TSTP Solution File: NUM409+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM409+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 : n005.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 10:37:13 EDT 2023
% Result : Theorem 0.19s 0.59s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 54
% Syntax : Number of formulae : 91 ( 20 unt; 42 typ; 0 def)
% Number of atoms : 147 ( 25 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 165 ( 67 ~; 67 |; 21 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 36 ( 26 >; 10 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 16 con; 0-3 aty)
% Number of variables : 78 ( 18 sgn; 40 !; 1 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
empty: $i > $o ).
tff(decl_24,type,
function: $i > $o ).
tff(decl_25,type,
ordinal: $i > $o ).
tff(decl_26,type,
epsilon_transitive: $i > $o ).
tff(decl_27,type,
epsilon_connected: $i > $o ).
tff(decl_28,type,
relation: $i > $o ).
tff(decl_29,type,
one_to_one: $i > $o ).
tff(decl_30,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_31,type,
relation_dom: $i > $i ).
tff(decl_32,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_33,type,
singleton: $i > $i ).
tff(decl_34,type,
transfinite_sequence: $i > $o ).
tff(decl_35,type,
transfinite_sequence_of: ( $i * $i ) > $o ).
tff(decl_36,type,
relation_rng: $i > $i ).
tff(decl_37,type,
subset: ( $i * $i ) > $o ).
tff(decl_38,type,
element: ( $i * $i ) > $o ).
tff(decl_39,type,
empty_set: $i ).
tff(decl_40,type,
relation_empty_yielding: $i > $o ).
tff(decl_41,type,
relation_non_empty: $i > $o ).
tff(decl_42,type,
with_non_empty_elements: $i > $o ).
tff(decl_43,type,
powerset: $i > $i ).
tff(decl_44,type,
esk1_3: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_46,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk4_1: $i > $i ).
tff(decl_48,type,
esk5_1: $i > $i ).
tff(decl_49,type,
esk6_0: $i ).
tff(decl_50,type,
esk7_0: $i ).
tff(decl_51,type,
esk8_0: $i ).
tff(decl_52,type,
esk9_0: $i ).
tff(decl_53,type,
esk10_0: $i ).
tff(decl_54,type,
esk11_0: $i ).
tff(decl_55,type,
esk12_0: $i ).
tff(decl_56,type,
esk13_0: $i ).
tff(decl_57,type,
esk14_0: $i ).
tff(decl_58,type,
esk15_0: $i ).
tff(decl_59,type,
esk16_0: $i ).
tff(decl_60,type,
esk17_0: $i ).
tff(decl_61,type,
esk18_0: $i ).
tff(decl_62,type,
esk19_0: $i ).
tff(decl_63,type,
esk20_0: $i ).
fof(t3_subset,axiom,
! [X1,X2] :
( element(X1,powerset(X2))
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(t2_xboole_1,axiom,
! [X1] : subset(empty_set,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
fof(d4_relat_1,axiom,
! [X1] :
( relation(X1)
=> ! [X2] :
( X2 = relation_dom(X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] : in(ordered_pair(X3,X4),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(t5_subset,axiom,
! [X1,X2,X3] :
~ ( in(X1,X2)
& element(X2,powerset(X3))
& empty(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(fc12_relat_1,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_relat_1) ).
fof(t65_relat_1,axiom,
! [X1] :
( relation(X1)
=> ( relation_dom(X1) = empty_set
<=> relation_rng(X1) = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t65_relat_1) ).
fof(d7_ordinal1,axiom,
! [X1] :
( ( relation(X1)
& function(X1) )
=> ( transfinite_sequence(X1)
<=> ordinal(relation_dom(X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_ordinal1) ).
fof(t45_ordinal1,conjecture,
! [X1] : transfinite_sequence_of(empty_set,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_ordinal1) ).
fof(d8_ordinal1,axiom,
! [X1,X2] :
( ( relation(X2)
& function(X2)
& transfinite_sequence(X2) )
=> ( transfinite_sequence_of(X2,X1)
<=> subset(relation_rng(X2),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_ordinal1) ).
fof(fc2_ordinal1,axiom,
( relation(empty_set)
& relation_empty_yielding(empty_set)
& function(empty_set)
& one_to_one(empty_set)
& empty(empty_set)
& epsilon_transitive(empty_set)
& epsilon_connected(empty_set)
& ordinal(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_ordinal1) ).
fof(c_0_12,plain,
! [X63,X64] :
( ( ~ element(X63,powerset(X64))
| subset(X63,X64) )
& ( ~ subset(X63,X64)
| element(X63,powerset(X64)) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t3_subset])]) ).
fof(c_0_13,plain,
! [X62] : subset(empty_set,X62),
inference(variable_rename,[status(thm)],[t2_xboole_1]) ).
fof(c_0_14,plain,
! [X15,X16,X17,X19,X20,X21,X23] :
( ( ~ in(X17,X16)
| in(ordered_pair(X17,esk1_3(X15,X16,X17)),X15)
| X16 != relation_dom(X15)
| ~ relation(X15) )
& ( ~ in(ordered_pair(X19,X20),X15)
| in(X19,X16)
| X16 != relation_dom(X15)
| ~ relation(X15) )
& ( ~ in(esk2_2(X15,X21),X21)
| ~ in(ordered_pair(esk2_2(X15,X21),X23),X15)
| X21 = relation_dom(X15)
| ~ relation(X15) )
& ( in(esk2_2(X15,X21),X21)
| in(ordered_pair(esk2_2(X15,X21),esk3_2(X15,X21)),X15)
| X21 = relation_dom(X15)
| ~ relation(X15) ) ),
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)],[d4_relat_1])])])])])]) ).
fof(c_0_15,plain,
! [X25,X26] : ordered_pair(X25,X26) = unordered_pair(unordered_pair(X25,X26),singleton(X25)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_16,plain,
! [X69,X70,X71] :
( ~ in(X69,X70)
| ~ element(X70,powerset(X71))
| ~ empty(X71) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t5_subset])]) ).
cnf(c_0_17,plain,
( element(X1,powerset(X2))
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
subset(empty_set,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
( in(esk2_2(X1,X2),X2)
| in(ordered_pair(esk2_2(X1,X2),esk3_2(X1,X2)),X1)
| X2 = relation_dom(X1)
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
fof(c_0_21,plain,
! [X13,X14] : unordered_pair(X13,X14) = unordered_pair(X14,X13),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_22,plain,
( ~ in(X1,X2)
| ~ element(X2,powerset(X3))
| ~ empty(X3) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,plain,
element(empty_set,powerset(X1)),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,plain,
( X2 = relation_dom(X1)
| in(esk2_2(X1,X2),X2)
| in(unordered_pair(unordered_pair(esk2_2(X1,X2),esk3_2(X1,X2)),singleton(esk2_2(X1,X2))),X1)
| ~ relation(X1) ),
inference(rw,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_25,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_26,plain,
( ~ empty(X1)
| ~ in(X2,empty_set) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,plain,
( X1 = relation_dom(X2)
| in(unordered_pair(singleton(esk2_2(X2,X1)),unordered_pair(esk2_2(X2,X1),esk3_2(X2,X1))),X2)
| in(esk2_2(X2,X1),X1)
| ~ relation(X2) ),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
relation(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]) ).
fof(c_0_29,plain,
! [X72] :
( ( relation_dom(X72) != empty_set
| relation_rng(X72) = empty_set
| ~ relation(X72) )
& ( relation_rng(X72) != empty_set
| relation_dom(X72) = empty_set
| ~ relation(X72) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t65_relat_1])])]) ).
cnf(c_0_30,plain,
( X1 = relation_dom(empty_set)
| in(esk2_2(empty_set,X1),X1)
| ~ empty(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
fof(c_0_31,plain,
! [X27] :
( ( ~ transfinite_sequence(X27)
| ordinal(relation_dom(X27))
| ~ relation(X27)
| ~ function(X27) )
& ( ~ ordinal(relation_dom(X27))
| transfinite_sequence(X27)
| ~ relation(X27)
| ~ function(X27) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d7_ordinal1])])]) ).
fof(c_0_32,negated_conjecture,
~ ! [X1] : transfinite_sequence_of(empty_set,X1),
inference(assume_negation,[status(cth)],[t45_ordinal1]) ).
fof(c_0_33,plain,
! [X28,X29] :
( ( ~ transfinite_sequence_of(X29,X28)
| subset(relation_rng(X29),X28)
| ~ relation(X29)
| ~ function(X29)
| ~ transfinite_sequence(X29) )
& ( ~ subset(relation_rng(X29),X28)
| transfinite_sequence_of(X29,X28)
| ~ relation(X29)
| ~ function(X29)
| ~ transfinite_sequence(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_ordinal1])])]) ).
cnf(c_0_34,plain,
( relation_rng(X1) = empty_set
| relation_dom(X1) != empty_set
| ~ relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_35,plain,
( relation_dom(empty_set) = empty_set
| ~ empty(X1)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_30]) ).
cnf(c_0_36,plain,
( transfinite_sequence(X1)
| ~ ordinal(relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_37,plain,
ordinal(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]) ).
cnf(c_0_38,plain,
function(empty_set),
inference(split_conjunct,[status(thm)],[fc2_ordinal1]) ).
fof(c_0_39,negated_conjecture,
~ transfinite_sequence_of(empty_set,esk20_0),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_32])])]) ).
cnf(c_0_40,plain,
( transfinite_sequence_of(X1,X2)
| ~ subset(relation_rng(X1),X2)
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,plain,
( relation_rng(empty_set) = empty_set
| ~ empty(X1)
| ~ empty(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_28])]) ).
cnf(c_0_42,plain,
( transfinite_sequence(empty_set)
| ~ empty(X1)
| ~ empty(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_35]),c_0_28]),c_0_37]),c_0_38])]) ).
cnf(c_0_43,negated_conjecture,
~ transfinite_sequence_of(empty_set,esk20_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_44,plain,
( transfinite_sequence_of(empty_set,X1)
| ~ empty(X2)
| ~ empty(X3) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_18]),c_0_28]),c_0_38])]),c_0_42]) ).
cnf(c_0_45,negated_conjecture,
( ~ empty(X1)
| ~ empty(X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_46,plain,
empty(empty_set),
inference(split_conjunct,[status(thm)],[fc12_relat_1]) ).
cnf(c_0_47,negated_conjecture,
~ empty(X1),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_48,plain,
$false,
inference(sr,[status(thm)],[c_0_46,c_0_47]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM409+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n005.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 : Fri Aug 25 17:36:23 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.19/0.59 % Version : CSE_E---1.5
% 0.19/0.59 % Problem : theBenchmark.p
% 0.19/0.59 % Proof found
% 0.19/0.59 % SZS status Theorem for theBenchmark.p
% 0.19/0.59 % SZS output start Proof
% See solution above
% 0.19/0.60 % Total time : 0.018000 s
% 0.19/0.60 % SZS output end Proof
% 0.19/0.60 % Total time : 0.021000 s
%------------------------------------------------------------------------------