TSTP Solution File: SET063+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET063+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n027.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 14:32:39 EDT 2023
% Result : Theorem 0.20s 0.65s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 43
% Syntax : Number of formulae : 57 ( 9 unt; 39 typ; 0 def)
% Number of atoms : 40 ( 9 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 39 ( 17 ~; 11 |; 6 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 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 : 34 ( 34 usr; 8 con; 0-3 aty)
% Number of variables : 23 ( 2 sgn; 17 !; 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 ).
fof(corollary_of_null_class_is_subclass,conjecture,
! [X1] :
( subclass(X1,null_class)
=> X1 = null_class ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',corollary_of_null_class_is_subclass) ).
fof(null_class_defn,axiom,
! [X1] : ~ member(X1,null_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',null_class_defn) ).
fof(extensionality,axiom,
! [X1,X2] :
( X1 = X2
<=> ( subclass(X1,X2)
& subclass(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',extensionality) ).
fof(subclass_defn,axiom,
! [X1,X2] :
( subclass(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',subclass_defn) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( subclass(X1,null_class)
=> X1 = null_class ),
inference(assume_negation,[status(cth)],[corollary_of_null_class_is_subclass]) ).
fof(c_0_5,plain,
! [X1] : ~ member(X1,null_class),
inference(fof_simplification,[status(thm)],[null_class_defn]) ).
fof(c_0_6,plain,
! [X17,X18] :
( ( subclass(X17,X18)
| X17 != X18 )
& ( subclass(X18,X17)
| X17 != X18 )
& ( ~ subclass(X17,X18)
| ~ subclass(X18,X17)
| X17 = X18 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[extensionality])])]) ).
fof(c_0_7,negated_conjecture,
( subclass(esk8_0,null_class)
& esk8_0 != null_class ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_8,plain,
! [X46] : ~ member(X46,null_class),
inference(variable_rename,[status(thm)],[c_0_5]) ).
fof(c_0_9,plain,
! [X10,X11,X12,X13,X14] :
( ( ~ subclass(X10,X11)
| ~ member(X12,X10)
| member(X12,X11) )
& ( member(esk1_2(X13,X14),X13)
| subclass(X13,X14) )
& ( ~ member(esk1_2(X13,X14),X14)
| subclass(X13,X14) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[subclass_defn])])])])])]) ).
cnf(c_0_10,plain,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
subclass(esk8_0,null_class),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
esk8_0 != null_class,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
~ member(X1,null_class),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( member(esk1_2(X1,X2),X1)
| subclass(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
~ subclass(null_class,esk8_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
cnf(c_0_16,plain,
subclass(null_class,X1),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET063+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sat Aug 26 09:18:04 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.62 start to proof: theBenchmark
% 0.20/0.65 % Version : CSE_E---1.5
% 0.20/0.65 % Problem : theBenchmark.p
% 0.20/0.65 % Proof found
% 0.20/0.65 % SZS status Theorem for theBenchmark.p
% 0.20/0.65 % SZS output start Proof
% See solution above
% 0.20/0.65 % Total time : 0.018000 s
% 0.20/0.65 % SZS output end Proof
% 0.20/0.65 % Total time : 0.022000 s
%------------------------------------------------------------------------------