TSTP Solution File: REL044-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : REL044-2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n010.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 13:36:25 EDT 2023
% Result : Unsatisfiable 2.38s 2.45s
% Output : CNFRefutation 2.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 27
% Syntax : Number of formulae : 96 ( 85 unt; 11 typ; 0 def)
% Number of atoms : 85 ( 84 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 : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 123 ( 10 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 ).
tff(decl_32,type,
sk3: $i ).
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(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(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(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(composition(complement(sk1),sk2),complement(sk3)) = complement(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_17) ).
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_18,negated_conjecture,
join(composition(sk3,converse(sk2)),sk1) != sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_18) ).
cnf(c_0_16,axiom,
converse(composition(X1,X2)) = composition(converse(X2),converse(X1)),
converse_multiplicativity_10 ).
cnf(c_0_17,axiom,
converse(converse(X1)) = X1,
converse_idempotence_8 ).
cnf(c_0_18,plain,
converse(composition(converse(X1),X2)) = composition(converse(X2),X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,axiom,
composition(X1,one) = X1,
composition_identity_6 ).
cnf(c_0_20,plain,
composition(converse(one),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_17]) ).
cnf(c_0_21,axiom,
join(composition(converse(X1),complement(composition(X1,X2))),complement(X2)) = complement(X2),
converse_cancellativity_11 ).
cnf(c_0_22,axiom,
join(X1,X2) = join(X2,X1),
maddux1_join_commutativity_1 ).
cnf(c_0_23,plain,
converse(one) = one,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,axiom,
zero = meet(X1,complement(X1)),
def_zero_13 ).
cnf(c_0_25,axiom,
meet(X1,X2) = complement(join(complement(X1),complement(X2))),
maddux4_definiton_of_meet_4 ).
cnf(c_0_26,plain,
join(complement(X1),composition(converse(X2),complement(composition(X2,X1)))) = complement(X1),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
composition(one,X1) = X1,
inference(rw,[status(thm)],[c_0_20,c_0_23]) ).
cnf(c_0_28,plain,
zero = complement(join(complement(X1),complement(complement(X1)))),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,axiom,
top = join(X1,complement(X1)),
def_top_12 ).
cnf(c_0_30,plain,
join(complement(X1),complement(X1)) = complement(X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_23]),c_0_27]) ).
cnf(c_0_31,plain,
complement(top) = zero,
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,axiom,
X1 = join(complement(join(complement(X1),complement(X2))),complement(join(complement(X1),X2))),
maddux3_a_kind_of_de_Morgan_3 ).
cnf(c_0_33,axiom,
join(X1,join(X2,X3)) = join(join(X1,X2),X3),
maddux2_join_associativity_2 ).
cnf(c_0_34,plain,
join(zero,zero) = zero,
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
join(complement(join(complement(X1),X2)),complement(join(complement(X1),complement(X2)))) = X1,
inference(rw,[status(thm)],[c_0_32,c_0_22]) ).
cnf(c_0_36,plain,
join(zero,join(zero,X1)) = join(zero,X1),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,plain,
join(zero,complement(complement(X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_29]),c_0_30]),c_0_31]),c_0_22]) ).
cnf(c_0_38,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_39,plain,
complement(complement(X1)) = X1,
inference(rw,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_40,plain,
join(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_30,c_0_39]) ).
cnf(c_0_41,plain,
join(X1,join(complement(X1),X2)) = join(top,X2),
inference(spm,[status(thm)],[c_0_33,c_0_29]) ).
cnf(c_0_42,plain,
join(X1,join(X2,complement(join(X1,X2)))) = top,
inference(spm,[status(thm)],[c_0_29,c_0_33]) ).
cnf(c_0_43,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_33,c_0_40]) ).
cnf(c_0_44,plain,
join(X1,join(X2,X3)) = join(X2,join(X3,X1)),
inference(spm,[status(thm)],[c_0_33,c_0_22]) ).
cnf(c_0_45,axiom,
converse(join(X1,X2)) = join(converse(X1),converse(X2)),
converse_additivity_9 ).
cnf(c_0_46,plain,
join(top,complement(complement(X1))) = join(X1,top),
inference(spm,[status(thm)],[c_0_41,c_0_29]) ).
cnf(c_0_47,plain,
join(top,complement(X1)) = top,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_30]),c_0_29]),c_0_22]) ).
cnf(c_0_48,plain,
join(X1,complement(join(complement(X1),X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_35]),c_0_22]) ).
cnf(c_0_49,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_44,c_0_40]) ).
cnf(c_0_50,plain,
converse(join(converse(X1),X2)) = join(X1,converse(X2)),
inference(spm,[status(thm)],[c_0_45,c_0_17]) ).
cnf(c_0_51,plain,
join(X1,top) = top,
inference(rw,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_52,plain,
join(X1,complement(join(X2,complement(X1)))) = X1,
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_53,plain,
join(X1,converse(complement(converse(X1)))) = converse(top),
inference(spm,[status(thm)],[c_0_50,c_0_29]) ).
cnf(c_0_54,plain,
join(top,X1) = top,
inference(spm,[status(thm)],[c_0_22,c_0_51]) ).
cnf(c_0_55,plain,
join(X1,join(complement(join(X2,complement(X1))),X3)) = join(X1,X3),
inference(spm,[status(thm)],[c_0_33,c_0_52]) ).
cnf(c_0_56,plain,
composition(converse(X1),complement(composition(X1,top))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_31]),c_0_38]) ).
cnf(c_0_57,plain,
converse(top) = top,
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_58,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_59,plain,
join(X1,complement(join(complement(X2),X1))) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_35]),c_0_39]) ).
cnf(c_0_60,axiom,
composition(join(X1,X2),X3) = join(composition(X1,X3),composition(X2,X3)),
composition_distributivity_7 ).
cnf(c_0_61,plain,
composition(top,complement(composition(top,top))) = zero,
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_62,plain,
converse(join(X1,converse(X2))) = join(converse(X1),X2),
inference(spm,[status(thm)],[c_0_45,c_0_17]) ).
cnf(c_0_63,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_58,c_0_25]),c_0_25]),c_0_25]),c_0_25]),c_0_25]) ).
cnf(c_0_64,plain,
join(X1,complement(join(X2,X1))) = join(X1,complement(X2)),
inference(spm,[status(thm)],[c_0_59,c_0_39]) ).
cnf(c_0_65,plain,
join(X1,join(X2,complement(join(X2,X1)))) = top,
inference(spm,[status(thm)],[c_0_42,c_0_22]) ).
cnf(c_0_66,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_22,c_0_38]) ).
cnf(c_0_67,plain,
join(complement(X1),complement(join(X2,X1))) = complement(X1),
inference(spm,[status(thm)],[c_0_52,c_0_39]) ).
cnf(c_0_68,negated_conjecture,
join(composition(complement(sk1),sk2),complement(sk3)) = complement(sk3),
goals_17 ).
cnf(c_0_69,axiom,
composition(X1,composition(X2,X3)) = composition(composition(X1,X2),X3),
composition_associativity_5 ).
cnf(c_0_70,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_60,c_0_61]),c_0_38]),c_0_54]),c_0_61]) ).
cnf(c_0_71,plain,
join(converse(zero),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_38]),c_0_17]) ).
cnf(c_0_72,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_63,c_0_22]),c_0_22]) ).
cnf(c_0_73,plain,
join(X1,complement(join(X1,X2))) = join(X1,complement(X2)),
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_64,c_0_65]),c_0_31]),c_0_66]),c_0_33]),c_0_22]),c_0_67]) ).
cnf(c_0_74,negated_conjecture,
join(complement(sk3),composition(complement(sk1),sk2)) = complement(sk3),
inference(rw,[status(thm)],[c_0_68,c_0_22]) ).
cnf(c_0_75,plain,
composition(X1,zero) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_70]) ).
cnf(c_0_76,plain,
converse(zero) = zero,
inference(spm,[status(thm)],[c_0_66,c_0_71]) ).
cnf(c_0_77,plain,
join(complement(join(complement(composition(X1,converse(X2))),complement(X3))),complement(join(complement(X3),complement(composition(complement(join(complement(X1),complement(composition(X3,X2)))),converse(X2)))))) = complement(join(complement(X3),complement(composition(complement(join(complement(X1),complement(composition(X3,X2)))),converse(X2))))),
inference(spm,[status(thm)],[c_0_72,c_0_17]) ).
cnf(c_0_78,negated_conjecture,
join(complement(sk3),complement(composition(complement(sk1),sk2))) = top,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_29]) ).
cnf(c_0_79,plain,
composition(zero,X1) = zero,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_75]),c_0_76]),c_0_76]) ).
cnf(c_0_80,plain,
complement(zero) = top,
inference(spm,[status(thm)],[c_0_29,c_0_38]) ).
cnf(c_0_81,negated_conjecture,
join(composition(sk3,converse(sk2)),sk1) != sk1,
goals_18 ).
cnf(c_0_82,negated_conjecture,
complement(join(sk1,complement(composition(sk3,converse(sk2))))) = zero,
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_77,c_0_78]),c_0_39]),c_0_39]),c_0_31]),c_0_79]),c_0_80]),c_0_51]),c_0_31]),c_0_66]),c_0_39]),c_0_31]),c_0_79]),c_0_80]),c_0_51]),c_0_31]),c_0_22]) ).
cnf(c_0_83,negated_conjecture,
join(sk1,composition(sk3,converse(sk2))) != sk1,
inference(rw,[status(thm)],[c_0_81,c_0_22]) ).
cnf(c_0_84,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_82]),c_0_66]),c_0_39]),c_0_83]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : REL044-2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Aug 25 18:54:05 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.17/0.56 start to proof: theBenchmark
% 2.38/2.45 % Version : CSE_E---1.5
% 2.38/2.45 % Problem : theBenchmark.p
% 2.38/2.45 % Proof found
% 2.38/2.45 % SZS status Theorem for theBenchmark.p
% 2.38/2.45 % SZS output start Proof
% See solution above
% 2.38/2.46 % Total time : 1.889000 s
% 2.38/2.46 % SZS output end Proof
% 2.38/2.46 % Total time : 1.891000 s
%------------------------------------------------------------------------------