TSTP Solution File: NUM390+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM390+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 : n007.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 10:37:10 EDT 2023
% Result : Theorem 0.19s 0.59s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 38
% Syntax : Number of formulae : 65 ( 10 unt; 31 typ; 0 def)
% Number of atoms : 100 ( 6 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 105 ( 39 ~; 34 |; 16 &)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 16 >; 4 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 15 con; 0-1 aty)
% Number of variables : 48 ( 0 sgn; 31 !; 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,
subset: ( $i * $i ) > $o ).
tff(decl_32,type,
element: ( $i * $i ) > $o ).
tff(decl_33,type,
empty_set: $i ).
tff(decl_34,type,
relation_empty_yielding: $i > $o ).
tff(decl_35,type,
relation_non_empty: $i > $o ).
tff(decl_36,type,
powerset: $i > $i ).
tff(decl_37,type,
esk1_1: $i > $i ).
tff(decl_38,type,
esk2_1: $i > $i ).
tff(decl_39,type,
esk3_0: $i ).
tff(decl_40,type,
esk4_0: $i ).
tff(decl_41,type,
esk5_0: $i ).
tff(decl_42,type,
esk6_0: $i ).
tff(decl_43,type,
esk7_0: $i ).
tff(decl_44,type,
esk8_0: $i ).
tff(decl_45,type,
esk9_0: $i ).
tff(decl_46,type,
esk10_0: $i ).
tff(decl_47,type,
esk11_0: $i ).
tff(decl_48,type,
esk12_0: $i ).
tff(decl_49,type,
esk13_0: $i ).
tff(decl_50,type,
esk14_0: $i ).
tff(decl_51,type,
esk15_0: $i ).
tff(decl_52,type,
esk16_0: $i ).
fof(t22_ordinal1,conjecture,
! [X1] :
( epsilon_transitive(X1)
=> ! [X2] :
( ordinal(X2)
=> ! [X3] :
( ordinal(X3)
=> ( ( subset(X1,X2)
& in(X2,X3) )
=> in(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_ordinal1) ).
fof(cc1_ordinal1,axiom,
! [X1] :
( ordinal(X1)
=> ( epsilon_transitive(X1)
& epsilon_connected(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).
fof(d2_ordinal1,axiom,
! [X1] :
( epsilon_transitive(X1)
<=> ! [X2] :
( in(X2,X1)
=> subset(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).
fof(t1_xboole_1,axiom,
! [X1,X2,X3] :
( ( subset(X1,X2)
& subset(X2,X3) )
=> subset(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
fof(t21_ordinal1,axiom,
! [X1] :
( epsilon_transitive(X1)
=> ! [X2] :
( ordinal(X2)
=> ( proper_subset(X1,X2)
=> in(X1,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_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(t7_ordinal1,axiom,
! [X1,X2] :
~ ( in(X1,X2)
& subset(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_ordinal1) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( epsilon_transitive(X1)
=> ! [X2] :
( ordinal(X2)
=> ! [X3] :
( ordinal(X3)
=> ( ( subset(X1,X2)
& in(X2,X3) )
=> in(X1,X3) ) ) ) ),
inference(assume_negation,[status(cth)],[t22_ordinal1]) ).
fof(c_0_8,plain,
! [X9] :
( ( epsilon_transitive(X9)
| ~ ordinal(X9) )
& ( epsilon_connected(X9)
| ~ ordinal(X9) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[cc1_ordinal1])])]) ).
fof(c_0_9,negated_conjecture,
( epsilon_transitive(esk14_0)
& ordinal(esk15_0)
& ordinal(esk16_0)
& subset(esk14_0,esk15_0)
& in(esk15_0,esk16_0)
& ~ in(esk14_0,esk16_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
fof(c_0_10,plain,
! [X13,X14,X15] :
( ( ~ epsilon_transitive(X13)
| ~ in(X14,X13)
| subset(X14,X13) )
& ( in(esk1_1(X15),X15)
| epsilon_transitive(X15) )
& ( ~ subset(esk1_1(X15),X15)
| epsilon_transitive(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)],[d2_ordinal1])])])])])]) ).
cnf(c_0_11,plain,
( epsilon_transitive(X1)
| ~ ordinal(X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
ordinal(esk16_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X36,X37,X38] :
( ~ subset(X36,X37)
| ~ subset(X37,X38)
| subset(X36,X38) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t1_xboole_1])]) ).
cnf(c_0_14,plain,
( subset(X2,X1)
| ~ epsilon_transitive(X1)
| ~ in(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
epsilon_transitive(esk16_0),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_16,plain,
! [X39,X40] :
( ~ epsilon_transitive(X39)
| ~ ordinal(X40)
| ~ proper_subset(X39,X40)
| in(X39,X40) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t21_ordinal1])])]) ).
fof(c_0_17,plain,
! [X17,X18] :
( ( subset(X17,X18)
| ~ proper_subset(X17,X18) )
& ( X17 != X18
| ~ proper_subset(X17,X18) )
& ( ~ subset(X17,X18)
| X17 = X18
| proper_subset(X17,X18) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[d8_xboole_0])])]) ).
cnf(c_0_18,plain,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
( subset(X1,esk16_0)
| ~ in(X1,esk16_0) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
fof(c_0_20,plain,
! [X57,X58] :
( ~ in(X57,X58)
| ~ subset(X58,X57) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t7_ordinal1])]) ).
cnf(c_0_21,plain,
( in(X1,X2)
| ~ epsilon_transitive(X1)
| ~ ordinal(X2)
| ~ proper_subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( X1 = X2
| proper_subset(X1,X2)
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( subset(X1,esk16_0)
| ~ subset(X1,X2)
| ~ in(X2,esk16_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
subset(esk14_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_25,negated_conjecture,
in(esk15_0,esk16_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_26,plain,
( ~ in(X1,X2)
| ~ subset(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
( X1 = X2
| in(X1,X2)
| ~ subset(X1,X2)
| ~ epsilon_transitive(X1)
| ~ ordinal(X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,negated_conjecture,
subset(esk14_0,esk16_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_29,negated_conjecture,
epsilon_transitive(esk14_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_30,negated_conjecture,
~ in(esk14_0,esk16_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_31,negated_conjecture,
~ in(esk15_0,esk14_0),
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_32,negated_conjecture,
esk14_0 = esk16_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_12])]),c_0_30]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM390+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
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 11:38:40 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
% 0.19/0.59 % Total time : 0.019000 s
% 0.19/0.59 % SZS output end Proof
% 0.19/0.59 % Total time : 0.021000 s
%------------------------------------------------------------------------------