TSTP Solution File: SET016-7 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET016-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% 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 14:32:08 EDT 2023
% Result : Unsatisfiable 0.18s 0.59s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 62
% Syntax : Number of formulae : 81 ( 18 unt; 53 typ; 0 def)
% Number of atoms : 40 ( 22 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 10 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 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 : 44 ( 44 usr; 12 con; 0-3 aty)
% Number of variables : 31 ( 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 ).
tff(decl_69,type,
member_of: $i > $i ).
tff(decl_70,type,
member_of1: $i > $i ).
tff(decl_71,type,
w: $i ).
tff(decl_72,type,
x: $i ).
tff(decl_73,type,
y: $i ).
tff(decl_74,type,
z: $i ).
cnf(ordered_pair,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',ordered_pair) ).
cnf(singleton_set,axiom,
unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
cnf(singleton_member_of_ordered_pair,axiom,
member(singleton(X1),ordered_pair(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_member_of_ordered_pair) ).
cnf(prove_ordered_pair_determines_components1_1,negated_conjecture,
ordered_pair(w,x) = ordered_pair(y,z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordered_pair_determines_components1_1) ).
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(only_member_in_singleton,axiom,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',only_member_in_singleton) ).
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(prove_ordered_pair_determines_components1_2,negated_conjecture,
member(w,universal_class),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordered_pair_determines_components1_2) ).
cnf(prove_ordered_pair_determines_components1_3,negated_conjecture,
w != y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ordered_pair_determines_components1_3) ).
cnf(c_0_9,axiom,
unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))) = ordered_pair(X1,X2),
ordered_pair ).
cnf(c_0_10,axiom,
unordered_pair(X1,X1) = singleton(X1),
singleton_set ).
cnf(c_0_11,axiom,
member(singleton(X1),ordered_pair(X1,X2)),
singleton_member_of_ordered_pair ).
cnf(c_0_12,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_9,c_0_10]),c_0_10]) ).
cnf(c_0_13,negated_conjecture,
ordered_pair(w,x) = ordered_pair(y,z),
prove_ordered_pair_determines_components1_1 ).
cnf(c_0_14,plain,
member(unordered_pair(X1,X1),unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_10]),c_0_12]) ).
cnf(c_0_15,negated_conjecture,
unordered_pair(unordered_pair(y,y),unordered_pair(y,unordered_pair(z,z))) = unordered_pair(unordered_pair(w,w),unordered_pair(w,unordered_pair(x,x))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_12]),c_0_12]) ).
cnf(c_0_16,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
unordered_pair_member ).
cnf(c_0_17,negated_conjecture,
member(unordered_pair(y,y),unordered_pair(unordered_pair(w,w),unordered_pair(w,unordered_pair(x,x)))),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,axiom,
( X1 = X2
| ~ member(X1,singleton(X2)) ),
only_member_in_singleton ).
cnf(c_0_19,axiom,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
unordered_pair2 ).
cnf(c_0_20,negated_conjecture,
( unordered_pair(w,unordered_pair(x,x)) = unordered_pair(y,y)
| unordered_pair(y,y) = unordered_pair(w,w) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
member(w,universal_class),
prove_ordered_pair_determines_components1_2 ).
cnf(c_0_22,plain,
( X1 = X2
| ~ member(X1,unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[c_0_18,c_0_10]) ).
cnf(c_0_23,negated_conjecture,
( unordered_pair(y,y) = unordered_pair(w,w)
| member(w,unordered_pair(y,y)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_24,negated_conjecture,
w != y,
prove_ordered_pair_determines_components1_3 ).
cnf(c_0_25,negated_conjecture,
unordered_pair(y,y) = unordered_pair(w,w),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_26,negated_conjecture,
( X1 = y
| ~ member(X1,unordered_pair(w,w)) ),
inference(spm,[status(thm)],[c_0_16,c_0_25]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_19]),c_0_21])]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET016-7 : TPTP v8.1.2. Bugfixed v7.3.0.
% 0.06/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 15:48:56 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.55 start to proof: theBenchmark
% 0.18/0.59 % Version : CSE_E---1.5
% 0.18/0.59 % Problem : theBenchmark.p
% 0.18/0.59 % Proof found
% 0.18/0.59 % SZS status Theorem for theBenchmark.p
% 0.18/0.59 % SZS output start Proof
% See solution above
% 0.18/0.60 % Total time : 0.034000 s
% 0.18/0.60 % SZS output end Proof
% 0.18/0.60 % Total time : 0.040000 s
%------------------------------------------------------------------------------