TSTP Solution File: NUM521+3 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : NUM521+3 : 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 : 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 10:38:22 EDT 2023
% Result : Theorem 0.20s 0.64s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 31
% Syntax : Number of formulae : 53 ( 10 unt; 23 typ; 0 def)
% Number of atoms : 107 ( 40 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 130 ( 53 ~; 48 |; 27 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 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 : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 25 ( 0 sgn; 12 !; 8 ?; 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,
esk1_2: ( $i * $i ) > $i ).
tff(decl_37,type,
esk2_2: ( $i * $i ) > $i ).
tff(decl_38,type,
esk3_1: $i > $i ).
tff(decl_39,type,
esk4_1: $i > $i ).
tff(decl_40,type,
esk5_3: ( $i * $i * $i ) > $i ).
tff(decl_41,type,
esk6_3: ( $i * $i * $i ) > $i ).
tff(decl_42,type,
esk7_3: ( $i * $i * $i ) > $i ).
tff(decl_43,type,
esk8_3: ( $i * $i * $i ) > $i ).
tff(decl_44,type,
esk9_0: $i ).
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/sandbox/benchmark/theBenchmark.p',m__) ).
fof(m_MulUnit,axiom,
! [X1] :
( aNaturalNumber0(X1)
=> ( sdtasdt0(X1,sz10) = X1
& X1 = sdtasdt0(sz10,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(m__2287,hypothesis,
~ ( xn != xp
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xn,X1) = xp )
| sdtlseqdt0(xn,xp) )
& xm != xp
& ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xm,X1) = xp )
| sdtlseqdt0(xm,xp) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2287) ).
fof(mLETotal,axiom,
! [X1,X2] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X2) )
=> ( sdtlseqdt0(X1,X2)
| ( X2 != X1
& sdtlseqdt0(X2,X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLETotal) ).
fof(mSortsC_01,axiom,
( aNaturalNumber0(sz10)
& sz10 != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(m__1837,hypothesis,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm)
& aNaturalNumber0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1837) ).
fof(m__1870,hypothesis,
~ ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xp,X1) = xn )
| sdtlseqdt0(xp,xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1870) ).
fof(m__2075,hypothesis,
~ ( ? [X1] :
( aNaturalNumber0(X1)
& sdtpldt0(xp,X1) = xm )
| sdtlseqdt0(xp,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2075) ).
fof(c_0_8,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__]) ).
fof(c_0_9,negated_conjecture,
! [X103,X104] :
( ( ~ aNaturalNumber0(X103)
| xn != sdtasdt0(xp,X103) )
& ~ doDivides0(xp,xn)
& ( ~ aNaturalNumber0(X104)
| xm != sdtasdt0(xp,X104) )
& ~ doDivides0(xp,xm) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).
fof(c_0_10,plain,
! [X21] :
( ( sdtasdt0(X21,sz10) = X21
| ~ aNaturalNumber0(X21) )
& ( X21 = sdtasdt0(sz10,X21)
| ~ aNaturalNumber0(X21) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).
fof(c_0_11,hypothesis,
! [X101,X102] :
( ( ~ aNaturalNumber0(X102)
| sdtpldt0(xm,X102) != xp
| ~ aNaturalNumber0(X101)
| sdtpldt0(xn,X101) != xp
| xn = xp
| xm = xp )
& ( ~ sdtlseqdt0(xm,xp)
| ~ aNaturalNumber0(X101)
| sdtpldt0(xn,X101) != xp
| xn = xp
| xm = xp )
& ( ~ aNaturalNumber0(X102)
| sdtpldt0(xm,X102) != xp
| ~ sdtlseqdt0(xn,xp)
| xn = xp
| xm = xp )
& ( ~ sdtlseqdt0(xm,xp)
| ~ sdtlseqdt0(xn,xp)
| xn = xp
| xm = xp ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2287])])])]) ).
fof(c_0_12,plain,
! [X49,X50] :
( ( X50 != X49
| sdtlseqdt0(X49,X50)
| ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X50) )
& ( sdtlseqdt0(X50,X49)
| sdtlseqdt0(X49,X50)
| ~ aNaturalNumber0(X49)
| ~ aNaturalNumber0(X50) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).
cnf(c_0_13,negated_conjecture,
( ~ aNaturalNumber0(X1)
| xn != sdtasdt0(xp,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
( sdtasdt0(X1,sz10) = X1
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
aNaturalNumber0(sz10),
inference(split_conjunct,[status(thm)],[mSortsC_01]) ).
cnf(c_0_16,hypothesis,
aNaturalNumber0(xp),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_17,negated_conjecture,
( ~ aNaturalNumber0(X1)
| xm != sdtasdt0(xp,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_18,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_19,hypothesis,
( xn = xp
| xm = xp
| ~ sdtlseqdt0(xm,xp)
| ~ sdtlseqdt0(xn,xp) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_20,plain,
( sdtlseqdt0(X1,X2)
| sdtlseqdt0(X2,X1)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,hypothesis,
aNaturalNumber0(xn),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_22,negated_conjecture,
xn != xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15]),c_0_16])]) ).
cnf(c_0_23,negated_conjecture,
xm != xp,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_14]),c_0_15]),c_0_16])]) ).
cnf(c_0_24,hypothesis,
~ sdtlseqdt0(xp,xn),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_25,hypothesis,
! [X100] :
( ( ~ aNaturalNumber0(X100)
| sdtpldt0(xp,X100) != xm )
& ~ sdtlseqdt0(xp,xm) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2075])])]) ).
cnf(c_0_26,hypothesis,
~ sdtlseqdt0(xm,xp),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_16]),c_0_21])]),c_0_22]),c_0_23]),c_0_24]) ).
cnf(c_0_27,hypothesis,
aNaturalNumber0(xm),
inference(split_conjunct,[status(thm)],[m__1837]) ).
cnf(c_0_28,hypothesis,
~ sdtlseqdt0(xp,xm),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_29,hypothesis,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_20]),c_0_27]),c_0_16])]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM521+3 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 16:53:41 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.20/0.64 % Version : CSE_E---1.5
% 0.20/0.64 % Problem : theBenchmark.p
% 0.20/0.64 % Proof found
% 0.20/0.64 % SZS status Theorem for theBenchmark.p
% 0.20/0.64 % SZS output start Proof
% See solution above
% 0.20/0.64 % Total time : 0.058000 s
% 0.20/0.64 % SZS output end Proof
% 0.20/0.64 % Total time : 0.062000 s
%------------------------------------------------------------------------------