TSTP Solution File: NUM414+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM414+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 : n017.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 0.17s 0.57s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 38
% Syntax : Number of formulae : 57 ( 7 unt; 34 typ; 0 def)
% Number of atoms : 72 ( 8 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 84 ( 35 ~; 27 |; 14 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 17 >; 5 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 17 con; 0-1 aty)
% Number of variables : 23 ( 0 sgn; 16 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
proper_subset: ( $i * $i ) > $o ).
tff(decl_24,type,
empty: $i > $o ).
tff(decl_25,type,
function: $i > $o ).
tff(decl_26,type,
ordinal: $i > $o ).
tff(decl_27,type,
epsilon_transitive: $i > $o ).
tff(decl_28,type,
epsilon_connected: $i > $o ).
tff(decl_29,type,
relation: $i > $o ).
tff(decl_30,type,
one_to_one: $i > $o ).
tff(decl_31,type,
ordinal_subset: ( $i * $i ) > $o ).
tff(decl_32,type,
subset: ( $i * $i ) > $o ).
tff(decl_33,type,
element: ( $i * $i ) > $o ).
tff(decl_34,type,
empty_set: $i ).
tff(decl_35,type,
relation_empty_yielding: $i > $o ).
tff(decl_36,type,
transfinite_sequence: $i > $o ).
tff(decl_37,type,
relation_non_empty: $i > $o ).
tff(decl_38,type,
powerset: $i > $i ).
tff(decl_39,type,
esk1_1: $i > $i ).
tff(decl_40,type,
esk2_0: $i ).
tff(decl_41,type,
esk3_0: $i ).
tff(decl_42,type,
esk4_0: $i ).
tff(decl_43,type,
esk5_0: $i ).
tff(decl_44,type,
esk6_0: $i ).
tff(decl_45,type,
esk7_0: $i ).
tff(decl_46,type,
esk8_0: $i ).
tff(decl_47,type,
esk9_0: $i ).
tff(decl_48,type,
esk10_0: $i ).
tff(decl_49,type,
esk11_0: $i ).
tff(decl_50,type,
esk12_0: $i ).
tff(decl_51,type,
esk13_0: $i ).
tff(decl_52,type,
esk14_0: $i ).
tff(decl_53,type,
esk15_0: $i ).
tff(decl_54,type,
esk16_0: $i ).
tff(decl_55,type,
esk17_0: $i ).
fof(t50_ordinal1,conjecture,
! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ proper_subset(X1,X2)
& X1 != X2
& ~ proper_subset(X2,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_ordinal1) ).
fof(connectedness_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
fof(redefinition_r1_ordinal1,axiom,
! [X1,X2] :
( ( ordinal(X1)
& ordinal(X2) )
=> ( ordinal_subset(X1,X2)
<=> subset(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(d8_xboole_0,axiom,
! [X1,X2] :
( proper_subset(X1,X2)
<=> ( subset(X1,X2)
& X1 != X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
fof(c_0_4,negated_conjecture,
~ ! [X1] :
( ordinal(X1)
=> ! [X2] :
( ordinal(X2)
=> ~ ( ~ proper_subset(X1,X2)
& X1 != X2
& ~ proper_subset(X2,X1) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[t50_ordinal1])]) ).
fof(c_0_5,plain,
! [X14,X15] :
( ~ ordinal(X14)
| ~ ordinal(X15)
| ordinal_subset(X14,X15)
| ordinal_subset(X15,X14) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[connectedness_r1_ordinal1])]) ).
fof(c_0_6,negated_conjecture,
( ordinal(esk16_0)
& ordinal(esk17_0)
& ~ proper_subset(esk16_0,esk17_0)
& esk16_0 != esk17_0
& ~ proper_subset(esk17_0,esk16_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
cnf(c_0_7,plain,
( ordinal_subset(X1,X2)
| ordinal_subset(X2,X1)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
ordinal(esk17_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X35,X36] :
( ( ~ ordinal_subset(X35,X36)
| subset(X35,X36)
| ~ ordinal(X35)
| ~ ordinal(X36) )
& ( ~ subset(X35,X36)
| ordinal_subset(X35,X36)
| ~ ordinal(X35)
| ~ ordinal(X36) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[redefinition_r1_ordinal1])])]) ).
cnf(c_0_10,negated_conjecture,
( ordinal_subset(X1,esk17_0)
| ordinal_subset(esk17_0,X1)
| ~ ordinal(X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,negated_conjecture,
ordinal(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_12,plain,
( subset(X1,X2)
| ~ ordinal_subset(X1,X2)
| ~ ordinal(X1)
| ~ ordinal(X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
( ordinal_subset(esk17_0,esk16_0)
| ordinal_subset(esk16_0,esk17_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
fof(c_0_14,plain,
! [X16,X17] :
( ( subset(X16,X17)
| ~ proper_subset(X16,X17) )
& ( X16 != X17
| ~ proper_subset(X16,X17) )
& ( ~ subset(X16,X17)
| X16 = X17
| proper_subset(X16,X17) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_xboole_0])])]) ).
cnf(c_0_15,negated_conjecture,
( subset(esk17_0,esk16_0)
| ordinal_subset(esk16_0,esk17_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_11]),c_0_8])]) ).
cnf(c_0_16,plain,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_17,negated_conjecture,
( subset(esk17_0,esk16_0)
| subset(esk16_0,esk17_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_15]),c_0_8]),c_0_11])]) ).
cnf(c_0_18,negated_conjecture,
esk16_0 != esk17_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
~ proper_subset(esk17_0,esk16_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,negated_conjecture,
subset(esk16_0,esk17_0),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19]) ).
cnf(c_0_21,negated_conjecture,
~ proper_subset(esk16_0,esk17_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_20]),c_0_18]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : NUM414+1 : TPTP v8.1.2. Released v3.2.0.
% 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.11/0.32 % Computer : n017.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Aug 25 09:33:25 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.17/0.55 start to proof: theBenchmark
% 0.17/0.57 % Version : CSE_E---1.5
% 0.17/0.57 % Problem : theBenchmark.p
% 0.17/0.57 % Proof found
% 0.17/0.57 % SZS status Theorem for theBenchmark.p
% 0.17/0.57 % SZS output start Proof
% See solution above
% 0.17/0.58 % Total time : 0.011000 s
% 0.17/0.58 % SZS output end Proof
% 0.17/0.58 % Total time : 0.014000 s
%------------------------------------------------------------------------------