TSTP Solution File: SET020+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET020+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n005.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 14:32:13 EDT 2023
% Result : Theorem 0.68s 0.76s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 45
% Syntax : Number of formulae : 67 ( 14 unt; 41 typ; 0 def)
% Number of atoms : 57 ( 32 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 51 ( 20 ~; 16 |; 12 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 47 ( 31 >; 16 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 36 ( 36 usr; 10 con; 0-3 aty)
% Number of variables : 31 ( 0 sgn; 16 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
subclass: ( $i * $i ) > $o ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
universal_class: $i ).
tff(decl_25,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_26,type,
singleton: $i > $i ).
tff(decl_27,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_28,type,
cross_product: ( $i * $i ) > $i ).
tff(decl_29,type,
first: $i > $i ).
tff(decl_30,type,
second: $i > $i ).
tff(decl_31,type,
element_relation: $i ).
tff(decl_32,type,
intersection: ( $i * $i ) > $i ).
tff(decl_33,type,
complement: $i > $i ).
tff(decl_34,type,
restrict: ( $i * $i * $i ) > $i ).
tff(decl_35,type,
null_class: $i ).
tff(decl_36,type,
domain_of: $i > $i ).
tff(decl_37,type,
rotate: $i > $i ).
tff(decl_38,type,
flip: $i > $i ).
tff(decl_39,type,
union: ( $i * $i ) > $i ).
tff(decl_40,type,
successor: $i > $i ).
tff(decl_41,type,
successor_relation: $i ).
tff(decl_42,type,
inverse: $i > $i ).
tff(decl_43,type,
range_of: $i > $i ).
tff(decl_44,type,
image: ( $i * $i ) > $i ).
tff(decl_45,type,
inductive: $i > $o ).
tff(decl_46,type,
sum_class: $i > $i ).
tff(decl_47,type,
power_class: $i > $i ).
tff(decl_48,type,
compose: ( $i * $i ) > $i ).
tff(decl_49,type,
identity_relation: $i ).
tff(decl_50,type,
function: $i > $o ).
tff(decl_51,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_52,type,
apply: ( $i * $i ) > $i ).
tff(decl_53,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk2_0: $i ).
tff(decl_55,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_56,type,
esk4_1: $i > $i ).
tff(decl_57,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_58,type,
esk6_1: $i > $i ).
tff(decl_59,type,
esk7_0: $i ).
tff(decl_60,type,
esk8_0: $i ).
tff(decl_61,type,
esk9_0: $i ).
tff(decl_62,type,
esk10_0: $i ).
fof(ordered_pair_defn,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',ordered_pair_defn) ).
fof(singleton_set_defn,axiom,
! [X1] : singleton(X1) = unordered_pair(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
fof(first_second,axiom,
! [X1,X2] :
( ( member(X1,universal_class)
& member(X2,universal_class) )
=> ( first(ordered_pair(X1,X2)) = X1
& second(ordered_pair(X1,X2)) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',first_second) ).
fof(unique_1st_and_2nd_in_pair_of_sets1,conjecture,
! [X3,X4,X1] :
( ( member(X3,universal_class)
& member(X4,universal_class)
& X1 = ordered_pair(X3,X4) )
=> ( first(X1) = X3
& second(X1) = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unique_1st_and_2nd_in_pair_of_sets1) ).
fof(c_0_4,plain,
! [X25,X26] : ordered_pair(X25,X26) = unordered_pair(singleton(X25),unordered_pair(X25,singleton(X26))),
inference(variable_rename,[status(thm)],[ordered_pair_defn]) ).
fof(c_0_5,plain,
! [X24] : singleton(X24) = unordered_pair(X24,X24),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
fof(c_0_6,plain,
! [X31,X32] :
( ( first(ordered_pair(X31,X32)) = X31
| ~ member(X31,universal_class)
| ~ member(X32,universal_class) )
& ( second(ordered_pair(X31,X32)) = X32
| ~ member(X31,universal_class)
| ~ member(X32,universal_class) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[first_second])])]) ).
cnf(c_0_7,plain,
ordered_pair(X1,X2) = unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_8,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_9,negated_conjecture,
~ ! [X3,X4,X1] :
( ( member(X3,universal_class)
& member(X4,universal_class)
& X1 = ordered_pair(X3,X4) )
=> ( first(X1) = X3
& second(X1) = X4 ) ),
inference(assume_negation,[status(cth)],[unique_1st_and_2nd_in_pair_of_sets1]) ).
cnf(c_0_10,plain,
( second(ordered_pair(X1,X2)) = X2
| ~ member(X1,universal_class)
| ~ member(X2,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_8]),c_0_8]) ).
fof(c_0_12,negated_conjecture,
( member(esk8_0,universal_class)
& member(esk9_0,universal_class)
& esk10_0 = ordered_pair(esk8_0,esk9_0)
& ( first(esk10_0) != esk8_0
| second(esk10_0) != esk9_0 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_13,plain,
( second(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))) = X2
| ~ member(X2,universal_class)
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,negated_conjecture,
member(esk9_0,universal_class),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,negated_conjecture,
esk10_0 = ordered_pair(esk8_0,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( first(ordered_pair(X1,X2)) = X1
| ~ member(X1,universal_class)
| ~ member(X2,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_17,negated_conjecture,
( second(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(esk9_0,esk9_0)))) = esk9_0
| ~ member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
member(esk8_0,universal_class),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_19,negated_conjecture,
esk10_0 = unordered_pair(unordered_pair(esk8_0,esk8_0),unordered_pair(esk8_0,unordered_pair(esk9_0,esk9_0))),
inference(rw,[status(thm)],[c_0_15,c_0_11]) ).
cnf(c_0_20,plain,
( first(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))) = X1
| ~ member(X2,universal_class)
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[c_0_16,c_0_11]) ).
cnf(c_0_21,negated_conjecture,
( first(esk10_0) != esk8_0
| second(esk10_0) != esk9_0 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_22,negated_conjecture,
second(esk10_0) = esk9_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_23,negated_conjecture,
( first(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(esk9_0,esk9_0)))) = X1
| ~ member(X1,universal_class) ),
inference(spm,[status(thm)],[c_0_20,c_0_14]) ).
cnf(c_0_24,negated_conjecture,
first(esk10_0) != esk8_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22])]) ).
cnf(c_0_25,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_18]),c_0_19]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET020+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.12/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.37 % Computer : n005.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Sat Aug 26 14:44:08 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.22/0.62 start to proof: theBenchmark
% 0.68/0.76 % Version : CSE_E---1.5
% 0.68/0.76 % Problem : theBenchmark.p
% 0.68/0.76 % Proof found
% 0.68/0.76 % SZS status Theorem for theBenchmark.p
% 0.68/0.76 % SZS output start Proof
% See solution above
% 0.68/0.77 % Total time : 0.130000 s
% 0.68/0.77 % SZS output end Proof
% 0.68/0.77 % Total time : 0.132000 s
%------------------------------------------------------------------------------