TSTP Solution File: NUM447+5 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM447+5 : 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 : n006.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 10:37:35 EDT 2023
% Result : Theorem 6.66s 6.71s
% Output : CNFRefutation 6.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 62
% Syntax : Number of formulae : 166 ( 22 unt; 45 typ; 0 def)
% Number of atoms : 706 ( 173 equ)
% Maximal formula atoms : 125 ( 5 avg)
% Number of connectives : 923 ( 338 ~; 405 |; 152 &)
% ( 4 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 47 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 63 ( 36 >; 27 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 35 ( 35 usr; 9 con; 0-3 aty)
% Number of variables : 178 ( 2 sgn; 65 !; 19 ?; 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,
xn: $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_0: $i ).
tff(decl_65,type,
esk20_0: $i ).
tff(decl_66,type,
esk21_0: $i ).
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddZero) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddNeg) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntZero) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
fof(mArSeq,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2)
& X2 != sz00 )
=> ! [X3] :
( X3 = szAzrzSzezqlpdtcmdtrp0(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ( aInteger0(X4)
& sdteqdtlpzmzozddtrp0(X4,X1,X2) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mArSeq) ).
fof(m__2046,hypothesis,
( aSet0(xS)
& ! [X1] :
( ( aElementOf0(X1,xS)
=> ? [X2] :
( aInteger0(X2)
& X2 != sz00
& isPrime0(X2)
& aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
| sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2)) ) )
& szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X1 ) )
& ( ? [X2] :
( aInteger0(X2)
& X2 != sz00
& isPrime0(X2)
& ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X2))
& ! [X3] :
( ( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2))
=> ( aInteger0(X3)
& ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
& aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
& sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
& ( ( aInteger0(X3)
& ( ? [X4] :
( aInteger0(X4)
& sdtasdt0(X2,X4) = sdtpldt0(X3,smndt0(sz00)) )
| aDivisorOf0(X2,sdtpldt0(X3,smndt0(sz00)))
| sdteqdtlpzmzozddtrp0(X3,sz00,X2) ) )
=> aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,X2)) ) ) )
=> szAzrzSzezqlpdtcmdtrp0(sz00,X2) = X1 ) )
=> aElementOf0(X1,xS) ) )
& xS = cS2043 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2046) ).
fof(m__,conjecture,
( ( ( ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(xn,X1) )
& aElementOf0(xn,sbsmnsldt0(xS)) )
=> ? [X1] :
( ( ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = xn ) )
| aDivisorOf0(X1,xn) )
& isPrime0(X1) ) )
& ( ? [X1] :
( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = xn )
& aDivisorOf0(X1,xn)
& isPrime0(X1) )
=> ( ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(xn,X1) )
| aElementOf0(xn,sbsmnsldt0(xS)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mMulZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulZero) ).
fof(mEquModRef,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2)
& X2 != sz00 )
=> sdteqdtlpzmzozddtrp0(X1,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquModRef) ).
fof(m__2106,hypothesis,
aInteger0(xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2106) ).
fof(mZeroDiv,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroDiv) ).
fof(mDivisor,axiom,
! [X1] :
( aInteger0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( aInteger0(X2)
& X2 != sz00
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X2,X3) = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivisor) ).
fof(mEquMod,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3)
& X3 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquMod) ).
fof(mDistrib,axiom,
! [X1,X2,X3] :
( ( aInteger0(X1)
& aInteger0(X2)
& aInteger0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X1,X2),X3) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X2,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDistrib) ).
fof(mMulOne,axiom,
! [X1] :
( aInteger0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulOne) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntOne) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aInteger0(X1)
& aInteger0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
fof(c_0_17,plain,
! [X15] :
( ( sdtpldt0(X15,sz00) = X15
| ~ aInteger0(X15) )
& ( X15 = sdtpldt0(sz00,X15)
| ~ aInteger0(X15) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
fof(c_0_18,plain,
! [X16] :
( ( sdtpldt0(X16,smndt0(X16)) = sz00
| ~ aInteger0(X16) )
& ( sz00 = sdtpldt0(smndt0(X16),X16)
| ~ aInteger0(X16) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])]) ).
cnf(c_0_19,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_20,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
fof(c_0_22,plain,
! [X5] :
( ~ aInteger0(X5)
| aInteger0(smndt0(X5)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])]) ).
fof(c_0_23,plain,
! [X90,X91,X92,X93,X94,X95] :
( ( aSet0(X92)
| X92 != szAzrzSzezqlpdtcmdtrp0(X90,X91)
| ~ aInteger0(X90)
| ~ aInteger0(X91)
| X91 = sz00 )
& ( aInteger0(X93)
| ~ aElementOf0(X93,X92)
| X92 != szAzrzSzezqlpdtcmdtrp0(X90,X91)
| ~ aInteger0(X90)
| ~ aInteger0(X91)
| X91 = sz00 )
& ( sdteqdtlpzmzozddtrp0(X93,X90,X91)
| ~ aElementOf0(X93,X92)
| X92 != szAzrzSzezqlpdtcmdtrp0(X90,X91)
| ~ aInteger0(X90)
| ~ aInteger0(X91)
| X91 = sz00 )
& ( ~ aInteger0(X94)
| ~ sdteqdtlpzmzozddtrp0(X94,X90,X91)
| aElementOf0(X94,X92)
| X92 != szAzrzSzezqlpdtcmdtrp0(X90,X91)
| ~ aInteger0(X90)
| ~ aInteger0(X91)
| X91 = sz00 )
& ( ~ aElementOf0(esk11_3(X90,X91,X95),X95)
| ~ aInteger0(esk11_3(X90,X91,X95))
| ~ sdteqdtlpzmzozddtrp0(esk11_3(X90,X91,X95),X90,X91)
| ~ aSet0(X95)
| X95 = szAzrzSzezqlpdtcmdtrp0(X90,X91)
| ~ aInteger0(X90)
| ~ aInteger0(X91)
| X91 = sz00 )
& ( aInteger0(esk11_3(X90,X91,X95))
| aElementOf0(esk11_3(X90,X91,X95),X95)
| ~ aSet0(X95)
| X95 = szAzrzSzezqlpdtcmdtrp0(X90,X91)
| ~ aInteger0(X90)
| ~ aInteger0(X91)
| X91 = sz00 )
& ( sdteqdtlpzmzozddtrp0(esk11_3(X90,X91,X95),X90,X91)
| aElementOf0(esk11_3(X90,X91,X95),X95)
| ~ aSet0(X95)
| X95 = szAzrzSzezqlpdtcmdtrp0(X90,X91)
| ~ aInteger0(X90)
| ~ aInteger0(X91)
| X91 = 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)],[mArSeq])])])])])]) ).
fof(c_0_24,hypothesis,
! [X113,X115,X117,X118,X119,X120,X121,X123,X124] :
( aSet0(xS)
& ( aInteger0(esk16_1(X113))
| ~ aElementOf0(X113,xS) )
& ( esk16_1(X113) != sz00
| ~ aElementOf0(X113,xS) )
& ( isPrime0(esk16_1(X113))
| ~ aElementOf0(X113,xS) )
& ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X113)))
| ~ aElementOf0(X113,xS) )
& ( aInteger0(X115)
| ~ aElementOf0(X115,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X113)))
| ~ aElementOf0(X113,xS) )
& ( aInteger0(esk17_2(X113,X115))
| ~ aElementOf0(X115,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X113)))
| ~ aElementOf0(X113,xS) )
& ( sdtasdt0(esk16_1(X113),esk17_2(X113,X115)) = sdtpldt0(X115,smndt0(sz00))
| ~ aElementOf0(X115,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X113)))
| ~ aElementOf0(X113,xS) )
& ( aDivisorOf0(esk16_1(X113),sdtpldt0(X115,smndt0(sz00)))
| ~ aElementOf0(X115,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X113)))
| ~ aElementOf0(X113,xS) )
& ( sdteqdtlpzmzozddtrp0(X115,sz00,esk16_1(X113))
| ~ aElementOf0(X115,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X113)))
| ~ aElementOf0(X113,xS) )
& ( ~ aInteger0(X118)
| sdtasdt0(esk16_1(X113),X118) != sdtpldt0(X117,smndt0(sz00))
| ~ aInteger0(X117)
| aElementOf0(X117,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X113)))
| ~ aElementOf0(X113,xS) )
& ( ~ aDivisorOf0(esk16_1(X113),sdtpldt0(X117,smndt0(sz00)))
| ~ aInteger0(X117)
| aElementOf0(X117,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X113)))
| ~ aElementOf0(X113,xS) )
& ( ~ sdteqdtlpzmzozddtrp0(X117,sz00,esk16_1(X113))
| ~ aInteger0(X117)
| aElementOf0(X117,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X113)))
| ~ aElementOf0(X113,xS) )
& ( szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X113)) = X113
| ~ aElementOf0(X113,xS) )
& ( aSet0(szAzrzSzezqlpdtcmdtrp0(sz00,X120))
| ~ aInteger0(X120)
| X120 = sz00
| ~ isPrime0(X120)
| aElementOf0(X119,xS) )
& ( aInteger0(X121)
| ~ aElementOf0(X121,szAzrzSzezqlpdtcmdtrp0(sz00,X120))
| ~ aInteger0(X120)
| X120 = sz00
| ~ isPrime0(X120)
| aElementOf0(X119,xS) )
& ( aInteger0(esk18_3(X119,X120,X121))
| ~ aElementOf0(X121,szAzrzSzezqlpdtcmdtrp0(sz00,X120))
| ~ aInteger0(X120)
| X120 = sz00
| ~ isPrime0(X120)
| aElementOf0(X119,xS) )
& ( sdtasdt0(X120,esk18_3(X119,X120,X121)) = sdtpldt0(X121,smndt0(sz00))
| ~ aElementOf0(X121,szAzrzSzezqlpdtcmdtrp0(sz00,X120))
| ~ aInteger0(X120)
| X120 = sz00
| ~ isPrime0(X120)
| aElementOf0(X119,xS) )
& ( aDivisorOf0(X120,sdtpldt0(X121,smndt0(sz00)))
| ~ aElementOf0(X121,szAzrzSzezqlpdtcmdtrp0(sz00,X120))
| ~ aInteger0(X120)
| X120 = sz00
| ~ isPrime0(X120)
| aElementOf0(X119,xS) )
& ( sdteqdtlpzmzozddtrp0(X121,sz00,X120)
| ~ aElementOf0(X121,szAzrzSzezqlpdtcmdtrp0(sz00,X120))
| ~ aInteger0(X120)
| X120 = sz00
| ~ isPrime0(X120)
| aElementOf0(X119,xS) )
& ( ~ aInteger0(X124)
| sdtasdt0(X120,X124) != sdtpldt0(X123,smndt0(sz00))
| ~ aInteger0(X123)
| aElementOf0(X123,szAzrzSzezqlpdtcmdtrp0(sz00,X120))
| ~ aInteger0(X120)
| X120 = sz00
| ~ isPrime0(X120)
| aElementOf0(X119,xS) )
& ( ~ aDivisorOf0(X120,sdtpldt0(X123,smndt0(sz00)))
| ~ aInteger0(X123)
| aElementOf0(X123,szAzrzSzezqlpdtcmdtrp0(sz00,X120))
| ~ aInteger0(X120)
| X120 = sz00
| ~ isPrime0(X120)
| aElementOf0(X119,xS) )
& ( ~ sdteqdtlpzmzozddtrp0(X123,sz00,X120)
| ~ aInteger0(X123)
| aElementOf0(X123,szAzrzSzezqlpdtcmdtrp0(sz00,X120))
| ~ aInteger0(X120)
| X120 = sz00
| ~ isPrime0(X120)
| aElementOf0(X119,xS) )
& ( szAzrzSzezqlpdtcmdtrp0(sz00,X120) != X119
| ~ aInteger0(X120)
| X120 = sz00
| ~ isPrime0(X120)
| aElementOf0(X119,xS) )
& xS = cS2043 ),
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)],[m__2046])])])])])]) ).
cnf(c_0_25,plain,
( smndt0(sz00) = sz00
| ~ aInteger0(smndt0(sz00)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21])]) ).
cnf(c_0_26,plain,
( aInteger0(smndt0(X1))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
( sdteqdtlpzmzozddtrp0(X1,X2,X3)
| X3 = sz00
| ~ aElementOf0(X1,X4)
| X4 != szAzrzSzezqlpdtcmdtrp0(X2,X3)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,hypothesis,
( aDivisorOf0(esk16_1(X1),sdtpldt0(X2,smndt0(sz00)))
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X1)))
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
smndt0(sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_21])]) ).
cnf(c_0_30,plain,
( X1 = sz00
| sdteqdtlpzmzozddtrp0(X2,X3,X1)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
| ~ aInteger0(X1)
| ~ aInteger0(X3) ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_31,hypothesis,
( szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X1)) = X1
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_32,hypothesis,
( aInteger0(esk16_1(X1))
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_33,hypothesis,
( esk16_1(X1) != sz00
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_34,hypothesis,
( aInteger0(X1)
| ~ aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2)))
| ~ aElementOf0(X2,xS) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_35,negated_conjecture,
~ ( ( ( ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(xn,X1) )
& aElementOf0(xn,sbsmnsldt0(xS)) )
=> ? [X1] :
( ( ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = xn ) )
| aDivisorOf0(X1,xn) )
& isPrime0(X1) ) )
& ( ? [X1] :
( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = xn )
& aDivisorOf0(X1,xn)
& isPrime0(X1) )
=> ( ? [X1] :
( aElementOf0(X1,xS)
& aElementOf0(xn,X1) )
| aElementOf0(xn,sbsmnsldt0(xS)) ) ) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_36,hypothesis,
( aDivisorOf0(esk16_1(X1),sdtpldt0(X2,sz00))
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X1)))
| ~ aElementOf0(X1,xS) ),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_37,hypothesis,
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2)))
| ~ sdteqdtlpzmzozddtrp0(X1,sz00,esk16_1(X2))
| ~ aInteger0(X1)
| ~ aElementOf0(X2,xS) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_38,hypothesis,
( sdteqdtlpzmzozddtrp0(X1,sz00,esk16_1(X2))
| ~ aElementOf0(X2,xS)
| ~ aElementOf0(X1,X2) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_21])]),c_0_32]),c_0_33]) ).
cnf(c_0_39,hypothesis,
( aInteger0(X1)
| ~ aElementOf0(X2,xS)
| ~ aElementOf0(X1,X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_31]) ).
cnf(c_0_40,hypothesis,
( X1 = sz00
| aElementOf0(X2,xS)
| szAzrzSzezqlpdtcmdtrp0(sz00,X1) != X2
| ~ aInteger0(X1)
| ~ isPrime0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_41,negated_conjecture,
! [X126,X127,X130] :
( ( aInteger0(esk20_0)
| aElementOf0(esk19_0,xS) )
& ( esk20_0 != sz00
| aElementOf0(esk19_0,xS) )
& ( aInteger0(esk21_0)
| aElementOf0(esk19_0,xS) )
& ( sdtasdt0(esk20_0,esk21_0) = xn
| aElementOf0(esk19_0,xS) )
& ( aDivisorOf0(esk20_0,xn)
| aElementOf0(esk19_0,xS) )
& ( isPrime0(esk20_0)
| aElementOf0(esk19_0,xS) )
& ( ~ aElementOf0(X130,xS)
| ~ aElementOf0(xn,X130)
| aElementOf0(esk19_0,xS) )
& ( ~ aElementOf0(xn,sbsmnsldt0(xS))
| aElementOf0(esk19_0,xS) )
& ( aInteger0(esk20_0)
| aElementOf0(xn,esk19_0) )
& ( esk20_0 != sz00
| aElementOf0(xn,esk19_0) )
& ( aInteger0(esk21_0)
| aElementOf0(xn,esk19_0) )
& ( sdtasdt0(esk20_0,esk21_0) = xn
| aElementOf0(xn,esk19_0) )
& ( aDivisorOf0(esk20_0,xn)
| aElementOf0(xn,esk19_0) )
& ( isPrime0(esk20_0)
| aElementOf0(xn,esk19_0) )
& ( ~ aElementOf0(X130,xS)
| ~ aElementOf0(xn,X130)
| aElementOf0(xn,esk19_0) )
& ( ~ aElementOf0(xn,sbsmnsldt0(xS))
| aElementOf0(xn,esk19_0) )
& ( aInteger0(esk20_0)
| aElementOf0(xn,sbsmnsldt0(xS)) )
& ( esk20_0 != sz00
| aElementOf0(xn,sbsmnsldt0(xS)) )
& ( aInteger0(esk21_0)
| aElementOf0(xn,sbsmnsldt0(xS)) )
& ( sdtasdt0(esk20_0,esk21_0) = xn
| aElementOf0(xn,sbsmnsldt0(xS)) )
& ( aDivisorOf0(esk20_0,xn)
| aElementOf0(xn,sbsmnsldt0(xS)) )
& ( isPrime0(esk20_0)
| aElementOf0(xn,sbsmnsldt0(xS)) )
& ( ~ aElementOf0(X130,xS)
| ~ aElementOf0(xn,X130)
| aElementOf0(xn,sbsmnsldt0(xS)) )
& ( ~ aElementOf0(xn,sbsmnsldt0(xS))
| aElementOf0(xn,sbsmnsldt0(xS)) )
& ( aInteger0(esk20_0)
| ~ aInteger0(X126)
| X126 = sz00
| ~ aInteger0(X127)
| sdtasdt0(X126,X127) != xn
| ~ isPrime0(X126) )
& ( esk20_0 != sz00
| ~ aInteger0(X126)
| X126 = sz00
| ~ aInteger0(X127)
| sdtasdt0(X126,X127) != xn
| ~ isPrime0(X126) )
& ( aInteger0(esk21_0)
| ~ aInteger0(X126)
| X126 = sz00
| ~ aInteger0(X127)
| sdtasdt0(X126,X127) != xn
| ~ isPrime0(X126) )
& ( sdtasdt0(esk20_0,esk21_0) = xn
| ~ aInteger0(X126)
| X126 = sz00
| ~ aInteger0(X127)
| sdtasdt0(X126,X127) != xn
| ~ isPrime0(X126) )
& ( aDivisorOf0(esk20_0,xn)
| ~ aInteger0(X126)
| X126 = sz00
| ~ aInteger0(X127)
| sdtasdt0(X126,X127) != xn
| ~ isPrime0(X126) )
& ( isPrime0(esk20_0)
| ~ aInteger0(X126)
| X126 = sz00
| ~ aInteger0(X127)
| sdtasdt0(X126,X127) != xn
| ~ isPrime0(X126) )
& ( ~ aElementOf0(X130,xS)
| ~ aElementOf0(xn,X130)
| ~ aInteger0(X126)
| X126 = sz00
| ~ aInteger0(X127)
| sdtasdt0(X126,X127) != xn
| ~ isPrime0(X126) )
& ( ~ aElementOf0(xn,sbsmnsldt0(xS))
| ~ aInteger0(X126)
| X126 = sz00
| ~ aInteger0(X127)
| sdtasdt0(X126,X127) != xn
| ~ isPrime0(X126) )
& ( aInteger0(esk20_0)
| ~ aDivisorOf0(X126,xn)
| ~ isPrime0(X126) )
& ( esk20_0 != sz00
| ~ aDivisorOf0(X126,xn)
| ~ isPrime0(X126) )
& ( aInteger0(esk21_0)
| ~ aDivisorOf0(X126,xn)
| ~ isPrime0(X126) )
& ( sdtasdt0(esk20_0,esk21_0) = xn
| ~ aDivisorOf0(X126,xn)
| ~ isPrime0(X126) )
& ( aDivisorOf0(esk20_0,xn)
| ~ aDivisorOf0(X126,xn)
| ~ isPrime0(X126) )
& ( isPrime0(esk20_0)
| ~ aDivisorOf0(X126,xn)
| ~ isPrime0(X126) )
& ( ~ aElementOf0(X130,xS)
| ~ aElementOf0(xn,X130)
| ~ aDivisorOf0(X126,xn)
| ~ isPrime0(X126) )
& ( ~ aElementOf0(xn,sbsmnsldt0(xS))
| ~ aDivisorOf0(X126,xn)
| ~ isPrime0(X126) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])])])]) ).
cnf(c_0_42,hypothesis,
( aDivisorOf0(esk16_1(X1),X2)
| ~ aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X1)))
| ~ aElementOf0(X1,xS) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_19]),c_0_34]) ).
cnf(c_0_43,hypothesis,
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2)))
| ~ aElementOf0(X2,xS)
| ~ aElementOf0(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_44,hypothesis,
( aElementOf0(X3,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2)))
| ~ aInteger0(X1)
| sdtasdt0(esk16_1(X2),X1) != sdtpldt0(X3,smndt0(sz00))
| ~ aInteger0(X3)
| ~ aElementOf0(X2,xS) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_45,hypothesis,
( X1 = sz00
| aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,X1),xS)
| ~ isPrime0(X1)
| ~ aInteger0(X1) ),
inference(er,[status(thm)],[c_0_40]) ).
cnf(c_0_46,hypothesis,
( isPrime0(esk16_1(X1))
| ~ aElementOf0(X1,xS) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_47,negated_conjecture,
( ~ aElementOf0(xn,sbsmnsldt0(xS))
| ~ aDivisorOf0(X1,xn)
| ~ isPrime0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_48,hypothesis,
( aDivisorOf0(esk16_1(X1),X2)
| ~ aElementOf0(X1,xS)
| ~ aElementOf0(X2,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_49,negated_conjecture,
( aElementOf0(xn,sbsmnsldt0(xS))
| ~ aElementOf0(X1,xS)
| ~ aElementOf0(xn,X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_50,hypothesis,
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2)))
| sdtasdt0(esk16_1(X2),X3) != sdtpldt0(X1,sz00)
| ~ aElementOf0(X2,xS)
| ~ aInteger0(X1)
| ~ aInteger0(X3) ),
inference(rw,[status(thm)],[c_0_44,c_0_29]) ).
cnf(c_0_51,hypothesis,
( aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X1)),xS)
| ~ aElementOf0(X1,xS) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_32]),c_0_33]) ).
fof(c_0_52,plain,
! [X26] :
( ( sdtasdt0(X26,sz00) = sz00
| ~ aInteger0(X26) )
& ( sz00 = sdtasdt0(sz00,X26)
| ~ aInteger0(X26) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])]) ).
fof(c_0_53,plain,
! [X38,X39] :
( ~ aInteger0(X38)
| ~ aInteger0(X39)
| X39 = sz00
| sdteqdtlpzmzozddtrp0(X38,X38,X39) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquModRef])]) ).
cnf(c_0_54,negated_conjecture,
( ~ aElementOf0(X1,xS)
| ~ aElementOf0(xn,X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_46]),c_0_49]) ).
cnf(c_0_55,hypothesis,
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2)))))
| sdtasdt0(esk16_1(szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2))),X3) != sdtpldt0(X1,sz00)
| ~ aElementOf0(X2,xS)
| ~ aInteger0(X1)
| ~ aInteger0(X3) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_56,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_52]) ).
cnf(c_0_57,plain,
( X2 = sz00
| sdteqdtlpzmzozddtrp0(X1,X1,X2)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_58,hypothesis,
aInteger0(xn),
inference(split_conjunct,[status(thm)],[m__2106]) ).
cnf(c_0_59,hypothesis,
( ~ aElementOf0(xn,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X1)))
| ~ aElementOf0(X1,xS) ),
inference(spm,[status(thm)],[c_0_54,c_0_51]) ).
cnf(c_0_60,hypothesis,
( aElementOf0(X1,szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2)))))
| sdtpldt0(X1,sz00) != sz00
| ~ aElementOf0(X2,xS)
| ~ aInteger0(esk16_1(szAzrzSzezqlpdtcmdtrp0(sz00,esk16_1(X2))))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_21])]) ).
fof(c_0_61,plain,
! [X28,X29] :
( ~ aInteger0(X28)
| ~ aInteger0(X29)
| sdtasdt0(X28,X29) != sz00
| X28 = sz00
| X29 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroDiv])]) ).
fof(c_0_62,plain,
! [X30,X31,X33,X34] :
( ( aInteger0(X31)
| ~ aDivisorOf0(X31,X30)
| ~ aInteger0(X30) )
& ( X31 != sz00
| ~ aDivisorOf0(X31,X30)
| ~ aInteger0(X30) )
& ( aInteger0(esk1_2(X30,X31))
| ~ aDivisorOf0(X31,X30)
| ~ aInteger0(X30) )
& ( sdtasdt0(X31,esk1_2(X30,X31)) = X30
| ~ aDivisorOf0(X31,X30)
| ~ aInteger0(X30) )
& ( ~ aInteger0(X33)
| X33 = sz00
| ~ aInteger0(X34)
| sdtasdt0(X33,X34) != X30
| aDivisorOf0(X33,X30)
| ~ aInteger0(X30) ) ),
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)],[mDivisor])])])])])]) ).
fof(c_0_63,plain,
! [X35,X36,X37] :
( ( ~ sdteqdtlpzmzozddtrp0(X35,X36,X37)
| aDivisorOf0(X37,sdtpldt0(X35,smndt0(X36)))
| ~ aInteger0(X35)
| ~ aInteger0(X36)
| ~ aInteger0(X37)
| X37 = sz00 )
& ( ~ aDivisorOf0(X37,sdtpldt0(X35,smndt0(X36)))
| sdteqdtlpzmzozddtrp0(X35,X36,X37)
| ~ aInteger0(X35)
| ~ aInteger0(X36)
| ~ aInteger0(X37)
| X37 = sz00 ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mEquMod])])]) ).
cnf(c_0_64,hypothesis,
( xn = sz00
| sdteqdtlpzmzozddtrp0(X1,X1,xn)
| ~ aInteger0(X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_65,hypothesis,
( sdtpldt0(xn,sz00) != sz00
| ~ aElementOf0(X1,xS) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_58])]),c_0_32]),c_0_51]) ).
cnf(c_0_66,negated_conjecture,
( isPrime0(esk20_0)
| aElementOf0(esk19_0,xS) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_67,negated_conjecture,
( aInteger0(esk20_0)
| aElementOf0(esk19_0,xS) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_68,negated_conjecture,
( aElementOf0(esk19_0,xS)
| esk20_0 != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_69,plain,
( X1 = sz00
| X2 = sz00
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_70,plain,
( sdtasdt0(X1,esk1_2(X2,X1)) = X2
| ~ aDivisorOf0(X1,X2)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_71,plain,
( aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2)))
| X3 = sz00
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_72,hypothesis,
( xn = sz00
| sdteqdtlpzmzozddtrp0(sz00,sz00,xn) ),
inference(spm,[status(thm)],[c_0_64,c_0_21]) ).
cnf(c_0_73,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_29]),c_0_21])]) ).
cnf(c_0_74,hypothesis,
( xn != sz00
| ~ aElementOf0(X1,xS) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_19]),c_0_58])]) ).
cnf(c_0_75,negated_conjecture,
( aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,esk20_0),xS)
| aElementOf0(esk19_0,xS) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_66]),c_0_67]),c_0_68]) ).
cnf(c_0_76,plain,
( esk1_2(sz00,X1) = sz00
| X1 = sz00
| ~ aDivisorOf0(X1,sz00)
| ~ aInteger0(esk1_2(sz00,X1))
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70])]),c_0_21])]) ).
cnf(c_0_77,plain,
( aInteger0(esk1_2(X1,X2))
| ~ aDivisorOf0(X2,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
cnf(c_0_78,hypothesis,
( xn = sz00
| aDivisorOf0(xn,sz00) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_29]),c_0_73]),c_0_58]),c_0_21])]) ).
cnf(c_0_79,negated_conjecture,
xn != sz00,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_74]) ).
fof(c_0_80,plain,
! [X23,X24,X25] :
( ( sdtasdt0(X23,sdtpldt0(X24,X25)) = sdtpldt0(sdtasdt0(X23,X24),sdtasdt0(X23,X25))
| ~ aInteger0(X23)
| ~ aInteger0(X24)
| ~ aInteger0(X25) )
& ( sdtasdt0(sdtpldt0(X23,X24),X25) = sdtpldt0(sdtasdt0(X23,X25),sdtasdt0(X24,X25))
| ~ aInteger0(X23)
| ~ aInteger0(X24)
| ~ aInteger0(X25) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDistrib])])]) ).
fof(c_0_81,plain,
! [X22] :
( ( sdtasdt0(X22,sz10) = X22
| ~ aInteger0(X22) )
& ( X22 = sdtasdt0(sz10,X22)
| ~ aInteger0(X22) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulOne])])]) ).
cnf(c_0_82,plain,
( esk1_2(sz00,X1) = sz00
| X1 = sz00
| ~ aDivisorOf0(X1,sz00)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_21])]) ).
cnf(c_0_83,hypothesis,
aDivisorOf0(xn,sz00),
inference(sr,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_84,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_85,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_81]) ).
cnf(c_0_86,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
cnf(c_0_87,hypothesis,
esk1_2(sz00,xn) = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_83]),c_0_58])]),c_0_79]) ).
cnf(c_0_88,plain,
( sdtpldt0(sdtasdt0(X1,X2),X1) = sdtasdt0(X1,sdtpldt0(X2,sz10))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86])]) ).
cnf(c_0_89,hypothesis,
sdtasdt0(xn,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_87]),c_0_83]),c_0_21])]) ).
cnf(c_0_90,hypothesis,
sdtasdt0(xn,sdtpldt0(sz00,sz10)) = sdtpldt0(sz00,xn),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_21]),c_0_58])]) ).
cnf(c_0_91,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_92,hypothesis,
sdtpldt0(sz00,xn) = sdtasdt0(xn,sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_86])]) ).
cnf(c_0_93,plain,
( sdtpldt0(X1,sdtasdt0(X1,X2)) = sdtasdt0(X1,sdtpldt0(sz10,X2))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_86])]) ).
fof(c_0_94,plain,
! [X13,X14] :
( ~ aInteger0(X13)
| ~ aInteger0(X14)
| sdtpldt0(X13,X14) = sdtpldt0(X14,X13) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_95,hypothesis,
sdtasdt0(xn,sz10) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_58])]) ).
cnf(c_0_96,plain,
( sdteqdtlpzmzozddtrp0(X2,X3,X1)
| X1 = sz00
| ~ aDivisorOf0(X1,sdtpldt0(X2,smndt0(X3)))
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_63]) ).
cnf(c_0_97,hypothesis,
sdtasdt0(xn,sdtpldt0(sz10,sz00)) = sdtpldt0(xn,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_89]),c_0_21]),c_0_58])]) ).
cnf(c_0_98,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_99,hypothesis,
sdtasdt0(xn,sdtpldt0(sz00,sz10)) = xn,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_90,c_0_92]),c_0_95]) ).
cnf(c_0_100,plain,
( X1 = sz00
| sdteqdtlpzmzozddtrp0(X2,sz00,X1)
| ~ aDivisorOf0(X1,sdtpldt0(X2,sz00))
| ~ aInteger0(X2)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_29]),c_0_21])]) ).
cnf(c_0_101,hypothesis,
sdtpldt0(xn,sz00) = xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_98]),c_0_99]),c_0_21]),c_0_86])]) ).
cnf(c_0_102,negated_conjecture,
( aElementOf0(xn,esk19_0)
| esk20_0 != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_103,negated_conjecture,
( isPrime0(esk20_0)
| aElementOf0(xn,esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_104,negated_conjecture,
( aInteger0(esk20_0)
| aElementOf0(xn,esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_105,plain,
( aElementOf0(X1,X4)
| X3 = sz00
| ~ aInteger0(X1)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| X4 != szAzrzSzezqlpdtcmdtrp0(X2,X3)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_106,hypothesis,
( X1 = sz00
| sdteqdtlpzmzozddtrp0(xn,sz00,X1)
| ~ aDivisorOf0(X1,xn)
| ~ aInteger0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_58])]) ).
cnf(c_0_107,negated_conjecture,
( aDivisorOf0(esk20_0,xn)
| aElementOf0(esk19_0,xS) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_108,negated_conjecture,
esk20_0 != sz00,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_68]),c_0_102]) ).
cnf(c_0_109,negated_conjecture,
( aElementOf0(esk19_0,xS)
| ~ aElementOf0(X1,xS)
| ~ aElementOf0(xn,X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_110,negated_conjecture,
( aDivisorOf0(esk20_0,xn)
| aElementOf0(xn,esk19_0) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_111,negated_conjecture,
( aElementOf0(xn,esk19_0)
| ~ aElementOf0(X1,xS)
| ~ aElementOf0(xn,X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_112,negated_conjecture,
( aElementOf0(szAzrzSzezqlpdtcmdtrp0(sz00,esk20_0),xS)
| aElementOf0(xn,esk19_0) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_103]),c_0_104]),c_0_102]) ).
cnf(c_0_113,plain,
( X1 = sz00
| aElementOf0(X2,szAzrzSzezqlpdtcmdtrp0(X3,X1))
| ~ sdteqdtlpzmzozddtrp0(X2,X3,X1)
| ~ aInteger0(X1)
| ~ aInteger0(X3)
| ~ aInteger0(X2) ),
inference(er,[status(thm)],[c_0_105]) ).
cnf(c_0_114,negated_conjecture,
( aElementOf0(esk19_0,xS)
| sdteqdtlpzmzozddtrp0(xn,sz00,esk20_0) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108]),c_0_67]) ).
cnf(c_0_115,negated_conjecture,
( aElementOf0(esk19_0,xS)
| ~ aElementOf0(xn,szAzrzSzezqlpdtcmdtrp0(sz00,esk20_0)) ),
inference(spm,[status(thm)],[c_0_109,c_0_75]) ).
cnf(c_0_116,negated_conjecture,
( aElementOf0(xn,esk19_0)
| sdteqdtlpzmzozddtrp0(xn,sz00,esk20_0) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_110]),c_0_108]),c_0_104]) ).
cnf(c_0_117,negated_conjecture,
( aElementOf0(xn,esk19_0)
| ~ aElementOf0(xn,szAzrzSzezqlpdtcmdtrp0(sz00,esk20_0)) ),
inference(spm,[status(thm)],[c_0_111,c_0_112]) ).
cnf(c_0_118,negated_conjecture,
aElementOf0(esk19_0,xS),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_114]),c_0_21]),c_0_58])]),c_0_108]),c_0_67]),c_0_115]) ).
cnf(c_0_119,negated_conjecture,
aElementOf0(xn,esk19_0),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_116]),c_0_21]),c_0_58])]),c_0_108]),c_0_104]),c_0_117]) ).
cnf(c_0_120,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_118]),c_0_119])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM447+5 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n006.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
% 0.19/0.34 % CPULimit : 300
% 0.19/0.34 % WCLimit : 300
% 0.19/0.34 % DateTime : Fri Aug 25 15:29:22 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 6.66/6.71 % Version : CSE_E---1.5
% 6.66/6.71 % Problem : theBenchmark.p
% 6.66/6.71 % Proof found
% 6.66/6.71 % SZS status Theorem for theBenchmark.p
% 6.66/6.71 % SZS output start Proof
% See solution above
% 6.66/6.72 % Total time : 6.151000 s
% 6.66/6.72 % SZS output end Proof
% 6.66/6.72 % Total time : 6.156000 s
%------------------------------------------------------------------------------