TSTP Solution File: SEU097+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU097+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 : n024.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 16:22:25 EDT 2023
% Result : Theorem 10.53s 10.60s
% Output : CNFRefutation 10.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 56
% Syntax : Number of formulae : 73 ( 11 unt; 52 typ; 0 def)
% Number of atoms : 37 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 11 ~; 7 |; 5 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 33 ( 27 >; 6 *; 0 +; 0 <<)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-2 aty)
% Number of functors : 34 ( 34 usr; 25 con; 0-2 aty)
% Number of variables : 28 ( 6 sgn; 16 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
ordinal: $i > $o ).
tff(decl_24,type,
element: ( $i * $i ) > $o ).
tff(decl_25,type,
epsilon_transitive: $i > $o ).
tff(decl_26,type,
epsilon_connected: $i > $o ).
tff(decl_27,type,
empty: $i > $o ).
tff(decl_28,type,
finite: $i > $o ).
tff(decl_29,type,
function: $i > $o ).
tff(decl_30,type,
relation: $i > $o ).
tff(decl_31,type,
natural: $i > $o ).
tff(decl_32,type,
powerset: $i > $i ).
tff(decl_33,type,
one_to_one: $i > $o ).
tff(decl_34,type,
positive_rationals: $i ).
tff(decl_35,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_36,type,
symmetric_difference: ( $i * $i ) > $i ).
tff(decl_37,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_38,type,
empty_set: $i ).
tff(decl_39,type,
relation_empty_yielding: $i > $o ).
tff(decl_40,type,
function_yielding: $i > $o ).
tff(decl_41,type,
being_limit_ordinal: $i > $o ).
tff(decl_42,type,
transfinite_sequence: $i > $o ).
tff(decl_43,type,
ordinal_yielding: $i > $o ).
tff(decl_44,type,
relation_non_empty: $i > $o ).
tff(decl_45,type,
subset: ( $i * $i ) > $o ).
tff(decl_46,type,
esk1_1: $i > $i ).
tff(decl_47,type,
esk2_0: $i ).
tff(decl_48,type,
esk3_0: $i ).
tff(decl_49,type,
esk4_0: $i ).
tff(decl_50,type,
esk5_0: $i ).
tff(decl_51,type,
esk6_0: $i ).
tff(decl_52,type,
esk7_0: $i ).
tff(decl_53,type,
esk8_0: $i ).
tff(decl_54,type,
esk9_1: $i > $i ).
tff(decl_55,type,
esk10_0: $i ).
tff(decl_56,type,
esk11_0: $i ).
tff(decl_57,type,
esk12_1: $i > $i ).
tff(decl_58,type,
esk13_0: $i ).
tff(decl_59,type,
esk14_0: $i ).
tff(decl_60,type,
esk15_0: $i ).
tff(decl_61,type,
esk16_0: $i ).
tff(decl_62,type,
esk17_1: $i > $i ).
tff(decl_63,type,
esk18_0: $i ).
tff(decl_64,type,
esk19_0: $i ).
tff(decl_65,type,
esk20_1: $i > $i ).
tff(decl_66,type,
esk21_0: $i ).
tff(decl_67,type,
esk22_0: $i ).
tff(decl_68,type,
esk23_0: $i ).
tff(decl_69,type,
esk24_0: $i ).
tff(decl_70,type,
esk25_0: $i ).
tff(decl_71,type,
esk26_0: $i ).
tff(decl_72,type,
esk27_0: $i ).
tff(decl_73,type,
esk28_0: $i ).
fof(t28_finset_1,conjecture,
! [X1,X2] :
( ( finite(X1)
& finite(X2) )
=> finite(symmetric_difference(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_finset_1) ).
fof(fc12_finset_1,axiom,
! [X1,X2] :
( finite(X1)
=> finite(set_difference(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_finset_1) ).
fof(fc9_finset_1,axiom,
! [X1,X2] :
( ( finite(X1)
& finite(X2) )
=> finite(set_union2(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc9_finset_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/sandbox/benchmark/theBenchmark.p',d6_xboole_0) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2] :
( ( finite(X1)
& finite(X2) )
=> finite(symmetric_difference(X1,X2)) ),
inference(assume_negation,[status(cth)],[t28_finset_1]) ).
fof(c_0_5,plain,
! [X27,X28] :
( ~ finite(X27)
| finite(set_difference(X27,X28)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc12_finset_1])]) ).
fof(c_0_6,negated_conjecture,
( finite(esk27_0)
& finite(esk28_0)
& ~ finite(symmetric_difference(esk27_0,esk28_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_7,plain,
! [X38,X39] :
( ~ finite(X38)
| ~ finite(X39)
| finite(set_union2(X38,X39)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc9_finset_1])]) ).
cnf(c_0_8,plain,
( finite(set_difference(X1,X2))
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
finite(esk28_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,plain,
! [X23,X24] : symmetric_difference(X23,X24) = set_union2(set_difference(X23,X24),set_difference(X24,X23)),
inference(variable_rename,[status(thm)],[d6_xboole_0]) ).
cnf(c_0_11,plain,
( finite(set_union2(X1,X2))
| ~ finite(X1)
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,negated_conjecture,
finite(set_difference(esk28_0,X1)),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,negated_conjecture,
finite(esk27_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
~ finite(symmetric_difference(esk27_0,esk28_0)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_15,plain,
symmetric_difference(X1,X2) = set_union2(set_difference(X1,X2),set_difference(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
( finite(set_union2(X1,set_difference(esk28_0,X2)))
| ~ finite(X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
finite(set_difference(esk27_0,X1)),
inference(spm,[status(thm)],[c_0_8,c_0_13]) ).
cnf(c_0_18,negated_conjecture,
~ finite(set_union2(set_difference(esk27_0,esk28_0),set_difference(esk28_0,esk27_0))),
inference(rw,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
finite(set_union2(set_difference(esk27_0,X1),set_difference(esk28_0,X2))),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU097+1 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n024.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 23 13:12:09 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 10.53/10.60 % Version : CSE_E---1.5
% 10.53/10.60 % Problem : theBenchmark.p
% 10.53/10.60 % Proof found
% 10.53/10.60 % SZS status Theorem for theBenchmark.p
% 10.53/10.60 % SZS output start Proof
% See solution above
% 10.53/10.61 % Total time : 10.013000 s
% 10.53/10.61 % SZS output end Proof
% 10.53/10.61 % Total time : 10.018000 s
%------------------------------------------------------------------------------