TSTP Solution File: SET985+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET985+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 : 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 14:36:32 EDT 2023
% Result : Theorem 0.19s 0.59s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 33 ( 9 unt; 10 typ; 0 def)
% Number of atoms : 58 ( 24 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 50 ( 15 ~; 23 |; 6 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 33 ( 3 sgn; 22 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
empty_set: $i ).
tff(decl_23,type,
empty: $i > $o ).
tff(decl_24,type,
subset: ( $i * $i ) > $o ).
tff(decl_25,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_26,type,
esk1_0: $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 ).
fof(t139_zfmisc_1,conjecture,
! [X1] :
( ~ empty(X1)
=> ! [X2,X3,X4] :
( ( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| subset(cartesian_product2(X2,X1),cartesian_product2(X4,X3)) )
=> subset(X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t139_zfmisc_1) ).
fof(t138_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
=> ( cartesian_product2(X1,X2) = empty_set
| ( subset(X1,X3)
& subset(X2,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t138_zfmisc_1) ).
fof(t113_zfmisc_1,axiom,
! [X1,X2] :
( cartesian_product2(X1,X2) = empty_set
<=> ( X1 = empty_set
| X2 = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t113_zfmisc_1) ).
fof(t2_xboole_1,axiom,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(fc1_xboole_0,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ~ empty(X1)
=> ! [X2,X3,X4] :
( ( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| subset(cartesian_product2(X2,X1),cartesian_product2(X4,X3)) )
=> subset(X2,X4) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t139_zfmisc_1])]) ).
fof(c_0_6,plain,
! [X10,X11,X12,X13] :
( ( subset(X10,X12)
| cartesian_product2(X10,X11) = empty_set
| ~ subset(cartesian_product2(X10,X11),cartesian_product2(X12,X13)) )
& ( subset(X11,X13)
| cartesian_product2(X10,X11) = empty_set
| ~ subset(cartesian_product2(X10,X11),cartesian_product2(X12,X13)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t138_zfmisc_1])])]) ).
fof(c_0_7,negated_conjecture,
( ~ empty(esk3_0)
& ( subset(cartesian_product2(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
| subset(cartesian_product2(esk4_0,esk3_0),cartesian_product2(esk6_0,esk5_0)) )
& ~ subset(esk4_0,esk6_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_8,plain,
( subset(X1,X2)
| cartesian_product2(X1,X3) = empty_set
| ~ subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,negated_conjecture,
( subset(cartesian_product2(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
| subset(cartesian_product2(esk4_0,esk3_0),cartesian_product2(esk6_0,esk5_0)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,negated_conjecture,
~ subset(esk4_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X8,X9] :
( ( cartesian_product2(X8,X9) != empty_set
| X8 = empty_set
| X9 = empty_set )
& ( X8 != empty_set
| cartesian_product2(X8,X9) = empty_set )
& ( X9 != empty_set
| cartesian_product2(X8,X9) = empty_set ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t113_zfmisc_1])])]) ).
cnf(c_0_12,plain,
( subset(X1,X2)
| cartesian_product2(X3,X1) = empty_set
| ~ subset(cartesian_product2(X3,X1),cartesian_product2(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,negated_conjecture,
( cartesian_product2(esk4_0,esk3_0) = empty_set
| subset(cartesian_product2(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
cnf(c_0_14,plain,
( X1 = empty_set
| X2 = empty_set
| cartesian_product2(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
( cartesian_product2(esk4_0,esk3_0) = empty_set
| cartesian_product2(esk3_0,esk4_0) = empty_set ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_10]) ).
fof(c_0_16,plain,
! [X18] : subset(empty_set,X18),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
cnf(c_0_17,negated_conjecture,
( esk4_0 = empty_set
| esk3_0 = empty_set ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_14]) ).
cnf(c_0_18,plain,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_19,negated_conjecture,
~ empty(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,negated_conjecture,
esk3_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_17]),c_0_18])]) ).
cnf(c_0_21,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc1_xboole_0]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET985+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
% 0.13/0.34 % 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 15:40:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.59 % Version : CSE_E---1.5
% 0.19/0.59 % Problem : theBenchmark.p
% 0.19/0.59 % Proof found
% 0.19/0.59 % SZS status Theorem for theBenchmark.p
% 0.19/0.59 % SZS output start Proof
% See solution above
% 0.19/0.59 % Total time : 0.006000 s
% 0.19/0.59 % SZS output end Proof
% 0.19/0.59 % Total time : 0.009000 s
%------------------------------------------------------------------------------