TSTP Solution File: SET090+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET090+1 : 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 : n020.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 14:32:56 EDT 2023
% Result : Theorem 0.19s 0.57s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 45
% Syntax : Number of formulae : 65 ( 11 unt; 41 typ; 0 def)
% Number of atoms : 53 ( 27 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 46 ( 17 ~; 17 |; 8 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 48 ( 32 >; 16 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 36 ( 36 usr; 9 con; 0-3 aty)
% Number of variables : 27 ( 3 sgn; 14 !; 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,
member_of: $i > $i ).
tff(decl_54,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk2_0: $i ).
tff(decl_56,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_57,type,
esk4_1: $i > $i ).
tff(decl_58,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_59,type,
esk6_1: $i > $i ).
tff(decl_60,type,
esk7_0: $i ).
tff(decl_61,type,
esk8_0: $i ).
tff(decl_62,type,
esk9_0: $i ).
fof(member_of_singleton,conjecture,
! [X1,X3] :
( ( member(X3,universal_class)
& X1 = singleton(X3) )
=> member_of(X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_singleton) ).
fof(member_singleton_singleton,axiom,
! [X2] :
( member(X2,universal_class)
=> singleton(member_of(singleton(X2))) = singleton(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_singleton_singleton) ).
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(c_0_4,negated_conjecture,
~ ! [X1,X3] :
( ( member(X3,universal_class)
& X1 = singleton(X3) )
=> member_of(X1) = X3 ),
inference(assume_negation,[status(cth)],[member_of_singleton]) ).
fof(c_0_5,plain,
! [X108] :
( ~ member(X108,universal_class)
| singleton(member_of(singleton(X108))) = singleton(X108) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[member_singleton_singleton])]) ).
fof(c_0_6,plain,
! [X24] : singleton(X24) = unordered_pair(X24,X24),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
fof(c_0_7,negated_conjecture,
( member(esk9_0,universal_class)
& esk8_0 = singleton(esk9_0)
& member_of(esk8_0) != esk9_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
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,plain,
( singleton(member_of(singleton(X1))) = singleton(X1)
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
esk8_0 = singleton(esk9_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( member(X1,unordered_pair(X3,X2))
| X1 != X2
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( unordered_pair(member_of(unordered_pair(X1,X1)),member_of(unordered_pair(X1,X1))) = unordered_pair(X1,X1)
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_9,c_0_10]),c_0_10]),c_0_10]) ).
cnf(c_0_14,negated_conjecture,
member(esk9_0,universal_class),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,negated_conjecture,
esk8_0 = unordered_pair(esk9_0,esk9_0),
inference(rw,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_16,plain,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,negated_conjecture,
unordered_pair(member_of(esk8_0),member_of(esk8_0)) = esk8_0,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_15]),c_0_15]) ).
cnf(c_0_19,negated_conjecture,
member(esk9_0,unordered_pair(X1,esk9_0)),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
cnf(c_0_20,negated_conjecture,
( X1 = member_of(esk8_0)
| ~ member(X1,esk8_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
member(esk9_0,esk8_0),
inference(spm,[status(thm)],[c_0_19,c_0_15]) ).
cnf(c_0_22,negated_conjecture,
member_of(esk8_0) != esk9_0,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET090+1 : TPTP v8.1.2. Bugfixed v7.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 09:19:29 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.54 start to proof: theBenchmark
% 0.19/0.57 % Version : CSE_E---1.5
% 0.19/0.57 % Problem : theBenchmark.p
% 0.19/0.57 % Proof found
% 0.19/0.57 % SZS status Theorem for theBenchmark.p
% 0.19/0.57 % SZS output start Proof
% See solution above
% 0.19/0.57 % Total time : 0.020000 s
% 0.19/0.57 % SZS output end Proof
% 0.19/0.57 % Total time : 0.024000 s
%------------------------------------------------------------------------------