TSTP Solution File: LAT247-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT247-1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n032.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 06:00:12 EDT 2023
% Result : Unsatisfiable 21.49s 21.63s
% Output : CNFRefutation 21.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 21
% Syntax : Number of formulae : 106 ( 95 unt; 7 typ; 0 def)
% Number of atoms : 106 ( 105 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 142 ( 25 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
meet: ( $i * $i ) > $i ).
tff(decl_23,type,
join: ( $i * $i ) > $i ).
tff(decl_24,type,
complement: $i > $i ).
tff(decl_25,type,
one: $i ).
tff(decl_26,type,
zero: $i ).
tff(decl_27,type,
b: $i ).
tff(decl_28,type,
a: $i ).
cnf(prove_distributivity_hypothesis,hypothesis,
meet(b,a) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity_hypothesis) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
cnf(associativity_of_meet,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',associativity_of_meet) ).
cnf(absorption2,axiom,
join(X1,meet(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).
cnf(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption1) ).
cnf(complement_join,axiom,
join(X1,complement(X1)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',complement_join) ).
cnf(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',idempotence_of_meet) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
cnf(complement_meet,axiom,
meet(X1,complement(X1)) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',complement_meet) ).
cnf(associativity_of_join,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',associativity_of_join) ).
cnf(idempotence_of_join,axiom,
join(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',idempotence_of_join) ).
cnf(equation_H61,axiom,
meet(join(X1,X2),join(X1,X3)) = join(X1,meet(join(X1,X2),join(meet(X1,X2),X3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H61) ).
cnf(meet_join_complement,axiom,
( complement(X1) = X2
| meet(X1,X2) != zero
| join(X1,X2) != one ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',meet_join_complement) ).
cnf(prove_distributivity,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity) ).
cnf(c_0_14,hypothesis,
meet(b,a) = a,
prove_distributivity_hypothesis ).
cnf(c_0_15,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_16,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_17,hypothesis,
meet(a,b) = a,
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,axiom,
join(X1,meet(X1,X2)) = X1,
absorption2 ).
cnf(c_0_19,hypothesis,
meet(a,meet(b,X1)) = meet(a,X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_21,axiom,
join(X1,complement(X1)) = one,
complement_join ).
cnf(c_0_22,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_23,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_24,hypothesis,
meet(a,meet(X1,b)) = meet(a,X1),
inference(spm,[status(thm)],[c_0_19,c_0_15]) ).
cnf(c_0_25,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_26,plain,
meet(X1,one) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,axiom,
meet(X1,complement(X1)) = zero,
complement_meet ).
cnf(c_0_28,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_16,c_0_22]) ).
cnf(c_0_29,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_30,hypothesis,
join(meet(X1,b),meet(a,X1)) = meet(X1,b),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_31,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_25]) ).
cnf(c_0_32,plain,
meet(one,X1) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_15]) ).
cnf(c_0_33,axiom,
join(X1,X1) = X1,
idempotence_of_join ).
cnf(c_0_34,hypothesis,
meet(a,complement(b)) = meet(a,zero),
inference(spm,[status(thm)],[c_0_19,c_0_27]) ).
cnf(c_0_35,plain,
meet(X1,zero) = zero,
inference(spm,[status(thm)],[c_0_28,c_0_27]) ).
cnf(c_0_36,plain,
join(X1,zero) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_27]) ).
cnf(c_0_37,plain,
meet(X1,meet(join(X1,X2),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_16,c_0_20]) ).
cnf(c_0_38,plain,
join(X1,join(X2,meet(X3,join(X1,X2)))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_23,c_0_29]) ).
cnf(c_0_39,hypothesis,
join(a,meet(b,join(X1,a))) = meet(b,join(X1,a)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_15]),c_0_25]),c_0_15]) ).
cnf(c_0_40,plain,
join(one,X1) = one,
inference(spm,[status(thm)],[c_0_20,c_0_32]) ).
cnf(c_0_41,plain,
join(X1,join(X1,X2)) = join(X1,X2),
inference(spm,[status(thm)],[c_0_29,c_0_33]) ).
cnf(c_0_42,axiom,
meet(join(X1,X2),join(X1,X3)) = join(X1,meet(join(X1,X2),join(meet(X1,X2),X3))),
equation_H61 ).
cnf(c_0_43,hypothesis,
meet(a,complement(b)) = zero,
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_44,plain,
join(zero,X1) = X1,
inference(spm,[status(thm)],[c_0_36,c_0_25]) ).
cnf(c_0_45,plain,
meet(X1,complement(join(X1,X2))) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_27]),c_0_35]) ).
cnf(c_0_46,hypothesis,
join(X1,meet(b,join(X1,a))) = join(X1,a),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_47,plain,
join(X1,join(X2,X1)) = join(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_20]),c_0_29]) ).
cnf(c_0_48,plain,
join(X1,join(complement(X1),X2)) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_21]),c_0_40]) ).
cnf(c_0_49,plain,
join(X1,one) = one,
inference(spm,[status(thm)],[c_0_41,c_0_21]) ).
cnf(c_0_50,hypothesis,
join(meet(b,X1),meet(a,X1)) = meet(b,X1),
inference(spm,[status(thm)],[c_0_23,c_0_19]) ).
cnf(c_0_51,plain,
meet(X1,meet(join(X2,X1),X3)) = meet(X1,X3),
inference(spm,[status(thm)],[c_0_16,c_0_31]) ).
cnf(c_0_52,hypothesis,
meet(join(a,complement(b)),join(a,X1)) = join(a,meet(join(a,complement(b)),X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_53,plain,
meet(X1,complement(meet(join(X1,X2),join(X1,X3)))) = zero,
inference(spm,[status(thm)],[c_0_45,c_0_42]) ).
cnf(c_0_54,hypothesis,
join(X1,meet(b,join(a,X1))) = join(a,X1),
inference(spm,[status(thm)],[c_0_46,c_0_25]) ).
cnf(c_0_55,plain,
join(X1,join(X2,meet(join(X1,X2),X3))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_29]) ).
cnf(c_0_56,plain,
join(X1,meet(join(X2,X1),join(meet(X1,X2),X3))) = meet(join(X2,X1),join(X1,X3)),
inference(spm,[status(thm)],[c_0_42,c_0_25]) ).
cnf(c_0_57,axiom,
( complement(X1) = X2
| meet(X1,X2) != zero
| join(X1,X2) != one ),
meet_join_complement ).
cnf(c_0_58,plain,
join(complement(X1),join(X2,X1)) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]),c_0_29]) ).
cnf(c_0_59,hypothesis,
join(meet(b,X1),meet(X1,a)) = meet(b,X1),
inference(spm,[status(thm)],[c_0_50,c_0_15]) ).
cnf(c_0_60,plain,
join(meet(X1,X2),meet(X1,meet(X2,X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_61,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_28,c_0_15]) ).
cnf(c_0_62,hypothesis,
meet(complement(b),join(a,meet(join(a,complement(b)),X1))) = meet(complement(b),join(a,X1)),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_63,hypothesis,
meet(X1,complement(meet(join(X1,X2),join(a,X1)))) = zero,
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_64,hypothesis,
meet(join(a,X1),join(a,complement(b))) = join(a,meet(join(a,complement(b)),X1)),
inference(spm,[status(thm)],[c_0_15,c_0_52]) ).
cnf(c_0_65,plain,
join(X1,meet(join(X1,X2),join(X2,X3))) = join(X1,X2),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_66,plain,
( complement(X1) = X2
| meet(X2,X1) != zero
| join(X1,X2) != one ),
inference(spm,[status(thm)],[c_0_57,c_0_15]) ).
cnf(c_0_67,hypothesis,
join(meet(b,X1),complement(meet(X1,a))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_25]) ).
cnf(c_0_68,plain,
join(meet(X1,X2),meet(X2,X1)) = meet(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_22]),c_0_16]),c_0_61]),c_0_16]),c_0_61]) ).
cnf(c_0_69,hypothesis,
meet(complement(b),join(a,complement(join(a,complement(b))))) = 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(spm,[status(thm)],[c_0_62,c_0_63]),c_0_36]),c_0_15]),c_0_34]),c_0_35]),c_0_29]),c_0_41]),c_0_64]),c_0_65]) ).
cnf(c_0_70,plain,
complement(complement(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_27]),c_0_25]),c_0_21])]) ).
cnf(c_0_71,plain,
join(X1,join(X2,complement(join(X2,X1)))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_47]),c_0_25]),c_0_29]) ).
cnf(c_0_72,hypothesis,
join(meet(b,X1),join(meet(b,meet(X1,complement(meet(X1,a)))),X2)) = join(meet(b,X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_67]),c_0_16]),c_0_32]),c_0_32]) ).
cnf(c_0_73,plain,
join(meet(X1,X2),complement(meet(X2,X1))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_68]),c_0_25]) ).
cnf(c_0_74,plain,
meet(zero,X1) = zero,
inference(spm,[status(thm)],[c_0_15,c_0_35]) ).
cnf(c_0_75,hypothesis,
join(a,complement(join(a,complement(b)))) = b,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_69]),c_0_70]),c_0_71])]) ).
cnf(c_0_76,hypothesis,
join(meet(b,X1),complement(meet(X1,meet(b,complement(meet(X1,a)))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_49]),c_0_16]),c_0_15]) ).
cnf(c_0_77,plain,
meet(X1,meet(complement(X1),X2)) = zero,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_27]),c_0_74]) ).
cnf(c_0_78,hypothesis,
meet(b,join(a,X1)) = join(a,meet(b,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_75]),c_0_45]),c_0_44]) ).
cnf(c_0_79,hypothesis,
join(b,a) = b,
inference(spm,[status(thm)],[c_0_23,c_0_17]) ).
cnf(c_0_80,hypothesis,
join(meet(b,X1),complement(meet(X1,meet(b,complement(meet(a,X1)))))) = one,
inference(spm,[status(thm)],[c_0_76,c_0_15]) ).
cnf(c_0_81,plain,
meet(X1,meet(X2,complement(X1))) = zero,
inference(spm,[status(thm)],[c_0_77,c_0_61]) ).
cnf(c_0_82,plain,
complement(zero) = one,
inference(spm,[status(thm)],[c_0_21,c_0_44]) ).
cnf(c_0_83,hypothesis,
meet(join(a,meet(b,X1)),X2) = meet(b,meet(join(a,X1),X2)),
inference(spm,[status(thm)],[c_0_16,c_0_78]) ).
cnf(c_0_84,hypothesis,
join(a,b) = b,
inference(rw,[status(thm)],[c_0_79,c_0_25]) ).
cnf(c_0_85,plain,
meet(X1,meet(X2,complement(meet(X1,X2)))) = zero,
inference(spm,[status(thm)],[c_0_27,c_0_16]) ).
cnf(c_0_86,hypothesis,
join(meet(b,meet(X1,complement(a))),complement(meet(X1,meet(b,complement(a))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]),c_0_26]),c_0_16]),c_0_15]) ).
cnf(c_0_87,hypothesis,
meet(b,meet(join(a,complement(b)),X1)) = meet(a,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_63]),c_0_36]),c_0_84]),c_0_15]),c_0_20]) ).
cnf(c_0_88,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_15]),c_0_16]) ).
cnf(c_0_89,hypothesis,
join(b,join(a,X1)) = join(b,X1),
inference(spm,[status(thm)],[c_0_29,c_0_79]) ).
cnf(c_0_90,hypothesis,
join(a,meet(complement(a),join(a,complement(b)))) = join(a,complement(b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_21]),c_0_26]),c_0_15]) ).
cnf(c_0_91,plain,
join(X1,join(X2,complement(X1))) = one,
inference(spm,[status(thm)],[c_0_48,c_0_25]) ).
cnf(c_0_92,plain,
( meet(X1,complement(meet(X2,X1))) = complement(X2)
| join(X2,meet(X1,complement(meet(X2,X1)))) != one ),
inference(spm,[status(thm)],[c_0_57,c_0_85]) ).
cnf(c_0_93,hypothesis,
complement(meet(b,meet(complement(a),join(a,complement(b))))) = one,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_87]),c_0_27]),c_0_88]),c_0_15]),c_0_44]) ).
cnf(c_0_94,hypothesis,
join(b,meet(complement(a),join(a,complement(b)))) = one,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]) ).
cnf(c_0_95,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
prove_distributivity ).
cnf(c_0_96,hypothesis,
meet(complement(a),join(a,complement(b))) = complement(b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_26]),c_0_26]),c_0_94])]) ).
cnf(c_0_97,negated_conjecture,
join(complement(a),complement(b)) != complement(a),
inference(rw,[status(thm)],[c_0_95,c_0_25]) ).
cnf(c_0_98,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_96]),c_0_97]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : LAT247-1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.09 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 300
% 0.09/0.28 % DateTime : Thu Aug 24 07:59:11 EDT 2023
% 0.09/0.28 % CPUTime :
% 0.13/0.45 start to proof: theBenchmark
% 21.49/21.63 % Version : CSE_E---1.5
% 21.49/21.63 % Problem : theBenchmark.p
% 21.49/21.63 % Proof found
% 21.49/21.63 % SZS status Theorem for theBenchmark.p
% 21.49/21.63 % SZS output start Proof
% See solution above
% 21.49/21.63 % Total time : 21.105000 s
% 21.49/21.63 % SZS output end Proof
% 21.49/21.63 % Total time : 21.108000 s
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