TSTP Solution File: SET793+4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET793+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 : n026.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 14:35:34 EDT 2023
% Result : Theorem 0.19s 0.59s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 37
% Syntax : Number of formulae : 66 ( 7 unt; 32 typ; 0 def)
% Number of atoms : 132 ( 6 equ)
% Maximal formula atoms : 19 ( 3 avg)
% Number of connectives : 149 ( 51 ~; 65 |; 23 &)
% ( 4 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 79 ( 29 >; 50 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-4 aty)
% Number of functors : 19 ( 19 usr; 3 con; 0-4 aty)
% Number of variables : 84 ( 1 sgn; 49 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
order: ( $i * $i ) > $o ).
tff(decl_23,type,
member: ( $i * $i ) > $o ).
tff(decl_24,type,
apply: ( $i * $i * $i ) > $o ).
tff(decl_25,type,
total_order: ( $i * $i ) > $o ).
tff(decl_26,type,
upper_bound: ( $i * $i * $i ) > $o ).
tff(decl_27,type,
lower_bound: ( $i * $i * $i ) > $o ).
tff(decl_28,type,
greatest: ( $i * $i * $i ) > $o ).
tff(decl_29,type,
least: ( $i * $i * $i ) > $o ).
tff(decl_30,type,
max: ( $i * $i * $i ) > $o ).
tff(decl_31,type,
min: ( $i * $i * $i ) > $o ).
tff(decl_32,type,
least_upper_bound: ( $i * $i * $i * $i ) > $o ).
tff(decl_33,type,
greatest_lower_bound: ( $i * $i * $i * $i ) > $o ).
tff(decl_34,type,
epred1_2: ( $i * $i ) > $o ).
tff(decl_35,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_36,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_37,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_38,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_39,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_40,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_43,type,
esk9_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_44,type,
esk10_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_45,type,
esk11_0: $i ).
tff(decl_46,type,
esk12_0: $i ).
tff(decl_47,type,
esk13_0: $i ).
tff(decl_48,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk15_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk16_2: ( $i * $i ) > $i ).
tff(decl_51,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk18_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk19_2: ( $i * $i ) > $i ).
fof(thIV5,conjecture,
! [X1,X2,X6] :
( ( total_order(X1,X2)
& max(X6,X1,X2) )
=> greatest(X6,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV5) ).
fof(total_order,axiom,
! [X1,X2] :
( total_order(X1,X2)
<=> ( order(X1,X2)
& ! [X3,X4] :
( ( member(X3,X2)
& member(X4,X2) )
=> ( apply(X1,X3,X4)
| apply(X1,X4,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',total_order) ).
fof(max,axiom,
! [X1,X2,X6] :
( max(X6,X1,X2)
<=> ( member(X6,X2)
& ! [X3] :
( ( member(X3,X2)
& apply(X1,X6,X3) )
=> X6 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',max) ).
fof(upper_bound,axiom,
! [X1,X2,X6] :
( upper_bound(X6,X1,X2)
<=> ! [X3] :
( member(X3,X2)
=> apply(X1,X3,X6) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',upper_bound) ).
fof(greatest,axiom,
! [X1,X2,X6] :
( greatest(X6,X1,X2)
<=> ( member(X6,X2)
& ! [X3] :
( member(X3,X2)
=> apply(X1,X3,X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',greatest) ).
fof(c_0_5,negated_conjecture,
~ ! [X1,X2,X6] :
( ( total_order(X1,X2)
& max(X6,X1,X2) )
=> greatest(X6,X1,X2) ),
inference(assume_negation,[status(cth)],[thIV5]) ).
fof(c_0_6,plain,
! [X10,X11,X12,X13,X14,X15] :
( ( order(X10,X11)
| ~ total_order(X10,X11) )
& ( ~ member(X12,X11)
| ~ member(X13,X11)
| apply(X10,X12,X13)
| apply(X10,X13,X12)
| ~ total_order(X10,X11) )
& ( member(esk1_2(X14,X15),X15)
| ~ order(X14,X15)
| total_order(X14,X15) )
& ( member(esk2_2(X14,X15),X15)
| ~ order(X14,X15)
| total_order(X14,X15) )
& ( ~ apply(X14,esk1_2(X14,X15),esk2_2(X14,X15))
| ~ order(X14,X15)
| total_order(X14,X15) )
& ( ~ apply(X14,esk2_2(X14,X15),esk1_2(X14,X15))
| ~ order(X14,X15)
| total_order(X14,X15) ) ),
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)],[total_order])])])])])]) ).
fof(c_0_7,negated_conjecture,
( total_order(esk11_0,esk12_0)
& max(esk13_0,esk11_0,esk12_0)
& ~ greatest(esk13_0,esk11_0,esk12_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).
fof(c_0_8,plain,
! [X50,X51,X52,X53,X54,X55,X56] :
( ( member(X52,X51)
| ~ max(X52,X50,X51) )
& ( ~ member(X53,X51)
| ~ apply(X50,X52,X53)
| X52 = X53
| ~ max(X52,X50,X51) )
& ( member(esk7_3(X54,X55,X56),X55)
| ~ member(X56,X55)
| max(X56,X54,X55) )
& ( apply(X54,X56,esk7_3(X54,X55,X56))
| ~ member(X56,X55)
| max(X56,X54,X55) )
& ( X56 != esk7_3(X54,X55,X56)
| ~ member(X56,X55)
| max(X56,X54,X55) ) ),
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)],[max])])])])])]) ).
cnf(c_0_9,plain,
( apply(X4,X1,X3)
| apply(X4,X3,X1)
| ~ member(X1,X2)
| ~ member(X3,X2)
| ~ total_order(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
total_order(esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
( member(X1,X2)
| ~ max(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
max(esk13_0,esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
( apply(esk11_0,X1,X2)
| apply(esk11_0,X2,X1)
| ~ member(X2,esk12_0)
| ~ member(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,negated_conjecture,
member(esk13_0,esk12_0),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
fof(c_0_15,plain,
! [X18,X19,X20,X21,X22,X23,X24] :
( ( ~ upper_bound(X20,X18,X19)
| ~ member(X21,X19)
| apply(X18,X21,X20) )
& ( member(esk3_3(X22,X23,X24),X23)
| upper_bound(X24,X22,X23) )
& ( ~ apply(X22,esk3_3(X22,X23,X24),X24)
| upper_bound(X24,X22,X23) ) ),
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_16,negated_conjecture,
( apply(esk11_0,esk13_0,X1)
| apply(esk11_0,X1,esk13_0)
| ~ member(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
( member(esk3_3(X1,X2,X3),X2)
| upper_bound(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,plain,
( X4 = X1
| ~ member(X1,X2)
| ~ apply(X3,X4,X1)
| ~ max(X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_19,plain,
( upper_bound(X3,X1,X2)
| ~ apply(X1,esk3_3(X1,X2,X3),X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,negated_conjecture,
( upper_bound(X1,X2,esk12_0)
| apply(esk11_0,esk3_3(X2,esk12_0,X1),esk13_0)
| apply(esk11_0,esk13_0,esk3_3(X2,esk12_0,X1)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,negated_conjecture,
( X1 = esk13_0
| ~ apply(esk11_0,esk13_0,X1)
| ~ member(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_18,c_0_12]) ).
cnf(c_0_22,negated_conjecture,
( upper_bound(esk13_0,esk11_0,esk12_0)
| apply(esk11_0,esk13_0,esk3_3(esk11_0,esk12_0,esk13_0)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
( esk3_3(esk11_0,esk12_0,esk13_0) = esk13_0
| upper_bound(esk13_0,esk11_0,esk12_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_17]) ).
cnf(c_0_24,negated_conjecture,
apply(esk11_0,esk13_0,esk13_0),
inference(spm,[status(thm)],[c_0_16,c_0_14]) ).
fof(c_0_25,plain,
! [X34,X35,X36,X37,X38,X39,X40] :
( ( member(X36,X35)
| ~ greatest(X36,X34,X35) )
& ( ~ member(X37,X35)
| apply(X34,X37,X36)
| ~ greatest(X36,X34,X35) )
& ( member(esk5_3(X38,X39,X40),X39)
| ~ member(X40,X39)
| greatest(X40,X38,X39) )
& ( ~ apply(X38,esk5_3(X38,X39,X40),X40)
| ~ member(X40,X39)
| greatest(X40,X38,X39) ) ),
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])])])])])]) ).
cnf(c_0_26,plain,
( apply(X2,X4,X1)
| ~ upper_bound(X1,X2,X3)
| ~ member(X4,X3) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_27,negated_conjecture,
upper_bound(esk13_0,esk11_0,esk12_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_23]),c_0_24])]) ).
cnf(c_0_28,plain,
( greatest(X3,X1,X2)
| ~ apply(X1,esk5_3(X1,X2,X3),X3)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( apply(esk11_0,X1,esk13_0)
| ~ member(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
( greatest(esk13_0,esk11_0,X1)
| ~ member(esk5_3(esk11_0,X1,esk13_0),esk12_0)
| ~ member(esk13_0,X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_31,plain,
( member(esk5_3(X1,X2,X3),X2)
| greatest(X3,X1,X2)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_32,negated_conjecture,
~ greatest(esk13_0,esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_14])]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET793+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 : n026.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 10:30:48 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.57 start to proof: theBenchmark
% 0.19/0.59 % Version : CSE_E---1.5
% 0.19/0.59 % Problem : theBenchmark.p
% 0.19/0.59 % Proof found
% 0.19/0.59 % SZS status Theorem for theBenchmark.p
% 0.19/0.59 % SZS output start Proof
% See solution above
% 0.19/0.60 % Total time : 0.018000 s
% 0.19/0.60 % SZS output end Proof
% 0.19/0.60 % Total time : 0.021000 s
%------------------------------------------------------------------------------