TSTP Solution File: SEU094+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU094+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 : n022.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 16:22:24 EDT 2023
% Result : Theorem 0.20s 0.57s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 57
% Syntax : Number of formulae : 86 ( 8 unt; 51 typ; 0 def)
% Number of atoms : 92 ( 0 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 94 ( 37 ~; 39 |; 9 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 26 >; 3 *; 0 +; 0 <<)
% Number of predicates : 19 ( 18 usr; 1 prp; 0-2 aty)
% Number of functors : 33 ( 33 usr; 25 con; 0-1 aty)
% Number of variables : 34 ( 0 sgn; 20 !; 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,
natural: $i > $o ).
tff(decl_32,type,
powerset: $i > $i ).
tff(decl_33,type,
one_to_one: $i > $o ).
tff(decl_34,type,
positive_rationals: $i ).
tff(decl_35,type,
empty_set: $i ).
tff(decl_36,type,
relation_empty_yielding: $i > $o ).
tff(decl_37,type,
union: $i > $i ).
tff(decl_38,type,
function_yielding: $i > $o ).
tff(decl_39,type,
being_limit_ordinal: $i > $o ).
tff(decl_40,type,
transfinite_sequence: $i > $o ).
tff(decl_41,type,
ordinal_yielding: $i > $o ).
tff(decl_42,type,
relation_non_empty: $i > $o ).
tff(decl_43,type,
subset: ( $i * $i ) > $o ).
tff(decl_44,type,
esk1_1: $i > $i ).
tff(decl_45,type,
esk2_1: $i > $i ).
tff(decl_46,type,
esk3_0: $i ).
tff(decl_47,type,
esk4_0: $i ).
tff(decl_48,type,
esk5_0: $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_1: $i > $i ).
tff(decl_54,type,
esk11_0: $i ).
tff(decl_55,type,
esk12_0: $i ).
tff(decl_56,type,
esk13_1: $i > $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_1: $i > $i ).
tff(decl_62,type,
esk19_0: $i ).
tff(decl_63,type,
esk20_0: $i ).
tff(decl_64,type,
esk21_1: $i > $i ).
tff(decl_65,type,
esk22_0: $i ).
tff(decl_66,type,
esk23_0: $i ).
tff(decl_67,type,
esk24_0: $i ).
tff(decl_68,type,
esk25_0: $i ).
tff(decl_69,type,
esk26_0: $i ).
tff(decl_70,type,
esk27_0: $i ).
tff(decl_71,type,
esk28_0: $i ).
tff(decl_72,type,
esk29_0: $i ).
fof(t13_finset_1,axiom,
! [X1,X2] :
( ( subset(X1,X2)
& finite(X2) )
=> finite(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t13_finset_1) ).
fof(t100_zfmisc_1,axiom,
! [X1] : subset(X1,powerset(union(X1))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t100_zfmisc_1) ).
fof(t24_finset_1,axiom,
! [X1] :
( finite(X1)
<=> finite(powerset(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t24_finset_1) ).
fof(t25_finset_1,conjecture,
! [X1] :
( ( finite(X1)
& ! [X2] :
( in(X2,X1)
=> finite(X2) ) )
<=> finite(union(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t25_finset_1) ).
fof(l22_finset_1,axiom,
! [X1] :
( ( finite(X1)
& ! [X2] :
( in(X2,X1)
=> finite(X2) ) )
=> finite(union(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l22_finset_1) ).
fof(t92_zfmisc_1,axiom,
! [X1,X2] :
( in(X1,X2)
=> subset(X1,union(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t92_zfmisc_1) ).
fof(c_0_6,plain,
! [X56,X57] :
( ~ subset(X56,X57)
| ~ finite(X57)
| finite(X56) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t13_finset_1])]) ).
fof(c_0_7,plain,
! [X55] : subset(X55,powerset(union(X55))),
inference(variable_rename,[status(thm)],[t100_zfmisc_1]) ).
cnf(c_0_8,plain,
( finite(X1)
| ~ subset(X1,X2)
| ~ finite(X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
subset(X1,powerset(union(X1))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X60] :
( ( ~ finite(X60)
| finite(powerset(X60)) )
& ( ~ finite(powerset(X60))
| finite(X60) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t24_finset_1])]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1] :
( ( finite(X1)
& ! [X2] :
( in(X2,X1)
=> finite(X2) ) )
<=> finite(union(X1)) ),
inference(assume_negation,[status(cth)],[t25_finset_1]) ).
cnf(c_0_12,plain,
( finite(X1)
| ~ finite(powerset(union(X1))) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
( finite(powerset(X1))
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,negated_conjecture,
! [X63] :
( ( in(esk29_0,esk28_0)
| ~ finite(esk28_0)
| ~ finite(union(esk28_0)) )
& ( ~ finite(esk29_0)
| ~ finite(esk28_0)
| ~ finite(union(esk28_0)) )
& ( finite(esk28_0)
| finite(union(esk28_0)) )
& ( ~ in(X63,esk28_0)
| finite(X63)
| finite(union(esk28_0)) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])]) ).
fof(c_0_15,plain,
! [X23] :
( ( in(esk2_1(X23),X23)
| ~ finite(X23)
| finite(union(X23)) )
& ( ~ finite(esk2_1(X23))
| ~ finite(X23)
| finite(union(X23)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l22_finset_1])])])]) ).
cnf(c_0_16,plain,
( finite(X1)
| ~ finite(union(X1)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,negated_conjecture,
( finite(esk28_0)
| finite(union(esk28_0)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_18,plain,
! [X79,X80] :
( ~ in(X79,X80)
| subset(X79,union(X80)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t92_zfmisc_1])]) ).
cnf(c_0_19,negated_conjecture,
( finite(X1)
| finite(union(esk28_0))
| ~ in(X1,esk28_0) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( in(esk2_1(X1),X1)
| finite(union(X1))
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,negated_conjecture,
finite(esk28_0),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,plain,
( subset(X1,union(X2))
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,plain,
( finite(union(X1))
| ~ finite(esk2_1(X1))
| ~ finite(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,negated_conjecture,
( finite(esk2_1(esk28_0))
| finite(union(esk28_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_25,negated_conjecture,
( in(esk29_0,esk28_0)
| ~ finite(esk28_0)
| ~ finite(union(esk28_0)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_26,negated_conjecture,
( ~ finite(esk29_0)
| ~ finite(esk28_0)
| ~ finite(union(esk28_0)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_27,plain,
( finite(X1)
| ~ finite(union(X2))
| ~ in(X1,X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_22]) ).
cnf(c_0_28,negated_conjecture,
finite(union(esk28_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_21])]) ).
cnf(c_0_29,negated_conjecture,
( in(esk29_0,esk28_0)
| ~ finite(union(esk28_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_21])]) ).
cnf(c_0_30,negated_conjecture,
( ~ finite(union(esk28_0))
| ~ finite(esk29_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_21])]) ).
cnf(c_0_31,negated_conjecture,
( finite(X1)
| ~ in(X1,esk28_0) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
in(esk29_0,esk28_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_28])]) ).
cnf(c_0_33,negated_conjecture,
~ finite(esk29_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_28])]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU094+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
% 0.13/0.34 % Computer : n022.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 : Wed Aug 23 19:07:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.54 start to proof: theBenchmark
% 0.20/0.57 % Version : CSE_E---1.5
% 0.20/0.57 % Problem : theBenchmark.p
% 0.20/0.57 % Proof found
% 0.20/0.57 % SZS status Theorem for theBenchmark.p
% 0.20/0.57 % SZS output start Proof
% See solution above
% 0.20/0.57 % Total time : 0.016000 s
% 0.20/0.57 % SZS output end Proof
% 0.20/0.57 % Total time : 0.020000 s
%------------------------------------------------------------------------------