TSTP Solution File: NUM456+6 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM456+6 : 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 : n025.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 10:37:40 EDT 2023
% Result : Theorem 0.20s 0.61s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 58
% Syntax : Number of formulae : 73 ( 6 unt; 55 typ; 0 def)
% Number of atoms : 183 ( 33 equ)
% Maximal formula atoms : 44 ( 10 avg)
% Number of connectives : 218 ( 53 ~; 51 |; 98 &)
% ( 10 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 31 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 74 ( 45 >; 29 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 45 ( 45 usr; 10 con; 0-3 aty)
% Number of variables : 41 ( 0 sgn; 27 !; 10 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
aInteger0: $i > $o ).
tff(decl_23,type,
sz00: $i ).
tff(decl_24,type,
sz10: $i ).
tff(decl_25,type,
smndt0: $i > $i ).
tff(decl_26,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(decl_27,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(decl_28,type,
aDivisorOf0: ( $i * $i ) > $o ).
tff(decl_29,type,
sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).
tff(decl_30,type,
isPrime0: $i > $o ).
tff(decl_31,type,
aSet0: $i > $o ).
tff(decl_32,type,
aElementOf0: ( $i * $i ) > $o ).
tff(decl_33,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(decl_34,type,
isFinite0: $i > $o ).
tff(decl_35,type,
cS1395: $i ).
tff(decl_36,type,
sdtbsmnsldt0: ( $i * $i ) > $i ).
tff(decl_37,type,
sdtslmnbsdt0: ( $i * $i ) > $i ).
tff(decl_38,type,
sbsmnsldt0: $i > $i ).
tff(decl_39,type,
stldt0: $i > $i ).
tff(decl_40,type,
szAzrzSzezqlpdtcmdtrp0: ( $i * $i ) > $i ).
tff(decl_41,type,
isOpen0: $i > $o ).
tff(decl_42,type,
isClosed0: $i > $o ).
tff(decl_43,type,
xS: $i ).
tff(decl_44,type,
cS2043: $i ).
tff(decl_45,type,
cS2076: $i ).
tff(decl_46,type,
xp: $i ).
tff(decl_47,type,
cS2200: $i ).
tff(decl_48,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk2_1: $i > $i ).
tff(decl_50,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_51,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_52,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_53,type,
esk6_1: $i > $i ).
tff(decl_54,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_55,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_56,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_57,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_58,type,
esk11_3: ( $i * $i * $i ) > $i ).
tff(decl_59,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_60,type,
esk13_1: $i > $i ).
tff(decl_61,type,
esk14_1: $i > $i ).
tff(decl_62,type,
esk15_1: $i > $i ).
tff(decl_63,type,
esk16_1: $i > $i ).
tff(decl_64,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_65,type,
esk18_3: ( $i * $i * $i ) > $i ).
tff(decl_66,type,
esk19_1: $i > $i ).
tff(decl_67,type,
esk20_1: $i > $i ).
tff(decl_68,type,
esk21_1: $i > $i ).
tff(decl_69,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_70,type,
esk23_1: $i > $i ).
tff(decl_71,type,
esk24_1: $i > $i ).
tff(decl_72,type,
esk25_2: ( $i * $i ) > $i ).
tff(decl_73,type,
esk26_1: $i > $i ).
tff(decl_74,type,
esk27_1: $i > $i ).
tff(decl_75,type,
esk28_0: $i ).
tff(decl_76,type,
esk29_0: $i ).
fof(m__2171,hypothesis,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X1] :
( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> ( aInteger0(X1)
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X1,sz10,xp) ) )
& ( ( aInteger0(X1)
& ( ? [X2] :
( aInteger0(X2)
& sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
| aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(X1,sz10,xp) ) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( aInteger0(X1)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) ) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
& ! [X1] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> aElementOf0(X1,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2171) ).
fof(m__2079,hypothesis,
( aSet0(sbsmnsldt0(xS))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( aInteger0(X1)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) ) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( X1 = sz10
| X1 = smndt0(sz10) ) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2079) ).
fof(m__2203,hypothesis,
? [X1] :
( aInteger0(X1)
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X1,sz10,xp)
& aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ~ ( X1 = sz10
| X1 = smndt0(sz10)
| aElementOf0(X1,cS2200) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2203) ).
fof(c_0_3,hypothesis,
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ! [X1] :
( ( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> ( aInteger0(X1)
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
& aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X1,sz10,xp) ) )
& ( ( aInteger0(X1)
& ( ? [X2] :
( aInteger0(X2)
& sdtasdt0(xp,X2) = sdtpldt0(X1,smndt0(sz10)) )
| aDivisorOf0(xp,sdtpldt0(X1,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(X1,sz10,xp) ) )
=> aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ) )
& aSet0(sbsmnsldt0(xS))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( aInteger0(X1)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) ) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
& ! [X1] :
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
=> aElementOf0(X1,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
inference(fof_simplification,[status(thm)],[m__2171]) ).
fof(c_0_4,hypothesis,
( aSet0(sbsmnsldt0(xS))
& ! [X1] :
( aElementOf0(X1,sbsmnsldt0(xS))
<=> ( aInteger0(X1)
& ? [X2] :
( aElementOf0(X2,xS)
& aElementOf0(X1,X2) ) ) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X1)
& ~ aElementOf0(X1,sbsmnsldt0(xS)) ) )
& ! [X1] :
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
<=> ( X1 = sz10
| X1 = smndt0(sz10) ) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
inference(fof_simplification,[status(thm)],[m__2079]) ).
fof(c_0_5,hypothesis,
! [X155,X157,X158,X159,X161,X162,X163,X164] :
( aInteger0(xp)
& xp != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& ( aInteger0(X155)
| ~ aElementOf0(X155,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aInteger0(esk26_1(X155))
| ~ aElementOf0(X155,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( sdtasdt0(xp,esk26_1(X155)) = sdtpldt0(X155,smndt0(sz10))
| ~ aElementOf0(X155,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( aDivisorOf0(xp,sdtpldt0(X155,smndt0(sz10)))
| ~ aElementOf0(X155,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( sdteqdtlpzmzozddtrp0(X155,sz10,xp)
| ~ aElementOf0(X155,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ aInteger0(X158)
| sdtasdt0(xp,X158) != sdtpldt0(X157,smndt0(sz10))
| ~ aInteger0(X157)
| aElementOf0(X157,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ aDivisorOf0(xp,sdtpldt0(X157,smndt0(sz10)))
| ~ aInteger0(X157)
| aElementOf0(X157,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& ( ~ sdteqdtlpzmzozddtrp0(X157,sz10,xp)
| ~ aInteger0(X157)
| aElementOf0(X157,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) )
& aSet0(sbsmnsldt0(xS))
& ( aInteger0(X159)
| ~ aElementOf0(X159,sbsmnsldt0(xS)) )
& ( aElementOf0(esk27_1(X159),xS)
| ~ aElementOf0(X159,sbsmnsldt0(xS)) )
& ( aElementOf0(X159,esk27_1(X159))
| ~ aElementOf0(X159,sbsmnsldt0(xS)) )
& ( ~ aInteger0(X161)
| ~ aElementOf0(X162,xS)
| ~ aElementOf0(X161,X162)
| aElementOf0(X161,sbsmnsldt0(xS)) )
& ( aInteger0(X163)
| ~ aElementOf0(X163,stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X163,sbsmnsldt0(xS))
| ~ aElementOf0(X163,stldt0(sbsmnsldt0(xS))) )
& ( ~ aInteger0(X163)
| aElementOf0(X163,sbsmnsldt0(xS))
| aElementOf0(X163,stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X164,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
| aElementOf0(X164,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS))) ),
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)],[c_0_3])])])])])]) ).
fof(c_0_6,hypothesis,
! [X125,X127,X128,X129,X130] :
( aSet0(sbsmnsldt0(xS))
& ( aInteger0(X125)
| ~ aElementOf0(X125,sbsmnsldt0(xS)) )
& ( aElementOf0(esk19_1(X125),xS)
| ~ aElementOf0(X125,sbsmnsldt0(xS)) )
& ( aElementOf0(X125,esk19_1(X125))
| ~ aElementOf0(X125,sbsmnsldt0(xS)) )
& ( ~ aInteger0(X127)
| ~ aElementOf0(X128,xS)
| ~ aElementOf0(X127,X128)
| aElementOf0(X127,sbsmnsldt0(xS)) )
& aSet0(stldt0(sbsmnsldt0(xS)))
& ( aInteger0(X129)
| ~ aElementOf0(X129,stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X129,sbsmnsldt0(xS))
| ~ aElementOf0(X129,stldt0(sbsmnsldt0(xS))) )
& ( ~ aInteger0(X129)
| aElementOf0(X129,sbsmnsldt0(xS))
| aElementOf0(X129,stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X130,stldt0(sbsmnsldt0(xS)))
| X130 = sz10
| X130 = smndt0(sz10) )
& ( X130 != sz10
| aElementOf0(X130,stldt0(sbsmnsldt0(xS))) )
& ( X130 != smndt0(sz10)
| aElementOf0(X130,stldt0(sbsmnsldt0(xS))) )
& stldt0(sbsmnsldt0(xS)) = cS2076 ),
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)],[c_0_4])])])])])]) ).
cnf(c_0_7,hypothesis,
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,hypothesis,
stldt0(sbsmnsldt0(xS)) = cS2076,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,hypothesis,
( aInteger0(esk28_0)
& aInteger0(esk29_0)
& sdtasdt0(xp,esk29_0) = sdtpldt0(esk28_0,smndt0(sz10))
& aDivisorOf0(xp,sdtpldt0(esk28_0,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(esk28_0,sz10,xp)
& aElementOf0(esk28_0,szAzrzSzezqlpdtcmdtrp0(sz10,xp))
& esk28_0 != sz10
& esk28_0 != smndt0(sz10)
& ~ aElementOf0(esk28_0,cS2200) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2203])])]) ).
cnf(c_0_10,hypothesis,
( X1 = sz10
| X1 = smndt0(sz10)
| ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,hypothesis,
( aElementOf0(X1,cS2076)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz10,xp)) ),
inference(rw,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_12,hypothesis,
aElementOf0(esk28_0,szAzrzSzezqlpdtcmdtrp0(sz10,xp)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_13,hypothesis,
( X1 = smndt0(sz10)
| X1 = sz10
| ~ aElementOf0(X1,cS2076) ),
inference(rw,[status(thm)],[c_0_10,c_0_8]) ).
cnf(c_0_14,hypothesis,
aElementOf0(esk28_0,cS2076),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,hypothesis,
esk28_0 != smndt0(sz10),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,hypothesis,
esk28_0 != sz10,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,hypothesis,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM456+6 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.33 % Computer : n025.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Fri Aug 25 16:30:52 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.57 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
% 0.20/0.62 % Total time : 0.036000 s
% 0.20/0.62 % SZS output end Proof
% 0.20/0.62 % Total time : 0.040000 s
%------------------------------------------------------------------------------