TSTP Solution File: NUM009-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM009-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n019.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 10:26:07 EDT 2023
% Result : Unsatisfiable 0.20s 0.63s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 115
% Syntax : Number of formulae : 122 ( 6 unt; 110 typ; 0 def)
% Number of atoms : 20 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 16 ( 8 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 183 ( 98 >; 85 *; 0 +; 0 <<)
% Number of predicates : 20 ( 19 usr; 1 prp; 0-5 aty)
% Number of functors : 91 ( 91 usr; 12 con; 0-5 aty)
% Number of variables : 8 ( 2 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
member: ( $i * $i ) > $o ).
tff(decl_23,type,
little_set: $i > $o ).
tff(decl_24,type,
f1: ( $i * $i ) > $i ).
tff(decl_25,type,
non_ordered_pair: ( $i * $i ) > $i ).
tff(decl_26,type,
singleton_set: $i > $i ).
tff(decl_27,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_28,type,
ordered_pair_predicate: $i > $o ).
tff(decl_29,type,
f2: $i > $i ).
tff(decl_30,type,
f3: $i > $i ).
tff(decl_31,type,
first: $i > $i ).
tff(decl_32,type,
f4: ( $i * $i ) > $i ).
tff(decl_33,type,
f5: ( $i * $i ) > $i ).
tff(decl_34,type,
second: $i > $i ).
tff(decl_35,type,
f6: ( $i * $i ) > $i ).
tff(decl_36,type,
f7: ( $i * $i ) > $i ).
tff(decl_37,type,
estin: $i ).
tff(decl_38,type,
intersection: ( $i * $i ) > $i ).
tff(decl_39,type,
complement: $i > $i ).
tff(decl_40,type,
union: ( $i * $i ) > $i ).
tff(decl_41,type,
domain_of: $i > $i ).
tff(decl_42,type,
f8: ( $i * $i ) > $i ).
tff(decl_43,type,
cross_product: ( $i * $i ) > $i ).
tff(decl_44,type,
converse: $i > $i ).
tff(decl_45,type,
rotate_right: $i > $i ).
tff(decl_46,type,
f9: ( $i * $i ) > $i ).
tff(decl_47,type,
f10: ( $i * $i ) > $i ).
tff(decl_48,type,
f11: ( $i * $i ) > $i ).
tff(decl_49,type,
flip_range_of: $i > $i ).
tff(decl_50,type,
f12: ( $i * $i ) > $i ).
tff(decl_51,type,
f13: ( $i * $i ) > $i ).
tff(decl_52,type,
f14: ( $i * $i ) > $i ).
tff(decl_53,type,
successor: $i > $i ).
tff(decl_54,type,
empty_set: $i ).
tff(decl_55,type,
universal_set: $i ).
tff(decl_56,type,
infinity: $i ).
tff(decl_57,type,
sigma: $i > $i ).
tff(decl_58,type,
f16: ( $i * $i ) > $i ).
tff(decl_59,type,
subset: ( $i * $i ) > $o ).
tff(decl_60,type,
f17: ( $i * $i ) > $i ).
tff(decl_61,type,
proper_subset: ( $i * $i ) > $o ).
tff(decl_62,type,
powerset: $i > $i ).
tff(decl_63,type,
relation: $i > $o ).
tff(decl_64,type,
f18: $i > $i ).
tff(decl_65,type,
single_valued_set: $i > $o ).
tff(decl_66,type,
f19: $i > $i ).
tff(decl_67,type,
f20: $i > $i ).
tff(decl_68,type,
f21: $i > $i ).
tff(decl_69,type,
function: $i > $o ).
tff(decl_70,type,
image: ( $i * $i ) > $i ).
tff(decl_71,type,
f22: ( $i * $i * $i ) > $i ).
tff(decl_72,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_73,type,
f23: ( $i * $i ) > $i ).
tff(decl_74,type,
f24: $i > $i ).
tff(decl_75,type,
f25: $i ).
tff(decl_76,type,
f26: $i > $i ).
tff(decl_77,type,
range_of: $i > $i ).
tff(decl_78,type,
f27: ( $i * $i ) > $i ).
tff(decl_79,type,
identity_relation: $i ).
tff(decl_80,type,
restrict: ( $i * $i ) > $i ).
tff(decl_81,type,
one_to_one_function: $i > $o ).
tff(decl_82,type,
apply: ( $i * $i ) > $i ).
tff(decl_83,type,
f28: ( $i * $i * $i ) > $i ).
tff(decl_84,type,
apply_to_two_arguments: ( $i * $i * $i ) > $i ).
tff(decl_85,type,
maps: ( $i * $i * $i ) > $o ).
tff(decl_86,type,
closed: ( $i * $i ) > $o ).
tff(decl_87,type,
compose: ( $i * $i ) > $i ).
tff(decl_88,type,
f29: ( $i * $i * $i ) > $i ).
tff(decl_89,type,
f30: ( $i * $i * $i ) > $i ).
tff(decl_90,type,
f31: ( $i * $i * $i ) > $i ).
tff(decl_91,type,
homomorphism: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_92,type,
f32: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_93,type,
f33: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_94,type,
associative: ( $i * $i ) > $o ).
tff(decl_95,type,
f34: ( $i * $i ) > $i ).
tff(decl_96,type,
f35: ( $i * $i ) > $i ).
tff(decl_97,type,
f36: ( $i * $i ) > $i ).
tff(decl_98,type,
identity: ( $i * $i * $i ) > $o ).
tff(decl_99,type,
f37: ( $i * $i * $i ) > $i ).
tff(decl_100,type,
inverse: ( $i * $i * $i * $i ) > $o ).
tff(decl_101,type,
f38: ( $i * $i * $i * $i ) > $i ).
tff(decl_102,type,
group: ( $i * $i ) > $o ).
tff(decl_103,type,
f39: ( $i * $i ) > $i ).
tff(decl_104,type,
f40: ( $i * $i ) > $i ).
tff(decl_105,type,
commutes: ( $i * $i ) > $o ).
tff(decl_106,type,
f41: ( $i * $i ) > $i ).
tff(decl_107,type,
f42: ( $i * $i ) > $i ).
tff(decl_108,type,
natural_numbers: $i ).
tff(decl_109,type,
f43: ( $i * $i ) > $i ).
tff(decl_110,type,
f44: $i > $i ).
tff(decl_111,type,
plus: $i ).
tff(decl_112,type,
f45: ( $i * $i ) > $i ).
tff(decl_113,type,
f46: ( $i * $i ) > $i ).
tff(decl_114,type,
f47: ( $i * $i ) > $i ).
tff(decl_115,type,
f48: ( $i * $i ) > $i ).
tff(decl_116,type,
f49: $i > $i ).
tff(decl_117,type,
times: $i ).
tff(decl_118,type,
f50: ( $i * $i ) > $i ).
tff(decl_119,type,
f51: ( $i * $i ) > $i ).
tff(decl_120,type,
f52: ( $i * $i ) > $i ).
tff(decl_121,type,
f53: ( $i * $i ) > $i ).
tff(decl_122,type,
f54: $i > $i ).
tff(decl_123,type,
prime_numbers: $i ).
tff(decl_124,type,
f55: $i > $i ).
tff(decl_125,type,
f56: $i > $i ).
tff(decl_126,type,
finite: $i > $o ).
tff(decl_127,type,
f57: $i > $i ).
tff(decl_128,type,
f58: $i > $i ).
tff(decl_129,type,
twin_prime_numbers: $i ).
tff(decl_130,type,
even_numbers: $i ).
tff(decl_131,type,
f59: $i > $i ).
cnf(a2,axiom,
( little_set(X1)
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',a2) ).
cnf(infinity2,axiom,
member(empty_set,infinity),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',infinity2) ).
cnf(natural_numbers6,axiom,
( member(X1,natural_numbers)
| ~ member(X1,f44(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM003-0.ax',natural_numbers6) ).
cnf(natural_numbers4,axiom,
( member(X1,natural_numbers)
| member(empty_set,f44(X1))
| ~ little_set(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM003-0.ax',natural_numbers4) ).
cnf(prove_zero_is_a_natural,negated_conjecture,
~ member(empty_set,natural_numbers),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_zero_is_a_natural) ).
cnf(c_0_5,axiom,
( little_set(X1)
| ~ member(X1,X2) ),
a2 ).
cnf(c_0_6,axiom,
member(empty_set,infinity),
infinity2 ).
cnf(c_0_7,axiom,
( member(X1,natural_numbers)
| ~ member(X1,f44(X1)) ),
natural_numbers6 ).
cnf(c_0_8,axiom,
( member(X1,natural_numbers)
| member(empty_set,f44(X1))
| ~ little_set(X1) ),
natural_numbers4 ).
cnf(c_0_9,plain,
little_set(empty_set),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_10,negated_conjecture,
~ member(empty_set,natural_numbers),
prove_zero_is_a_natural ).
cnf(c_0_11,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9])]),c_0_10]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM009-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 15:57:58 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.59 start to proof: theBenchmark
% 0.20/0.63 % Version : CSE_E---1.5
% 0.20/0.63 % Problem : theBenchmark.p
% 0.20/0.63 % Proof found
% 0.20/0.63 % SZS status Theorem for theBenchmark.p
% 0.20/0.63 % SZS output start Proof
% See solution above
% 0.20/0.64 % Total time : 0.027000 s
% 0.20/0.64 % SZS output end Proof
% 0.20/0.64 % Total time : 0.034000 s
%------------------------------------------------------------------------------