TSTP Solution File: SEU160+2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SEU160+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/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 16:22:55 EDT 2023
% Result : Theorem 0.17s 0.59s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 44
% Syntax : Number of formulae : 67 ( 11 unt; 38 typ; 0 def)
% Number of atoms : 66 ( 41 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 60 ( 23 ~; 28 |; 5 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 28 ( 2 sgn; 19 !; 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_0: $i ).
tff(decl_57,type,
esk21_0: $i ).
tff(decl_58,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_59,type,
esk23_2: ( $i * $i ) > $i ).
fof(t39_zfmisc_1,conjecture,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(l4_zfmisc_1,lemma,
! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
fof(t69_enumset1,lemma,
! [X1] : unordered_pair(X1,X1) = singleton(X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(l32_xboole_1,lemma,
! [X1,X2] :
( set_difference(X1,X2) = empty_set
<=> subset(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).
fof(reflexivity_r1_tarski,axiom,
! [X1,X2] : subset(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(t4_boole,axiom,
! [X1] : set_difference(empty_set,X1) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
fof(c_0_6,negated_conjecture,
~ ! [X1,X2] :
( subset(X1,singleton(X2))
<=> ( X1 = empty_set
| X1 = singleton(X2) ) ),
inference(assume_negation,[status(cth)],[t39_zfmisc_1]) ).
fof(c_0_7,lemma,
! [X136,X137] :
( ( ~ subset(X136,singleton(X137))
| X136 = empty_set
| X136 = singleton(X137) )
& ( X136 != empty_set
| subset(X136,singleton(X137)) )
& ( X136 != singleton(X137)
| subset(X136,singleton(X137)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l4_zfmisc_1])])]) ).
fof(c_0_8,lemma,
! [X220] : unordered_pair(X220,X220) = singleton(X220),
inference(variable_rename,[status(thm)],[t69_enumset1]) ).
fof(c_0_9,negated_conjecture,
( ( esk20_0 != empty_set
| ~ subset(esk20_0,singleton(esk21_0)) )
& ( esk20_0 != singleton(esk21_0)
| ~ subset(esk20_0,singleton(esk21_0)) )
& ( subset(esk20_0,singleton(esk21_0))
| esk20_0 = empty_set
| esk20_0 = singleton(esk21_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
cnf(c_0_10,lemma,
( X1 = empty_set
| X1 = singleton(X2)
| ~ subset(X1,singleton(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,lemma,
unordered_pair(X1,X1) = singleton(X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
( subset(esk20_0,singleton(esk21_0))
| esk20_0 = empty_set
| esk20_0 = singleton(esk21_0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,negated_conjecture,
( esk20_0 != empty_set
| ~ subset(esk20_0,singleton(esk21_0)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_14,lemma,
! [X131,X132] :
( ( set_difference(X131,X132) != empty_set
| subset(X131,X132) )
& ( ~ subset(X131,X132)
| set_difference(X131,X132) = empty_set ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l32_xboole_1])]) ).
cnf(c_0_15,negated_conjecture,
( esk20_0 != singleton(esk21_0)
| ~ subset(esk20_0,singleton(esk21_0)) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,lemma,
( X1 = empty_set
| X1 = unordered_pair(X2,X2)
| ~ subset(X1,unordered_pair(X2,X2)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_11]) ).
cnf(c_0_17,negated_conjecture,
( esk20_0 = empty_set
| esk20_0 = unordered_pair(esk21_0,esk21_0)
| subset(esk20_0,unordered_pair(esk21_0,esk21_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_11]),c_0_11]) ).
fof(c_0_18,plain,
! [X146] : subset(X146,X146),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[reflexivity_r1_tarski])]) ).
cnf(c_0_19,negated_conjecture,
( esk20_0 != empty_set
| ~ subset(esk20_0,unordered_pair(esk21_0,esk21_0)) ),
inference(rw,[status(thm)],[c_0_13,c_0_11]) ).
cnf(c_0_20,lemma,
( subset(X1,X2)
| set_difference(X1,X2) != empty_set ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,negated_conjecture,
( esk20_0 != unordered_pair(esk21_0,esk21_0)
| ~ subset(esk20_0,unordered_pair(esk21_0,esk21_0)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_11]),c_0_11]) ).
cnf(c_0_22,negated_conjecture,
( unordered_pair(esk21_0,esk21_0) = esk20_0
| esk20_0 = empty_set ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,plain,
subset(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_24,plain,
! [X208] : set_difference(empty_set,X208) = empty_set,
inference(variable_rename,[status(thm)],[t4_boole]) ).
cnf(c_0_25,negated_conjecture,
( set_difference(esk20_0,unordered_pair(esk21_0,esk21_0)) != empty_set
| esk20_0 != empty_set ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,negated_conjecture,
esk20_0 = empty_set,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).
cnf(c_0_27,plain,
set_difference(empty_set,X1) = empty_set,
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU160+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.11 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.15/0.32 % Computer : n011.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Wed Aug 23 13:56:52 EDT 2023
% 0.15/0.33 % CPUTime :
% 0.17/0.55 start to proof: theBenchmark
% 0.17/0.59 % Version : CSE_E---1.5
% 0.17/0.59 % Problem : theBenchmark.p
% 0.17/0.59 % Proof found
% 0.17/0.59 % SZS status Theorem for theBenchmark.p
% 0.17/0.59 % SZS output start Proof
% See solution above
% 0.17/0.59 % Total time : 0.029000 s
% 0.17/0.59 % SZS output end Proof
% 0.17/0.59 % Total time : 0.033000 s
%------------------------------------------------------------------------------