TSTP Solution File: NUM547+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM547+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n005.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 10:38:36 EDT 2023
% Result : Theorem 0.19s 0.58s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 41
% Syntax : Number of formulae : 58 ( 11 unt; 34 typ; 0 def)
% Number of atoms : 107 ( 22 equ)
% Maximal formula atoms : 39 ( 4 avg)
% Number of connectives : 142 ( 59 ~; 57 |; 19 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 45 ( 27 >; 18 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 7 con; 0-3 aty)
% Number of variables : 34 ( 1 sgn; 22 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
aSet0: $i > $o ).
tff(decl_23,type,
aElement0: $i > $o ).
tff(decl_24,type,
aElementOf0: ( $i * $i ) > $o ).
tff(decl_25,type,
isFinite0: $i > $o ).
tff(decl_26,type,
slcrc0: $i ).
tff(decl_27,type,
isCountable0: $i > $o ).
tff(decl_28,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(decl_29,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(decl_30,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(decl_31,type,
szNzAzT0: $i ).
tff(decl_32,type,
sz00: $i ).
tff(decl_33,type,
szszuzczcdt0: $i > $i ).
tff(decl_34,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(decl_35,type,
iLess0: ( $i * $i ) > $o ).
tff(decl_36,type,
sbrdtbr0: $i > $i ).
tff(decl_37,type,
szmzizndt0: $i > $i ).
tff(decl_38,type,
szmzazxdt0: $i > $i ).
tff(decl_39,type,
slbdtrb0: $i > $i ).
tff(decl_40,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(decl_41,type,
xk: $i ).
tff(decl_42,type,
xS: $i ).
tff(decl_43,type,
xT: $i ).
tff(decl_44,type,
xx: $i ).
tff(decl_45,type,
esk1_1: $i > $i ).
tff(decl_46,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk3_3: ( $i * $i * $i ) > $i ).
tff(decl_48,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_49,type,
esk5_1: $i > $i ).
tff(decl_50,type,
esk6_2: ( $i * $i ) > $i ).
tff(decl_51,type,
esk7_2: ( $i * $i ) > $i ).
tff(decl_52,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_53,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk10_1: $i > $i ).
tff(decl_55,type,
esk11_3: ( $i * $i * $i ) > $i ).
fof(m__,conjecture,
? [X1] : aElementOf0(X1,slbdtsldtrb0(xS,xk)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mDefSub,axiom,
! [X1] :
( aSet0(X1)
=> ! [X2] :
( aSubsetOf0(X2,X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
=> aElementOf0(X3,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(mDefSel,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aElementOf0(X2,szNzAzT0) )
=> ! [X3] :
( X3 = slbdtsldtrb0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aSubsetOf0(X4,X1)
& sbrdtbr0(X4) = X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSel) ).
fof(mDefEmp,axiom,
! [X1] :
( X1 = slcrc0
<=> ( aSet0(X1)
& ~ ? [X2] : aElementOf0(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefEmp) ).
fof(m__2227,hypothesis,
( aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& slbdtsldtrb0(xS,xk) != slcrc0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2227) ).
fof(m__2202,hypothesis,
aElementOf0(xk,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202) ).
fof(m__2202_02,hypothesis,
( aSet0(xS)
& aSet0(xT)
& xk != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2202_02) ).
fof(c_0_7,negated_conjecture,
~ ? [X1] : aElementOf0(X1,slbdtsldtrb0(xS,xk)),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_8,plain,
! [X13,X14,X15,X16] :
( ( aSet0(X14)
| ~ aSubsetOf0(X14,X13)
| ~ aSet0(X13) )
& ( ~ aElementOf0(X15,X14)
| aElementOf0(X15,X13)
| ~ aSubsetOf0(X14,X13)
| ~ aSet0(X13) )
& ( aElementOf0(esk2_2(X13,X16),X16)
| ~ aSet0(X16)
| aSubsetOf0(X16,X13)
| ~ aSet0(X13) )
& ( ~ aElementOf0(esk2_2(X13,X16),X13)
| ~ aSet0(X16)
| aSubsetOf0(X16,X13)
| ~ aSet0(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)],[mDefSub])])])])])]) ).
fof(c_0_9,plain,
! [X110,X111,X112,X113,X114,X115] :
( ( aSet0(X112)
| X112 != slbdtsldtrb0(X110,X111)
| ~ aSet0(X110)
| ~ aElementOf0(X111,szNzAzT0) )
& ( aSubsetOf0(X113,X110)
| ~ aElementOf0(X113,X112)
| X112 != slbdtsldtrb0(X110,X111)
| ~ aSet0(X110)
| ~ aElementOf0(X111,szNzAzT0) )
& ( sbrdtbr0(X113) = X111
| ~ aElementOf0(X113,X112)
| X112 != slbdtsldtrb0(X110,X111)
| ~ aSet0(X110)
| ~ aElementOf0(X111,szNzAzT0) )
& ( ~ aSubsetOf0(X114,X110)
| sbrdtbr0(X114) != X111
| aElementOf0(X114,X112)
| X112 != slbdtsldtrb0(X110,X111)
| ~ aSet0(X110)
| ~ aElementOf0(X111,szNzAzT0) )
& ( ~ aElementOf0(esk11_3(X110,X111,X115),X115)
| ~ aSubsetOf0(esk11_3(X110,X111,X115),X110)
| sbrdtbr0(esk11_3(X110,X111,X115)) != X111
| ~ aSet0(X115)
| X115 = slbdtsldtrb0(X110,X111)
| ~ aSet0(X110)
| ~ aElementOf0(X111,szNzAzT0) )
& ( aSubsetOf0(esk11_3(X110,X111,X115),X110)
| aElementOf0(esk11_3(X110,X111,X115),X115)
| ~ aSet0(X115)
| X115 = slbdtsldtrb0(X110,X111)
| ~ aSet0(X110)
| ~ aElementOf0(X111,szNzAzT0) )
& ( sbrdtbr0(esk11_3(X110,X111,X115)) = X111
| aElementOf0(esk11_3(X110,X111,X115),X115)
| ~ aSet0(X115)
| X115 = slbdtsldtrb0(X110,X111)
| ~ aSet0(X110)
| ~ aElementOf0(X111,szNzAzT0) ) ),
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)],[mDefSel])])])])])]) ).
fof(c_0_10,negated_conjecture,
! [X123] : ~ aElementOf0(X123,slbdtsldtrb0(xS,xk)),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])]) ).
fof(c_0_11,plain,
! [X7,X8,X9] :
( ( aSet0(X7)
| X7 != slcrc0 )
& ( ~ aElementOf0(X8,X7)
| X7 != slcrc0 )
& ( ~ aSet0(X9)
| aElementOf0(esk1_1(X9),X9)
| X9 = slcrc0 ) ),
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)],[mDefEmp])])])])])]) ).
cnf(c_0_12,plain,
( aSet0(X1)
| ~ aSubsetOf0(X1,X2)
| ~ aSet0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,hypothesis,
aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)),
inference(split_conjunct,[status(thm)],[m__2227]) ).
cnf(c_0_14,plain,
( aSet0(X1)
| X1 != slbdtsldtrb0(X2,X3)
| ~ aSet0(X2)
| ~ aElementOf0(X3,szNzAzT0) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,negated_conjecture,
~ aElementOf0(X1,slbdtsldtrb0(xS,xk)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( aElementOf0(esk1_1(X1),X1)
| X1 = slcrc0
| ~ aSet0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,hypothesis,
slbdtsldtrb0(xS,xk) != slcrc0,
inference(split_conjunct,[status(thm)],[m__2227]) ).
cnf(c_0_18,hypothesis,
( aSet0(slbdtsldtrb0(xS,xk))
| ~ aSet0(slbdtsldtrb0(xT,xk)) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
( aSet0(slbdtsldtrb0(X1,X2))
| ~ aElementOf0(X2,szNzAzT0)
| ~ aSet0(X1) ),
inference(er,[status(thm)],[c_0_14]) ).
cnf(c_0_20,hypothesis,
aElementOf0(xk,szNzAzT0),
inference(split_conjunct,[status(thm)],[m__2202]) ).
cnf(c_0_21,hypothesis,
aSet0(xT),
inference(split_conjunct,[status(thm)],[m__2202_02]) ).
cnf(c_0_22,negated_conjecture,
~ aSet0(slbdtsldtrb0(xS,xk)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_23,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]),c_0_21])]),c_0_22]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM547+1 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n005.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 : Fri Aug 25 17:02:23 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 0.19/0.58 % Version : CSE_E---1.5
% 0.19/0.58 % Problem : theBenchmark.p
% 0.19/0.58 % Proof found
% 0.19/0.58 % SZS status Theorem for theBenchmark.p
% 0.19/0.58 % SZS output start Proof
% See solution above
% 0.19/0.59 % Total time : 0.021000 s
% 0.19/0.59 % SZS output end Proof
% 0.19/0.59 % Total time : 0.025000 s
%------------------------------------------------------------------------------