TSTP Solution File: SET122-7 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET122-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n009.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 14:33:12 EDT 2023
% Result : Unsatisfiable 0.58s 0.82s
% Output : CNFRefutation 0.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 61
% Syntax : Number of formulae : 88 ( 19 unt; 51 typ; 0 def)
% Number of atoms : 55 ( 31 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 29 ( 11 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 67 ( 41 >; 26 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 42 ( 42 usr; 10 con; 0-3 aty)
% Number of variables : 52 ( 14 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,
member_of: $i > $i ).
tff(decl_70,type,
member_of1: $i > $i ).
tff(decl_71,type,
y: $i ).
tff(decl_72,type,
x: $i ).
cnf(ordered_pair,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(unordered_pair_equals_singleton1,axiom,
( member(X1,universal_class)
| unordered_pair(X2,X1) = singleton(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unordered_pair_equals_singleton1) ).
cnf(singleton_is_null_class,axiom,
( member(X1,universal_class)
| singleton(X1) = null_class ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_is_null_class) ).
cnf(existence_of_1st_and_2nd_3,axiom,
( member(ordered_pair(first(X1),second(X1)),cross_product(universal_class,universal_class))
| second(X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_1st_and_2nd_3) ).
cnf(prove_corollary_2_to_OP_determines_components2_1,negated_conjecture,
~ member(y,universal_class),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_OP_determines_components2_1) ).
cnf(existence_of_1st_and_2nd_5,axiom,
( ordered_pair(first(X1),second(X1)) = X1
| second(X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_1st_and_2nd_5) ).
cnf(corollary_2_to_cartesian_product,axiom,
( member(X2,universal_class)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_to_cartesian_product) ).
cnf(commutativity_of_unordered_pair,axiom,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_unordered_pair) ).
cnf(prove_corollary_2_to_OP_determines_components2_2,negated_conjecture,
second(ordered_pair(x,y)) != ordered_pair(x,y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary_2_to_OP_determines_components2_2) ).
cnf(c_0_10,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_11,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_12,axiom,
( member(X1,universal_class)
| unordered_pair(X2,X1) = singleton(X2) ),
unordered_pair_equals_singleton1 ).
cnf(c_0_13,axiom,
( member(X1,universal_class)
| singleton(X1) = null_class ),
singleton_is_null_class ).
cnf(c_0_14,axiom,
( member(ordered_pair(first(X1),second(X1)),cross_product(universal_class,universal_class))
| second(X1) = X1 ),
existence_of_1st_and_2nd_3 ).
cnf(c_0_15,plain,
unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))) = ordered_pair(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_11]) ).
cnf(c_0_16,negated_conjecture,
~ member(y,universal_class),
prove_corollary_2_to_OP_determines_components2_1 ).
cnf(c_0_17,plain,
( unordered_pair(X2,X1) = unordered_pair(X2,X2)
| member(X1,universal_class) ),
inference(rw,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_18,axiom,
( ordered_pair(first(X1),second(X1)) = X1
| second(X1) = X1 ),
existence_of_1st_and_2nd_5 ).
cnf(c_0_19,axiom,
( member(X2,universal_class)
| ~ member(ordered_pair(X1,X2),cross_product(X3,X4)) ),
corollary_2_to_cartesian_product ).
cnf(c_0_20,plain,
( unordered_pair(X1,X1) = null_class
| member(X1,universal_class) ),
inference(rw,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_21,plain,
( second(X1) = X1
| member(unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))),cross_product(universal_class,universal_class)) ),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_22,negated_conjecture,
unordered_pair(X1,y) = unordered_pair(X1,X1),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,axiom,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
commutativity_of_unordered_pair ).
cnf(c_0_24,plain,
( second(X1) = X1
| unordered_pair(unordered_pair(first(X1),first(X1)),unordered_pair(first(X1),unordered_pair(second(X1),second(X1)))) = X1 ),
inference(rw,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_25,plain,
( member(X2,universal_class)
| ~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),cross_product(X3,X4)) ),
inference(rw,[status(thm)],[c_0_19,c_0_15]) ).
cnf(c_0_26,negated_conjecture,
unordered_pair(y,y) = null_class,
inference(spm,[status(thm)],[c_0_16,c_0_20]) ).
cnf(c_0_27,negated_conjecture,
second(ordered_pair(x,y)) != ordered_pair(x,y),
prove_corollary_2_to_OP_determines_components2_2 ).
cnf(c_0_28,plain,
( second(X1) = X1
| member(unordered_pair(unordered_pair(y,first(X1)),unordered_pair(first(X1),unordered_pair(y,second(X1)))),cross_product(universal_class,universal_class)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_22]),c_0_23]) ).
cnf(c_0_29,plain,
( unordered_pair(unordered_pair(y,first(X1)),unordered_pair(first(X1),unordered_pair(y,second(X1)))) = X1
| second(X1) = X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_22]),c_0_23]),c_0_22]),c_0_23]) ).
cnf(c_0_30,negated_conjecture,
~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,null_class)),cross_product(X2,X3)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_16]) ).
cnf(c_0_31,negated_conjecture,
second(unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y)))) != unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(y,y))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_15]),c_0_15]) ).
cnf(c_0_32,plain,
( second(X1) = X1
| member(X1,cross_product(universal_class,universal_class)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_33,negated_conjecture,
~ member(unordered_pair(unordered_pair(X1,X1),unordered_pair(null_class,X1)),cross_product(X2,X3)),
inference(spm,[status(thm)],[c_0_30,c_0_23]) ).
cnf(c_0_34,negated_conjecture,
member(unordered_pair(unordered_pair(null_class,x),unordered_pair(x,x)),cross_product(universal_class,universal_class)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_26]),c_0_23]),c_0_23]) ).
cnf(c_0_35,negated_conjecture,
~ member(unordered_pair(unordered_pair(null_class,X1),unordered_pair(X1,X1)),cross_product(X2,X3)),
inference(spm,[status(thm)],[c_0_33,c_0_23]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_34,c_0_35]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SET122-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% 0.08/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.36 % Computer : n009.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 08:55:05 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.61 start to proof: theBenchmark
% 0.58/0.82 % Version : CSE_E---1.5
% 0.58/0.82 % Problem : theBenchmark.p
% 0.58/0.82 % Proof found
% 0.58/0.82 % SZS status Theorem for theBenchmark.p
% 0.58/0.82 % SZS output start Proof
% See solution above
% 0.58/0.82 % Total time : 0.197000 s
% 0.58/0.82 % SZS output end Proof
% 0.58/0.82 % Total time : 0.203000 s
%------------------------------------------------------------------------------