TSTP Solution File: SET041-3 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET041-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n012.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 14:32:26 EDT 2023
% Result : Unsatisfiable 0.21s 0.62s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 81
% Syntax : Number of formulae : 91 ( 9 unt; 75 typ; 0 def)
% Number of atoms : 27 ( 6 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 13 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 122 ( 66 >; 56 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-5 aty)
% Number of functors : 62 ( 62 usr; 9 con; 0-5 aty)
% Number of variables : 19 ( 0 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,
a_function: $i ).
tff(decl_95,type,
a: $i ).
tff(decl_96,type,
another_function: $i ).
cnf(apply_for_composition1,axiom,
( subset(apply(X3,apply(X1,X2)),apply(compose(X3,X1),X2))
| ~ function(X1)
| ~ member(X2,domain_of(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply_for_composition1) ).
cnf(member_of_domain,hypothesis,
member(a,domain_of(a_function)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_domain) ).
cnf(a_function,hypothesis,
function(a_function),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_function) ).
cnf(two_sets_equal,axiom,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',two_sets_equal) ).
cnf(apply_for_composition2,axiom,
( subset(apply(compose(X2,X1),X3),apply(X2,apply(X1,X3)))
| ~ function(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apply_for_composition2) ).
cnf(prove_apply_for_composition3,negated_conjecture,
apply(another_function,apply(a_function,a)) != apply(compose(another_function,a_function),a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_apply_for_composition3) ).
cnf(c_0_6,axiom,
( subset(apply(X3,apply(X1,X2)),apply(compose(X3,X1),X2))
| ~ function(X1)
| ~ member(X2,domain_of(X1)) ),
apply_for_composition1 ).
cnf(c_0_7,hypothesis,
member(a,domain_of(a_function)),
member_of_domain ).
cnf(c_0_8,hypothesis,
function(a_function),
a_function ).
cnf(c_0_9,axiom,
( X1 = X2
| ~ subset(X1,X2)
| ~ subset(X2,X1) ),
two_sets_equal ).
cnf(c_0_10,hypothesis,
subset(apply(X1,apply(a_function,a)),apply(compose(X1,a_function),a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8])]) ).
cnf(c_0_11,hypothesis,
( apply(compose(X1,a_function),a) = apply(X1,apply(a_function,a))
| ~ subset(apply(compose(X1,a_function),a),apply(X1,apply(a_function,a))) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,axiom,
( subset(apply(compose(X2,X1),X3),apply(X2,apply(X1,X3)))
| ~ function(X1) ),
apply_for_composition2 ).
cnf(c_0_13,negated_conjecture,
apply(another_function,apply(a_function,a)) != apply(compose(another_function,a_function),a),
prove_apply_for_composition3 ).
cnf(c_0_14,hypothesis,
apply(compose(X1,a_function),a) = apply(X1,apply(a_function,a)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_8])]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET041-3 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n012.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 12:16:55 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 0.21/0.62 % Version : CSE_E---1.5
% 0.21/0.62 % Problem : theBenchmark.p
% 0.21/0.62 % Proof found
% 0.21/0.62 % SZS status Theorem for theBenchmark.p
% 0.21/0.62 % SZS output start Proof
% See solution above
% 0.21/0.62 % Total time : 0.039000 s
% 0.21/0.62 % SZS output end Proof
% 0.21/0.62 % Total time : 0.045000 s
%------------------------------------------------------------------------------