TSTP Solution File: SEU161+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU161+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n011.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 16:22:56 EDT 2023
% Result : Theorem 0.19s 0.56s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 43
% Syntax : Number of formulae : 61 ( 12 unt; 38 typ; 0 def)
% Number of atoms : 36 ( 16 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 26 ( 13 ~; 7 |; 2 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 73 ( 33 >; 40 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 33 ( 33 usr; 5 con; 0-4 aty)
% Number of variables : 29 ( 0 sgn; 18 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
in: ( $i * $i ) > $o ).
tff(decl_23,type,
proper_subset: ( $i * $i ) > $o ).
tff(decl_24,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_25,type,
set_union2: ( $i * $i ) > $i ).
tff(decl_26,type,
set_intersection2: ( $i * $i ) > $i ).
tff(decl_27,type,
subset: ( $i * $i ) > $o ).
tff(decl_28,type,
singleton: $i > $i ).
tff(decl_29,type,
empty_set: $i ).
tff(decl_30,type,
powerset: $i > $i ).
tff(decl_31,type,
cartesian_product2: ( $i * $i ) > $i ).
tff(decl_32,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_33,type,
union: $i > $i ).
tff(decl_34,type,
set_difference: ( $i * $i ) > $i ).
tff(decl_35,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_36,type,
empty: $i > $o ).
tff(decl_37,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk2_1: $i > $i ).
tff(decl_39,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_40,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
esk6_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_43,type,
esk7_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_44,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
esk9_3: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
esk10_3: ( $i * $i * $i ) > $i ).
tff(decl_47,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_48,type,
esk12_3: ( $i * $i * $i ) > $i ).
tff(decl_49,type,
esk13_3: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_51,type,
esk15_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk16_3: ( $i * $i * $i ) > $i ).
tff(decl_53,type,
esk17_0: $i ).
tff(decl_54,type,
esk18_0: $i ).
tff(decl_55,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_56,type,
esk20_2: ( $i * $i ) > $i ).
tff(decl_57,type,
esk21_0: $i ).
tff(decl_58,type,
esk22_0: $i ).
tff(decl_59,type,
esk23_2: ( $i * $i ) > $i ).
fof(t46_zfmisc_1,conjecture,
! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(commutativity_k2_xboole_0,axiom,
! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(t12_xboole_1,lemma,
! [X1,X2] :
( subset(X1,X2)
=> set_union2(X1,X2) = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(l2_zfmisc_1,lemma,
! [X1,X2] :
( subset(singleton(X1),X2)
<=> in(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l2_zfmisc_1) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2] :
( in(X1,X2)
=> set_union2(singleton(X1),X2) = X2 ),
inference(assume_negation,[status(cth)],[t46_zfmisc_1]) ).
fof(c_0_6,negated_conjecture,
( in(esk21_0,esk22_0)
& set_union2(singleton(esk21_0),esk22_0) != esk22_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_7,lemma,
! [X222] : unordered_pair(X222,X222) = singleton(X222),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
cnf(c_0_8,negated_conjecture,
set_union2(singleton(esk21_0),esk22_0) != esk22_0,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X13,X14] : set_union2(X13,X14) = set_union2(X14,X13),
inference(variable_rename,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(c_0_11,lemma,
! [X153,X154] :
( ~ subset(X153,X154)
| set_union2(X153,X154) = X154 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[t12_xboole_1])]) ).
cnf(c_0_12,negated_conjecture,
set_union2(unordered_pair(esk21_0,esk21_0),esk22_0) != esk22_0,
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
set_union2(X1,X2) = set_union2(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,lemma,
( set_union2(X1,X2) = X2
| ~ subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,lemma,
! [X129,X130] :
( ( ~ subset(singleton(X129),X130)
| in(X129,X130) )
& ( ~ in(X129,X130)
| subset(singleton(X129),X130) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l2_zfmisc_1])]) ).
cnf(c_0_16,negated_conjecture,
set_union2(esk22_0,unordered_pair(esk21_0,esk21_0)) != esk22_0,
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,lemma,
( set_union2(X1,X2) = X1
| ~ subset(X2,X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_13]) ).
cnf(c_0_18,lemma,
( subset(singleton(X1),X2)
| ~ in(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,negated_conjecture,
~ subset(unordered_pair(esk21_0,esk21_0),esk22_0),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,lemma,
( subset(unordered_pair(X1,X1),X2)
| ~ in(X1,X2) ),
inference(rw,[status(thm)],[c_0_18,c_0_9]) ).
cnf(c_0_21,negated_conjecture,
in(esk21_0,esk22_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU161+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Aug 23 20:04:07 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.53 start to proof: theBenchmark
% 0.19/0.56 % Version : CSE_E---1.5
% 0.19/0.56 % Problem : theBenchmark.p
% 0.19/0.56 % Proof found
% 0.19/0.56 % SZS status Theorem for theBenchmark.p
% 0.19/0.56 % SZS output start Proof
% See solution above
% 0.19/0.56 % Total time : 0.024000 s
% 0.19/0.56 % SZS output end Proof
% 0.19/0.56 % Total time : 0.028000 s
%------------------------------------------------------------------------------