TSTP Solution File: SEU167+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU167+3 : 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 : 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 16:23:00 EDT 2023
% Result : Theorem 0.19s 0.57s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 12
% Syntax : Number of formulae : 25 ( 4 unt; 9 typ; 0 def)
% Number of atoms : 39 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 38 ( 15 ~; 12 |; 7 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 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 : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn; 20 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
empty: $i > $o ).
tff(decl_23,type,
subset: ( $i * $i ) > $o ).
tff(decl_24,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_25,type,
esk1_0: $i ).
tff(decl_26,type,
esk2_0: $i ).
tff(decl_27,type,
esk3_0: $i ).
tff(decl_28,type,
esk4_0: $i ).
tff(decl_29,type,
esk5_0: $i ).
tff(decl_30,type,
esk6_0: $i ).
fof(t1_xboole_1,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(t118_zfmisc_1,axiom,
! [X1,X2,X3] :
( subset(X1,X2)
=> ( subset(cartesian_product2(X1,X3),cartesian_product2(X2,X3))
& subset(cartesian_product2(X3,X1),cartesian_product2(X3,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_zfmisc_1) ).
fof(t119_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t119_zfmisc_1) ).
fof(c_0_3,plain,
! [X15,X16,X17] :
( ~ subset(X15,X16)
| ~ subset(X16,X17)
| subset(X15,X17) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
fof(c_0_4,plain,
! [X8,X9,X10] :
( ( subset(cartesian_product2(X8,X10),cartesian_product2(X9,X10))
| ~ subset(X8,X9) )
& ( subset(cartesian_product2(X10,X8),cartesian_product2(X10,X9))
| ~ subset(X8,X9) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t118_zfmisc_1])])]) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( subset(X1,X2)
& subset(X3,X4) )
=> subset(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
inference(assume_negation,[status(cth)],[t119_zfmisc_1]) ).
cnf(c_0_6,plain,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_3]) ).
cnf(c_0_7,plain,
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X2))
| ~ subset(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
fof(c_0_8,negated_conjecture,
( subset(esk3_0,esk4_0)
& subset(esk5_0,esk6_0)
& ~ subset(cartesian_product2(esk3_0,esk5_0),cartesian_product2(esk4_0,esk6_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
cnf(c_0_9,plain,
( subset(X1,cartesian_product2(X2,X3))
| ~ subset(X1,cartesian_product2(X4,X3))
| ~ subset(X4,X2) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_10,plain,
( subset(cartesian_product2(X1,X2),cartesian_product2(X1,X3))
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_11,negated_conjecture,
~ subset(cartesian_product2(esk3_0,esk5_0),cartesian_product2(esk4_0,esk6_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
( subset(cartesian_product2(X1,X2),cartesian_product2(X3,X4))
| ~ subset(X1,X3)
| ~ subset(X2,X4) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,negated_conjecture,
subset(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
subset(esk5_0,esk6_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU167+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 23 15:12:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 0.19/0.57 % Version : CSE_E---1.5
% 0.19/0.57 % Problem : theBenchmark.p
% 0.19/0.57 % Proof found
% 0.19/0.57 % SZS status Theorem for theBenchmark.p
% 0.19/0.57 % SZS output start Proof
% See solution above
% 0.19/0.57 % Total time : 0.006000 s
% 0.19/0.57 % SZS output end Proof
% 0.19/0.57 % Total time : 0.008000 s
%------------------------------------------------------------------------------