TSTP Solution File: SEU147+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU147+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/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 16:22:46 EDT 2023
% Result : Theorem 0.19s 0.55s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 16
% Syntax : Number of formulae : 34 ( 9 unt; 11 typ; 0 def)
% Number of atoms : 65 ( 34 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 65 ( 23 ~; 31 |; 6 &)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 8 >; 5 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 40 ( 1 sgn; 23 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
singleton: $i > $i ).
tff(decl_24,type,
powerset: $i > $i ).
tff(decl_25,type,
subset: ( $i * $i ) > $o ).
tff(decl_26,type,
empty_set: $i ).
tff(decl_27,type,
empty: $i > $o ).
tff(decl_28,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_29,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_30,type,
esk3_0: $i ).
tff(decl_31,type,
esk4_0: $i ).
tff(decl_32,type,
esk5_2: ( $i * $i ) > $i ).
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(t3_xboole_1,axiom,
! [X1] :
( subset(X1,empty_set)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_1) ).
fof(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(t1_zfmisc_1,conjecture,
powerset(empty_set) = singleton(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_zfmisc_1) ).
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,
! [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,
! [X26] :
( ~ subset(X26,empty_set)
| X26 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_xboole_1])]) ).
fof(c_0_7,plain,
! [X13,X14,X15,X16,X17,X18] :
( ( ~ in(X15,X14)
| subset(X15,X13)
| X14 != powerset(X13) )
& ( ~ subset(X16,X13)
| in(X16,X14)
| X14 != powerset(X13) )
& ( ~ in(esk2_2(X17,X18),X18)
| ~ subset(esk2_2(X17,X18),X17)
| X18 = powerset(X17) )
& ( in(esk2_2(X17,X18),X18)
| subset(esk2_2(X17,X18),X17)
| X18 = powerset(X17) ) ),
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_zfmisc_1])])])])])]) ).
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,
( X1 = empty_set
| ~ subset(X1,empty_set) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
( in(esk2_2(X1,X2),X2)
| subset(esk2_2(X1,X2),X1)
| X2 = powerset(X1) ),
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,plain,
( esk2_2(empty_set,X1) = empty_set
| X1 = powerset(empty_set)
| in(esk2_2(empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_13,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t1_zfmisc_1])]) ).
cnf(c_0_14,plain,
( esk2_2(empty_set,singleton(X1)) = empty_set
| esk2_2(empty_set,singleton(X1)) = X1
| singleton(X1) = powerset(empty_set) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,negated_conjecture,
powerset(empty_set) != singleton(empty_set),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_16,plain,
! [X22] : subset(X22,X22),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_17,plain,
( in(X1,X3)
| X1 != X2
| X3 != singleton(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,plain,
( X2 = powerset(X1)
| ~ in(esk2_2(X1,X2),X2)
| ~ subset(esk2_2(X1,X2),X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_19,plain,
esk2_2(empty_set,singleton(empty_set)) = empty_set,
inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_14])]),c_0_15]) ).
cnf(c_0_20,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
in(X1,singleton(X1)),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_17])]) ).
cnf(c_0_22,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]),c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU147+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 20:03:36 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.53 start to proof: theBenchmark
% 0.19/0.55 % Version : CSE_E---1.5
% 0.19/0.55 % Problem : theBenchmark.p
% 0.19/0.55 % Proof found
% 0.19/0.55 % SZS status Theorem for theBenchmark.p
% 0.19/0.55 % SZS output start Proof
% See solution above
% 0.19/0.55 % Total time : 0.007000 s
% 0.19/0.55 % SZS output end Proof
% 0.19/0.55 % Total time : 0.010000 s
%------------------------------------------------------------------------------