TSTP Solution File: NUM518+3 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM518+3 : 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 : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 10:38:19 EDT 2023
% Result : Theorem 0.20s 0.67s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 58
% Syntax : Number of formulae : 134 ( 36 unt; 38 typ; 0 def)
% Number of atoms : 412 ( 160 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 461 ( 145 ~; 179 |; 114 &)
% ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 17 >; 17 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 33 ( 33 usr; 21 con; 0-3 aty)
% Number of variables : 93 ( 0 sgn; 50 !; 15 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
aNaturalNumber0: $i > $o ).
tff(decl_23,type,
sz00: $i ).
tff(decl_24,type,
sz10: $i ).
tff(decl_25,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(decl_26,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(decl_27,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(decl_28,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(decl_29,type,
iLess0: ( $i * $i ) > $o ).
tff(decl_30,type,
doDivides0: ( $i * $i ) > $o ).
tff(decl_31,type,
sdtsldt0: ( $i * $i ) > $i ).
tff(decl_32,type,
isPrime0: $i > $o ).
tff(decl_33,type,
xn: $i ).
tff(decl_34,type,
xm: $i ).
tff(decl_35,type,
xp: $i ).
tff(decl_36,type,
xk: $i ).
tff(decl_37,type,
xr: $i ).
tff(decl_38,type,
esk1_2: ( $i * $i ) > $i ).
tff(decl_39,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_40,type,
esk3_1: $i > $i ).
tff(decl_41,type,
esk4_1: $i > $i ).
tff(decl_42,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_43,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_44,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_45,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_46,type,
esk9_0: $i ).
tff(decl_47,type,
esk10_0: $i ).
tff(decl_48,type,
esk11_0: $i ).
tff(decl_49,type,
esk12_0: $i ).
tff(decl_50,type,
esk13_0: $i ).
tff(decl_51,type,
esk14_0: $i ).
tff(decl_52,type,
esk15_0: $i ).
tff(decl_53,type,
esk16_0: $i ).
tff(decl_54,type,
esk17_0: $i ).
tff(decl_55,type,
esk18_0: $i ).
tff(decl_56,type,
esk19_0: $i ).
tff(decl_57,type,
esk20_0: $i ).
tff(decl_58,type,
esk21_0: $i ).
tff(decl_59,type,
esk22_0: $i ).
fof(m__1860,hypothesis,
( xp != sz00
& xp != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& xp = sdtasdt0(X1,X2) )
| doDivides0(X1,xp) ) )
=> ( X1 = sz10
| X1 = xp ) )
& isPrime0(xp)
& ? [X1] :
( aNaturalNumber0(X1)
& sdtasdt0(xn,xm) = sdtasdt0(xp,X1) )
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(mPrimDiv,axiom,
! [X1] :
( ( aNaturalNumber0(X1)
& X1 != sz00
& X1 != sz10 )
=> ? [X2] :
( aNaturalNumber0(X2)
& doDivides0(X2,X1)
& isPrime0(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPrimDiv) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(mDefPrime,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( isPrime0(X1)
<=> ( X1 != sz00
& X1 != sz10
& ! [X2] :
( ( aNaturalNumber0(X2)
& doDivides0(X2,X1) )
=> ( X2 = sz10
| X2 = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
fof(m__,conjecture,
( ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xp,X1) )
| doDivides0(xp,xn)
| ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xp,X1) )
| doDivides0(xp,xm) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(m__2645,hypothesis,
( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& ? [X1] :
( aNaturalNumber0(X1)
& sdtsldt0(xn,xr) = sdtasdt0(xp,X1) )
& doDivides0(xp,sdtsldt0(xn,xr)) )
| ( ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xp,X1) )
& doDivides0(xp,xm) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2645) ).
fof(mMulCanc,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( X1 != sz00
=> ! [X2,X3] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtasdt0(X1,X2) = sdtasdt0(X1,X3)
| sdtasdt0(X2,X1) = sdtasdt0(X3,X1) )
=> X2 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulCanc) ).
fof(m__2487,hypothesis,
( ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xr,X1) )
& doDivides0(xr,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2487) ).
fof(m__2342,hypothesis,
( aNaturalNumber0(xr)
& ? [X1] :
( aNaturalNumber0(X1)
& xk = sdtasdt0(xr,X1) )
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ! [X1] :
( ( aNaturalNumber0(X1)
& ( ? [X2] :
( aNaturalNumber0(X2)
& xr = sdtasdt0(X1,X2) )
| doDivides0(X1,xr) ) )
=> ( X1 = sz10
| X1 = xr ) )
& isPrime0(xr) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).
fof(m__2504,hypothesis,
( ~ ( ( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
=> sdtsldt0(xn,xr) = xn )
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(sdtsldt0(xn,xr),X1) = xn )
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2504) ).
fof(mDivMin,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( doDivides0(X1,X2)
& doDivides0(X1,sdtpldt0(X2,X3)) )
=> doDivides0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivMin) ).
fof(m_AddZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtpldt0(X1,sz00) = X1
& X1 = sdtpldt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
fof(mDefDiv,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( doDivides0(X1,X2)
<=> ? [X3] :
( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(mLETran,axiom,
! [X1,X2,X3] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2)
& aNaturalNumber0(X3) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X3) )
=> sdtlseqdt0(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLETran) ).
fof(mMonMul2,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( X1 != sz00
=> sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul2) ).
fof(mZeroMul,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X1 = sz00
| X2 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroMul) ).
fof(m__1870,hypothesis,
~ ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xp,X1) = xn )
| sdtlseqdt0(xp,xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
fof(m_MulZero,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz00) = sz00
& sz00 = sdtasdt0(sz00,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).
fof(c_0_20,hypothesis,
! [X96,X97] :
( xp != sz00
& xp != sz10
& ( ~ aNaturalNumber0(X97)
| xp != sdtasdt0(X96,X97)
| ~ aNaturalNumber0(X96)
| X96 = sz10
| X96 = xp )
& ( ~ doDivides0(X96,xp)
| ~ aNaturalNumber0(X96)
| X96 = sz10
| X96 = xp )
& isPrime0(xp)
& aNaturalNumber0(esk9_0)
& sdtasdt0(xn,xm) = sdtasdt0(xp,esk9_0)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1860])])])])]) ).
fof(c_0_21,plain,
! [X86] :
( ( aNaturalNumber0(esk4_1(X86))
| ~ aNaturalNumber0(X86)
| X86 = sz00
| X86 = sz10 )
& ( doDivides0(esk4_1(X86),X86)
| ~ aNaturalNumber0(X86)
| X86 = sz00
| X86 = sz10 )
& ( isPrime0(esk4_1(X86))
| ~ aNaturalNumber0(X86)
| X86 = sz00
| X86 = sz10 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mPrimDiv])])])]) ).
cnf(c_0_22,hypothesis,
( X1 = sz10
| X1 = xp
| ~ doDivides0(X1,xp)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_23,plain,
( doDivides0(esk4_1(X1),X1)
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_24,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_25,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,hypothesis,
xp != sz10,
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_27,plain,
! [X83,X84] :
( ( X83 != sz00
| ~ isPrime0(X83)
| ~ aNaturalNumber0(X83) )
& ( X83 != sz10
| ~ isPrime0(X83)
| ~ aNaturalNumber0(X83) )
& ( ~ aNaturalNumber0(X84)
| ~ doDivides0(X84,X83)
| X84 = sz10
| X84 = X83
| ~ isPrime0(X83)
| ~ aNaturalNumber0(X83) )
& ( aNaturalNumber0(esk3_1(X83))
| X83 = sz00
| X83 = sz10
| isPrime0(X83)
| ~ aNaturalNumber0(X83) )
& ( doDivides0(esk3_1(X83),X83)
| X83 = sz00
| X83 = sz10
| isPrime0(X83)
| ~ aNaturalNumber0(X83) )
& ( esk3_1(X83) != sz10
| X83 = sz00
| X83 = sz10
| isPrime0(X83)
| ~ aNaturalNumber0(X83) )
& ( esk3_1(X83) != X83
| X83 = sz00
| X83 = sz10
| isPrime0(X83)
| ~ aNaturalNumber0(X83) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefPrime])])])])]) ).
fof(c_0_28,negated_conjecture,
~ ( ? [X1] :
( aNaturalNumber0(X1)
& xn = sdtasdt0(xp,X1) )
| doDivides0(xp,xn)
| ? [X1] :
( aNaturalNumber0(X1)
& xm = sdtasdt0(xp,X1) )
| doDivides0(xp,xm) ),
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_0_29,hypothesis,
( esk4_1(xp) = xp
| esk4_1(xp) = sz10
| ~ aNaturalNumber0(esk4_1(xp)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]),c_0_25]),c_0_26]) ).
cnf(c_0_30,plain,
( aNaturalNumber0(esk4_1(X1))
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,plain,
( X1 != sz10
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_32,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
fof(c_0_33,hypothesis,
( ( aNaturalNumber0(esk22_0)
| aNaturalNumber0(sdtsldt0(xn,xr)) )
& ( xm = sdtasdt0(xp,esk22_0)
| aNaturalNumber0(sdtsldt0(xn,xr)) )
& ( doDivides0(xp,xm)
| aNaturalNumber0(sdtsldt0(xn,xr)) )
& ( aNaturalNumber0(esk22_0)
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( xm = sdtasdt0(xp,esk22_0)
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( doDivides0(xp,xm)
| xn = sdtasdt0(xr,sdtsldt0(xn,xr)) )
& ( aNaturalNumber0(esk22_0)
| aNaturalNumber0(esk21_0) )
& ( xm = sdtasdt0(xp,esk22_0)
| aNaturalNumber0(esk21_0) )
& ( doDivides0(xp,xm)
| aNaturalNumber0(esk21_0) )
& ( aNaturalNumber0(esk22_0)
| sdtsldt0(xn,xr) = sdtasdt0(xp,esk21_0) )
& ( xm = sdtasdt0(xp,esk22_0)
| sdtsldt0(xn,xr) = sdtasdt0(xp,esk21_0) )
& ( doDivides0(xp,xm)
| sdtsldt0(xn,xr) = sdtasdt0(xp,esk21_0) )
& ( aNaturalNumber0(esk22_0)
| doDivides0(xp,sdtsldt0(xn,xr)) )
& ( xm = sdtasdt0(xp,esk22_0)
| doDivides0(xp,sdtsldt0(xn,xr)) )
& ( doDivides0(xp,xm)
| doDivides0(xp,sdtsldt0(xn,xr)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2645])])]) ).
fof(c_0_34,negated_conjecture,
! [X116,X117] :
( ( ~ aNaturalNumber0(X116)
| xn != sdtasdt0(xp,X116) )
& ~ doDivides0(xp,xn)
& ( ~ aNaturalNumber0(X117)
| xm != sdtasdt0(xp,X117) )
& ~ doDivides0(xp,xm) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).
cnf(c_0_35,plain,
( isPrime0(esk4_1(X1))
| X1 = sz00
| X1 = sz10
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_36,hypothesis,
( esk4_1(xp) = sz10
| esk4_1(xp) = xp ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_24])]),c_0_25]),c_0_26]) ).
cnf(c_0_37,plain,
~ isPrime0(sz10),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_31]),c_0_32])]) ).
fof(c_0_38,plain,
! [X29,X30,X31] :
( ( sdtasdt0(X29,X30) != sdtasdt0(X29,X31)
| X30 = X31
| ~ aNaturalNumber0(X30)
| ~ aNaturalNumber0(X31)
| X29 = sz00
| ~ aNaturalNumber0(X29) )
& ( sdtasdt0(X30,X29) != sdtasdt0(X31,X29)
| X30 = X31
| ~ aNaturalNumber0(X30)
| ~ aNaturalNumber0(X31)
| X29 = sz00
| ~ aNaturalNumber0(X29) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulCanc])])])]) ).
fof(c_0_39,hypothesis,
( aNaturalNumber0(esk18_0)
& xn = sdtasdt0(xr,esk18_0)
& doDivides0(xr,xn) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2487])]) ).
fof(c_0_40,hypothesis,
! [X104,X105] :
( aNaturalNumber0(xr)
& aNaturalNumber0(esk12_0)
& xk = sdtasdt0(xr,esk12_0)
& doDivides0(xr,xk)
& xr != sz00
& xr != sz10
& ( ~ aNaturalNumber0(X105)
| xr != sdtasdt0(X104,X105)
| ~ aNaturalNumber0(X104)
| X104 = sz10
| X104 = xr )
& ( ~ doDivides0(X104,xr)
| ~ aNaturalNumber0(X104)
| X104 = sz10
| X104 = xr )
& isPrime0(xr) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2342])])])])]) ).
fof(c_0_41,hypothesis,
( aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& sdtsldt0(xn,xr) != xn
& aNaturalNumber0(sdtsldt0(xn,xr))
& xn = sdtasdt0(xr,sdtsldt0(xn,xr))
& aNaturalNumber0(esk19_0)
& sdtpldt0(sdtsldt0(xn,xr),esk19_0) = xn
& sdtlseqdt0(sdtsldt0(xn,xr),xn) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2504])])]) ).
cnf(c_0_42,hypothesis,
( doDivides0(xp,xm)
| sdtsldt0(xn,xr) = sdtasdt0(xp,esk21_0) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_43,negated_conjecture,
~ doDivides0(xp,xm),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
fof(c_0_44,plain,
! [X75,X76,X77] :
( ~ aNaturalNumber0(X75)
| ~ aNaturalNumber0(X76)
| ~ aNaturalNumber0(X77)
| ~ doDivides0(X75,X76)
| ~ doDivides0(X75,sdtpldt0(X76,X77))
| doDivides0(X75,X77) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDivMin])]) ).
cnf(c_0_45,hypothesis,
esk4_1(xp) = xp,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_24])]),c_0_25]),c_0_26]),c_0_37]) ).
cnf(c_0_46,plain,
( X2 = X3
| X1 = sz00
| sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_47,hypothesis,
xn = sdtasdt0(xr,esk18_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_48,hypothesis,
aNaturalNumber0(esk18_0),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_49,hypothesis,
aNaturalNumber0(xr),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_50,hypothesis,
xr != sz00,
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_51,hypothesis,
xn = sdtasdt0(xr,sdtsldt0(xn,xr)),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_52,hypothesis,
sdtsldt0(xn,xr) = sdtasdt0(xp,esk21_0),
inference(sr,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_53,hypothesis,
aNaturalNumber0(sdtsldt0(xn,xr)),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_54,plain,
( doDivides0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ doDivides0(X1,X2)
| ~ doDivides0(X1,sdtpldt0(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_55,hypothesis,
doDivides0(xp,xp),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_45]),c_0_24])]),c_0_25]),c_0_26]) ).
fof(c_0_56,plain,
! [X15] :
( ( sdtpldt0(X15,sz00) = X15
| ~ aNaturalNumber0(X15) )
& ( X15 = sdtpldt0(sz00,X15)
| ~ aNaturalNumber0(X15) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).
cnf(c_0_57,hypothesis,
sdtlseqdt0(sdtsldt0(xn,xr),xn),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_58,hypothesis,
( X1 = esk18_0
| sdtasdt0(xr,X1) != xn
| ~ aNaturalNumber0(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]),c_0_49])]),c_0_50]) ).
cnf(c_0_59,hypothesis,
sdtasdt0(xr,sdtasdt0(xp,esk21_0)) = xn,
inference(rw,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_60,hypothesis,
aNaturalNumber0(sdtasdt0(xp,esk21_0)),
inference(rw,[status(thm)],[c_0_53,c_0_52]) ).
fof(c_0_61,plain,
! [X62,X63,X65] :
( ( aNaturalNumber0(esk2_2(X62,X63))
| ~ doDivides0(X62,X63)
| ~ aNaturalNumber0(X62)
| ~ aNaturalNumber0(X63) )
& ( X63 = sdtasdt0(X62,esk2_2(X62,X63))
| ~ doDivides0(X62,X63)
| ~ aNaturalNumber0(X62)
| ~ aNaturalNumber0(X63) )
& ( ~ aNaturalNumber0(X65)
| X63 != sdtasdt0(X62,X65)
| doDivides0(X62,X63)
| ~ aNaturalNumber0(X62)
| ~ aNaturalNumber0(X63) ) ),
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_62,hypothesis,
( doDivides0(xp,X1)
| ~ doDivides0(xp,sdtpldt0(xp,X1))
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_24])]) ).
cnf(c_0_63,plain,
( sdtpldt0(X1,sz00) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_56]) ).
cnf(c_0_64,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
fof(c_0_65,plain,
! [X46,X47,X48] :
( ~ aNaturalNumber0(X46)
| ~ aNaturalNumber0(X47)
| ~ aNaturalNumber0(X48)
| ~ sdtlseqdt0(X46,X47)
| ~ sdtlseqdt0(X47,X48)
| sdtlseqdt0(X46,X48) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])]) ).
cnf(c_0_66,hypothesis,
sdtlseqdt0(sdtasdt0(xp,esk21_0),xn),
inference(rw,[status(thm)],[c_0_57,c_0_52]) ).
cnf(c_0_67,hypothesis,
sdtasdt0(xp,esk21_0) = esk18_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60])]) ).
fof(c_0_68,plain,
! [X58,X59] :
( ~ aNaturalNumber0(X58)
| ~ aNaturalNumber0(X59)
| X58 = sz00
| sdtlseqdt0(X59,sdtasdt0(X59,X58)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul2])]) ).
cnf(c_0_69,hypothesis,
( doDivides0(xp,xm)
| aNaturalNumber0(esk21_0) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
fof(c_0_70,plain,
! [X34,X35] :
( ~ aNaturalNumber0(X34)
| ~ aNaturalNumber0(X35)
| sdtasdt0(X34,X35) != sz00
| X34 = sz00
| X35 = sz00 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])]) ).
cnf(c_0_71,plain,
( X1 = sdtasdt0(X2,esk2_2(X2,X1))
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_72,hypothesis,
doDivides0(xp,sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_55]),c_0_64]),c_0_24])]) ).
cnf(c_0_73,plain,
( aNaturalNumber0(esk2_2(X1,X2))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_74,plain,
( sdtlseqdt0(X1,X3)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X3)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_75,hypothesis,
sdtlseqdt0(esk18_0,xn),
inference(rw,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_76,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_77,plain,
( X1 = sz00
| sdtlseqdt0(X2,sdtasdt0(X2,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_78,hypothesis,
aNaturalNumber0(esk21_0),
inference(sr,[status(thm)],[c_0_69,c_0_43]) ).
fof(c_0_79,hypothesis,
! [X99] :
( ( ~ aNaturalNumber0(X99)
| sdtpldt0(xp,X99) != xn )
& ~ sdtlseqdt0(xp,xn) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1870])])]) ).
cnf(c_0_80,plain,
( X1 = sz00
| X2 = sz00
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| sdtasdt0(X1,X2) != sz00 ),
inference(split_conjunct,[status(thm)],[c_0_70]) ).
cnf(c_0_81,hypothesis,
sdtasdt0(xp,esk2_2(xp,sz00)) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_24]),c_0_64])]) ).
cnf(c_0_82,hypothesis,
aNaturalNumber0(esk2_2(xp,sz00)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_72]),c_0_64]),c_0_24])]) ).
cnf(c_0_83,hypothesis,
( sdtlseqdt0(X1,xn)
| ~ sdtlseqdt0(X1,esk18_0)
| ~ aNaturalNumber0(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76]),c_0_48])]) ).
cnf(c_0_84,hypothesis,
( esk21_0 = sz00
| sdtlseqdt0(xp,esk18_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_67]),c_0_24]),c_0_78])]) ).
cnf(c_0_85,hypothesis,
~ sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[c_0_79]) ).
cnf(c_0_86,hypothesis,
esk2_2(xp,sz00) = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]),c_0_24])]),c_0_25]) ).
cnf(c_0_87,hypothesis,
esk21_0 = sz00,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_84]),c_0_24])]),c_0_85]) ).
cnf(c_0_88,hypothesis,
sdtasdt0(xp,sz00) = sz00,
inference(rw,[status(thm)],[c_0_81,c_0_86]) ).
fof(c_0_89,plain,
! [X22] :
( ( sdtasdt0(X22,sz00) = sz00
| ~ aNaturalNumber0(X22) )
& ( sz00 = sdtasdt0(sz00,X22)
| ~ aNaturalNumber0(X22) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])]) ).
cnf(c_0_90,hypothesis,
esk18_0 = sz00,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_87]),c_0_88]) ).
cnf(c_0_91,negated_conjecture,
( ~ aNaturalNumber0(X1)
| xn != sdtasdt0(xp,X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_92,plain,
( sdtasdt0(X1,sz00) = sz00
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_89]) ).
cnf(c_0_93,hypothesis,
sdtasdt0(xr,sz00) = xn,
inference(rw,[status(thm)],[c_0_47,c_0_90]) ).
cnf(c_0_94,negated_conjecture,
sz00 != xn,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_64]),c_0_24])]) ).
cnf(c_0_95,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_49])]),c_0_94]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM518+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Aug 25 14:18:26 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 0.20/0.67 % Version : CSE_E---1.5
% 0.20/0.67 % Problem : theBenchmark.p
% 0.20/0.67 % Proof found
% 0.20/0.67 % SZS status Theorem for theBenchmark.p
% 0.20/0.67 % SZS output start Proof
% See solution above
% 0.20/0.68 % Total time : 0.103000 s
% 0.20/0.68 % SZS output end Proof
% 0.20/0.68 % Total time : 0.107000 s
%------------------------------------------------------------------------------