TSTP Solution File: SET938+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET938+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 : n028.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 14:36:22 EDT 2023
% Result : Theorem 0.19s 0.78s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 20
% Syntax : Number of formulae : 59 ( 18 unt; 14 typ; 0 def)
% Number of atoms : 119 ( 22 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 121 ( 47 ~; 58 |; 10 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 10 >; 9 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-3 aty)
% Number of variables : 105 ( 7 sgn; 41 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_24,type,
symmetric_difference: ( $i * $i ) > $i ).
tff(decl_25,type,
powerset: $i > $i ).
tff(decl_26,type,
subset: ( $i * $i ) > $o ).
tff(decl_27,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_28,type,
empty: $i > $o ).
tff(decl_29,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_30,type,
esk2_3: ( $i * $i * $i ) > $i ).
tff(decl_31,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_32,type,
esk4_0: $i ).
tff(decl_33,type,
esk5_0: $i ).
tff(decl_34,type,
esk6_0: $i ).
tff(decl_35,type,
esk7_0: $i ).
fof(d1_zfmisc_1,axiom,
! [X1,X2] :
( X2 = powerset(X1)
<=> ! [X3] :
( in(X3,X2)
<=> subset(X3,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(d2_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_union2(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
| in(X4,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(t86_zfmisc_1,conjecture,
! [X1,X2] : subset(set_union2(powerset(set_difference(X1,X2)),powerset(set_difference(X2,X1))),powerset(symmetric_difference(X1,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t86_zfmisc_1) ).
fof(d6_xboole_0,axiom,
! [X1,X2] : symmetric_difference(X1,X2) = set_union2(set_difference(X1,X2),set_difference(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_xboole_0) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(c_0_6,plain,
! [X11,X12,X13,X14,X15,X16] :
( ( ~ in(X13,X12)
| subset(X13,X11)
| X12 != powerset(X11) )
& ( ~ subset(X14,X11)
| in(X14,X12)
| X12 != powerset(X11) )
& ( ~ in(esk1_2(X15,X16),X16)
| ~ subset(esk1_2(X15,X16),X15)
| X16 = powerset(X15) )
& ( in(esk1_2(X15,X16),X16)
| subset(esk1_2(X15,X16),X15)
| X16 = powerset(X15) ) ),
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])])])])])]) ).
fof(c_0_7,plain,
! [X27,X28,X29,X30,X31] :
( ( ~ subset(X27,X28)
| ~ in(X29,X27)
| in(X29,X28) )
& ( in(esk3_2(X30,X31),X30)
| subset(X30,X31) )
& ( ~ in(esk3_2(X30,X31),X31)
| subset(X30,X31) ) ),
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)],[d3_tarski])])])])])]) ).
cnf(c_0_8,plain,
( subset(X1,X3)
| ~ in(X1,X2)
| X2 != powerset(X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| X3 != powerset(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,plain,
! [X18,X19,X20,X21,X22,X23,X24,X25] :
( ( ~ in(X21,X20)
| in(X21,X18)
| in(X21,X19)
| X20 != set_union2(X18,X19) )
& ( ~ in(X22,X18)
| in(X22,X20)
| X20 != set_union2(X18,X19) )
& ( ~ in(X22,X19)
| in(X22,X20)
| X20 != set_union2(X18,X19) )
& ( ~ in(esk2_3(X23,X24,X25),X23)
| ~ in(esk2_3(X23,X24,X25),X25)
| X25 = set_union2(X23,X24) )
& ( ~ in(esk2_3(X23,X24,X25),X24)
| ~ in(esk2_3(X23,X24,X25),X25)
| X25 = set_union2(X23,X24) )
& ( in(esk2_3(X23,X24,X25),X25)
| in(esk2_3(X23,X24,X25),X23)
| in(esk2_3(X23,X24,X25),X24)
| X25 = set_union2(X23,X24) ) ),
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)],[d2_xboole_0])])])])])]) ).
cnf(c_0_11,plain,
( in(X3,X2)
| ~ subset(X1,X2)
| ~ in(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( subset(X1,X2)
| ~ in(X1,powerset(X2)) ),
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(er,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( in(esk3_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,plain,
( subset(X1,X2)
| ~ in(esk3_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_16,plain,
( in(X1,X3)
| ~ in(X1,X2)
| X3 != set_union2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
( in(X1,X2)
| ~ in(X3,powerset(X2))
| ~ in(X1,X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_18,plain,
( in(esk3_2(X1,X2),X1)
| in(X1,powerset(X2)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_19,negated_conjecture,
~ ! [X1,X2] : subset(set_union2(powerset(set_difference(X1,X2)),powerset(set_difference(X2,X1))),powerset(symmetric_difference(X1,X2))),
inference(assume_negation,[status(cth)],[t86_zfmisc_1]) ).
cnf(c_0_20,plain,
( in(X1,powerset(X2))
| ~ in(esk3_2(X1,X2),X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_21,plain,
( in(X1,set_union2(X2,X3))
| ~ in(X1,X3) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( in(powerset(X1),powerset(X2))
| in(X3,X1)
| ~ in(X3,esk3_2(powerset(X1),X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_23,negated_conjecture,
~ subset(set_union2(powerset(set_difference(esk6_0,esk7_0)),powerset(set_difference(esk7_0,esk6_0))),powerset(symmetric_difference(esk6_0,esk7_0))),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
fof(c_0_24,plain,
! [X33,X34] : symmetric_difference(X33,X34) = set_union2(set_difference(X33,X34),set_difference(X34,X33)),
inference(variable_rename,[status(thm)],[d6_xboole_0]) ).
cnf(c_0_25,plain,
( in(X1,powerset(set_union2(X2,X3)))
| ~ in(esk3_2(X1,set_union2(X2,X3)),X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
( in(esk3_2(esk3_2(powerset(X1),X2),X3),X1)
| in(esk3_2(powerset(X1),X2),powerset(X3))
| in(powerset(X1),powerset(X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_18]) ).
cnf(c_0_27,negated_conjecture,
~ subset(set_union2(powerset(set_difference(esk6_0,esk7_0)),powerset(set_difference(esk7_0,esk6_0))),powerset(symmetric_difference(esk6_0,esk7_0))),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
symmetric_difference(X1,X2) = set_union2(set_difference(X1,X2),set_difference(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
( in(esk3_2(powerset(X1),X2),powerset(set_union2(X3,X1)))
| in(powerset(X1),powerset(X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
fof(c_0_30,plain,
! [X7,X8] : set_union2(X7,X8) = set_union2(X8,X7),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_0_31,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X2 != set_union2(X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_32,negated_conjecture,
~ subset(set_union2(powerset(set_difference(esk6_0,esk7_0)),powerset(set_difference(esk7_0,esk6_0))),powerset(set_union2(set_difference(esk6_0,esk7_0),set_difference(esk7_0,esk6_0)))),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_33,plain,
in(powerset(X1),powerset(powerset(set_union2(X2,X1)))),
inference(spm,[status(thm)],[c_0_20,c_0_29]) ).
cnf(c_0_34,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,plain,
( in(X1,X2)
| in(X1,X3)
| ~ in(X1,set_union2(X3,X2)) ),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_36,negated_conjecture,
in(esk3_2(set_union2(powerset(set_difference(esk6_0,esk7_0)),powerset(set_difference(esk7_0,esk6_0))),powerset(set_union2(set_difference(esk6_0,esk7_0),set_difference(esk7_0,esk6_0)))),set_union2(powerset(set_difference(esk6_0,esk7_0)),powerset(set_difference(esk7_0,esk6_0)))),
inference(spm,[status(thm)],[c_0_32,c_0_14]) ).
cnf(c_0_37,negated_conjecture,
~ in(esk3_2(set_union2(powerset(set_difference(esk6_0,esk7_0)),powerset(set_difference(esk7_0,esk6_0))),powerset(set_union2(set_difference(esk6_0,esk7_0),set_difference(esk7_0,esk6_0)))),powerset(set_union2(set_difference(esk6_0,esk7_0),set_difference(esk7_0,esk6_0)))),
inference(spm,[status(thm)],[c_0_32,c_0_15]) ).
cnf(c_0_38,plain,
( in(X1,powerset(set_union2(X2,X3)))
| ~ in(X1,powerset(X3)) ),
inference(spm,[status(thm)],[c_0_17,c_0_33]) ).
cnf(c_0_39,plain,
in(powerset(X1),powerset(powerset(set_union2(X1,X2)))),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_40,negated_conjecture,
( in(esk3_2(set_union2(powerset(set_difference(esk6_0,esk7_0)),powerset(set_difference(esk7_0,esk6_0))),powerset(set_union2(set_difference(esk6_0,esk7_0),set_difference(esk7_0,esk6_0)))),powerset(set_difference(esk7_0,esk6_0)))
| in(esk3_2(set_union2(powerset(set_difference(esk6_0,esk7_0)),powerset(set_difference(esk7_0,esk6_0))),powerset(set_union2(set_difference(esk6_0,esk7_0),set_difference(esk7_0,esk6_0)))),powerset(set_difference(esk6_0,esk7_0))) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,negated_conjecture,
~ in(esk3_2(set_union2(powerset(set_difference(esk6_0,esk7_0)),powerset(set_difference(esk7_0,esk6_0))),powerset(set_union2(set_difference(esk6_0,esk7_0),set_difference(esk7_0,esk6_0)))),powerset(set_difference(esk7_0,esk6_0))),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,plain,
( in(X1,powerset(set_union2(X2,X3)))
| ~ in(X1,powerset(X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_39]) ).
cnf(c_0_43,negated_conjecture,
in(esk3_2(set_union2(powerset(set_difference(esk6_0,esk7_0)),powerset(set_difference(esk7_0,esk6_0))),powerset(set_union2(set_difference(esk6_0,esk7_0),set_difference(esk7_0,esk6_0)))),powerset(set_difference(esk6_0,esk7_0))),
inference(sr,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_44,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_42]),c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET938+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n028.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 08:50:07 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.78 % Version : CSE_E---1.5
% 0.19/0.78 % Problem : theBenchmark.p
% 0.19/0.78 % Proof found
% 0.19/0.78 % SZS status Theorem for theBenchmark.p
% 0.19/0.78 % SZS output start Proof
% See solution above
% 0.19/0.79 % Total time : 0.206000 s
% 0.19/0.79 % SZS output end Proof
% 0.19/0.79 % Total time : 0.209000 s
%------------------------------------------------------------------------------