TSTP Solution File: SET976+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET976+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n013.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 14:36:30 EDT 2023
% Result : Theorem 0.20s 0.59s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 17
% Syntax : Number of formulae : 44 ( 8 unt; 13 typ; 0 def)
% Number of atoms : 84 ( 27 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 89 ( 36 ~; 38 |; 10 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 7 >; 5 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 64 ( 7 sgn; 29 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_24,type,
singleton: $i > $i ).
tff(decl_25,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_26,type,
empty: $i > $o ).
tff(decl_27,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_28,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_29,type,
esk2_0: $i ).
tff(decl_30,type,
esk3_0: $i ).
tff(decl_31,type,
esk4_0: $i ).
tff(decl_32,type,
esk5_0: $i ).
tff(decl_33,type,
esk6_0: $i ).
tff(decl_34,type,
esk7_0: $i ).
fof(t129_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,singleton(X4)))
<=> ( in(X1,X3)
& X2 = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t129_zfmisc_1) ).
fof(l55_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
<=> ( in(X1,X3)
& in(X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( in(ordered_pair(X1,X2),cartesian_product2(X3,singleton(X4)))
<=> ( in(X1,X3)
& X2 = X4 ) ),
inference(assume_negation,[status(cth)],[t129_zfmisc_1]) ).
fof(c_0_5,plain,
! [X20,X21,X22,X23] :
( ( in(X20,X22)
| ~ in(ordered_pair(X20,X21),cartesian_product2(X22,X23)) )
& ( in(X21,X23)
| ~ in(ordered_pair(X20,X21),cartesian_product2(X22,X23)) )
& ( ~ in(X20,X22)
| ~ in(X21,X23)
| in(ordered_pair(X20,X21),cartesian_product2(X22,X23)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l55_zfmisc_1])])]) ).
fof(c_0_6,plain,
! [X16,X17] : ordered_pair(X16,X17) = unordered_pair(unordered_pair(X16,X17),singleton(X16)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_7,negated_conjecture,
( ( ~ in(ordered_pair(esk4_0,esk5_0),cartesian_product2(esk6_0,singleton(esk7_0)))
| ~ in(esk4_0,esk6_0)
| esk5_0 != esk7_0 )
& ( in(esk4_0,esk6_0)
| in(ordered_pair(esk4_0,esk5_0),cartesian_product2(esk6_0,singleton(esk7_0))) )
& ( esk5_0 = esk7_0
| in(ordered_pair(esk4_0,esk5_0),cartesian_product2(esk6_0,singleton(esk7_0))) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
fof(c_0_8,plain,
! [X9,X10,X11,X12,X13,X14] :
( ( ~ in(X11,X10)
| X11 = X9
| X10 != singleton(X9) )
& ( X12 != X9
| in(X12,X10)
| X10 != singleton(X9) )
& ( ~ in(esk1_2(X13,X14),X14)
| esk1_2(X13,X14) != X13
| X14 = singleton(X13) )
& ( in(esk1_2(X13,X14),X14)
| esk1_2(X13,X14) = X13
| X14 = singleton(X13) ) ),
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)],[d1_tarski])])])])])]) ).
cnf(c_0_9,plain,
( in(X1,X2)
| ~ in(ordered_pair(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
( esk5_0 = esk7_0
| in(ordered_pair(esk4_0,esk5_0),cartesian_product2(esk6_0,singleton(esk7_0))) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,negated_conjecture,
( ~ in(ordered_pair(esk4_0,esk5_0),cartesian_product2(esk6_0,singleton(esk7_0)))
| ~ in(esk4_0,esk6_0)
| esk5_0 != esk7_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X3,X1),singleton(X3)),cartesian_product2(X4,X2)) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
( esk7_0 = esk5_0
| in(unordered_pair(unordered_pair(esk4_0,esk5_0),singleton(esk4_0)),cartesian_product2(esk6_0,singleton(esk7_0))) ),
inference(rw,[status(thm)],[c_0_11,c_0_10]) ).
cnf(c_0_16,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( in(X1,X2)
| ~ in(ordered_pair(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,negated_conjecture,
( in(esk4_0,esk6_0)
| in(ordered_pair(esk4_0,esk5_0),cartesian_product2(esk6_0,singleton(esk7_0))) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,negated_conjecture,
( esk7_0 != esk5_0
| ~ in(esk4_0,esk6_0)
| ~ in(unordered_pair(unordered_pair(esk4_0,esk5_0),singleton(esk4_0)),cartesian_product2(esk6_0,singleton(esk7_0))) ),
inference(rw,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_20,negated_conjecture,
esk5_0 = esk7_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_21,plain,
( in(X1,X2)
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4)) ),
inference(rw,[status(thm)],[c_0_17,c_0_10]) ).
cnf(c_0_22,negated_conjecture,
( in(esk4_0,esk6_0)
| in(unordered_pair(unordered_pair(esk4_0,esk5_0),singleton(esk4_0)),cartesian_product2(esk6_0,singleton(esk7_0))) ),
inference(rw,[status(thm)],[c_0_18,c_0_10]) ).
cnf(c_0_23,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(esk4_0,esk7_0),singleton(esk4_0)),cartesian_product2(esk6_0,singleton(esk7_0)))
| ~ in(esk4_0,esk6_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_20])]) ).
cnf(c_0_24,negated_conjecture,
in(esk4_0,esk6_0),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
( in(ordered_pair(X1,X3),cartesian_product2(X2,X4))
| ~ in(X1,X2)
| ~ in(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_26,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_27,negated_conjecture,
~ in(unordered_pair(unordered_pair(esk4_0,esk7_0),singleton(esk4_0)),cartesian_product2(esk6_0,singleton(esk7_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]) ).
cnf(c_0_28,plain,
( in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),cartesian_product2(X2,X4))
| ~ in(X3,X4)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_25,c_0_10]) ).
cnf(c_0_29,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_26])]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET976+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n013.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 16:19:32 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.20/0.59 % Version : CSE_E---1.5
% 0.20/0.59 % Problem : theBenchmark.p
% 0.20/0.59 % Proof found
% 0.20/0.59 % SZS status Theorem for theBenchmark.p
% 0.20/0.59 % SZS output start Proof
% See solution above
% 0.20/0.60 % Total time : 0.009000 s
% 0.20/0.60 % SZS output end Proof
% 0.20/0.60 % Total time : 0.012000 s
%------------------------------------------------------------------------------