TSTP Solution File: SET083+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET083+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 : n031.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 14:32:53 EDT 2023
% Result : Theorem 0.21s 0.62s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 45
% Syntax : Number of formulae : 68 ( 14 unt; 40 typ; 0 def)
% Number of atoms : 64 ( 31 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 55 ( 19 ~; 20 |; 12 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 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 : 35 ( 35 usr; 9 con; 0-3 aty)
% Number of variables : 31 ( 4 sgn; 17 !; 1 ?; 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 ).
fof(singleton_identified_by_element1,conjecture,
! [X1,X2] :
( ( singleton(X1) = singleton(X2)
& member(X1,universal_class) )
=> X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton_identified_by_element1) ).
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(unordered_pair_defn,axiom,
! [X3,X1,X2] :
( member(X3,unordered_pair(X1,X2))
<=> ( member(X3,universal_class)
& ( X3 = X1
| X3 = X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).
fof(regularity,axiom,
! [X1] :
( X1 != null_class
=> ? [X3] :
( member(X3,universal_class)
& member(X3,X1)
& disjoint(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',regularity) ).
fof(null_class_defn,axiom,
! [X1] : ~ member(X1,null_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',null_class_defn) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( ( singleton(X1) = singleton(X2)
& member(X1,universal_class) )
=> X1 = X2 ),
inference(assume_negation,[status(cth)],[singleton_identified_by_element1]) ).
fof(c_0_6,negated_conjecture,
( singleton(esk8_0) = singleton(esk9_0)
& member(esk8_0,universal_class)
& esk8_0 != esk9_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_7,plain,
! [X24] : singleton(X24) = unordered_pair(X24,X24),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
fof(c_0_8,plain,
! [X19,X20,X21] :
( ( member(X19,universal_class)
| ~ member(X19,unordered_pair(X20,X21)) )
& ( X19 = X20
| X19 = X21
| ~ member(X19,unordered_pair(X20,X21)) )
& ( X19 != X20
| ~ member(X19,universal_class)
| member(X19,unordered_pair(X20,X21)) )
& ( X19 != X21
| ~ member(X19,universal_class)
| member(X19,unordered_pair(X20,X21)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[unordered_pair_defn])])]) ).
cnf(c_0_9,negated_conjecture,
singleton(esk8_0) = singleton(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
unordered_pair(esk9_0,esk9_0) = unordered_pair(esk8_0,esk8_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_10]) ).
fof(c_0_13,plain,
! [X101] :
( ( member(esk6_1(X101),universal_class)
| X101 = null_class )
& ( member(esk6_1(X101),X101)
| X101 = null_class )
& ( disjoint(esk6_1(X101),X101)
| X101 = null_class ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[regularity])])])]) ).
cnf(c_0_14,negated_conjecture,
( X1 = esk9_0
| ~ member(X1,unordered_pair(esk8_0,esk8_0)) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
( member(esk6_1(X1),X1)
| X1 = null_class ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,plain,
( member(X1,unordered_pair(X3,X2))
| X1 != X2
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,negated_conjecture,
( esk6_1(unordered_pair(esk8_0,esk8_0)) = esk9_0
| unordered_pair(esk8_0,esk8_0) = null_class ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_18,plain,
! [X1] : ~ member(X1,null_class),
inference(fof_simplification,[status(thm)],[null_class_defn]) ).
cnf(c_0_19,plain,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_20,negated_conjecture,
member(esk8_0,universal_class),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_21,negated_conjecture,
( unordered_pair(esk8_0,esk8_0) = null_class
| member(esk9_0,unordered_pair(esk8_0,esk8_0)) ),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
esk8_0 != esk9_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_23,plain,
! [X46] : ~ member(X46,null_class),
inference(variable_rename,[status(thm)],[c_0_18]) ).
cnf(c_0_24,negated_conjecture,
member(esk8_0,unordered_pair(X1,esk8_0)),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,negated_conjecture,
unordered_pair(esk8_0,esk8_0) = null_class,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_21]),c_0_22]) ).
cnf(c_0_26,plain,
~ member(X1,null_class),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET083+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
% 0.13/0.36 % Computer : n031.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Sat Aug 26 09:25:08 EDT 2023
% 0.13/0.36 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 0.21/0.62 % Version : CSE_E---1.5
% 0.21/0.62 % Problem : theBenchmark.p
% 0.21/0.62 % Proof found
% 0.21/0.62 % SZS status Theorem for theBenchmark.p
% 0.21/0.62 % SZS output start Proof
% See solution above
% 0.21/0.62 % Total time : 0.024000 s
% 0.21/0.62 % SZS output end Proof
% 0.21/0.62 % Total time : 0.028000 s
%------------------------------------------------------------------------------