TSTP Solution File: NUM450+6 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM450+6 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/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 10:37:37 EDT 2023
% Result : Theorem 0.20s 0.65s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 55
% Syntax : Number of formulae : 75 ( 4 unt; 52 typ; 0 def)
% Number of atoms : 441 ( 65 equ)
% Maximal formula atoms : 116 ( 19 avg)
% Number of connectives : 578 ( 160 ~; 176 |; 196 &)
% ( 18 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 65 ( 11 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 77 ( 46 >; 31 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 42 ( 42 usr; 6 con; 0-3 aty)
% Number of variables : 101 ( 0 sgn; 66 !; 26 ?; 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,
esk1_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk2_1: $i > $i ).
tff(decl_48,type,
esk3_2: ( $i * $i ) > $i ).
tff(decl_49,type,
esk4_3: ( $i * $i * $i ) > $i ).
tff(decl_50,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_51,type,
esk6_1: $i > $i ).
tff(decl_52,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_53,type,
esk8_2: ( $i * $i ) > $i ).
tff(decl_54,type,
esk9_2: ( $i * $i ) > $i ).
tff(decl_55,type,
esk10_2: ( $i * $i ) > $i ).
tff(decl_56,type,
esk11_3: ( $i * $i * $i ) > $i ).
tff(decl_57,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_58,type,
esk13_1: $i > $i ).
tff(decl_59,type,
esk14_1: $i > $i ).
tff(decl_60,type,
esk15_1: $i > $i ).
tff(decl_61,type,
esk16_1: $i > $i ).
tff(decl_62,type,
esk17_2: ( $i * $i ) > $i ).
tff(decl_63,type,
esk18_3: ( $i * $i * $i ) > $i ).
tff(decl_64,type,
esk19_1: $i > $i ).
tff(decl_65,type,
esk20_1: $i > $i ).
tff(decl_66,type,
esk21_1: $i > $i ).
tff(decl_67,type,
esk22_2: ( $i * $i ) > $i ).
tff(decl_68,type,
esk23_1: $i > $i ).
tff(decl_69,type,
esk24_1: $i > $i ).
tff(decl_70,type,
esk25_2: ( $i * $i ) > $i ).
tff(decl_71,type,
esk26_2: ( $i * $i ) > $i ).
tff(decl_72,type,
esk27_2: ( $i * $i ) > $i ).
tff(decl_73,type,
esk28_1: $i > $i ).
fof(m__,conjecture,
? [X1] :
( aInteger0(X1)
& X1 != sz00
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,X1))
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz10,X1))
=> ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz10)) )
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X2,sz10,X1) ) )
& ( ( aInteger0(X2)
& ( ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz10)) )
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(X2,sz10,X1) ) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz10,X1)) ) ) )
=> ( ( aSet0(sbsmnsldt0(xS))
& ! [X2] :
( aElementOf0(X2,sbsmnsldt0(xS))
<=> ( aInteger0(X2)
& ? [X3] :
( aElementOf0(X3,xS)
& aElementOf0(X2,X3) ) ) ) )
=> ( ! [X2] :
( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X2)
& ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
=> ( ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz10,X1))
=> aElementOf0(X2,stldt0(sbsmnsldt0(xS))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X1),stldt0(sbsmnsldt0(xS))) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
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/sandbox/benchmark/theBenchmark.p',m__2079) ).
fof(m__2144,hypothesis,
( 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,stldt0(sbsmnsldt0(xS)))
=> ? [X2] :
( aInteger0(X2)
& X2 != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ) )
& ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(sbsmnsldt0(xS))) ) )
& isOpen0(stldt0(sbsmnsldt0(xS)))
& isClosed0(sbsmnsldt0(xS))
& 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,stldt0(sbsmnsldt0(xS)))
=> ? [X2] :
( aInteger0(X2)
& X2 != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ) )
& ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(sbsmnsldt0(xS))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2144) ).
fof(c_0_3,negated_conjecture,
~ ? [X1] :
( aInteger0(X1)
& X1 != sz00
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,X1))
& ! [X2] :
( ( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz10,X1))
=> ( aInteger0(X2)
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz10)) )
& aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz10)))
& sdteqdtlpzmzozddtrp0(X2,sz10,X1) ) )
& ( ( aInteger0(X2)
& ( ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = sdtpldt0(X2,smndt0(sz10)) )
| aDivisorOf0(X1,sdtpldt0(X2,smndt0(sz10)))
| sdteqdtlpzmzozddtrp0(X2,sz10,X1) ) )
=> aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz10,X1)) ) ) )
=> ( ( aSet0(sbsmnsldt0(xS))
& ! [X2] :
( aElementOf0(X2,sbsmnsldt0(xS))
<=> ( aInteger0(X2)
& ? [X3] :
( aElementOf0(X3,xS)
& aElementOf0(X2,X3) ) ) ) )
=> ( ! [X2] :
( aElementOf0(X2,stldt0(sbsmnsldt0(xS)))
<=> ( aInteger0(X2)
& ~ aElementOf0(X2,sbsmnsldt0(xS)) ) )
=> ( ! [X2] :
( aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz10,X1))
=> aElementOf0(X2,stldt0(sbsmnsldt0(xS))) )
| aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X1),stldt0(sbsmnsldt0(xS))) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[m__])]) ).
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,
( 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,stldt0(sbsmnsldt0(xS)))
=> ? [X2] :
( aInteger0(X2)
& X2 != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ) )
& ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(sbsmnsldt0(xS))) ) )
& isOpen0(stldt0(sbsmnsldt0(xS)))
& isClosed0(sbsmnsldt0(xS))
& 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,stldt0(sbsmnsldt0(xS)))
=> ? [X2] :
( aInteger0(X2)
& X2 != sz00
& aSet0(szAzrzSzezqlpdtcmdtrp0(X1,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
& sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(X1)) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(X1)))
| sdteqdtlpzmzozddtrp0(X3,X1,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2)) ) )
& ! [X3] :
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(X1,X2))
=> aElementOf0(X3,stldt0(sbsmnsldt0(xS))) )
& aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,X2),stldt0(sbsmnsldt0(xS))) ) ) ),
inference(fof_simplification,[status(thm)],[m__2144]) ).
fof(c_0_6,negated_conjecture,
! [X155,X156,X158,X159,X160,X162,X163,X164,X165] :
( ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz10,X155))
| ~ aInteger0(X155)
| X155 = sz00 )
& ( aInteger0(X156)
| ~ aElementOf0(X156,szAzrzSzezqlpdtcmdtrp0(sz10,X155))
| ~ aInteger0(X155)
| X155 = sz00 )
& ( aInteger0(esk26_2(X155,X156))
| ~ aElementOf0(X156,szAzrzSzezqlpdtcmdtrp0(sz10,X155))
| ~ aInteger0(X155)
| X155 = sz00 )
& ( sdtasdt0(X155,esk26_2(X155,X156)) = sdtpldt0(X156,smndt0(sz10))
| ~ aElementOf0(X156,szAzrzSzezqlpdtcmdtrp0(sz10,X155))
| ~ aInteger0(X155)
| X155 = sz00 )
& ( aDivisorOf0(X155,sdtpldt0(X156,smndt0(sz10)))
| ~ aElementOf0(X156,szAzrzSzezqlpdtcmdtrp0(sz10,X155))
| ~ aInteger0(X155)
| X155 = sz00 )
& ( sdteqdtlpzmzozddtrp0(X156,sz10,X155)
| ~ aElementOf0(X156,szAzrzSzezqlpdtcmdtrp0(sz10,X155))
| ~ aInteger0(X155)
| X155 = sz00 )
& ( ~ aInteger0(X159)
| sdtasdt0(X155,X159) != sdtpldt0(X158,smndt0(sz10))
| ~ aInteger0(X158)
| aElementOf0(X158,szAzrzSzezqlpdtcmdtrp0(sz10,X155))
| ~ aInteger0(X155)
| X155 = sz00 )
& ( ~ aDivisorOf0(X155,sdtpldt0(X158,smndt0(sz10)))
| ~ aInteger0(X158)
| aElementOf0(X158,szAzrzSzezqlpdtcmdtrp0(sz10,X155))
| ~ aInteger0(X155)
| X155 = sz00 )
& ( ~ sdteqdtlpzmzozddtrp0(X158,sz10,X155)
| ~ aInteger0(X158)
| aElementOf0(X158,szAzrzSzezqlpdtcmdtrp0(sz10,X155))
| ~ aInteger0(X155)
| X155 = sz00 )
& ( aSet0(sbsmnsldt0(xS))
| ~ aInteger0(X155)
| X155 = sz00 )
& ( aInteger0(X160)
| ~ aElementOf0(X160,sbsmnsldt0(xS))
| ~ aInteger0(X155)
| X155 = sz00 )
& ( aElementOf0(esk27_2(X155,X160),xS)
| ~ aElementOf0(X160,sbsmnsldt0(xS))
| ~ aInteger0(X155)
| X155 = sz00 )
& ( aElementOf0(X160,esk27_2(X155,X160))
| ~ aElementOf0(X160,sbsmnsldt0(xS))
| ~ aInteger0(X155)
| X155 = sz00 )
& ( ~ aInteger0(X162)
| ~ aElementOf0(X163,xS)
| ~ aElementOf0(X162,X163)
| aElementOf0(X162,sbsmnsldt0(xS))
| ~ aInteger0(X155)
| X155 = sz00 )
& ( aInteger0(X164)
| ~ aElementOf0(X164,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X155)
| X155 = sz00 )
& ( ~ aElementOf0(X164,sbsmnsldt0(xS))
| ~ aElementOf0(X164,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X155)
| X155 = sz00 )
& ( ~ aInteger0(X165)
| aElementOf0(X165,sbsmnsldt0(xS))
| aElementOf0(X165,stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X155)
| X155 = sz00 )
& ( aElementOf0(esk28_1(X155),szAzrzSzezqlpdtcmdtrp0(sz10,X155))
| ~ aInteger0(X155)
| X155 = sz00 )
& ( ~ aElementOf0(esk28_1(X155),stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X155)
| X155 = sz00 )
& ( ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X155),stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X155)
| X155 = sz00 ) ),
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_7,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])])])])])]) ).
fof(c_0_8,hypothesis,
! [X131,X133,X134,X135,X136,X138,X140,X141,X142,X143,X145,X146,X147,X148,X150,X152,X153,X154] :
( aSet0(sbsmnsldt0(xS))
& ( aInteger0(X131)
| ~ aElementOf0(X131,sbsmnsldt0(xS)) )
& ( aElementOf0(esk20_1(X131),xS)
| ~ aElementOf0(X131,sbsmnsldt0(xS)) )
& ( aElementOf0(X131,esk20_1(X131))
| ~ aElementOf0(X131,sbsmnsldt0(xS)) )
& ( ~ aInteger0(X133)
| ~ aElementOf0(X134,xS)
| ~ aElementOf0(X133,X134)
| aElementOf0(X133,sbsmnsldt0(xS)) )
& ( aInteger0(X135)
| ~ aElementOf0(X135,stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X135,sbsmnsldt0(xS))
| ~ aElementOf0(X135,stldt0(sbsmnsldt0(xS))) )
& ( ~ aInteger0(X135)
| aElementOf0(X135,sbsmnsldt0(xS))
| aElementOf0(X135,stldt0(sbsmnsldt0(xS))) )
& ( aInteger0(esk21_1(X136))
| ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
& ( esk21_1(X136) != sz00
| ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
& ( aSet0(szAzrzSzezqlpdtcmdtrp0(X136,esk21_1(X136)))
| ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
& ( aInteger0(X138)
| ~ aElementOf0(X138,szAzrzSzezqlpdtcmdtrp0(X136,esk21_1(X136)))
| ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
& ( aInteger0(esk22_2(X136,X138))
| ~ aElementOf0(X138,szAzrzSzezqlpdtcmdtrp0(X136,esk21_1(X136)))
| ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
& ( sdtasdt0(esk21_1(X136),esk22_2(X136,X138)) = sdtpldt0(X138,smndt0(X136))
| ~ aElementOf0(X138,szAzrzSzezqlpdtcmdtrp0(X136,esk21_1(X136)))
| ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
& ( aDivisorOf0(esk21_1(X136),sdtpldt0(X138,smndt0(X136)))
| ~ aElementOf0(X138,szAzrzSzezqlpdtcmdtrp0(X136,esk21_1(X136)))
| ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
& ( sdteqdtlpzmzozddtrp0(X138,X136,esk21_1(X136))
| ~ aElementOf0(X138,szAzrzSzezqlpdtcmdtrp0(X136,esk21_1(X136)))
| ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
& ( ~ aInteger0(X141)
| sdtasdt0(esk21_1(X136),X141) != sdtpldt0(X140,smndt0(X136))
| ~ aInteger0(X140)
| aElementOf0(X140,szAzrzSzezqlpdtcmdtrp0(X136,esk21_1(X136)))
| ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
& ( ~ aDivisorOf0(esk21_1(X136),sdtpldt0(X140,smndt0(X136)))
| ~ aInteger0(X140)
| aElementOf0(X140,szAzrzSzezqlpdtcmdtrp0(X136,esk21_1(X136)))
| ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
& ( ~ sdteqdtlpzmzozddtrp0(X140,X136,esk21_1(X136))
| ~ aInteger0(X140)
| aElementOf0(X140,szAzrzSzezqlpdtcmdtrp0(X136,esk21_1(X136)))
| ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X142,szAzrzSzezqlpdtcmdtrp0(X136,esk21_1(X136)))
| aElementOf0(X142,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
& ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X136,esk21_1(X136)),stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X136,stldt0(sbsmnsldt0(xS))) )
& isOpen0(stldt0(sbsmnsldt0(xS)))
& isClosed0(sbsmnsldt0(xS))
& aSet0(sbsmnsldt0(xS))
& ( aInteger0(X143)
| ~ aElementOf0(X143,sbsmnsldt0(xS)) )
& ( aElementOf0(esk23_1(X143),xS)
| ~ aElementOf0(X143,sbsmnsldt0(xS)) )
& ( aElementOf0(X143,esk23_1(X143))
| ~ aElementOf0(X143,sbsmnsldt0(xS)) )
& ( ~ aInteger0(X145)
| ~ aElementOf0(X146,xS)
| ~ aElementOf0(X145,X146)
| aElementOf0(X145,sbsmnsldt0(xS)) )
& ( aInteger0(X147)
| ~ aElementOf0(X147,stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X147,sbsmnsldt0(xS))
| ~ aElementOf0(X147,stldt0(sbsmnsldt0(xS))) )
& ( ~ aInteger0(X147)
| aElementOf0(X147,sbsmnsldt0(xS))
| aElementOf0(X147,stldt0(sbsmnsldt0(xS))) )
& ( aInteger0(esk24_1(X148))
| ~ aElementOf0(X148,stldt0(sbsmnsldt0(xS))) )
& ( esk24_1(X148) != sz00
| ~ aElementOf0(X148,stldt0(sbsmnsldt0(xS))) )
& ( aSet0(szAzrzSzezqlpdtcmdtrp0(X148,esk24_1(X148)))
| ~ aElementOf0(X148,stldt0(sbsmnsldt0(xS))) )
& ( aInteger0(X150)
| ~ aElementOf0(X150,szAzrzSzezqlpdtcmdtrp0(X148,esk24_1(X148)))
| ~ aElementOf0(X148,stldt0(sbsmnsldt0(xS))) )
& ( aInteger0(esk25_2(X148,X150))
| ~ aElementOf0(X150,szAzrzSzezqlpdtcmdtrp0(X148,esk24_1(X148)))
| ~ aElementOf0(X148,stldt0(sbsmnsldt0(xS))) )
& ( sdtasdt0(esk24_1(X148),esk25_2(X148,X150)) = sdtpldt0(X150,smndt0(X148))
| ~ aElementOf0(X150,szAzrzSzezqlpdtcmdtrp0(X148,esk24_1(X148)))
| ~ aElementOf0(X148,stldt0(sbsmnsldt0(xS))) )
& ( aDivisorOf0(esk24_1(X148),sdtpldt0(X150,smndt0(X148)))
| ~ aElementOf0(X150,szAzrzSzezqlpdtcmdtrp0(X148,esk24_1(X148)))
| ~ aElementOf0(X148,stldt0(sbsmnsldt0(xS))) )
& ( sdteqdtlpzmzozddtrp0(X150,X148,esk24_1(X148))
| ~ aElementOf0(X150,szAzrzSzezqlpdtcmdtrp0(X148,esk24_1(X148)))
| ~ aElementOf0(X148,stldt0(sbsmnsldt0(xS))) )
& ( ~ aInteger0(X153)
| sdtasdt0(esk24_1(X148),X153) != sdtpldt0(X152,smndt0(X148))
| ~ aInteger0(X152)
| aElementOf0(X152,szAzrzSzezqlpdtcmdtrp0(X148,esk24_1(X148)))
| ~ aElementOf0(X148,stldt0(sbsmnsldt0(xS))) )
& ( ~ aDivisorOf0(esk24_1(X148),sdtpldt0(X152,smndt0(X148)))
| ~ aInteger0(X152)
| aElementOf0(X152,szAzrzSzezqlpdtcmdtrp0(X148,esk24_1(X148)))
| ~ aElementOf0(X148,stldt0(sbsmnsldt0(xS))) )
& ( ~ sdteqdtlpzmzozddtrp0(X152,X148,esk24_1(X148))
| ~ aInteger0(X152)
| aElementOf0(X152,szAzrzSzezqlpdtcmdtrp0(X148,esk24_1(X148)))
| ~ aElementOf0(X148,stldt0(sbsmnsldt0(xS))) )
& ( ~ aElementOf0(X154,szAzrzSzezqlpdtcmdtrp0(X148,esk24_1(X148)))
| aElementOf0(X154,stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X148,stldt0(sbsmnsldt0(xS))) )
& ( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X148,esk24_1(X148)),stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X148,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_5])])])])])]) ).
cnf(c_0_9,negated_conjecture,
( X1 = sz00
| ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X1),stldt0(sbsmnsldt0(xS)))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,hypothesis,
stldt0(sbsmnsldt0(xS)) = cS2076,
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,hypothesis,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,esk21_1(X1)),stldt0(sbsmnsldt0(xS)))
| ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,hypothesis,
( aElementOf0(X1,stldt0(sbsmnsldt0(xS)))
| X1 != sz10 ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
( X1 = sz00
| ~ aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,X1),cS2076)
| ~ aInteger0(X1) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,hypothesis,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(X1,esk21_1(X1)),cS2076)
| ~ aElementOf0(X1,cS2076) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_10]),c_0_10]) ).
cnf(c_0_15,hypothesis,
aElementOf0(sz10,cS2076),
inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_10])]) ).
cnf(c_0_16,hypothesis,
( aInteger0(esk21_1(X1))
| ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_17,hypothesis,
( esk21_1(X1) != sz00
| ~ aElementOf0(X1,stldt0(sbsmnsldt0(xS))) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_18,negated_conjecture,
( esk21_1(sz10) = sz00
| ~ aInteger0(esk21_1(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_19,hypothesis,
( aInteger0(esk21_1(X1))
| ~ aElementOf0(X1,cS2076) ),
inference(rw,[status(thm)],[c_0_16,c_0_10]) ).
cnf(c_0_20,hypothesis,
( esk21_1(X1) != sz00
| ~ aElementOf0(X1,cS2076) ),
inference(rw,[status(thm)],[c_0_17,c_0_10]) ).
cnf(c_0_21,hypothesis,
esk21_1(sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_15])]) ).
cnf(c_0_22,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM450+6 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/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 : Fri Aug 25 15:11:17 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.59 start to proof: theBenchmark
% 0.20/0.65 % Version : CSE_E---1.5
% 0.20/0.65 % Problem : theBenchmark.p
% 0.20/0.65 % Proof found
% 0.20/0.65 % SZS status Theorem for theBenchmark.p
% 0.20/0.65 % SZS output start Proof
% See solution above
% 0.20/0.66 % Total time : 0.056000 s
% 0.20/0.66 % SZS output end Proof
% 0.20/0.66 % Total time : 0.061000 s
%------------------------------------------------------------------------------