TSTP Solution File: SEU173+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU173+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 : 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 16:23:04 EDT 2023
% Result : Theorem 0.20s 0.70s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 52
% Syntax : Number of formulae : 72 ( 4 unt; 47 typ; 0 def)
% Number of atoms : 86 ( 6 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 96 ( 35 ~; 33 |; 12 &)
% ( 7 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 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 : 40 ( 40 usr; 5 con; 0-4 aty)
% Number of variables : 51 ( 1 sgn; 34 !; 0 ?; 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_0: $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_0: $i ).
tff(decl_63,type,
esk24_1: $i > $i ).
tff(decl_64,type,
esk25_2: ( $i * $i ) > $i ).
tff(decl_65,type,
esk26_2: ( $i * $i ) > $i ).
tff(decl_66,type,
esk27_2: ( $i * $i ) > $i ).
tff(decl_67,type,
esk28_1: $i > $i ).
tff(decl_68,type,
esk29_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(l71_subset_1,conjecture,
! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> in(X3,X2) )
=> element(X1,powerset(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l71_subset_1) ).
fof(t7_boole,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& empty(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
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(d3_tarski,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( in(X3,X1)
=> in(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(c_0_5,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_6,negated_conjecture,
~ ! [X1,X2] :
( ! [X3] :
( in(X3,X1)
=> in(X3,X2) )
=> element(X1,powerset(X2)) ),
inference(assume_negation,[status(cth)],[l71_subset_1]) ).
fof(c_0_7,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_5])])]) ).
fof(c_0_8,plain,
! [X275,X276] :
( ~ in(X275,X276)
| ~ empty(X276) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_boole])]) ).
fof(c_0_9,negated_conjecture,
! [X160] :
( ( ~ in(X160,esk18_0)
| in(X160,esk19_0) )
& ~ element(esk18_0,powerset(esk19_0)) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
cnf(c_0_10,plain,
( element(X1,X2)
| empty(X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( ~ in(X1,X2)
| ~ empty(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X30,X31,X32,X33,X34,X35] :
( ( ~ in(X32,X31)
| subset(X32,X30)
| X31 != powerset(X30) )
& ( ~ subset(X33,X30)
| in(X33,X31)
| X31 != powerset(X30) )
& ( ~ in(esk3_2(X34,X35),X35)
| ~ subset(esk3_2(X34,X35),X34)
| X35 = powerset(X34) )
& ( in(esk3_2(X34,X35),X35)
| subset(esk3_2(X34,X35),X34)
| X35 = powerset(X34) ) ),
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_13,plain,
! [X74,X75,X76,X77,X78] :
( ( ~ subset(X74,X75)
| ~ in(X76,X74)
| in(X76,X75) )
& ( in(esk11_2(X77,X78),X77)
| subset(X77,X78) )
& ( ~ in(esk11_2(X77,X78),X78)
| subset(X77,X78) ) ),
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_14,negated_conjecture,
~ element(esk18_0,powerset(esk19_0)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( element(X1,X2)
| ~ in(X1,X2) ),
inference(csr,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
( in(X1,X3)
| ~ subset(X1,X2)
| X3 != powerset(X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( in(X1,esk19_0)
| ~ in(X1,esk18_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_18,plain,
( in(esk11_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
~ in(esk18_0,powerset(esk19_0)),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,plain,
( in(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_21,plain,
( subset(X1,X2)
| ~ in(esk11_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_22,negated_conjecture,
( subset(esk18_0,X1)
| in(esk11_2(esk18_0,X1),esk19_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
~ subset(esk18_0,esk19_0),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU173+2 : 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
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 23 19:10:36 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.70 % Version : CSE_E---1.5
% 0.20/0.70 % Problem : theBenchmark.p
% 0.20/0.70 % Proof found
% 0.20/0.70 % SZS status Theorem for theBenchmark.p
% 0.20/0.70 % SZS output start Proof
% See solution above
% 0.20/0.71 % Total time : 0.131000 s
% 0.20/0.71 % SZS output end Proof
% 0.20/0.71 % Total time : 0.135000 s
%------------------------------------------------------------------------------