TSTP Solution File: SEU106+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU106+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 : n026.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 16:22:27 EDT 2023
% Result : Theorem 0.20s 0.67s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 41
% Syntax : Number of formulae : 70 ( 12 unt; 35 typ; 0 def)
% Number of atoms : 97 ( 9 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 113 ( 51 ~; 40 |; 11 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 29 >; 7 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 6 con; 0-2 aty)
% Number of variables : 46 ( 1 sgn; 30 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
empty: $i > $o ).
tff(decl_24,type,
finite: $i > $o ).
tff(decl_25,type,
preboolean: $i > $o ).
tff(decl_26,type,
cup_closed: $i > $o ).
tff(decl_27,type,
diff_closed: $i > $o ).
tff(decl_28,type,
powerset: $i > $i ).
tff(decl_29,type,
element: ( $i * $i ) > $o ).
tff(decl_30,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_31,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_32,type,
symmetric_difference: ( $i * $i ) > $i ).
tff(decl_33,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_34,type,
empty_set: $i ).
tff(decl_35,type,
cap_closed: $i > $o ).
tff(decl_36,type,
relation: $i > $o ).
tff(decl_37,type,
function: $i > $o ).
tff(decl_38,type,
one_to_one: $i > $o ).
tff(decl_39,type,
epsilon_transitive: $i > $o ).
tff(decl_40,type,
epsilon_connected: $i > $o ).
tff(decl_41,type,
ordinal: $i > $o ).
tff(decl_42,type,
natural: $i > $o ).
tff(decl_43,type,
subset: ( $i * $i ) > $o ).
tff(decl_44,type,
esk1_1: $i > $i ).
tff(decl_45,type,
esk2_0: $i ).
tff(decl_46,type,
esk3_0: $i ).
tff(decl_47,type,
esk4_1: $i > $i ).
tff(decl_48,type,
esk5_0: $i ).
tff(decl_49,type,
esk6_1: $i > $i ).
tff(decl_50,type,
esk7_1: $i > $i ).
tff(decl_51,type,
esk8_0: $i ).
tff(decl_52,type,
esk9_1: $i > $i ).
tff(decl_53,type,
esk10_1: $i > $i ).
tff(decl_54,type,
esk11_1: $i > $i ).
tff(decl_55,type,
esk12_1: $i > $i ).
tff(decl_56,type,
esk13_0: $i ).
fof(t10_finsub_1,axiom,
! [X1] :
( preboolean(X1)
<=> ! [X2,X3] :
( ( in(X2,X1)
& in(X3,X1) )
=> ( in(set_union2(X2,X3),X1)
& in(set_difference(X2,X3),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_finsub_1) ).
fof(t100_xboole_1,axiom,
! [X1,X2] : set_difference(X1,X2) = symmetric_difference(X1,set_intersection2(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_xboole_1) ).
fof(t95_xboole_1,axiom,
! [X1,X2] : set_intersection2(X1,X2) = symmetric_difference(symmetric_difference(X1,X2),set_union2(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t95_xboole_1) ).
fof(t17_finsub_1,conjecture,
! [X1] :
( ~ empty(X1)
=> ( ! [X2] :
( element(X2,X1)
=> ! [X3] :
( element(X3,X1)
=> ( in(symmetric_difference(X2,X3),X1)
& in(set_union2(X2,X3),X1) ) ) )
=> preboolean(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_finsub_1) ).
fof(t1_subset,axiom,
! [X1,X2] :
( in(X1,X2)
=> element(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(idempotence_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(c_0_6,plain,
! [X55,X56,X57,X58] :
( ( in(set_union2(X56,X57),X55)
| ~ in(X56,X55)
| ~ in(X57,X55)
| ~ preboolean(X55) )
& ( in(set_difference(X56,X57),X55)
| ~ in(X56,X55)
| ~ in(X57,X55)
| ~ preboolean(X55) )
& ( in(esk11_1(X58),X58)
| preboolean(X58) )
& ( in(esk12_1(X58),X58)
| preboolean(X58) )
& ( ~ in(set_union2(esk11_1(X58),esk12_1(X58)),X58)
| ~ in(set_difference(esk11_1(X58),esk12_1(X58)),X58)
| preboolean(X58) ) ),
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)],[t10_finsub_1])])])])])]) ).
fof(c_0_7,plain,
! [X53,X54] : set_difference(X53,X54) = symmetric_difference(X53,set_intersection2(X53,X54)),
inference(variable_rename,[status(thm)],[t100_xboole_1]) ).
fof(c_0_8,plain,
! [X86,X87] : set_intersection2(X86,X87) = symmetric_difference(symmetric_difference(X86,X87),set_union2(X86,X87)),
inference(variable_rename,[status(thm)],[t95_xboole_1]) ).
fof(c_0_9,negated_conjecture,
~ ! [X1] :
( ~ empty(X1)
=> ( ! [X2] :
( element(X2,X1)
=> ! [X3] :
( element(X3,X1)
=> ( in(symmetric_difference(X2,X3),X1)
& in(set_union2(X2,X3),X1) ) ) )
=> preboolean(X1) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t17_finsub_1])]) ).
cnf(c_0_10,plain,
( preboolean(X1)
| ~ in(set_union2(esk11_1(X1),esk12_1(X1)),X1)
| ~ in(set_difference(esk11_1(X1),esk12_1(X1)),X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,plain,
set_difference(X1,X2) = symmetric_difference(X1,set_intersection2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
set_intersection2(X1,X2) = symmetric_difference(symmetric_difference(X1,X2),set_union2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_13,negated_conjecture,
! [X62,X63] :
( ~ empty(esk13_0)
& ( in(symmetric_difference(X62,X63),esk13_0)
| ~ element(X63,esk13_0)
| ~ element(X62,esk13_0) )
& ( in(set_union2(X62,X63),esk13_0)
| ~ element(X63,esk13_0)
| ~ element(X62,esk13_0) )
& ~ preboolean(esk13_0) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])])]) ).
cnf(c_0_14,plain,
( preboolean(X1)
| ~ in(set_union2(esk11_1(X1),esk12_1(X1)),X1)
| ~ in(symmetric_difference(esk11_1(X1),symmetric_difference(symmetric_difference(esk11_1(X1),esk12_1(X1)),set_union2(esk11_1(X1),esk12_1(X1)))),X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
cnf(c_0_15,negated_conjecture,
( in(symmetric_difference(X1,X2),esk13_0)
| ~ element(X2,esk13_0)
| ~ element(X1,esk13_0) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_16,negated_conjecture,
~ preboolean(esk13_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_17,plain,
! [X65,X66] :
( ~ in(X65,X66)
| element(X65,X66) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_subset])]) ).
fof(c_0_18,plain,
! [X36] : set_union2(X36,X36) = X36,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[idempotence_k2_xboole_0])]) ).
cnf(c_0_19,negated_conjecture,
( ~ element(symmetric_difference(symmetric_difference(esk11_1(esk13_0),esk12_1(esk13_0)),set_union2(esk11_1(esk13_0),esk12_1(esk13_0))),esk13_0)
| ~ element(esk11_1(esk13_0),esk13_0)
| ~ in(set_union2(esk11_1(esk13_0),esk12_1(esk13_0)),esk13_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_20,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,negated_conjecture,
( in(set_union2(X1,X2),esk13_0)
| ~ element(X2,esk13_0)
| ~ element(X1,esk13_0) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,plain,
set_union2(X1,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( ~ element(esk11_1(esk13_0),esk13_0)
| ~ in(symmetric_difference(symmetric_difference(esk11_1(esk13_0),esk12_1(esk13_0)),set_union2(esk11_1(esk13_0),esk12_1(esk13_0))),esk13_0)
| ~ in(set_union2(esk11_1(esk13_0),esk12_1(esk13_0)),esk13_0) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( in(X1,esk13_0)
| ~ element(X1,esk13_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
( ~ element(set_union2(esk11_1(esk13_0),esk12_1(esk13_0)),esk13_0)
| ~ element(symmetric_difference(esk11_1(esk13_0),esk12_1(esk13_0)),esk13_0)
| ~ element(esk11_1(esk13_0),esk13_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_15]),c_0_24]) ).
cnf(c_0_26,negated_conjecture,
( ~ element(symmetric_difference(esk11_1(esk13_0),esk12_1(esk13_0)),esk13_0)
| ~ element(esk11_1(esk13_0),esk13_0)
| ~ in(set_union2(esk11_1(esk13_0),esk12_1(esk13_0)),esk13_0) ),
inference(spm,[status(thm)],[c_0_25,c_0_20]) ).
cnf(c_0_27,negated_conjecture,
( ~ element(esk11_1(esk13_0),esk13_0)
| ~ in(set_union2(esk11_1(esk13_0),esk12_1(esk13_0)),esk13_0)
| ~ in(symmetric_difference(esk11_1(esk13_0),esk12_1(esk13_0)),esk13_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_20]) ).
cnf(c_0_28,negated_conjecture,
( ~ element(esk11_1(esk13_0),esk13_0)
| ~ element(esk12_1(esk13_0),esk13_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_21]),c_0_15]) ).
cnf(c_0_29,negated_conjecture,
( ~ element(esk11_1(esk13_0),esk13_0)
| ~ in(esk12_1(esk13_0),esk13_0) ),
inference(spm,[status(thm)],[c_0_28,c_0_20]) ).
cnf(c_0_30,negated_conjecture,
( ~ in(esk12_1(esk13_0),esk13_0)
| ~ in(esk11_1(esk13_0),esk13_0) ),
inference(spm,[status(thm)],[c_0_29,c_0_20]) ).
cnf(c_0_31,plain,
( in(esk12_1(X1),X1)
| preboolean(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_32,negated_conjecture,
~ in(esk11_1(esk13_0),esk13_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_16]) ).
cnf(c_0_33,plain,
( in(esk11_1(X1),X1)
| preboolean(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU106+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34 % Computer : n026.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 : Thu Aug 24 01:24:31 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 0.20/0.67 % Version : CSE_E---1.5
% 0.20/0.67 % Problem : theBenchmark.p
% 0.20/0.67 % Proof found
% 0.20/0.67 % SZS status Theorem for theBenchmark.p
% 0.20/0.67 % SZS output start Proof
% See solution above
% 0.20/0.67 % Total time : 0.075000 s
% 0.20/0.67 % SZS output end Proof
% 0.20/0.67 % Total time : 0.078000 s
%------------------------------------------------------------------------------