TSTP Solution File: SEU089+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU089+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 : n013.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 16:22:23 EDT 2023
% Result : Theorem 0.23s 0.56s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 55
% Syntax : Number of formulae : 70 ( 10 unt; 52 typ; 0 def)
% Number of atoms : 35 ( 3 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 27 ( 10 ~; 6 |; 8 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 26 >; 6 *; 0 +; 0 <<)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-2 aty)
% Number of functors : 34 ( 34 usr; 26 con; 0-3 aty)
% Number of variables : 23 ( 0 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,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_32,type,
powerset: $i > $i ).
tff(decl_33,type,
natural: $i > $o ).
tff(decl_34,type,
one_to_one: $i > $o ).
tff(decl_35,type,
positive_rationals: $i ).
tff(decl_36,type,
cartesian_product3: ( $i * $i * $i ) > $i ).
tff(decl_37,type,
empty_set: $i ).
tff(decl_38,type,
relation_empty_yielding: $i > $o ).
tff(decl_39,type,
function_yielding: $i > $o ).
tff(decl_40,type,
being_limit_ordinal: $i > $o ).
tff(decl_41,type,
transfinite_sequence: $i > $o ).
tff(decl_42,type,
ordinal_yielding: $i > $o ).
tff(decl_43,type,
relation_non_empty: $i > $o ).
tff(decl_44,type,
subset: ( $i * $i ) > $o ).
tff(decl_45,type,
esk1_1: $i > $i ).
tff(decl_46,type,
esk2_0: $i ).
tff(decl_47,type,
esk3_0: $i ).
tff(decl_48,type,
esk4_0: $i ).
tff(decl_49,type,
esk5_0: $i ).
tff(decl_50,type,
esk6_0: $i ).
tff(decl_51,type,
esk7_0: $i ).
tff(decl_52,type,
esk8_0: $i ).
tff(decl_53,type,
esk9_1: $i > $i ).
tff(decl_54,type,
esk10_0: $i ).
tff(decl_55,type,
esk11_0: $i ).
tff(decl_56,type,
esk12_1: $i > $i ).
tff(decl_57,type,
esk13_0: $i ).
tff(decl_58,type,
esk14_0: $i ).
tff(decl_59,type,
esk15_0: $i ).
tff(decl_60,type,
esk16_0: $i ).
tff(decl_61,type,
esk17_1: $i > $i ).
tff(decl_62,type,
esk18_0: $i ).
tff(decl_63,type,
esk19_0: $i ).
tff(decl_64,type,
esk20_1: $i > $i ).
tff(decl_65,type,
esk21_0: $i ).
tff(decl_66,type,
esk22_0: $i ).
tff(decl_67,type,
esk23_0: $i ).
tff(decl_68,type,
esk24_0: $i ).
tff(decl_69,type,
esk25_0: $i ).
tff(decl_70,type,
esk26_0: $i ).
tff(decl_71,type,
esk27_0: $i ).
tff(decl_72,type,
esk28_0: $i ).
tff(decl_73,type,
esk29_0: $i ).
fof(t20_finset_1,conjecture,
! [X1,X2,X3] :
( ( finite(X1)
& finite(X2)
& finite(X3) )
=> finite(cartesian_product3(X1,X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_finset_1) ).
fof(fc14_finset_1,axiom,
! [X1,X2] :
( ( finite(X1)
& finite(X2) )
=> finite(cartesian_product2(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc14_finset_1) ).
fof(d3_zfmisc_1,axiom,
! [X1,X2,X3] : cartesian_product3(X1,X2,X3) = cartesian_product2(cartesian_product2(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_zfmisc_1) ).
fof(c_0_3,negated_conjecture,
~ ! [X1,X2,X3] :
( ( finite(X1)
& finite(X2)
& finite(X3) )
=> finite(cartesian_product3(X1,X2,X3)) ),
inference(assume_negation,[status(cth)],[t20_finset_1]) ).
fof(c_0_4,plain,
! [X27,X28] :
( ~ finite(X27)
| ~ finite(X28)
| finite(cartesian_product2(X27,X28)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fc14_finset_1])]) ).
fof(c_0_5,negated_conjecture,
( finite(esk27_0)
& finite(esk28_0)
& finite(esk29_0)
& ~ finite(cartesian_product3(esk27_0,esk28_0,esk29_0)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
cnf(c_0_6,plain,
( finite(cartesian_product2(X1,X2))
| ~ finite(X1)
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
finite(esk28_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X22,X23,X24] : cartesian_product3(X22,X23,X24) = cartesian_product2(cartesian_product2(X22,X23),X24),
inference(variable_rename,[status(thm)],[d3_zfmisc_1]) ).
cnf(c_0_9,negated_conjecture,
finite(esk29_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
( finite(cartesian_product2(X1,esk28_0))
| ~ finite(X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_11,negated_conjecture,
finite(esk27_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,negated_conjecture,
~ finite(cartesian_product3(esk27_0,esk28_0,esk29_0)),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,plain,
cartesian_product3(X1,X2,X3) = cartesian_product2(cartesian_product2(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
( finite(cartesian_product2(X1,esk29_0))
| ~ finite(X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_9]) ).
cnf(c_0_15,negated_conjecture,
finite(cartesian_product2(esk27_0,esk28_0)),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,negated_conjecture,
~ finite(cartesian_product2(cartesian_product2(esk27_0,esk28_0),esk29_0)),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.16 % Problem : SEU089+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.17 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.16/0.38 % Computer : n013.cluster.edu
% 0.16/0.38 % Model : x86_64 x86_64
% 0.16/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.38 % Memory : 8042.1875MB
% 0.16/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.38 % CPULimit : 300
% 0.16/0.38 % WCLimit : 300
% 0.16/0.38 % DateTime : Wed Aug 23 14:20:47 EDT 2023
% 0.16/0.38 % CPUTime :
% 0.23/0.55 start to proof: theBenchmark
% 0.23/0.56 % Version : CSE_E---1.5
% 0.23/0.56 % Problem : theBenchmark.p
% 0.23/0.56 % Proof found
% 0.23/0.56 % SZS status Theorem for theBenchmark.p
% 0.23/0.56 % SZS output start Proof
% See solution above
% 0.23/0.56 % Total time : 0.009000 s
% 0.23/0.56 % SZS output end Proof
% 0.23/0.56 % Total time : 0.011000 s
%------------------------------------------------------------------------------