TSTP Solution File: NUM504+1 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM504+1 : 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 : n029.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 10:38:09 EDT 2023
% Result : Theorem 0.67s 0.81s
% Output : CNFRefutation 0.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 30
% Syntax : Number of formulae : 66 ( 17 unt; 20 typ; 0 def)
% Number of atoms : 171 ( 59 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 205 ( 80 ~; 91 |; 24 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 13 >; 9 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn; 22 !; 0 ?; 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 ).
fof(mDefQuot,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( X1 != sz00
& doDivides0(X1,X2) )
=> ! [X3] :
( X3 = sdtsldt0(X2,X1)
<=> ( aNaturalNumber0(X3)
& X2 = sdtasdt0(X1,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefQuot) ).
fof(mMulComm,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(mLEAsym,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( ( sdtlseqdt0(X1,X2)
& sdtlseqdt0(X2,X1) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLEAsym) ).
fof(m__1860,hypothesis,
( isPrime0(xp)
& doDivides0(xp,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(m__2306,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).
fof(m__2414,hypothesis,
( sdtasdt0(xn,xm) != sdtasdt0(xp,xm)
& sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm))
& sdtasdt0(xp,xm) != sdtasdt0(xp,xk)
& sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2414) ).
fof(mSortsB_02,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> aNaturalNumber0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
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(mSortsC,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
fof(c_0_10,plain,
! [X64,X65,X66] :
( ( aNaturalNumber0(X66)
| X66 != sdtsldt0(X65,X64)
| X64 = sz00
| ~ doDivides0(X64,X65)
| ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X65) )
& ( X65 = sdtasdt0(X64,X66)
| X66 != sdtsldt0(X65,X64)
| X64 = sz00
| ~ doDivides0(X64,X65)
| ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X65) )
& ( ~ aNaturalNumber0(X66)
| X65 != sdtasdt0(X64,X66)
| X66 = sdtsldt0(X65,X64)
| X64 = sz00
| ~ doDivides0(X64,X65)
| ~ aNaturalNumber0(X64)
| ~ aNaturalNumber0(X65) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])]) ).
fof(c_0_11,plain,
! [X14,X15] :
( ~ aNaturalNumber0(X14)
| ~ aNaturalNumber0(X15)
| sdtasdt0(X14,X15) = sdtasdt0(X15,X14) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).
fof(c_0_12,plain,
! [X42,X43] :
( ~ aNaturalNumber0(X42)
| ~ aNaturalNumber0(X43)
| ~ sdtlseqdt0(X42,X43)
| ~ sdtlseqdt0(X43,X42)
| X42 = X43 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])]) ).
cnf(c_0_13,plain,
( X1 = sdtasdt0(X2,X3)
| X2 = sz00
| X3 != sdtsldt0(X1,X2)
| ~ doDivides0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,hypothesis,
doDivides0(xp,sdtasdt0(xn,xm)),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_15,plain,
( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_17,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_18,hypothesis,
xk = sdtsldt0(sdtasdt0(xn,xm),xp),
inference(split_conjunct,[status(thm)],[m__2306]) ).
cnf(c_0_19,plain,
( X1 = X2
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2)
| ~ sdtlseqdt0(X1,X2)
| ~ sdtlseqdt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,hypothesis,
sdtlseqdt0(sdtasdt0(xn,xm),sdtasdt0(xp,xm)),
inference(split_conjunct,[status(thm)],[m__2414]) ).
cnf(c_0_21,hypothesis,
sdtasdt0(xn,xm) != sdtasdt0(xp,xm),
inference(split_conjunct,[status(thm)],[m__2414]) ).
cnf(c_0_22,plain,
( sdtasdt0(X1,sdtsldt0(X2,X1)) = X2
| X1 = sz00
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_13]) ).
cnf(c_0_23,hypothesis,
doDivides0(xp,sdtasdt0(xm,xn)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]),c_0_17])]) ).
cnf(c_0_24,hypothesis,
sdtsldt0(sdtasdt0(xm,xn),xp) = xk,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_15]),c_0_16]),c_0_17])]) ).
cnf(c_0_25,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
fof(c_0_26,plain,
! [X6,X7] :
( ~ aNaturalNumber0(X6)
| ~ aNaturalNumber0(X7)
| aNaturalNumber0(sdtasdt0(X6,X7)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).
cnf(c_0_27,plain,
( aNaturalNumber0(X1)
| X3 = sz00
| X1 != sdtsldt0(X2,X3)
| ~ doDivides0(X3,X2)
| ~ aNaturalNumber0(X3)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_28,hypothesis,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_29,hypothesis,
( sdtasdt0(xm,xn) = sdtasdt0(xp,xk)
| xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xm,xn)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_25])]) ).
cnf(c_0_30,plain,
( aNaturalNumber0(sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
( X1 = sz00
| aNaturalNumber0(sdtsldt0(X2,X1))
| ~ doDivides0(X1,X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X2) ),
inference(er,[status(thm)],[c_0_27]) ).
cnf(c_0_32,hypothesis,
( ~ sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xm,xn))
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_15]),c_0_17]),c_0_16])]) ).
cnf(c_0_33,hypothesis,
( sdtasdt0(xm,xn) = sdtasdt0(xp,xk)
| xp = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_16]),c_0_17])]) ).
cnf(c_0_34,hypothesis,
sdtlseqdt0(sdtasdt0(xp,xm),sdtasdt0(xp,xk)),
inference(split_conjunct,[status(thm)],[m__2414]) ).
cnf(c_0_35,hypothesis,
( xp = sz00
| aNaturalNumber0(xk)
| ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_14]),c_0_18]),c_0_25])]) ).
cnf(c_0_36,hypothesis,
( xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xp,xk))
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
cnf(c_0_37,hypothesis,
( xp = sz00
| aNaturalNumber0(xk) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_30]),c_0_17]),c_0_16])]) ).
fof(c_0_38,plain,
! [X81,X82] :
( ( X81 != sz00
| ~ isPrime0(X81)
| ~ aNaturalNumber0(X81) )
& ( X81 != sz10
| ~ isPrime0(X81)
| ~ aNaturalNumber0(X81) )
& ( ~ aNaturalNumber0(X82)
| ~ doDivides0(X82,X81)
| X82 = sz10
| X82 = X81
| ~ isPrime0(X81)
| ~ aNaturalNumber0(X81) )
& ( aNaturalNumber0(esk3_1(X81))
| X81 = sz00
| X81 = sz10
| isPrime0(X81)
| ~ aNaturalNumber0(X81) )
& ( doDivides0(esk3_1(X81),X81)
| X81 = sz00
| X81 = sz10
| isPrime0(X81)
| ~ aNaturalNumber0(X81) )
& ( esk3_1(X81) != sz10
| X81 = sz00
| X81 = sz10
| isPrime0(X81)
| ~ aNaturalNumber0(X81) )
& ( esk3_1(X81) != X81
| X81 = sz00
| X81 = sz10
| isPrime0(X81)
| ~ aNaturalNumber0(X81) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefPrime])])])])]) ).
cnf(c_0_39,hypothesis,
( xp = sz00
| ~ aNaturalNumber0(sdtasdt0(xp,xm)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_30]),c_0_25])]),c_0_37]) ).
cnf(c_0_40,plain,
( X1 != sz00
| ~ isPrime0(X1)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_41,plain,
aNaturalNumber0(sz00),
inference(split_conjunct,[status(thm)],[mSortsC]) ).
cnf(c_0_42,hypothesis,
isPrime0(xp),
inference(split_conjunct,[status(thm)],[m__1860]) ).
cnf(c_0_43,hypothesis,
xp = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_30]),c_0_17]),c_0_25])]) ).
cnf(c_0_44,plain,
~ isPrime0(sz00),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_40]),c_0_41])]) ).
cnf(c_0_45,hypothesis,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43]),c_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUM504+1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Aug 25 13:54:54 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.60 start to proof: theBenchmark
% 0.67/0.81 % Version : CSE_E---1.5
% 0.67/0.81 % Problem : theBenchmark.p
% 0.67/0.81 % Proof found
% 0.67/0.81 % SZS status Theorem for theBenchmark.p
% 0.67/0.81 % SZS output start Proof
% See solution above
% 0.67/0.81 % Total time : 0.202000 s
% 0.67/0.81 % SZS output end Proof
% 0.67/0.81 % Total time : 0.206000 s
%------------------------------------------------------------------------------