TSTP Solution File: SET096+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET096+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 : n006.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 14:33:00 EDT 2023
% Result : Theorem 2.69s 2.94s
% Output : CNFRefutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 46
% Syntax : Number of formulae : 75 ( 13 unt; 40 typ; 0 def)
% Number of atoms : 95 ( 36 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 90 ( 30 ~; 38 |; 15 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 51 ( 0 sgn; 26 !; 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(two_subsets_of_singleton,conjecture,
! [X1,X2] :
( subclass(X1,singleton(X2))
=> ( X1 = null_class
| singleton(X2) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',two_subsets_of_singleton) ).
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(regularity,axiom,
! [X1] :
( X1 != null_class
=> ? [X3] :
( member(X3,universal_class)
& member(X3,X1)
& disjoint(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',regularity) ).
fof(singleton_set_defn,axiom,
! [X1] : singleton(X1) = unordered_pair(X1,X1),
file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/SET005+0.ax',unordered_pair_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(c_0_6,negated_conjecture,
~ ! [X1,X2] :
( subclass(X1,singleton(X2))
=> ( X1 = null_class
| singleton(X2) = X1 ) ),
inference(assume_negation,[status(cth)],[two_subsets_of_singleton]) ).
fof(c_0_7,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])])])])])]) ).
fof(c_0_8,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])])])]) ).
fof(c_0_9,negated_conjecture,
( subclass(esk8_0,singleton(esk9_0))
& esk8_0 != null_class
& singleton(esk9_0) != esk8_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_10,plain,
! [X24] : singleton(X24) = unordered_pair(X24,X24),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
cnf(c_0_11,plain,
( member(X3,X2)
| ~ subclass(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( member(esk6_1(X1),X1)
| X1 = null_class ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
subclass(esk8_0,singleton(esk9_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_15,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_16,plain,
( X1 = null_class
| member(esk6_1(X1),X2)
| ~ subclass(X1,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
subclass(esk8_0,unordered_pair(esk9_0,esk9_0)),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
esk8_0 != null_class,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
( member(esk1_2(X1,X2),X1)
| subclass(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_21,negated_conjecture,
member(esk6_1(esk8_0),unordered_pair(esk9_0,esk9_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_22,plain,
( subclass(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_23,plain,
( esk1_2(unordered_pair(X1,X2),X3) = X2
| esk1_2(unordered_pair(X1,X2),X3) = X1
| subclass(unordered_pair(X1,X2),X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
esk6_1(esk8_0) = esk9_0,
inference(spm,[status(thm)],[c_0_19,c_0_21]) ).
cnf(c_0_25,plain,
( esk1_2(unordered_pair(X1,X2),X3) = X2
| subclass(unordered_pair(X1,X2),X3)
| ~ member(X1,X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
member(esk9_0,esk8_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_24]),c_0_18]) ).
fof(c_0_27,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])])]) ).
cnf(c_0_28,negated_conjecture,
singleton(esk9_0) != esk8_0,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_29,negated_conjecture,
( esk1_2(unordered_pair(esk9_0,X1),esk8_0) = X1
| subclass(unordered_pair(esk9_0,X1),esk8_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
( X1 = X2
| ~ subclass(X1,X2)
| ~ subclass(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_31,negated_conjecture,
unordered_pair(esk9_0,esk9_0) != esk8_0,
inference(rw,[status(thm)],[c_0_28,c_0_14]) ).
cnf(c_0_32,negated_conjecture,
( subclass(unordered_pair(esk9_0,X1),esk8_0)
| ~ member(X1,esk8_0) ),
inference(spm,[status(thm)],[c_0_22,c_0_29]) ).
cnf(c_0_33,negated_conjecture,
~ subclass(unordered_pair(esk9_0,esk9_0),esk8_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_17]),c_0_31]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_26]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET096+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n006.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sat Aug 26 15:06:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 2.69/2.94 % Version : CSE_E---1.5
% 2.69/2.94 % Problem : theBenchmark.p
% 2.69/2.94 % Proof found
% 2.69/2.94 % SZS status Theorem for theBenchmark.p
% 2.69/2.94 % SZS output start Proof
% See solution above
% 2.69/2.94 % Total time : 2.377000 s
% 2.69/2.94 % SZS output end Proof
% 2.69/2.94 % Total time : 2.380000 s
%------------------------------------------------------------------------------