TSTP Solution File: SET080-6 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET080-6 : 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 : n016.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 14:32:51 EDT 2023
% Result : Unsatisfiable 0.19s 0.59s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 54
% Syntax : Number of formulae : 66 ( 12 unt; 47 typ; 0 def)
% Number of atoms : 28 ( 2 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 13 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 65 ( 39 >; 26 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 38 ( 38 usr; 8 con; 0-3 aty)
% Number of variables : 17 ( 4 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 ).
cnf(inductive1,axiom,
( member(null_class,X1)
| ~ inductive(X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',inductive1) ).
cnf(omega_is_inductive1,axiom,
inductive(omega),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',omega_is_inductive1) ).
cnf(prove_null_class_in_its_singleton_1,negated_conjecture,
~ member(null_class,singleton(null_class)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_null_class_in_its_singleton_1) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
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(unordered_pair3,axiom,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',unordered_pair3) ).
cnf(class_elements_are_sets,axiom,
subclass(X1,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
cnf(c_0_7,axiom,
( member(null_class,X1)
| ~ inductive(X1) ),
inductive1 ).
cnf(c_0_8,axiom,
inductive(omega),
omega_is_inductive1 ).
cnf(c_0_9,negated_conjecture,
~ member(null_class,singleton(null_class)),
prove_null_class_in_its_singleton_1 ).
cnf(c_0_10,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_11,axiom,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
subclass_members ).
cnf(c_0_12,plain,
member(null_class,omega),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_13,negated_conjecture,
~ member(null_class,unordered_pair(null_class,null_class)),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,axiom,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
unordered_pair3 ).
cnf(c_0_15,plain,
( member(null_class,X1)
| ~ subclass(omega,X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,axiom,
subclass(X1,universal_class),
class_elements_are_sets ).
cnf(c_0_17,negated_conjecture,
~ member(null_class,universal_class),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET080-6 : 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
% 0.15/0.34 % Computer : n016.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Sat Aug 26 12:33:26 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.59 % Version : CSE_E---1.5
% 0.19/0.59 % Problem : theBenchmark.p
% 0.19/0.59 % Proof found
% 0.19/0.59 % SZS status Theorem for theBenchmark.p
% 0.19/0.59 % SZS output start Proof
% See solution above
% 0.19/0.60 % Total time : 0.016000 s
% 0.19/0.60 % SZS output end Proof
% 0.19/0.60 % Total time : 0.021000 s
%------------------------------------------------------------------------------