TSTP Solution File: SEU171+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU171+2 : 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 : n029.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 16:23:03 EDT 2023
% Result : Theorem 0.19s 0.67s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 55
% Syntax : Number of formulae : 86 ( 14 unt; 48 typ; 0 def)
% Number of atoms : 118 ( 26 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 128 ( 48 ~; 40 |; 18 &)
% ( 8 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 86 ( 42 >; 44 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 41 ( 41 usr; 6 con; 0-4 aty)
% Number of variables : 55 ( 0 sgn; 38 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
proper_subset: ( $i * $i ) > $o ).
tff(decl_24,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_25,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_26,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_27,type,
subset: ( $i * $i ) > $o ).
tff(decl_28,type,
singleton: $i > $i ).
tff(decl_29,type,
empty_set: $i ).
tff(decl_30,type,
powerset: $i > $i ).
tff(decl_31,type,
empty: $i > $o ).
tff(decl_32,type,
element: ( $i * $i ) > $o ).
tff(decl_33,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_34,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_35,type,
union: $i > $i ).
tff(decl_36,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_37,type,
subset_complement: ( $i * $i ) > $i ).
tff(decl_38,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_39,type,
are_equipotent: ( $i * $i ) > $o ).
tff(decl_40,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_41,type,
esk2_1: $i > $i ).
tff(decl_42,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_43,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_44,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
esk6_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_46,type,
esk7_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_47,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_48,type,
esk9_3: ( $i * $i * $i ) > $i ).
tff(decl_49,type,
esk10_3: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_51,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_52,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_53,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk15_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_56,type,
esk17_1: $i > $i ).
tff(decl_57,type,
esk18_1: $i > $i ).
tff(decl_58,type,
esk19_0: $i ).
tff(decl_59,type,
esk20_1: $i > $i ).
tff(decl_60,type,
esk21_0: $i ).
tff(decl_61,type,
esk22_1: $i > $i ).
tff(decl_62,type,
esk23_2: ( $i * $i ) > $i ).
tff(decl_63,type,
esk24_2: ( $i * $i ) > $i ).
tff(decl_64,type,
esk25_2: ( $i * $i ) > $i ).
tff(decl_65,type,
esk26_0: $i ).
tff(decl_66,type,
esk27_0: $i ).
tff(decl_67,type,
esk28_0: $i ).
tff(decl_68,type,
esk29_1: $i > $i ).
tff(decl_69,type,
esk30_2: ( $i * $i ) > $i ).
fof(d2_subset_1,axiom,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_subset_1) ).
fof(t50_subset_1,conjecture,
! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t50_subset_1) ).
fof(t6_boole,axiom,
! [X1] :
( empty(X1)
=> X1 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(rc1_xboole_0,axiom,
? [X1] : empty(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(d4_xboole_0,axiom,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
fof(t8_boole,axiom,
! [X1,X2] :
~ ( empty(X1)
& X1 != X2
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(d5_subset_1,axiom,
! [X1,X2] :
( element(X2,powerset(X1))
=> subset_complement(X1,X2) = set_difference(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).
fof(c_0_7,plain,
! [X1,X2] :
( ( ~ empty(X1)
=> ( element(X2,X1)
<=> in(X2,X1) ) )
& ( empty(X1)
=> ( element(X2,X1)
<=> empty(X2) ) ) ),
inference(fof_simplification,[status(thm)],[d2_subset_1]) ).
fof(c_0_8,negated_conjecture,
~ ! [X1] :
( X1 != empty_set
=> ! [X2] :
( element(X2,powerset(X1))
=> ! [X3] :
( element(X3,X1)
=> ( ~ in(X3,X2)
=> in(X3,subset_complement(X1,X2)) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t50_subset_1])]) ).
fof(c_0_9,plain,
! [X266] :
( ~ empty(X266)
| X266 = empty_set ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t6_boole])]) ).
fof(c_0_10,plain,
empty(esk19_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[rc1_xboole_0])]) ).
fof(c_0_11,plain,
! [X1,X2,X3] :
( X3 = set_difference(X1,X2)
<=> ! [X4] :
( in(X4,X3)
<=> ( in(X4,X1)
& ~ in(X4,X2) ) ) ),
inference(fof_simplification,[status(thm)],[d4_xboole_0]) ).
fof(c_0_12,plain,
! [X275,X276] :
( ~ empty(X275)
| X275 = X276
| ~ empty(X276) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t8_boole])]) ).
fof(c_0_13,plain,
! [X37,X38] :
( ( ~ element(X38,X37)
| in(X38,X37)
| empty(X37) )
& ( ~ in(X38,X37)
| element(X38,X37)
| empty(X37) )
& ( ~ element(X38,X37)
| empty(X38)
| ~ empty(X37) )
& ( ~ empty(X38)
| element(X38,X37)
| ~ empty(X37) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_14,negated_conjecture,
( esk26_0 != empty_set
& element(esk27_0,powerset(esk26_0))
& element(esk28_0,esk26_0)
& ~ in(esk28_0,esk27_0)
& ~ in(esk28_0,subset_complement(esk26_0,esk27_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
cnf(c_0_15,plain,
( X1 = empty_set
| ~ empty(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
empty(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_17,plain,
! [X109,X110] :
( ~ element(X110,powerset(X109))
| subset_complement(X109,X110) = set_difference(X109,X110) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d5_subset_1])]) ).
fof(c_0_18,plain,
! [X100,X101,X102,X103,X104,X105,X106,X107] :
( ( in(X103,X100)
| ~ in(X103,X102)
| X102 != set_difference(X100,X101) )
& ( ~ in(X103,X101)
| ~ in(X103,X102)
| X102 != set_difference(X100,X101) )
& ( ~ in(X104,X100)
| in(X104,X101)
| in(X104,X102)
| X102 != set_difference(X100,X101) )
& ( ~ in(esk16_3(X105,X106,X107),X107)
| ~ in(esk16_3(X105,X106,X107),X105)
| in(esk16_3(X105,X106,X107),X106)
| X107 = set_difference(X105,X106) )
& ( in(esk16_3(X105,X106,X107),X105)
| in(esk16_3(X105,X106,X107),X107)
| X107 = set_difference(X105,X106) )
& ( ~ in(esk16_3(X105,X106,X107),X106)
| in(esk16_3(X105,X106,X107),X107)
| X107 = set_difference(X105,X106) ) ),
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)],[c_0_11])])])])])]) ).
cnf(c_0_19,plain,
( X1 = X2
| ~ empty(X1)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
( in(X1,X2)
| empty(X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,negated_conjecture,
element(esk28_0,esk26_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,negated_conjecture,
esk26_0 != empty_set,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
empty_set = esk19_0,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_24,plain,
( subset_complement(X2,X1) = set_difference(X2,X1)
| ~ element(X1,powerset(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_25,negated_conjecture,
element(esk27_0,powerset(esk26_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_26,plain,
( in(X1,X3)
| in(X1,X4)
| ~ in(X1,X2)
| X4 != set_difference(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_27,plain,
( esk19_0 = X1
| ~ empty(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_28,negated_conjecture,
( empty(esk26_0)
| in(esk28_0,esk26_0) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_29,negated_conjecture,
esk26_0 != esk19_0,
inference(rw,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,negated_conjecture,
~ in(esk28_0,subset_complement(esk26_0,esk27_0)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_31,negated_conjecture,
subset_complement(esk26_0,esk27_0) = set_difference(esk26_0,esk27_0),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_32,plain,
( in(X1,set_difference(X2,X3))
| in(X1,X3)
| ~ in(X1,X2) ),
inference(er,[status(thm)],[c_0_26]) ).
cnf(c_0_33,negated_conjecture,
in(esk28_0,esk26_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_34,negated_conjecture,
~ in(esk28_0,set_difference(esk26_0,esk27_0)),
inference(rw,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,negated_conjecture,
( in(esk28_0,set_difference(esk26_0,X1))
| in(esk28_0,X1) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_36,negated_conjecture,
~ in(esk28_0,esk27_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU171+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 14:08:07 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.19/0.67 % Version : CSE_E---1.5
% 0.19/0.67 % Problem : theBenchmark.p
% 0.19/0.67 % Proof found
% 0.19/0.67 % SZS status Theorem for theBenchmark.p
% 0.19/0.67 % SZS output start Proof
% See solution above
% 0.19/0.68 % Total time : 0.107000 s
% 0.19/0.68 % SZS output end Proof
% 0.19/0.68 % Total time : 0.110000 s
%------------------------------------------------------------------------------