TSTP Solution File: SET814+4 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET814+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 : n008.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 14:35:39 EDT 2023
% Result : Theorem 152.58s 152.55s
% Output : CNFRefutation 152.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 40
% Syntax : Number of formulae : 64 ( 4 unt; 35 typ; 0 def)
% Number of atoms : 92 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 104 ( 41 ~; 42 |; 13 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 60 ( 31 >; 29 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 27 ( 27 usr; 4 con; 0-3 aty)
% Number of variables : 59 ( 0 sgn; 28 !; 1 ?; 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,
on: $i ).
tff(decl_35,type,
set: $i > $o ).
tff(decl_36,type,
member_predicate: $i ).
tff(decl_37,type,
strict_well_order: ( $i * $i ) > $o ).
tff(decl_38,type,
strict_order: ( $i * $i ) > $o ).
tff(decl_39,type,
least: ( $i * $i * $i ) > $o ).
tff(decl_40,type,
apply: ( $i * $i * $i ) > $o ).
tff(decl_41,type,
initial_segment: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
suc: $i > $i ).
tff(decl_43,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_44,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_45,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_46,type,
esk4_1: $i > $i ).
tff(decl_47,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_48,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_50,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_51,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk11_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk13_2: ( $i * $i ) > $i ).
tff(decl_56,type,
esk14_0: $i ).
fof(thI3,axiom,
! [X1,X2,X9] :
( ( subset(X1,X2)
& subset(X2,X9) )
=> subset(X1,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thI3) ).
fof(ordinal_number,axiom,
! [X1] :
( member(X1,on)
<=> ( set(X1)
& strict_well_order(member_predicate,X1)
& ! [X3] :
( member(X3,X1)
=> subset(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+4.ax',ordinal_number) ).
fof(thV14,conjecture,
! [X1] :
( member(X1,on)
=> subset(sum(X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thV14) ).
fof(sum,axiom,
! [X3,X1] :
( member(X3,sum(X1))
<=> ? [X5] :
( member(X5,X1)
& member(X3,X5) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',sum) ).
fof(subset,axiom,
! [X1,X2] :
( subset(X1,X2)
<=> ! [X3] :
( member(X3,X1)
=> member(X3,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).
fof(c_0_5,plain,
! [X93,X94,X95] :
( ~ subset(X93,X94)
| ~ subset(X94,X95)
| subset(X93,X95) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[thI3])]) ).
fof(c_0_6,plain,
! [X47,X48,X49] :
( ( set(X47)
| ~ member(X47,on) )
& ( strict_well_order(member_predicate,X47)
| ~ member(X47,on) )
& ( ~ member(X48,X47)
| subset(X48,X47)
| ~ member(X47,on) )
& ( member(esk4_1(X49),X49)
| ~ set(X49)
| ~ strict_well_order(member_predicate,X49)
| member(X49,on) )
& ( ~ subset(esk4_1(X49),X49)
| ~ set(X49)
| ~ strict_well_order(member_predicate,X49)
| member(X49,on) ) ),
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)],[ordinal_number])])])])])]) ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( member(X1,on)
=> subset(sum(X1),X1) ),
inference(assume_negation,[status(cth)],[thV14]) ).
cnf(c_0_8,plain,
( subset(X1,X3)
| ~ subset(X1,X2)
| ~ subset(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_9,plain,
( subset(X1,X2)
| ~ member(X1,X2)
| ~ member(X2,on) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_10,negated_conjecture,
( member(esk14_0,on)
& ~ subset(sum(esk14_0),esk14_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_11,plain,
( subset(X1,X2)
| ~ member(X2,on)
| ~ member(X3,X2)
| ~ subset(X1,X3) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,negated_conjecture,
member(esk14_0,on),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_13,plain,
! [X35,X36,X38,X39,X40] :
( ( member(esk2_2(X35,X36),X36)
| ~ member(X35,sum(X36)) )
& ( member(X35,esk2_2(X35,X36))
| ~ member(X35,sum(X36)) )
& ( ~ member(X40,X39)
| ~ member(X38,X40)
| member(X38,sum(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)],[sum])])])])])]) ).
fof(c_0_14,plain,
! [X10,X11,X12,X13,X14] :
( ( ~ subset(X10,X11)
| ~ member(X12,X10)
| member(X12,X11) )
& ( member(esk1_2(X13,X14),X13)
| subset(X13,X14) )
& ( ~ member(esk1_2(X13,X14),X14)
| subset(X13,X14) ) ),
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_15,negated_conjecture,
( subset(X1,esk14_0)
| ~ member(X2,esk14_0)
| ~ subset(X1,X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
( member(esk2_2(X1,X2),X2)
| ~ member(X1,sum(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_17,plain,
( subset(X1,X2)
| ~ member(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_18,plain,
( member(esk1_2(X1,X2),X1)
| subset(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_19,plain,
( member(X3,X2)
| ~ subset(X1,X2)
| ~ member(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
( member(X1,esk2_2(X1,X2))
| ~ member(X1,sum(X2)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,negated_conjecture,
( subset(X1,esk14_0)
| ~ member(X2,sum(esk14_0))
| ~ subset(X1,esk2_2(X2,esk14_0)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_22,plain,
subset(X1,X1),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( member(X1,X2)
| ~ member(X1,sum(X3))
| ~ subset(esk2_2(X1,X3),X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( subset(esk2_2(X1,esk14_0),esk14_0)
| ~ member(X1,sum(esk14_0)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
( member(X1,esk14_0)
| ~ member(X1,sum(esk14_0)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,negated_conjecture,
( member(esk1_2(sum(esk14_0),X1),esk14_0)
| subset(sum(esk14_0),X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_18]) ).
cnf(c_0_27,negated_conjecture,
~ subset(sum(esk14_0),esk14_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_28,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_26]),c_0_27]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET814+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 : n008.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 12:40:32 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 152.58/152.55 % Version : CSE_E---1.5
% 152.58/152.55 % Problem : theBenchmark.p
% 152.58/152.55 % Proof found
% 152.58/152.55 % SZS status Theorem for theBenchmark.p
% 152.58/152.55 % SZS output start Proof
% See solution above
% 152.58/152.55 % Total time : 151.983000 s
% 152.58/152.55 % SZS output end Proof
% 152.58/152.55 % Total time : 151.993000 s
%------------------------------------------------------------------------------