TSTP Solution File: SET038-3 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET038-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/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 14:32:25 EDT 2023
% Result : Unsatisfiable 2.61s 2.72s
% Output : CNFRefutation 2.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 97
% Syntax : Number of formulae : 143 ( 23 unt; 76 typ; 0 def)
% Number of atoms : 139 ( 32 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 146 ( 74 ~; 72 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 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 : 63 ( 63 usr; 10 con; 0-5 aty)
% Number of variables : 91 ( 8 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_domain: $i ).
tff(decl_96,type,
a_range: $i ).
tff(decl_97,type,
a: $i ).
cnf(maps2,axiom,
( domain_of(X1) = X2
| ~ maps(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',maps2) ).
cnf(a_mapping,hypothesis,
maps(a_function,a_domain,a_range),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_mapping) ).
cnf(domain2,axiom,
( member(f8(X1,X2),X2)
| ~ member(X1,domain_of(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',domain2) ).
cnf(ordered_pair,axiom,
ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair) ).
cnf(singleton_set,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',singleton_set) ).
cnf(member_of_domain,hypothesis,
member(a,a_domain),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_domain) ).
cnf(apply_for_functions1,axiom,
( apply(X3,X1) = X2
| ~ little_set(X1)
| ~ little_set(X2)
| ~ function(X3)
| ~ member(ordered_pair(X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_for_functions1) ).
cnf(ordered_pair_predicate3,axiom,
( X1 = ordered_pair(f2(X1),f3(X1))
| ~ ordered_pair_predicate(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate3) ).
cnf(relation1,axiom,
( ordered_pair_predicate(X2)
| ~ relation(X1)
| ~ member(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',relation1) ).
cnf(maps1,axiom,
( function(X1)
| ~ maps(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',maps1) ).
cnf(ordered_pair_predicate1,axiom,
( little_set(f2(X1))
| ~ ordered_pair_predicate(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate1) ).
cnf(ordered_pair_predicate2,axiom,
( little_set(f3(X1))
| ~ ordered_pair_predicate(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair_predicate2) ).
cnf(function1,axiom,
( relation(X1)
| ~ function(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',function1) ).
cnf(property_of_first,axiom,
( first(ordered_pair(X1,X2)) = X1
| ~ little_set(X1)
| ~ little_set(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_first) ).
cnf(domain3,axiom,
( X1 = first(f8(X1,X2))
| ~ member(X1,domain_of(X2)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',domain3) ).
cnf(maps3,axiom,
( subset(range_of(X1),X3)
| ~ maps(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',maps3) ).
cnf(range_of4,axiom,
( member(X1,range_of(X2))
| ~ little_set(X1)
| ~ ordered_pair_predicate(X3)
| ~ member(X3,X2)
| X1 != second(X3) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',range_of4) ).
cnf(second_component_is_small,axiom,
( little_set(second(X1))
| ~ ordered_pair_predicate(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',second_component_is_small) ).
cnf(property_of_second,axiom,
( second(ordered_pair(X1,X2)) = X2
| ~ little_set(X1)
| ~ little_set(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_of_second) ).
cnf(subset1,axiom,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',subset1) ).
cnf(prove_mapping_in_range,negated_conjecture,
~ member(apply(a_function,a),a_range),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_mapping_in_range) ).
cnf(c_0_21,axiom,
( domain_of(X1) = X2
| ~ maps(X1,X2,X3) ),
maps2 ).
cnf(c_0_22,hypothesis,
maps(a_function,a_domain,a_range),
a_mapping ).
cnf(c_0_23,axiom,
( member(f8(X1,X2),X2)
| ~ member(X1,domain_of(X2)) ),
domain2 ).
cnf(c_0_24,hypothesis,
domain_of(a_function) = a_domain,
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,axiom,
ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
ordered_pair ).
cnf(c_0_26,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
singleton_set ).
cnf(c_0_27,hypothesis,
( member(f8(X1,a_function),a_function)
| ~ member(X1,a_domain) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,hypothesis,
member(a,a_domain),
member_of_domain ).
cnf(c_0_29,axiom,
( apply(X3,X1) = X2
| ~ little_set(X1)
| ~ little_set(X2)
| ~ function(X3)
| ~ member(ordered_pair(X1,X2),X3) ),
apply_for_functions1 ).
cnf(c_0_30,plain,
ordered_pair(X1,X2) = non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,axiom,
( X1 = ordered_pair(f2(X1),f3(X1))
| ~ ordered_pair_predicate(X1) ),
ordered_pair_predicate3 ).
cnf(c_0_32,axiom,
( ordered_pair_predicate(X2)
| ~ relation(X1)
| ~ member(X2,X1) ),
relation1 ).
cnf(c_0_33,hypothesis,
member(f8(a,a_function),a_function),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,axiom,
( function(X1)
| ~ maps(X1,X2,X3) ),
maps1 ).
cnf(c_0_35,plain,
( apply(X3,X1) = X2
| ~ little_set(X2)
| ~ little_set(X1)
| ~ function(X3)
| ~ member(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)),X3) ),
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,plain,
( X1 = non_ordered_pair(non_ordered_pair(f2(X1),f2(X1)),non_ordered_pair(f2(X1),f3(X1)))
| ~ ordered_pair_predicate(X1) ),
inference(rw,[status(thm)],[c_0_31,c_0_30]) ).
cnf(c_0_37,axiom,
( little_set(f2(X1))
| ~ ordered_pair_predicate(X1) ),
ordered_pair_predicate1 ).
cnf(c_0_38,axiom,
( little_set(f3(X1))
| ~ ordered_pair_predicate(X1) ),
ordered_pair_predicate2 ).
cnf(c_0_39,hypothesis,
( ordered_pair_predicate(f8(a,a_function))
| ~ relation(a_function) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_40,axiom,
( relation(X1)
| ~ function(X1) ),
function1 ).
cnf(c_0_41,hypothesis,
function(a_function),
inference(spm,[status(thm)],[c_0_34,c_0_22]) ).
cnf(c_0_42,axiom,
( first(ordered_pair(X1,X2)) = X1
| ~ little_set(X1)
| ~ little_set(X2) ),
property_of_first ).
cnf(c_0_43,axiom,
( X1 = first(f8(X1,X2))
| ~ member(X1,domain_of(X2)) ),
domain3 ).
cnf(c_0_44,axiom,
( subset(range_of(X1),X3)
| ~ maps(X1,X2,X3) ),
maps3 ).
cnf(c_0_45,axiom,
( member(X1,range_of(X2))
| ~ little_set(X1)
| ~ ordered_pair_predicate(X3)
| ~ member(X3,X2)
| X1 != second(X3) ),
range_of4 ).
cnf(c_0_46,axiom,
( little_set(second(X1))
| ~ ordered_pair_predicate(X1) ),
second_component_is_small ).
cnf(c_0_47,axiom,
( second(ordered_pair(X1,X2)) = X2
| ~ little_set(X1)
| ~ little_set(X2) ),
property_of_second ).
cnf(c_0_48,plain,
( apply(X1,f2(X2)) = f3(X2)
| ~ function(X1)
| ~ ordered_pair_predicate(X2)
| ~ member(X2,X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_38]) ).
cnf(c_0_49,hypothesis,
ordered_pair_predicate(f8(a,a_function)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41])]) ).
cnf(c_0_50,plain,
( first(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))) = X1
| ~ little_set(X2)
| ~ little_set(X1) ),
inference(rw,[status(thm)],[c_0_42,c_0_30]) ).
cnf(c_0_51,hypothesis,
( first(f8(X1,a_function)) = X1
| ~ member(X1,a_domain) ),
inference(spm,[status(thm)],[c_0_43,c_0_24]) ).
cnf(c_0_52,axiom,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
subset1 ).
cnf(c_0_53,hypothesis,
subset(range_of(a_function),a_range),
inference(spm,[status(thm)],[c_0_44,c_0_22]) ).
cnf(c_0_54,plain,
( member(second(X1),range_of(X2))
| ~ ordered_pair_predicate(X1)
| ~ member(X1,X2) ),
inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_45]),c_0_46]) ).
cnf(c_0_55,plain,
( second(non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2))) = X2
| ~ little_set(X2)
| ~ little_set(X1) ),
inference(rw,[status(thm)],[c_0_47,c_0_30]) ).
cnf(c_0_56,hypothesis,
apply(a_function,f2(f8(a,a_function))) = f3(f8(a,a_function)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_33]),c_0_41]),c_0_49])]) ).
cnf(c_0_57,plain,
( f2(X1) = first(X1)
| ~ ordered_pair_predicate(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_36]),c_0_37]),c_0_38]) ).
cnf(c_0_58,hypothesis,
first(f8(a,a_function)) = a,
inference(spm,[status(thm)],[c_0_51,c_0_28]) ).
cnf(c_0_59,hypothesis,
( member(X1,a_range)
| ~ member(X1,range_of(a_function)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_60,hypothesis,
member(second(f8(a,a_function)),range_of(a_function)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_33]),c_0_49])]) ).
cnf(c_0_61,plain,
( f3(X1) = second(X1)
| ~ ordered_pair_predicate(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_36]),c_0_37]),c_0_38]) ).
cnf(c_0_62,hypothesis,
f3(f8(a,a_function)) = apply(a_function,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_49])]) ).
cnf(c_0_63,hypothesis,
member(second(f8(a,a_function)),a_range),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_64,hypothesis,
second(f8(a,a_function)) = apply(a_function,a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_49])]) ).
cnf(c_0_65,negated_conjecture,
~ member(apply(a_function,a),a_range),
prove_mapping_in_range ).
cnf(c_0_66,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_63,c_0_64]),c_0_65]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET038-3 : TPTP v8.1.2. Released v1.0.0.
% 0.13/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 08:59:28 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 2.61/2.72 % Version : CSE_E---1.5
% 2.61/2.72 % Problem : theBenchmark.p
% 2.61/2.72 % Proof found
% 2.61/2.72 % SZS status Theorem for theBenchmark.p
% 2.61/2.72 % SZS output start Proof
% See solution above
% 2.61/2.73 % Total time : 2.144000 s
% 2.61/2.73 % SZS output end Proof
% 2.61/2.73 % Total time : 2.150000 s
%------------------------------------------------------------------------------