TSTP Solution File: NUM412+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM412+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 : n026.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 10:37:14 EDT 2023
% Result : Theorem 0.21s 0.62s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 44
% Syntax : Number of formulae : 67 ( 8 unt; 39 typ; 0 def)
% Number of atoms : 87 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 99 ( 40 ~; 37 |; 12 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 21 >; 6 *; 0 +; 0 <<)
% Number of predicates : 16 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 18 con; 0-2 aty)
% Number of variables : 43 ( 3 sgn; 24 !; 0 ?; 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,
transfinite_sequence: $i > $o ).
tff(decl_31,type,
transfinite_sequence_of: ( $i * $i ) > $o ).
tff(decl_32,type,
relation_rng: $i > $i ).
tff(decl_33,type,
subset: ( $i * $i ) > $o ).
tff(decl_34,type,
tseq_dom_restriction: ( $i * $i ) > $i ).
tff(decl_35,type,
relation_dom_restriction: ( $i * $i ) > $i ).
tff(decl_36,type,
element: ( $i * $i ) > $o ).
tff(decl_37,type,
empty_set: $i ).
tff(decl_38,type,
relation_empty_yielding: $i > $o ).
tff(decl_39,type,
relation_non_empty: $i > $o ).
tff(decl_40,type,
with_non_empty_elements: $i > $o ).
tff(decl_41,type,
powerset: $i > $i ).
tff(decl_42,type,
esk1_1: $i > $i ).
tff(decl_43,type,
esk2_1: $i > $i ).
tff(decl_44,type,
esk3_0: $i ).
tff(decl_45,type,
esk4_0: $i ).
tff(decl_46,type,
esk5_0: $i ).
tff(decl_47,type,
esk6_0: $i ).
tff(decl_48,type,
esk7_0: $i ).
tff(decl_49,type,
esk8_0: $i ).
tff(decl_50,type,
esk9_0: $i ).
tff(decl_51,type,
esk10_0: $i ).
tff(decl_52,type,
esk11_0: $i ).
tff(decl_53,type,
esk12_0: $i ).
tff(decl_54,type,
esk13_0: $i ).
tff(decl_55,type,
esk14_0: $i ).
tff(decl_56,type,
esk15_0: $i ).
tff(decl_57,type,
esk16_0: $i ).
tff(decl_58,type,
esk17_0: $i ).
tff(decl_59,type,
esk18_0: $i ).
tff(decl_60,type,
esk19_0: $i ).
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/sandbox/benchmark/theBenchmark.p',d8_ordinal1) ).
fof(dt_m1_ordinal1,axiom,
! [X1,X2] :
( transfinite_sequence_of(X2,X1)
=> ( relation(X2)
& function(X2)
& transfinite_sequence(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m1_ordinal1) ).
fof(t48_ordinal1,conjecture,
! [X1,X2] :
( transfinite_sequence_of(X2,X1)
=> ! [X3] :
( ordinal(X3)
=> transfinite_sequence_of(tseq_dom_restriction(X2,X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_ordinal1) ).
fof(t47_ordinal1,axiom,
! [X1,X2] :
( subset(X1,X2)
=> ! [X3] :
( transfinite_sequence_of(X3,X1)
=> transfinite_sequence_of(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_ordinal1) ).
fof(dt_k2_ordinal1,axiom,
! [X1,X2] :
( ( relation(X1)
& function(X1)
& transfinite_sequence(X1)
& ordinal(X2) )
=> transfinite_sequence_of(tseq_dom_restriction(X1,X2),relation_rng(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_ordinal1) ).
fof(c_0_5,plain,
! [X12,X13] :
( ( ~ transfinite_sequence_of(X13,X12)
| subset(relation_rng(X13),X12)
| ~ relation(X13)
| ~ function(X13)
| ~ transfinite_sequence(X13) )
& ( ~ subset(relation_rng(X13),X12)
| transfinite_sequence_of(X13,X12)
| ~ relation(X13)
| ~ function(X13)
| ~ transfinite_sequence(X13) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_ordinal1])])]) ).
fof(c_0_6,plain,
! [X18,X19] :
( ( relation(X19)
| ~ transfinite_sequence_of(X19,X18) )
& ( function(X19)
| ~ transfinite_sequence_of(X19,X18) )
& ( transfinite_sequence(X19)
| ~ transfinite_sequence_of(X19,X18) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_m1_ordinal1])])]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X2] :
( transfinite_sequence_of(X2,X1)
=> ! [X3] :
( ordinal(X3)
=> transfinite_sequence_of(tseq_dom_restriction(X2,X3),X1) ) ),
inference(assume_negation,[status(cth)],[t48_ordinal1]) ).
fof(c_0_8,plain,
! [X54,X55,X56] :
( ~ subset(X54,X55)
| ~ transfinite_sequence_of(X56,X54)
| transfinite_sequence_of(X56,X55) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t47_ordinal1])])]) ).
fof(c_0_9,plain,
! [X14,X15] :
( ~ relation(X14)
| ~ function(X14)
| ~ transfinite_sequence(X14)
| ~ ordinal(X15)
| transfinite_sequence_of(tseq_dom_restriction(X14,X15),relation_rng(X14)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[dt_k2_ordinal1])]) ).
cnf(c_0_10,plain,
( subset(relation_rng(X1),X2)
| ~ transfinite_sequence_of(X1,X2)
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_11,plain,
( function(X1)
| ~ transfinite_sequence_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( relation(X1)
| ~ transfinite_sequence_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,plain,
( transfinite_sequence(X1)
| ~ transfinite_sequence_of(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_14,negated_conjecture,
( transfinite_sequence_of(esk18_0,esk17_0)
& ordinal(esk19_0)
& ~ transfinite_sequence_of(tseq_dom_restriction(esk18_0,esk19_0),esk17_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_15,plain,
( transfinite_sequence_of(X3,X2)
| ~ subset(X1,X2)
| ~ transfinite_sequence_of(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,plain,
( transfinite_sequence_of(tseq_dom_restriction(X1,X2),relation_rng(X1))
| ~ relation(X1)
| ~ function(X1)
| ~ transfinite_sequence(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
( subset(relation_rng(X1),X2)
| ~ transfinite_sequence_of(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13]) ).
cnf(c_0_18,negated_conjecture,
transfinite_sequence_of(esk18_0,esk17_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
( transfinite_sequence_of(tseq_dom_restriction(X1,X2),X3)
| ~ subset(relation_rng(X1),X3)
| ~ transfinite_sequence(X1)
| ~ relation(X1)
| ~ ordinal(X2)
| ~ function(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
subset(relation_rng(esk18_0),esk17_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
transfinite_sequence(esk18_0),
inference(spm,[status(thm)],[c_0_13,c_0_18]) ).
cnf(c_0_22,negated_conjecture,
relation(esk18_0),
inference(spm,[status(thm)],[c_0_12,c_0_18]) ).
cnf(c_0_23,negated_conjecture,
function(esk18_0),
inference(spm,[status(thm)],[c_0_11,c_0_18]) ).
cnf(c_0_24,negated_conjecture,
~ transfinite_sequence_of(tseq_dom_restriction(esk18_0,esk19_0),esk17_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_25,negated_conjecture,
( transfinite_sequence_of(tseq_dom_restriction(esk18_0,X1),esk17_0)
| ~ ordinal(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_22]),c_0_23])]) ).
cnf(c_0_26,negated_conjecture,
ordinal(esk19_0),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM412+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n026.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 13:46:02 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.58 start to proof: theBenchmark
% 0.21/0.62 % Version : CSE_E---1.5
% 0.21/0.62 % Problem : theBenchmark.p
% 0.21/0.62 % Proof found
% 0.21/0.62 % SZS status Theorem for theBenchmark.p
% 0.21/0.62 % SZS output start Proof
% See solution above
% 0.21/0.63 % Total time : 0.032000 s
% 0.21/0.63 % SZS output end Proof
% 0.21/0.63 % Total time : 0.036000 s
%------------------------------------------------------------------------------