TSTP Solution File: SET135-6 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET135-6 : 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 : n017.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 14:33:15 EDT 2023
% Result : Unsatisfiable 0.21s 0.61s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 62
% Syntax : Number of formulae : 89 ( 15 unt; 51 typ; 0 def)
% Number of atoms : 65 ( 17 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 47 ( 20 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 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 : 42 ( 42 usr; 11 con; 0-3 aty)
% Number of variables : 46 ( 7 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,
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(complement2,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
cnf(prove_corollary_3_to_member_of_triple_1,negated_conjecture,
member(u,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_3_to_member_of_triple_1) ).
cnf(prove_corollary_3_to_member_of_triple_2,negated_conjecture,
set_builder(x,set_builder(u,set_builder(z,null_class))) = null_class,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_3_to_member_of_triple_2) ).
cnf(union,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
cnf(intersection2,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
cnf(complement1,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
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(unordered_pair2,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair2) ).
cnf(c_0_11,axiom,
union(singleton(X1),X2) = set_builder(X1,X2),
definition_of_set_builder ).
cnf(c_0_12,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_13,axiom,
( member(X1,complement(X2))
| member(X1,X2)
| ~ member(X1,universal_class) ),
complement2 ).
cnf(c_0_14,negated_conjecture,
member(u,universal_class),
prove_corollary_3_to_member_of_triple_1 ).
cnf(c_0_15,negated_conjecture,
set_builder(x,set_builder(u,set_builder(z,null_class))) = null_class,
prove_corollary_3_to_member_of_triple_2 ).
cnf(c_0_16,plain,
union(unordered_pair(X1,X1),X2) = set_builder(X1,X2),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,axiom,
complement(intersection(complement(X1),complement(X2))) = union(X1,X2),
union ).
cnf(c_0_18,negated_conjecture,
( member(u,complement(X1))
| member(u,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
complement(intersection(complement(unordered_pair(x,x)),complement(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))))) = 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_15,c_0_16]),c_0_16]),c_0_16]),c_0_17]),c_0_17]),c_0_17]) ).
cnf(c_0_20,axiom,
( member(X1,X3)
| ~ member(X1,intersection(X2,X3)) ),
intersection2 ).
cnf(c_0_21,negated_conjecture,
( member(u,intersection(complement(unordered_pair(x,x)),complement(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))))))
| member(u,null_class) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,axiom,
( ~ member(X1,complement(X2))
| ~ member(X1,X2) ),
complement1 ).
cnf(c_0_23,negated_conjecture,
( member(u,complement(complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))))
| member(u,null_class) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
( member(u,null_class)
| ~ member(u,complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,axiom,
( member(X1,X2)
| ~ member(X1,intersection(X2,X3)) ),
intersection1 ).
cnf(c_0_26,negated_conjecture,
( member(u,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))
| member(u,null_class) ),
inference(spm,[status(thm)],[c_0_24,c_0_18]) ).
cnf(c_0_27,negated_conjecture,
( member(u,complement(unordered_pair(u,u)))
| member(u,null_class) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_28,axiom,
( X1 = null_class
| intersection(X1,regular(X1)) = null_class ),
regularity2 ).
cnf(c_0_29,negated_conjecture,
( member(u,null_class)
| ~ member(u,unordered_pair(u,u)) ),
inference(spm,[status(thm)],[c_0_22,c_0_27]) ).
cnf(c_0_30,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
unordered_pair2 ).
cnf(c_0_31,plain,
( X1 = null_class
| member(X2,X1)
| ~ member(X2,null_class) ),
inference(spm,[status(thm)],[c_0_25,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
member(u,null_class),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_14])]) ).
cnf(c_0_33,negated_conjecture,
( X1 = null_class
| member(u,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_34,negated_conjecture,
( complement(X1) = null_class
| ~ member(u,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_33]) ).
cnf(c_0_35,negated_conjecture,
( ~ member(X1,null_class)
| ~ member(u,X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_34]) ).
cnf(c_0_36,negated_conjecture,
~ member(u,X1),
inference(spm,[status(thm)],[c_0_35,c_0_32]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_18,c_0_36]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SET135-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.07/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n017.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 15:29:41 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 0.21/0.61 % Version : CSE_E---1.5
% 0.21/0.61 % Problem : theBenchmark.p
% 0.21/0.61 % Proof found
% 0.21/0.61 % SZS status Theorem for theBenchmark.p
% 0.21/0.61 % SZS output start Proof
% See solution above
% 0.21/0.61 % Total time : 0.021000 s
% 0.21/0.61 % SZS output end Proof
% 0.21/0.61 % Total time : 0.026000 s
%------------------------------------------------------------------------------