TSTP Solution File: RNG109+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : RNG109+1 : 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 : n013.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 13:49:13 EDT 2023
% Result : Theorem 4.53s 4.62s
% Output : CNFRefutation 4.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 73
% Syntax : Number of formulae : 220 ( 46 unt; 44 typ; 0 def)
% Number of atoms : 644 ( 151 equ)
% Maximal formula atoms : 52 ( 3 avg)
% Number of connectives : 805 ( 337 ~; 352 |; 82 &)
% ( 9 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 80 ( 38 >; 42 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 33 ( 33 usr; 6 con; 0-4 aty)
% Number of variables : 255 ( 0 sgn; 108 !; 8 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
aElement0: $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,
aSet0: $i > $o ).
tff(decl_29,type,
aElementOf0: ( $i * $i ) > $o ).
tff(decl_30,type,
sdtpldt1: ( $i * $i ) > $i ).
tff(decl_31,type,
sdtasasdt0: ( $i * $i ) > $i ).
tff(decl_32,type,
aIdeal0: $i > $o ).
tff(decl_33,type,
sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).
tff(decl_34,type,
aNaturalNumber0: $i > $o ).
tff(decl_35,type,
sbrdtbr0: $i > $i ).
tff(decl_36,type,
iLess0: ( $i * $i ) > $o ).
tff(decl_37,type,
doDivides0: ( $i * $i ) > $o ).
tff(decl_38,type,
aDivisorOf0: ( $i * $i ) > $o ).
tff(decl_39,type,
aGcdOfAnd0: ( $i * $i * $i ) > $o ).
tff(decl_40,type,
misRelativelyPrime0: ( $i * $i ) > $o ).
tff(decl_41,type,
slsdtgt0: $i > $i ).
tff(decl_42,type,
xa: $i ).
tff(decl_43,type,
xb: $i ).
tff(decl_44,type,
xc: $i ).
tff(decl_45,type,
xI: $i ).
tff(decl_46,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_47,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_48,type,
esk3_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_49,type,
esk4_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_50,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_51,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_52,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_53,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_54,type,
esk9_1: $i > $i ).
tff(decl_55,type,
esk10_1: $i > $i ).
tff(decl_56,type,
esk11_1: $i > $i ).
tff(decl_57,type,
esk12_2: ( $i * $i ) > $i ).
tff(decl_58,type,
esk13_4: ( $i * $i * $i * $i ) > $i ).
tff(decl_59,type,
esk14_2: ( $i * $i ) > $i ).
tff(decl_60,type,
esk15_2: ( $i * $i ) > $i ).
tff(decl_61,type,
esk16_2: ( $i * $i ) > $i ).
tff(decl_62,type,
esk17_3: ( $i * $i * $i ) > $i ).
tff(decl_63,type,
esk18_3: ( $i * $i * $i ) > $i ).
tff(decl_64,type,
esk19_2: ( $i * $i ) > $i ).
tff(decl_65,type,
esk20_2: ( $i * $i ) > $i ).
fof(mDivision,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2)
& X2 != sz00 )
=> ? [X3,X4] :
( aElement0(X3)
& aElement0(X4)
& X1 = sdtpldt0(sdtasdt0(X3,X2),X4)
& ( X4 != sz00
=> iLess0(sbrdtbr0(X4),sbrdtbr0(X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivision) ).
fof(mMulUnit,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulUnit) ).
fof(mSortsC_01,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(mUnNeZr,axiom,
sz10 != sz00,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mUnNeZr) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aElement0(X3) )
=> sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(mAddZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(mAddInvr,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtpldt0(X1,smndt0(X1)) = sz00
& sz00 = sdtpldt0(smndt0(X1),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddInvr) ).
fof(mSortsC,axiom,
aElement0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(mSortsU,axiom,
! [X1] :
( aElement0(X1)
=> aElement0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsU) ).
fof(mDefMod,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aIdeal0(X3) )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aElementOf0(sdtpldt0(X1,smndt0(X2)),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefMod) ).
fof(mDefPrIdeal,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( X2 = slsdtgt0(X1)
<=> ( aSet0(X2)
& ! [X3] :
( aElementOf0(X3,X2)
<=> ? [X4] :
( aElement0(X4)
& sdtasdt0(X1,X4) = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefPrIdeal) ).
fof(mPrIdeal,axiom,
! [X1] :
( aElement0(X1)
=> aIdeal0(slsdtgt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mPrIdeal) ).
fof(mMulAsso,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aElement0(X3) )
=> sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(m__2203,hypothesis,
( aElementOf0(sz00,slsdtgt0(xa))
& aElementOf0(xa,slsdtgt0(xa))
& aElementOf0(sz00,slsdtgt0(xb))
& aElementOf0(xb,slsdtgt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2203) ).
fof(m__2091,hypothesis,
( aElement0(xa)
& aElement0(xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2091) ).
fof(mMulZero,axiom,
! [X1] :
( aElement0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
fof(mSortsB,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> aElement0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(mAMDistr,axiom,
! [X1,X2,X3] :
( ( aElement0(X1)
& aElement0(X2)
& aElement0(X3) )
=> ( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
& sdtasdt0(sdtpldt0(X2,X3),X1) = sdtpldt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
fof(mDefSSum,axiom,
! [X1,X2] :
( ( aSet0(X1)
& aSet0(X2) )
=> ! [X3] :
( X3 = sdtpldt1(X1,X2)
<=> ( aSet0(X3)
& ! [X4] :
( aElementOf0(X4,X3)
<=> ? [X5,X6] :
( aElementOf0(X5,X1)
& aElementOf0(X6,X2)
& sdtpldt0(X5,X6) = X4 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSSum) ).
fof(mDefIdeal,axiom,
! [X1] :
( aIdeal0(X1)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> ( ! [X3] :
( aElementOf0(X3,X1)
=> aElementOf0(sdtpldt0(X2,X3),X1) )
& ! [X3] :
( aElement0(X3)
=> aElementOf0(sdtasdt0(X3,X2),X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
fof(mDefGCD,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ! [X3] :
( aGcdOfAnd0(X3,X1,X2)
<=> ( aDivisorOf0(X3,X1)
& aDivisorOf0(X3,X2)
& ! [X4] :
( ( aDivisorOf0(X4,X1)
& aDivisorOf0(X4,X2) )
=> doDivides0(X4,X3) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefGCD) ).
fof(mDefDvs,axiom,
! [X1] :
( aElement0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( aElement0(X2)
& doDivides0(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDvs) ).
fof(m__2129,hypothesis,
aGcdOfAnd0(xc,xa,xb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2129) ).
fof(m__,conjecture,
? [X1] :
( aElementOf0(X1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& X1 != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aElement0(X1)
& aElement0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aElement0(X3)
& sdtasdt0(X1,X3) = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
fof(m__2110,hypothesis,
( xa != sz00
| xb != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2110) ).
fof(c_0_29,plain,
! [X82,X83] :
( ( aElement0(esk14_2(X82,X83))
| ~ aElement0(X82)
| ~ aElement0(X83)
| X83 = sz00 )
& ( aElement0(esk15_2(X82,X83))
| ~ aElement0(X82)
| ~ aElement0(X83)
| X83 = sz00 )
& ( X82 = sdtpldt0(sdtasdt0(esk14_2(X82,X83),X83),esk15_2(X82,X83))
| ~ aElement0(X82)
| ~ aElement0(X83)
| X83 = sz00 )
& ( esk15_2(X82,X83) = sz00
| iLess0(sbrdtbr0(esk15_2(X82,X83)),sbrdtbr0(X83))
| ~ aElement0(X82)
| ~ aElement0(X83)
| X83 = sz00 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivision])])])]) ).
fof(c_0_30,plain,
! [X24] :
( ( sdtasdt0(X24,sz10) = X24
| ~ aElement0(X24) )
& ( X24 = sdtasdt0(sz10,X24)
| ~ aElement0(X24) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulUnit])])]) ).
cnf(c_0_31,plain,
( X1 = sdtpldt0(sdtasdt0(esk14_2(X1,X2),X2),esk15_2(X1,X2))
| X2 = sz00
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_32,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_33,plain,
aElement0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_34,plain,
sz10 != sz00,
inference(split_conjunct,[status(thm)],[mUnNeZr]) ).
fof(c_0_35,plain,
! [X12,X13] :
( ~ aElement0(X12)
| ~ aElement0(X13)
| sdtpldt0(X12,X13) = sdtpldt0(X13,X12) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])]) ).
cnf(c_0_36,plain,
( sdtpldt0(esk14_2(X1,sz10),esk15_2(X1,sz10)) = X1
| ~ aElement0(esk14_2(X1,sz10))
| ~ aElement0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33])]),c_0_34]) ).
cnf(c_0_37,plain,
( aElement0(esk14_2(X1,X2))
| X2 = sz00
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,plain,
( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_39,plain,
( sdtpldt0(esk14_2(X1,sz10),esk15_2(X1,sz10)) = X1
| ~ aElement0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_33])]),c_0_34]) ).
cnf(c_0_40,plain,
( sdtpldt0(esk15_2(X1,sz10),esk14_2(X1,sz10)) = X1
| ~ aElement0(esk15_2(X1,sz10))
| ~ aElement0(esk14_2(X1,sz10))
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_41,plain,
( aElement0(esk15_2(X1,X2))
| X2 = sz00
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_42,plain,
! [X14,X15,X16] :
( ~ aElement0(X14)
| ~ aElement0(X15)
| ~ aElement0(X16)
| sdtpldt0(sdtpldt0(X14,X15),X16) = sdtpldt0(X14,sdtpldt0(X15,X16)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])]) ).
cnf(c_0_43,plain,
( sdtpldt0(esk15_2(X1,sz10),esk14_2(X1,sz10)) = X1
| ~ aElement0(esk14_2(X1,sz10))
| ~ aElement0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_33])]),c_0_34]) ).
fof(c_0_44,plain,
! [X17] :
( ( sdtpldt0(X17,sz00) = X17
| ~ aElement0(X17) )
& ( X17 = sdtpldt0(sz00,X17)
| ~ aElement0(X17) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])]) ).
fof(c_0_45,plain,
! [X18] :
( ( sdtpldt0(X18,smndt0(X18)) = sz00
| ~ aElement0(X18) )
& ( sz00 = sdtpldt0(smndt0(X18),X18)
| ~ aElement0(X18) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddInvr])])]) ).
cnf(c_0_46,plain,
( sdtpldt0(sdtpldt0(X1,X2),X3) = sdtpldt0(X1,sdtpldt0(X2,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_47,plain,
( sdtpldt0(esk15_2(X1,sz10),esk14_2(X1,sz10)) = X1
| ~ aElement0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_37]),c_0_33])]),c_0_34]) ).
cnf(c_0_48,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_49,plain,
( sz00 = sdtpldt0(smndt0(X1),X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_50,plain,
aElement0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_51,plain,
! [X7] :
( ~ aElement0(X7)
| aElement0(smndt0(X7)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsU])]) ).
cnf(c_0_52,plain,
( sdtpldt0(esk15_2(X1,sz10),sdtpldt0(esk14_2(X1,sz10),X2)) = sdtpldt0(X1,X2)
| ~ aElement0(esk14_2(X1,sz10))
| ~ aElement0(esk15_2(X1,sz10))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
fof(c_0_53,plain,
! [X72,X73,X74] :
( ( ~ sdteqdtlpzmzozddtrp0(X72,X73,X74)
| aElementOf0(sdtpldt0(X72,smndt0(X73)),X74)
| ~ aElement0(X72)
| ~ aElement0(X73)
| ~ aIdeal0(X74) )
& ( ~ aElementOf0(sdtpldt0(X72,smndt0(X73)),X74)
| sdteqdtlpzmzozddtrp0(X72,X73,X74)
| ~ aElement0(X72)
| ~ aElement0(X73)
| ~ aIdeal0(X74) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefMod])])]) ).
cnf(c_0_54,plain,
( smndt0(sz00) = sz00
| ~ aElement0(smndt0(sz00)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50])]) ).
cnf(c_0_55,plain,
( aElement0(smndt0(X1))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_51]) ).
fof(c_0_56,plain,
! [X100,X101,X102,X104,X105,X106,X108] :
( ( aSet0(X101)
| X101 != slsdtgt0(X100)
| ~ aElement0(X100) )
& ( aElement0(esk18_3(X100,X101,X102))
| ~ aElementOf0(X102,X101)
| X101 != slsdtgt0(X100)
| ~ aElement0(X100) )
& ( sdtasdt0(X100,esk18_3(X100,X101,X102)) = X102
| ~ aElementOf0(X102,X101)
| X101 != slsdtgt0(X100)
| ~ aElement0(X100) )
& ( ~ aElement0(X105)
| sdtasdt0(X100,X105) != X104
| aElementOf0(X104,X101)
| X101 != slsdtgt0(X100)
| ~ aElement0(X100) )
& ( ~ aElementOf0(esk19_2(X100,X106),X106)
| ~ aElement0(X108)
| sdtasdt0(X100,X108) != esk19_2(X100,X106)
| ~ aSet0(X106)
| X106 = slsdtgt0(X100)
| ~ aElement0(X100) )
& ( aElement0(esk20_2(X100,X106))
| aElementOf0(esk19_2(X100,X106),X106)
| ~ aSet0(X106)
| X106 = slsdtgt0(X100)
| ~ aElement0(X100) )
& ( sdtasdt0(X100,esk20_2(X100,X106)) = esk19_2(X100,X106)
| aElementOf0(esk19_2(X100,X106),X106)
| ~ aSet0(X106)
| X106 = slsdtgt0(X100)
| ~ aElement0(X100) ) ),
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)],[mDefPrIdeal])])])])])]) ).
cnf(c_0_57,plain,
( sdtpldt0(esk15_2(X1,sz10),sdtpldt0(esk14_2(X1,sz10),X2)) = sdtpldt0(X1,X2)
| ~ aElement0(esk15_2(X1,sz10))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_37]),c_0_33])]),c_0_34]) ).
cnf(c_0_58,plain,
( sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aElementOf0(sdtpldt0(X1,smndt0(X2)),X3)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_59,plain,
smndt0(sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_50])]) ).
cnf(c_0_60,plain,
( aElementOf0(X3,X4)
| ~ aElement0(X1)
| sdtasdt0(X2,X1) != X3
| X4 != slsdtgt0(X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_61,plain,
( sdtpldt0(esk15_2(X1,sz10),sdtpldt0(esk14_2(X1,sz10),X2)) = sdtpldt0(X1,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_41]),c_0_33])]),c_0_34]) ).
cnf(c_0_62,plain,
( sdteqdtlpzmzozddtrp0(X1,sz00,X2)
| ~ aIdeal0(X2)
| ~ aElementOf0(sdtpldt0(X1,sz00),X2)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_50])]) ).
cnf(c_0_63,plain,
( aElementOf0(sdtasdt0(X1,X2),slsdtgt0(X1))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_60])]) ).
cnf(c_0_64,plain,
( X1 = sdtasdt0(sz10,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_65,plain,
( X1 = sdtpldt0(sz00,X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_66,plain,
( sdtpldt0(esk15_2(X1,sz10),esk14_2(X1,sz10)) = sdtpldt0(X1,sz00)
| ~ aElement0(esk14_2(X1,sz10))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_48]),c_0_50])]) ).
cnf(c_0_67,plain,
( sdtasdt0(X1,esk18_3(X1,X2,X3)) = X3
| ~ aElementOf0(X3,X2)
| X2 != slsdtgt0(X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_68,plain,
( aElement0(esk18_3(X1,X2,X3))
| ~ aElementOf0(X3,X2)
| X2 != slsdtgt0(X1)
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_69,plain,
( sdteqdtlpzmzozddtrp0(sz00,sz00,X1)
| ~ aIdeal0(X1)
| ~ aElementOf0(sz00,X1) ),
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_62,c_0_49]),c_0_59]),c_0_59]),c_0_50]),c_0_50])]) ).
cnf(c_0_70,plain,
( aElementOf0(X1,slsdtgt0(sz10))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_33])]) ).
fof(c_0_71,plain,
! [X110] :
( ~ aElement0(X110)
| aIdeal0(slsdtgt0(X110)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPrIdeal])]) ).
cnf(c_0_72,plain,
( sdtpldt0(sz00,sdtpldt0(X1,X2)) = sdtpldt0(X1,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_65]),c_0_50])]) ).
cnf(c_0_73,plain,
( sdtpldt0(esk15_2(X1,sz10),esk14_2(X1,sz10)) = sdtpldt0(X1,sz00)
| ~ aElement0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_37]),c_0_33])]),c_0_34]) ).
fof(c_0_74,plain,
! [X21,X22,X23] :
( ~ aElement0(X21)
| ~ aElement0(X22)
| ~ aElement0(X23)
| sdtasdt0(sdtasdt0(X21,X22),X23) = sdtasdt0(X21,sdtasdt0(X22,X23)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])]) ).
fof(c_0_75,plain,
! [X10,X11] :
( ~ aElement0(X10)
| ~ aElement0(X11)
| aElement0(sdtasdt0(X10,X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
cnf(c_0_76,plain,
( sdtasdt0(X1,esk18_3(X1,slsdtgt0(X1),X2)) = X2
| ~ aElementOf0(X2,slsdtgt0(X1))
| ~ aElement0(X1) ),
inference(er,[status(thm)],[c_0_67]) ).
cnf(c_0_77,hypothesis,
aElementOf0(xa,slsdtgt0(xa)),
inference(split_conjunct,[status(thm)],[m__2203]) ).
cnf(c_0_78,hypothesis,
aElement0(xa),
inference(split_conjunct,[status(thm)],[m__2091]) ).
cnf(c_0_79,plain,
( aElement0(esk18_3(X1,slsdtgt0(X1),X2))
| ~ aElementOf0(X2,slsdtgt0(X1))
| ~ aElement0(X1) ),
inference(er,[status(thm)],[c_0_68]) ).
fof(c_0_80,plain,
! [X29] :
( ( sdtasdt0(X29,sz00) = sz00
| ~ aElement0(X29) )
& ( sz00 = sdtasdt0(sz00,X29)
| ~ aElement0(X29) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulZero])])]) ).
cnf(c_0_81,plain,
( sdteqdtlpzmzozddtrp0(sz00,sz00,slsdtgt0(sz10))
| ~ aIdeal0(slsdtgt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_50])]) ).
cnf(c_0_82,plain,
( aIdeal0(slsdtgt0(X1))
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_71]) ).
fof(c_0_83,plain,
! [X8,X9] :
( ~ aElement0(X8)
| ~ aElement0(X9)
| aElement0(sdtpldt0(X8,X9)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).
cnf(c_0_84,plain,
( sdtpldt0(sz00,sdtpldt0(X1,sz00)) = sdtpldt0(X1,sz00)
| ~ aElement0(esk14_2(X1,sz10))
| ~ aElement0(esk15_2(X1,sz10))
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
fof(c_0_85,plain,
! [X25,X26,X27] :
( ( sdtasdt0(X25,sdtpldt0(X26,X27)) = sdtpldt0(sdtasdt0(X25,X26),sdtasdt0(X25,X27))
| ~ aElement0(X25)
| ~ aElement0(X26)
| ~ aElement0(X27) )
& ( sdtasdt0(sdtpldt0(X26,X27),X25) = sdtpldt0(sdtasdt0(X26,X25),sdtasdt0(X27,X25))
| ~ aElement0(X25)
| ~ aElement0(X26)
| ~ aElement0(X27) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAMDistr])])]) ).
cnf(c_0_86,plain,
( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_74]) ).
cnf(c_0_87,plain,
( aElement0(sdtasdt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_88,hypothesis,
sdtasdt0(xa,esk18_3(xa,slsdtgt0(xa),xa)) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78])]) ).
cnf(c_0_89,hypothesis,
aElement0(esk18_3(xa,slsdtgt0(xa),xa)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_77]),c_0_78])]) ).
cnf(c_0_90,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aElement0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_80]) ).
cnf(c_0_91,plain,
( aElementOf0(sdtpldt0(X1,smndt0(X2)),X3)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aIdeal0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_92,plain,
sdteqdtlpzmzozddtrp0(sz00,sz00,slsdtgt0(sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_33])]) ).
cnf(c_0_93,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_59]),c_0_50])]) ).
fof(c_0_94,plain,
! [X38,X39,X40,X41,X44,X45,X46,X47,X49,X50] :
( ( aSet0(X40)
| X40 != sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(X39) )
& ( aElementOf0(esk3_4(X38,X39,X40,X41),X38)
| ~ aElementOf0(X41,X40)
| X40 != sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(X39) )
& ( aElementOf0(esk4_4(X38,X39,X40,X41),X39)
| ~ aElementOf0(X41,X40)
| X40 != sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(X39) )
& ( sdtpldt0(esk3_4(X38,X39,X40,X41),esk4_4(X38,X39,X40,X41)) = X41
| ~ aElementOf0(X41,X40)
| X40 != sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(X39) )
& ( ~ aElementOf0(X45,X38)
| ~ aElementOf0(X46,X39)
| sdtpldt0(X45,X46) != X44
| aElementOf0(X44,X40)
| X40 != sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(X39) )
& ( ~ aElementOf0(esk5_3(X38,X39,X47),X47)
| ~ aElementOf0(X49,X38)
| ~ aElementOf0(X50,X39)
| sdtpldt0(X49,X50) != esk5_3(X38,X39,X47)
| ~ aSet0(X47)
| X47 = sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(X39) )
& ( aElementOf0(esk6_3(X38,X39,X47),X38)
| aElementOf0(esk5_3(X38,X39,X47),X47)
| ~ aSet0(X47)
| X47 = sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(X39) )
& ( aElementOf0(esk7_3(X38,X39,X47),X39)
| aElementOf0(esk5_3(X38,X39,X47),X47)
| ~ aSet0(X47)
| X47 = sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(X39) )
& ( sdtpldt0(esk6_3(X38,X39,X47),esk7_3(X38,X39,X47)) = esk5_3(X38,X39,X47)
| aElementOf0(esk5_3(X38,X39,X47),X47)
| ~ aSet0(X47)
| X47 = sdtpldt1(X38,X39)
| ~ aSet0(X38)
| ~ aSet0(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)],[mDefSSum])])])])])]) ).
cnf(c_0_95,plain,
( aElement0(sdtpldt0(X1,X2))
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_83]) ).
cnf(c_0_96,plain,
( sdtpldt0(sz00,sdtpldt0(X1,sz00)) = sdtpldt0(X1,sz00)
| ~ aElement0(esk15_2(X1,sz10))
| ~ aElement0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_37]),c_0_33])]),c_0_34]) ).
cnf(c_0_97,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
| ~ aElement0(X1)
| ~ aElement0(X2)
| ~ aElement0(X3) ),
inference(split_conjunct,[status(thm)],[c_0_85]) ).
cnf(c_0_98,plain,
( sdtasdt0(X1,sdtasdt0(X2,sz10)) = sdtasdt0(X1,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_86]),c_0_33])]),c_0_87]) ).
cnf(c_0_99,hypothesis,
( sdtasdt0(xa,sdtasdt0(esk18_3(xa,slsdtgt0(xa),xa),X1)) = sdtasdt0(xa,X1)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_88]),c_0_89]),c_0_78])]) ).
cnf(c_0_100,plain,
( sdtasdt0(X1,sdtasdt0(X2,sz00)) = sz00
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_86]),c_0_50])]),c_0_87]) ).
cnf(c_0_101,plain,
( aElementOf0(sz00,slsdtgt0(sz10))
| ~ aIdeal0(slsdtgt0(sz10)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_59]),c_0_93]),c_0_50])]) ).
fof(c_0_102,plain,
! [X60,X61,X62,X63,X64] :
( ( aSet0(X60)
| ~ aIdeal0(X60) )
& ( ~ aElementOf0(X62,X60)
| aElementOf0(sdtpldt0(X61,X62),X60)
| ~ aElementOf0(X61,X60)
| ~ aIdeal0(X60) )
& ( ~ aElement0(X63)
| aElementOf0(sdtasdt0(X63,X61),X60)
| ~ aElementOf0(X61,X60)
| ~ aIdeal0(X60) )
& ( aElementOf0(esk9_1(X64),X64)
| ~ aSet0(X64)
| aIdeal0(X64) )
& ( aElement0(esk11_1(X64))
| aElementOf0(esk10_1(X64),X64)
| ~ aSet0(X64)
| aIdeal0(X64) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X64),esk9_1(X64)),X64)
| aElementOf0(esk10_1(X64),X64)
| ~ aSet0(X64)
| aIdeal0(X64) )
& ( aElement0(esk11_1(X64))
| ~ aElementOf0(sdtpldt0(esk9_1(X64),esk10_1(X64)),X64)
| ~ aSet0(X64)
| aIdeal0(X64) )
& ( ~ aElementOf0(sdtasdt0(esk11_1(X64),esk9_1(X64)),X64)
| ~ aElementOf0(sdtpldt0(esk9_1(X64),esk10_1(X64)),X64)
| ~ aSet0(X64)
| aIdeal0(X64) ) ),
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)],[mDefIdeal])])])])])]) ).
cnf(c_0_103,plain,
( aElementOf0(X5,X6)
| ~ aElementOf0(X1,X2)
| ~ aElementOf0(X3,X4)
| sdtpldt0(X1,X3) != X5
| X6 != sdtpldt1(X2,X4)
| ~ aSet0(X2)
| ~ aSet0(X4) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_104,plain,
( aSet0(X1)
| X1 != slsdtgt0(X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_105,plain,
( sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_46]),c_0_50])]),c_0_95]) ).
cnf(c_0_106,plain,
( sdtpldt0(sz00,sdtpldt0(X1,sz00)) = sdtpldt0(X1,sz00)
| ~ aElement0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_41]),c_0_33])]),c_0_34]) ).
cnf(c_0_107,plain,
( sdtpldt0(sdtasdt0(X1,X2),sz00) = sdtasdt0(X1,sdtpldt0(X2,sz00))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_90]),c_0_50])]) ).
cnf(c_0_108,hypothesis,
sdtasdt0(xa,sz10) = xa,
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_98,c_0_99]),c_0_88]),c_0_89]),c_0_78]),c_0_33])]) ).
cnf(c_0_109,hypothesis,
( sdtpldt0(sdtasdt0(xa,X1),xa) = sdtasdt0(xa,sdtpldt0(X1,esk18_3(xa,slsdtgt0(xa),xa)))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_88]),c_0_89]),c_0_78])]) ).
cnf(c_0_110,hypothesis,
sdtasdt0(xa,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_99]),c_0_89]),c_0_78]),c_0_50])]) ).
cnf(c_0_111,plain,
( aElementOf0(sz00,slsdtgt0(X1))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_90]),c_0_50])]) ).
cnf(c_0_112,plain,
aElementOf0(sz00,slsdtgt0(sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_82]),c_0_33])]) ).
cnf(c_0_113,plain,
( aElementOf0(sdtpldt0(X3,X1),X2)
| ~ aElementOf0(X1,X2)
| ~ aElementOf0(X3,X2)
| ~ aIdeal0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_114,hypothesis,
aElementOf0(xb,slsdtgt0(xb)),
inference(split_conjunct,[status(thm)],[m__2203]) ).
fof(c_0_115,plain,
! [X92,X93,X94,X95,X96] :
( ( aDivisorOf0(X94,X92)
| ~ aGcdOfAnd0(X94,X92,X93)
| ~ aElement0(X92)
| ~ aElement0(X93) )
& ( aDivisorOf0(X94,X93)
| ~ aGcdOfAnd0(X94,X92,X93)
| ~ aElement0(X92)
| ~ aElement0(X93) )
& ( ~ aDivisorOf0(X95,X92)
| ~ aDivisorOf0(X95,X93)
| doDivides0(X95,X94)
| ~ aGcdOfAnd0(X94,X92,X93)
| ~ aElement0(X92)
| ~ aElement0(X93) )
& ( aDivisorOf0(esk17_3(X92,X93,X96),X92)
| ~ aDivisorOf0(X96,X92)
| ~ aDivisorOf0(X96,X93)
| aGcdOfAnd0(X96,X92,X93)
| ~ aElement0(X92)
| ~ aElement0(X93) )
& ( aDivisorOf0(esk17_3(X92,X93,X96),X93)
| ~ aDivisorOf0(X96,X92)
| ~ aDivisorOf0(X96,X93)
| aGcdOfAnd0(X96,X92,X93)
| ~ aElement0(X92)
| ~ aElement0(X93) )
& ( ~ doDivides0(esk17_3(X92,X93,X96),X96)
| ~ aDivisorOf0(X96,X92)
| ~ aDivisorOf0(X96,X93)
| aGcdOfAnd0(X96,X92,X93)
| ~ aElement0(X92)
| ~ aElement0(X93) ) ),
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)],[mDefGCD])])])])])]) ).
cnf(c_0_116,plain,
( aElementOf0(sdtpldt0(X1,X2),sdtpldt1(X3,X4))
| ~ aElementOf0(X2,X4)
| ~ aElementOf0(X1,X3)
| ~ aSet0(X4)
| ~ aSet0(X3) ),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_103])]) ).
cnf(c_0_117,plain,
( aSet0(slsdtgt0(X1))
| ~ aElement0(X1) ),
inference(er,[status(thm)],[c_0_104]) ).
cnf(c_0_118,plain,
( sdtpldt0(X1,sz00) = sdtpldt0(sz00,X1)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_50])]) ).
cnf(c_0_119,hypothesis,
sdtpldt0(xa,sz00) = sdtasdt0(xa,sdtpldt0(sz10,sz00)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_33]),c_0_78])]) ).
cnf(c_0_120,hypothesis,
sdtpldt0(sz00,xa) = xa,
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_109,c_0_65]),c_0_110]),c_0_88]),c_0_50]),c_0_89])]) ).
cnf(c_0_121,plain,
( sdtasdt0(X1,esk18_3(X1,slsdtgt0(X1),sz00)) = sz00
| ~ aElement0(X1) ),
inference(spm,[status(thm)],[c_0_76,c_0_111]) ).
cnf(c_0_122,plain,
aElement0(esk18_3(sz10,slsdtgt0(sz10),sz00)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_112]),c_0_33])]) ).
cnf(c_0_123,hypothesis,
( aElementOf0(sdtpldt0(xb,X1),slsdtgt0(xb))
| ~ aIdeal0(slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xb)) ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_124,hypothesis,
aElement0(xb),
inference(split_conjunct,[status(thm)],[m__2091]) ).
fof(c_0_125,plain,
! [X90,X91] :
( ( aElement0(X91)
| ~ aDivisorOf0(X91,X90)
| ~ aElement0(X90) )
& ( doDivides0(X91,X90)
| ~ aDivisorOf0(X91,X90)
| ~ aElement0(X90) )
& ( ~ aElement0(X91)
| ~ doDivides0(X91,X90)
| aDivisorOf0(X91,X90)
| ~ aElement0(X90) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDvs])])])]) ).
cnf(c_0_126,plain,
( aDivisorOf0(X1,X2)
| ~ aGcdOfAnd0(X1,X3,X2)
| ~ aElement0(X3)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_127,hypothesis,
aGcdOfAnd0(xc,xa,xb),
inference(split_conjunct,[status(thm)],[m__2129]) ).
cnf(c_0_128,hypothesis,
( aElementOf0(sdtpldt0(xa,X1),slsdtgt0(xa))
| ~ aIdeal0(slsdtgt0(xa))
| ~ aElementOf0(X1,slsdtgt0(xa)) ),
inference(spm,[status(thm)],[c_0_113,c_0_77]) ).
fof(c_0_129,negated_conjecture,
~ ? [X1] :
( aElementOf0(X1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& X1 != sz00 ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_130,plain,
( aElementOf0(sdtpldt0(X1,sz00),sdtpldt1(X2,slsdtgt0(X3)))
| ~ aElementOf0(X1,X2)
| ~ aSet0(X2)
| ~ aElement0(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_111]),c_0_117]) ).
cnf(c_0_131,hypothesis,
sdtasdt0(xa,sdtpldt0(sz10,sz00)) = xa,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_119]),c_0_120]),c_0_78])]) ).
fof(c_0_132,plain,
! [X19,X20] :
( ~ aElement0(X19)
| ~ aElement0(X20)
| sdtasdt0(X19,X20) = sdtasdt0(X20,X19) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
cnf(c_0_133,plain,
esk18_3(sz10,slsdtgt0(sz10),sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_121]),c_0_122]),c_0_33])]) ).
cnf(c_0_134,hypothesis,
( aElementOf0(sdtpldt0(xb,X1),slsdtgt0(xb))
| ~ aElementOf0(X1,slsdtgt0(xb)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_82]),c_0_124])]) ).
fof(c_0_135,plain,
! [X86,X87,X89] :
( ( aElement0(esk16_2(X86,X87))
| ~ doDivides0(X86,X87)
| ~ aElement0(X86)
| ~ aElement0(X87) )
& ( sdtasdt0(X86,esk16_2(X86,X87)) = X87
| ~ doDivides0(X86,X87)
| ~ aElement0(X86)
| ~ aElement0(X87) )
& ( ~ aElement0(X89)
| sdtasdt0(X86,X89) != X87
| doDivides0(X86,X87)
| ~ aElement0(X86)
| ~ aElement0(X87) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefDiv])])])])]) ).
cnf(c_0_136,plain,
( doDivides0(X1,X2)
| ~ aDivisorOf0(X1,X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_137,hypothesis,
aDivisorOf0(xc,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_78]),c_0_124])]) ).
cnf(c_0_138,plain,
( aElement0(X1)
| ~ aDivisorOf0(X1,X2)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_139,hypothesis,
( aElementOf0(sdtpldt0(xa,X1),slsdtgt0(xa))
| ~ aElementOf0(X1,slsdtgt0(xa)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_82]),c_0_78])]) ).
cnf(c_0_140,plain,
( sdtpldt0(sdtasdt0(X1,X2),X1) = sdtasdt0(X1,sdtpldt0(X2,sz10))
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_32]),c_0_33])]) ).
fof(c_0_141,negated_conjecture,
! [X111] :
( ~ aElementOf0(X111,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| X111 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_129])]) ).
cnf(c_0_142,hypothesis,
( aElementOf0(xa,sdtpldt1(slsdtgt0(xa),slsdtgt0(X1)))
| ~ aSet0(slsdtgt0(xa))
| ~ aElement0(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_77]),c_0_119]),c_0_131]) ).
cnf(c_0_143,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_132]) ).
cnf(c_0_144,plain,
sdtasdt0(sz10,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_133]),c_0_33])]) ).
cnf(c_0_145,hypothesis,
aElementOf0(sdtpldt0(xb,sz00),slsdtgt0(xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_111]),c_0_124])]) ).
cnf(c_0_146,plain,
( sdtasdt0(X1,esk16_2(X1,X2)) = X2
| ~ doDivides0(X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_135]) ).
cnf(c_0_147,hypothesis,
doDivides0(xc,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137]),c_0_124])]) ).
cnf(c_0_148,hypothesis,
aElement0(xc),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_137]),c_0_124])]) ).
cnf(c_0_149,plain,
( aElement0(esk16_2(X1,X2))
| ~ doDivides0(X1,X2)
| ~ aElement0(X1)
| ~ aElement0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_135]) ).
cnf(c_0_150,plain,
( aElementOf0(X1,slsdtgt0(X1))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_32]),c_0_33])]) ).
cnf(c_0_151,hypothesis,
aElementOf0(sdtpldt0(xa,xa),slsdtgt0(xa)),
inference(spm,[status(thm)],[c_0_139,c_0_77]) ).
cnf(c_0_152,hypothesis,
sdtpldt0(xa,xa) = sdtasdt0(xa,sdtpldt0(sz10,sz10)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_108]),c_0_33]),c_0_78])]) ).
cnf(c_0_153,negated_conjecture,
( X1 = sz00
| ~ aElementOf0(X1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(split_conjunct,[status(thm)],[c_0_141]) ).
cnf(c_0_154,hypothesis,
( aElementOf0(xa,sdtpldt1(slsdtgt0(xa),slsdtgt0(X1)))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_142,c_0_117]),c_0_78])]) ).
cnf(c_0_155,plain,
sdtasdt0(sz00,sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_143,c_0_144]),c_0_50]),c_0_33])]) ).
cnf(c_0_156,plain,
( sdtasdt0(sz10,sdtasdt0(X1,X2)) = sdtasdt0(X1,X2)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_64]),c_0_33])]) ).
cnf(c_0_157,hypothesis,
sdtasdt0(xb,esk18_3(xb,slsdtgt0(xb),sdtpldt0(xb,sz00))) = sdtpldt0(xb,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_145]),c_0_124])]) ).
cnf(c_0_158,hypothesis,
aElement0(esk18_3(xb,slsdtgt0(xb),sdtpldt0(xb,sz00))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_145]),c_0_124])]) ).
cnf(c_0_159,hypothesis,
sdtasdt0(xc,esk16_2(xc,xb)) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_146,c_0_147]),c_0_124]),c_0_148])]) ).
cnf(c_0_160,hypothesis,
aElement0(esk16_2(xc,xb)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_147]),c_0_124]),c_0_148])]) ).
cnf(c_0_161,plain,
( aElementOf0(sdtpldt0(X1,X2),sdtpldt1(X3,slsdtgt0(X2)))
| ~ aElementOf0(X1,X3)
| ~ aSet0(X3)
| ~ aElement0(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_150]),c_0_117]) ).
cnf(c_0_162,hypothesis,
aElementOf0(sdtasdt0(xa,sdtpldt0(sz10,sz10)),slsdtgt0(xa)),
inference(rw,[status(thm)],[c_0_151,c_0_152]) ).
cnf(c_0_163,negated_conjecture,
xa = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_153,c_0_154]),c_0_124])]) ).
cnf(c_0_164,plain,
sdtasdt0(sz00,sdtpldt0(sz10,sz10)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_155]),c_0_93]),c_0_33]),c_0_50])]) ).
cnf(c_0_165,hypothesis,
sdtasdt0(sz10,sdtpldt0(xb,sz00)) = sdtpldt0(xb,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_157]),c_0_158]),c_0_124])]) ).
cnf(c_0_166,plain,
( sdtasdt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtasdt0(X1,X3),sdtasdt0(X1,X2))
| ~ aElement0(X3)
| ~ aElement0(X2)
| ~ aElement0(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_97]),c_0_87]),c_0_87]) ).
cnf(c_0_167,hypothesis,
sdtasdt0(sz10,xb) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_156,c_0_159]),c_0_160]),c_0_148])]) ).
cnf(c_0_168,hypothesis,
( aElementOf0(sdtpldt0(sz00,X1),sdtpldt1(slsdtgt0(sz00),slsdtgt0(X1)))
| ~ aSet0(slsdtgt0(sz00))
| ~ aElement0(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_162]),c_0_163]),c_0_164]),c_0_163]),c_0_163]) ).
cnf(c_0_169,hypothesis,
sdtpldt0(xb,sz00) = sdtpldt0(sz00,xb),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165,c_0_166]),c_0_144]),c_0_167]),c_0_50]),c_0_124]),c_0_33])]) ).
cnf(c_0_170,hypothesis,
( xa != sz00
| xb != sz00 ),
inference(split_conjunct,[status(thm)],[m__2110]) ).
cnf(c_0_171,negated_conjecture,
( X1 = sz00
| ~ aElementOf0(X1,sdtpldt1(slsdtgt0(sz00),slsdtgt0(xb))) ),
inference(spm,[status(thm)],[c_0_153,c_0_163]) ).
cnf(c_0_172,hypothesis,
( aElementOf0(sdtpldt0(sz00,X1),sdtpldt1(slsdtgt0(sz00),slsdtgt0(X1)))
| ~ aElement0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_168,c_0_117]),c_0_50])]) ).
cnf(c_0_173,hypothesis,
sdtpldt0(sz00,xb) = xb,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_169]),c_0_124])]) ).
cnf(c_0_174,hypothesis,
xb != sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_170,c_0_163])]) ).
cnf(c_0_175,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_172]),c_0_173]),c_0_124])]),c_0_174]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : RNG109+1 : 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
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Aug 27 01:53:17 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 4.53/4.62 % Version : CSE_E---1.5
% 4.53/4.62 % Problem : theBenchmark.p
% 4.53/4.62 % Proof found
% 4.53/4.62 % SZS status Theorem for theBenchmark.p
% 4.53/4.62 % SZS output start Proof
% See solution above
% 4.59/4.64 % Total time : 4.066000 s
% 4.59/4.64 % SZS output end Proof
% 4.59/4.64 % Total time : 4.070000 s
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