TSTP Solution File: SET801+4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET801+4 : 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 : n013.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 14:35:36 EDT 2023
% Result : Theorem 0.20s 0.79s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 51
% Syntax : Number of formulae : 81 ( 5 unt; 47 typ; 0 def)
% Number of atoms : 131 ( 0 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 152 ( 55 ~; 65 |; 20 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 101 ( 42 >; 59 *; 0 +; 0 <<)
% Number of predicates : 16 ( 15 usr; 1 prp; 0-4 aty)
% Number of functors : 32 ( 32 usr; 5 con; 0-4 aty)
% Number of variables : 93 ( 3 sgn; 44 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
subset: ( $i * $i ) > $o ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
equal_set: ( $i * $i ) > $o ).
tff(decl_25,type,
power_set: $i > $i ).
tff(decl_26,type,
intersection: ( $i * $i ) > $i ).
tff(decl_27,type,
union: ( $i * $i ) > $i ).
tff(decl_28,type,
empty_set: $i ).
tff(decl_29,type,
difference: ( $i * $i ) > $i ).
tff(decl_30,type,
singleton: $i > $i ).
tff(decl_31,type,
unordered_pair: ( $i * $i ) > $i ).
tff(decl_32,type,
sum: $i > $i ).
tff(decl_33,type,
product: $i > $i ).
tff(decl_34,type,
order: ( $i * $i ) > $o ).
tff(decl_35,type,
apply: ( $i * $i * $i ) > $o ).
tff(decl_36,type,
total_order: ( $i * $i ) > $o ).
tff(decl_37,type,
upper_bound: ( $i * $i * $i ) > $o ).
tff(decl_38,type,
lower_bound: ( $i * $i * $i ) > $o ).
tff(decl_39,type,
greatest: ( $i * $i * $i ) > $o ).
tff(decl_40,type,
least: ( $i * $i * $i ) > $o ).
tff(decl_41,type,
max: ( $i * $i * $i ) > $o ).
tff(decl_42,type,
min: ( $i * $i * $i ) > $o ).
tff(decl_43,type,
least_upper_bound: ( $i * $i * $i * $i ) > $o ).
tff(decl_44,type,
greatest_lower_bound: ( $i * $i * $i * $i ) > $o ).
tff(decl_45,type,
epred1_2: ( $i * $i ) > $o ).
tff(decl_46,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_48,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk4_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk5_2: ( $i * $i ) > $i ).
tff(decl_51,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_52,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_53,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_54,type,
esk9_3: ( $i * $i * $i ) > $i ).
tff(decl_55,type,
esk10_3: ( $i * $i * $i ) > $i ).
tff(decl_56,type,
esk11_3: ( $i * $i * $i ) > $i ).
tff(decl_57,type,
esk12_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_58,type,
esk13_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_59,type,
esk14_0: $i ).
tff(decl_60,type,
esk15_0: $i ).
tff(decl_61,type,
esk16_0: $i ).
tff(decl_62,type,
esk17_0: $i ).
tff(decl_63,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_64,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_65,type,
esk20_2: ( $i * $i ) > $i ).
tff(decl_66,type,
esk21_2: ( $i * $i ) > $i ).
tff(decl_67,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_68,type,
esk23_2: ( $i * $i ) > $i ).
fof(thIV13,conjecture,
! [X6,X4] :
( order(X6,X4)
=> ! [X3] :
( subset(X3,X4)
=> ! [X8] :
( greatest(X8,X6,X3)
<=> ( member(X8,X3)
& least_upper_bound(X8,X3,X6,X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV13) ).
fof(greatest,axiom,
! [X6,X4,X8] :
( greatest(X8,X6,X4)
<=> ( member(X8,X4)
& ! [X3] :
( member(X3,X4)
=> apply(X6,X3,X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',greatest) ).
fof(upper_bound,axiom,
! [X6,X4,X8] :
( upper_bound(X8,X6,X4)
<=> ! [X3] :
( member(X3,X4)
=> apply(X6,X3,X8) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',upper_bound) ).
fof(least_upper_bound,axiom,
! [X1,X3,X6,X4] :
( least_upper_bound(X1,X3,X6,X4)
<=> ( member(X1,X3)
& upper_bound(X1,X6,X3)
& ! [X8] :
( ( member(X8,X4)
& upper_bound(X8,X6,X3) )
=> apply(X6,X1,X8) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',least_upper_bound) ).
fof(c_0_4,negated_conjecture,
~ ! [X6,X4] :
( order(X6,X4)
=> ! [X3] :
( subset(X3,X4)
=> ! [X8] :
( greatest(X8,X6,X3)
<=> ( member(X8,X3)
& least_upper_bound(X8,X3,X6,X4) ) ) ) ),
inference(assume_negation,[status(cth)],[thIV13]) ).
fof(c_0_5,plain,
! [X72,X73,X74,X75,X76,X77,X78] :
( ( member(X74,X73)
| ~ greatest(X74,X72,X73) )
& ( ~ member(X75,X73)
| apply(X72,X75,X74)
| ~ greatest(X74,X72,X73) )
& ( member(esk8_3(X76,X77,X78),X77)
| ~ member(X78,X77)
| greatest(X78,X76,X77) )
& ( ~ apply(X76,esk8_3(X76,X77,X78),X78)
| ~ member(X78,X77)
| greatest(X78,X76,X77) ) ),
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)],[greatest])])])])])]) ).
fof(c_0_6,negated_conjecture,
( order(esk14_0,esk15_0)
& subset(esk16_0,esk15_0)
& ( ~ greatest(esk17_0,esk14_0,esk16_0)
| ~ member(esk17_0,esk16_0)
| ~ least_upper_bound(esk17_0,esk16_0,esk14_0,esk15_0) )
& ( member(esk17_0,esk16_0)
| greatest(esk17_0,esk14_0,esk16_0) )
& ( least_upper_bound(esk17_0,esk16_0,esk14_0,esk15_0)
| greatest(esk17_0,esk14_0,esk16_0) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
cnf(c_0_7,plain,
( apply(X3,X1,X4)
| ~ member(X1,X2)
| ~ greatest(X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,negated_conjecture,
( least_upper_bound(esk17_0,esk16_0,esk14_0,esk15_0)
| greatest(esk17_0,esk14_0,esk16_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X56,X57,X58,X59,X60,X61,X62] :
( ( ~ upper_bound(X58,X56,X57)
| ~ member(X59,X57)
| apply(X56,X59,X58) )
& ( member(esk6_3(X60,X61,X62),X61)
| upper_bound(X62,X60,X61) )
& ( ~ apply(X60,esk6_3(X60,X61,X62),X62)
| upper_bound(X62,X60,X61) ) ),
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)],[upper_bound])])])])])]) ).
cnf(c_0_10,negated_conjecture,
( least_upper_bound(esk17_0,esk16_0,esk14_0,esk15_0)
| apply(esk14_0,X1,esk17_0)
| ~ member(X1,esk16_0) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
( member(esk6_3(X1,X2,X3),X2)
| upper_bound(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X104,X105,X106,X107,X108,X109,X110,X111,X112] :
( ( member(X104,X105)
| ~ least_upper_bound(X104,X105,X106,X107) )
& ( upper_bound(X104,X106,X105)
| ~ least_upper_bound(X104,X105,X106,X107) )
& ( ~ member(X108,X107)
| ~ upper_bound(X108,X106,X105)
| apply(X106,X104,X108)
| ~ least_upper_bound(X104,X105,X106,X107) )
& ( member(esk12_4(X109,X110,X111,X112),X112)
| ~ member(X109,X110)
| ~ upper_bound(X109,X111,X110)
| least_upper_bound(X109,X110,X111,X112) )
& ( upper_bound(esk12_4(X109,X110,X111,X112),X111,X110)
| ~ member(X109,X110)
| ~ upper_bound(X109,X111,X110)
| least_upper_bound(X109,X110,X111,X112) )
& ( ~ apply(X111,X109,esk12_4(X109,X110,X111,X112))
| ~ member(X109,X110)
| ~ upper_bound(X109,X111,X110)
| least_upper_bound(X109,X110,X111,X112) ) ),
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)],[least_upper_bound])])])])])]) ).
cnf(c_0_13,plain,
( upper_bound(X3,X1,X2)
| ~ apply(X1,esk6_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
( least_upper_bound(esk17_0,esk16_0,esk14_0,esk15_0)
| upper_bound(X1,X2,esk16_0)
| apply(esk14_0,esk6_3(X2,esk16_0,X1),esk17_0) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
( upper_bound(X1,X2,X3)
| ~ least_upper_bound(X1,X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( apply(X2,X4,X1)
| ~ upper_bound(X1,X2,X3)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,negated_conjecture,
upper_bound(esk17_0,esk14_0,esk16_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]) ).
cnf(c_0_18,plain,
( member(X1,X2)
| ~ greatest(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_19,negated_conjecture,
( member(esk17_0,esk16_0)
| greatest(esk17_0,esk14_0,esk16_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_20,plain,
( greatest(X3,X1,X2)
| ~ apply(X1,esk8_3(X1,X2,X3),X3)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_21,negated_conjecture,
( apply(esk14_0,X1,esk17_0)
| ~ member(X1,esk16_0) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_22,negated_conjecture,
( ~ greatest(esk17_0,esk14_0,esk16_0)
| ~ member(esk17_0,esk16_0)
| ~ least_upper_bound(esk17_0,esk16_0,esk14_0,esk15_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_23,negated_conjecture,
member(esk17_0,esk16_0),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
( greatest(esk17_0,esk14_0,X1)
| ~ member(esk8_3(esk14_0,X1,esk17_0),esk16_0)
| ~ member(esk17_0,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
( member(esk8_3(X1,X2,X3),X2)
| greatest(X3,X1,X2)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_26,plain,
( upper_bound(esk12_4(X1,X2,X3,X4),X3,X2)
| least_upper_bound(X1,X2,X3,X4)
| ~ member(X1,X2)
| ~ upper_bound(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_27,negated_conjecture,
( ~ least_upper_bound(esk17_0,esk16_0,esk14_0,esk15_0)
| ~ greatest(esk17_0,esk14_0,esk16_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23])]) ).
cnf(c_0_28,negated_conjecture,
greatest(esk17_0,esk14_0,esk16_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_23])]) ).
cnf(c_0_29,plain,
( least_upper_bound(X2,X3,X1,X4)
| ~ apply(X1,X2,esk12_4(X2,X3,X1,X4))
| ~ member(X2,X3)
| ~ upper_bound(X2,X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_30,plain,
( least_upper_bound(X1,X2,X3,X4)
| apply(X3,X5,esk12_4(X1,X2,X3,X4))
| ~ upper_bound(X1,X3,X2)
| ~ member(X5,X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
~ least_upper_bound(esk17_0,esk16_0,esk14_0,esk15_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
cnf(c_0_32,plain,
( least_upper_bound(X1,X2,X3,X4)
| ~ upper_bound(X1,X3,X2)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_17]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET801+4 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n013.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 : Sat Aug 26 15:07:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.63 start to proof: theBenchmark
% 0.20/0.79 % Version : CSE_E---1.5
% 0.20/0.79 % Problem : theBenchmark.p
% 0.20/0.79 % Proof found
% 0.20/0.79 % SZS status Theorem for theBenchmark.p
% 0.20/0.79 % SZS output start Proof
% See solution above
% 0.20/0.80 % Total time : 0.147000 s
% 0.20/0.80 % SZS output end Proof
% 0.20/0.80 % Total time : 0.150000 s
%------------------------------------------------------------------------------