TSTP Solution File: SET978+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET978+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 : n009.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 : 5
% Number of leaves : 13
% Syntax : Number of formulae : 24 ( 3 unt; 10 typ; 0 def)
% Number of atoms : 31 ( 7 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 32 ( 15 ~; 9 |; 4 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 4 >; 2 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 30 ( 4 sgn; 20 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
empty: $i > $o ).
tff(decl_23,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_24,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_25,type,
singleton: $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(t131_zfmisc_1,conjecture,
! [X1,X2,X3,X4] :
( X1 != X2
=> ( disjoint(cartesian_product2(singleton(X1),X3),cartesian_product2(singleton(X2),X4))
& disjoint(cartesian_product2(X3,singleton(X1)),cartesian_product2(X4,singleton(X2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t131_zfmisc_1) ).
fof(t127_zfmisc_1,axiom,
! [X1,X2,X3,X4] :
( ( disjoint(X1,X2)
| disjoint(X3,X4) )
=> disjoint(cartesian_product2(X1,X3),cartesian_product2(X2,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t127_zfmisc_1) ).
fof(t17_zfmisc_1,axiom,
! [X1,X2] :
( X1 != X2
=> disjoint(singleton(X1),singleton(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_zfmisc_1) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( X1 != X2
=> ( disjoint(cartesian_product2(singleton(X1),X3),cartesian_product2(singleton(X2),X4))
& disjoint(cartesian_product2(X3,singleton(X1)),cartesian_product2(X4,singleton(X2))) ) ),
inference(assume_negation,[status(cth)],[t131_zfmisc_1]) ).
fof(c_0_4,negated_conjecture,
( esk3_0 != esk4_0
& ( ~ disjoint(cartesian_product2(singleton(esk3_0),esk5_0),cartesian_product2(singleton(esk4_0),esk6_0))
| ~ disjoint(cartesian_product2(esk5_0,singleton(esk3_0)),cartesian_product2(esk6_0,singleton(esk4_0))) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
fof(c_0_5,plain,
! [X9,X10,X11,X12] :
( ( ~ disjoint(X9,X10)
| disjoint(cartesian_product2(X9,X11),cartesian_product2(X10,X12)) )
& ( ~ disjoint(X11,X12)
| disjoint(cartesian_product2(X9,X11),cartesian_product2(X10,X12)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t127_zfmisc_1])])]) ).
cnf(c_0_6,negated_conjecture,
( ~ disjoint(cartesian_product2(singleton(esk3_0),esk5_0),cartesian_product2(singleton(esk4_0),esk6_0))
| ~ disjoint(cartesian_product2(esk5_0,singleton(esk3_0)),cartesian_product2(esk6_0,singleton(esk4_0))) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
( disjoint(cartesian_product2(X1,X3),cartesian_product2(X2,X4))
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( disjoint(cartesian_product2(X3,X1),cartesian_product2(X4,X2))
| ~ disjoint(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_9,plain,
! [X17,X18] :
( X17 = X18
| disjoint(singleton(X17),singleton(X18)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t17_zfmisc_1])]) ).
cnf(c_0_10,negated_conjecture,
~ disjoint(singleton(esk3_0),singleton(esk4_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_7]),c_0_8]) ).
cnf(c_0_11,plain,
( X1 = X2
| disjoint(singleton(X1),singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_12,negated_conjecture,
esk3_0 != esk4_0,
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_13,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET978+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n009.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 08:10:05 EDT 2023
% 0.13/0.34 % 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
% 0.20/0.59 % Total time : 0.007000 s
% 0.20/0.59 % SZS output end Proof
% 0.20/0.59 % Total time : 0.009000 s
%------------------------------------------------------------------------------