TSTP Solution File: NUM011-1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM011-1 : 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 : n026.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 10:26:08 EDT 2023
% Result : Unsatisfiable 0.20s 0.64s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 125
% Syntax : Number of formulae : 152 ( 23 unt; 111 typ; 0 def)
% Number of atoms : 65 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 26 ~; 24 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 183 ( 98 >; 85 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-5 aty)
% Number of functors : 92 ( 92 usr; 13 con; 0-5 aty)
% Number of variables : 51 ( 14 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 ).
tff(decl_132,type,
f75: $i ).
cnf(successor,axiom,
successor(X1) = union(X1,singleton_set(X1)),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',successor) ).
cnf(singleton_set,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',singleton_set) ).
cnf(prove_zero_is_first,negated_conjecture,
empty_set = successor(f75),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_zero_is_first) ).
cnf(union,axiom,
union(X1,X2) = complement(intersection(complement(X1),complement(X2))),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',union) ).
cnf(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ little_set(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',complement2) ).
cnf(empty_set,axiom,
~ member(X1,empty_set),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',empty_set) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',intersection1) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',complement1) ).
cnf(a2,axiom,
( little_set(X1)
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',a2) ).
cnf(a_natural_number,hypothesis,
member(f75,natural_numbers),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_natural_number) ).
cnf(choice2,axiom,
( X1 = empty_set
| member(f26(X1),X1)
| ~ little_set(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',choice2) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',intersection2) ).
cnf(non_ordered_pair3,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X3 ),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',non_ordered_pair3) ).
cnf(infinity2,axiom,
member(empty_set,infinity),
file('/export/starexec/sandbox/benchmark/Axioms/SET003-0.ax',infinity2) ).
cnf(c_0_14,axiom,
successor(X1) = union(X1,singleton_set(X1)),
successor ).
cnf(c_0_15,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
singleton_set ).
cnf(c_0_16,negated_conjecture,
empty_set = successor(f75),
prove_zero_is_first ).
cnf(c_0_17,plain,
successor(X1) = union(X1,non_ordered_pair(X1,X1)),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,axiom,
union(X1,X2) = complement(intersection(complement(X1),complement(X2))),
union ).
cnf(c_0_19,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ little_set(X1) ),
complement2 ).
cnf(c_0_20,negated_conjecture,
empty_set = complement(intersection(complement(f75),complement(non_ordered_pair(f75,f75)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_21,axiom,
~ member(X1,empty_set),
empty_set ).
cnf(c_0_22,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_23,negated_conjecture,
( member(X1,intersection(complement(f75),complement(non_ordered_pair(f75,f75))))
| ~ little_set(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_24,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_25,negated_conjecture,
( member(X1,complement(f75))
| ~ little_set(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,axiom,
( little_set(X1)
| ~ member(X1,X2) ),
a2 ).
cnf(c_0_27,hypothesis,
member(f75,natural_numbers),
a_natural_number ).
cnf(c_0_28,negated_conjecture,
~ member(X1,f75),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_29,axiom,
( X1 = empty_set
| member(f26(X1),X1)
| ~ little_set(X1) ),
choice2 ).
cnf(c_0_30,hypothesis,
little_set(f75),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_32,negated_conjecture,
f75 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30])]) ).
cnf(c_0_33,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X3 ),
non_ordered_pair3 ).
cnf(c_0_34,axiom,
member(empty_set,infinity),
infinity2 ).
cnf(c_0_35,negated_conjecture,
( member(X1,complement(non_ordered_pair(empty_set,empty_set)))
| ~ little_set(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_23]),c_0_32]),c_0_32]) ).
cnf(c_0_36,plain,
( member(X1,non_ordered_pair(X2,X1))
| ~ little_set(X1) ),
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_37,plain,
little_set(empty_set),
inference(spm,[status(thm)],[c_0_26,c_0_34]) ).
cnf(c_0_38,negated_conjecture,
~ member(X1,non_ordered_pair(empty_set,empty_set)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_35]),c_0_26]) ).
cnf(c_0_39,plain,
member(empty_set,non_ordered_pair(X1,empty_set)),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_38,c_0_39]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM011-1 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Aug 25 13:36:47 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.64 % Version : CSE_E---1.5
% 0.20/0.64 % Problem : theBenchmark.p
% 0.20/0.64 % Proof found
% 0.20/0.64 % SZS status Theorem for theBenchmark.p
% 0.20/0.64 % SZS output start Proof
% See solution above
% 0.20/0.64 % Total time : 0.053000 s
% 0.20/0.64 % SZS output end Proof
% 0.20/0.64 % Total time : 0.060000 s
%------------------------------------------------------------------------------