TSTP Solution File: SEU117+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU117+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 : n016.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 16:22:30 EDT 2023
% Result : Theorem 0.18s 0.56s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 38
% Syntax : Number of formulae : 57 ( 9 unt; 32 typ; 0 def)
% Number of atoms : 81 ( 8 equ)
% Maximal formula atoms : 26 ( 3 avg)
% Number of connectives : 88 ( 32 ~; 32 |; 17 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 25 >; 4 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 35 ( 2 sgn; 24 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
empty_set: $i ).
tff(decl_23,type,
empty: $i > $o ).
tff(decl_24,type,
cup_closed: $i > $o ).
tff(decl_25,type,
diff_closed: $i > $o ).
tff(decl_26,type,
preboolean: $i > $o ).
tff(decl_27,type,
finite: $i > $o ).
tff(decl_28,type,
element: ( $i * $i ) > $o ).
tff(decl_29,type,
in: ( $i * $i ) > $o ).
tff(decl_30,type,
powerset: $i > $i ).
tff(decl_31,type,
subset: ( $i * $i ) > $o ).
tff(decl_32,type,
finite_subsets: $i > $i ).
tff(decl_33,type,
cap_closed: $i > $o ).
tff(decl_34,type,
relation: $i > $o ).
tff(decl_35,type,
function: $i > $o ).
tff(decl_36,type,
one_to_one: $i > $o ).
tff(decl_37,type,
epsilon_transitive: $i > $o ).
tff(decl_38,type,
epsilon_connected: $i > $o ).
tff(decl_39,type,
ordinal: $i > $o ).
tff(decl_40,type,
natural: $i > $o ).
tff(decl_41,type,
esk1_1: $i > $i ).
tff(decl_42,type,
esk2_0: $i ).
tff(decl_43,type,
esk3_0: $i ).
tff(decl_44,type,
esk4_1: $i > $i ).
tff(decl_45,type,
esk5_1: $i > $i ).
tff(decl_46,type,
esk6_1: $i > $i ).
tff(decl_47,type,
esk7_1: $i > $i ).
tff(decl_48,type,
esk8_1: $i > $i ).
tff(decl_49,type,
esk9_0: $i ).
tff(decl_50,type,
esk10_0: $i ).
tff(decl_51,type,
esk11_0: $i ).
tff(decl_52,type,
esk12_0: $i ).
tff(decl_53,type,
esk13_2: ( $i * $i ) > $i ).
fof(t32_finsub_1,conjecture,
! [X1,X2] :
( element(X2,finite_subsets(X1))
=> element(X2,powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t32_finsub_1) ).
fof(fc2_finsub_1,axiom,
! [X1] :
( ~ empty(finite_subsets(X1))
& cup_closed(finite_subsets(X1))
& diff_closed(finite_subsets(X1))
& preboolean(finite_subsets(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_finsub_1) ).
fof(d5_finsub_1,axiom,
! [X1,X2] :
( preboolean(X2)
=> ( X2 = finite_subsets(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( subset(X3,X1)
& finite(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_finsub_1) ).
fof(dt_k5_finsub_1,axiom,
! [X1] : preboolean(finite_subsets(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_finsub_1) ).
fof(t2_subset,axiom,
! [X1,X2] :
( element(X1,X2)
=> ( empty(X2)
| in(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2] :
( element(X2,finite_subsets(X1))
=> element(X2,powerset(X1)) ),
inference(assume_negation,[status(cth)],[t32_finsub_1]) ).
fof(c_0_7,plain,
! [X1] :
( ~ empty(finite_subsets(X1))
& cup_closed(finite_subsets(X1))
& diff_closed(finite_subsets(X1))
& preboolean(finite_subsets(X1)) ),
inference(fof_simplification,[status(thm)],[fc2_finsub_1]) ).
fof(c_0_8,plain,
! [X53,X54,X55,X56] :
( ( subset(X55,X53)
| ~ in(X55,X54)
| X54 != finite_subsets(X53)
| ~ preboolean(X54) )
& ( finite(X55)
| ~ in(X55,X54)
| X54 != finite_subsets(X53)
| ~ preboolean(X54) )
& ( ~ subset(X56,X53)
| ~ finite(X56)
| in(X56,X54)
| X54 != finite_subsets(X53)
| ~ preboolean(X54) )
& ( ~ in(esk13_2(X53,X54),X54)
| ~ subset(esk13_2(X53,X54),X53)
| ~ finite(esk13_2(X53,X54))
| X54 = finite_subsets(X53)
| ~ preboolean(X54) )
& ( subset(esk13_2(X53,X54),X53)
| in(esk13_2(X53,X54),X54)
| X54 = finite_subsets(X53)
| ~ preboolean(X54) )
& ( finite(esk13_2(X53,X54))
| in(esk13_2(X53,X54),X54)
| X54 = finite_subsets(X53)
| ~ preboolean(X54) ) ),
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)],[d5_finsub_1])])])])])]) ).
fof(c_0_9,plain,
! [X19] : preboolean(finite_subsets(X19)),
inference(variable_rename,[status(thm)],[dt_k5_finsub_1]) ).
fof(c_0_10,plain,
! [X6,X7] :
( ~ element(X6,X7)
| empty(X7)
| in(X6,X7) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t2_subset])]) ).
fof(c_0_11,negated_conjecture,
( element(esk12_0,finite_subsets(esk11_0))
& ~ element(esk12_0,powerset(esk11_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
fof(c_0_12,plain,
! [X21] :
( ~ empty(finite_subsets(X21))
& cup_closed(finite_subsets(X21))
& diff_closed(finite_subsets(X21))
& preboolean(finite_subsets(X21)) ),
inference(variable_rename,[status(thm)],[c_0_7]) ).
cnf(c_0_13,plain,
( subset(X1,X2)
| ~ in(X1,X3)
| X3 != finite_subsets(X2)
| ~ preboolean(X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
preboolean(finite_subsets(X1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( empty(X2)
| in(X1,X2)
| ~ element(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
element(esk12_0,finite_subsets(esk11_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
~ empty(finite_subsets(X1)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
fof(c_0_18,plain,
! [X44,X45] :
( ( ~ element(X44,powerset(X45))
| subset(X44,X45) )
& ( ~ subset(X44,X45)
| element(X44,powerset(X45)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
cnf(c_0_19,plain,
( subset(X1,X2)
| ~ in(X1,finite_subsets(X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_13]),c_0_14])]) ).
cnf(c_0_20,negated_conjecture,
in(esk12_0,finite_subsets(esk11_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_21,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_22,negated_conjecture,
subset(esk12_0,esk11_0),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
~ element(esk12_0,powerset(esk11_0)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
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
% 0.00/0.11 % Problem : SEU117+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.32 % Computer : n016.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Wed Aug 23 15:10:07 EDT 2023
% 0.12/0.32 % CPUTime :
% 0.18/0.54 start to proof: theBenchmark
% 0.18/0.56 % Version : CSE_E---1.5
% 0.18/0.56 % Problem : theBenchmark.p
% 0.18/0.56 % Proof found
% 0.18/0.56 % SZS status Theorem for theBenchmark.p
% 0.18/0.56 % SZS output start Proof
% See solution above
% 0.18/0.57 % Total time : 0.011000 s
% 0.18/0.57 % SZS output end Proof
% 0.18/0.57 % Total time : 0.014000 s
%------------------------------------------------------------------------------