TSTP Solution File: SET800+4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET800+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 : 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 0.61s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 53
% Syntax : Number of formulae : 72 ( 8 unt; 49 typ; 0 def)
% Number of atoms : 89 ( 0 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 95 ( 29 ~; 30 |; 24 &)
% ( 3 <=>; 9 =>; 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 : 34 ( 34 usr; 7 con; 0-4 aty)
% Number of variables : 62 ( 3 sgn; 45 !; 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_0: $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 ).
tff(decl_70,type,
esk25_2: ( $i * $i ) > $i ).
fof(thIV12,conjecture,
! [X6,X4] :
( order(X6,X4)
=> ! [X9,X10] :
( ( subset(X9,X4)
& subset(X10,X4)
& subset(X9,X10) )
=> ! [X11,X12] :
( ( greatest_lower_bound(X11,X9,X6,X4)
& greatest_lower_bound(X12,X10,X6,X4) )
=> apply(X6,X12,X11) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV12) ).
fof(greatest_lower_bound,axiom,
! [X1,X3,X6,X4] :
( greatest_lower_bound(X1,X3,X6,X4)
<=> ( member(X1,X3)
& lower_bound(X1,X6,X3)
& ! [X8] :
( ( member(X8,X4)
& lower_bound(X8,X6,X3) )
=> apply(X6,X8,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',greatest_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(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(c_0_4,negated_conjecture,
~ ! [X6,X4] :
( order(X6,X4)
=> ! [X9,X10] :
( ( subset(X9,X4)
& subset(X10,X4)
& subset(X9,X10) )
=> ! [X11,X12] :
( ( greatest_lower_bound(X11,X9,X6,X4)
& greatest_lower_bound(X12,X10,X6,X4) )
=> apply(X6,X12,X11) ) ) ),
inference(assume_negation,[status(cth)],[thIV12]) ).
fof(c_0_5,plain,
! [X118,X119,X120,X121,X122,X123,X124,X125,X126] :
( ( member(X118,X119)
| ~ greatest_lower_bound(X118,X119,X120,X121) )
& ( lower_bound(X118,X120,X119)
| ~ greatest_lower_bound(X118,X119,X120,X121) )
& ( ~ member(X122,X121)
| ~ lower_bound(X122,X120,X119)
| apply(X120,X122,X118)
| ~ greatest_lower_bound(X118,X119,X120,X121) )
& ( member(esk13_4(X123,X124,X125,X126),X126)
| ~ member(X123,X124)
| ~ lower_bound(X123,X125,X124)
| greatest_lower_bound(X123,X124,X125,X126) )
& ( lower_bound(esk13_4(X123,X124,X125,X126),X125,X124)
| ~ member(X123,X124)
| ~ lower_bound(X123,X125,X124)
| greatest_lower_bound(X123,X124,X125,X126) )
& ( ~ apply(X125,esk13_4(X123,X124,X125,X126),X123)
| ~ member(X123,X124)
| ~ lower_bound(X123,X125,X124)
| greatest_lower_bound(X123,X124,X125,X126) ) ),
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_lower_bound])])])])])]) ).
fof(c_0_6,negated_conjecture,
( order(esk14_0,esk15_0)
& subset(esk16_0,esk15_0)
& subset(esk17_0,esk15_0)
& subset(esk16_0,esk17_0)
& greatest_lower_bound(esk18_0,esk16_0,esk14_0,esk15_0)
& greatest_lower_bound(esk19_0,esk17_0,esk14_0,esk15_0)
& ~ apply(esk14_0,esk19_0,esk18_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_7,plain,
! [X13,X14,X15,X16,X17] :
( ( ~ subset(X13,X14)
| ~ member(X15,X13)
| member(X15,X14) )
& ( member(esk1_2(X16,X17),X16)
| subset(X16,X17) )
& ( ~ member(esk1_2(X16,X17),X17)
| subset(X16,X17) ) ),
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_8,plain,
( member(X1,X2)
| ~ greatest_lower_bound(X1,X2,X3,X4) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,negated_conjecture,
greatest_lower_bound(esk18_0,esk16_0,esk14_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,plain,
! [X68,X69,X70,X71,X72,X73,X74] :
( ( ~ lower_bound(X70,X68,X69)
| ~ member(X71,X69)
| apply(X68,X70,X71) )
& ( member(esk7_3(X72,X73,X74),X73)
| lower_bound(X74,X72,X73) )
& ( ~ apply(X72,X74,esk7_3(X72,X73,X74))
| lower_bound(X74,X72,X73) ) ),
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])])])])])]) ).
cnf(c_0_11,plain,
( lower_bound(X1,X2,X3)
| ~ greatest_lower_bound(X1,X3,X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_12,negated_conjecture,
greatest_lower_bound(esk19_0,esk17_0,esk14_0,esk15_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_14,negated_conjecture,
member(esk18_0,esk16_0),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_15,plain,
( apply(X2,X1,X4)
| ~ lower_bound(X1,X2,X3)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,negated_conjecture,
lower_bound(esk19_0,esk14_0,esk17_0),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( member(esk18_0,X1)
| ~ subset(esk16_0,X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
subset(esk16_0,esk17_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,negated_conjecture,
( apply(esk14_0,esk19_0,X1)
| ~ member(X1,esk17_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
member(esk18_0,esk17_0),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
~ apply(esk14_0,esk19_0,esk18_0),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET800+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
% 0.13/0.34 % 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 09:36:47 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.61 % Version : CSE_E---1.5
% 0.20/0.61 % Problem : theBenchmark.p
% 0.20/0.61 % Proof found
% 0.20/0.61 % SZS status Theorem for theBenchmark.p
% 0.20/0.61 % SZS output start Proof
% See solution above
% 0.20/0.61 % Total time : 0.042000 s
% 0.20/0.61 % SZS output end Proof
% 0.20/0.61 % Total time : 0.045000 s
%------------------------------------------------------------------------------