TSTP Solution File: SET798+4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET798+4 : 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 : n018.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 14:35:35 EDT 2023
% Result : Theorem 0.20s 0.60s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 51
% Syntax : Number of formulae : 67 ( 4 unt; 48 typ; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 59 ( 18 ~; 18 |; 13 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 33 ( 33 usr; 6 con; 0-4 aty)
% Number of variables : 46 ( 0 sgn; 29 !; 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_0: $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 ).
tff(decl_69,type,
esk24_2: ( $i * $i ) > $i ).
fof(thIV10,conjecture,
! [X6,X4] :
( order(X6,X4)
=> ! [X3,X5] :
( ( subset(X3,X4)
& subset(X5,X4)
& subset(X3,X5) )
=> ! [X8] :
( lower_bound(X8,X6,X5)
=> lower_bound(X8,X6,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV10) ).
fof(lower_bound,axiom,
! [X6,X4,X8] :
( lower_bound(X8,X6,X4)
<=> ! [X3] :
( member(X3,X4)
=> apply(X6,X8,X3) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',lower_bound) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).
fof(c_0_3,negated_conjecture,
~ ! [X6,X4] :
( order(X6,X4)
=> ! [X3,X5] :
( ( subset(X3,X4)
& subset(X5,X4)
& subset(X3,X5) )
=> ! [X8] :
( lower_bound(X8,X6,X5)
=> lower_bound(X8,X6,X3) ) ) ),
inference(assume_negation,[status(cth)],[thIV10]) ).
fof(c_0_4,plain,
! [X64,X65,X66,X67,X68,X69,X70] :
( ( ~ lower_bound(X66,X64,X65)
| ~ member(X67,X65)
| apply(X64,X66,X67) )
& ( member(esk7_3(X68,X69,X70),X69)
| lower_bound(X70,X68,X69) )
& ( ~ apply(X68,X70,esk7_3(X68,X69,X70))
| lower_bound(X70,X68,X69) ) ),
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)],[lower_bound])])])])])]) ).
fof(c_0_5,negated_conjecture,
( order(esk14_0,esk15_0)
& subset(esk16_0,esk15_0)
& subset(esk17_0,esk15_0)
& subset(esk16_0,esk17_0)
& lower_bound(esk18_0,esk14_0,esk17_0)
& ~ lower_bound(esk18_0,esk14_0,esk16_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])]) ).
cnf(c_0_6,plain,
( apply(X2,X1,X4)
| ~ lower_bound(X1,X2,X3)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
lower_bound(esk18_0,esk14_0,esk17_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X9,X10,X11,X12,X13] :
( ( ~ subset(X9,X10)
| ~ member(X11,X9)
| member(X11,X10) )
& ( member(esk1_2(X12,X13),X12)
| subset(X12,X13) )
& ( ~ member(esk1_2(X12,X13),X13)
| subset(X12,X13) ) ),
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)],[subset])])])])])]) ).
cnf(c_0_9,plain,
( lower_bound(X2,X1,X3)
| ~ apply(X1,X2,esk7_3(X1,X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_10,negated_conjecture,
( apply(esk14_0,esk18_0,X1)
| ~ member(X1,esk17_0) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_11,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
subset(esk16_0,esk17_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,negated_conjecture,
( lower_bound(esk18_0,esk14_0,X1)
| ~ member(esk7_3(esk14_0,X1,esk18_0),esk17_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
( member(X1,esk17_0)
| ~ member(X1,esk16_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,negated_conjecture,
( lower_bound(esk18_0,esk14_0,X1)
| ~ member(esk7_3(esk14_0,X1,esk18_0),esk16_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,plain,
( member(esk7_3(X1,X2,X3),X2)
| lower_bound(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_17,negated_conjecture,
~ lower_bound(esk18_0,esk14_0,esk16_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET798+4 : 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
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 15:05:00 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.60 % Version : CSE_E---1.5
% 0.20/0.60 % Problem : theBenchmark.p
% 0.20/0.60 % Proof found
% 0.20/0.60 % SZS status Theorem for theBenchmark.p
% 0.20/0.60 % SZS output start Proof
% See solution above
% 0.20/0.60 % Total time : 0.028000 s
% 0.20/0.60 % SZS output end Proof
% 0.20/0.60 % Total time : 0.031000 s
%------------------------------------------------------------------------------