TSTP Solution File: SET093+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET093+1 : TPTP v8.1.2. Bugfixed v7.3.0.
% 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 14:32:58 EDT 2023
% Result : Theorem 0.21s 0.58s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 43
% Syntax : Number of formulae : 53 ( 10 unt; 40 typ; 0 def)
% Number of atoms : 16 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 3 ~; 0 |; 1 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 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 : 35 ( 35 usr; 8 con; 0-3 aty)
% Number of variables : 11 ( 2 sgn; 8 !; 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 ).
fof(corollary_2_to_singletons_are_sets,conjecture,
! [X1] :
( singleton(member_of(X1)) = X1
=> member(X1,universal_class) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',corollary_2_to_singletons_are_sets) ).
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,axiom,
! [X1,X2] : member(unordered_pair(X1,X2),universal_class),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',unordered_pair) ).
fof(c_0_3,negated_conjecture,
~ ! [X1] :
( singleton(member_of(X1)) = X1
=> member(X1,universal_class) ),
inference(assume_negation,[status(cth)],[corollary_2_to_singletons_are_sets]) ).
fof(c_0_4,negated_conjecture,
( singleton(member_of(esk8_0)) = esk8_0
& ~ member(esk8_0,universal_class) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
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,
! [X22,X23] : member(unordered_pair(X22,X23),universal_class),
inference(variable_rename,[status(thm)],[unordered_pair]) ).
cnf(c_0_7,negated_conjecture,
singleton(member_of(esk8_0)) = esk8_0,
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]) ).
cnf(c_0_9,plain,
member(unordered_pair(X1,X2),universal_class),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
unordered_pair(member_of(esk8_0),member_of(esk8_0)) = esk8_0,
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,negated_conjecture,
~ member(esk8_0,universal_class),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_12,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET093+1 : TPTP v8.1.2. Bugfixed v7.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n031.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 10:29:38 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.21/0.56 start to proof: theBenchmark
% 0.21/0.58 % Version : CSE_E---1.5
% 0.21/0.58 % Problem : theBenchmark.p
% 0.21/0.58 % Proof found
% 0.21/0.58 % SZS status Theorem for theBenchmark.p
% 0.21/0.58 % SZS output start Proof
% See solution above
% 0.21/0.59 % Total time : 0.008000 s
% 0.21/0.59 % SZS output end Proof
% 0.21/0.59 % Total time : 0.012000 s
%------------------------------------------------------------------------------