TSTP Solution File: SET016+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET016+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 : 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 14:32:07 EDT 2023
% Result : Theorem 0.78s 0.86s
% Output : CNFRefutation 0.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 47
% Syntax : Number of formulae : 75 ( 20 unt; 42 typ; 0 def)
% Number of atoms : 63 ( 31 equ)
% Maximal formula atoms : 11 ( 1 avg)
% Number of connectives : 47 ( 17 ~; 19 |; 8 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 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 : 37 ( 37 usr; 11 con; 0-3 aty)
% Number of variables : 50 ( 9 sgn; 24 !; 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 ).
tff(decl_61,type,
esk9_0: $i ).
tff(decl_62,type,
esk10_0: $i ).
tff(decl_63,type,
esk11_0: $i ).
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(ordered_pair_determines_components1,conjecture,
! [X7,X1,X2,X5] :
( ( ordered_pair(X7,X1) = ordered_pair(X2,X5)
& member(X7,universal_class) )
=> X7 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair_determines_components1) ).
fof(ordered_pair_defn,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',ordered_pair_defn) ).
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,axiom,
! [X1,X2] : member(unordered_pair(X1,X2),universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',unordered_pair) ).
fof(c_0_5,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])])]) ).
fof(c_0_6,negated_conjecture,
~ ! [X7,X1,X2,X5] :
( ( ordered_pair(X7,X1) = ordered_pair(X2,X5)
& member(X7,universal_class) )
=> X7 = X2 ),
inference(assume_negation,[status(cth)],[ordered_pair_determines_components1]) ).
fof(c_0_7,plain,
! [X25,X26] : ordered_pair(X25,X26) = unordered_pair(singleton(X25),unordered_pair(X25,singleton(X26))),
inference(variable_rename,[status(thm)],[ordered_pair_defn]) ).
fof(c_0_8,plain,
! [X24] : singleton(X24) = unordered_pair(X24,X24),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
cnf(c_0_9,plain,
( member(X1,unordered_pair(X2,X3))
| X1 != X2
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_10,plain,
! [X22,X23] : member(unordered_pair(X22,X23),universal_class),
inference(variable_rename,[status(thm)],[unordered_pair]) ).
fof(c_0_11,negated_conjecture,
( ordered_pair(esk8_0,esk9_0) = ordered_pair(esk10_0,esk11_0)
& member(esk8_0,universal_class)
& esk8_0 != esk10_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
cnf(c_0_12,plain,
ordered_pair(X1,X2) = unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( member(X1,unordered_pair(X1,X2))
| ~ member(X1,universal_class) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
member(unordered_pair(X1,X2),universal_class),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
ordered_pair(esk8_0,esk9_0) = ordered_pair(esk10_0,esk11_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_13]) ).
cnf(c_0_18,plain,
member(unordered_pair(X1,X2),unordered_pair(unordered_pair(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
unordered_pair(unordered_pair(esk10_0,esk10_0),unordered_pair(esk10_0,unordered_pair(esk11_0,esk11_0))) = unordered_pair(unordered_pair(esk8_0,esk8_0),unordered_pair(esk8_0,unordered_pair(esk9_0,esk9_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_17]),c_0_17]) ).
cnf(c_0_20,negated_conjecture,
member(esk8_0,universal_class),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_21,plain,
( X1 = X2
| X1 = X3
| ~ member(X1,unordered_pair(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_22,negated_conjecture,
member(unordered_pair(esk10_0,esk10_0),unordered_pair(unordered_pair(esk8_0,esk8_0),unordered_pair(esk8_0,unordered_pair(esk9_0,esk9_0)))),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
member(esk8_0,unordered_pair(esk8_0,X1)),
inference(spm,[status(thm)],[c_0_14,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( unordered_pair(esk8_0,unordered_pair(esk9_0,esk9_0)) = unordered_pair(esk10_0,esk10_0)
| unordered_pair(esk10_0,esk10_0) = unordered_pair(esk8_0,esk8_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
( unordered_pair(esk10_0,esk10_0) = unordered_pair(esk8_0,esk8_0)
| member(esk8_0,unordered_pair(esk10_0,esk10_0)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,negated_conjecture,
esk8_0 != esk10_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_27,plain,
( member(X1,unordered_pair(X3,X2))
| X1 != X2
| ~ member(X1,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_28,negated_conjecture,
unordered_pair(esk10_0,esk10_0) = unordered_pair(esk8_0,esk8_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_25]),c_0_26]) ).
cnf(c_0_29,plain,
( member(X1,unordered_pair(X2,X1))
| ~ member(X1,universal_class) ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_30,negated_conjecture,
( X1 = esk10_0
| ~ member(X1,unordered_pair(esk8_0,esk8_0)) ),
inference(spm,[status(thm)],[c_0_21,c_0_28]) ).
cnf(c_0_31,negated_conjecture,
member(esk8_0,unordered_pair(X1,esk8_0)),
inference(spm,[status(thm)],[c_0_29,c_0_20]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET016+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n031.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 10:52:08 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.78/0.86 % Version : CSE_E---1.5
% 0.78/0.86 % Problem : theBenchmark.p
% 0.78/0.86 % Proof found
% 0.78/0.86 % SZS status Theorem for theBenchmark.p
% 0.78/0.86 % SZS output start Proof
% See solution above
% 0.78/0.87 % Total time : 0.284000 s
% 0.78/0.87 % SZS output end Proof
% 0.78/0.87 % Total time : 0.288000 s
%------------------------------------------------------------------------------