference(spm,[status(thm)],[c_0_52,c_0_51]) ).
cnf(c_0_58,plain,
join(X1,complement(join(X1,complement(X2)))) = join(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_40]),c_0_40]),c_0_34]),c_0_55]) ).
cnf(c_0_59,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_60,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_58]),c_0_43]) ).
cnf(c_0_61,plain,
join(X1,converse(complement(converse(X1)))) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_30]),c_0_59]) ).
cnf(c_0_62,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_39]) ).
cnf(c_0_63,axiom,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
composition_distributivity_7 ).
cnf(c_0_64,negated_conjecture,
join(sk2,one) = one,
goals_18 ).
cnf(c_0_65,plain,
join(X1,complement(converse(complement(converse(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_32]),c_0_62]) ).
cnf(c_0_66,plain,
join(X1,composition(X2,X1)) = composition(join(one,X2),X1),
inference(spm,[status(thm)],[c_0_63,c_0_28]) ).
cnf(c_0_67,negated_conjecture,
join(one,sk2) = one,
inference(rw,[status(thm)],[c_0_64,c_0_23]) ).
cnf(c_0_68,plain,
join(X1,converse(complement(converse(complement(X1))))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_65]),c_0_18]),c_0_18]) ).
cnf(c_0_69,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_70,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_71,negated_conjecture,
join(X1,composition(sk2,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_28]) ).
cnf(c_0_72,plain,
join(X1,composition(converse(complement(one)),X1)) = composition(top,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_61]),c_0_24]) ).
cnf(c_0_73,plain,
composition(top,converse(X1)) = converse(composition(X1,top)),
inference(spm,[status(thm)],[c_0_17,c_0_59]) ).
cnf(c_0_74,plain,
join(complement(X1),converse(complement(converse(X1)))) = complement(X1),
inference(spm,[status(thm)],[c_0_68,c_0_40]) ).
cnf(c_0_75,plain,
converse(composition(X1,converse(X2))) = composition(X2,converse(X1)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_76,negated_conjecture,
join(sk1,one) = one,
goals_17 ).
cnf(c_0_77,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_69,c_0_26]),c_0_26]),c_0_26]),c_0_26]),c_0_26]) ).
cnf(c_0_78,negated_conjecture,
join(X1,join(X2,composition(sk2,X1))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_79,plain,
join(X1,composition(X1,complement(one))) = composition(X1,top),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_72]),c_0_73]),c_0_18]),c_0_17]),c_0_18]) ).
cnf(c_0_80,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_55,c_0_74]),c_0_40]),c_0_23]),c_0_65]) ).
cnf(c_0_81,negated_conjecture,
join(X1,composition(X1,converse(sk2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_71]),c_0_18]),c_0_75]) ).
cnf(c_0_82,negated_conjecture,
join(one,sk1) = one,
inference(rw,[status(thm)],[c_0_76,c_0_23]) ).
cnf(c_0_83,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_77,c_0_23]),c_0_23]) ).
cnf(c_0_84,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_60,c_0_23]) ).
cnf(c_0_85,negated_conjecture,
join(composition(sk2,top),complement(one)) = join(sk2,complement(one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_23]) ).
cnf(c_0_86,negated_conjecture,
join(complement(one),complement(sk2)) = complement(sk2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_67]),c_0_23]) ).
cnf(c_0_87,plain,
converse(complement(converse(X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_40,c_0_80]) ).
cnf(c_0_88,negated_conjecture,
join(X1,composition(converse(sk2),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_81]),c_0_28]),c_0_28]) ).
cnf(c_0_89,negated_conjecture,
join(X1,composition(sk1,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_82]),c_0_28]) ).
cnf(c_0_90,plain,
join(complement(join(complement(composition(converse(X1),X2)),complement(X3))),complement(join(complement(X3),complement(composition(converse(X1),complement(join(complement(X2),complement(composition(X1,X3))))))))) = complement(join(complement(X3),complement(composition(converse(X1),complement(join(complement(X2),complement(composition(X1,X3)))))))),
inference(spm,[status(thm)],[c_0_83,c_0_18]) ).
cnf(c_0_91,negated_conjecture,
join(complement(one),complement(composition(sk2,top))) = complement(sk2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_84]),c_0_86]) ).
cnf(c_0_92,plain,
complement(converse(X1)) = converse(complement(X1)),
inference(spm,[status(thm)],[c_0_18,c_0_87]) ).
cnf(c_0_93,negated_conjecture,
join(X1,composition(X1,sk2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_88]),c_0_18]),c_0_17]),c_0_18]) ).
cnf(c_0_94,negated_conjecture,
join(X1,composition(X1,converse(sk1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_89]),c_0_18]),c_0_75]) ).
cnf(c_0_95,negated_conjecture,
join(X1,join(X2,composition(sk1,X1))) = join(X2,X1),
inference(spm,[status(thm)],[c_0_70,c_0_89]) ).
cnf(c_0_96,negated_conjecture,
composition(converse(sk2),sk2) = converse(sk2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(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_90,c_0_91]),c_0_20]),c_0_92]),c_0_32]),c_0_62]),c_0_92]),c_0_40]),c_0_32]),c_0_40]),c_0_39]),c_0_40]),c_0_93]),c_0_32]),c_0_40]),c_0_39]),c_0_40]) ).
cnf(c_0_97,negated_conjecture,
join(X1,composition(converse(sk1),X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_94]),c_0_28]),c_0_28]) ).
cnf(c_0_98,plain,
join(X1,join(complement(X1),X2)) = top,
inference(rw,[status(thm)],[c_0_42,c_0_56]) ).
cnf(c_0_99,negated_conjecture,
join(composition(sk1,top),complement(one)) = join(sk1,complement(one)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_79]),c_0_23]) ).
cnf(c_0_100,negated_conjecture,
join(complement(one),complement(sk1)) = complement(sk1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_82]),c_0_23]) ).
cnf(c_0_101,axiom,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
composition_associativity_5 ).
cnf(c_0_102,negated_conjecture,
converse(sk2) = sk2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_96]),c_0_18]),c_0_96]) ).
cnf(c_0_103,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_52,c_0_97]),c_0_18]),c_0_17]),c_0_18]) ).
cnf(c_0_104,plain,
join(complement(X1),join(X2,X1)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_36]),c_0_34]) ).
cnf(c_0_105,negated_conjecture,
join(complement(one),complement(composition(sk1,top))) = complement(sk1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_99]),c_0_84]),c_0_100]) ).
cnf(c_0_106,plain,
join(composition(X1,converse(X2)),converse(X3)) = converse(join(composition(X2,converse(X1)),X3)),
inference(spm,[status(thm)],[c_0_49,c_0_75]) ).
cnf(c_0_107,plain,
composition(join(X1,converse(X2)),converse(X3)) = converse(composition(X3,join(converse(X1),X2))),
inference(spm,[status(thm)],[c_0_17,c_0_52]) ).
cnf(c_0_108,plain,
join(composition(X1,X2),composition(X3,composition(X4,X2))) = composition(join(X1,composition(X3,X4)),X2),
inference(spm,[status(thm)],[c_0_63,c_0_101]) ).
cnf(c_0_109,negated_conjecture,
composition(sk2,sk2) = sk2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_102]),c_0_102]) ).
cnf(c_0_110,plain,
join(complement(one),composition(converse(X1),complement(X1))) = complement(one),
inference(spm,[status(thm)],[c_0_27,c_0_20]) ).
cnf(c_0_111,negated_conjecture,
converse(complement(sk2)) = complement(sk2),
inference(spm,[status(thm)],[c_0_92,c_0_102]) ).
cnf(c_0_112,plain,
converse(complement(one)) = complement(one),
inference(spm,[status(thm)],[c_0_92,c_0_24]) ).
cnf(c_0_113,negated_conjecture,
join(X1,join(composition(X1,sk1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_103]) ).
cnf(c_0_114,plain,
join(X1,join(X2,X3)) = join(X3,join(X1,X2)),
inference(spm,[status(thm)],[c_0_23,c_0_34]) ).
cnf(c_0_115,plain,
join(complement(X1),join(X2,join(X3,X1))) = top,
inference(spm,[status(thm)],[c_0_104,c_0_34]) ).
cnf(c_0_116,negated_conjecture,
composition(converse(sk1),sk1) = converse(sk1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(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_90,c_0_105]),c_0_20]),c_0_92]),c_0_32]),c_0_62]),c_0_92]),c_0_40]),c_0_32]),c_0_40]),c_0_39]),c_0_40]),c_0_103]),c_0_32]),c_0_40]),c_0_39]),c_0_40]) ).
cnf(c_0_117,plain,
converse(join(composition(X1,converse(X2)),composition(X1,X3))) = converse(composition(X1,join(converse(X2),X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_17]),c_0_106]),c_0_107]) ).
cnf(c_0_118,negated_conjecture,
composition(sk2,converse(X1)) = converse(composition(X1,sk2)),
inference(spm,[status(thm)],[c_0_17,c_0_102]) ).
cnf(c_0_119,negated_conjecture,
composition(join(X1,composition(X2,sk2)),sk2) = composition(join(X1,X2),sk2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_63]) ).
cnf(c_0_120,negated_conjecture,
join(complement(one),composition(complement(sk2),sk2)) = complement(one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_40]) ).
cnf(c_0_121,plain,
composition(converse(X1),complement(one)) = converse(composition(complement(one),X1)),
inference(spm,[status(thm)],[c_0_19,c_0_112]) ).
cnf(c_0_122,negated_conjecture,
join(X1,composition(join(X1,X2),sk1)) = join(X1,composition(X2,sk1)),
inference(spm,[status(thm)],[c_0_113,c_0_63]) ).
cnf(c_0_123,plain,
join(complement(X1),complement(join(complement(X2),join(complement(X1),complement(join(complement(X1),X2)))))) = join(complement(X1),X2),
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_114]),c_0_23]) ).
cnf(c_0_124,negated_conjecture,
join(X1,join(complement(composition(X1,sk1)),X2)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_103]),c_0_114]) ).
cnf(c_0_125,plain,
composition(converse(X1),top) = converse(composition(top,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_59]) ).
cnf(c_0_126,negated_conjecture,
converse(sk1) = sk1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_116]),c_0_18]),c_0_116]) ).
cnf(c_0_127,plain,
join(composition(X1,converse(X2)),composition(X1,X3)) = composition(X1,join(converse(X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_117]),c_0_18]) ).
cnf(c_0_128,negated_conjecture,
converse(composition(complement(sk2),sk2)) = composition(sk2,complement(sk2)),
inference(spm,[status(thm)],[c_0_118,c_0_111]) ).
cnf(c_0_129,negated_conjecture,
composition(complement(sk2),sk2) = composition(complement(one),sk2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_120]),c_0_86]) ).
cnf(c_0_130,negated_conjecture,
converse(composition(complement(one),sk2)) = composition(sk2,complement(one)),
inference(spm,[status(thm)],[c_0_121,c_0_102]) ).
cnf(c_0_131,negated_conjecture,
join(X1,composition(complement(X1),sk1)) = join(X1,composition(top,sk1)),
inference(spm,[status(thm)],[c_0_122,c_0_30]) ).
cnf(c_0_132,negated_conjecture,
join(X1,complement(composition(complement(X1),sk1))) = complement(composition(complement(X1),sk1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_124]),c_0_32]),c_0_62]),c_0_23]) ).
cnf(c_0_133,negated_conjecture,
converse(composition(top,sk1)) = composition(sk1,top),
inference(spm,[status(thm)],[c_0_125,c_0_126]) ).
cnf(c_0_134,negated_conjecture,
join(one,join(sk1,X1)) = join(one,X1),
inference(spm,[status(thm)],[c_0_34,c_0_82]) ).
cnf(c_0_135,negated_conjecture,
join(X1,join(composition(X1,sk2),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_93]) ).
cnf(c_0_136,plain,
join(composition(X1,X2),composition(X1,X3)) = composition(X1,join(X2,X3)),
inference(spm,[status(thm)],[c_0_127,c_0_18]) ).
cnf(c_0_137,negated_conjecture,
composition(sk2,composition(sk2,X1)) = composition(sk2,X1),
inference(spm,[status(thm)],[c_0_101,c_0_109]) ).
cnf(c_0_138,negated_conjecture,
composition(sk2,complement(sk2)) = composition(sk2,complement(one)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_128,c_0_129]),c_0_130]) ).
cnf(c_0_139,negated_conjecture,
join(X1,complement(composition(top,sk1))) = complement(composition(complement(X1),sk1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_131]),c_0_60]),c_0_132]) ).
cnf(c_0_140,negated_conjecture,
composition(converse(X1),sk1) = converse(composition(sk1,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_126]) ).
cnf(c_0_141,negated_conjecture,
converse(complement(composition(top,sk1))) = complement(composition(sk1,top)),
inference(spm,[status(thm)],[c_0_92,c_0_133]) ).
cnf(c_0_142,negated_conjecture,
join(one,complement(sk1)) = join(top,one),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_30]),c_0_23]) ).
cnf(c_0_143,negated_conjecture,
join(X1,composition(join(X1,X2),sk2)) = join(X1,composition(X2,sk2)),
inference(spm,[status(thm)],[c_0_135,c_0_63]) ).
cnf(c_0_144,negated_conjecture,
join(X1,join(complement(composition(X1,sk2)),X2)) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_93]),c_0_114]) ).
cnf(c_0_145,negated_conjecture,
composition(sk2,join(X1,composition(sk2,X2))) = composition(sk2,join(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_136]) ).
cnf(c_0_146,plain,
join(complement(X1),composition(X2,complement(composition(converse(X2),X1)))) = complement(X1),
inference(spm,[status(thm)],[c_0_27,c_0_18]) ).
cnf(c_0_147,negated_conjecture,
join(complement(X1),complement(composition(sk2,X1))) = complement(composition(sk2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_71]),c_0_23]) ).
cnf(c_0_148,negated_conjecture,
composition(sk2,join(complement(sk2),X1)) = composition(sk2,join(complement(one),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_138]),c_0_136]) ).
cnf(c_0_149,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_139]),c_0_92]),c_0_140]),c_0_92]),c_0_18]),c_0_141]) ).
cnf(c_0_150,negated_conjecture,
join(one,complement(sk1)) = top,
inference(rw,[status(thm)],[c_0_142,c_0_56]) ).
cnf(c_0_151,negated_conjecture,
join(X1,composition(complement(X1),sk2)) = join(X1,composition(top,sk2)),
inference(spm,[status(thm)],[c_0_143,c_0_30]) ).
cnf(c_0_152,negated_conjecture,
join(X1,complement(composition(complement(X1),sk2))) = complement(composition(complement(X1),sk2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_144]),c_0_32]),c_0_62]),c_0_23]) ).
cnf(c_0_153,negated_conjecture,
converse(composition(top,sk2)) = composition(sk2,top),
inference(spm,[status(thm)],[c_0_125,c_0_102]) ).
cnf(c_0_154,negated_conjecture,
composition(converse(X1),sk2) = converse(composition(sk2,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_102]) ).
cnf(c_0_155,negated_conjecture,
converse(composition(sk1,sk2)) = composition(sk2,sk1),
inference(spm,[status(thm)],[c_0_118,c_0_126]) ).
cnf(c_0_156,negated_conjecture,
composition(sk2,complement(composition(sk2,X1))) = composition(sk2,complement(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_146]),c_0_102]),c_0_147]) ).
cnf(c_0_157,negated_conjecture,
composition(sk2,complement(composition(sk1,sk2))) = composition(sk2,complement(sk1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_148,c_0_149]),c_0_40]),c_0_149]),c_0_40]),c_0_20]) ).
cnf(c_0_158,negated_conjecture,
join(X1,join(composition(sk2,X1),X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_71]) ).
cnf(c_0_159,negated_conjecture,
join(X1,composition(complement(sk1),X1)) = composition(top,X1),
inference(spm,[status(thm)],[c_0_66,c_0_150]) ).
cnf(c_0_160,negated_conjecture,
converse(complement(sk1)) = complement(sk1),
inference(spm,[status(thm)],[c_0_92,c_0_126]) ).
cnf(c_0_161,negated_conjecture,
join(X1,complement(composition(top,sk2))) = complement(composition(complement(X1),sk2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_151]),c_0_60]),c_0_152]) ).
cnf(c_0_162,negated_conjecture,
converse(complement(composition(top,sk2))) = complement(composition(sk2,top)),
inference(spm,[status(thm)],[c_0_92,c_0_153]) ).
cnf(c_0_163,negated_conjecture,
converse(composition(sk2,composition(sk1,sk2))) = composition(sk2,composition(sk1,sk2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_101]) ).
cnf(c_0_164,negated_conjecture,
composition(sk2,composition(sk1,sk2)) = composition(sk2,sk1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_156]),c_0_40]),c_0_40]) ).
cnf(c_0_165,negated_conjecture,
converse(composition(sk2,sk1)) = composition(sk1,sk2),
inference(spm,[status(thm)],[c_0_154,c_0_126]) ).
cnf(c_0_166,negated_conjecture,
composition(sk1,sk2) != meet(sk1,sk2),
goals_19 ).
cnf(c_0_167,negated_conjecture,
join(X1,complement(join(X2,composition(sk2,X1)))) = join(X1,complement(X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_158,c_0_84]),c_0_158]) ).
cnf(c_0_168,negated_conjecture,
join(X1,composition(X1,complement(sk1))) = composition(X1,top),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_159]),c_0_73]),c_0_18]),c_0_75]),c_0_160]) ).
cnf(c_0_169,negated_conjecture,
join(X1,complement(composition(sk2,top))) = complement(composition(sk2,complement(X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_161]),c_0_92]),c_0_154]),c_0_92]),c_0_18]),c_0_162]) ).
cnf(c_0_170,negated_conjecture,
composition(sk2,sk1) = composition(sk1,sk2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_163,c_0_164]),c_0_165]),c_0_164]) ).
cnf(c_0_171,negated_conjecture,
composition(sk1,sk2) != complement(join(complement(sk1),complement(sk2))),
inference(rw,[status(thm)],[c_0_166,c_0_26]) ).
cnf(c_0_172,negated_conjecture,
join(complement(sk1),complement(sk2)) = complement(composition(sk1,sk2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_167,c_0_168]),c_0_169]),c_0_40]),c_0_170]) ).
cnf(c_0_173,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_171,c_0_172]),c_0_40])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : REL028-2 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 19:03:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 3.14/3.25 % Version : CSE_E---1.5
% 3.14/3.25 % Problem : theBenchmark.p
% 3.14/3.25 % Proof found
% 3.14/3.25 % SZS status Theorem for theBenchmark.p
% 3.14/3.25 % SZS output start Proof
% See solution above
% 3.14/3.26 % Total time : 2.679000 s
% 3.14/3.26 % SZS output end Proof
% 3.14/3.26 % Total time : 2.682000 s
%------------------------------------------------------------------------------