TSTP Solution File: SET129-6 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET129-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n014.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 14:33:14 EDT 2023
% Result : Unsatisfiable 0.20s 0.60s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 67
% Syntax : Number of formulae : 108 ( 23 unt; 52 typ; 0 def)
% Number of atoms : 113 ( 24 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 112 ( 55 ~; 57 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 67 ( 40 >; 27 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 43 ( 43 usr; 12 con; 0-3 aty)
% Number of variables : 57 ( 5 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
subclass: ( $i * $i ) > $o ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
not_subclass_element: ( $i * $i ) > $i ).
tff(decl_25,type,
universal_class: $i ).
tff(decl_26,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_27,type,
singleton: $i > $i ).
tff(decl_28,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_29,type,
cross_product: ( $i * $i ) > $i ).
tff(decl_30,type,
first: $i > $i ).
tff(decl_31,type,
second: $i > $i ).
tff(decl_32,type,
element_relation: $i ).
tff(decl_33,type,
intersection: ( $i * $i ) > $i ).
tff(decl_34,type,
complement: $i > $i ).
tff(decl_35,type,
union: ( $i * $i ) > $i ).
tff(decl_36,type,
symmetric_difference: ( $i * $i ) > $i ).
tff(decl_37,type,
restrict: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
null_class: $i ).
tff(decl_39,type,
domain_of: $i > $i ).
tff(decl_40,type,
rotate: $i > $i ).
tff(decl_41,type,
flip: $i > $i ).
tff(decl_42,type,
inverse: $i > $i ).
tff(decl_43,type,
range_of: $i > $i ).
tff(decl_44,type,
domain: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
range: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
image: ( $i * $i ) > $i ).
tff(decl_47,type,
successor: $i > $i ).
tff(decl_48,type,
successor_relation: $i ).
tff(decl_49,type,
inductive: $i > $o ).
tff(decl_50,type,
omega: $i ).
tff(decl_51,type,
sum_class: $i > $i ).
tff(decl_52,type,
power_class: $i > $i ).
tff(decl_53,type,
compose: ( $i * $i ) > $i ).
tff(decl_54,type,
single_valued_class: $i > $o ).
tff(decl_55,type,
identity_relation: $i ).
tff(decl_56,type,
function: $i > $o ).
tff(decl_57,type,
regular: $i > $i ).
tff(decl_58,type,
apply: ( $i * $i ) > $i ).
tff(decl_59,type,
choice: $i ).
tff(decl_60,type,
one_to_one: $i > $o ).
tff(decl_61,type,
subset_relation: $i ).
tff(decl_62,type,
diagonalise: $i > $i ).
tff(decl_63,type,
cantor: $i > $i ).
tff(decl_64,type,
operation: $i > $o ).
tff(decl_65,type,
compatible: ( $i * $i * $i ) > $o ).
tff(decl_66,type,
homomorphism: ( $i * $i * $i ) > $o ).
tff(decl_67,type,
not_homomorphism1: ( $i * $i * $i ) > $i ).
tff(decl_68,type,
not_homomorphism2: ( $i * $i * $i ) > $i ).
tff(decl_69,type,
set_builder: ( $i * $i ) > $i ).
tff(decl_70,type,
u: $i ).
tff(decl_71,type,
x: $i ).
tff(decl_72,type,
y: $i ).
tff(decl_73,type,
z: $i ).
cnf(definition_of_set_builder,axiom,
union(singleton(X1),X2) = set_builder(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_of_set_builder) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(prove_members_of_built_triple_1,negated_conjecture,
member(u,set_builder(x,set_builder(y,set_builder(z,null_class)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_members_of_built_triple_1) ).
cnf(union,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
cnf(subclass_members,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(intersection3,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).
cnf(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
cnf(unordered_pair_member,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair_member) ).
cnf(prove_members_of_built_triple_4,negated_conjecture,
u != z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_members_of_built_triple_4) ).
cnf(prove_members_of_built_triple_3,negated_conjecture,
u != y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_members_of_built_triple_3) ).
cnf(intersection1,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
cnf(regularity2,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',regularity2) ).
cnf(prove_members_of_built_triple_2,negated_conjecture,
u != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_members_of_built_triple_2) ).
cnf(c_0_15,axiom,
union(singleton(X1),X2) = set_builder(X1,X2),
definition_of_set_builder ).
cnf(c_0_16,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_17,negated_conjecture,
member(u,set_builder(x,set_builder(y,set_builder(z,null_class)))),
prove_members_of_built_triple_1 ).
cnf(c_0_18,plain,
union(unordered_pair(X1,X1),X2) = set_builder(X1,X2),
inference(rw,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(c_0_20,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_21,negated_conjecture,
member(u,complement(intersection(complement(unordered_pair(x,x)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))))))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_18]),c_0_18]),c_0_19]),c_0_19]),c_0_19]) ).
cnf(c_0_22,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_23,negated_conjecture,
( member(u,X1)
| ~ subclass(complement(intersection(complement(unordered_pair(x,x)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))))),X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_25,negated_conjecture,
~ member(u,intersection(complement(unordered_pair(x,x)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))))),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_26,axiom,
( member(X1,intersection(X2,X3))
| ~ member(X1,X2)
| ~ member(X1,X3) ),
intersection3 ).
cnf(c_0_27,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
complement2 ).
cnf(c_0_28,negated_conjecture,
member(u,universal_class),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_29,negated_conjecture,
( ~ member(u,complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))))
| ~ member(u,complement(unordered_pair(x,x))) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
( member(u,complement(X1))
| member(u,X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
( member(u,complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))))
| ~ member(u,complement(unordered_pair(x,x))) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_32,negated_conjecture,
( ~ member(u,intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))
| ~ member(u,complement(unordered_pair(x,x))) ),
inference(spm,[status(thm)],[c_0_22,c_0_31]) ).
cnf(c_0_33,negated_conjecture,
( ~ member(u,complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))
| ~ member(u,complement(unordered_pair(x,x)))
| ~ member(u,complement(unordered_pair(y,y))) ),
inference(spm,[status(thm)],[c_0_32,c_0_26]) ).
cnf(c_0_34,negated_conjecture,
( member(u,complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))
| ~ member(u,complement(unordered_pair(x,x)))
| ~ member(u,complement(unordered_pair(y,y))) ),
inference(spm,[status(thm)],[c_0_33,c_0_30]) ).
cnf(c_0_35,negated_conjecture,
( ~ member(u,intersection(complement(unordered_pair(z,z)),complement(null_class)))
| ~ member(u,complement(unordered_pair(x,x)))
| ~ member(u,complement(unordered_pair(y,y))) ),
inference(spm,[status(thm)],[c_0_22,c_0_34]) ).
cnf(c_0_36,negated_conjecture,
( ~ member(u,complement(unordered_pair(x,x)))
| ~ member(u,complement(unordered_pair(y,y)))
| ~ member(u,complement(unordered_pair(z,z)))
| ~ member(u,complement(null_class)) ),
inference(spm,[status(thm)],[c_0_35,c_0_26]) ).
cnf(c_0_37,negated_conjecture,
( member(u,unordered_pair(z,z))
| ~ member(u,complement(unordered_pair(x,x)))
| ~ member(u,complement(unordered_pair(y,y)))
| ~ member(u,complement(null_class)) ),
inference(spm,[status(thm)],[c_0_36,c_0_30]) ).
cnf(c_0_38,negated_conjecture,
( member(u,unordered_pair(y,y))
| member(u,unordered_pair(z,z))
| ~ member(u,complement(unordered_pair(x,x)))
| ~ member(u,complement(null_class)) ),
inference(spm,[status(thm)],[c_0_37,c_0_30]) ).
cnf(c_0_39,negated_conjecture,
( member(u,unordered_pair(z,z))
| member(u,unordered_pair(y,y))
| member(u,null_class)
| ~ member(u,complement(unordered_pair(x,x))) ),
inference(spm,[status(thm)],[c_0_38,c_0_30]) ).
cnf(c_0_40,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
unordered_pair_member ).
cnf(c_0_41,negated_conjecture,
( member(u,unordered_pair(x,x))
| member(u,unordered_pair(y,y))
| member(u,unordered_pair(z,z))
| member(u,null_class) ),
inference(spm,[status(thm)],[c_0_39,c_0_30]) ).
cnf(c_0_42,negated_conjecture,
u != z,
prove_members_of_built_triple_4 ).
cnf(c_0_43,negated_conjecture,
( member(u,unordered_pair(y,y))
| member(u,unordered_pair(x,x))
| member(u,null_class) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_44,negated_conjecture,
u != y,
prove_members_of_built_triple_3 ).
cnf(c_0_45,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_46,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
regularity2 ).
cnf(c_0_47,negated_conjecture,
( member(u,unordered_pair(x,x))
| member(u,null_class) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_43]),c_0_44]) ).
cnf(c_0_48,negated_conjecture,
u != x,
prove_members_of_built_triple_2 ).
cnf(c_0_49,plain,
( X1 = null_class
| member(X2,X1)
| ~ member(X2,null_class) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,negated_conjecture,
member(u,null_class),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_47]),c_0_48]) ).
cnf(c_0_51,negated_conjecture,
( X1 = null_class
| member(u,X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_52,negated_conjecture,
( complement(X1) = null_class
| ~ member(u,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_51]) ).
cnf(c_0_53,negated_conjecture,
( ~ member(X1,null_class)
| ~ member(u,X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_52]) ).
cnf(c_0_54,negated_conjecture,
~ member(u,X1),
inference(spm,[status(thm)],[c_0_53,c_0_50]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_30,c_0_54]),c_0_54]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET129-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n014.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 15:53:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.60 % Version : CSE_E---1.5
% 0.20/0.60 % Problem : theBenchmark.p
% 0.20/0.60 % Proof found
% 0.20/0.60 % SZS status Theorem for theBenchmark.p
% 0.20/0.60 % SZS output start Proof
% See solution above
% 0.20/0.60 % Total time : 0.024000 s
% 0.20/0.60 % SZS output end Proof
% 0.20/0.60 % Total time : 0.028000 s
%------------------------------------------------------------------------------