TSTP Solution File: SET879+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET879+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 : n032.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 14:36:06 EDT 2023
% Result : Theorem 0.13s 0.48s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 28 ( 4 unt; 9 typ; 0 def)
% Number of atoms : 51 ( 34 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 57 ( 25 ~; 21 |; 5 &)
% ( 6 <=>; 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 : 8 ( 5 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn; 19 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
singleton: $i > $i ).
tff(decl_24,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_25,type,
empty: $i > $o ).
tff(decl_26,type,
esk1_2: ( $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 ).
fof(l34_zfmisc_1,axiom,
! [X1,X2] :
( set_difference(singleton(X1),X2) = singleton(X1)
<=> ~ in(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l34_zfmisc_1) ).
fof(t20_zfmisc_1,conjecture,
! [X1,X2] :
( set_difference(singleton(X1),singleton(X2)) = singleton(X1)
<=> X1 != X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_zfmisc_1) ).
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_3,plain,
! [X1,X2] :
( set_difference(singleton(X1),X2) = singleton(X1)
<=> ~ in(X1,X2) ),
inference(fof_simplification,[status(thm)],[l34_zfmisc_1]) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( set_difference(singleton(X1),singleton(X2)) = singleton(X1)
<=> X1 != X2 ),
inference(assume_negation,[status(cth)],[t20_zfmisc_1]) ).
fof(c_0_5,plain,
! [X6,X7,X8,X9,X10,X11] :
( ( ~ in(X8,X7)
| X8 = X6
| X7 != singleton(X6) )
& ( X9 != X6
| in(X9,X7)
| X7 != singleton(X6) )
& ( ~ in(esk1_2(X10,X11),X11)
| esk1_2(X10,X11) != X10
| X11 = singleton(X10) )
& ( in(esk1_2(X10,X11),X11)
| esk1_2(X10,X11) = X10
| X11 = singleton(X10) ) ),
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])])])])])]) ).
fof(c_0_6,plain,
! [X13,X14] :
( ( set_difference(singleton(X13),X14) != singleton(X13)
| ~ in(X13,X14) )
& ( in(X13,X14)
| set_difference(singleton(X13),X14) = singleton(X13) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])]) ).
fof(c_0_7,negated_conjecture,
( ( set_difference(singleton(esk4_0),singleton(esk5_0)) != singleton(esk4_0)
| esk4_0 = esk5_0 )
& ( set_difference(singleton(esk4_0),singleton(esk5_0)) = singleton(esk4_0)
| esk4_0 != esk5_0 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_8,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( set_difference(singleton(X1),X2) != singleton(X1)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
( set_difference(singleton(esk4_0),singleton(esk5_0)) = singleton(esk4_0)
| esk4_0 != esk5_0 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
( esk4_0 = esk5_0
| set_difference(singleton(esk4_0),singleton(esk5_0)) != singleton(esk4_0) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( in(X1,X2)
| set_difference(singleton(X1),X2) = singleton(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
~ in(esk4_0,singleton(esk5_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).
cnf(c_0_15,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_16,negated_conjecture,
esk5_0 = esk4_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
cnf(c_0_17,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_15])]) ).
cnf(c_0_18,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_16]),c_0_17])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET879+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.10 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.28 % Computer : n032.cluster.edu
% 0.11/0.28 % Model : x86_64 x86_64
% 0.11/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.28 % Memory : 8042.1875MB
% 0.11/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Sat Aug 26 13:17:14 EDT 2023
% 0.11/0.29 % CPUTime :
% 0.13/0.46 start to proof: theBenchmark
% 0.13/0.47 % Version : CSE_E---1.5
% 0.13/0.47 % Problem : theBenchmark.p
% 0.13/0.47 % Proof found
% 0.13/0.48 % SZS status Theorem for theBenchmark.p
% 0.13/0.48 % SZS output start Proof
% See solution above
% 0.13/0.48 % Total time : 0.005000 s
% 0.13/0.48 % SZS output end Proof
% 0.13/0.48 % Total time : 0.007000 s
%------------------------------------------------------------------------------