TSTP Solution File: SET983+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET983+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n021.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 14:36:31 EDT 2023
% Result : Theorem 0.20s 0.59s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 15
% Syntax : Number of formulae : 27 ( 7 unt; 12 typ; 0 def)
% Number of atoms : 50 ( 11 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 55 ( 20 ~; 21 |; 10 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 5 >; 5 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 46 ( 0 sgn; 30 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_24,type,
empty: $i > $o ).
tff(decl_25,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_26,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_27,type,
esk2_0: $i ).
tff(decl_28,type,
esk3_0: $i ).
tff(decl_29,type,
esk4_0: $i ).
tff(decl_30,type,
esk5_0: $i ).
tff(decl_31,type,
esk6_0: $i ).
tff(decl_32,type,
esk7_0: $i ).
tff(decl_33,type,
esk8_0: $i ).
fof(d3_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_intersection2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(t137_zfmisc_1,conjecture,
! [X1,X2,X3,X4,X5] :
( ( in(X1,cartesian_product2(X2,X3))
& in(X1,cartesian_product2(X4,X5)) )
=> in(X1,cartesian_product2(set_intersection2(X2,X4),set_intersection2(X3,X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t137_zfmisc_1) ).
fof(t123_zfmisc_1,axiom,
! [X1,X2,X3,X4] : cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t123_zfmisc_1) ).
fof(c_0_3,plain,
! [X10,X11,X12,X13,X14,X15,X16,X17] :
( ( in(X13,X10)
| ~ in(X13,X12)
| X12 != set_intersection2(X10,X11) )
& ( in(X13,X11)
| ~ in(X13,X12)
| X12 != set_intersection2(X10,X11) )
& ( ~ in(X14,X10)
| ~ in(X14,X11)
| in(X14,X12)
| X12 != set_intersection2(X10,X11) )
& ( ~ in(esk1_3(X15,X16,X17),X17)
| ~ in(esk1_3(X15,X16,X17),X15)
| ~ in(esk1_3(X15,X16,X17),X16)
| X17 = set_intersection2(X15,X16) )
& ( in(esk1_3(X15,X16,X17),X15)
| in(esk1_3(X15,X16,X17),X17)
| X17 = set_intersection2(X15,X16) )
& ( in(esk1_3(X15,X16,X17),X16)
| in(esk1_3(X15,X16,X17),X17)
| X17 = set_intersection2(X15,X16) ) ),
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)],[d3_xboole_0])])])])])]) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X3,X4,X5] :
( ( in(X1,cartesian_product2(X2,X3))
& in(X1,cartesian_product2(X4,X5)) )
=> in(X1,cartesian_product2(set_intersection2(X2,X4),set_intersection2(X3,X5))) ),
inference(assume_negation,[status(cth)],[t137_zfmisc_1]) ).
cnf(c_0_5,plain,
( in(X1,X4)
| ~ in(X1,X2)
| ~ in(X1,X3)
| X4 != set_intersection2(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
fof(c_0_6,plain,
! [X22,X23,X24,X25] : cartesian_product2(set_intersection2(X22,X23),set_intersection2(X24,X25)) = set_intersection2(cartesian_product2(X22,X24),cartesian_product2(X23,X25)),
inference(variable_rename,[status(thm)],[t123_zfmisc_1]) ).
fof(c_0_7,negated_conjecture,
( in(esk4_0,cartesian_product2(esk5_0,esk6_0))
& in(esk4_0,cartesian_product2(esk7_0,esk8_0))
& ~ in(esk4_0,cartesian_product2(set_intersection2(esk5_0,esk7_0),set_intersection2(esk6_0,esk8_0))) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_8,plain,
( in(X1,set_intersection2(X2,X3))
| ~ in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
cartesian_product2(set_intersection2(X1,X2),set_intersection2(X3,X4)) = set_intersection2(cartesian_product2(X1,X3),cartesian_product2(X2,X4)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
~ in(esk4_0,cartesian_product2(set_intersection2(esk5_0,esk7_0),set_intersection2(esk6_0,esk8_0))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( in(X1,cartesian_product2(set_intersection2(X2,X3),set_intersection2(X4,X5)))
| ~ in(X1,cartesian_product2(X3,X5))
| ~ in(X1,cartesian_product2(X2,X4)) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,negated_conjecture,
in(esk4_0,cartesian_product2(esk7_0,esk8_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
in(esk4_0,cartesian_product2(esk5_0,esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET983+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 12:48:41 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.57 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 : 0.012000 s
% 0.20/0.60 % SZS output end Proof
% 0.20/0.60 % Total time : 0.014000 s
%------------------------------------------------------------------------------