TSTP Solution File: SET873+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET873+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 14:36:05 EDT 2023
% Result : Theorem 0.21s 0.61s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 15
% Syntax : Number of formulae : 31 ( 10 unt; 10 typ; 0 def)
% Number of atoms : 44 ( 24 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 38 ( 15 ~; 14 |; 4 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 6 >; 4 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 1 sgn; 24 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_24,type,
singleton: $i > $i ).
tff(decl_25,type,
empty: $i > $o ).
tff(decl_26,type,
subset: ( $i * $i ) > $o ).
tff(decl_27,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_28,type,
esk2_0: $i ).
tff(decl_29,type,
esk3_0: $i ).
tff(decl_30,type,
esk4_0: $i ).
tff(decl_31,type,
esk5_0: $i ).
fof(l21_zfmisc_1,axiom,
! [X1,X2] :
( subset(set_union2(singleton(X1),X2),X2)
=> in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l21_zfmisc_1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(t13_zfmisc_1,conjecture,
! [X1,X2] :
( set_union2(singleton(X1),singleton(X2)) = singleton(X1)
=> X1 = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_zfmisc_1) ).
fof(d1_tarski,axiom,
! [X1,X2] :
( X2 = singleton(X1)
<=> ! [X3] :
( in(X3,X2)
<=> X3 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(c_0_5,plain,
! [X20,X21] :
( ~ subset(set_union2(singleton(X20),X21),X21)
| in(X20,X21) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l21_zfmisc_1])]) ).
fof(c_0_6,plain,
! [X6,X7] : set_union2(X6,X7) = set_union2(X7,X6),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2] :
( set_union2(singleton(X1),singleton(X2)) = singleton(X1)
=> X1 = X2 ),
inference(assume_negation,[status(cth)],[t13_zfmisc_1]) ).
fof(c_0_8,plain,
! [X8,X9,X10,X11,X12,X13] :
( ( ~ in(X10,X9)
| X10 = X8
| X9 != singleton(X8) )
& ( X11 != X8
| in(X11,X9)
| X9 != singleton(X8) )
& ( ~ in(esk1_2(X12,X13),X13)
| esk1_2(X12,X13) != X12
| X13 = singleton(X12) )
& ( in(esk1_2(X12,X13),X13)
| esk1_2(X12,X13) = X12
| X13 = singleton(X12) ) ),
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])])])])])]) ).
cnf(c_0_9,plain,
( in(X1,X2)
| ~ subset(set_union2(singleton(X1),X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,negated_conjecture,
( set_union2(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_7])])]) ).
fof(c_0_12,plain,
! [X24] : subset(X24,X24),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_13,plain,
( X1 = X3
| ~ in(X1,X2)
| X2 != singleton(X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( in(X1,X2)
| ~ subset(set_union2(X2,singleton(X1)),X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,negated_conjecture,
set_union2(singleton(esk4_0),singleton(esk5_0)) = singleton(esk4_0),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
( X1 = X2
| ~ in(X1,singleton(X2)) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
in(esk5_0,singleton(esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16])]) ).
cnf(c_0_19,negated_conjecture,
esk4_0 != esk5_0,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SET873+1 : TPTP v8.1.2. Released v3.2.0.
% 0.09/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.15/0.36 % Computer : n021.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sat Aug 26 09:02:26 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.21/0.59 start to proof: theBenchmark
% 0.21/0.61 % Version : CSE_E---1.5
% 0.21/0.61 % Problem : theBenchmark.p
% 0.21/0.61 % Proof found
% 0.21/0.61 % SZS status Theorem for theBenchmark.p
% 0.21/0.61 % SZS output start Proof
% See solution above
% 0.21/0.61 % Total time : 0.006000 s
% 0.21/0.61 % SZS output end Proof
% 0.21/0.61 % Total time : 0.008000 s
%------------------------------------------------------------------------------